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meat journal
l^^r/ A IN
^OTED TO THE SCIENTIFIC ^^r>^ AND ENGINEERING
»ECTS OF ELECTRICAL COMMUNICATION
U M E XXXV JANUARY 1956 tf k k--- • ' t. N U M B E R-lv
DiflPused Emitter and Base Silicon Transistors J ^' ^ '^ ^ ^^^°
M. TANENBAUM AND D. E. THOMAS 1
A High-Frequency Diffused Base Germanium Transistor c. a. lee 23
Waveguide Investigations with Millimicrosecond Pulses
a. c. beck 35
Experiments on the Regeneration of Binary Microwave Pulses
o. B. delange 67
Crossbar Tandem as a Long Distance Switching System
a. O. ADAM 91
Growing Waves Due to Transverse Velocities
J. R. pierce and l. r. walker 109
Coupled Helices j. s. cook, r. kompfner and c. f. quatb 127
Statistical Techniques for Reducing the Experiment Time in Re-
liability Studies MILTON sobel 179
A Class of Binary Signaling Alphabets david slepian 203
Bell System Technical Papers Not Published in This Journal 235
Recent Bell System Monographs 242
Contributors to This Issue 244
COPYRIGHT 1956 AMERICAN TELEPHONE AND TELEGRAPH COMPANY
; , * -^ -^ f - -.r » ' J " -' •
THE BELL SYSTEM TECHNICAL JOURNAL
ADVISORY BOARD
F. E. K A P P E L, President, Western Electric Company
M. J. KELLY, President, Bell Telephone Laboratories
E. J. McNEELY, Executive Vice President, American
Telephone and Telegraph Company
EDITORIAL COMMITTEE
B. MCMILLAN, Chairman H. R. HUNTLEY
A. J. BUSCH F. R. LACK
A. C. DICKIESON J. R. PIERCE
R. L. DIETZOLD H. V. SCHMIDT
K. E. GOULD C. E. SCHOOLEY
E. L GREEN G. N. THAYER
EDITORIAL STAFF
J. D. TEBO, Editor
M. E. s T R I E B Y, Managing Editor
R. L. SHEPHERD, Production Editor
THE" BELL SYSTEM TECHNICAL JOURNAL is pubUshed six times
a year by the American Telephone and Telegraph Company, 195 Broadway,
New York 7, N. Y. Cleo F. Craig, President; S. Whitney Landon, Secretary;
John J. Scanlon, Treasurer. Subscriptions are accepted at $3.00 per year.
Single copies are 75 cents each. The foreign postage is 65 cents per year or 11
cents per copy. Printed in U. S. A.
THE BELL SYSTEM
TECHNICAL JOURNAL
VOLUME XXXV JANUARY 1956 number 1
Copyright 1956, American Telephone and Telegraph Company
Diffused Emitter and Base Silicon
Transistors*
By M. TANENBAUM and D. E. THOMAS
(Manuscript received October 21, 1955)
Silicon n-p-n transistors have been made in which the base and emitter
regions were produced by diffusing impurities from the vapor phase. Tran-
sistors with base layers 3.8 X 10~ -cm thick have been made. The diffusion
techniques and the processes for making electrical contact to the structures
are described.
The electrical characteristics of a transistor with a maximum alpha of
0.97 and an alpha-cutoff of 120 mc/sec are presented. The manner in which
some of the electrical parameters are determined by the distribution of the
doping impurities is discussed. Design data for the diffused emitter, dif-
fused base structure is calcidated and compared with the rneasured char-
acteristics.
INTRODUCTION
The necessity of thin base layers for high-frequency operation of tran-
sistors has long been apparent. One of the most appealing techniques for
controlling the distribution of impurities in a semiconductor is the dif-
fusion of the impurity into the solid semiconductor. The diffusion co-
efficients of Group III acceptors and Group V donors into germanium
and silicon are sufficiently low at judiciously selected temperatures so
* A portion of the material of this paper was presented at the Semiconductor
Device Conference of the Institute of Radio Engineers, Philadelphia, Pa., June,
1955.
2 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
that it is possible to envision transistors with base layer thicknesses of a
micron and frequency response of several thousand megacycles per
second.
A major deterent to the application of diffusion to silicon transistor
fabrication in the past was the drastic decrease in lifetime which generally
occurs when silicon is heated to the high temperatures required for dif-
fusion. There was also insufficient knowledge of the diffusion parameters
to permit the preparation of structures with controlled layer thicknesses
and desired dopings. Recently the investigations of C. S. Fuller and co-
workers have produced detailed information concerning the diffusion of
Group III and Group V elements in silicon. This information has made
possible the controlled fabrication of transistors with base layers suffi-
ciently thin that high alphas are obtained even though the lifetime has
been reduced to a fraction of a microsecond. In a cooperative program
with Fuller, diffusion structures were produced which have permitted
the fabrication of transistors whose electrical behavior closely approxi-
mates the behavior anticipated from the design. This paper describes
these techniques which have resulted in high alpha silicon transistors
with alpha-cutoff of over 100 mc/sec.
1.0 FABRICATION OF THE TRANSISTORS
Fuller's work has shown that in silicon the diffusion coefficient of a
Group III acceptor is usually 10 to 100 times larger than that of the
Group V donor in the same row in the periodic table at the same tem-
peratures. These experiments were performed in evacuated silica tubes
using the Group III and Group V elements as the source of diffusant.
Under these conditions a particular steady state surface concentration
of the diffusant is produced and the depth of diffusion is sensitive to
this concentration as well as to the diffusion coefficient. The experiments
show that the effective steady state surface concentration of the donor
impurities produced under these conditions is ten to one hundred times
greater than that of the acceptor impurities. Thus, by the simultaneous
diffusion of selected donor and acceptor impurities into n-type silicon
an n-p-n structure will result. The first n-la,yer forms because the surface
concentration of the donor is greater than that of the acceptor. The
p-laycr is protluced because the acceptor diffuses faster than the donor
and gets ahead of it. The final n-region is simply the original background
doping of the n-type silicon sample. It has been possible to produce n-p-n
structures by the simultaneous diffusion of several combinations of
donors and acceptors. Often, however, the diffusion coefficients and
surface concentrations of the donors and acceptors are such that opti-
1 C. S. Fuller, private communication.
DIFFUSED EMITTER AND BASE SILICON TRANSISTORS 3
mum layer thicknesses (see Sections 3 and 4) are not produced by simul-
taneous diffusion. In this case, one of the impurities is started ahead of
the other in a prior diffusion, and then the other impurity is diffused
in a second operation.
With the proper choice of diffusion temperatures and times it has been
possible to make n-p-n structures with base layer thicknesses of 2 X 10~*
cm. The uniformity of the layers in a given specimen is better than ten
per cent of the layer thickness. Fig. 1 illustrates the uniformity of the
layers. This figure is an enlarged photograph of a view perpendicular
to the surface of the specimen. A bevel which makes an angle of five
degrees with the original surface has been polished on the specimen. This
angle magnifies the layer thickness by 11.5. The layer is defined by an
etchant which preferentially stains p-type silicon^ and the width of the
layer is measured with a calibrated microscope.
After diffusion the entire surface of the silicon wafer is covered with
the diffused n- and p-type layers, see Fig. 2(a). Electrical contact must
now be made to the three regions of the device. The base contact can
be made by polishing a bevel on the specimen to expose and magnify
the base layer and then alloying a lead to this region by the same tech-
f.^ *f^'- *;
'>i
i * /i
n-TfPE DIFFUSED LAV^ER
fo-t^^E*OiFFUSED LAYER
i»#
OF^GIt^L n-TYPE
CRYSTAl.
I 1 EQUIVALENT TO 2 X lO"'* CM
LAYER THICKNESS
Fig- 1 — Angle section of a double diffused silicon wafer. The p-type center
ayer is approximately 2 X 10-< cm thick.
4 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
niques employed in the fabrication of grown junction transistors. Fig.
2(b). However, a much simpler technique has been evolved. If the sur-
face concentration of the donor diffusant is maintained below a certain
critical value, it is possible to alloy an aluminum wire directly through
the diffused n-type layer and thus make effective contact to the base
layer, Fig. 2(c). Since the resistivity of the original silicon wafer is one
to five ohm-cm, the aluminum will be rectifying to this region. It has
been experimentally shown that if the surface concentration of the
donor diffusant is less than the critical value mentioned above, the
aluminum will also be rectifying to the diffused n-type region and the
contact becomes merely an extension of the base layer. The n-layers
produced by diffusing from elemental antimony are below the critical
concentration and the direct aluminum alloying technique is feasible.
-n + TYPE DIFFUSED LAYER
-p-TYPE DIFFUSED LAYER
n +
n+
-ALUMINUM WIRE
p + ALUMINUM DOPED
REGROWTH LAYER
n-TYPE
(b)
,^- ALUMINUM WIRE
P + ALUMINUM DOPED
, REGROWTH LAYER
^M'nY ^-i-r
n-TYPE
(c)
Fig. 2 — ■ Schematic illustralioii of (a) double diffused n-p-n wafer, (b) angle
section method of making base contact, and (c) direct alloying method of making
base contact.
DIFFUSED EMITTER AND BASE SILICON TRANSISTORS
AU-Sb PLATED
POINT
VAPORIZED Al
LINE
0.005 CM WIDE
t MM
Fig. 3 — Mounted double diffused transistor.
Contact to the emitter layer is achieved by alloying a film of gold
containing a small amount of antimony. Since this alloy will produce
an n-type regrowth layer, it is only necessary to insure that the gold-
antimony film does not alloy through the p-type base layer, thus shorting
the emitter to the collector. This is controlled by limiting the amount of
gold-antimony alloy which is available by using a thin evaporated film
or by electroplating a thin film of gold-antimony alloy on an inert metal
point and alloying this structure to the emitter layer.
Ohmic, contact to the collector is produced by alloying the silicon
wafer to an inert metal tab plated with a gold-antimony alloy.
6 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
The transistors whose characteristics are reported in this paper were
prepared from 3 ohm-cm n-type siHcon using antimony and ahmiinum
as the diffusants. The base contact was produced by evaporating alumi-
num through a mask so that a hne approximately 0.005 X 0.015 cm in
o
lateral dimensions and 100,000 A thick was formed on the surface. This
aluminum line was alloyed through the emitter layer in a subsequent
operation. The wafer was then alloyed onto the plated kovar tab. A
small area approximately 0.015 cm in diameter was masked around the
line and the wafer was etched to remove the unwanted layers. The unit
was then mounted in a header. Electrical contact to the collector was
made by soldering to the kovar tab. Contact to the base was made with
a tungsten point pressure contact to the alloyed aluminum. Contact
to the emitter was made by bringing a gold-antimony plated tungsten
point into pressure contact with the emitter layer. The gold-antimony
plate was then alloyed by passing a controlled electrical pulse between
the plated point and the transistor collector lead. Fig. 3 is a photograph
of a mounted unit.
2.0 ELECTRICAL CHARACTERISTICS
The frequency cutoffs of experimental double diffused silicon tran-
sistors fabricated as described above are an order of magnitude higher
than the known cutoff frequencies of earlier silicon transistors. This is
shown in Fig. 4 which gives the measured common base and common
emitter current gains for one of these units as a function of frequency.
The common base short-circuit current gain is seen to have a cutoff fre-
quency of about 120 mc/sec. The common emitter short-circuit current
gain is shown on the same figure. The low-freciuency current gain is
better than thirty decibels and the cutoff frequency which is indicated
by the freciuency at which the gain is 3 db below its low-frequency
value is 3 mc/sec. This is an exceptionally large common emitter band-
width for a thirty db common emitter current gain and is of the same
order of magnitude as that obtained with the highest frequency ger-
manium transistors (e.q., p-n-i-p or tetrode) which had been made
prior to the diffused base germanium transistor.
^ Tlio iiicroasp in (•oiiiinon haso current gain ahovc unity (indicated by current
gain in decibels being positive) in the vicinity of 50 mc/sec is caused by a reactance
gain error in the common base measurement. This error is caused by a combination
of the emitter to ground parasitic capacitance and the i)ositive reactance com-
ponent of the transistor input impedance resulting from phase shift in the ali)ha
current gain.
' C. A. Lee, A High-Frequency Diffused Base Germanium Transistor, see
page 23.
DIFFUSED EMITTER AND BASE SILICON TRANSISTORS
z
<
o
I-
z
LJ
a.
cr
D
O
40
30
20
(0
-\0
-20
-30
Ie =
3 MA
Vc
= 10 VOLTS
COMMON^
EMITTER
N
'OCCB — ^ ^^
OCq = 0.9716
['=^"=106MC
l-Ofg
\ facb = i20MC
\
COMMON
BASE
\
\
\
0.1 0.2 0.5 1.0 2 6 10 20 50 100 200
FREQUENCY IN MEGACYCLES PER SECOND
500 1000
Fig. 4 — ■ Short-circuit current gain of a double diffused silicon n-p-n transistor
as a function of frequency in the common emitter and common base connections.
Fig. 5 shows a high-freciueiicy lumped constant equivalent circuit
for the double diffused silicon transistor whose current gain cutoff char-
acteristic is shown in Fig. 4. External parasitic capacitances have been
omitted from the circuit. The configuration is the conventional one for
junction transistors with two exceptions. A series resistance rj has been
added in the emitter circuit to account for contact resistance resulting
from the fact that the present emitter point contacts are not perfectly
ohmic. A second resistance r/ has been added in the collector circuit to
account for the ohmic resistance of the n-type silicon between the col-
lector terminal and the effective collector junction. This resistance exists
in all junction transistors but in larger area low frequency junction
transistors its effect on alpha-cutoff is sufficiently small so that it has
been ignored in equivalent circuits of these devices. The collector RC
Ce = TmmF
Pq -]AU)
Cc = 0.52//^F r ' _ ,50 co
Tg = 150;
a
J^C(
•Le
'%=QOCO
COMMON BASE CURRENT
GAIN CUT-OFF FREQUENCY
■ 120 MC
Ic = 3 MA
Vc = 10 VOLTS
Fig. 5 ~ High-frequency lumped constant equivalent circuit for a double
diffused silicon n-p-n transistor.
8
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
cutoff caused by the collector capacitance and the combined collector
body resistance and base resistance is an order of magnitude higher
than the measured alpha cutoff frequency and therefore is not too serious
in impairing the very high-frecjuency performance of the transistor.
This is due to the low capacitance of the collector junction which is
seen to be approximately 0.5 mmf at 10 volts collector voltage. The
base resistance of this transistor is less than 100 ohms which is quite low
and compares very favorably with the best low frequency transistors
reported previously.
The low-frequency characteristics of the double diffused silicon tran-
sistor are very similar to those of other junction transistors. This is il-
lustrated in Fig. 6 where the static collector characteristics of one of
these transistors are given. At zero emitter current the collector current
is too small to be seen on the scale of this figure. The collector current
45
40
35
30
25
20
15
10
-5
le=0
2
4 6
8
10
12
]
J
14/
^
J^
^
y^
^
2 4 6 8 10 12 14
CURRENT, If, IN MILUAMPERES
Fig. 6 — Collector characteristics of a double diffused silicon n-p-n tran-
sistor.
DIFFUSED EMITTER AND BASE SILICON TRANSISTORS
9
0.98
0.94
0.90
0.86
a
0.82
0.78
0.74
0.70
T=150°C,
^
^
^
^
^
7
<^
y
^
^
^
\
/
9/
y
24, 5M
65-W
/>
7
/24.5
t35^y\
7
15ol
/
/
1
1
1
_L.
1
1
1
,1
0.1 0.2 0.4 0.6 1 2 4 6 8 10 20
CURRENT, Ig, IN MILLIAMPERES
Fig. 7 — Alpha as a function of emitter current and temperature for a double
diffused silicon n-p-n transistor.
under this condition does not truly saturate but collector junction re-
sistance is very high. Collector junction resistances of 50 megohms at
reverse biases of 50 volts are common.
The continuous power dissipation permissible with these units is also
shown in Fig. 6. The figure shows dissipation of 200 milliwatts and the
units have been operated at 400 milliwatts without damage. As illus-
trated in Fig. 3 no special provision has been made for power dissipation
and it would appear from the performance obtained to date that powers
of a few watts could be handled by these iniits with relatively minor
provisions for heat dissipation. However, it can also be seen from Fig. 6
that at low collector voltages alpha decreases rapidly as the emitter
current is increased. The transistor is, therefore, non-linear in this
range of emitter currents and collector voltages. In many applications,
this non-linearity may limit the operating range of the device to values
below those which would be permissible from the point of view of con-
tinuous power dissipation.
Fig. 7 gives the magnitude of alpha as a function of emitter current
for a fixed collector voltage of 10 volts and a number of ambient tem-
peratures. These curves are presented to illustrate the stability of the
parameters of the double diffused silicon transistor at increased ambient
temperatures. Over the range from 1 to 15 milliamperes emitter current
and 25°C to 150°C ambient temperature, alpha is seen to change only
10 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
by approximately 2 per cent. This amounts to only 150 parts per million
change in alpha per degree centigrade change in ambient temperature.
The decrease in alpha at low emitter currents shown in Fig. 7 has been
observed in every double diffused silicon transistor which has been made
to date. Although this effect is not completely understood at present it
could be caused by recombination centers in the base layer that can
be saturated at high injection levels. Such saturation would result in an
increase in effective lifetime and a corresponding increase in alpha. The
large increase in alpha with temperature at low emitter currents is con-
sistent with this proposal. It has also been observed that shining a strong
light on the transistor will produce an appreciable increase in alpha at
low emitter currents but has little effect at high emitter currents. A
strong light would also be expected to saturate recombination centers
which are active at low emitter currents and this behavior is also con-
sistent with the above proposal.
3.0 DISCUSSION OF THE TRANSISTOR STRUCTURE
Although the low frequency electrical characteristics of the double
diffused silicon transistor which are presented in Section 2 are quite
similar to those usually obtained in junction transistors, the structure
of the double diffused transistor is sufficiently different from that of the
grown junction or alloy transistor that a discussion of some design
principles is warranted. This section is devoted to a general discussion
of the factors which determine the electrical characteristics of the tran-
sistors. In Section 4 the general ideas of Section 3 are applied in a more
specialized fashion to the double diffused structure and a detailed cal-
culation of electrical parameters is presented.
One essential difference between the double diffused transistor and
grown junction or alloy transistors arises from the manner in which the
impurities are distributed in the three active regions. In the ideal case
of a double-doped grown junction transistor or an alloy transistor the
concentration of impurities in a given region is essentially uniform and
the transition from one conductivity type to another at the emitter and
collector junctions is abrupt giving rise to step junctions. On the other
hand in the double diffused structure the distribution of impurities is
more closely described by the error function complement and the emitter
and collector junctions are graded. Tlu\se differences can have an appre-
ciable influence on the electrical beha\'ior of the transistors.
Fig. 8(a) shows the probable distribution of donor impurities, No ,
and acceptor impurities, A''^ , in a double diffused n-p-n. Fig. 8(b) is a
DIFFUSED EMITTER AND BASE SILICON TRANSISTORS
11
DONORS
ACCEPTORS
DISTANCE
(a)
DISTANCE *•
(b)
Fig. 8 — Diagrammatic representation of (a) donor and acceptor distributions
and (b) uncompensated impuritj- distribution in a double diffused n-p-n tran-
sistor.
plot of Nd — Na which would result from the distribution in Fig. 8(a).
Kromer has shown that a nonuniform distribution of impurities in a
semiconductor will produce electric fields which can influence the flow
of electrons and holes. For example, in the base region the fields between
the emitter junction, Xe , and the minimum in the Nd — Na curve, x',
will retard the flow of electrons toward the collector while the fields
between this minimum and the collector jvmction, Xc , will accelerate the
flow of electrons toward the collector. These base laj^er fields will affect
the transit time of minority carriers across the base and thus contribute
* H. Kromer, On Diffusion and Drift Transistor Theory I, II, III, Archiv. der
Electr. Ubertragung, 8, pp. 223-228, pp. 363-369, pp. 499-504, 1954.
12 THE BELL SYSTEM TECHNICAL JOUENAL, JANUARY 1956
to the fre(iuency response of the transistor. In addition the base re-
sistance will be dependent on the distribution of both diffusants. These
three factors are discussed in detail below.
Moll and Ross have determined that the minority current, /,„ , that
will flow into the base region of a transistor if the base is doped in a non-
uniform manner is given by
f N(x) dx
where rii is the carrier concentration in intrinsic material, q is the elec-
tronic charge, V is the applied voltage, Dm is the diffusion coefficient of
the minority carriers, and the integral represents the total number of
uncompensated impurities in the base. The primary assumptions in this
derivation are (1) planar junctions, (2) no recombination in the base
region, and (3) a boundary condition at the collector junction that the
minority carrier density at this point equals zero. It is also assumed that
the minority carrier concentration in the base region just adjacent to the
emitter junction is equal to the equilibrium minority carrier density at
this point multiplied by the Boltzman factor exp (qV/kT). It is of special
interest to note that Im depends only on the total number of uncom-
pensated impurities in the base and not on the manner in which they
are distributed.
In the double diffused transistor, it has been convenient from the
point of ease of fabrication to make the emitter layer approximately the
same thickness as the base layer. It has been observed that heating sili-
con to high temperatures degrades the lifetime of n- and p-type silicon
in a similar manner. Both base and emitter layers have experienced the
same heat treatment and to a first approximation it can be assumed that
the lifetime in the two regions will be essentially the same. Thus as-
sumptions (1) and (2) should also apply to current flow from base to
emitter. If we assume that the surface recombination \'elocity at the
free surface of the emitter is infinite, then this imposes a boundary
condition at this side of the emitter which under conditions of forward
bias on the emitter is equivalent to assumption (3). Thus an equation
of the form of (3.1) should also give the minority current flow from base
to emitter. Since the emitter efficiency, y, is given by
^ J. Tj. Moll and I. M. Ross, The J)opendencc of Transistor Paramotors on tlie
Distribution of Base Layer liesistivity, Proc. I.R.E. in press.
8 G. Bemski, private comnmnication.
DIFFUSED EMITTER AND BASE SILICON TRANSISTORS 13
/m (emitter to base)
-y = . . .
/^(emitter to base) + /„j(base to emitter)
proper substitution of (3.1) will give the emitter efficiency of the double
diffused n-p-n transistor,
1
7 =
J-'n
Z).^''^-^"^
dx
p .6 (3.2)
\ (No - iVj dx
In (3.2), Dp is the diffusion coefficient of holes in the emitter, /)„ is the
diffusion coefficient of electrons in the base and the ratio of integrals is
the ratio of total uncompensated doping in the base to that in the
emitter.
A calculation of transit time is more difficult. Kromer has studied
the case of an aiding field which reduces transit time of minority carriers
across the base region and thus increases frequency response. In the
double diffused transistor the situation is more complex. Near the
emitter side of the base region the field is retarding (Region R, see Fig. 8)
and becomes aiding (Region A) only after the base region doping reaches
a maximum. The case of retarding fields has been studied by Lee and
by MoU.^ At present, the case for a base region containing both types of
fields has not been solved. However, at the present state of knowledge
some speculations about transit time can be made.
The two factors of primary importance are the magnitude of the
built-in fields and the distance over which they extend. In the double
diffused transistor, the widths of regions R and A are determined by the
surface concentrations and diffusion coefficients of the diffusants. It
Can be shown by numerical computation that if region R constitutes no
more than 30-40 per cent of the entire base layer width, then the overall
effect of the built-in fields will be to aid the transport of minority car-
riers and to produce a reduction in transit time. In addition the absolute
magnitude of region R is important. If the point x' should occur within
an effective Debye length from the emitter junction, i.e., if x' is located
in the space charge region associated with the emitter junction, then the
retarding fields can be neglected.
The base resistance can also be calculated from surface concentrations
and diffusion coefficients of the impurities. This is done by considering
the base layer as a conducting sheet and determining the sheet con-
' J. L. Moll, private communication.
14 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
ductivity from the total number of uncompensated impurities per square
centimeter of sheet and the approjiriate moliility weighted to account
for impurity scattering.
4.0 CALCULATION OF DESIGN PARAMETERS
To calculate the parameters which determine emitter efficiency, transit
time, and base resistance it is assumed that the distribution of uncom-
pensated impurities is given by
N(x) = Nicrfc f - N-2erJc^ + Nz (4.1)
where A^i and A^2 are the surface concentrations of the emitter and base
impurity diffusants respectively, Li and L^ are their respective diffusion
lengths, and Nz is the original doping of the semiconductor into which
the impurities are diffused. The impurity diffusion lengths are defined as
Li = 2 V/M and L2 = 2 ^Ddo (4.2)
where the D's are the respective diffusion coefficients and the f's are the
diffusion times.
Equation (4.1) can be reduced to
r(^) = Ti erfc I - Ta erfc X^ + 1 (4.3)
where
For cases of interest here, r(^) will be zero at two points, a and 13,
and will have one minimum at ^'. In the transistor structure the emitter
junction occurs at ^ = ^v and the collector junction occurs at ^ = (3.
Thus the base width is determined by 13 — a. The extent of aiding and
retarding fields in the base is determined by ^'. The integral of (4.3)
from 0 to a, I\ , and from o to ^, I2 , are the integrals of interest in (3.2)
and thus determine emitter efficiency. In addition I2 is the integral from
which base resistance can be calculated.
The calculations which follow apply only for values of ri/r2 and To
greater than ten. Some of the simplifying assumptions which are made
will not apply at lower values of these parameters where the distribution
of both diffusants as well as the background doping affect the structure
in all three regions of the device.
DIFFUSED EMITTER AND BASE SILICON TRANSISTORS
15
4.1 Base Width
From Fig. 8 and (4.3) it can be seen that for r2 ^ 10, a is essentially
independent of r2 and is primarily a function of T1/T2 and X. Fig. 9 is a
plot of a versus ri/r2 with X as the parameter. The particular plot is for
r2 = 10 . Although as stated a is essentially independent of r2 , at lower
values of r2, a may not exist for the larger values of X, i.e., the p-layer
does not form.
In the same manner, it can be seen that ^ is essentially independent of
T]/T2 and is a function only of r2 and X. Fig. 10 is a plot of /3 versus F^
with X as a parameter. This plot is for Ti/Fo = 10 and at larger Fi/Fo ,
/3 may not exist at large X.
10"
\0'
10
r2=)o''
///
//
/
^
::i
ll
r /
/
m
0/ /
'
>
/os/
1
i
1
///
'o.e/
/
f 0.7/
/
///
/
/
<.e
I
w.
W
/
/
/
1.0
1.4
1.8
2.2 2.6
a
3.0
3.4
3.8
Fig. 9 — Emitter layer thickness (in reduced units) as a function of the ratio
of the surface concentrations of the diffusing impurities (ri/r2) and the ratio of
their diffusion lengths (X).
16
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
The base width
W = ^ — a
can be obtained from Figs. 9 and 10. a, 13 and iv can be converted to
centimeters by nuiltiplying by the appropriate value of Li .
4.2 Emitter Efficiency
With the hmits a and /3 determined above, the integrals h and 1 2 can
be calculated. Examination of the integrals shows that h is closely pro-
portional to ri/r2 and also to r2 . On the other hand I2 is closely propor-
tional to r2 and essentially independent of ri/r2 . Thus, the ratio of
/2//1 which determines 7 depends primarily on ri/r2 . Fig. 11 is a plot
of the constant /2//1 contours in the ri/T2 — X plane for lo/h ii^ the
range from — 1.0 to —0.01. The graph is for r2 = 10 . Since from (3.2)
7 =
1
1 _ ^h
Dnh
(4.4)
for an n-p-n transistor, and assuming Dp/Dn = /^ for silicon, then
to'
(0-
10'
10
1'
1
\=
..J\
0.6-
0.5-
::ffl
M
\u
|6 In
1 1°
1
\\\
(
0.2
0.1
'///
///
0.01/
ill
7
/
/
///
/
/
/
10
20 50
100 200
500 1000
Fig. 10 — (Collector junction dopth (in rodurod units) as a function of the sur-
face concuMit.ration (in reduced units) of llie dilfusaiit wliicli determines the con-
ductivity type of the l)ase layer (I'.') and liie ratio of tlie dilTusioii lengths (X) of
the tAvo diffusing inii)urifies.
DIFFUSED EMITTER AND BASE SILICON TRANSISTORS
10"
17
10
H
Ta
10
10
r2 = io'*
2
w
\v
V
2
?
1
^
1
\\
\
t
^.
\
\I2/I
1
2
V
,\
N-0
VO.05
02
-i.o\
-0.3S^
32X^0
'\
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Fig. 11 — ^Dependence of emitter efficiency upon diffusant surface concentra-
tions and diffusion lengths. The lines of constant /2//1 are essentially lines of
constant emitter efficiency. The ordinate is the ratio of surface concentrations of
the two diffusants and the abscissa is the ratio of their diffusion lengths.
/2//1 = — 1.0 corresponds to a 7 of 0.75 and /2//1 = —0.01 corresponds
to a 7 of 0.997.
4.. 3 Base Resistance
It was indicated above that I2 depends principally on r2 and X. Fig. 12
is a plot of the constant I2 contours in the r2 — X plane for I2 in the range
from —10^ to —10. The graph is for Ti/To = 10. The base layer sheet
conductivity, cjb , can be calculated from these data as
Qb = —qtihTjiNz
(4.5)
where q, L\ and A^3 are as defined above and /I is a mobility properly
weighted to account for impurity scattering in the non-uniformly doped
base region. The units of gb are mhos per square.
18
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
10-
1 2= -10,00^
/
/
7/
1
/
-5000/
r
/ /
//
/
/
/ -1000/
//
//
/ / 1
2
1
/
/-5oa
/ /
/ /
/ 1
^/^^
/
/
/
/I
^/
/ /
1 1
10
/
/
//
v.
/-ioy
V
11
/ /
/
/,
//
/-/ ,
(I
5
//
/,
-^
/J
/
V/
/
2
^
^
^
f^
u
10
102
r
/ /
^
/
/
^
5
— 1
0
^/
V
r
10
/
/
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Fig. 12 — Dependence of base layer sheet condiictivitj^ on diffusant surface
concentrations and diffusion lengths. The lines of constant Ii are essentiallj' lines
of constant base sheet conductivity. The ordinate is the surface concentration
(in reduced units) of the diffusant which determines the conductivity type of the
base layer and the abscissa is the ratio of the diffusion lengths of the two difi'using
impurities.
4.4 Transit Time
With a knowledge of where the minimum value, ^', of (4.3) occurs,
it is possible to calculate over what fraction of the base width the fields
are retarding. The interesting quantity here is
13 - a
^ is a function of ri/r2 and X and varies only very slowly with ri/r2 .
a is also a function of ri/r2 and X and varies only slowly with ri/r2 .
The most rapidly changing part of bJi is l^ which depends primarily on
r2 as noted above. Fig. 13 is a plot of the constant LR contours in the
r2 — X plane for values of A/2 in the range 0.1 to 0.3. This graph is
DIFFUSED EMITTER AND BASE SILICON TRANSISTORS
19
lor data with ri/r2 = 10. As ri/r2 increases at constant r2 and X, AR
decreases slightly. At ri/r2 = 10\ the average change in AR is a decrease
of about 25 per cent for constant r2 and X when AR ^ 0.3. The error is
larger for values of AR greater than 0.3. It was noted above that when
AR becomes greater than 0.3, the retarding fields become dominant.
Therefore, this region is of slight interest in the design of a high frequency
transistor.
4.5 A Sample Design
By superimposing Figs. 11, 12 and 13 the ranges of r2 , ri/r2 and X
which are consistent with desired values of y, gt and AR can be deter-
0.7
Fig. 1.3 — Dependence of the built-in field distribution on concentrations and
diffusion lengths. The lines of constant aR indicate the fraction of the base layer
thickness over which built-in fields are retarding. The ordinate is the surface
concentration (in reduced units) of the diffusant which determines the conductiv-
ity type of the base layer and the abscissa is the ratio of the diffusion lengths of
the two diffusing impurities.
20 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
mined by the area enclosed by the specified contour lines. It is also
possible to compare the measured parameters of a specific device and
observe how closely they agree with what is predicted from the estimated
concentrations and diffusion coefficients. This is done below for the
transistor described in Sections 1 and 2.
The comparison is complicated by the fact that the exact values of the
surface concentrations and diffusion coefficients are not known {Precisely
enough at present to permit an accurate evaluation of the design theory.
However, the following values of concentrations and diffusion coefficients
are thought to be realistic for this transistor.
iVi = 5 X 10^' /)i = 3 X 10"'' /i = 5.7 X lO'
iV2 = 4 X 10'' Di = 2.5 X 10"" t^= 1.2 X lO'
Nz = 10''
From these values it is seen that
Ti/ra = 12.5; r, = 400; X = 0.6
From Fig. 9, a = 1.9 and from Fig. 10, /3 = 3.6 and therefore w = 1.7.
Measurement of the emitter and base layer dimensions showed that these
layers were approximately the same thickness which was 3.8 X 10" cm.
Thus the ifieasured ratio of emitter width to base width of unity is in
good agreement with the ^'alue of 1.1 predicted from the assumed con-
centrations and diffusion coefficients.
From Fig. 11, lo/h ~ —0.01. If this value is substituted into (4.4),
7 = 0.997. This compares with a measured maximum alpha of 0.972.
From Fig. 12, lo = —15. Assuming an average hole mobility of 350
cm' /volt. sec. and evaluating Li from the measured emitter thickness
and the calculated a, (4.5) gives a value of gb = 1.7 X 10^ mhos per
square. The geometry of the emitter and base contacts as shown in Fig.
3 makes it difficult to calculate the effective base resistance from the
sheet conductivity even at very small emitter currents. In addition at
the very high inje{;tion levels at which these transistors are operated the
calculation of effective base resistance becomes very difficult. However,
from the geometr}^ it would be expected that the effective base re-
sistance would l)c no greater than 0.1 of the sheet resistivity or 600 ohms.
This is about seven times larger than the measured \'alue of 80 ohms
reported in Section 2.
From Fig. b3, A/^ is approximately 0.20. Thus there should be an over-
all aiding elfect of the built-in fields. In addition the impurity gradient
at the emitter junction is believed to be approximately lO'Vcm and the
DIFFUSED EMITTER AND BASE SILICON TRANSISTORS 21
space charge associated with this gradient will extend approximately
2 X 10 ■' cm into the base region. The base thickness over which re-
tarding fields extend is AR times the base width or 7.6 X 10~^ cm. Thus
the first quarter of region R will be space charge and can be neglected.
The frequency cutoff from pure diffusion transit is given by
2A3D ,. ,
where W is the measured base layer thickness. Assuming D — 25 cmVsec
for electrons in the base region, ,/'„ = (w mc/sec. Since the measured
cutoff was 120 mc/sec, the predicted aiding effect of the built-in field
is evidently present.
These computations illustrate how the measured electrical parameters
can be used to check the values of the surface concentrations and dif-
fusion coefficients. Conversely knowledge of the concentrations and
diffusion coefficients aid in the design of devices which will have pre-
scribed electrical parameters. The agreement in the case of the transistor
described above is not perfect and indicates errors in the proposed values
of the concentrations and diffusion coefficients. However, it is sufficiently
close to be encouraging and indicate the value of the calculations.
The discussion of design has been limited to a very few of the important
parameters. Junction capacitances, emitter and collector resistances are
among the other important characteristics which have been omitted
here. Presumably all of these quantities can be calculated if the detailed
structure of the device is known and the structure should be susceptible
to the type of analysis used above. Another fact, which has been ignored,
is that these transistors were operated at high injection levels and a low
level analysis of electrical parameters was used. All of these other factors
must be considered for a detailed understanding of the device. The object
of this last section has been to indicate one path which the more detailed
analysis might take.
5.0 CONCLUSIONS
By means of multiple diffusion, it has been possible to produce silicon
transistors with alpha-cutoff above 100 mc/sec. Refinements of the
described technicjues offer the possibility of even higher frequency per-
formance. These transistors show the other advantages expected from
silicon such as low saturation currents and satisfactory operation at
high temperatures.
The structure of the double diffused transistor is susceptible to design
22 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
analysis in a fashion similar to that which has been applied to other junc-
tion transistors. The non-uniform distribution of impurities produces
significant electrical effects which can be controlled to enhance appre-
cial)ly the high-frequency behavior of the devices.
The extreme control inherent in the use of diffusion to distribute im-
purities in a semiconductor structure suggests that this technique will
become one of the most valuable in the fabrication of semiconductor
devices.
ACKNOWLEDGEMENT
The authors are indebted to several people who contributed to the
work described in this paper. In particular, the double diffused silicon
from which the transistors were prepared was supplied by C. S. Fuller
and J. A. Ditzenberger. The data on diffusion coefficients and concen-
trations were also obtained by them.
P. W. Foy and G. Kaminsky assisted in the fabrication and mounting
of the transistors and J. M. Klein aided in the electrical characterization.
The computations of the various solutions of the diffusion equation, (4.3),
were performed by Francis Maier. In addition many valuable discussions
with C. A. Lee, G. Weinreich, J. L. Moll, and G. C. Dacey helped formu-
late many of the ideas presented herein.
A High-Frequency Diffused Base
Gernianiuni Transistor
By CHARLES A. LEE
(Manuscript received November 15, 1955)
Techniques of impurity diffusion and alloying have been developed which
make possible the construction of p-n-p junction transistors utilizing a
diffused surface layer as a base region. An important Jeature is the high
degree of dimensional control obtainable. Diffusion has the advantages of
being able to produce uniform large area junctions which may be utilized in
high power devices, and very thin surface layers which may be utilized in
high-frequency devices.
Transistors have been made in germanium which typically have alphas
of 0.98 and alpha-cutoff frequencies of 500 mcls. The fabrication, electrical
characterization, and design considerations of these transistors are dis-
cussed.
INTRODUCTION
Recent work ■ concerning diffusion of impurities into germanium
and silicon prompted the suggestion that the dimensional control in-
herent in these processes be utilized to make high-frecjuency transistors.
One of the critical dimensions of junction transistors, which in many
cases seriously restricts their upper freciuency limit of operation, is the
thickness of the base region. A considerable advance in transistor proper-
ties can be accomplished if it is possible to reduce this dimension one or
two orders of magnitude. The diffusion constants of ordinary donors
and acceptors in germanium are such that, with'n realizable tempera-
tures and times, the depth of diffused surface layers may be as small as
10" cm. Already in the present works layers slightly less than 1 micron
(10~ cm) thick have been made and utilized in transistors. Moreover,
the times and temperatures required to produce 1 micron surface laj^ers
permit good control of the depth of penetration and the concentration
of the diffusant in the surface layer with techniciues described below.
If one considers making a transistor whose base region consists of such
23
24 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
a diffused surface layer, several problems become immediately apparent :
(1) Control of body resistivity and lifetime during the diffusion heat-
ing cycle.
(2) Control of the surface concentration of the diffusant.
(3) INIaking an emitter on the surface of a thin diffused layer and
controlling the depth of penetration.
(4) Making an ohmic base contact to the diffused surface layer.
One approach to the solution of these problems in germanium which has
enabled us to make transistors with alpha-cutoff frequencies in excess
of 500 mc/sec is described in the main body of the paper.
An important characteristic feature of the diffusion technique is that
it produces an impurity gradient in the base region of the transistor.
This impurity gradiant produces a "built-in" electric field in such a
direction as to aid the transport of minority carriers from emitter to
collector. Such a drift field may considerably enhance the frequency
response of a transistor for given physical dimensions.
The capabilities of these new techniques are only partially realized
by their application to the making of high frequency transistors, and
even in this field their potential has not been completely explored. For
example, with these techniques applied to making a p-n-i-p structure
the possibility of constructing transistor amplifiers with usable gain at
frequencies in excess of 1,000 mc/sec now seems feasible.
DESCRIPTION OF TRANSISTOR FABRICATION AND PHYSICAL CHARACTERIS-
TICS
As starting material for a p-n-p structure, p-type germanium of 0.8
ohm-cm resistivity was used. From the single crystal ingot rectangular
bars were cut and then lapped and polished to the approximate dimen-
sions: 200 X 60 X 15 mils. After a slight etch, the bars were washed in
deionized water and placed in a vacuum oven for the diffusion of an
n-type impurity into the surface. The vacuum oven consisted of a small
molybdenum capsule heated by radiation from a tungsten coil and sur-
rounded by suitable radiation shields made also of molybdenum. The
capsule could be baked out at about 1,900°C in order that impurities
detrimental to the electrical characteristics of the germaniinn be evapo-
rated to sufficiently low levels.
As a source of n-type impurity to be placed with the p-type bars in
the molybdenum oven, arsenic doped germanium was used. The rela-
tively high vapor pressure of the arsenic was reduced to a desirable range
(about lO"* nun of Ilg) by diluting it in germanium. The use of ger-
manium eliminated any additional problems of contamination by the
A HIGH-FREQUENCY DIFFUSED BASE GERMANIUM TRANSISTOR 25
dilutant, and provided a convenient means of determining the degree of
dilution by a measurement of the conductivity. The arsenic concentra-
tions used in the source crystal were typically of the order of 10 '-10^^/cc.
These concentrations were rather high compared to the concentrations
desired in the diffused surface layers since compensation had to be made
for losses of arsenic due to the imperfect fit of the cover on the capsule
and due to some chemical reaction and adsorption which occurred on the
internal surfaces of the capsule.
The layers obtained after diffusion were then evaluated for sheet con-
ductivity and thickness. To measure the sheet conductivity a four-point
probe method^ was used. An island of the surface layer was formed by
masking and etching to reveal the junction between the surface layer
and the p-type body. The island was then biased in the reverse direction
with respect to the body thus effectively isolating it electrically during
the measurement of its sheet conductivity. The thickness of the surface
layer was obtained by first lapping at a small angle to the original surface
(3^-2°~l°) and locating the junction on the beveled surface with a thermal
probe; then multiplying the tangent of the angle between the two sur-
faces by the distance from the edge of the bevel to the junction gives the
desired thickness. Another particularly convenient method of measuring
the thickness' is to place a half silvered mirror parallel to the original sur-
face and count fringes, of the sodium D-Yme for example, from the edge
of the bevel to the junction. Typically the transistors described here
were prepared from diffused layers with a sheet conductivity of about
200 ohms/square, and a layer thickness of (1.5 ± 0.3) X 10~ cm.
When the surface layer had been evaluated, the emitter and base con-
tacts were made using techniques of vacuum evaporation and alloying.
o
For the emitter, a film of aluminum approximately 1,000 A thick was
evaporated onto the surface through a mask which defined an emitter
area of 1 X 2 mils. The bar with the evaporated aluminum was then
placed on a strip heater in a hydrogen atmosphere and momentarily
brought up to a temperature sufficient to alloy the alimiinum. The
emitter having been thus formed, the bar was again placed in the masking
jig and a film of gold-antimony alloy from 3,000 to 4,000 A thick was
evaporated onto the surface. This film was identical in area to the
emitter, and was placed parallel to and 0.5 to 1 mil away from the
emitter. The bar was again placed on the heater strip and heated to the
gold-germanium eutectic temperature, thus forming the ohmic base
contact. The masking jig was constructed to permit the simultaneous
evaporation of eight pairs of contacts on each bar. Thus, using a 3-mil
diamond saw, a bar could be cut into eight units.
20
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
Each unit, with an alloyed emitter and base contact, was then soldered
to a platinum tab with indium, a sufficient quantity of indium being-
used to alloy through the n-type surface layer on the back of the unit.
One of the last steps was to mask the emitter and base contacts with a
6- to 8-mil diameter dot of wax and form a small area collector junction
by etching the unit attached to the platinum tab, in CP4. After washing
in solvents to remove the wax, the unit was mounted in a header designed
to allow electrolytically pointed wire contacts to be made to the base and
emitter areas of the transistor. These spring contacts were made of 1-mil
phosphor bronze wire.
ELECTRICAL CHARACTERIZATION
Of the parameters that characterize the performance of a transistor,
one of the most important is the short circuit current gain (alpha) ver-
sus frequency. The measured variation of a and q:/(1 — a) (short-circuit
current gain in the grounded emitter circuit) as a function of frequency
for a typical unit is shown in Fig. 1 . For comparison the same parameters
for an exceptionally good unit are shown in Fig. 2.
In order that the alpha-cutoff frequency be a measure of the transit
time of minority carriers through the active regions of the transistor, any
resistance-capacity cutoffs, of the emitter and collector circuits, must lie
considerably higher than the measured /„ . In the emitter circuit, an
external contact resistance to the aluminum emitter of the order of 10
U1
_J
LU
eg
o
lij
Q
•4U
(
30
20
>-(
— ,
4.3
MC
UNIT 0-3 p-
n-p
Ge
Ie = 2 MA
Vc =-10 VOLTS
ao= 0.982
' 1
s
S. 1-a
6 DB
OCT/>
PER ^'
VE
■>
^s
1 0
0
-10
l«l
w
>
\
46
3 M(
1
;
^
*
0.1 0.2 0.4 0,6 1 2 4 6 8 10 20 40 60 100 200 400 1000
FREQUENCY IN MEGACYCLES PER SECOND
Fig. 1 — The grounded emitter and grounded base response versus frequency
for a typical unit.
A HIGH-FREQUENCY DIFFUSED BASE GERMANIUM TRANSISTOR 27
40
30
10
_l
LU
5 20
o
LJJ
Q
10
o-
^
«
3.4 M
C
UNIT M-2 p-r
Ie = 2MA
1-p
Ge
N
-— oc
1 \-oc
Vc=-10 VOLTS
OCo- 0.980
6Db\
PER A
OCTAVE
^N
^'s
oc
i-C
v^ 540 MC
^\
\
-10
0.1 0.2 0.4 0.6 1 2 4 6 e 10 20 40 60 100 200 400 1000
FREQUENCY IN MEGACYCLES PER SECOND
Fig. 2 — The grounded emitter and grounded base response versus frequency
for an exceptionally good unit.
to 20 ohms and a junction transition capacity of 1 fx^xid were measured.
The displacement current which flows through this transition capacity
reduces the emitter efficiency and must be kept small relative to the
injected hole current. With 1 milliampere of ciu"rent flowing through the
emitter junction, and conseciuently an emitter resistance of 26 ohms,
I the emitter cutoff for this transistor was above 6,000 mc/sec. One can
now see that the emitter area must be small and the current density
high to attain a high emitter cutoff freciuency. The fact that a low base
resistance requires a high level of doping in the base region, and thus a
high emitter transition capacity, restricts one to small areas and high
current densities.
In the collector circuit capacities of 0.5 to 0.8 ^l^xid at a collector volt-
age of — 10 volts were measured. There was a spreading resistance in the
collector body of about 100 ohms which was the result of the small
emitter area. The base resistance was approximately 100 ohms. If the
phase shift and attenuation due to the transport of minority carriers
through the base region w^ere small at the collector cutoff frequency, the
(effective base resistance would be decreased by the factor (1 —a). The
collector cutoff frequency is then given by
where Cc = collector transition capacity
and Re = collector body spreading resistance.
28 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
However, in the transistors described here the base region produces the
major contribution to the observed alpha-cutoff frequency and it is more
appropriate to use the expression
2irCcin + Re)
where n = base resistance. This cutoff frequency could be raised by in-
creasing the collector voltage, but the allowable power dissipation in the
mounting determines an upper limit for this voltage. It should b noted
that an increase in the doping of the collector material would raise the
cutoff since the spreading resistance is inversely proportional to Na ,
while the junction capacity for constant collector voltage is only pro-
portional to Na .
The low-frequency alpha of the transistor ranged from 0.95 to 0.99
with some exceptional units as high as 0.998. The factors to be con-
sidered here are the emitter efficiency y and the transport factor (3.
The transport factor is dependent upon the lifetime in the base region,
the recombination velocity at the surface immediately surrounding the
emitter, and the geometry. The geometrical factor of the ratio of the
emitter dimensions to the base layer thickness is > 10, indicating that
solutions for a planar geometry may be assumed.^ If a lifetime in the base
region of 1 microsecond and a surface recombination velocity of 2,000
cm/sec is assumed a perturbation calculation gives
iS = 0.995
The high value of ^ obtained with what is estimated to be a low base
region lifetime and a high surface recombination velocity indicates that
the observed low frecjuency alpha is most probably limited by the
emitter injection efficiency. As for the emitter injection efficiency, within
the accuracy to which the impurity concentrations in the emitter re-
growth layer and the base region are known, together with the thick-
nesses of these two regions, the calculated efficiency is consistent with
the experimentally observed values.
Considerations of Transit Time
An examination of what agreement (^xists between the alpha-cutoff
frequency and the physical measurements of the base region involves
the me(;hanism of transport of minority carriers through the active
regions of the transistor. The "active regions" include the space charge
A HIGH-FREQUENCY DIFFUSED BASE GERMANIUM TRANSISTOR 29
region of the collector junction. The transit time through this region
is no longer a negligible factor. A short calculation will show that with
— 10 volts on the collector junction, the space charger layer is about
4 X 10"^ cm thick and that the frequency cutoff associated with trans-
port through this region is approximately 3,000 mc/sec.
The remaining problem is the transport of minority carriers through
the base region. Depending upon the boundary conditions existing at the
surface of the germanium during the diffusion process, considerable
gradients of the impurity density in the surface layer are possible. How-
ever, the problem of what boundary conditions existed during the diffu-
sion process employed in the fabrication of these transistors w^ill not be
discussed here because of the many uncertainties involved. Some quali-
tative idea is necessary though of how electric fields arising from impurity
gradients may affect the frequency behavior of a transistor in the limit
of low injection.
If one assumes a constant electric field as would result from an ex-
ponential impurity gradient in the base region of a transistor, then the
continuity eciuation may be solved for the distribution of minority
carriers.* From the hole distribution one can obtain an expression for
the transport factor j3 and it has the form
/3 = e"
r? sinh Z -{- Z cosh Z
where
1, Ne IqE
^"2^^iV; = 2^^'
z ^ [i^ + ,r'
IV'
Ne = donor density in base region at emitter junction
Nc = donor density in base region at collector junction
E = electric field strength
Dp = diffusion constant for holes
w = width of the base layer
30
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
A plot of this function for various values of rj is shown in Fig. 3. For ?? = 0,
the above expression reduces to the well known case of a uniformly doped
base region. The important feature to be noted in Fig. 3 is that relatively
small gradients of the impurity distribution in the base layer can produce
a considerable enhancement of the frequency response.
It is instructive to calculate what the alpha-cutoff f recjuency would be
for a base region with a uniform distribution of impurity. The effective
thickness of the base layer may be estimated by decreasing the measured
thickness of the surface layer by the penetration of the space charge
region of the collector and the depth of the alloyed emitter structure.
Using a value for the diffusion constant of holes in the base region appro-
priate to a donor density of about 10 Vcc,
300 mc/s ^fa^ 800 mc/s
This result implies that the frecjuency enhancement due to "built-in"
fields is at most a factor of two. In addition it was observed that the
alpha-cutoff frequency was a function of the emitter current as shown
in Fig. 4. This variation indicates that at least intermediate injection
<Si
£L
'^ ^ 77 siNhZ +Z coshz
Z=(L5z5+772)'/2
0.8
0.6
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V
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1
1
1
\
\
1
1
>
1
1
1
1
_L
0.1
0.2
0.4 0.6 0.8 1
6 8 10
20
40 60 80 100
w2
<^-U} -g- , (RADIANS)
Fig. .3 — The variation of | i3 | ver.sii.s frequency for various values of a uniform
drift field in the base region.
A HIGH-FREQUENCY DIFFUSED BASE GERMANIUM TRANSISTOR 31
in
_i
LU
m
o
LU
a
z
b
n
=7^"
'^^-^^
S— 1'
i
f
\
^ '
'
; Q ■ ■_;;;; -t
Fv
Rl
k
-5
UNIT 0-3 p-n-p Ge
o Ie = 2 MA
A Ie=0.8MA
D Ig=0.4MA
\
k^
^
\
\
\
10
Vc
= -K
) VOLTS
1
1
\
1
1
1
10
20
30 40 50 60 80 100 200 300 400
FREQUENCY IN MEGACYCLES PER SECOND
600 800 1000
Fig. 4
current.
The variation of the alpha-cutoff frequency as a function of emitter
levels exist in the range of emitter current shown in Fig. 4. The conclu-
sion to be drawn then is that electric fields produced by impurity
gradients in the base region are not the dominant factor in the transport
of minority carriers in these transistors.
The emitter current for a low level of injection could not be deter-
mined by measuring /„ versus /« because the high input impedance at
very low levels was shorted by the input capacity of the header and
socket. Thus at very small emitter currents the measured cutoff fre-
quency was due to an emitter cutoff and was roughly proportional to
the emitter current. At /e ^ 1 ma this effect is small, but here at least
intermediate levels of injection already exist.
A further attempt to measure the effect of any "built-in" fields by
turning the transistor around and measuring the inverse alpha proved
fruitless for two reasons. The unfavorable geometrical factor of a large
collector area an a small emitter area as well as a poor injection effi-
ciency gave an alpha of only
a
= 0.1
Secondly, the injection efficiency turns out in this case to be proportional
to oT^^'^ giving a cutoff freciuency of less than 1 mc/sec. The sciuare-root
dependence of the injection efficiency on freciuency may be readily seen.
The electron current injected into the collector body may be expressed as
Je = qDnN
1 -)- iu^Te
1/2
where q = electronic charge
32 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
Dn ^ diffusion constant of electrons
Vi = voltage across collector junction
Tic = density of electrons on the p-type side of the collector junction
Te = lifetime of electrons in collector body
Le = diffusion length of electrons in the collector body
Since the inverse cutoff frequency is well below that associated with the
base region, we may regard the injected hole current as independent of
the frequency in this region. The injection efficiency is low so that
7 ;^ ^ « 1
J e
Thus at a frequency where
then
cor,
»1
I
-1/2
An interesting feature of these transistors was the very high current
densities at which the emitter could be operated without appreciable loss
of injection efficiency. Fig. 5 shows the transmission of a 50 millimicro-
second pulse up to currents of 18 milliamperes which corresponds to a
current density of 1800 amperes/cm". The injection efficiency should
remain high as long as the electron density at the emitter edge of the
base region remains small compared to the acceptor density in the
emitter regrowth layer. When high injection levels are reached the in-
jected hole density at the emitter greatly exceeds the donor density in th(>
base region. In order to preserve charge neutrality then
p ^ n
where p = hole density
n = electron density
As the inject(Hl hole density is raised still further the electron density
will eventually become comparable to the acceptor density in the
emitter regrowth layer. Tlie density of acceptors in the emitter regrowth
A HIGH-FREQUENCY DIFFUSED BASE GERMANIUM TRANSISTOR 33
30 46 60 75 90
TIME IN MILLIMICROSECONDS
>"
0
9
"^
V
4
'^
\^
/
18
V
/
-15
15
30 45 60 75 90
TIME IN MILLIMICROSECONDS
105
120
136
Fig. 5 — Transmission of a 50 millimicrosecond pulse at emitter currents up
to 18 ma by a typical unit. (Courtesy of F. K. Bowers).
region is of the order of
and this is to be compared with injected hole density at the base region
iside of the emitter junction. The relation between the injected hole
density and the current density may be approximated by^
J.
w
where pi = hole density at emitter side of base region
w = width of base region
jA short calculation indicates that the emitter efficiency should remain
'high at a current density of an order of magnitude higher than 1,800
|amp/cm'. The measurements were not carried to higher current densities
jbecause the voltage drop across the spreading resistance in the collector
was producing saturation of the collector junction.
CONCLUSIONS
Impurity diffusion is an extremely powerful tool for the fabrication
of high frequency transistors. Moreover, of the 50-odd transistors which
34 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
were made in the laboratory, the characteristics were remarkably uni-
form considering the ^•ariations usually encountered at such a stage of
development. It appears that diffusion process is sufficiently controllable
that the thickness of the base region can be reduced to half that of the
units described here. Therefore, with no change in the other design
parameters, outside of perhaps a different mounting, units with a 1000
mc/s cutoff frequency should be possible.
ACKNOWLEDGMENT
The author wishes to acknowledge the help of P. W. Foy and W. Wieg-
mann who aided in the construction of the transistors, D. E. Thomas who
designed the electrical equipment needed to characterize these units,
and J. Klein who helped with the electrical measurements. The numerical
evaluation of alpha for drift fields was done by Lillian Lee whose as-
sistance is gratefully acknowledged.
REFERENCES
1. C. S. Fuller, Phys. Rev., 86, pp. 136-137, 1952.
2. J. Saby and W. C. Dunlap, Jr., Phys. Rev., 90, p. 630, 1953.
3. W. Shocklej', private communication.
4. H. Kromer, Archiv. der Elek. tlbertragung, 8, No. 5, pp. 223-228, 1954.
5. R. A. Logan and M. Schwartz, Phys. Rev., 96, p. 46, 1954
6. L. B. Valdes, Proc. I.R.E., 42, pp. 420-427, 1954.
7. W. L. Bond and F. M. Smits, to be published.
8. E. S. Rittner, Pnys. Rev., 94, p. 1161, 1954.
9. W. M. Webster, Proc. I.R.E., 42, p. 914, 1954.
10. J. M. Early, B.S.T.J., 33, pp. 517-533, 1954.
Waveguide Investigations with
Millimicrosecond Pulses
By A. C. BECK
(Manuscript received October 11, 1955)
Pulse techniques have been used for many waveguide testing 'puryoses.
The importance of increased resolution hy means of short pulses has led to
the development of equipment to generate, receive and display pidses about
5 or 6 millimicroseconds lo7ig. The equipment is briefly described and its
resolution and measuring range are discussed. Domi7ia7it mode waveguide
and antenna tests are described, and illustrated. Applications to midtimode
waveguides are then considered. Mode separation, delay distortion and its
equalization, and mode conversion are discussed, and examples are given.
The resolution obtained with this equipment provides information that is
difficult to get by any other means, and its use has proved to be very helpfid
in ivaveguide investigations.
CONTENTS
1 . Introduction 35
2. Pulse Generation 36
3. Receiver and Indicator 41
4. Resolution and Measuring Range 42
5. Dominant Mode Waveguide Tests 43
6. Testing Antenna Installations 45
7. Separation of Modes on a Time Basis 48
8. Delay Distortion 52
9. Delay Distortion Ecjualization 54
10. Measuring Mode Conversion from Isolated Sources 57
11. Measuring Distril)uted Mode Conversion in 1 ong Waveguides 61
12. Concluding Remarks 65
1. INTRODUCTION
Pulse testing techniques have been employed to advantage in wave-
guide investigations in numerous ways. The importance of better resolu-
tion through the use of short pulses has always been apparent and, from
the first, eciuipment was employed which used as short a pulse as pos-
sible. Radar-type apparatus using magnetrons and a pulse width of
about one-tenth microsecond has seen considerable use in waveguide
research, and many of the results have been published.' • -
35
36 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
To improve the resolution, work was initiated some time ago by S. E.
Miller to obtain measuring equipment which would operate with much
shorter pulses. As a result, pulses about 5 or 6 millimicroseconds long
became available at a frequency of 9,000 mc. In a pulse of this length
there are less than 100 cycles of radio frequency energy, and the signal
occupies less than ten feet of path length in the transmission medium.
The RF bandwidth required is about 500 mc. In order to obtain such
bandwidths, traveling wave tubes were developed by J. R. Pierce and
members of the Electronics Research Department of the Laboratories.
The completed amplifiers were designed by W. W. Mumford. N. J.
Pierce, R. W. Dawson and J. W. Bell assisted in the design and construc-
tion phases, and G. D. Mandeville has been closely associated in all of
this work.
2. PULSE GENERATION
These millimicrosecond pulses have been produced by two different
types of generators. In the first equipment, a regenerative pulse gener-
ator of the type suggested by C. C. Cutler of the Laboratories was used.^
This was a very useful device, although somewhat complicated and hard
to keep in adjustment. A brief description of it will permit comparisons
with a simpler generator which was developed a little later.
A block diagram of the regenerative pulse generator is shown in Fig. 1.
The fundamental part of the system is the feedback loop drawn with
heavy lines in the lower central part of the figure. This includes a travel-
ing wave amplifier, a waveguide delay line about sixty feet long, a crystal
expander, a band-pass filter, and an attenuator. This combination forms
an oscillator which produces very short pulses of microwave energy.
Between pulses, the expander makes the feedback loop loss too high for
oscillation. Each time the pulse circulates around the loop it tends to
shorten, due to the greater amplification of its narrower upper part
caused by the expander action, until it uses the entire available band
width. A 500-mc gaussian band-pass filter is used in the feedback loop,^
of this generator to determine the final bandwidth. An automatic gain
control operates with the expander to limit the pulse amplitude, thus
preventing amplifier compression from reducing the available expansion.
To get enough separation between outgoing pulses for reflected pulse
measurements with waveguides, the repetition rate would need to be
too low for a practical delay fine length in the loop. Therefore a r2.8-mc
fundamental rate was chosen, and a gated traveling wave {\\\)v ampfifier
was used to reduce it to a 100-kc rate at the output. This amplifier is
kept in a cutoff condition for 127 pulses, and then a gate pulse restores
I
i
t
WAVEGUIDE TESTING WITH MILLIMIf'ROSECOND PULSES
37
it to the normal amplifying condition for fifty millimicroseconds, during
which time the 128th pulse is passed on to the output of the generator
as shown on Fig. 1.
The synchronizing system is also shown on Fig. 1. A 100-kc quartz
crystal controlled oscillator with three cathode follower outputs is the
basis of the system. One output goes through a seven stage multiplier
to get a 12.8-mc signal, which is used to control a pulser for synchroniz-
ing the circulating loop. Another output controls the gate pulser for the
output traveling wave amplifier. Accurate timing of the gate pulse is
obtained by adding the 12.8-mc pulses through a buffer amplifier to the
gate pulser. The third output synchronizes the indicator oscilloscope
sweep to give a steady pattern on the screen.
Although this equipment was fairly satisfactory and served for many
OSCILLATOR
AND CATHODE
FOLLOWERS
100 KC
I 1
MULTIPLIER
100 KC TO
12.8 MC
SYNC
PULSER
0.02 A SEC
12.8 MC
500 MC
BANDPASS
FILTER
GATE
PULSER
0.05 USEC
100 KC
A
BUFFER
AMPLIFIER
"1
CRYSTAL
EXPANDER
U
AGC I
WAVEGUIDE
DELAY
LINE
TW TUBE
■Y^
MILLI/iSEC/
9000 MC/'
PULSES
12.8 MC RATE
MlLLIyUSEC
9000 MC
PULSES
100 KC RATE
GATED
TW TUBE
SYNC SIGNAL TO
INDICATOR SCOPE
Fig. 1 — Block diagram of the regenerative pulse generator.
38 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
testing purposes, it was rather complex and there were some problems
in its construction and use. It was difficult to obtain suitable microwave
crystals to match the waveguide at low levels in the expander. Tliis
would make it even more difficult to build this type of pulse generator
for higher frequency ranges. Stability also proved to be a problem. The
frequency multiplier had to be very well constructed to avoid phase
shift due to drifting. The gate pulser also required care in design and
construction in order to get a stable and flat output pulse. It was some-
what troublesome to keep the gain adjusted for proper operation, and
the gate pulse time adjustment required some attention. The pulse
frequency could not be changed. For these reasons, and in order to get
a smaller, lighter and less complicated pulse generator, work was carried
out to produce pulses of about the same length by a simpler method.
If the gated output amplifier of Fig. 1 were to have a CW instead of a
pulsed input, a pulse of microwave energy would nevertheless appear at
the output because of the presence of the gating pulse. This gating pulse
is applied to the beam forming electrode of the tube to obtain the gating
action. If the beam forming electrode could be pulsed from cutoff to its
normal operating potential for a very short time, very short pulses of
output energy could be obtained from a continuous input signal. How-
ever, it is difficult to obtain millimicrosecond video gating pulses of suf-
ficient amplitude for this purpose at a 100-kc repetition rate.
A traveling-wave tube amplifies normally only when the helix is
within a small voltage range around its rated dc operating value. For
voltages either above or below this range, the tube is cut off. When the
helix voltage is raised through this range into the cutoff region beyond
it, and then brought back again, two pulses are obtained, one during a
small part of the rise time and the other during a small part of the return
time. If the rise and fall times are steep, very short pulses can be
obtained. Fig. 2 shows the pulse envelopes photographed from the
indicator scope screen when this is done. For the top trace, the helix was
biased 300 volts negatively from its normal operating potential, then
pulsed to its correct operating range for about 80 millimicroseconds,
during which time normal amplification of the CW input signal was ob-
tained. The effect of further increasing the helix video pulse amplitude
in the positive direction is shown by the succeeding lower traces. The
envelope dips in the middle, then two separated pulses remain — one
during a part of the rise time and one during a part of the fall time of
helix voltage. The pulses shown on the bottom trace have shortened to
about six millimicroseconds in length. The helix pulse had a positive
amplitude of about 500 volts for this trace.
1
WAVEGUIDE TESTIXG WITH MILUMICROSErOXD PULSES
39
Since only one of these pulses can be used to get the desired repetition
rate, it is necessary to eliminate the other pulse. This is done in a simi-
lar manner to that used for gating out the undesired pulses in the re-
generative pulse generator. However, it is not necessary to use another
amplifier, as was required there, since the same tube can be used for
this purpose, as well as for producing the microwave pulses. Its beam
forming electrode is biased negatively about 250 volts with respect to
the cathode, and then is pulsed to the normal operating potential for
about 50 millimicroseconds during the time of the first short pulse ob-
tained by gating the helix. Thus, the beam forming electrode potential
has been returned to the cutoff value during the second helix pulse,
which is therefore eliminated.
Il A block diagram of the resulting double-gated pulse generator is
shown in Fig. 3. Comparison with Fig. 1 shows that it is simpler
than the regenerative pulse generator, and it has also proved more
satisfactory in operation. It can be used at any frequency where a sig-
nal source and a traveling-wave amplifier are available, and the pulse
Fig. 2 — Envelopes of microwave pulses at the output of a traveling wave am-
lifier with continuous wave input and helix gating. The gating voltage is higher
or the lower traces.
40
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
frequency can be set anywhere within the bandwidth of the travehng-
wave ampUfier by tuning the klystron oscillator.
The pulse center frequency is shifted from that of the klystron os-
cillator frequency by this helix gating process. An over-simphfied but
helpful explanation of this effect can be obtained by considering that
the microwave signal voltage on the helix causes a bunching of the elec-
tron stream. This^ bunching has the same periodicity as the microwave
signal voltage when the dc helix potential is held constant. However,
since the helix voltage is continuously increased in the positive direction
during the time of the first pulse, the average velocity of the last bunches
of electrons becomes higher than that of the earlier bunches in the pulse,
because the later electrons come along at the time of higher positive
helix voltage. This tends to shorten the total length of the series of
bunches, resulting in a shorter w^avelength at the output end of the
helix and therefore a higher output microwave frequency. On the second
pulse, obtained when the helix voltage returns toward zero, the process
is reversed, the bunching is stretched out, and the frequency is de-
creased. This second pulse is, however, gated out in this arrangement
by the beam-forming electrode pulsing voltage. The result for this
particular tube and pulse length is an effective output frequency ap-
proximately 150 mc higher than the oscillator frequency, but this figure
is not constant over the range of pulse frequencies available within the
amplifier bandwidth.
OSCILLATOR AND
CATHODE FOLLOWERS
100 KC
KLYSTRON
OSCILLATOR
9000 MC
BEAM FORMING
ELECTRODE
PULSER
HELIX
PULSER
^
PULSED
TW TUBE
MILLI/aSEC
9000 MC
PULSES
SYNC SIGNAL TO
INDICATOR SCOPE
Fig. 3 — Block diugram of the double-gated traveling wave tube millimicro-
second pulse generator.
WAVEGUIDE TESTING WITH MILLIMICROSECOND PULSES
41
3. RECEIVER AND INDICATOR
The receiving equipment is shown in Fig. 4. It uses two traveUng-
wave amplifiers in cascade. A wide band detector and a video amplifier
then follow, and the signal envelope is displayed by connecting it to
the vertical deflecting plates of a 5 XP type oscilloscope tube. The
video amplifier now consists of two Hewlett Packard wide band dis-
tributed amplifiers, having a baseband width of about 175 mc. The
second one of these has been modified to give a higher output voltage.
The sweep circuits for this oscilloscope have been built especially for
this use, and produce a sweep speed in the order of 6 feet per micro-
second. An intensity pulser is used to eliminate the return trace. These
parts of the system are controlled by a synchronizing output from the
pulse generator 100-kc oscillator. A precision phase shifter is used at
the receiver for the same purpose that a range unit is employed in radar
systems. This has a dial, calibrated in millimicroseconds, which moves
the position of a pulse appearing on the scope and makes accurate
measurement of pulse delay time possible.
Fig. 4 also shows the appearance of the pulses obtained with this
equipment. The pulse on the left-hand side of this trace came from the
PULSE
SIGNAL
9000 MC
SYNC
SIGNAL
100 KC
TW TUBES
VIDEO
AMPLIFIER
INTENSITY
PULSER
0.05/USEC
100 KC
PRECISION
PHASE
SHIFTER
SWEEP
GENERATOR
DOUBLE-GATED
PULSE
REGENERATIVE
PULSE
Fig. 4 — Block diagram of millimicrosecond pulse receiver and indicator. The
idicator trace photograph shows pulses from each type of generator.
42
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
newer double-gated pulse generator, while the pulse on the right was
produced by the regenerative pulse generator. It can be seen that they
appear to have about the same pulse width and shape. This is partly
due to the fact that the video amplifier bandwidth is not c^uite adequate
to show the actual shape, since in both cases the pulses are slightly
shorter than can be correctly reproduced through this amplifier. The
ripples on the base line following the pulses are also due to the video
amplifier characteristics when used with such short pulses.
4. RESOLUTION AND MEASURING RANGE
Fig. 5 shows a piece of equipment which was placed between the pulse
generator and the receiver to show the resolution which can be obtained.
This waveguide hybrid junction has its branch marked 1 connected to
the pulse generator and branch 3 connected to the receiver. If the two
side branches marked 2 and 4 were terminated, substantially no energy
would be transmitted from the pulser straight through to the receiver.
However, a short circuit placed on either side branch will send energy
through the system to the receiver. Two short circuits were so placed
that the one on branch 4 was 4 feet farther away from the hybiid junc-
tion than the one on branch 2. The pulse appearing first is produced l)y
a signal traveling from the pulse generator to the short circuit on branch
2 and then through to the receiver, as shown by the path drawn with
short dashes. A second pulse is produced by the signal which travels
BRANCH
2
SHORT
CIRCUIT
BRANCH
FROM
PULSER
TO
RECEIVER
FIRST PULSE PATH
SECOND PULSE PATH
SHORT
CIRCUIT
DOUBLE-GATED PULSES
REGENERATIVE PULSES
Fig. 5 — W;iv(!guicle hyhriil ciicuil- uscxl to demonstrate resululion of milli-
microsecond pulses. Trace photographs of pulses from each type of generator ;iie
shown.
WAVEGUIDE TESTING WITH MILLIMICROSECOND PULSES
43
TO RECEIVER
\
TE° IN 3"DIAM copper GUIDE (ISO FT LONG)
Fig. 6 — Waveguide arrangement and oscilloscope trace photos showing pres-
ence and location of defective joint. The dominant mode (TEn) was used with its
polarization changed 90 degrees for the two trace photos.
from the pulse generator through branch 4 to the short circuit and then
to the receiver as shown by the long dashed line. This pulse has traveled
8 feet farther in the waveguide than the first pulse. This would be equiva-
lent to seeing separate radar echoes from two targets about 4 feet apart.
Resolution tests made in this way \vith the pulses from the regenerative
pulse generator, and from the double-gated pulse generator, are shown
on Fig. 5. With our video amplifier and viewing equipment, there is
no appreciable difference in the resolution obtained using either type
of pulse generator.
The measuring range is determined by the power output of the gated
amplifier at saturation and by the noise figure of the first tube in the
receiver. In this equipment the saturation level is about 1 watt, and the
noise figure of the first receiver tube is rather poor. As a result, received
pulses about 70 db below the outgoing pulse can be observed, which is
I enough range for many measurement purposes.
5. DOMINANT MODE WAVEGUIDE TESTS
Fig. 6 shows the use of this equipment to test 3'^ round waveguides
such as those installed between radio repeater equipment and an an-
tenna. This particular 150-foot line had very good soldered joints and was
thought to be electrically very smooth. The signal is sent in through a
transducer to produce the dominant TEn mode. The receiver is con-
nected through a directional coupler on the sending end to look for any
44 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
Fig. 7 — Defective joint caused by imperfect soldering which gave the reflec-
tion shown on Fig. 6.
reflections from imperfections in the line. The overloaded signal at the
left of the oscilloscope trace is produced by leakage directly through
the directional coupler. The overloaded signal on the other end of this
trace is produced by the reflection from the short circuit piston at the
far end of the waveguide. The signal between these two, which is about
45 db down from the input signal, is produced by an imperfect joint
in the waveguide. The signal polarization was oriented so that a maxi-
mum reflection was obtained in the case of the lower trace. In the
other trace, the polarization was changed by 90°. It is seen that this
particular joint produces a stronger reflection for one polarization than
for the other. By use of the precision phase shifter in the receiver the
exact location of this defect was found and the particular joint that was
at fault was sawed out. Fig. 7 shows this joint after the pipe had been
cut in half through the middle. The guide is quite smooth on the inside
in spite of the discoloration of some solder that is shown here, but on
the left-hand side of the illustration the open crack is seen where the
solder did not run in properly. This causes the reflected pulse that shows
on the trace. The fact that this crack is less than a semi-circumference
in length causes the echo to be stronger for one polarization than for the
other.
WAVEGUIDE TESTING WITH MILLIMICROSECOND PULSES
45
Fig. 8 shows the same test for a 3" diameter ahiminum waveguide
250 feet long. This line was mounted horizontally in the test building
with compression couplings used at the joints. The line expanded on
warm days hut the friction of the mounting supports was so great that
it pulled open at some of the joints when the temperature returned to
normal. These open joints produced reflected pulses from 40 to 50 db
down, which are shown here. They come at intervals equal to the length
of one section of pipe, about 12 feet. Some of these show polarization
effects where the crack was more open on one side than on the other,
but others are almost independent of polarization. These two photo-
graphs of the trace were taken with the polarization changed 90°.
Fig. 9 shows the same test for a 3" diameter galvanized iron wave-
guide. This line had shown fairly high loss using CW for measure-
ments. The existence of a great many echoes from random distances
indicates a rough interior finish in the waveguide. Fig. 10 shows the
kind of inperfections in the zinc coating used for galvanizing which
caused these reflections.
6. TESTING ANTENNA INSTALLATIONS
The use of this equipment in testing waveguide and antenna installa-
tions for microwave radio repeater systems is shown in Fig. 11. This
particular work was done in cooperation wdth A. B. Crawford's antenna
research group at Holmdel, who designed the antenna system. A direc-
tional coupler was used to observe energy reflections from the system
under test. In this installation a 3" diameter round guide carrying the
TEu mode was used to feed the antenna. Two different waveguide
TE,, IN 3"D1AM aluminum GUIDE (250 FT LONG)
Fig. 8 — Reflections from several defective joints in a dominant (TEn) mode
waveguide. The two trace photos are for polarizations differing by 90 degrees.
46
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
TO RECEIVER ^n
^— a^IS^rv^
i— ^
TE
■^-^Bi
21
I
10
TE,° IN 3" DIAM GALVANIZED IRON GUIDE (250 FT LONG)
Fig. 9 ■ — Multiple reflections from a dominant (TEn) mode waveguide with a
rough inside surface. The two trace photos are for polarizations differing by 90 I
degrees.
joints are shown here. In addition, a study was being made of the re-
turn loss of the transition piece at the throat of the antenna which •
connected the 3" waveguide to the square section of the horn. The I
waveguide sections are about 10 feet long. The overloaded pulse at the
left on the traces is the leakage through the directional coupler. The
Fig. 10 — Rough inside surface of a galvanized iron waveguide which produced
the reflections shown on Fig. 9.
I
WAVEGUIDE TESTING WITH MILLIMICROSECOND PULSES
47
other echoes are associated with the parts of the system from which
they came by the dashed Hues and arrows on the figure. A clamped
joint in the line gave the reflection shown next following the initial
overloaded pulse. A well made threaded coupling in which the ends of
the pipe butted squarel,y is seen to have a very much lower reflection,
scarcely observable on this trace. Since there is ahvays reflection from
the mouth and upper reflector parts of this kind of antenna, it is not
possible to measure a throat transition piece alone by conventional CW
methods, as the total reflected power from the system is measured.
Here, use of the resolution of this short pulse equipment completely
separated the reflection of the transition piece from all other reflections
and made a measurement of its performance possible. In this particular
case, the reflection from the transition is more than 50 db down from
the incident signal which represents very good design. As can be seen,
OPEN APERTURE
FIBERGLASS COVER
OVER APERTURE
REFLECTION APPEARS
-^TO COME FROM 16 FT
N FRONT OF HORN MOUTH
DIRECTIONAL TRANSDUCER CLAMPED THREADED ROUND-TO
COUPLER JOINT COUPLING SQUARE
TRANSITION
Fig. 11 — Waveguide and antenna arrangement with trace photos showing re-
flections from joints, transition section, and cover.
48 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
the reflection from the parabohc reflector and mouth is also finite low,
and this characterizes a good antenna installation.
The extra reflected pulse on the right of the lower trace on Fig. 11
appeared when a fiberglas weatherproof cover was installed over the
open mouth of the horn. This cover by itself would normally produce a
troublesome reflection. However, in this antenna, it is a continuation of
one of the side walls of the horn. Consequently, outgoing signals strike
it at an oblique angle. Reflected energy from it is not focused by the
parabolic section back at the waveguide, so the overall reflected power
in the waveguide was found to be rather low. However, measuring it
with this equipment, we found that an extra reflection appeared to
come from a point 16 feet out in front of the mouth of the horn when the
cover was in place. This is accounted for by the fact that energy re-
flected obliquely from this cover bounces back and forth inside the
horn before getting back into the waveguide, thus traveling the extra
distance that makes the measurement seem to show that it comes from
16 feet out in front.
7. SEPARATION OF MODES ON A TIME BASIS
If a pulse of energy is introduced into a moderate length of round
waveguide to excite a number of modes which travel with different
group velocities, and then observed farther along the line, or reflected
from a piston at the end and observed at the beginning, separate pulses
will be seen corresponding to each mode that is sent. This is illustrated
! t r
t t
TE„ TMo,TE2,
TM„ TE3,
(TEoi)
^NOT EXCITED
TO RECEIVER
=^
^-^
=^^
t
;ft
t
TMj,
TE4I TE,2
TM02
TM3, AND
TE5, TOO
WEAK TO
SHOW
TE,
•^^ "
PROBE 3 DIAM ROUND GUIDE
COUPLING (WILL SUPPORT 12 MODES)
Fig. 12 — Arrangement for showing mode separation on a time basis in a multi-
mode waveguide. The pulses in the trace ])]io(o have all traveled to the iiisloii and
back. The earlier outgoing pulse due to direelional coupler unbalance is not shown.
WAVEGUIDE TESTING WITH MILLIMICROSECOND PULSES
49
in Fig. 12. In this arrangement energy was sent into the round line from
a probe inserted in the side of the guide. This couples to all of the 12
modes which can be supported, with the exception of the TEoi circular
electric mode. The sending end of the round guide was terminated. A
directional coupler is connected to the sending probe so that the return
from the piston at the far end can be observed on the receiver. Because
of the different time that each mode takes to travel one round trip in
this waveguide, which was 258 feet long, separate pulses are seen for
each mode. The pulses in this figure have been marked to show which
mode is being received.
The time of each pulse referred to the outgoing pulse was measured
and found to check very well with the calculated time. The formula for
the time of transit in the waveguide for any mode is:
T =
0.98322V'1 - VnJ
[where T = time in millimicroseconds
L = length of pulse travel in feet
Vnm ^^ A /Ac
X = operating wavelength in air
Ac = cutoff wavelength of guide for the mode involved.
[ Table I — Calculated and Measured Value of Time for One
Round Trip
Time in Millimicroseconds
Mode Designation
Calculated
Measured
1
TEn
545
545
2
TMoi
561
561
3
TE,i
587
587
4
TMn
634
634
5
TEoi
634
.
6
TE31
665
665
7
TM21
795
793
8
TE4:
835
838
9
TE12
838
10
TM„2
890
890
11
TMn
1461
—
12
TE51
1519
—
50 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
The calculated and measured \'alue of time for one round trip is given
in Table I.
In this experiment the operating wavelength was 3.35 centimeters
This was obtained by measurements based on group velocit}' in a num-
ber of guides as well as information about the pulse generator com-
ponents. It represents an effective wa\'elength giving correct time of
travel. The pulse occupies such a wide bandwidth that a measurement
of its wavelength is difficult by the usual means.
The dashes in the measured column indicate that the mode was not
excited by the probe or was too weak to measure. These modes do not
appear on the oscilloscope trace photograph.
The relative pulse heights can be calculated from a knowledge of the
probe coupling factors and the line loss. The probe coupling factors as
given by M. Aronoff in unpublished work are expressed by the following
For TE„„, modes:
P = 2.390 r—^
i
For TM„^ modes:
TV- L a -.
j\. nm ^ "flu
X X
P = 1.195€„ — -
where
P = ratio of probe coupling power in mode nm to that in mode TEn
n = first index of mode being calculated
Knm = Bessel function zero value for mode being calculated = Td/\c
X = wavelength in air
X(, = wavelength in the guide for the mode involved '
Xc = cutoff wavelength of guide for the mode involved
€„ = 1 for w = 0
€„ = 2 for n ?^ 0 ,
d = waveguide diameter
Formulas for guide loss as given by S. A. Schelkunoff on page 390 of
his book Elect romagnelir Waves for this case where the resistivity of the
aluminum guide is 4.14 X 10~^ ohms per cm cube are:
WAVEGUIDE TESTING WITH MILLIMICROSECOND PULSES 51
For TE„,„ modes:
a = 3.805 ! — 2 2 + V.an ) (1 " Vnm)
\l\n,n — n /
For TM„,„ modes:
a = 3.805(1 - VnJy'''
where:
a = attemiation of this aluminum guide in db
n — first index of mode being calculated
Knm — Bessel function zero value for mode being calculated = TrtZ/Xc
Vnm = A/Ac
X = operating wavelength in air
Xc = cutoff wavelength of guide for the mode involved
d = waveguide diameter
Table II gives the calculated probe coupling factor, line loss, and rela-
tive pulse height for each mode. In the calculation of the latter, wave
elUpticity and loss due to mode conversion were neglected, but the heat
loss given by the preceding formulas has been increased 20 per cent for
all modes, to take account of surface roughness. Relative pulse heights
were obtained by subtracting the relative line loss from twice the rela-
tive probe coupling factor. The relative line loss is the number in the
itable minus 2.33 db, the loss for the TEn mode.
The actual pulse heights on the photo of the trace on Fig. 12 are in
fair agreement with these calculated values. Differences are probably
due to polarization rotation in the guide (wave ellipticity) and conver-
sion to other modes, effects which were neglected in the calculations,
and which are different for different modes.
Calculated pulse heights with this guide length, except for modes
near cutoff, vary less than the probe coupling factors, because line loss
is high when tight probe coupling exists. This is to be expected, since
both are the result of high fields near the guide walls.
The table of round trip travel time shows that the TE41 and TE12
modes are separated by only three millimicroseconds after the round
trip in this waveguide. They would not be resolved as separate pulses
by this e(iuipment. However, the table of calculated pulse heights shows
that the TE41 pulse should be about 22 db higher than the TE12 pulse.
52
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
Table II — Calculated Probe Coupling Factor, Line Loss and
Pulse Height for Each Mode
Mode
Mode
Relative Probe
1.2 X Theoretical
Calculated Relatix e
Number
Designation
Coupling Factor,
db
Line Loss, db
Pulse Heights, db
1
TEu
0
2.33
0
2
TMoi
+0.32
4.88
-1.91
3
TE2,
+2.86
4.85
+3.20
4
TMu
+2.80
5.51
+2.42
5
TEo,
— 00
1.73
— 00
6
TE31
+4.82
8.21
+3.76
7
TM2,
+ 1.82
6.92
-0.95
8
TE41
+6.80
13.86
+2.07
9
TE12
-8.73
4.70
-19.83
10
TM02
-1.68
7.74
-8.77
11
TMsi
-0.82
12.71
-12.02
12
TE51
+ 10.14
32.09
-9.48
Since the TE12 pulse is so weak, it would not show on the trace even if
it were resolved on a time basis. Coupling to the TM02 mode is rather
weak, and the gain was increased somewhat at its position on the trace
to show its time location.
8. DELAY distortion
Another effect of the wide bandwidth of the pulses used with this
equipment can be observed in Fig. 12. The pulses that have traveled
for a longer time in the guide are in the modes closer to cutoff, and are
on the right-hand side of the oscilloscope trace. They are broadened
and distorted compared with the ones on the left-hand side. This effect
is due to delay distortion in the guide. This can be explained by refer-
ence to Fig. 13. On this figure the ratio of group velocity to the velocity
in an unbounded medium is shown plotted as a function of frequency
for each of the modes that can be propagated. The bandwidth of the
transmitted pulse is indicated by the vertical shaded area. It will he
noticed that the spacing of the pulses on the oscilloscope trace on Fig.
12 from left to right in time corresponds to the spacing of the group
velocity curves in the bandwidth of the pulse from top to bottom. De-
lay distortion on these curves is shown by the slope of the line across
the pulse bandwidth. If the line were horizontal, showing the same group
velocity at all points in the band, there would be no delay distortion.
The greater the difference in group A-elocity at the two edges of the
band, the greater the delay distortion. The curves of Fig. 13 indicate
WAVEGUIDE TESTING WITH MILLIMICROSECOND PULSES
53
I that there should be increasing amounts of delay distortion reading
ifrom top to bottom for the pulse bandwidth used in these experiments.
;The effect of this delay distortion is to cause a broadening of the pulse.
Examination of the pulse pattern of Fig. 12 shows that the later pulses
corresponding in mode designation to the lower curves of Fig. 13 do in-
deed show a broadening due to the increased delay distortion. One
method of reducing the effect of delay distortion is to use frequency
division multiplex so that each signal uses a smaller bandwidth. Another
way, suggested by D. H. Ring, is to invert the band in a section of the
waveguide between one pair of repeaters compared with that between
an adjacent pair of repeaters so that the slope is, in effect, placed in the
opposite direction, and delay distortion tends to cancel out, to a first
order at least.
The (luantitative magnitude of delay distortion has been expressed
by S. Darlington in terms of the modulating base-band frequency
needed to generate two side frequencies which suffer a relative phase
error of 180° in traversing the line. This would cause cancellation of a
single frequency AM signal, and severe distortion using any of the
1.0
PULSE BANDWIDTH
— >.
<—
^^
^—
UJ
^0.9
Q.
</)
OI
mo.8
u.
z
^0.7
1-
o
O
>
o
^ 0.5
>-
o
3 0.4
m
>
^0.3
o
(r
o
^0.2
o
io.,
0
■^^H;;^
. —
/^
o^^
^
^
^
^^
/
/
y
\a
X
y
/
^
^
/
/
/
6
^
/
7
/
f
//
<
f/>
\
^-'^'fA
y^.
/
/
1
/
1
'L
f4
//
1
/
/
1
1
/A
'/
//
//
L
^i
/ 1
7
\\
1
3 4
FREQUENCY
5 6 7 8 9 10
IN KILOMEGACYCLES PER SECOND
12
1 Fig. 1.3 — Theoretical group velocity vs. frequency curves for the 3" diameter
ivaveguide used for the tests shown on Fig. 12. The vertical shaded area gives the
bandwidth for the millimicrosecond pulses employed in that arrangement.
54 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
ordinary modulation methods. Darlington gives this formula:
^) ^^^^
iLLi/ Vnm
where :
jB = base bandwidth for 180° out of phase sidebands
/ = operating frequency (in same units as jB)
X = wavelength in air
L = waveguide length (in same units as X)
Vnm = X/Xe
Xc = cutoff wavelength for the mode involved
With this equipment, the base bandwidth of the pulse is about 175
mc, and when/5 from the formula above is about equal to or less than
this, pulse distortion should be observed. The following Table III gives
fB calculated from this formula for the arrangement shown on Fig. 12.
It is interesting to note that pulses in the TMu and TE31 modes, for
which jB is less than the 175-mc pulse bandwidth, are broadened, but
not badly distorted. For the higher modes, where jB is much less than
175 mc, broadening and severe distortion are evident. Another example
is given in the next section.
9. DELAY DISTORTION EQUALIZATION
If the distance which a pulse travels in a waveguide is increased, its
delay distortion also increases. Since the group velocity at one edge of
the band is different than at the other edge of the band, the amount
by which the two edges get out of phase with each other increases with
the total length of travel, causing increased distortion and pulse broaden-
ing. The Darlington formula in the previous section shows that jB
varies inversely as the square root of the length of travel. This efTect
is shown on Fig. 14. In this arrangement the transmitter was connected
to the end of a 3" diameter round waveguide 107 feet long through a
small hole in the end plate. A mode filter was used so that only the
TEoi mode would be transmitted in this Avaveguide. Through another
small hole in the end plate polarized 90° from the first one, and rotated
90° around tlu^ plate, a directional coupler was connected as shown.
The direct through guide of this directional coupler could be short cir-
cuited with a waveguide shorting switch. Energy reflected from this
fl
WAVEGUIDE TESTING WITH MILLIMICROSECOND PULSES
55
Table III -
— Calculatee
> Values of fB foe the Arrangement
Shown in Fig. 1
2
Mode Number
Mode Designation
/B Megacycles
Remarks
1
TEn
324.0
2
TMoi
237.7
3
TEn
174.9
4
TMu
124.1
5
TEoi
124.1
Not excited
6
TE31
105.2
7
TMoi
65.9
8
TE41
59.1
9
TEi,
58.6
Veiy weakly excited
10
TMoo
51.8
11
TM3:
21.3
Not observed
12
TE51
20.0
Not observed
NUMBER OF
R(
3UND TRIPS
TAPERED
DELAY
DISTORTION
EQUALIZER
WAVEGUIDE
SHORTING
SWITCH
1/
'M
^
te;
>T0 RECEIVER
NOT EQUALIZED
(SWITCH CLOSED)
EQUALIZED
(SWITCH OPEN)
TEqiIN 3 DIAM ROUND GUIDE
(107 FT LONG)
Fig. 14 — The left-hand series of pulses shows the build up of delay distortion
with increasing number of round trips in a long waveguide. The right-hand series
shows the im]irovement obtained with the tapered delay distortion equalizer
shown at the right.
56
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
switch was then taken through the directional coupler to the receiver
as shown by the output arrow. The series of pulses at the left-hand
photograph of the oscilloscope traces was taken with this waveguide i
shorting switch closed. The top pulse shows the direct leakage across
the inside of the end plate before it has traveled through the 3" round
guide. The next pulse is marked one round trip, having gone therefore
214 feet in the TEoi mode in the round waveguide. The successive pulses
have traveled more round trips as shown by the number in the center
between the two photographs. The effect of increased delay distortion
broadening and distorting the pulse can be seen as the numbers increase.
The values of fB from the Darlington formula in the previous section
for these lengths are given in Table IV.
It will be noticed that pulse broadening, and eventually severe dis-
tortion, occurs as fB decreases much below the 175-mc pulse band-
width. The effect is gradual, and not too bad a pulse shape is seen until
fB is about half the pulse bandwidth, although broadening is very
evident earlier.
When the waveguide short-circuiting switch was opened so that the
tapered delay distortion equalizer was used to reflect the energy, in-
stead of the switch, the series of pulses at the right was observed on
the indicator. It will be noted that there is much less distortion of these,
pulses, particularly toward the bottom of the series. The ones at the top,
have less distortion than would be expected, probably because of fre-,
quency modulation of the injected pulse. The equalizer consists of a
long gradually tapered section of waveguide which has its size reduced
to a point beyond cutoff for the frequencies involved. Reflection takes
place at the point of cutoff in this tapered guide. For the high frequency
part of the pulse bandwidth, this point is farther away from the short-
ing switch than for the low frequency part of the bandwidth. Conse-
quently, the high frequency part of the pulse travels farther in one round
trip into this tapered section and back than the low frequency part of
Table IV — Values of fB from the Darlington Formula
FOR the Arrangement Show^n in Fig. 14
li
Round Trip Number
JB Megacycles
Round Trip Number
fB Megacycles
1
2
3
4
5
185.8
131.4
107.3
92.9
83.1
6
7
8
9
10
75.8
70.2
65.7
61.9
58.7
j
1
1
WAVEGUIDE TESTING WITH MILLIMICROSECOND PULSES 57
he pulse. This increased time of travel compensates for the shorter
ime of travel of the high frequency edge of the band in the 3" round
.vaveguide, so equalization takes place. Since this waveguide close to
cutoff introduces considerable delay distortion by itself, the taper effect
nust be made larger in order to secure the equalization. This can be
ilone by making the taper sufficiently gradual. This type of equalizer
ntroduces a rather high loss in the system. For this reason it might
le used to predistort the signal at an early level in a repeater system,
ilqualization by this method was suggested by J. R. Pierce.
.0. MEASURING MODE CONVERSION FROM ISOLATED SOURCES
I One of the important uses of this equipment has been for the meas-
irement of mode conversion. W. D. Warters has cooperated in develop-
ng techniques and carrying out such measurements. One of the prob-
ems in the design of mode filters used for suppressing all modes except
;he circular electric ones in round multimode guides is mode conversion.
Since these mode filters have circular symmetry, conversion can take
alace only to circular electric modes of order higher than the TEoi mode.
This conversion is, however, a troublesome one, since these higher
Drder circular modes cannot be suppressed by the usual type of filter.
An arrangement for measuring mode conversion at such mode filters
rom the TEoi to the TE02 mode is being used with the short pulse equip-
:nent. This employs a 400-foot long section of the b" diameter line. Be-
ause the coupled- line transducer available had too high a loss to TE02 , a
3ombined TEoi — TE02 transducer was assembled. It uses one-half of
:he round waveguide to couple to each mode. Fig. 15 shows this device.
The use of this transducer and line is illustrated in Fig. 16. Pulses in
:he TEoi mode are sent into the waveguide by the upper section of the
transducer as shown. Some of the TEoi energy goes directly across to
ohe TE02 transducer and appears as the outgoing pulse with a level
down about 32 db. This is useful as a time reference in the system and
s shown as the outgoing pulse in the photo of the oscilloscope trace
ibove. The main energy in the TEoi mode propagates down the line as
hown by dashed line 2, which is the path of this wave. Most of
ohis energy goes all the way to the reflecting piston at the far end and
ohen returns to the TE02 transducer where it gives a pulse which is
narked TEoi round trip on the trace photograph above. Two thirds of
;he way from the sending end to the piston, the mode filter being meas-
ired is inserted in the line. When the TEoi mode energy comes to this
node filter, a small amount of it is converted to the TE02 mode. This
58
THE BELL SYSTEM TECHNICAL JOURNAL
Fig. 15 — A special experimental transducer for injecting the TEoi mode and'
receiving the converted TE02 mode in a 5" diameter waveguide.
continues to the piston by path 4 (with dashed Hnes and crosses)
and then returns and is received by the TE02 part of the transducer.
This appears on the trace photo as the TE02 first conversion. When the
main TEoi energy reflected by the piston comes back to the mode filter,
conversion again takes place to TE02 • This is shown by path 3 hav-
ing dashed lines and circles. This returns to the TE02 part of the trans-
ducer and appears on the trace photo as the TE02 second conversion.
In addition, a small amount of energy in the TE02 mode is generated
by the TEoi upper part of the transducer. It is shown by path 5, having'
OUTGOING PULSE
TEoi
ROUND
TRIP
TE02
SECOND
CONVERSION
TE02
FIRST
CONVERSION
TE02
ROUND
TRIP
'
MODE FILTER
Fig. 16 — Trace photos and waveguide paths traveled when measuring TEoi,
to TE02 mode conversion at a mode filter with the transducer shown on Fig. 15
All
WAVEGUIDE TESTING WITH MILLIMICROSECOND PULSES 59
jihort dashes. This goes down through the waveguide to the far end
Ijiston and back, and is received by the TE02 transducer and shown as
[he pulse marked TE02 round trip. The pulse marked TEoi round trip
las a time separation from the outgoing pulse which is determined by
,he group velocity of TEoi waves going one round trip in the guide. The
|rEo2 round trip pulse appears at a time corresponding to the group
/elocity of the TE02 mode going one round trip in the guide. Spacing the
node filter two-thirds of the way down produces the two conversion
:)ulses equally spaced between these two as shown in Fig. 16. The first
ponversion pulse appears at a time which is the sum of the time taken
or the TEoi to go down to the filter and the TE02 to go from the filter
uo the piston and back to the receiver. Because of the slower velocity
bf the TE02 , this appears at the time shown, since it was in the TE02
node for a longer time than it was in the TEoi mode. The second con-
[/ersion, which happened when TEoi came back to the mode filter, comes
jiarlier in time than the first conversion, since the path for this signal
ivas in the TEoi mode longer than it was in the TE02 mode. This arrange-
,nent gives very good time separation, and makes possible a measure-
Inent of the amount of mode conversion taking place in the mode filters,
viode conversion from TEoi to TE02 as low as 50 to 55 db down, can be
neasured with this equipment.
Randomly spaced single discontinuities in long waveguides can be
ocated by this technique if they are separated far enough to give in-
lividually resolved short pulses in the converted mode. Fig. 17 shows
CONVERSION
FIRST CONVERSION AT FAR END SECOND CONVERSION
AT NEAR END SQUEEZED AT NEAR END
SQUEEZED SECTION SECTION SQUEEZED SECTION
TO RECEIVER
TEJo — *- TEq, TE2, -• »- TE,o NEAR END 250 FT OF FAR END
TRANSDUCER COUPLED LINE SQUEEZED 3"DIAM ROUND SQUEEZED
TRANSDUCER SECTION GUIDE SECTION
Fig. 17 — Arrangement used to explain the measurement and location of mode
onversion from isolated sources. A deliberately squeezed section was placed
t each end of the long waveguide, producing the pulses shown in the trace photo.
60 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
an arrangement having oval sections deliberately placed in the wave- '
guide in order to explain the method. Pure TEoi excitation is vised, and
the converted TE21 mode observed with a coupled line transducer giv- ;
ing an output for that mode alone. ;
Let us consider first what would happen with the far-end squeezed;
section alone, omitting the near-end squeezed section from considera- •
tion. The injected TEoi mode signal would then travel down the 250 ,
feet of 3" diameter round waveguide to the far end with substantially,
no mode conversion at the level being measured. At this point it goes
through the squeezed section. Conversion now takes place from the TEou,
mode to the TE21 mode. Both these modes after reflection from the piston
travel back up the waveguide to the sending end. The group velocity
of the TE21 mode is higher than the group velocity of the TEoi mode, so
energy in these two modes separates, and if a coupling system were
used to receive energy in both modes, two pulses would appear, with at
time separation between them. In this case, since the receiver is con-
nected to the line through the coupled line transducer which is responsive
only to the TE21 mode, only one pulse is seen, that due to this mode
alone. This is the center pulse in the trace photograph at the top of
Fig. 17. If only one mode conversion point at the far end of the guide
exists, only this one pulse is seen at the receiver. It would be spaced a
distance away from the injected outgoing pulse that corresponds m:^
time to one trip of the TEoi mode down to the far end and one trip of ||
the TE21 mode from the far end back to the receiver.
Now let us consider what would happen if the near-end squeezed sec-
tion alone were present. When the TEqi wave passes the oval section!
just beyond the coupled line transducer, conversion takes place, andi
the energy travels down the line in both the TEoi and the TE21 modes,:;
at a higher group velocity in the TE21 mode. These two signals are re-
flected by the piston at the far end and return to the sending end. The
TE21 signal comes through the coupled line transducer and appears as
the pulse at the left of the photo shown on Fig. 17. Now the TEoi energy
has lagged behind the TE21 energy, and when it gets back to the near-
end squeezed section, a second mode conversion takes place, and TE21
mode energy is produced which comes through the coupled line trans-:
ducer and appears at the receiver at the time of the right hand pulse.
The spacing between these two pulses is equal to the difference in round
trip times between the two modes.
In general, for a single conversion source occurring at any point in
the line, two pulses will appear on the scope. The spacing between these
pulses corresponds to the difference in group velocity between the modes.
WAVEGUIDE TESTING AVITH MILLIMICROSECOND PULSES 61
{from the point of the discontiimity down to the piston at the far end,
land then back to the discontinuity. If the discontinuity is at the far
lend, this time difference becomes zero, and a single pulse is seen. By
i [making a measurement of the pulse spacing, the location of a single
i icon version point can be determined.
[ In the arrangement illustrated in Fig. 17, two isolated sources of
j conversion existed. They were spaced far enough apart so that they
\ were resolved by this equipment, and all three pulses were observed.
The two outside pulses were due to the first conversion point. The center
pulse was caused by the other squeeze, which was right at the reflecting
|:)iston. If this conversion point had been located back some distance
rom the piston, it would have produced two conversion pulses whose
'spacing could be used to determine the location of the conversion point.
I The coupled-line transducers are calibrated for coupling loss by send-
ng the pulse through a directional coupler into the branch normally
ised for the output to the receiver. This gives a return loss from the
lirectional coupler equal to twice the transducer loss plus the round
rip line loss.
1. MEASURING DISTRIBUTED MODE CONVERSION IN LONG WAVEGUIDES
; Measurements of mode conversion from TEoi to a number of other
nodes have been made with 5" diameter guides using this equipment,
rhe arrangement of Fig. 18 was set up for this purpose. This is the same
IS Fig. 17, except that a long taper was used at the input end of the 5"
waveguide, and a movable piston installed at the remote end.
One of the converted modes studied with this apparatus arrange-
uent was the TMu mode, which is produced by bends in the guide,
rhis mode has the same velocity in the waveguide as the TEoi mode.
Therefore energy components converted at different points in the line
tay in phase with the injected TEoi mode from which they are converted,
rhere is never any time separation between these modes, and a single
TO RECEIVER
■ I ■■'■ '■■■ ^
^^i
Si
TEro— *TE^, COUPLED LINE -^^p^P, 5„ 0,^^^ MOVABLE
TRANSDUCER TRANSDUCER HOLMDEL LINE PISTON
FOR THE MODE
BEING MEASURED
Fig. 18 — Arrangement used for measuring mode conversion in the 5" diameter
aveguides at Holmdel.
62
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
narrow pulse like the transmitted one is all that appears on the indicator
oscilloscope. It is not possible from this to get any information about
the location or extent of the conversion points in the line. Moving the
far end piston does not change the relative phases of the modes, so no
changes are seen in indicator pattern or pulse level as the piston is
moved. For the Holmdel waveguides, which are about 500 feet long,
the total round trip T]\In mode converted level varies from 32 to 36 db
below the input TEoi mode level over a frequency range from 8,800 to
9,600 mc per second.
All the other modes have velocities that are different than that of
the TEoi mode. ^Vhen mode conversion takes place at many closely
spaced points along the waveguide, the pulses from the various sources
overlap, and phasing effects take place. In general, a filled-in pulse
much longer than the injected one is observed. The maximum possible,
but not necessary, pulse length is equal to the difference in time re-
quired for the TEoi mode and the converted mode to travel the total
waveguide length being observed. The phasing effects within the broad-
ened pulse change its height and shape as a function of frequency and
line length.
Measurements of mode conversion from TEoi to TE31 in these wave-
guides illustrate distributed sources and piston phasing effects. The
TE3, mode has a group velocity 1.4 per cent slower than the TEoi mode.
For a full round trip in the 500-foot lines, assuming conversion at the
imput end, this causes a time separation of about two and one half
pulse widths between these two modes. The received pulse is about two
and a half times as long as the injected pulse, indicating rather closely
spaced sources over the whole line length. For one far-end piston posi-
tion, the received pattern is shown as the upper trace in Fig. 19. As
the piston is moved, the center depressed part of the trace gradually
ImK. 10 — Hocoivcd pulsr patterns willi llic .irraiijicnuMit of Fig. IS used for
studying conversion to tlie Tlvn mode.
WAVEGUIDE TESTING WITH MILLIMICROSECOND PULSES 63
rises until the pattern shown in the lower trace is seen. As the piston
is moved farther in the same direction the trace gradually changes to
have the appearance of the upper photo again. Moving the far-end
piston changes the phase of energy on the return trip, and thus it can
be made to add to, or nearly cancel out, conversion components that
originated ahead of the piston. When the time separation becomes
great enough to prevent overlapping in the pulse ^^^dth, phasing effects
cannot take place, therefore, the beginning and end of the spread-out
received pulse are not affected by moving the piston. Energy converted
at the sending end of the guide travels the full round trip to the piston
and back in the slower TE31 mode, and thus appears at the latest time,
which is at the right-hand end of the received pulse. Conversion at the
piston end returns at the center of the pulse, and conversion on the
return trip comes at earlier times, at the left-hand part of the pulse.
The TEoi mode has less loss in the guide than the TE31 mode. Since the
energy in the earlier part of the received pulse spent a greater part of
the trip in the lower loss TEoi mode before conversion, the output is
higher here, and slopes off toward the right, where the later returning
energy has gone for a longer distance in the higher loss mode. The pulse
height at the maximum shows the converted energy from that part of
the line to be between 30 and 35 db below the incident TEoi energy
level over the measured band\\ddth.
Measurements of mode conversion from TEoi to TE21 in these wave-
guides show these same effects, and also a phasing effect as a function
of frequency. The TE21 mode has a group velocity 2.4 per cent faster
than the TEoi mode. For a full round trip in the guides, this is a time
separation of about four pulse mdths between the modes. At one fre-
quency and one far-end piston position, the TE21 response shown as the
top trace of Fig. 20 was obtained. Moving the far-end piston gradually
changed this to the second trace from the top, and further piston mo-
tion changed it back again. This is the same kind of piston phasing effect
observed in the TE31 mode conversion studies. The irregular top of this
broadened pulse indicates fewer conversion points than for the TE31
mode, or phasing effects along the guide length. Since the TE21 mode
has a higher group velocity' than the TEoi mode, energy converted at
the beginning of the guide returns at the earlier or left-hand part of the
pulse, and conversions on the return trip, having traveled longer in
the slower TEoi mode, are on the right-hand side of the pulse. This is
just the reverse of the situation for the TE31 mode. Since the loss in the
TE21 mode is higher than in the TEoi mode, the right side of this broad-
ened pulse is higher than the left side, as the energy in the left side has
64
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
gone further in the higher loss TE21 mode. Conversions from the piston
end of the guide return in the center of the pulse, and only in this re-
gion do piston phasing effects appear. As the frequency is changed the '
pattern changes, until it reaches the extreme shape shown in the next-
to-the-bottom trace, with this narrower pulse coming at a time corre-
sponding to the center of the broadened pulse at the top. Further fre-
quency change in the same direction returns the shape to that of the
top traces. At the frequency giving the received pulse shown on the
next-to-the-bottom trace, moving the far-end piston causes a gradual
change to the shape shown on the lowest trace. This makes it appear
as if the mode conversion were coming almost entirely from the part of
the guide near the piston end at this frequency. The upper traces appear
to show that more energy is converted at the transducer end of the
waveguide at that frequency. It would seem that at certain frequencies
some phase cancellation is taking place between conversion points
spaced closely enough to overlap within the pulse width . At frequencies
between the ones giving traces like this, the appearance is more like
that shown for the TE31 mode on Fig. 19 except for the slope across the
top of the pulse being reversed. The highest part of this TEoi pulse is
Fiff. 20 — Received pulse patterns witli the urrangemeiit of Fig. 18 used for
studying conversion to the TE21 mode.
WAVEGUIDE TESTING WITH MILLIMICKOSECOND PULSES 65
24 to 27 db below the injected TEoi pulse level for the 5" diameter
Holmdel waveguides.
12. CONCLUDING REMARKS
The high resolution obtainable with this millimicrosecond pulse
equipment provides information difficult to obtain by any other means.
These examples of its use in waveguide investigations indicate the
possibilities of the method in research, design and testing procedures.
It is being used for many other similar purposes in addition to the illus-
tratio)is given here, and no doubt many more uses will be found for
such short pulses in the future.
REFERENCES
1. S. E. Miller and A. C. Beck, Low-loss Waveguide Transmission, Proc. I.R.E.,
41, pp. 348-358, March, 1953.
2. S. E. Miller, Waveguide As a Communication Medium, B. S. T. J., 33, pp. 1209-
1265, Nov., 1954.
3. C. C. Cutler, The Regenerative Pulse Generator, Proc. I.R.E., 43, pp. 140-
148, Feb., 1955.
4. S. E. Miller, Coupled WaveTheory and Waveguide Applications, B. S. T. J., 33,
pp. 661-719, May, 1954.
Experiments on the Regeneration of
Binary Microwave Pulses
By O. E. DeLANGE
(Manuscript received September 7, 1955)
A sifnple device has been produced for regenerating binary pulses directly
at microwave frequencies. To determine the capabilities of such devices one
of them was included in a circidating test loop in which pidse groups were
passed through the device a large number of titnes. Residts indicate that
even in the presence of serious noise and bandwidth limitations pidses can
be regenerated many times and still shotv no noticeable deterioration. Pic-
tures of circulated pidses are included which illustrate performance of the
regenerator.
INTRODUCTION
The chief advantage of a transmission system employing Ijinary pulses
resides in the possibility of regenerating such pulses at intervals along
the route of transmission to prevent the accumulation of distortion due
to noise, bandwidth limitations and other effects. This makes it possible
to take the total allowable deterioration of signal in each section of a
long relay system rather than having to make each link sufficiently good
to prevent total accumulated distortion from becoming excessive. This
has been pointed out by a number of writers. i--
W. M. GoodalP has shown the feasibility of transmitting television
signals in binary form. Such transmission reciuires a considerable amount
of bandwidth; a seven digit system, for example, would require trans-
mission of seventy million pulses per second. This need for wide bands
makes the microwave range an attractive one in which to work. S. E.
Miller* has pointed out that a binary system employing regeneration
might prove to be especially advantageous in waveguide transmission.
1 B. M. Oliver, J. R. Pierce and, C. E. Shannon, The Pliilosophv of PCM, Proc.
I. R.E., Nov., 1948.
'^ L. A. Meacham and Iv Peterson, An Experimental Multichannel Pulse Code
Modulation System of Toll Quality, B. S. T. J., Jan. 1948.
' W. M. Goodall, Television l)y Pulse Code Modulation, B. S. T. J., Jan., 1951.
* S. E. Miller, Waveguide as a Communication Medium, B. S. T. J., Nov., 1954.
67
68 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
INPUT
FILTER
AUTOMATIC
GAIN
CONTROL
REGENERATOR
DETECTOR
TIMING
WAVE
GENERATOR
FILTER
OUTPUT
Fig. 1 — A typical regenerative repeater shown in block form.
That the Bell System is interested in the long-distance transmission
of television and other broad-band signals is evident from the number
of miles of such broad-band circuits, both coaxial cable and microwave
radio, ^ now in service. These circuits provide high-grade transmission
because each repeater was designed to have a very fiat frequency charac-
teristic and linear phase over a considerable bandwidth. Furthermore,
these characteristics are very carefully maintained. For a binary pulse
system employing regeneration the requirements on flatness of band and
linearity of phase can be relaxed to a considerable degree. The compo-
nents for such a system should, therefore, be simpler and less expensive
to build and maintain. Reduced maintenance costs might well prove to
be the chief virtue of the binary system.
Since the chief advantage of a binary system lies in the possibility of
regeneration it is obvious that a very important part of such a system is
the regenerative repeater employed. Fig. 1 shows in block form a typical
broad-band, microwave repeater. Here the input, which might come from
either a radio antenna or from a waveguide, is first passed through a
proper microwave filter then amplified, probably by a traveling-wave
amplifier. The amplified pulses of energy are regenerated, filtered, am-
plified and sent on to the next repeater. The experiment to be described
here deals primarily with the block labeled "Regenerator" on Fig. 1.
In these first experiments one of our main objectives was to keep the
repeater as simple as possible. This suggests regeneration of pulses
directly at microwave frequency, which for this experiment was chosen
to be 4 kmc. It was suggested by J. R. Pierce and W. D. Lewis, both of
Bell Telephone Laboratories, that further simplification might be made
possible by accepting only partial instead of complete regeneration.
This suggestion was adopted.
For the case of complete regeneration each incoming pulse inaugurates
a new pulse, perfect in shape and correctly timed to be sent on to the
'A. A. Roetken, K. D. Smith and R. W. Friis, The TD-2 System, B. S. T. J.,
Oct., 1951, Part II.
REGENERATION OF BINARY MICROWAVE PULSES 69
next repeater. Thus noise and other disturbing effects are completely
eliminated and the output of each repeater is identical to the original
signal which entered the system. For the case of partial regeneration
incoming pulses are retimed and reshaped only as well as is possible with
simple equipment. Obviously the difference between complete and partial
. regeneration is one of degree.
One object of the experiment was to determine how well such a partial
regenerator would function and what price must be paid for employing
partial instead of complete regeneration. The regenerator developed
consists simply of a waveguide hybrid junction with a silicon crystal
diode in each side arm. It appears to meet the requirement of simplicity
in that it combines the functions of amplitude slicing and pulse retiming
in one unit. A detailed description of this unit will be given later. Al-
though the purpose of this experiment was to determine what could be
accomplished in a very simple repeater we must keep in mind that
superior performance would be obtained from a regenerator which ap-
proached more nearly the ideal. For some applications the better re-
generator might result in a more economical system even though the
regenerator itself might be more complicated and more expensive to
produce.
METHOD OF TESTING
The regeneration of pulses consists of two functions. The first function
is that of removing amplitude distortions, the second is that of restoring
each pulse to its proper time. The retiming problem divides into two
[parts the first of which is the actual retiming process and the second
! that of obtaining the proper timing pulses with which to perform this
lifunction. In a practical commercial system timing information at a
[repeater would probably be derived from the incoming signal pulses.
There are a number of problems involved in this recovery of timing
pulses. These are being studied at the present time but were avoided in
the experiment described here by deriving such information from the
local synchronizing gear.
Since the device we are dealing with only partially regenerates pulses
it is not enough to study the performance of a single unit — we should
•like to have a large number operating in tandem so that we can observe
'what happens to pulses as they pass through one after another of these
Tegenerators. To avoid the necessity of building a large number of units
the pulse circulating technique of simulating a chain of repeaters was
j employed. Fig. 2 shows this circulating loop in block form.
70
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
HYBRID
JUNCTION
' NO. 3
CW
OSCILLATOR
(4 KMC)
TRAVELING WAVE
AMPLIFIER
(NOISE GENERATOR)
Fig. 2 — The circulating loop.
To provide RF test pulses for this loop the output of a 4 kmc, cw
oscillator is gated by baseband pulse groups in a microwave gate or
modulator. The resultant microwa\-e pulses are fed into the loop (heavy
line) through hybrid junction No. 1. They are then amplified by a trav-
eling-wave amplifier the output of which is coupled to the pulse regen-
erator through another hybrid junction (No. 2). The purpose of this
hybrid is to provide a position for monitoring the input to the regen-
erator. A monitoring position at the output of the regenerator is pro-
vided by a third hybrid, the main output of which feeds a considerable
length of waveguide which provides the necessary loop delay. At the far
end of the waveguide another hybrid (No. 4) makes it possible to feed
noise, which is derived from a traveling-wave amplifier, into the loop.
The combined output after passing through a band pass filter is ampli-
REGENEKATION OF BINARY MICROWAVE PULSES
71
fied by another traveling-wave amplifier and fed back into the loop in-
put thus completing the circuit.
The synchronizing equipment starts out with an oscillator going at
approximately 78 kc. A pulse generator is locked in step with this os-
cillator. The output of the pulser is a negative 3 microsecond pulse as
shown in Fig. 3A. After being amplified to a level of about 75 volts
this pulse is applied to the helix of the first traveling-wave tube to re-
I duce the gain of this tube during the 3-microsecond interval. Out of each
12.8/xsec interval pulses are allowed to circulate for O.S/xsec but are blocked
I for the remaining 3Msec thus allowing the loop to return to the quiescent
i condition once during each period as shown on Figs. 3A and 3C.
The S^sec pulse also synchronizes a short-pulse generator. This unit
delivers pulses which are about 25 millimicroseconds long at the base
and spaced by 12.8/isec, i.e., Avith a repetition frequency of 78 kc. See
Fig. 3B.
In order to simulate a PCM system it was decided to circulate pulse
CIRCULATING INTERVAL
9.8/ZS
QUENCHING
INTERVAL
-3//S-*|
(A) GATING CYCLE
(B) SHORT SYNCHRONIZING PULSES
--24 GROUPS OF PULSES
(C) CIRCULATING PULSE GROUPS
GROUP GROUP GROUP
1 2 3
lOOMyUS
^ k ^^-o.4;uS-^^ I (D) PULSE GROUPS (EXPANDED)
■ ' |300M/US| I I
I
(E) TIMING WAVE (40MC) EXPANDED
0
TIME
Fig. 3 — Timing events in the circulating loop.
72 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
groups rather than individual pulses through the system. These were
derived from the pulse group generator which is capable of delivering
any number up to 5 pulses for each short input pulse. These pulses are
about 15 milli-microseconds long at the base and spaced 25 milli-micro-
seconds apart. The amplitude of each of these pulses can be adjusted
independently to any value from zero to full amplitude making it pos-
sible to set up any combination of the five pulses. These are the pulses
which are used to gate, or modulate, the output of the 4-kmc oscillator.
The total delay around the waveguide loop including TW tubes, etc.,'
was 0.4)usec or 400 milli-microseconds. This was sufficient to allow time
between pulse groups and yet short enough that groups could circulate
24 times in the available 9.8jLtsec interval. This can be seen from Figs.
3C and 3D. The latter figure shows an expanded view of circulating
pulse groups. The pulses in Group 1 are inserted into the loop at the
beginning of each gating cycle, the remaining groups result from circu-
lation around the loop.
When all five pulses are present in the pulse groups the pulse repeti-
tion frequency is 40 mc. (Pulse interval 25 milli-microseconds). For this
condition timing pulses should be supplied to the regenerator at the rate
of 40 million per second. These pulses are supplied continuously and not
in groups as is the case with the circulating pulses. See Fig. BE. In order
to maintain time coincidence between the circulating pulses and the tim-
ing pulses the delay around the loop must be adjusted to be an exact
multiple of the pulse spacing. In this experiment the loop delay is equal
to 16-pulse intervals. Since timing pulses are obtained by harmonic
generation from the quenching frequency as will be discussed later this
frequency must be an exact submultiple of pulse repetition frequency.
In this experiment the ratio is 512 to 1.
Although the above discussion is based on a five-pulse group and
40-mc repetition frequency it turned out that for most of the experi-
ments described here it was preferable to drop out every other pulse,
leaving three to a group and resulting in a 20-mc repetition frequency.
The one exception to this is the limited-band-width experiment which
will be described later. -
For all of the experiments described here timing pulses were derived
from the 78-kc quenching frequency by harmonic generation. A pulse
with a width of 25 milli-microseconds and with a 78-kc repetition fre-
quency as shown in Fig. 3B supplied the input to the timing wave gen-
erator. This generator consists of several stages of limiting amplifiers all
tuned to 20 mc, followed by a locked-in 20-mc oscillator. The output of
the amplifier consists of a train of 20-mc sine waves with constant ampli-
til
REGENERATION OF BINARY MICROWAVE PULSES 73
tude for most of the 12.8Msec period but falling off somewhat at the end
of the period. This-train locks in the oscillator which oscillates at a con-
stant amplitude over the whole period and at a frequency of 20 mc.
Timing pulses obtained from the cathode circuit of the oscillator tube
pro^'ided the timing waves for most of the experiments. For the experi-
ment where a 40-mc timing wave was required it was obtained from the,
20 mc train by means of a frequency doubler. For this case it is necessary
for the output of the timing wave generator to remain constant in ampli-
tude and fixed in phase for the 512-pulse interval between synchronizing
pulses.
In spite of the stringent requirements placed upon the timing equip-
ment it functioned well and maintained synchronism over adequately
long periods of time without adjustment.
PERFORMANCE OF REGENERATOR
Performance of the regenerator under various conditions is recorded
on the accompanying illustrations of recovered pulse envelopes. The
first experiment was to determine the effects of disturbances which arise
at only one point in a system. Such effects were simulated by adding
disturbances along with the group of pulses as they were fed into the
circulating loop from the modulator. This is equivalent to having them
occur at only the first repeater of the chain.
Some of the first experiments also involved the use of extraneous
pulses to represent noise or distortion since these pulses could be syn-
chronized and thus studied more readily than could random effects. In
, Fig. 4A the first pulse at the left represents a desired digit pulse with
' its amplitude increased by a burst of noise, the second pulse represents
' a clean digit pulse, and the third pulse a burst of noise. This group is at
1 the input to the regenerator. Fig. 4B shows the same group of pulses
' after traversing the regenerator once. The pulses are seen to be shortened
due to the gating, or retiming, action. There is also seen to be some ampli-
tude correction, i.e. the two desired pulses are of more nearly the same
j amplitude and the undesired pulse has been reduced in relative ampli-
tude. After a few trips through the regenerator the pulse group was
rendered practically perfect and remained so for the rest of the twenty-
four trips around the loop. Fig. 4C shows the group after 24 trips. In
'another experiment pulses were circulated for 100 trips without deteri-
oration. Nothing was found to indicate that regeneration could not be
repeated indefinitely.
Figs. 5 A and 5B represent the same conditions as those of 4 A and 4B
74 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
Fig. 4 — Effect of regeneration on disturbances which occur at only one re-
peater. A — Input to regenerator, original signal. B — Output of regenerator,
first trip. C — Output of regenerator, 24th trip.
Fig. 5 — l']ffect of regeneration on disturbances which occur at only one re-
peater. A — Input to regenerator, first four groups. B — Output of regenerator,
first four groups. C — Output of regenerator, increased input level.
REGENERATION OF BINARY MICROWAVE PULSES
75
Fig. 6 — Effect of regeneration on disturbances which occur at only one re-
peater. A — Input to regenerator, original signal. B — ^ Output of regenerator,
first trip. C • — Oi^tput of regenerator, 24th trip.
except that the oscilloscope sweep has been contracted in order to show
the progressive effects produced by repeated passage of the signal through
the regenerator. Fig. 5B shows that after the pulses have passed through
the regenerator only twice all visible effects of the disturbances have
been removed. Fig. 5C shows the effect of simply increasing the RF
pulse input to the regenerator by approximately 4 db. The small "noise"
pulse which in the previous case was quickly dropped out because of
being below the slicing level has now come up above the slicing level
and so builds up to full amplitude after only a few trips through the
regenerator. Note that in the cases shown in Figs. 4 and 5 discrimination
against unwanted pulses has been purely on an amplitude basis since
the gate has been unblocked to pulses with amplitudes above the slicing
level whenever one of these distiu'bing pulses was present.
For Fig. 6A conditions are the same as for Fig. 4A except that an ad-
ditional pulse has been added to simulate intersymbol noise or inter-
ference. Fig. 6B indicates that after only one trip through the regenerator
the effect of the added pulse is very small. After a few trips the effect
is completely eliminated leaving a practically perfect group which con-
tinues on for 24 trips as shown by Fig. 6C. For the intersymbol pulse,
discrimination is on a time basis since this interference occurs at a time
76
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
Fig. 7 — Effect of regenerating in amplitude without retiming. A — Outputof
regenerator, no timing, firt trip. B — Output of regenerator, no timing, 10th trip.
Output of regenerator, no timing, 23rd trip.
when no gating pulse is present and hence finds the gate blocked regard-
less of amplitude.
To show the need for retiming the pictures shown on Figs. 7 and 8
were taken. These were taken with the amplitude slicer in operation but
with the pulses not being retimed. Figs. 7A, 7B and 7C, respectively,
show the output of the slicer for the first, tenth and twenty-third trips.
After ten trips, there is noticeable time jitter caused by residual noise
in the system; after 23 trips this jitter has become severe though pulses
are still recognizable. It should be pointed out that for this experiment
no noise was purposely added to the system and hence the signal-to-
noise ratio was much better than that which would probably be encoun-
tered in an operating system. For such a system we would expect time
jitter effects to build up much more rapidly. For Fig. 8 conditions are
the same as for Fig. 7 except that the pulse spacing is decreased by the
addition of an extra pulse at the input. Now, after ten trips, time jitter
is bad and after 23 trips the pulse group has become little more than a
smear. This increased distortion is probably due to the fact that less
jitter is now required to cause overlap of pulses. There may also be some
effects due to change of duty cycle. For Fig. 9 there was neither slicing
nor retiming of pulses. Here, pulse groups deteriorate very rapidly to
nothing more than blobs of energy. Note that there is an increase of
i
REGENERATION OF BINARY MICROWAVE PULSES
77
Fig. 8 — ■ Effect of regenerating in amplitude without retiming. A — Output of
regenerator, no timing, first trip. B — Output of regenerator, no timing, 10th
trip. C — Output of regenerator, no timing, 23rd trip.
Fig. 9 — Pulses circulating through the loop without regeneration. A — Origi-
nal input. B — 4th trip without regeneration. C — 20th to 24th trip without re-
generation.
'8
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
iWWWMMMWWIWWMilJflM^ II . rlilllT- i \m....: iniTiinr- IH.
Fig. 10 — The regeneration of band-limited pulses. A — Input to regenerator,
first two groups. B — Output of regenerator, first two groups. C — Output of
regenerator, 24th trip.
amplitude with each trip around the loop indicating that loop gain was
slightly greater than unity. Without the sheer it is difficult to set the
gain to exactly unity and the amplitude tends to either increase or de- :
crease depending upon whether the gain is greater or less than unity.
Results indicated by the pictures of Fig 9 are possibly not typical of a
properly functioning system but do show what happened in this par- .
ticular sj^stem when regeneration was dispensed with.
Another important function of regeneration is that of overcoming .
band-limiting effects. Figs. 10 and 11 show what can be accomplished. .
For this experiment the pulse groups inserted into the loop were as shown i|
at the left in Fig. lOA. These pulses were 15 milli-microseconds wide at
the base and spaced by 25 milli-microseconds which corresponds to a j
repetition frequency of 40 mc. After passing through a band-pass filter
these pulses were distorted to the extent shown at the right in Fig. lOA.
From the characteristic of the filter, as shown on Fig. 12, it is seen that
the bandwidth employed is not very different from the theoretical min-
imum required for double sideband transmission. This minimum char-
acteristic is shown by the dashed lines on Fig. 12. Fig. lOB shows that
at the output of the regenerator the effects of band limiting have been
removed. This is borne out by Fig. IOC which shows that after 24 trips
the code group was still practically perfect. It should l)e pointed out
that the pulses traversed the filter once for each trip around the loop,
REGENERATION OF BINARY MICROWAVE PULSES
79
Fig. 11 — The regeneration of band-limited pulses. A — Input to regenerator,
first two groups. B — Output of regenerator, first two groups. C — Output of re-
generator, 24th trip.
that is for each trip the input to the regenerator was as shown at the right
of Fig. lOA and the output as shown by Fig. lOB. It is important to
note that Fig. 12 represents the frequency characteristic of a single hnk
of the simulated system. The pictures of Fig. 11 show the same experi-
ment but this time with a different code group. Any code group which
we could set up with our five digit pulses was transmitted equally well.
In order to determine the breaking point of the experimental system,
broad-band noise obtained from a traveling-wave amplifier was added
into the system as shown on Fig. 2. The breaking point of the system is
the noise level which is just sufficient to start producing errors at the
output of the system.* The noise is seen to be band-limited in exactly
the same way as the signal. With the system adjusted to operate properly
the level of added noise was increased to the point where errors became
barely discernible after 24 trips around the loop. Noise level was now
reduced slightly (no errors discernible) and the ratio of rms signal to rms
noise measured. Fig. 13A shows the input to the regenerator for the 23rd
and 24th trips with this amount of noise added. Note that the noise has
* The type of noise employed has a Gaussian amplitude distribution and there-
fore there was actually no definite breaking point — the rate at which errors Oc-
curred increased continuously as noise amplitude was increased. The breaking
point was taken as the noise level at which errors became barely discernible on
the viewing oscilloscope. More accurate measurements made in other experiments
indicate that this is a fairly satisfactory criterion.
80 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
28
24
IT)
aJ2o
03
O
16
to
If)
g 12
a.
UJ
5 8
ll
1 —
1
\
i
A
\
^
1
1
1
1
1
/
<
\
1
1
1
/
/
\
1
/
<
V h*
--20 M
1
--20MC *]
1/
v.
1
/
1
■~ TX^
^
■rrD*^
/J
3950 3960 3970 3980 3990 4000 4010 4020 4030 4040
FREQUENCY IN MEGACYCLES PER SECOND
Fig. 12 — Characteristics of the band-pass microwave filter.
m %
I
JYYYYYYTin
Fig. 13. — The regeneration of pulses in the presence of broad-hand, random
noise added at each repeater. A — Ini)ut to regenerator, 23rd and 24th trijis,
broad-band noise added. B — Ini)ut to regenerator, 23rd and 24th trips, no added
noise. C — 20-mc timing wave.
\
KEGENERATION OF BINARY MICROWAVE PULSES
81
Fig. 14 — The regeneration of pulses in the presence of interference occurring
at each repeater. A — Original signal with added moduhited carrier interference.
B — Input to regenerator, 24th trip, niochilatod carrier interference. C — Output
of regenerator, 24th trip, modulated carrier interference.
produced a considerable broadening of the oscilloscope trace. Fig. 13B
shows the same pulse groups with no added noise. These photographs are
included to give some idea as to how bad the noise was at the l;)reaking
point of the system. Of course maximum noise peaks occur rather infre-
quently and do not show on the photograph. At the output of the re-
generator effects due to noise were barely discernible. This output looked
so much like that shown at Fig. 14C that no separate photograph is
shown for it.
Figs. 14A, 14B and 14C show the effects of a different type of inter-
ference upon the system. This disturbance was produced by adding into
the system a carrier of exactly the same frequency as the signal carrier
(4 kmc) but modulated by a 14-mc wave, a frequency in the same order
as the pulse rate. Here again the level of the interference was adjusted
to be just below the l)reaking point of the system. A comparison between
Figs. 14B and 14C gives convincing evidence that the regenerator has
substantially restored the waveform.
For the case of the interfering signal a ratio of signal to interference
of 10 db on a peak-to-peak basis was measured when the interference
was just below the breaking point of the system. This, of course, is 4 db
above the theoretical value for a perfect regenerator. For the case of
82 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
broad-band random noise an rms signal to noise ratio of 20 dl) was meas-
ured.* This compares Avith a ratio of 18 db as measured by Messrs.
Meacham and Peterson for a system employing complete regeneration
and a single repeater, f
Recently, A. F. Dietrich repeated the circulating loop experiment at
a radio frequency of 11 kmc. His determinations of required signal-to-
noise ratios are substantially the same as those reported here. From the
various experiments we conclude that for a long chain of properly func-
tioning regenerative repeaters of i-he type discussed here practically
perfect transmission is obtained as long as the signal-to-noise ratio at
the input to each repeater is 20 db or better on an rms basis. In an operat-
ing system it might be desirable to increase this ratio to 23 db to take
care of deficiencies in automatic gain controls, power changes, etc.
From the experiments we also conclude that the price we pay for using
partial instead of complete regeneration is about 3 to 4 db increase in
the required signal-to-noise ratio. In a radio system which provides a
fading margin this penalty would be less since the probability that two
or more adjacent links will reach maximum fades simultaneously is very '
small. Under these conditions only one repeater at a time would be near
the breaking point and the system would behave much as though the
repeater provided complete regeneration.
TIMING
Although we have considered the problem of retiming of signal pulses
up to now we have not discussed the problem of obtaining the necessary '
timing pulses to perform this function, but have simpl}^ assumed that a
source of such pulses was available. As w^as mentioned earlier timing I
pulses would probably be derived from the signal pulses in a practical »^
system. These pulses would be fed into some narrow band amplifier
tuned to pulse repetition frequency. The output of this circuit could be
made to be a sine wave at repetition frequency if gaps between the input
pulses were not too great. Timing pulses could be derived from this sine
wave. This timing equipment could be similar to that used in these ex-
periments and described earlier. Further study of the problems of ob-
taining timing information is being made.
* For Gaussian noise it is not possible to specif.y a theoretical value of minimum
S/N ratio without specifying the tolerable percentage of errors. For the number of
errors detectable on the oscilloscope it seems rasonable to assume a 12 db peak
factor for the noise. The peak factor for the signal is 3 db. The 6 db peak S/N
which would be required for an ideal regenerator then becomes 15 db on an rms
basis.
t L. A. Meacham and E. Peterson, B. S. T. J., p. 43, Jan., 1948.
"
KEGENERATION OF BINARY MICROWAVE PULSES
83
' GATING
PULSE
INPUT
OUTPUT
Fig. 15A — Low-frequency equivalent of the partial regenerator.
DESCRIPTION OF REGENERATOR
This device regenerates pulses by performing on them the operations
of ''slicing" and retiming.
An ideal slicer is a device with an input-output characteristics such as
shown by the dashed lines of Fig. 15C. It is seen that for all input levels
below the so-called slicing level transmission through the device is zero
but that for all amplitudes greater than this value the output level is
finite and constant. Thus, all input voltages which are less than the slic-
ing level have no effect upon the output whereas all input voltages
greater than the slicing level produce the same amplitude of output.
Normally conditions are adjusted so that the slicing level is at one-half
INPUT LEVEL
Fig. 15B — Characteristics of the separate branches with ditterential bias.
84
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
INPUT LEVEL
Fig. 15C — Resultant output with differential bias.
BRANCH 2
BRANCH 1
RESULTANT
INPUT LEVEL
Fig. 15D — Characteristics of the separate branches and resultant output with
equal biases.
of peak pulse amplitude — then at the output of the slicer there will be
no effect whatsoever from disturbances unless these disturbances exceed
half of the pulse amplitude. It is this slicing action which removes the
amplitude effects of noise. Time jitter effects are removed by retiming,
i.e., the device is made to have high loss regardless of input level except
at those times when a gating pulse is present.
Fig. 15A shows schematically a low-frequency equivalent of the re-
generator used in these experiments. Here an input line divides into two
identical branches isolated from each other and each with a diode shunted
across it. The outputs of the two branches are recombined through neces-
sary isolators to form a single output. The phase of one branch is re-
versed before recombination, so that the final output is the difference
between the two individual outputs.
Fig. 15B shows the input-output characteristics of the two branches
when the diodes are biased back to be non-conducting by means of bias
voltages Vi and V2 respectively. For low levels the input-output char-
acteristic of both branches will be linear and have a 45° slope. As soon
REGENEKATION OF BINARY MICROWAVE PULSES
85
as the input voltage in a branch reaches a vakie equal to that of the back
bias the diode will start to conduct, thus absorbing power and decrease
the slope of the characteristic. The output of Branch 1 starts to flatten
off when the input reaches the value Vi , while the output of Branch 2
does not flatten until the input reaches the value V2 . The combined
output, which is equal to the differences of the two branch outputs, is
then that shown by the solid line of Fig. 15C and is seen to have a transi-
tion region between a low output and a high output level. If the two
branches are accurately balanced and if the signal voltage is large com-
pared to the differential bias V2 — Vi the transition becomes sharp and
the device is a good slicer.
If the two diodes are equally biased as shown on Fig. 15D the outputs
of the two branches should be nearly equal regardless of input and the
total output, which is the difference between the two branch outputs,
will always be small.
Fig. 16 shows a microwave equivalent of the circuit of Fig. 15A. In
the microwave structure lengths of wave-guide replace the wire lines and
branching, recombining and isolation are accomplished by means of
hybrid junctions. The hybrid shown here is of the type known as the lA
junction.
Fig. 17 shows another equivalent microwave structure employing only
one hybrid. This is the type used in the experiments described here. The
[output consists of the combined energies reflected from the two side
jarms of the junction. With the junction connected as shown phase rela-
Itionships are such that the output is the difference between the reflec-
GATING
PULSE
^(— r-V\^^^
RF
INPUT ARM
PROBE
TERMINATION
I
ARM 4
I— vw-^
Fig. 16 — Microwave regenerator.
86
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
tions from the two side arms so that when conditions in the two arms
are identical there is no output. The crystal diodes coupled to the side
arms are equivalent to those shunted across the two lines of Fig. 15A.
Fig. 18, which is a plot of the measured input-output characteristic
of the regenerator used in the loop test, shows how the device acts as a
combined sheer and retimer. Curve A, ol)tained with equal biases on the
two diodes, is the characteristic with no gating pulse applied i.e. the
diodes are normally biased in this manner. It is seen that this condition
produces the maximum of loss through the device. By shifting one diode
bias so as to produce a differential of 0.5 volt the characteristic changes
to that of Curve B. This differential bias can be supplied by the timing
pulse in such a way that this pulse shifts the characteristic from that
shown at A to that shown at B thus decreasing the loss through the de-
vice by some 12 to 15 db during the time the pulse is present. In this way
the regenerator is made to act as a gate — though not an ideal one.
We see from curve B that with the differential bias the device has the
characteristic of a slicer — though again not ideal. For lower levels of
input there is a region over which the input-output characteristic is
square law with a one db change of input producing a two db change of
output. This region is followed by another in which limiting is fairly
pronounced. At the 8-db input level, which is the point at which limiting
sets in, the loss through the regenerator was measured to be approxi-
mately 12 db. The characteristic shown was found to be reproducible
both in these experiments at 4 kmc and in those bj'- A. F. Dietrich at
11 kmc.
For a perfect slicer only an infinitesimal change of input level is re-
GATING
PULSE
■AAV-i_
ARM 2
RF
OUTPUT
Fig, 17 — Microwave regenerator employing a single hybrid junction.
REGENERATION OF BINARY MICROWAVE PULSES
87
ID
m
o
LU
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D
3
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-10
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-14
-16
-18
-20
-22
-24
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V2 = 0
<--
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LOSS
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6 8 10 12
INPUT LEVEL IN DECIBELS
14
16
18
Fig. 18 — Static characteristics of the regenerator employed in these experiments.
f}uired to change the output from zero to maximum. The input level at
which this transition takes place is the slicing level and has a very defi-
nite value. For a characteristic such as that shown on Fig. 18 this point
is not at all definite and the question arises as to how one determines the
slicing level for such a device. Obviously this point should be somewhere
on the portion of the characteristic where expansion takes place. In the
case of the circulating loop the slicing level is the level for which total
gain around the loop is exactly etiual to unity. Why this is so can be seen
from Fig. 19 which is a plot of gain \'ersus input level for a repeater
containing a sheer with a characteristic as shown by curve B of Fig. 18.
Amplifiers are necessary in the loop to make up for loss through the re-
generator and other components. For Fig. 11) we assume that these
amplifiers have been adjusted so that gain around the loop is exactly
unity for an input pulse having a peak amplitude corresponding to the
88
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
-3
-2-1 0 1 2 3 4 5
INPUT LEVEL IN DECIBELS ABOVE SLICING LEVEL
Fig 19 — Gain characteristics of u repeater providing partial regeneration.
point F' of Fig. 18. On Fig. 19 all other levels are shown in reference to
this unity-gain value.
From Fig. 19 it is obvious that a pulse which starts out in the loop
with a peak amplitude exactly equal to the reference, or slicing level,
will continue to circulate without change of amplitude since for this
level there is unity gain around the loop. A pulse with amplitude greater
than the slicing level will have its amplitude increased by each passage
through a regenerator until it eventually reaches a value of +6 db. It
will continue to circulate at this amplitude, for here also the gain around
the loop isVmity.* Any pulse with peak amplitude less than the reference
level will have its amplitude decreased by successive trips through the
regenerator and eventually go to zero. We also see that the greater the
departure of the amplitude of a pulse from the slicing level the more
effect the regenerator has upon it. This means that the device acts much
more powerfully on low level noise than on noise with pulse peaks near
the slicing level. As examples consider first the case of noise peaks only
1 db below slicing level at the input (peak S/N = 7 db). At this level
there is a 1 db loss through the repeater so that at the output the noise
peaks will be 2 db below reference to give a *S/A^ ratio of 8 db. Next
* Note that llic ^-fi-dl) level is at a point of stable equilibrium whereas at the
slicing level C(iuilil)rium is unstable.
REGENERATION OF BINARY MICROWAVE PULSES 89
consider noise with a peak level 5 db below slicing level (S/N =11 db)
at the input. The loss at this level is 5 db resulting in a noise level 10 db
below reference to give a S/N ratio of 16 db. We see that a 4 db improve-
ment in S/N ratio at the input results in an 8 db improvement in this
ratio at the output.
Everything which was said above concerning the circulating loop ap-
plies equally to a chain of identical repeaters. To set the effective slicing
level at half amplitude at each repeater in a chain one would first find
two points on the sheer characteristics such as P and P' of Fig. 18. The
point P should be in the region of expansion and P' in the limiting region.
Also the points should be so chosen that a 6 db increase of input from
that at point P results in a 6 db increase in output at the point P'. If
now at each repeater we adjust pulse peak amplitude at the sheer input
to a value corresponding to that at point P' we will have unity gain
from one repeater to the next at levels corresponding to pulse peaks.
We will also have unity gain at levels corresponding to one half of pulse
amplitude. The effective slicing level is thus set at half amplitude. Ob-
viously the procedure for setting the slicing level at some value other
than half amplitude would be practically the same. It should be pointed
out that although half amplitude is the preferred slicing level for base-
band pulses this is not the case for carrier pulses. W. R. Bennett of Bell
Telephone Laboratories has shown that for carrier pulses the probability
that noise of a given power will reduce signal pulses below half amplitude
is less than the probability that this same noise will exceed half ampli-
tude. This comes about from the fact that for effective cancellation there
must be a 180° phase relationship between noise and pulse carrier. For
this reason the slicing level should be set slightly above half amplitude
for a carrier pulse system.
The difference in performance between a perfect sheer and one with
characteristics such as shown on Fig. 18 are as follows: For the perfect
sheer no effects from noise or other disturbances are passed from one
repeater to the next. For the case of the imperfect regenerator some ef-
fects are passed on and so tend to accumulate in a chain of repeaters.
To prevent this accumulated noise from building up to the breaking
point of the system it is necessary to make the signal-to-noise ratio at
each repeater somewhat better than that which would be required with
the ideal sheer. For the case of random noise the required S/N ratio
seems to be about 5 or 6 db above the theoretical value. This is due in
part to sheer deficiency and in part to other system imperfections.
90 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 19o()
CONCLUSIONS
It is possible to build a simple device for regenerating pulses directly
at microwave frequencies. A long chain of repeaters employing this
regenerator should perform satisfactorily as long as the rms signal-to-
noise ratio at each repeater is maintained at a value of 20 db or greater.
There are a number of remaining problems which must be solved before
we have a complete regenerative repeater. Some of these problems are:
(1) Recovery of information for retiming from the incoming pulse train;
(2) Automatic gain or level control to set the slicing level at each re-
peater; (3) Simple, reliable, economical, broad-band microwave ampli-
fiers. (4) Proper filters — both for transmitting and receiving. Traveling-
wave tube development should eventually result in amplifiers which
will meet all of the requirements set forth in (3) above. Any improve-
ments which can be made in the regenerator without adding undue
complications would also be advantageous.
ACKNOWLEDGMENTS
A. F. Dietrich assisted in setting up the equipment described here and
in many other ways. The experiment would not have been possible with-
out traveling-wave tubes and amplifiers which were obtained through
the cooperation of M. E. Hines, C. C. Cutler and their associates. I wish
to thank W. M. Goodall, and J. R. Pierce for many valuable suggestions.
Crossbar Tandem as a Long Distance
Switching System
By A. O. ADAM
(Manuscript received March 4, 1955)
Major toll switching features are being added to the crossbar tandem
switching system for use at many of the important long distance switching
centers of the nationwide network. These include automatic selection of one
of several alternate routes to a 'particular destination, storing and sending
forward digits as required, highly flexible code conversion for transmitting
digits different from those received, and a translating arrangement to select
the most direct route to a destination. The system is designed to serve both
operator and customer dialed long distance traffic.
INTRODUCTION
The crossbar tandem switching system,^ originally designed for switch-
ing between local dial offices, will now play an important role in nation-
wide dialing. New features are now available or are being developed that
will permit this system to switch all types of traffic. As a result, crossbar
[ tandem offices will have widespread use at many of the important switch-
ing centers of the nationwide switching network.
This paper briefly reviews the crossbar tandem switching system and
its application for local switching, followed by discussion of the general
aspects of the nationwide switching plan and of the major new features
required to adapt crossbar tandem to this plan.
CROSSBAR TANDEM OFFICES USED FOR LOCAL SWITCHING
Crossbar tandem offices are now used in many of the large metropolitan
areas throughout the country for interconnecting all types of local dial
offices. In these applications they perform three major functions. Basi-
cally, they permit economies in trunking by combining small amounts of
91
02 THE BELL SYSTEM TECHXIf AL JOURNAL, JANUARY 1956
traffic to and from the local offices into larger amounts for routing over
common triuik groups to gain increased efficiency resulting in fewer over-
all trunks.
A second important function is to permit handling calls economically
between different types of local offices which are not compatible from the
standpoint of intercommunication by direct pulsing. Crossbar tandem
offices serve to connect these offices and to supply the conversion from
one type of pulsing to another where such incompatibilities exist.
The third major function is that of centralization of equipment or
services. For example, centralization of expensive charging equipment at
a crossbar tandem office results in efficient use of such equipment and
over-all lower cost as compared with furnishing this equipment at each
local office requiring it. Examples of such equipment are remote control
of zone registration and centralized automatic message accounting.^ Cen-
tralization of other services such as weather bureau, time-of-day and
similar services can be furnished.
The first crossbar tandem offices were installed in 1941 in New York,
Detroit and San Francisco. These offices were equipped to interconnect
local panel and No. 1 crossbar central offices in the metropolitan areas,
and to complete calls to manual central offices in the same areas. The war
years slowed both development and production and it was not until the
late 40's that many features now in use were placed in service. These
later features enable customers in step-by-step local central offices on the
fringes of the metropolitan areas to interconnect on a direct dialing basis
with metropolitan area customers in panel, crossbar, manual and step-
by-step central offices. This same development also permitted central
offices in strictly step-by-step areas to be interconnected by a crossbar
tandem office where direct interconnecting was not economical. Facilities
were also made available in the crossbar tandem system for completing
calls from switchboards where operators use dials or multifrequency key
pulsing sets.
Since a crossbar tandem office usually has access to all of the local
offices in the area in which it is installed, it is attractive for handling
short and long haul terminating traffic. The addition of toll terminal
equipment at Gotham Tandem in New York City in 1947 permitted
operators in New York State and northern New Jersey as well as distant
operators to dial or key pulse directly into the tandem equipment for
completion of calls to approximately 350 central offices in the New York
metropolitan area. This method of completing these calls without the
aid of the inward operators was a major advance in using tandem switch-
ing ecjuipment for speeding completion of out-of-town calls.
CROSSBAR TANDEM AS A TOLL SWITCHING SYSTEM
93
CROSSBAR TANDEM SWITCHING ARRANGEMENT
The connections in a crossbar tandem office are established through
crossbar switches mounted on incoming trunk link and outgoing office
link frames shown on Fig. 1. The connections set up through these
switches are controlled by equipment common to the crossbar tandem
office which is held only long enough to set up each individual connec-
tion. Senders and markers are the major common control circuits.
The sender's function is to register the digits of the called number,
transmit the called office code to the marker and then, as subsequently
directed by the marker, control the outpulsing to the next office.
The marker's function is to receive the code digits from the sender
for translation, return information to the sender concerning the de-
tails of the call, select an idle outgoing trunk to the called destination
and close the transmission path through the crossbar switches from the
incoming to the outgoing trunk.
GENERAL ASPECTS OF NATIONWIDE DIALING
Operator distance dialing, now used extensively throughout the
country, as well as customer direct distance dialing are based on the
division of the United States and Canada into numbering plan areas,
interconnected by a national network through some 225 Control Switch-
ing Points (CSP's) equipped with automatic toll switching systems.
^ An essential element of the nationwide dialing program is a universal
numbering plan^ wherein each customer will have a distinctive number
which does not conflict with the number of any other customer. The
method employed is to divide the United States and Canada geographi-
INCOMING
TRUNK FROM
ORIGINATING
OFFICE
TANDEM
TRUNK
TRUNK LINK FRAME
9 ?
TRUNK LINK
CONNECTOR
SENDER LINK
SENDER LINK
CONTROL CIRCUIT
SENDER
OFFICE LINK FRAME
<? 9
OFFICE LINK
CONNECTOR
J 4_
MARKER
CONNECTOR
OUTGOING
TRUNK
MARKER
Fig. 1 — Crossbar tandem switching arrangement.
94 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
cally into more than 100 numbering plan areas and to give each of these
a distinctive three digit code with either a 1 or 0 as the middle digit.
Each numbering plan area will contain 500 or fewer local central offices
each of which will be assigned a distinctive three-digit office code.
Thus each of the telephones in the United States and Canada will have,
for distance dialing purposes, a distinct identity consisting of a three
digit area code, an office code of two letters and a numeral, and a sta-
tion number of four digits. Under this plan, a customer will dial 7 digits
to reach another customer in the same numbering area and 10 digits to
reach a customer in a different numbering area.
A further reciuirement for nationwide dialing of long distance calls is
a fundamental plan"* for automatic toll switching. The plan provides a
systematic method of interconnecting all the local central offices and
toll switching centers in the United States and Canada. As shown on
Fig. 2, several local central offices or "end offices" are served by a single
toll center or toll point that has trunks to a "home" primary center
which serves a group of toll centers. Each primary center, has trunks to
a "home" sectional center which serves a larger area of the country.
Similuj-ly, the entire toll dialing territory is divided into eleven very
large areas called regions, each having a regional center to serve all the
sectional centers in the region. One of the regional centers, probably
St. Louis, Missouri, will be designated the national center. The homing
arrangements are such that it is not necessary for end offices, toll centers,
toll points and primary centers to home on the next higher ranking
office since the complete final route chain is not necessary. For example,
end offices may be served directly from any of the higher ranking switch-
ing centers also shown in Fig. 2.
Collectively, the national center, the regional centers, the sectional
centers and the primary centers will constitute the control switching
points for nationwide dialing. The basic switching centers and homing
arrangements are illustrated in Fig. 3.
TANDEM CROSSBAR FEATURES FOR NATIONWIDE DIALING
The broad objective in developing new features for crossbar tandem
is to provide a toll switching system that can be used in cities where
the large capacity and the full versatilit}^ of the No. 4 toll crossbar
switching system-'' may not be economical.
The application of crossbar tandem two-wire switching systems at
primary and sectional centers has been made possible by the extended
use of high speed carrier systems. The echoes at the 2-wire crossbar
tandem switching offices can be effectively reduced by providing a high
CROSSBAR TANDEM AS A TOLL SWITCHING SYSTEM
95
office balance and by the use of impedance compensators and fixed pads.
A well balanced two-wire switching system, proper assignment of inter-
toll trunk losses, and the use of carrier circuits with high speed of propa-
gation will permit through switching Mdth little or no impairment from
an echo standpoint.
The new features for crossbar tandem will provide arrangements
necessary for operation at control switching points (CSP's). These in-
clude automatic alternate routing, the ability to store and send forward
TP
e
I I NC = NATIONAL CENTER
RC = REGIONAL CENTER
/\ SC = SECTIONAL CENTER
( J PC = PRIMARY CENTER
Fig. 2 — Homing arrangement for local central offices and toll centers.
TC = TOLL CENTER
TP = TOLL POINT
EG = END OFFICE
96
CROSSBAR TANDEM AS A TOLL SWITCHING SYSTEM
97
digits as required, highly flexible code conversion (transmitting forward
i different digits for the area or office code instead of the dialed digits),
prefixing digits ahead of the called office code, and six-digit translation.
ALTERNATE ROUTING
The control switching points will be interconnected by a final or
"backbone" network of intertoll trunks engineered so that very few
calls will be delayed. In addition, direct circuits between individual
switching offices of all classes will be provided as warranted by the
traffic density. These are called "high-usage" groups and are not en-
gineered to handle all the traffic offered to them during the busy hour.
Traffic offered to a high-usage group which finds all trunks busy will be
automatically rerouted to alternate routes®-^ consisting of other high-
usage groups or to the final trunk group. The abi.ity of the crossbar
tandem equipment at the control switching point to select one of several
alternate routes automatically, when all choices in the first route are
busy, contributes to the economy of the plant and provides additional
protection against complete interruption of service when all circuits on
a particular route are out of service.
Fig. 4 shows a hypothetical example of alternate routing when a
crossbar tandem office at South Bend, Indiana, receives a call destined
for ^Youngstown, Ohio. To select an idle path, using this plan, the
switching equipment at South Bend first tests the direct trunks to
Youngstown. If these are all busy, it tests the direct trunks to Cleveland
where the call would be completed over the final group to Youngstown.
If the group to Cleveland is also busy, South Bend would test the group
CHICAGO
SOUTH BEND
CROSSBAR
TANDEM
CLEVELAND
-YOUNGSTOWN
ITT5BURGH
Fig. 4 — Toll network — alternate routing.
98
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
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CROSSBAR TANDEM AS A TOLL SWITCHING SYSTEM 99
to Pittsburgh and on its last attempt it would test the final group to
Indianapolis. If the call were routed to Pittsburgh or Indianapolis, the
switching equipment at these points would attempt by first choice and
alternate routes to reach Youngstown. The final choice backbone route
would be via Indianapolis, Chicago, St. Louis, Pittsburgh, Cleveland to
Youngstown. Should all the trunks in any of the final groups tested be
busy no further attempt to complete the call is made. It is unlikely
that so many alternate routes would be provided in actual practice
since crossbar tandem can test only a maximum of 240 trunks on each
call and, in the case illustrated, the final trunk group to Indianapolis
may be quite large.
The method employed by the crossbar tandem marker in selecting
the direct route and subsequent alternate routes is shown in simplified
form on Fig. 5. As a result of the translating operation, the marker
selects the first choice route relay, corresponding to the called destina-
tion. Each route relay has a number of contacts which are connected to
supply all the information recjuired for proper routing of the call. Several
of these contacts are used to indicate the equipment location of the
trunks and the number of trunks to be tested. The marker tests all of
the trunks in the direct route and if they are busy, the search for an
idle trunk continues in the first alternate route which is brought into
play from the "route advance" cross-connection shown on the sketch.
As many as three alternate routes in addition to the first choice route
can be tested in this manner.
STORING AND SENDING FORWARD DIGITS AS REQUIRED
The crossbar tandem equipment at control switching points must
store all the digits received and send forward as many as are required to
complete the call.
The called number recorded at a switching point is in the form of
ABX-XXXX if the call is to be completed in the same numbering
plan area. If the called destination is in another area, the area code
XOX or XIX precedes the 7 digit number. The area codes XOX or XIX
and the local office code ABX are the digits used for routing purposes
and are sufficient to complete the call regardless of the number of switch-
ing points involved. Each control switching point is arranged to ad-
vance the call towards its destination when these codes are received.
If the next switching point is not in the numbering area of the called
telephone, the complete ten-digit number is needed to advance the
call toward its destination. If the next switching point is in the num-
100 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
bering area of the called telephone the area code is not needed and seven
digits will suffice for completing the call.
For example, suppose a call is originated by a customer in South
Bend, Indiana, destined for customer NAtional 4-1234 in Washington,
D.C. If it is assumed that the route to Washington is via a switching
center in Pittsburgh, then the crossbar tandem equipment at South
Bend pulses forward to Pittsburgh 202-NA4-1234, 202 being the area
code for the District of Columbia. Pittsburgh in turn will delete the
area code and send NA4-1234 to the District of Columbia terminating
area.
As another example, suppose the crossbar tandem office at South
Bend receives a call from some foreign area destined to a nearby step-
by-step end office in Michigan. The crossbar tandem equipment re-
ceives and stores a ten-digit number comprising the area code and the-
seven digits for the office code and station number. Assuming that
direct trunks to the step-by-step end office in Michigan are available,
the area code and office code are deleted and the line number only is
pulsed forward. To meet all conditions, the equipment is arranged to
permit deletion of either the first three, four, five or six digits of a ten-
digit number.
CODE CONVERSION
At the present time, some step-by-step primary centers reach other
offices by the use of routing codes that are different from those assigned
under the national numbering plan. This arrangement is used to obtain
economies in switching equipment of the step-by-step plant and is
accetpable with operator originated calls. However, with the intro-
duction of customer direct distance dialing, it is essential that the codes
used by customers be in accordance with the national numbering plan.
The crossbar tandem control switching point must then automatically
provide the routing codes needed by the intermediate step-by-step
primary centers. This is accomplished by the code conversion feature
which substitutes the arbitrary digits required to reach the called office
through the step-by-step systems. Fig. 6 illustrates an application of
this feature. It shows a crossbar tandem office arranged for completing
calls through a step-by-step toll center to a local central office, GArden
8, in an adjacent area. A call reaching the crossbar tandem office for a
customer in this office arrives with the national number, 218-GA8-1234.
To complete this call, the crossbar tandem equipment deletes the area
code 218 and pulses forward the local office code and number. If the
«
CROSSBAK TANDEM AS A TOLL SWITCHING SYSTEM
101
call is switched to an alternate route via the step-by-step primary
center, it will be necessary for the crossbar tandem equipment to delete
the area code 218 and substitute the arbitrary digits 062 to direct the
call through the switches at the primary center, since the toll center
requires the full seven digit number for completing the call.
PREFIXING DIGITS
It may be necessary to route a call from one area to another and back
to the original area for completion. Such a situation arises on a call
from Amarillo to Lubbock, Texas, both in area 915 when the crossbar
tandem switching equipment finds all of the direct paths from Amarillo
to Lubbock busy as illustrated on Fig. 7. The call could be routed to
Lubbock via Oklahoma City which is in area 405. A seven-digit number
for example, MAin 2-1234, is received in the crossbar tandem office at
Amarillo. Assuming that the call is to be switched out of the 915 area
through the 405 area and back to the 915 area for completion, it is
necessary for the crossbar tandem office in Amarillo to prefix 915 to the
MAin 2-1234 number so that the switching equipment in Oklahoma
City will know that the call is for the 915 area and not for the 405 area.
Prefixing digits may also be needed at crossbar tandem offices to
route calls through step-by-step primary centers. The crossbar tandem
office in Fig. 8 receives the seven digit number MA2-1234 for a call to a
701
AREA
218
AREA
NUMBER
RECEIVED
218-GA8-1234
CROSSBAR
TANDEM
NUMBER
OUTPULSED
062-GA8-1234
STEP-BY-STEP
PRIMARY CENTER
ALTERNATE
ROUTE
DIRECT
ROUTE
GA8-I234
i^
GA8-t234
SX S
TOLL
CENTER
GA8-1234
LOCAL
CUSTOMER
Fig. 6 — Code conversion.
102
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
customer in the Madison office in the same area. However, since the
toll center needs the full seven digit number for completing the call and
since the step-by-step switches at the primary center "use up" two
digits (04) for its switching, the crossbar tandem equipment must
prefix 04 to the seven digit number.
METHOD OF DETERMINING DIGITS TO BE TRANSMITTED
The circuitry involved for transmitting digits as received, prefixing,
code conversion and for deletion involves both marker and sender
functions. The senders have ten registers (1 to 10) for storing incoming
digits and three registers (A A, AB, AC) for storing the arbitrary digits
that are used for prefixing and code conversion.
On a ten-digit call into a crossbar tandem switchmg center the area
code XOX, the office code ABX and the station number XXXX are
stored in the inpulsing or receiving registers of the sender. The code
digits XOX-ABX are sent to the marker which translates them to
determine which of the digits received by the sender should be outpulsed.
It also determines whether arbitrary digits should be transmitted ahead
of the digits received and, if so, the value of the arbitrary digits to be
stored in the sender registers AA, AB and AC. Case 1 of Fig. 9 assumes
that a ten-digit number has been stored in the sender registers 1 to 10
915
AREA
INCOMING
TOLL CALL
LOCAL
OFFICE
AMARILLO
CROSSBAR
TANDEM
OFFICE
NUMBER
RECEIVED
MA2-1234
405
AREA
^<
■^
.-^
^^o^^
.-^^^"J^^'
OKLAHOMA CITY
TOLL OFFICE
LUBBOCK
TOLL
OFFICE
MA 2
LOCAL
CO.
CUSTOMER
MA 2-1234
Fig. 7 — Prefixing.
CROSSBAR TANDEM AS A TOLL SWITCHING SYSTEM
103
and that the marker has mformed the sender the called number is to be
sent as received. The outpulsing control circuit is connected to each
register in turn through the steering circuit SI, S2, etc. and sends the
digits stored.
Case 2 illustrates a situation where the sender has stored ten digits
in registers 1 to 10 and received information from the marker to delete
the digits in registers 1 to 3 inclusive and to substitute the arbitrary
digits stored in registers AA, AB and AC. The outpulsing circuit is
first connected to register AA through steering circuit PSl, then to AB
through PS2, continuing in a left to right sequence until all digits are
outpulsed.
Case 3 covers a condition where the sender has stored seven digits and
has obtained information from the marker to prefix the two digits
stored in registers AB and AC. Outpulsing begins at the AB register
through steering circuit PS2 and then advances through steering circuit
PS3 to the AC register, continuing in a left to right seciuence until all
digits have been transmitted.
These are only a few of the many combinations that are used to give
the crossbar tandem control switching equipment complete pulsing
flexibility.
SIX-DIGIT TRANSLATION
Six-digit translation will be another feature added to the crossbar
tandem system. When only three digits are translated, it is necessary to
direct all calls to a foreign area over a single route. The ability to trans-
late six digits permits the establishment of two or more routes from the
switching center to or towards the foreign area. This is shown in Fig.
LOCAL
OFFICE
NUMBER OUTPULSED
04-MA2-1234
MADISON
OFFICE
MA2-I234
CROSSBAR
TANDEM
t
■ »
'
' — 1 n
MA2-
1
1234
EIVED
4
4
1
1
TOLL
CENTER
— >-
MADISON 2-
1234
STEP-BY-STEP
PRIMARY CENTER
Fig. 8 — Prefixing.
104 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
f/l
10 with Madison and Milwaukee, Wisconsin, in area 414 and Belle
Plaine Crossbar Tandem in Chicago, Illinois, in area 312. An economical
trunking plan may provide for direct circuits from Chicago to each
place. If only three-digit translation were provided in the Chicago
switching equipment, the route to both places would be selected as a
result of the translation of the 414 area code alone and, therefore, calls
to central offices reached through Madison, would need to be routed
via Milwaukee. This involves not only the extra trunk mileage, ])ut
also the use of an extra switching point. With six-digit translation, both
the area code and the central office code are analyzed, making it
possible to select the direct route to either city.
Six-digit translation in crossbar tandem will involve primarily the
use of a foreign area translator and a marker. The translator will have
a capacity for translation of five foreign areas and for 60 routes to each
area. Since the translator holding time is very short, one translator is
sufficient to handle all of the calls requiring six-digit translation, but
two are always provided for hazard and maintenance reasons.
On a call requiring six-digit translation the first three digits are
CASE 1 ^
DIGITS RECEIVED
t
2
3
-IMPULSING
4 5
REGISTERS -
6 7
8
9
10
\
X
0
X
A
B
X
X
X
X
X
.
.
;
i.
OUTPULSING
CONTROL
;Si
: Sd
S J
Sa -
S3
So
. S /
- So
b» * oiu
CASE 2
DIGITS RECEIVED
OUTPULSING
CONTROL
0
DIGITS CODE CONVERTED
AA AB AC
;: PS1
X'
PS2 ;:PS3 ;:S4 ):S6 ~:S6 ;;S7 ::S8
10
59 ;:S10
CASE 3
DIGITS RECEIVED
DIGITS PREFIXED
AB AC
B'
C
OUTPULSING
CONTROL
i PS2 : : P
B
PS3 •:SI ':S2 ::S3 :;S4 : : S5 :'S6 ■;S7
Fig. 9 — Method used for outpulsing digits.
CROSSBAR TANDEM AS A TOLL SWITCHING SYSTEM
105
translated in the marker and the second three digits in a foreign area
translator which is associated with the marker. Fig. 11 shows, in simpli-
fied form, how this translation is accomplished.
The first three digits, corresponding to the area code, are received by
a relay code tree in the marker which translates it into one of a thousand
code points. This code point is cross-connected to the particular relay of
the five area relays A(3-A4 which has been assigned to the called area.
A foreign area translator is now connected to the marker and a corre-
sponding area relay is operated in it. The translator also receives the
called office code from the sender via the marker and by means of a
relay code tree similar to that in the marker translates the office code
to one of a thousand code points. This code point plus the area relay is
sufficient to determine the actual route to be used. As shown on the
sketch, wires from each of the code points are threaded through trans-
formers, two for each area. When the marker is ready to receive the
route information, a surge of current is sent through one of these threaded
wires which produces a voltage in the output winding to ionize the
T- and U- tubes. Only the tubes associated with the area involved in
the translation pass current to operate one each of the eight T- and U-
relays. This information is passed to the marker and registered on
corresponding tens and units relays. These operate a route relay which
WISCONSIN
MICH.
J
ILLINOIS
CHICAGO =
' f BELLE \
1 AREA IplaINeJ
\312 I
^- — 1
I N D.
ROUTE WITHOUT 6 DIGIT TRANSLATION
ROUTE WITH 6 DIGIT TRANSLATION
Fig. 10 — Six-digit translation.
106 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
Fig. 11 — Method used for foreign area translation.
CROSSBAR TANDEM AS A TOLL SWITCHING SYSTEM 107
provides all the information necessary for routing the call to the central
office involved.
CUSTOMER DIRECT DISTANCE DIALING
Crossbar tandem will provide arrangements permitting customers in
step-by-step offices to dial their own calls anywhere in the country.
Centralized automatic message accounting previously mentioned will
be used for charging purposes. While the basic plan for direct distance
dialing provides for the dialing of either seven or ten digits, it will be
necessary for the customer in step-by-step areas to prefix a three-digit
directing code, such as 112, to the called number. This directing code
is required to direct the call through the step-by-step switches to the
crossbar tandem office so that the seven or ten digit number can be
registered in the crossbar tandem office.
When a customer in a step-by-step office originates a call to a distant
customer whose national number is 915-CH3-1234, he first dials the
directing code 112 and then the ten-digit number. The dialing of 112
causes the selectors in the step-by-step office to select an outgoing trunk
to the crossbar tandem office. The incoming trunk in the crossbar tandem
office has quick access to a three-digit register. The register must be
connected during the interval between the last digit of the directing
code and the first digit of the national number to insure registration of
this number. This arrangement is used to permit the customer to dial
all digits without delay and avoids the use of a second dial tone. If this
arrangement were not used, the customer would be required to wait
after dialing the 112 until the trunk in the tandem crossbar office could
gain access to a sender through the sender link circuit which would
then signal the customer to resume dialing by returning dial tone.
After recording the 915 area code digits in the case assumed, the
CH3-1234 portion of the number is registered directly in the tandem
sender which has been connected to the trunk while the customer was
dialing 915. When the sender is attached to the trunk, it signals the
three-digit register to transfer the 915 area code digits to it via a con-
nector circuit. Thus when dialing is complete, the entire number 915-
CH3-1234 is registered in the sender.
Crossbar tandem is being arranged to serve customers of panel and
No. 1 crossbar offices for direct distance dialing. At the present time,
ten digit direct distance dialing is not available to these customers
because the digit storing equipments in these offices are limited to
eight digits. Developments now under way, will provide arrangements
for expanding the digit capacity in the local offices so that ultirnately
108 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
calls from custoniers in panel and No. 1 crossbar offices may be routed
through crossbar tandem cr other equivalent offices to telephones
anywhere in the country.
CONCLUSION
The new features developed for crossbar tandem will adapt it to
switching all types of traffic at many important switching centers of
the nationwide toll network. Of the 225 important toll switching centers
now contemplated, it is expected that about 80 of these will be ecjuipped
with crossbar tandem.
REFERENCES
1. Collis, R. E., Crossbar Tandem System, A.I.E.E. Trans., 69, pp. 997-1004, 1950.
2. King, G. v.. Centralized Automatic Message Accounting, B.S.T.J., 33, pp.
1331-1342, 1952.
3. Nunn, W. H., Nationwide Numbering Plan, B.S.T.J., 31, pp. 851-859, 1952.
4. Pilliod, J. J., Fundamental Plans for Toll Telephone Plant, B. S.T.J. , 31, pp.
832-850, 1952.
5. Shipley, F. F., Automatic Toll Switching Systems, B.S.T.J., 31, pp. 860-882,
1952.
6. Truitt, C. J., Traffic Engineering Techniques for Determining Trunk Require-
ments in Alternate Routing Trunk Networks, B.S.T.J., 33, pp. 277-302, 1954.
7. Clos, C, Automatic Alternate Routing of Telephone Traffic, Bell Laboratories
Record, 32, pp. 51-57, Feb. 1954.
Growing Waves Due to Transverse
Velocities
By J. R. PIERCE and L. R. WALKER
(Manuscript received March 30, 1955)
This paper treats propagation of slow waves in two-dimensional neu-
tralized electron floiv in which all electrons have the same velocity in the
direction of propagation hut in which there are streams of two or more veloci-
ties normal to the direction of propagation. In a finite beam in which
' electrons are reflected elastically at the boundaries and in which equal dc
currents are carried by electrons with transverse velocities -\-Ui and — Wi ,
there is an antisi/mmetrical growing ivave if
Up ~ {rUi/Wf
and a symmetrical growing wave if
y-
i{Tu,/wy
Here cop is plasma frequency for the total charge density and W is beam
width.
INTKODUCTION
i It is well-known that there can be growing waves in electron flow when
the flow is composed of several streams of electrons having different
velocities in the direction of propagation of the waves. ' While Birdsall
considers the case of growing waves in electron flow consisting of streams
which cross one another, the growing waves which he finds apparently
occur when two streams have different components of velocity in the
direction of propagation.
This paper shows that there can be growing waves in electron flow
consisting of two or more streams with the same component of velocity
in the direction of wave propagation but with different components of
velocity transverse to the direction of propagation. Such growing Avaves
can exist when the electric field varies in strength across the flow. Such
waves could result in the amplification of noise fluctuations in electron
' flow. They could also be used to amplify signals.
109
110 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
Actual electron flow as it occurs in practical tubes can exhibit trans-
verse velocities. For instance, in Brillouin flow, ' • if we consider electron
motion in a coordinate system rotating with the Larmor frequency we
see that electrons with transverse velocities are free to cross the beam
repeatedly, being reflected at the boundaries of the beam. The trans-
verse \-elocities may be completely disorganized thermal velocities, or
they may be larger and better-organized velocities due to aberrations at
the edges of the cathode or at lenses or apertures. Two-dimensional
Brillouin flow allows similar transverse motions.
It would be difficult to treat the case of Brillouin or Brillouin-like flow
with transverse velocities. Here, simpler cases with transverse velocities
will be considered. The first case treated is that of infinite ion-neutra-
lized two-dimensional flow with transverse velocities. The second case
treated is that of two-dimensional flow in a beam of finite width in which
the electrons are elastically reflected at the boundaries of the beam.
Growing waves are found in both cases, and the rate of growth may be
large.
In the case of the finite beam both an antisymmetric mode and a
symmetric mode are possible. Here, it appears, the current density
required for a growing wave in the symmetric mode is about ^^ times
as great as the current density required for a growing wa^•e in the anti-
symmetric mode. Hence, as the current is increased, the first growing
waves to arise might be antisymmetric modes, which could couple to a
symmetrical resonator or helix only through a lack of symmetry or
through high-level effects.
1 . Infinite two-dimensional flow
Consider a two-dimensional problem in which the potential varies
sinusoidally in the y direction, as exp{—j^z) in the z direction and as exp
(jut) with time. Let there be two electron streams, each of a negative
charge po and each moving with the velocity ?/o in the z direction, but
with velocities Wi and —ih respectively in the y direction. Let us denote
ac quantities pertaining to the first stream by subscripts 1 and ac quan-
tities pertaining to the second stream by subscripts 2. The ac charge
density will be denoted by p, the ac velocity in the y direction by y,
and the ac velocity in the z direction by i. We will use linearized or
small-signal equations of motion.^ We will denote differentiation with
respect to ?/ by the operator D.
The equation of continuity gives
jupi = -D(piUi + po?yi) + j|8(piWo + pnii) (1.1)1
jcopo = -D{-p-iHi -\- pi)lj':d + il3(P2''o + Poi2) (1.2)
t;
GROWING WAVES DUE TO TRANSVERSE VELOCITIES 111
Let US define
dx = i(co - ^u,) + u,D (1.3)
do = ./(w - i8wo) - uj) (1.4)
We can then rewrite (1.1) and (1.2) as
f/iPi = Poi-Diji + j(3zi) (1.5)
dopi = Pi^{ — Dy2 + .7/3i2) (1.0)
We will assume that we are dealing ^^•ith slow waves and can use a po-
tential V to describe the field. We can thus write the linearized equations
of motion in the form
r/iii = -j-^F (1.7)
m
d2h = -j-^V (1.8)
m
drlji = - DV (1.9)
m
d,y, = 1 DV (1.10)
w
From (1.5) to (1.10) we obtain
^m = ~ PoiD' - ^')V (1.11)
m
d'p2= --poiD'- ^')V (1.12)
m
Now, Poisson's equation is
{D' - ^')V = _^L±£! (1.13)
From (1.11) to (1.13) we obtain
{D' - /3^)y = - Kco/ (^1 + ^^ (D' - /3^)7 (1.14)
9 ^
— Z— po
2 m
Wp =
e
Here Wp is the plasma frequency for the charge of both beams.
(1.15)
112 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
Either
or else
(2)' - /3')7 = 0
— C0„" (c/l" + ^2")
^ 2 di^ d.}
We will consider this second case.
W(< should note from (1.3) and (1.4) that
d{ = u^-D^ - (co - /5(/„)" + 2yD(co - |8?/.o)«i
^2^ = ?<i-D" - (co - ^ihf - 2jD{o^ - l3uo)ui
di' + f/o' = 2{u{D' - (co - iSwo)']
rfiW = [uiD' + (co - /3;/„)T
Thus, (1.17) becomes
(1.16)
(1.17)
(1.18)
(1.19)
(1.20)
(1.21)
(1.22)
WD"" + (co - j8mo)2]^
If the quantities involved vary sinusoidally with y as cos ru or sin yy,
-co,
\u{lf - (co - /3ao)']
then
Our equation becomes
D'
-7
(1.23)
CO
P L
1 +
CO — jS'Uo
T^Wi^
_ /co - 13^0 Y"
\ 7^1 /
(1.24)
What happens if we have many transverse velocities? If we refer back
to (1.14) we see that we will have an equation of the form
1 = E - 14
2^pn
2 I din + C?2n
d^d ^ J ^^-^''^
"In (fin /
Here cop„^ is a plasma frequency based on the density of electrons having
transverse velocities ±Un . Equation (1.25) can be written
(co - |(3//o)""|
i = E
A^
'M„2 r _ (g, - /3uo)2-['^
L 7-'"n^ J
(1.2())
GROWING WAVES DUE TO TRANSVERSE VELOCITIES
113
(u;-/3Uo
Fig. 1
Suppose we plot the left-hand and the right-hand sides of (1.26) versus
(co — ^Uo)- The general appearance of the left-hand and right-hand sides
of (1.26) is indicated in Fig. 1 for the case of two velocities Un . There
will always be two unattenuated waves at values of (w — /3wo) > y Ug
where Ue is the extreme value of lu; these correspond to intersections 3
and 3' in Fig. 2. The other waves, two per value of Un , may be unat-
tenuated or a pair of increasing and decreasing waves, depending on the
values of the parameters. If
CO
pn
-yhir?
> 1
there will be at least one pair of increasing and decreasing waves.
It is not clear what will happen for a Maxwellian distribution of veloci-
ties. However, we must remember that various aberrations might give a
very different, strongly peaked velocity distribution.
Let us consider the amount of gain in the case of one pair of transverse
velocities, ±i/i . The equation is now
2 2
7 Ui
C0„2
[
1 +
CO — |3wo
)•]
[ ■ - (^OI
(1.27)
Let
/5 = ^+i^
Wo Wo
(1.28)
114 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
1 .u
0.9
0.8
\
\
0.7
0.6
\
\
\,
\
^
0.5
0.4
0.3
\^
\
>s.
\
V
0.2
\
>
\
0.1
\
\
0
\
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
v2
m
Fig. 2
This relation defines e. Equation (1.27) becomes
2 2
0}J
1 - e^
(1 + e^)^ ^'-''^
In Fig. 2, e is plotted versus the parameter y^Ui/oip^. We see that as the
parameter falls below unity, e increases, at first rapidly, and then more
slowly, reaching a value of ±1 as the parameter goes to zero (as cop'
goes to infinity, for instance).
It will be shown in Section 2 of this paper that these results for infinite
flow are in some degree an approximation to the results for flow in narrow
beams. It is therefore of interest to see what results they yield if applied
to a beam of finite width.
If the beam has a length L, the voltage gain is
The gain G in db is
G = 8.7 '^ € db
Wo
(1.30)
(1.31)
GROWING WAVES DUE TO TRANSVERSE VELOCITIES 115
Let the width of the beam be W. We let
Thus, for n = 1, there is a half -cycle variation across the beam. From
(1.31) and (1.32)
G = 27.s(^^^\ne db (1.33)
Now L/uo is the time it takes the electrons to go from one end of the
beam to the other, while W/ui is the time it takes the electrons to cross
the beam. If the electrons cross the beam A'' times
iV = ^4 (1-34)
Thus,
G = 27.SNnedb (1.35)
While for a given value of e the gain is higher if we make the phase
vary many times across the beam, i.e., if we make n large, we should
note that to get any gain at all we must have
2 . //iTTUlV
0)r> >
(1.36)
W
If we increase oop , which is proportional to current density, so that cop
passes through this value, the gain will rise sharply just after cOp" passes
through this value and will rise less rapidly thereafter.
.?. A Two-Dimensional Beam of Finite Width.
Let us assume a beam of finite width in the ^/-direction ; the boundaries
lying a,t y = ±^o • It will be assumed also that electrons incident upon
these boundaries are elastically reflected, so that electrons of the incident
stream (1 or 2) are converted into those of the other stream (2 or 1). The
condition of elastic reflection implies that
yi = -h (2.1)
Zi = 22 Sit y = ±2/0 (2.2)
and, in addition, that
Pi = p2 at y = ±?/o . (2.3)
since there is no change in the number of electrons at the boundary.
116 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
The equations of motion and of continuity (1.7-1.12) may be satisfied
by introducing a single quantity, ^, such that
V = dx dzV (2.4)
ii = -J - /3 d, ^2^ (2.5)
m
zi = —j — di di\p (2.6)
m
yi=-d, d^Dyp (2.7)
m
112=- di d^Di^ (2.8)
m
Pi
m
poiD' - ^') dirl^ (2.9)
P2 = -- Po(i)' - n di'rl^ (2.10)
m
Then, if we introduce the symbol, 12, for co — jSuo
yi + y^ = 2j-d,d2D^yp (2.11) '
m
h- Z2 = 2j - di diUiD^ (2.12)
m
PI - P2 = 2j- po{D' - l3')uiQDi^ (2.13)
m
It is clear that if
Drjy = D^xl^ = 0 y = ±yo (2.14)
the conditions for elastic reflection will be satisfied. The equation satis-
fied by rf/ may now be found from Poisson's equation, (1-13), and is
{D' - /3^) dx' di^P = '-^{D'- fi'){d,' + di)^l.
we
or
{D' - ^')[{u,'D' + ny + coJiu.'D' - n')] = 0 (2.15)
which is of the sixth degree in D. So far four boundary conditions have,
been imposed. The remaining necessary pair arise from matching the
GROWING WAVES DUE TO TRANSVERSE VELOCITIES 117
internal fields to the external ones. For y > ijo
V = Voe-'^'-e~^" (2.16)
and
Similarlv
^ + i37 = 0 at 2/ = 2/0
dy
dV
— - ^V = 0 at y = -7/0 (2.17)
dy
The most familiar procedure now would be to look for solutions of
(2,15) of the form, e''^. This would give the sextic for c
(c' - /3')[(WiV + nY + a;/(niV - n')] = 0 (2.18)
with the roots c = ±|8, ±ci , ±C2 , let us s^y. We could then express \p
as a linear combination of these six solutions and adjust the coefficients
to satisfy the six boundary equations. In this way a characteristic equa-
tion for l3 would be obtained. From the S3anmetry of the problem this
has the general form F(l3, Ci) = F(i3, C2), where Ci and Co are found from
; (2.18). The discussion of the problem in these terms is rather laborious
and, if we are concerned mainly with examining qualitatively the onset
of increasing waves, another approach serves better.
From the symmetry of the equations and of the boundary conditions
we see that there are solutions for \p (and consequently for V and p)
which are even in y and again some which are odd in y. Consider first the
even solutions. We will assume that there is an even function, ^i(y),
periodic in y with period 2yo , which coincides with \l/(y) in the open
interval, —yo<y<yo and that \pi(:y) has a Fourier cosine series repre-
sentation :
hiy) = E c„ cos \ny X„ = — n = 0, 1, 2, • • • (2.19)
1 yo
yp inside the interval satisfies (2.15), so we assume that ypiiy) obeys
(D^ - ^')[{u,'D' + ^'f + o.,\u,'D' - ^-)^,
+00
(2.20)
= Z) 5(2/ - 2m + lyo)
where 6 is the familiar 5-function. Since D\p and D^\p are required to vanish
at the ends of the interval and \l/, D'^ and Z)V are even it follows that all
118 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
of these functions are continuous. We assume that xpi = \l/, D\pi = D\l/,
DVi = D~\p, D% = D^yp and D% = D*xl/ at the ends of the intervals.
From (2.20), Wi'D^i ^ -H as y ^ ijo .
Since
2 8iy - 2m + lyo) = ^ + - £ (-1)" cos Ky (2.21)
we obtain from (2.20)
/ 1
2?/oi/'i
,/32ff(i22 - Wp2)
+ 2i;(-l)" ^"^'"^
Since
^ + ^F = (Z) + /3)(t.x^Z)^ + fi^)V,
using (2.4), the condition for matching to the external field,
dV
^ + /37 = 0,
dy
yields, using D\p = DV = 0 and Ui*D^\f/ = — i^, the relation
(ui'D' + fi')Vi = 3^/3 at 2/ = 2/0 .
Applying this to (2.22), we then obtain, finally,
yo ^ 1
+ 2Z
r (^2 4- X„2)[(i22 - Ml2X„2)2 - cOp2(Q2 + ,,^2X„2)]
(2.22)
(2.23)
For the odd solution we use a function, yp2(y), equal to ;/'(?/) in — //o <
y < yo and representable by a sine series. To ensure the vanishing of D^p
and 7)V at ?/ = ±?/o it is appropriate to use the functions, sin n„y, where
Mn = (n -\- l'2)ir/yo . The period is now iyo and we define \p2(y) in /yo <
y < 32/0 by the relation i;'2(2/) = ^{2yo — y) and in — 32/o < 2/ < — 2/o by
^2(2/) = ^{ — '^Uo — y)- Thus, we write
00
1^2(2/) = 2 C?n sin UnV Hn = (w + 3^)^7/0
0
^2(2/) ^^i" ho supposed to satisfy
GROWING "WAVES DUE TO TRANSVERSE VELOCITIES 119
+M (2.24)
= 2 [^(y - 4m + lyo) - Ky - 4m - lyo)]
m=— 00
The extended definition of i/'2 (outside — /yo <y < ijo) is such that we may
again take \pi = \p, , D% = DV at the ends of the interval. ?/i*DVi is
still equal to — }4 at ij = ijo . Now
+ 00
£ [5(y - 4m + iW - ^(y — 4m - l^/o)]
(2.25)
= — 2 (—1)" sin /i„?/
2/0
so from (2.24) we may find
v^L = -T (-l)"sin/xnj/ , ^
Matching to the external field as before gives
and applied to (2.26) we have
00 /rfi 2 2\2
_y^ = y (^ - uinn) , .
The equations (2.23) and (2.27) for the even and odd modes may be
rewritten using the following reduced variables.
. = ^«
IT
1 _ Wj/0 _ Wo
(2.23) becomes
^' 4- 2 y ^ (n' - k^ _ _ .
and (2.27) transforms to
„^ 2^ + (n + 3^)2 [{n + 1^)2 - /c2]2 - s\{n + 3^)^ + k'] (2 99)
= — tt;?
120
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
We shall assume in considering (2.28) and (2.29) that the beam is
sufficiently wide for the transit of an electron from one side to the other
to take a few RF cycles. The number of cycles is in fact, coz/o/ttwi , and,
hence, from the definition of z, we see that for values of A: less than 2,
perhaps, z is certainly positive.
Let us consider (2.29) first since it proves to be the simpler case. If we
transfer the term ttz to the right hand side, it follo^^•s from the observa-
tion that z is positive (for modest values of h), that it is necessary to
make the sum negative. The sum may be studied qualitatively by sketch-
ing in the k^ — d' plane the lines on which the individual terms go to
infinity, given by
[(n + 3^)^ - k'f
8' =
(n -f K)' + k'
(2.30)
3.5
Fig. 3
GROWING WAVES DUE TO TRANSVERSE VELOCITIES
121
77
0.4
0.3
0.2 0.4 0.6 0.8 1.0
1.2 1.4
(X/TT
1.6
1.8 2.0 2.2 2.4
Fig. 4
Fig. 3 shows a few such curves (n = 0, 1, 2). To the right of such curves
the individual term in question is negative, except on the Hne, k^ =
{n + V^) , where it attains the value of zero. Approaching the curves
from the right the terms go to — oo . On the left of the curves the func-
tion is positive and goes to + oo as the curve is approached from the
10
...
/
/
/
/
J,
L
/
/
/
/
/
/
L
/
/
/
/
Y
/
/=,
/
A
V
/
/
/
'
\
/
A
-0
1
/
\
/
y
/
\
^^
A
><
■^
^^
>C
^
"\
^
'^
^
3 4 5 6 7 8 9
Fig. 5
J 22 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 195G
left. Clearly in the regions marked + which lie to the left of every curve
given by (2.30), the sum is positive and we cannot have roots. Let us
examine the sum in the region to the right of the n = 0 curve and to the
left of all others. On the line, A;^ = J4» the sum is positive, since the first
term is zero. On any other line, k' = constant, the sum goes from + °°
at the n = 1 curve monotonically to — oo at the n = 0 curve, so that
somewhere it must pass through 0. This enables us to draw the zero-
sum contours qualitatively in this region and they are indicated in Fig. 3.
We are now in a position to follow the variation in the sum as k varies
at fixed 5 . It is readily seen that for 5 < 0.25, because —wz is negative
in the region under consideration, there will be four real roots, tw^o for
positive, two for negative k. For 5' slightly greater than 0.25, the sum has
Fig. 6A
GROWING WAVES DUE TO TRANSVERSE VELOCITIES 123
a deep minimum for k = 0, so that there are still four real roots unless z
is very large. For z fixed, as 5^ increases, the depth of the minimum de-
creases and there will finally occur a 5" for which the minimum is so shal-
low that two of the real roots disappear. Call z(0) the value of ziork = 0,
write the sum as 2(5^ k^) and suppose that 2(5o^ 0) = —irziO), then for
small k we have
S(5^ e) = -«(0) + (6^ - 8o') §, + k'§,= -«(0) -"^ k
do^ dk^ Ua
as
dB dk^
^ = ^± / ".^(^-^0^) +
'^ a/
dk' y
The roots become complex when
aA-2
S.2 J 2 (Ul/Uo)
0 = do —
52 as
d8^ dB
Since Ui/uq may be considered small (say 10 per cent) it is sufficient to
look for the values of 5o^.
When k = 0 we have
-TZ = 2X)
2z
z (n + y,y
z^ + 52
irz"
z'-\-in-\- y^r (n -1- y^y- - s'
' H ^ + i ^
0 \in + 3^)2 - 52 ^ (n + 1^)2 + zy
(5 tan -Kb -\- z tanh irz)
z" + 52
Fig. 4 shows the solution of this equation for various 2(0) or oiyo/iruo .
Clearly the threshold 5 is rather insensitive to variations in uyo/ir^io .
Equation (2.28) may be examined by a similar method, but here some
complications arise. Fig. 5 shows the infinity curves for n = 0, 1, 2, 3;
the n = 0 term being of the form k^/k^ — 8^. The lowest critical region
in 5^ is the neighborhood of the point fc^ = 6^ = ]^i, which is the intersec-
tion of the n = 0 and n = 1 lines. To obtain an idea of the behavior of
124 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 195G
the left hand side (l.h.s.) of (2.28) in this area we first see how the point
k^ = f = 1^ can be approached so that the l.h.s. remains finite. If we
put k^ = H + £ and a' = ^ + ce and expand the first two dominant
terms of (2.28), then adjust c to keep the result finite as f -^ 0 we find
= 1 3^' - 5
^ ~ 4 32^ + 1
c varies from — % to \i as z goes from 0 to c» , changing sign at 2^ = %.
Every curve for which the l.h.s. is constant makes quadratic contact with
the Jine 5" — V3 = c(/v" — ]i) at Jc' = 5' = I/3. If we remember that
the l.h.s. is positive for A;' = 0, 0 < 5" < 1 and for A;^ = 1, 0 < 5^ < 1,
1
2
lik
3
w-oX
k^
/
1
y( I
3
SHADED AREAS //
NEGATIVE yV
X /'
/ //
/ /I
/ / /
X
\
n = i^v
0
3
3
Fig. 6B
GROWING WAVES DUE TO TRANSVERSE VELOCITIES 125
since there are no negative terms in the sum for these ranges and again
that the l.h.s. must change sign between the n = 0 and n — I Unes for
any k^ in the range 0 < k^ < 1 (since it varies from T oo to ±0°), this
information may be combined with that about the immediate vicinity
of 5 = k = V^ to enable us to draw a Hue on which the l.h.s. is zero.
This is indicated in Figs. 6A and 6B for small z and large z respec-
tively. It will be seen that the zero curve and, in fact, all curves on which
the l.h.s. is equal to a negative constant are required to have a vertical
tangent at some point. This point may be above or below /c^ = ^ (de-
pending upon the sign of c or the size of z) but always at a 3^ > ^. For
5 < H there are no regions where roots can arise as we can readily see
by considering how the l.h.s. varies with k"^ at fixed 5^ For a fixed d^ > }/s
we have, then, either for k^ > ]4 or k^ < V^, according to the size of z,
a negative minimum which becomes indefinitely deep as 5^ -^ ^. Thus,
since the negative terms on the right-hand side are not sensitive to small
changes in 5^, we must expect to find, for a fixed value of the l.h.s., two
real solutions of (2.28) for some values of 5^ and no real solutions for some
larger value of 5 , since the negative minimum of the l.h.s. may be made
as shallow as we like by increasing 6". By continuity then we expect to
find pairs of complex roots in this region. Rather oddly these roots, which
will exist certainly for 5' sufficiently close to V^ + 0, will disappear if
5^ is sufficiently increased.
REFERENCES
1. L. S. Nergaard, Analysis of a Simple Model of a Two-Beam Growing-Wave
Tube, RCA Review, 9, pp. 585-601, Dec, 1948.
2. J. R. Pierce and W. B. Hebenstreit, A New Type of High-Frequency Amplifier,
B. S. T. J., 28, pp. 23-51, Jan., 1949.
3. A. V. Haeff, The Electron-Wave Tube — A Novel Method of Generation and
Amplification of Microwave Energy, Proc. I.R.E., 37, pp. 4-10, Jan., 1949.
4. G. G. Macfarlg,ne and H. G. Hay, Wave Propagation in a Slipping Stream of
Electrons, Proc. Physical Society Sec. B, 63, pp. 409-427, June, 1950.
5. P. Gurnard and H. Huber, Etude E.xp^rimentale de L'Interaction par Ondes
de Chargd^d'Espace au Sein d'Un Faisceau Electronique se Deplagant dans
Des Champs Electrique et Magn^tique Croisfe, Annales de Radio^lectricite,
7, pp. 252-278, Oct., 1952.
6. C. K. Birdsall, Double Stream Amplification Due to Interaction Between Two
Oblique Electron Streams, Technical Report No. 24, Electronics Research
Laboratory, Stanford University.
7. L. Brillouin, A Theorem of Larmor and Its Importance for Electrons in Mag-
netic Fields, Phys. Rev., 67, pp. 260-266, 1945.
8. J. R. Pierce, Theory and Design of Electron Beams, 2nd Ed., Chapter 9, Van
Nostrand, 1954.
9. J. R. Pierce, Traveling-Wave Tubes, Van Nostrand, 1950.
Coupled Helices
By J. S. COOK, R. KOMPFNER and C. F. QUATE
(Received September 21, 1955)
An analysis of coupled helices is presented, using the transmission line
approach and also the field approach, with the objective of providing the
tube designer and the microwave circuit engineer with a basis for approxi-
mate calcidations. Devices based on the presence of only one mode of propa-
gation are briefly described; and methods for establishing such a mode are
given. Devices depending on the simultaneous presence of both modes, that
is, depending on the beat wave phenomenon, are described; some experi-
mental results are cited in support of the view that a novel and useful class of
coupling elements has been discovered.
CONTENTS
1. Introduction 129
2. Theory of Coupled Helices 132
2.1 Introduction 132
2.2 Transmission Line Equations 133
2.3 Solution for Synchronous Helices 135
2.4 Non-Synchronous Helix Solutions 137
2.5 A Look at the Fields 139
2.6 A Simple Estimate of b and x 141
2.7 Strength of Coupling versus Frequency 142
2.8 Field Solutions 144
. 2.9 Bifilar Helix 146
2.10 Effect of Dielectric Material between Helices 148
2.11 The Conditions for Maximum Power Transfer 151
2.12 Mode Impedance 152
3. Applications of Coupled Helices 154
3.1 Excitation of Pure Modes 156
3.1.1 Direct Excitation 156
3.1.2 Tapered Coupler 157
3.1.3 Stepped Coupler 158
3.2 Low Noise Transverse Field Amplifier 159
3.3 Dispersive Traveling Wave Tube 159
3.4 Devices Using Both Modes 161
3.4.1 Coupled Helix Transducer 161
3.4.2 Coupled-Helix Attenuator 165
4. Conclusion 167
Appendix
I Solution of Field Equations 168
II Finding r I73
III Complete Power Transfer 175
127
128 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
GLOSSARY OF SYMBOLS
a Mean radius of inner helix
h Mean radius of outer helix
h Capacitive coupling coefficient
Bio, 20 shunt susceptance of inner and outer helices, respectively
Bi, 2 Shunt susceptance plus mutual susceptance of inner and outer
helices, respectively, Bm + Bm , Boo + B^
Bm Mutual susceptance of two coupled helices
c Velocity of light in free space
d Radial separation between helices, h-a
D Directivity of helix coupler
E Electric field intensity
F Maximum fraction of power transferable from one coupled helix
to the other
F(ya) Impedance parameter
7i, 2 RF current in inner and outer helix, respectively
K Impedance in terms of longitudinal electric field on helix axis
and axial power flow
L ]\Iinimum axial distance required for maximum energy transfer
from one coupled helix to the other, X6/2
Axial power flow along helix circuit
Radial coordinate
Radius where longitudinal component of electric field is zero for
transverse mode (about midway between a and b)
Return loss
Radial separation betw^een helix and adjacent conducting shield
Time
RF potential of inner and outer helices, respectively •
Inductive coupling coefficient
Series reactance of inner and outer helices, respectively
Series reactance plus mutual reactance of inner and outer helices,
respectively, Xio + Xm , X20 + Xm
Mutual reactance of two coupled helices
Axial coordinate
Impedance of inner and outer helix, respectively
Attenuation constant of inner and outer helices, respectively
General circuit phase constant; or mean circuit phase constant.
Free space phase constant
Axial phase constant of inner and outer helices in absence of
coupling, V^ioXio , VBioXio
p
r
f
R
s
t
F1.2
X
Xva, 20
Xl, 2
Xm
Z
Zil, 2
Oil, 2
^0
^10. 20
COUPLED HELICES 129
181 , 2 May be considered as axial phase constant of inner and outer
helices, respectively
(Sft Beat phase constant
jSc Coupling phase constant, (identical with ^b when /3i = JS2)
I3ce Coupling phase constant when there is dielectric material be-
tween the helices
/3d Difference phase constant, [ /3i — /32 [
(8f Axial phase constant of single helix in presence of dielectric
^t, ( Axial phase constant of transverse and longitudinal modes, re-
spectively
7 Radial phase constant
jt, ( Radial phase constant of transverse and longitudinal modes,
respectively
r Axial propagation constant
Tt. ( Axial propagation constant for transverse and longitudinal
coupled-helix modes, respectively
e Dielectric constant
e' Relative dielectric constant, e/eq
En Dielectric constant of free space
X General circuit wavelength; or mean circuit wavelength, \/XiX2
Xo Free space wavelength
Xi, 2 Axial wavelength on inner and outer helix, respectively
X6 Beat wavelength
Xc Coupling wavelength (identical with Xb when (5i = /So)
yj/ Helix pitch angle
i/'i, 2 Pitch angle of inner and outer helix, respectively
CO Angular frequency
1. INTRODUCTION
Since their first appearance, traveling-wave tubes have changed only
very little. In particular, if we divide the tube, somewhat arbitrarily,
into circuit and beam, the most widely used circuit is still the helix, and
the most widely used transition from the circuits outside the tube to the
circuit inside is from waveguide to a short stub or antenna which, in
turn, is attached to the helix, either directly or through a few turns of
increased pitch. Feedback of signal energy along the helix is prevented
by means of loss, either distributed along the whole helix or localized
somewhere near the middle. The helix is most often supported along its
whole length by glass or ceramic rods, which also serve to carry a con-
ducting coating ("aquadag"), acting as the localized loss.
We therefore find the following circuit elements within the tube en-
velope, fixed and inaccessible once and for all after it has been sealed off:
130 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
1 . The helix itself, determining the beam voltage for optimum beam-
circuit interaction ;
2. The helix ends and matching stubs, etc., all of which have to be
positioned very precisely with relation to the waveguide circuits in
order to obtain a reproducible match ;
3. The loss, in the form of "aquadag" on the support rods, which
greatly influences the tube performance by its position and distril)ution.
In spite of the enormous bandwidth over which the traveling-wave
tube is potentially capable of operating — a feature new in the field of
microwave amplifier tubes — it turns out that the positioning of the tube
in the external circuits and the necessary matching adjustments are
rather critical; moreover the overall bandwidths achieved are far short
of the obtainable maximum.
Another fact, experimentally observed and well-founded in theory,
rounds off the situation: The electro-magnetic field surrounding a helix,
i.e., the slow wave, under normal conditions, does not radiate, and is
confined to the close vicinity of the helix, falling off in intensity nearly
exponentially with distance from the helix. A typical traveling-wave
tube, in which the helix is supported by ceramic rods, and the whole
enclosed by the glass envelope, is thus practically inaccessible as far as
RF fields are concerned, with the exception of the ends of the helix,
where provision is made for matching to the outside circuits. Placing
objects such as conductors, dielectrics or distributed loss close to the
tube is, in general, observed to have no effect whatsoever.
In the course of an experimental investigation into the propagation of
space charge waves in electron beams it was desired to couple into a long
helix at any point chosen along its length. Because of the feebleness of
the RF fields outside the helix surrounded by the conventional sup-
ports and the envelope, this seemed a rather difficult task. Nevertheless,
if accomplished, such a coupling would have other and even more im-
portant applications; and a good deal of thought was given to the
problem.
Coupled concentric helices were found to provide the solution to the
problem of coupling into and out of a helix at any particular point, and to
a number of other problems too.
Concentric coupled helices have been considered by J. R. Pierce,
who has ti'cated the problem mainly with transverse fields in mind.
Such fields were thought to be useful in low-noise traveling-wave tube
devices. Pierce's analysis treats the helices as transmission lines coupled
uniformly over their length by means of nuitual distributed capacitance
and inductance. Pierce also recognized that it is necessary to wind the
COUPLED HELICES l,']!
two helices in opposite directions in order to obtain well defined trans-
verse and axial wave modes which are well separated in respect to their
velocities of propagation.
Pierce did not then give an estimate of the velocity separation which
might be attainable with practical helices, nor did anybody (as far as we
are aware) then know how strong a coupling one might obtain with such
heUces.
It was, therefore, a considerable (and gratifying) surprise^' ^ to find
that concentric helices of practically realizable dimensions and separa-
tions are, indeed, very strongly coupled when, and these are the im-
portant points,
(a) They have very nearly equal velocities of propagation when un-
coupled, and when
(b) They are wound in opposite senses.
It was found that virtually complete power transfer from outer to
inner helix (or vice versa) could be effected over a distance of the order
of one helix wavelength (normally between i^fo and 3^^o of a free-space
wavelength.
It was also found that it was possible to make a transition from a co-
axial transmission line to a short (outer) helix and thence through the
glass surrounding an inner helix, which was fairly good over quite a con-
siderable bandwidth. Such a transition also acted as a directional coupler,
RF power coming from the coaxial line being transferred to the inner
helix predominantly in one direction.
Thus, one of the shortcomings of the "conventional" helix traveling-
wave tube, namely the necessary built-in accuracy of the matching
parameters, was overcome by means of the new type of coupler that
might evolve around coupled helix-to-helix systems.
Other constructional and functional possibilities appeared as the
work progressed, such as coupled-helix attenuators, various tj^pes of
broadband couplers, and schemes for exciting pure transverse (slow) or
longitudinal (fast) waves on coupled helices.
One central fact emerged from all these considerations: by placing
part of the circuit outside the tube envelope with complete independence
from the helix terminations inside the tube, coupled helices give back to
the circuit designer a freedom comparable only with that obtained at
much lower frequencies. For example, it now appears entirely possible
to make one type of traveling wave tube to cover a variety of frequency
bands, each band requiring merely different couplers or outside helices,
the tube itself remaining unchanged.
Moreover, one tube may now be made to fulfill a number of different
132 THE BELL SYSTEM TECHNICAI- JOURNAL, JANUARY 1956
functions; this is made possible by the freedom with which couplers
and attenuators can be placed at any chosen point along the tube.
Considerable work in this field has been done elsewhere. Reference
will be made to it wherever possible. However, only that work with
which the authors have been intimately connected will be fully reported
here. In particular, the effect of the electron beam on the wave propaga-
tion phenomena will not be considered.
2. THEORY OF COUPLED HELICES
2.1 Introduction
In the past, considerable success has been attained in the under-
standing of traveling wave tube behavior by means of the so-called
"transmission-line" approach to the theory. In particular, J. R, Pierce
used it in his initial analysis and was thus able to present the solution
of the so-called traveling-wave tube equations in the form of 4 waves,
one of which is an exponentially growing forward traveling wave basic
to the operation of the tube as an amplifier.
This transmission-line approach considers the helix — or any slow-
wave circuit for that matter — as a transmission line with distributed
capacitance and inductance with which an electron beam interacts.
As the first approximation, the beam is assumed to be moving in an RF
field of uniform intensity across the beam.
In this way very simple expressions for the coupling parameter and
gain, etc., are obtained, which give one a good appreciation of the
physically relevant quantities.
A number of factors, such as the effect of space charge, the non-uniform
distribution of the electric field, the variation of circuit impedance with
frequency, etc., can, in principle, be calculated and their effects can be
superimposed, so to speak, on the relatively simple expressions deriving
from the simple transmission line theory. This has, in fact, been done and
is, from the design engineer's point of view, quite satisfactory.
However, phj^sicists are bound to be unhappy over this state of
affairs. In the beginning was Maxwell, and therefore the proper point to
start from is Maxwell.
So-called "Field" theories of traveling-w^ave tubes, based on Maxwell's
equation, solved with the appropriate boundary conditions, have been
worked out and their main importance is that they largely confirm the
results obtained by the inexact transmission line theory. It is, however,
in the nature of things that field theories cannot give answers in terms of
COUPLED HELICES 133
simple closed expressions of any generality. The best that can be done
is in the form of curves, with step-wise increases of particular param-
eters. These can be of considerable value in particular cases, and when
exactness is essential.
In this paper we shall proceed by giving the "transmission-line" type
theory first, together with the elaborations that are necessary to arrive
at an estimate of the strength of coupling possible with coaxial helices.
The "field" type theory will be used whenever the other theory fails, or
is inadequate. Considerable physical insight can be gotten with the use
of the transmission-line theory; nevertheless recourse to field theory is
necessary in a number of cases, as will be seen.
It will be noted that in all the calculations to be presented the presence
of an electron beam is left out of account. This is done for two reasons:
Its inclusion would enormously complicate the theory, and, as will
eventually be shown, it would modify our conclusions only very slightly.
Moreover, in practically all cases which we shall consider, the helices are
so tightly coupled that the velocities of the two normal modes of propaga-
tion are very different, as will be shown. Thus, only when the beam
velocity is very near to either one or the other wave velocity, will
growing-wave interaction take place between the beam and the helices.
In this case conventional traveling wave tube theory may be used.
A theory of coupled helices in the presence of an electron beam has
been presented by Wade and Rynn,^ who treated the case of weakly
coupled helices and arrived at conclusions not at variance with our views.
2.2 Transmission Line Equations
Following Pierce we describe two lossless helices by their distributed
series reactances Xio and A'20 and their distributed shunt susceptances
Bio and ^20 . Thus their phase constants are
/3io = V^ioA'io
Let these helices be coupled by means of a mutual distributed reac-
tance Xm and a mutual susceptance B^ , both of which are, in a way
which will be described later, functions of the geometry.
Let waves in the coupled system be described by the factor
jut — Tj;
e e
\v
here the F's are the propagation constants to be found.
134 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
The transmission line equations may be written:
r/i - jB,V, + jB„y2 = 0
rFi - iXi/i + jXJo = 0
r/o - JB0V2 + jB„yi = 0
TV2 - jXJa + jXJ, - 0
where
B, - 5io + 5«
Bo = B20 + Bm
X2 = X20 -f" Xm
1 1 and 1 2 are eliminated from the (2.2.1) and we find
F2 ^ + (r- + XiBi + x^Bj
Fi
F2
(2.2.1)
X\Bm + B%Xm
+ (r- + X2S2 + x^Bj
XlBm + 5lX„
(2.2.2)
(2.2.3)
These two equations are then multipUed together and an expression for
r of the 4th degree is obtained :
r' + (XiBi + X2B2 + 2Z,„Bjr'
+ (X1Z2 - Xj){B,B2 - Bj) = 0
We now define a number of dimensionless quantities:
(2.2.4)
B,
BiB.
Xm
= h' = (eapacitive coupling coefficient)'
= X = (inductive coupling coefficient)
XiXo
B\Xi = ^1, B2X2 = (82'
X1B1X2B2 = 13^ = (mean phase constant)
With these substitutions we obtain the general equation for T~
T' = 13'
2 \(3-r ^ I3{' ^
y 4v^2'^^/3i^
_ (2.2.5)
+ 26.r - (1 - .r-)(l - U')
COUPLED HELICES 135
(2.2.6)
If we make the same substitutions in (2.2.2) we find
Fi T ZiL /3(/3i?> + /3o:r) .
where the Z's are the impedances of the heUces, i.e.,
Z,. = VXJB,
2.3 Solution for Synchronous Helices
Let us consider the particular case where (Si = (S-z = |S. From (2.2.5)
we obtain
r' = -I3\l + xb db (x + b)] (2.3.1)
Each of the above values of T" characterizes a normal mode of propaga-
tion involving both helices. The two square roots of each T" represent
waves going in the positive and negative directions. We shall consider
only the positive roots of T , denoted Tt and Tt , which represent the
forward traveling waves.
Ttj = i/3Vl + xb ± {x + b) (2.3.2)
If a: > 0 and 6 > 0
I r, I > |/3i, I r,| < 1^1
Thus Vt represents a normal mode of propagation which is slower than
the propagation velocity of either helix alone and can be called the
"slow" wave. Similarly T( represents a "fast" wave. We shall find that,
in fact, X and b are numerically equal in most cases of interest to us; we
therefore write the expressions for the propagation constants
r. = M^ + H(-^ + b)]
(2.3.3)
r. = Ml - Viix + b)]
If we substitute (2.3.3) into (2.2.6) for the case where /3i = (82 = /3 and
assume, for simplicity, that the helix self-impedances are equal, we find
that for r = Tt
Y% _
for r = T;
F2
-— = -f 1
Yx ^
136 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
Thus, the slow wave is characterized by equal voltages of unlike sign on
the two helices, and the fast wave by equal voltages of like sign. It fol-
lows that the electric field in the annular region between two such coupled
concentric helices will be transverse for the slow wave and longitudinal
for the fast. For this reason the slow and fast modes are often referred
to as the transverse and longitudinal modes, respectively, as indi-
cated by our subscripts.
It should be noted here that we arbitrarily chose h and x positive. A
different choice of signs cannot alter the fact that the transverse mode is
the slower and the longitudinal mode is the faster of the two.
Apart from the interest in the separate existence of the fast and slow
waves as such, another object of interest is the phenomenon of the simul-
taneous existence of both waves and the interference, or spatial beating,
between them.
Let V2 denote the voltage on the outer hehx; and let Vi , the voltage
on the inner halix, be zero at z = 0. Then we have, omitting the common
factor e'" ,
(2.3.4)
Since at 2 = 0, Fi = 0, Vn = — V(^ . For the case we have considered we
have found Fa = — V^ and Vn = V^ . We can write (2.3.4) as
Fi = I {e~'^' - e-^n
V, = ^ {e''^' + e-'n
(2.3.5)
F2 can be written
= Ye-"'''''^''^''' cos [-jj^(r, - Vi)z\
In the case when x = 6, and /Si = /32 = /8
F2 = Ye"'^' cos Wiix + h)^z\ (2.3.6)
Correspondingly, it can be shown that the voltage on the inner helix is
y, = j\Tfr^^' sin Wiix + h)^z\ (2.3.7)
The last tAvo equations exhibit clearly what we have called the spatial
beat phenomonou, a wave-like transfer of power from one helix to thc^
COUPLED HELICES . 137
other and back. We started, arbitrarily, with all the voltage on the outer
helix at 2 = 0, and none on the inner; after a distance, z', which makes
the argument of the cosine x/2, there is no voltage on the outer helix
and all is on the inner.
To conform with published material let us define what we shall call
the "coupling phase-constant" as
^, = ^{h + x) (2.3.8)
From (2.3.3) we find that for (Si = ^2 = |S, and x = h,
Tt - Ti = jl3c
2.4 Non-Synchronous Helix Solutions
Let us now go back to the more general case where the propagation
velocities of the (uncoupled) helices are not equal. Eciuation (2.2.5) can
be written:
Further, let us define
(2.4.1)
r- = -^- [1 + (1/2)A + xb ±
V(l + xb)A + (1/4)A2 + (6 + xy]
where
L /3 _
In the case where x = h, (2.4.1) has an exact root.
r,, , = j^ [Vl + A/4 ± 1/2 Va + (a; + by] (2.4.2)
We shall be interested in the difference between Tt and Tt,
Tt-Tf = j^ Va + (x + by- (2.4.3)
Now we substitute for A and find
Tt- Tc = j V(^i - ^2y + ^M& + 4' (2.4.4)
Let us define the "beat phase-constant" as:
Pb = V(/3i - /32)2 + nb + xy
so that
r, - r, = jA (2.4.5)
(3a = \ i5i - iSo
138 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
and call this the "difference phase-constant," i.e., the hase constant cor-
responding to two uncoupled waves of the same frequency but differing
phase velocities. We can thus state the relation between these phase
constants :
^b' = &I + ^c (2.4.6)
This relation is identical (except for notation) with expression (33) in
S. E. Miller's paper. ^ In this paper Miller also gives expressions for the
voltage amplitudes in two coupled transmission systems in the case of
unequal phase velocities. It turns out that in such a case the power trans-
fer from one system to the other is necessarily incomplete. This is of
particular interest to us, in connection with a number of practical
schemes. In our notation it is relatively simple, and we can state it by
saying that the maximum fraction of power transferred is
(2.4.7)
or, in more detail,
iS/ + iSc- (^1 - iS2)- + ^Kh + xY
This relationship can be shown to be a good approximation from (2.2.6),
(2.3.4), (2.4.2), on the assumption that h ^ x and Zx 'PH Z2 , and the
further assumption that the system is lossless; that is,
I 72 I ^ + I Fi I ^ = constant (2.4.8)
We note that the phase velocity difference gives rise to two phenomena :
It reduces the coupling w^avelength and it reduces the amount of power
that can be transferred from one helix to the other.
Something should be said about the case where the two helix imped-
ances are not equal, since this, indeed, is usually the case with coupled
concentric helices. Equation (2.4.8) becomes:
I F2 1 _^ \Vx\_ ^ (3Qj^g^^j^^ (2.4.9)
Z2 Z\
Using this relation it is found from (2.3.4) that
F2 , /Zi
FiT z,
(1 ± Vl - /^) (2.4.10)
When Ihis is combined with (2.2.6) it is found that the impedances droj)
out with the voltages, and that "F" is a function of the |S's only. In other
COUPLED HELICES 139
words, complete power transfer occurs when ,81 = /So regardless of the
relative impedances of the helices.
The reader will remember that (3io and (820 , not jSi and ^o , were defined
as the phase constants of the helices in the absence of each other. If the
assumption that h ^ x is maintained, it will be found that all of the de-
rived relationships hold true when (Sno is substituted for /3„ . In other
words, throughout the paper, /3i and /So may be treated as the phase con-
stants of the inner and outer helices, respectively. In particular it should
be noted that if these ciuantities are to be measured experimentally each
helix must be kept in the same environment as if the helices were coupled ;
onl}^ the other helix may be removed. That is, if there is dielectric in the
annular region between the coupled helices, /Si and ^2 must each be
measured in the presence of that dielectric.
Miller also has treated the case of lossy coupled transmission systems.
The expressions are lengthy and complicated and we believe that no
substantial error is made in simply applying his conclusions to our case.
If the attenuation constants ai and ao of the two transmission systems
(helices) are equal, no change is required in our expressions; when they
are unequal the total available power (in both helices) is most effectively
reduced when
^4^'^l (2.4.11)
Pc
This fact may be made use of in designing coupled helix attenuators.
2.5 A Look at the Fields
It may be advantageous to consider sketches of typical field distribu-
tions in coupled helices, as in Fig. 2.1, before we go on to derive a quanti-
tative estimate of the coupling factors actually obtainable in practice.
Fig. 2.1(a) shows, diagrammatically, electric field lines when the
coupled helices are excited in the fast or "longitudinal" mode. To set up
this mode only, one has to supply voltages of like sign and equal ampli-
tudes to both helices. For this reason, this mode is also sometimes called
the "(+-f) mode."
Fig. 2.1(b) shows the electric field lines when the helices are excited in
the slow or "transverse" mode. This is the kind of field required in the
transverse interaction type of traveling wave tube. In order to excite
this mode it is necessary to supply voltages of equal amplitude and
opposite signs to the helices and for this reason it is sometimes called the
"(-| — ) mode." One way of exciting this mode consists in connecting one
140 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
helix to one of the two conductors of a balanced transmission line
("Lecher"-line) and the other hehx to the other.
Fig. 2.1(c) shows the electric field configuration when fast and slow
modes are both present and equally strongly excited. We can imagine
the two helices being excited by a voltage source connected to the outer
(a) FAST WAVE (longitudinal)
(b) SLOW WAVE (transverse)
(C) fast and slow waves combined SHOWING SPATIAL "BEAT" PHENOMENON
Fig. 2.1 — Typical electric field distributions in coupled coaxial helices when
thej^ are excited in: (a) the in-phase or lonfritudinal mode, (b) the out-of-phase or
transverse mode, and (c) both modes equally.
COUPLED HELICES 141
helix only at the far left side of the sketch. One, perfectly legitimate,
view of the situation is that the RF power, initially all on the outer helix,
leaks into the inner helix because of the coupling between them, and then
leaks back to the outer helix, and so forth.
Apart from noting the appearance of the stationary spatial beat (or
interference) phenomenon these additional facts are of interest:
1) It is a simple matter to excite such a beat- wave, for instance, by
connecting a lead to either one or the other of the helices, and
2) It should be possible to discontinue either one of the helices, at
points where there is no current (voltage) on it, without causing reflec-
tions.
2.6 A Simple Estimate of h and x
How strong a coupling can one expect from concentric helices in prac-
tice? Quantitatively, this is expressed by the values of the coupling fac-
tors X and h, which we shall now proceed to estimate.
A first crude estimate is based on the fact that slow-wave fields are
known to fall off in intensity somewhat as c where (3 is the phase con-
stant of the wave and r the distance from the surface guiding the slow
wave. Thus a unit charge placed, say, on the inner helix, will induce a
charge of opposite sign and of magnitude
-Pib-a)
on the outer helix. Here h = mean radius of the outer helix and a =
mean radius of the inner. We note that the shunt mutual admittance
coupling factor is negative, irrespective of the directions in which the
helices are wound. Because of the similarity of the magnetic and electric
field distributions a current flowing on the inner helix will induce a simi-
larly attenuated current, of amplitude
on the outer helix. The direction of the induced current will depend on
whether the helices are woimd in the same sense or not, and it turns out
(as one can verify by reference to the low-freciuency case of coaxial
coupled coils) that the series mutual impedance coupling factor is nega-
tive when the helices are oppositely wound.
In order to obtain the greatest possible coupling between concentric
helices, both coupling factors should have the same sign. This then re-
fiuires that the helices should be wound in opposite directions, as has
been pointed out by Pierce.
When the distance between the two helices goes to zero, that is to say,
142 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
.if they lie in the same surface, it is clear that both coupling factors h and x
will go to unity.
As pointed out earlier in Section 2.3, the choice of sign for h is arbi-
trary. However, once a sign for h has been chosen, the sign of x is neces-
sarily the opposite when the helices are wound in the same direction, and
vice versa. We shall choose, therefore,
the sign of the latter depending on whether the helices are wound in the
same direction or not.
In the case of unequal velocities, (5, the propagation constant, would
be given by
1^ = VM~2 (2.6.2)
2.7 Strength of Coupling versus Frequency
The exponential variation of coupling factors with respect to frequency
(since /3 = co/y) has an important consequence. Consider the expression
for the coupling phase constant
/3. = I3{b + x) (2.3.8)
or
l/3e| = 2/3^"^^'""^ (2.7.1)
The coupling wavelength, which is defined as
Ac
is, therefore,
27r
(2.7.2)
or
Xc- -e
X, = ;^ g(2./x)u.-«) (2.7.3)
where X is the (slowed-down) RF wavelength on either helix. It is con-
venient to multiply both sides of (2.7.1) with a, the inner helix radius,
in order to obtain a dimensionless relation between /3c and /3:
^,a = 2/3ac~^''"''°^"" (2.7.4)
This relalion is j)l()Ued on Fig. 2.2 for several values of b/a.
COUPLED HELICES
143
3.00
2.75
2.50
2.25
2.00
/3ca
1.75
1.50
1.25
i.OO
0.75
0.50
0.25
^^
— -
/
/
/
/
/
/
/
/
/
l-y
/
/
/
/
/
J
/
/
/
/(/Jc3)max
/
/
/
/
/
1
/
/
/
/
/
^
/
b
= 1.5
/
/
/
/
f
^
,
V
/
^^
'"
\
1
-\
"^^^ — 1
75
L
2.0
■\
/
"^
■-^
3.0
— -
0.5
1.5
2.0
2.5
/3a
3.0
3.5 4.0
4.5
5.0
Fig. 2.2 — Coupling pliase-constant plotted as a function of the single helix
phase-constant for synchronous helices for several values of b/a. These curves
are based on simple estimates made in Section 2.7.
There are two opposing tendencies determining the actual physical
length of a coupling beat-wavelength:
1) It tends to grow with the RF wavelength, being proportional to it
in the first instance;
2) Because of the tighter coupling possible as the RF wavelength
increases in relation to the heli.x-to-helix distance, the coupling beat-
wavelength tends to shrink.
Therefore, there is a region where these tendencies cancel each other,
and where one would expect to find little change of the coupling beat-
wavelength for a considerable change of RF freciuency. In other words,
the "bandwidth" over which the beat-wavelength stays nearly constant
can be large.
This is a situation naturally very desirable and favorable for any
device in which we rely on power transfer from one helix to the other by
144 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
means of a length of overlap between them an integral number of half
beat-wavelengths long. Ob^'iously, one will design the helices in such a
way as to take advantage of this situation.
Optimiun conditions are easily obtained by dijfferentiating ^c with
respect to (3 and setting d^c/d^ equal to zero. This gives for the optimum
conditions
^opt —
1
b — a
(2.7.5)
or
Pc opt
2e
h — a
= 2e ')8opt
(2.7.6)
Equation (2.7.5), then, determines the ratio of the helix radii if it is re-
quired that deviations from a chosen operating frequency shall have
least effect.
2.8 Field Solutions
In treating the problem of coaxial coupled helices from the transmis-
sion line point of view one important fact has not been considered,
namely, the dispersive character of the phase constants of the separate
helices, /3i and fS-i . By dispersion we mean change of phase velocity with
frequency. If the dispersion of the inner and outer helices were the same
it would be of little consequence. It is well known, however, that the
dispersion of a helical transmission line is a function of the ratio of helix
radius to wavelength, and thus becomes a parameter to be considered.
When the theory of wave propagation on a helix was solved by means of
Maxwell's equations subject to the boundary condition of a helically
conducting cylindrical sheath, the phenomenon of dispersion first made
its appearance. It is clear, therefore, that a more complete theory of
/i
'V^ 'TV
Fig. 2.3 — ShoMtli liolix arrangement on which the field equations are based.
COUPLED HELICES 145
coupled helices will require similar treatment, namely, Maxwell's equa-
tions solved now with the boundary conditions of two cylindrical heli-
cally conducting sheaths. As shown on Fig. 2.3, the inner helix is specified
by its radius a and the angle 1^1 made by the direction of conductivity
with a plane perpendicular to the axis; and the outer helix by its radius
h (not to be confused with the mutual coupling coefficient 5) and its
corresponding pitch angle i/'-j . We note here that oppositely wound helices
require opposite signs for the angles \f/i and i/'o ; and, further, that helices
with equal phase velocities will ha\'e pitch angles of about the same
absolute magnitude.
The method of solving Maxwell's equations subject to the above men-
tioned boundary conditions is given in Appendix I. We restrict our-
selves here to giving some of the results in graphical form.
The most universally used parameter in traveling-wave tube design is
a combination of parameters:
/3oa cot \pi
where (So = 27r/Xo , Xo being the free-space wavelength, a the radius of
the inner helix, and xpi the pitch angle of the inner helix. The inner helix
is chosen here in preference to the outer helix because, in practice, it will
be part of a traveling-wave tube, that is to say, inside the tube envelope.
Thus, it is not only less accessible and changeable, but determines the
important aspects of a traveling-wave tube, such as gain, power output,
and efficiency.
The theory gives solutions in terms of radial propagation constants
which we shall denote jt and yt (bj^ analogy with the transverse and
longitudinal modes of the transmission line theory). These propagation
constants are related to the axial propagation constants ^t and j3( by
Of course, in transmission line theory there is no such thing as a radial
propagation constant. The propagation constant derived there and de-
noted r corresponds here to the axial propagation constant j^. By
analogy with (2.4.5) the beat phase constant should be written
How^ever, in practice ^0 is usually much smaller than j3 and Ave can there-
fore write with little error
iSfc = 7e — li
for the beat phase constant. For practical purposes it is convenient to
146 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
J.OU
_^^
1
3i.Z0
COT ^2 _ „„„
;:^
^
COTV'i
-0.90..
\
!^
-0.82,^
^
:J^
2.80
>^
<r
Q 2.40
^2.00
^
/.
^
//
/
^
|=,.25
1. 60
1.20
i
///
0.80
0.5
1.0
2.0 2.5
/io a COT ^,
3.0
3.5
4.0
4.5
Fig. 2.4.1 — Beat phase-constant plotted as a function of /3oa cot i^i • These
curves result from the solution of the field equations given in the appendix. For
hi a = 1.25.
normalize in terms of the inner helix radius, a:
jSbO
7<a — 7/a
This has been plotted as a function of /5o a cot i/'i in Fig. 2.4, which
should be compared with Fig. 2.2. It will be seen that there is considerable
agreement between the results of the two methods,
2.9 Bifilar Helix
The failure of the transmission line theory to take into account dis-
persion is well illustrated in the case of the bifilar helix. Here we have
two identical helices wound in the same sense, and at the same radius.
If the two wires are fed in phase we have the normal mode characterized
by the sheath helix model whose propagation constant is the familiar
Curve A of Fig. 2.5. If the two wires of the helix are fed out of phase we
have the bifilar mode; and, since that is a two wure transmission system,
we shall have a TEM mode which, in the absence of dielectric, propa-
gates along the wire with the velocity of light. Hence, the propagation
constant for this mode is simplj' /3oa cot \p and gives rise to the horizontal
COUPLED HELICES
147
1.80
1.60
(0
n 1.40
<5.
I
to
t.OO
0.80
0.60
b.
^
^>.
"^
"a"'"
A
s
^
N.
\.
\^
i
&
\
\
^
■^
0.82
w
^ = -0.98
COT^,
^
0.90
^V
^
//
/
\
\
v
J,
/
\
\
\,
t
\
f
\
f
0.5
1.0
1.5
2.0 2.5
/3oaCOTi^,
3.0
3.5
4.0
4.5
Fig. 2.4.2 — Beat phase-constant plotted as a function of /3oa cot ^i-i . These
curves result from the solution of the field equations given in the appendix. For
hia = 1.5.
line of Curve B in Fig. 2.5. Again the coupling phase constant j3c is given
by the difference of the individual phase constants:
^cO- — /3oa cot \f/ — ya
(2.9.1)
which is plotted in Fig. 2.6. Now note that when /So <3C 7 this equation is
accurate, for it represents a solution of the field equations for the helix.
From the simple unsophisticated transmission line point of view no
coupling between the two helices would, of course, have been expected,
since the two helices are identical in every way and their mutual capacity
and inductance should then be equal and opposite.
Experiments confirm the essential correctness of (2.9.1). In one experi-
ment, which was performed to measure the coupling wavelength for the
l)ifilar helices, we used helices with a cot 1/' = 3.49 and a radius of 0.036
cm which gave a value, at 3,000 mc, of ^oa cot i^ = 0.51 . In these experi-
ments the coupling length, L, defined by
(/3oa cot xp — 7a) — = TT
a
was measured to be 15.7o as compared to a value of 13.5a from Fig. 2.6.
At 4,000 mc the measured coupling length was 14.6a as compared to
148 THE BELL vSYSTEM TECHNICAL JOURNAL, JANUARY 1956
1.20
b
a
1.76
^
^^
^
^
X,
/
y
^
^
S.
X
1.00
/
V
\
^.
-\
/
/
\
P>
•^.82
0.80
r —
\
^
<5.
COT^
COT^
N
^ = -0.9
1
k^
"^^^
0.90
(0 0.60
a >s^
X
<0
'^ 0.40
^
.
0.20
0
<
D
0
5
1
0
1
5
2
.0
2
.5
^1
3.0
3.5
4.0
4
Fig. 2.4.3 — Beat phase-constant plotted as a function of ^^a cot -^x . These
curves result from the solution of the field equations given in the appendix. For
hi a = 1.75.
12.6a computed from Fig. 2.6, thus confirming the theoretical prediction
rather well. The slight increase in coupling length is attributable to the
dielectric loading of the helices which were supported in quartz tubing.
The dielectric tends to decrease the dispersion and hence reduce /3,. . This
is discussed further in the next section.
2.10 Effect of Dielectric Material hetween Helices
In many cases which are of interest in practice there is dielectric ma-
terial between the helices. In particular when coupled helices are used
with traveling-wave tubes, the tube envelope, which may be of glass,
quartz, or ceramic, all but fills the space between the two helices.
It is therefore of interest to know whether such dielectric makes any
difference to the estimates at which we arrived earlier. We should not be
surprised to find the coupling strengthened by the presence of the di-
electric, because it is known that dielectrics tend to rob RF fields from
the surrounding space, leading to an increase in the energy flow through
the dielectric. On the other hand, tlio dielectric tends to bind the fields
closer to the conducting medium. To find a qualitative answer to this
question we have calculated the relative coupling phase constants for
two sheath helices of infinite radius separated by a distance "d" for 1)
COUPLED HELICES
149
1.00
b
-a-^.u
^
^^
^
^
j^
^
COT Tp2
^
^
C 0.60
)^
1 0.40
m
y
^
COT }^,
^ 1
>
-^
S^
^
. ,
—
-0.
90
=-
--
V
^,
i
^
^0^
98
0.20
1
0
1
(
3
0
5
1
0
1
5
2
0
>oac
2.5
3
.0
3
.5
4
0
4.
Fig. 2.4.4 — Beat phase-constant plotted as a function of /3oa cot ^i . These
curves result from the solution of the field equations given in the appendix. For
b/a = 2.0.
the case with dielectric between them having a relative dielectric con-
stant e' = 4, and 2) the case of no dielectric. The pitch angles of the two
helices were \p and —xp, respectively; i.e., the helices were assumed to be
synchronous, and wound in the opposite sense.
■ Fig. 2.7 shows a plot of the ratio of /3,,.//3, to ^d^ versus /3o (f//2) cotiA,
1.00
0.80
to
n
«5. 0.60
II
m
i 0.40
0.20
b
a-o.u
^y
^
><
^
y
COT ^2
^
\>^
^--
COT 5^,
-^
r
/,
^
^
==^
"^^
N^
^^
y^
^
^
^
f/
^
^
N.
^
-c
).90
-^
r
\
-^
_
-o.s
?8
,
^
0.5
1.0
f.5
2.0 2.5
/JoacoT;^,
3.0
3.5
4.0
4.5
Fig. 2.4.5 — ■ Beat phase-constant plotted as a function of (3o« cot ^\ . These
curves result from the solution of the field equations given in the appendix. For
Va = 3.0.
150 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
2.4
0.5 ).0 1.5 2.0 2.
5 3.0 3.5
/3oaCOT^
4.0 4.5
Fig. 2.5 — Propagation constants for a bifilar helix plotted as a function of
/3oa cot i/-! . The curves illustrate, (A) the dispersive character of the in-phase
mode and, (B) the non-dispersive character of the out-of -phase mode.
where ^^ is the coupling phase-constant in the presence of dielectric,
/3j is the phase-constant of each helix alone in the presence of the same
dielectric, ^c is the coupling phase-constant with no dielectric, and (3 is
the phase constant of each helix in free space. In many cases of interest
/3o(d/2) cot lA is greater than 1.2. Then
3£ + 1"
_2£' + 2_
g—(v'2« '+2-2)^0 (dl2) cot \l/
(2.10.1)
Appearing in the same figure is a similar plot for the case when there is a
conducting shield inside the inner helix and outside the outer, and
separated a distance, "s," from the helices. Note that
c? = 6 — a.
It appears from these calculations that the effect of the presence of
dielectric between the helices depends largely on the parameter /So (d/2)
cot \{/. For values of this parameter larger than 0.3 the coupling wave-
length tends to increase in terms of circuit wavelength. For values smaller
than 0.3 the opposite tends to happen. Note that the curve representing
(2.10.1) is a fair approximation down to /3o(c?/2) cot i/' = 0.6 to the curve
representing the exact solution of the field equations. J. W. Sullivan, in
unpublished work, has drawn similar conclusions.
COUPLED HELICES
151
2.11 The Conditions for Maximum Power Transfer
The transmission line theory has led us to expect that the most efficient
power transfer will take place if the phase velocities on the two helices,
prior to coupling, are the same. Again, this would be true were it not for
the dispersion of the helices. To evaluate this effect we have used the
field equation to determine the parameter of the coupled helices which
gives maximum power transfer. To do this we searched for combinations
of parameters which give an equal current flow in the helix sheath for
either the longitudinal mode or the transverse mode. This was suggested
by L. Stark, who reasoned that if the currents were equal for the indi-
vidual modes the beat phenomenon would give points of zero RF current
on the helix.
The values of cot T/'2/cot 4/i which are required to produce this condi-
tion are plotted in Fig. 2.8 for various values of b/a. Also there are shown
values of cot ^2/cot \{/i required to give equal axial velocities for the helices
before they are coupled. It can be seen that the uncoupled velocity of the
inner helix must be slightly slower than that of the outer.
A word of caution is* necessary for these curves have been plotted
without considering the effects of dielectric loading, and this can have a
rather marked effect on the parameters which we have been discussing.
The significant point brought out by this calculation is that the optimum
u.^o
r
N
0.24
0.20
/
\
\
/
N
<D
/
\,
/
N
/
N^
0
^ 0.12
\
\^
~j
■^v
CD
^■^^^
0
0.08
f-
^-
-^
0.04
0
04 0.8 1.2 1.6 2.0 2.4
/3oaCOT J^,
2.8
3.2
3.6
4.0
Fig. 2.6 — The coupling phase-constant which results from the two possible
modes of propagation on a bifilar helix shown as a function of jSoo cot i/-! .
152 THE BELL SYSTEM TECHXICAL JOURNAL, JANUARY 1956
2.6
2.4
2.2
2.0
i.8
1.6
u
1.4
i.2
1.0
0.8
0.6
0.4
0.2
PROPAGATION
DIRECTION
\
\
^,
\
L
VA
\
s
PLANE SHEATH -^^^^"'^ XdiELECTRIC,
HELICES \^^r e'
CONDUCTING
SHIELD
\
\
\
s=oo
\
\,
APPROXIMATION
^^
^,
s
\
"N
'^
\
^
"^^^
■^^
o.t
0.2 0.3
0.4 0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
/iofcOT^^
Fig. 2.7 — ^ The effect of dielectric material between coupled infinite radius
sheath helices on their relative coupling phase-constant shown as a function of
fiod/2 cot \pi . The effect of shielding on this relation is also indicated.
condition for coupling is not necessarily associated with equal \'elocities
on the uncoupled helices.
2.12 Mode Impedance
Before leaving the general theor_y of coupled helices something should
be said regarding the impedance their modes present to an electron beam
traveling either along their axis or through the annular space between
them. The field solutions for cross woimd, coaxiall}^ coupled helices,
which are given in Appendix I, have been used to compute the imped-
ances of the transverse and longitudinal modes. The impedance, /v, is
defined, as usual, in terms of the longitudinal field on the axis and the
power flow along the system.
COUPLED HELICES
153
K =
F{ya)
In Fig. 2.9, Fiya), for various I'atios of inner to outer radius, is plotted
for both the transverse and longitudinal modes together with the value
of F{ya) for the single helix {b/a = co). We see that the longitudinal
mode has a higher impedance with cross wound coupled helices than
does a single helix. We call attention here to the fact that this is the
same phenomenon which is encountered in the contrawound helix^, where
the structure consists of two oppositely wound helices of the same radius.
As defined here, the transverse mode has a lower impedance than the
single helix. This, however, is not the most significant comparison; for
it is the transverse field midway between helices which is of interest in
the transverse mode. The factor relating the impedance in terms of the
transverse field between helices to the longitudinal field cni the axis is
Er (f)/Ei(0), where f is the radius at which the longitudinal component
of the electric field E^ , is zero for the transverse mode. This factor,
plotted in Fig. 2.10 as a function of /3oa cot \l/r , shows that the impedance
in. terms of the transverse field at f is interestingly high.
1.00
0.72
1.6 2.0 2.4
/3o a COT Ifi
4.0
Fig. 2.8 — The values of cot ^^./cot \pi required for complete power transfer
plotted as a function of /3tia cot \pi for several values of b/a. For comparison, the
value of cot ^2/cot \//i required for equal velocities on inner and outer helices is also
shown.
154 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
F(ra)
7.0
6.5
6.0
5.5
5.0
4.5
4.0
3.5
•
3.0
2.5
2.0
1.5
1.0
0.5
0.5 (.0 (.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
/SoaCOTii',
Fig. 2.9 — ■ Impedance parameter, F(ya), associated with both transverse and
longitudinal modes shown for several values of b/a. Also shown is F{ya) for a
single helix.
It is also of interest to consider the impedance of the longitudinal
mode in terms of the longitudinal field between the two helices. The
factor, ^/(f)/£'/(0), relating this to the axial impedance is plotted in
Fig. 2.11. We see that rather high impedances can also be obtained with
the longitudinal field midway between helices. This, in conjunction with
a hollow electron beam, should provide efficient amplification.
LONGITUDINAL WAVE
V
COT U/2
\
\^. V
\
\
\ "^
^=-0.90
k \
\
COT U/^
V \
\
\
b.ooV ^
\
\
\
a
\
\
^
\
\
\
\-o\
\
\
\
\
\
\
\
>
\
\
\
\
\
\
\
\
\
L \
i
\
\
\
\
\
\
\
\
\
V
\
\
,25\
yp
\
\
\
XT'
\
\
\
\
\
^
\ '
\
\
\
\
\
\
\ '
1
\
\
\
\
\
\
\
\
k
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\ \
\
%
\
N,
\
\
\
\
s
>
\
\
\
\,
V,
^.0
\\
\
N
s^5
\
\
1
\
\
1=1.2^
^^^
^
^^
^
'""'^-^
^^
"^^
>.,
'-
^^
^
■
^^
^==^
3. APPLICATION OF COUPLED HELICES
When we come to describe devices which make use of coupled helices
we find that they fall, quite naturally, into two separate classes. One
COUPLED HELICES
155
class contains those devices which depend on the presence of only one of
the two normal modes of propagation. The other class of devices depends
on the simultaneous presence, in roughly equal amounts, of both normal
modes of propagation, and is, in general, characterized by the words
"spatial beating." Since spatial beating implies energy surging to and
fro between inner and outer helix, there is no special problem in exciting
both modes simultaneously. Power fed exclusively to one or the other
/bo a COT jfi,
Fiji;. 2.10 — The relation l)et\veen the impedance in terms of the transverse
field between conpled helices excited in the out-of -phase mode, and the impedance
in terms of the longitudinal field on the axis shown as a function of /3oa cot tpi .
156
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
helix will inevitably excite both modes equally. When it is desired to
excite one mode exclusively a more difficult problem has to be solved.
Therefore, in section 3.1 we shall first discuss methods of exciting one
mode only before going on to discuss in sections 3.2 and 3.3 devices
using one mode only.
In section 3.4 we shall discuss devices depending on the simultaneous
presence of both modes.
3.1 Excitation of Pure Modes
3.1.1 Direct Excitation
In order to set up one or the other normal mode on coupled helices,
voltages with specific phase and amplitudes (or corresponding currents)
E|(f)
E|(o)
10^
5
10^
10^
10'
10
10"
COT
ip?
■ — = -0.90
COT i^,
1
/
/
1
'
l-.o/
1
L
L
1
/
J
l\.2b
/
J
/ J
/
^
'^
3 A
/ho a COT 1fi^
Fig. 2.11 — -The relation Ijetween the impedance in terms of the longitudinal
field between couj)led helices excited in the in-phase mode, and the impedance in
terms of the longitudinal field on the axis shown as a function of /3offl cot \pi .
COUPLED HELICES 157
have to be supplied to each helix at the input end. A natural way of doing
this might be by means of a two-conductor balanced transmission line
(Lecher-line), one conductor being connected to the inner helix, the other
to the outer helix. Such an arrangement would cause something like the
transverse (-| — ) mode to be set up on the helices. If the two con-
ductors and the balanced line can be shielded from each other starting
some distance from the helices then it is, in principle, possible to intro-
duce arbitrary amounts of extra delay into one of the conductors. A delay
of one half period would then cause the longitudinal ( + + ) mode to be
set up in the helices. Clearly such a coupling scheme would not be
broad-band since a frequency-independent delay of one half period is not
realizable.
Other objections to both of these schemes are: Balanced lines are not
generally used at microwave frequencies; it is difficult to bring leads
through the envelope of a TWT without causing reflection of RF energy
and without unduly encumbering the mechanical design of the tube plus
circuits; both schemes are necessarily inexact because helices having
different radii will, in general, require different voltages at either input
in order to be excited in a pure mode.
Thus the practicability, and success, of any general scheme based on
the existence of a pure transverse or a pure longitudinal mode on coupled
helices will depend to a large extent on whether elegant coupling means
are available. Such means are indeed in existence as will be shown in the
next sections.
3.1.2 Tapered Coupler
A less direct but more elegant means of coupling an external circuit
to either normal mode of a double helix arrangement is by the use of the
so-called "tapered" coupler.^' ^' ^^ By appropriately tapering the relative
propagation velocities of the inner and outer helices, outside the inter-
action region, one can excite either normal mode by coupling to one
helix only.
The principle of this coupler is based on the fact that any two coupled
transmission lines support two, and only two, normal modes, regardless
of their relative phase velocities. These normal modes are characterized
by unequal wave amplitudes on the two lines if the phase velocities are
not equal. Indeed the greater the phase velocity difference and /or
the smaller the coupling coefficient between the lines, the more their
wave amplitudes diverge. Furthermore, the wave amplitude on the line
with the slower phase velocity is greater for the out-of-phase or trans-
verse normal mode, and the wave amplitude on the faster line is greater
158 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 195G
for the longitudinal normal mode. As the ratio of phase constant to
coupling constant approaches infinity, the ratio of the wave amplitudes
on the two lines does also. Finally, if the phase velocities of, or coupling
between, two coupled helices are changed gradually along their length
the normal modes existing on the pair roughly maintain their identity
evan though they change their character. Thus, by properly tapering the
phase velocities and coupling strength of any two coupled helices one
can cause the two normal modes to become two separate waves, one
existing on each helix.
For instance, if one desires to extract a signal propagating in the in-
phase, or longitudinal, normal mode from two concentric helices of equal
phase velocity, one might gradually increase the pitch of the outer helix
and decrease that of the inner, and at the same time increase the diameter
of the outer helix to decrease the coupling, until the longitudinal mode
exists as a wave on the outer helix only. At such a point the outer helix
may be connected to a coaxial line and the signal brought out.
This kind of coupler has the advantage of being frequency insensitive ;
and, perhaps, operable over bandwidths upwards of two octaves. It
has the disadvantage of being electrically, and sometimes physically,
quite long.
3.1.3 Stepped Coupler
There is yet a third way to excite only one normal mode on a double
helix. This scheme consists of a short length at each end of the outer helix,
for instance, which has a pitch slightly different from the rest. This
has been called a "stepped" coupler.
The principle of the stepped coupler is this: If two coupled transmis-
sion lines have unlike phase velocities then a wave initiated in one line
can never be completely transferred to the other, as has been shown in
Section 2.4. The greater the velocity difference the less will be the maxi-
mum transfer. One can choose a velocity difference such that the maxi-
mum power transfer is just one half the initial power. It is a characteristic
of incomplete power transfer that at the point where the maximum trans-
fer occurs the waves on the two lines are exactly either in-phase or out-of-
phase, depending on which helix was initially excited. Thus, the condi-
tions for a normal mode on two equal-velocity helices can be produced
at the maximum transfer point of two unlike velocity helices by initiating
a wave on only one of them. If at that point the helix pitches are changed
to give equal phase velocities in both helices, with equal current or volt-
age amplitude on both helices, either one or the other of the two normal
modes will be propagated on the two helices from there on. Although the
COUPLED HELICES 159
pitch and length of such a stepped coupler are rather critical, the re-
quirements are indicated in the equations in Section 2.4.
The useful bandwidth of the stepped coupler is not as great as that
of the tapered variety, but may be as much as an octave. It has however
the advantage of being very much shorter and simpler than the tapered
coupler.
3.2 Low-Noise Transverse-Field Amplifier
r One application of coupled helices which has been suggested from the
very beginning is for a transverse field amplifier with low noise factor.
In such an amplifier the EF structure is required to produce a field which
is purely transverse at the position of the beam. For the transverse mode
there is always such a cylindrical surface where the longitudinal field is
zero and this can be obtained from the field equation of Appendix II.
In Fig. 3.1 we have plotted the value of the radius f at which the longi-
tudinal field is zero for various parameters. The significant feature of
this plot is that the radius which specifies zero longitudinal field is not
constant with frequency. At frequencies away from the design frequency
the electron beam will be in a position where interaction with longitudinal
components might become important and thus shotnoise power will be
introduced into the circuit. Thus the bandwidth of the amplifier over
which it has a good noise factor would tend to be limited. However, this
effect can be reduced by using the smallest practicable value of b/a.
Section 2.12 indicates that the impedance of the transverse mode is
very high, and thus this structure should be well suited for transverse
field amplifiers.
3.3 Dispersive Traveling-Wave Tube
Large bandwidth is not always essential in microwave amplifiers. In
particular, the enormous bandwidth over which the traveling-wave tube
is potentially capable of amplifying has so far found little application,
while relatively narrow bandwidths (although quite wide by previous
standards) are of immediate interest. Such a relatively narrow band, if
it is an inherent electronic property of the tube, makes matching the
tube to the external circuits easier. It may permit, for instance, the use
of non-reciprocal attenuation by means of ferrites in the ferromagnetic
resonance region. It obviates filters designed to deliberately reduce the
band in certain applications. Last, but not least, it offers the possibility
of trading bandwidth for gain and efficiency.
A very simple method of making a traveling-wave tube narrow-band
160 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
0.5
1.W
1.8
^
^
1.7
COT \p.
_^
^
^
<^
T^ = -0.
COT ^,
82^
^
^
^
^
l=-
1.6
^
^
^
-0.90
^
^
^
^
*
1.5
— -
-0.9
8
'
^-' '
^
^
1.4
-^
COT ^i'2
^-^ = -0.82
COT UJ^ ,
-0.9j
,
^-
1.3
.
—
"ZH
' 1
-0.98
1.2
_
"71
| = ,.25
—
^=
CO'
r 1//.
— T-"
H
COT 5^,
= -0.82 -
-0.90 ■
' /
^
1
/
/
i.n
-0
.98
~
1.0
1.5
2.0
2.5 3.0
/3o a COT j^.
3.5
4.0
4.5
5.0
Fig. 3.1 — The radius r at which the longitudinal field is zero for transversely
excited coupled coaxial helices.
is by using a dispersive circuit, (i.e. one in which the phase velocity varies
significantly with frequency). Thus, we obtain an amplifier that can be
limed by varying the beam voltage; being dispersive we should also
expect a low group velocity and therefore higher circuit impedance.
Calculations of the phase velocities of the normal modes of coupled
concentric helices presented in the appendix show that the fast, longitu-
dinal or (+ + ) mode is highly dispersive. Given the geometry of two
such coupled helices and the relevant data on an electron beam, namely
current, voltage and beam radius, it is possible to arrive at an estimate
of the dependence of gain on frecjuency.
Experiments with such a tube showed a Ijandwidth 3.8 times larger
than the simple estimate would show. This we ascribe to the presence
COUPLED HELICES 161
of the dielectric between the helices in the actual tube, and to the neglect
of power propagated in the form of spatial harmonics.
Nevertheless, the tube operated satisfactorily with distributed non-
reciprocal ferrite attenuation along the whole helix and gave, at the
center frequency of 4,500 mc/s more than 40 db stable gain.
The gain fell to zero at 3,950 mc/s at one end of the band and at
4,980 mc/s at the other. The forward loss was 12 db. The backward
loss was of the order of 50 db at the maximum gain frequency.
3.4 Devices Using Both Modes
In this section we shall discuss applications of the coupled-helix princi-
ple which depend for their function on the simultaneous presence of both
the transverse and the longitudinal modes. When present in substantially
equal magnitude a spatial beat-phenomenon takes place, that is, RF
power transfers back and forth between inner and outer helix.
Thus, there are points, periodic with distance along each helix, where
there is substantially no current or voltage; at these points a helix can be
terminated, cut-off, or connected to external circuits without detriment.
The main object, then, of all devices discussed in this section is power
transfer from one helix to the other; and, as will be seen, this can be ac-
complished in a remarkably efficient, elegant, and broad-band manner.
3.4.1 Coupled-Helix Transducer
It is, by now, a well known fact that a good match can be obtained
between a coaxial line and a helix of proportions such as used in TWT's. A
wire helix in free space has an effective impedance of the order of 100
ohms. A conducting shield near the helix, however, tends to reduce the
helix impedance, and a value of 70 or even 50 ohms is easily attained.
Pro\'ided that the transition region between the coaxial line and the
helix does not present too abrupt a change in geometry or impedance,
relatively good transitions, operable over bandwidths of several octaves,
can l)e made, and are used in practice to feed into and out of tubes em-
ploying helices such as TWT's and backward-wave oscillators.
One particularly awkward point remains, namely, the necessity to lead
the coaxial line through the tube envelope. This is a complication in
manufacture and reciuires careful positioning and dimensioning of the
helix and other tube parts.
Coupled helices offer an opportunity to overcome this difficulty in the
form of the so-called coupled-helix transducer, a sketch of which is
shown in Fig. 3.2. As has been shown in Section 2.3, with helices having
162
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
the same velocity an overlap of one half of a beat wavelength will result
in a 100 per cent power transfer from one helix to the other. A signal in-
troduced into the outer helix at point A by means of the coaxial line will
be all on the inner helix at point B, nothing remaining on the outer helix.
At that point the outer helix can be discontinued, or cut off; since there
is no power there, the seemingly violent discontinuity represented by the
'open" end of the helix will cause no reflection of power. In practice, un-
fortunately, there are always imperfections to consider, and there will
often be some power left at the end of the coupler helix. Thus, it is de-
sirable to terminate the outer helix at this point non-reflectively, as, for
instance, by a resistive element of the right value, or by connecting to it
another matched coaxial line which in turn is then non-reflectively ter-
minated.
It will be seen, therefore, that the coupled-helix transducer can, in
principle, be made into an efficient device for coupling RF energy from
a coaxial line to a helix contained in a dielectric envelope such as a glass
tube. The inner helix will be energized predominantly in one direction,
namely, the one away from the input connection. Conversely, energy
traveling initially in the inner helix will be transferred to the outer, and
made available as output in the respective coaxial line. Such a coupled-
helix transducer can be moved along the tube, if required. As long as the
outer helix completely overlaps the inner, operation as described above
should be assured. By this means a new flexibility in design, operation
and adjustment of traveling-wave tubes is obtained which could not be
achieved by any other known form of traveling-wave tube transducer.
Naturally, the applications of the coupled-helix transducer are not
restricted to TWT's only, nor to 100 per cent power transfer. To obtain
Fig. 3.2 — A simple coupled helix transducer.
COUPLED HELICES 1G3
power transfer of proportions other than 100 per cent two possibilities
are open: either one can reduce the length of the synchronous coupling
helix appropriately, or one can deliberately make the helices non-syn-
chronous. In the latter case, a considerable measure of broad-banding
can be obtained by making the length of overlap again equal to one half
of a beat-wavelength, while the fraction of power transferred is deter-
mined by the difference of the helix velocities according to 2.4.7. An
application of the principle of the coupled-helix transducer to a variable
delay line has been described by L. Stark in an unpublished memo-
randum.
Turning again to the complete power transfer case, we may ask:
How broad is such a coupler?
In Section 2.7 we have discussed how the radial falling-off of the RF
energy near a helix can be used to broad-band coupled-helix devices
which depend on relative constancy of beat-wavelength as frequency
is varied. On the assumption that there exists a perfect broad-band match
between a coaxial line and a helix, one can calculate the performance of
a coupled-helix transducer of the type shown in Fig. 3.2.
Let us define a center frequency co, at which the outer helix is exactly
one half beat-wavelength, \b , long. If oj is the frequency of minimum
beat wavelength then at frequencies coi and co2 , larger and smaller,
respectively, than co, the outer helix will be a fraction 5 shorter than
}i\b , (Section 2.7). Let a voltage amplitude, Vo , exist at the point where
the outer helix is joined to the coaxial line. Then the magnitude of the
voltage at the other end of the outer helix will be | F2 • sin (x5/2) | which
means that the power has not been completely transferred to the inner
helix. Let us assume complete reflection at this end of the outer helix.
Then all but a fraction of the reflected power will be transferred to the
inner helix in a reverse direction. Thus, we have a first estimate for the
"directivity" defined as the ratio of forward to backward power (in db)
introduced into the inner helix:
D =
10 log sin"
(3.4.1.1)
We have assumed a perfect match between coaxial line and outer helix;
thus the power reflected back into the coaxial line is proportional to
sin^(x5/2). Thus the reflectivity defined as the ratio of reflected to
incident power is given in db by
i^ = 10 log sin' ^ (3.4.1.2)
164 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
For the sake of definiteness, let us choose actual figures: let /3a = 2.0.
and hi a = 1.5. And let us, arbitrarily, demand that R always be less than
-20 db.
This gives sin (7r5/2) < 0.316 and 7r5/2 < 18.42° or 0.294 radians,
8 < 0.205. With the optimum value of (Sea = 1.47, this gives the mini-
mum permissible value of I3ca of 1.47/(1 + 0.205) = 1.22. From the
graph on Fig. 2.2 this corresponds to values of jSa of 1.00 and 3.50.
Therefore, the reflected power is down 20 db over a frequency range of
aj2/aji = 3,5 to one. Over the same range, the directivity is better than
10 to one. Suppose a directivity of better than 20 db were required.
This requires sin (7r5/2) = 0.10, 8 = 0.0638 and is obtained over a fre-
quency range of approximately two to one. Over the same range, the
reflected power would be down by 40 db.
In the above example the full bandwidth possibilities have not been
used since the coupler has been assumed to have optimum length when
jSctt is maximum. If the coupler is made longer so that when I3ca is maxi-
mum it is electrically short of optimum to the extent permissible by
the quality requirements, then the minimum allowable (S^a becomes even
smaller. Thus, for h/a =1.5 and directivity 20 db or greater the rea-
lizable bandwidth is nearly three to one.
When the coupling helix is non-reflectively terminated at both ends,
either by means of two coaxial lines or a coaxial line at one end and a
resistive element at the other, the directivity is, ideally, infinite, irrespec-
tive of frequency; and, similarly, there will be no reflections. The power
transfer to the inner helix is simply proportional to cos (t8/2). Thus,
under the conditions chosen for the example given above, the coupled-
helix transducer can approach the ideal transducer over a considerable
range of frequencies.
So far, we have inspected the performance and bandwith of the
coupled-helix transducer from the most optimistic theoretical point of
view. Although a more realistic approach does not change the essence
of our conclusions, it does modify them. For instance, we have neglected
dispersion on the helices. Dispersion tends to reduce the maximum at-
tainable bandwidth as can be seen if Fig. 2.4.2 rather than Fig. 2.2 is
used in the example cited above. The dielectric that exists in the annular
region between coupled concentric helices in most practical couplers
may also affect the bandwidth.
In practice, the performance^ of coupled-hc^lix transducers has been
short of the ideal. In the first place, the match from a coaxial line to a
helix is not perfect. Secondly, a not inappreciable fraction of the RF
power on a real wire helix is propagated in the form of spatial harmonic
COUPLED HELICES
165
28
26
24
22
20
18
)6
in
_i
LU
m (4
u
12
10
r\
\
\
\
\
' * /
' * /
1 t /
[\
n
[ 1
I
1 1
\j
^
\
Wf
\
1
\
\
I /
I /
\ /
\1^
U~
/
/
/
\
.'
1
A
\J
\-
/ \
\
A
/
Vi
\
\
\
1
1
/
1
p
OUPLER DIRECTIVITY
ETURN LOSS
\
\
1
J
\
A
V
I
/
l
1.5
2.5 3 4
FREQUENCY IN KILOMEGACYCLES
Fig. 3.3 — • The return loss and directivity of an experimental 100 per cent
coupled-helix transducer.
wave components which have variations with angle around the helix-
axis, and coupling between such components on two helices wound in
opposite directions must be small. Finally, there are the inevitable me-
chanical inaccuracies and misalignments.
Fig. 3.3 shows the results of measurements on a coupled-helix trans-
ducer with no termination at the far end.
3.4.2 Coupled-Helix Attenuator
In most TWT's the need arises for a region of heavy attenuation
somewhere between input and output; this serves to isolate input and
output, and prevents oscillations due to feedback along the circuit. Be-
cause of the large bandwidth over which most TWT's are inherently
capable of amplifying, substantial attenuation, say at least 60 db, is
166 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
required over a bandwidth of maybe 2 octaves, or even more. Further-
more, such attenuation should present a very good match to a wave on
the heHx, particularly to a wave traveling backwards from the output
of the tube since such a wave will be amplified by the output section of
the tube.
Another requirement is that the attenuator should be physically as
short as possible so as not to increase the length of the tube unneces-
sarily.
Finally, such attenuation might, with advantage, be made movable
during the operation of the tube in order to obtain optimum performance,
perhaps in respect of power output, or linearity, or some other aspect.
Coupled-helix attenuators promise to perform these functions satis-
factorily.
A length of outer helix (synchronous with the inner helix) one half of a
beat wavelength long, terminated at either end non-reflectively, forms a
very simple, short, and elegant solution of the coupled-helix attenuator
problem. A notable weakness of this form of attenuator is its relatively
narrow bandwidth. Proceeding, as before, on the assumption that the
attenuator is a fraction 8 larger or smaller than half a beat wavelength
at frequencies coi and W2 on either side of the center frequency co, we find
that the fraction of power transferred from the inner helix to the attenu-
ator is then given by (1 — sin" (ir8/2)). The attenuation is thus simply
A = sin^ (I)
For helices of the same proportions as used before in Section 3.4.1, we
find that this will give an attenuation of at least 20 db over a frequency
band of two to one. At the center frequency, coo , the attenuation is in-
finite; — in theory.
Thus to get higher attenuation, it would be necessary to arrange for a
sufficient number of such attenuators in tandem along the TWT. More-
over, by properly staggering their lengths within certain ranges a wdder
attenuation band may be achieved. The success of such a scheme largely
depends on the ability to terminate the helix ends non-reflectively. Con-
siderable work has been done in this direction, but complete success is
not yet in sight.
Another basically different scheme for a coupled-helix attenuator rests
on the use of distributed attenuation along the coupling helix. The diffi-
culty with any such scheme lies in the fact that unequal attenuation in
the two coupled helices reduces the coupling between them and the moi'c
they differ in respect to attenuation, the less the coupling. Naturally, one
COUPLED HELICES 167
would wish to have as Httle attenuation as practicable associated with
the inner helix (inside the TWT). This requires the attenuating element
to be associated with the outer helix. Miller has shown that the maxi-
mum total power reduction in coupled transmission systems is obtained
when
ai — 0:2
where ai and 012 are the attenuation constants in the respective systems,
and ^b the beat phase constant. If the inner helix is assumed to be loss-
less, the attenuation constant of the outer helix has to be effectively equal
to the beat wave phase constant. It turns out that 60 db of attenuation
requires about 3 beat wavelengths (in practice 10 to 20 helix wave-
lengths). The total length of a typical TWT is only 3 or 4 times that,
and it will be seen, therefore, that this scheme may not be practical as
the only means of providing loss.
Experiments carried out Avith outer helices of various resistivities and
thicknesses by K. M. Poole (then at the Clarendon Laboratory, Oxford,
England) tend to confirm this conclusion. P. D. Lacy" has described a
coupled helix attenuator which uses a multifilar helix of resistance
material together with a resistive sheath between the helices.
Experiments were performed at Bell Telephone Laboratories with a
TWT using a resistive sheath (graphite on paper) placed between the
outer helix and the quartz tube enclosing the inner helix. The attenua-
tions were found to be somewhat less than estimated theoretically. The
attenuator helix was movable in the axial direction and it w^as instructive
to observe the influence of attenuator position on the power output from
the tube, particularly at the highest attainable power level. As one might
expect, as the power level is raised, the attenuator has to be moA-ed nearer
to the input end of the tube in order to obtain maximum gain and power
output. In the limit, the attenuator helix has to be placed right close to
the input end, a position which does not coincide with that for maximum
low-level signal gain. Thus, the potential usefulness of the feature of
mobility of coupled-helix elements has been demonstrated.
4. CONCLUSION
In this paper we have made an attempt to develop and collect together
a considerable body of information, partly in the form of equations,
partl}^ in the form of graphs, which should be of some help to workers
in the field of microwave tubes and devices. Because of the crudity of the
assumptions, precise agreement between theory and experiment has not
168 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
been att-aiiu>(l iiur can it l)c expected. Nevertheless, the kind of physical
phenomena occurring with coupled helices are, at least, qualitatively
described here and should permit one to develop and construct various
types of (lexices with fair chance of success.
ACKNOWLEDGEMENTS
As a final note the authors wish to express their appreciation for the
patient work of Mrs. C. A. Lambert in computing the curves, and to
G. E. Korb for taking the experimental data.
Appendix i
i. solution of field equations
In this section there is presented the field equations for a transmission
system consisting of two helices aligned with a common axis. The propa-
gation properties and impedance of such a transmission system are dis-
cussed for various ratios of the outer helix radius to the inner helix radius.
This system is capable of propagating two modes and as previously
pointed out one mode is characterized by a longitudinal field midway
between the two helices and the other is characterized by a transverse
field midway between the tw^o helices.
The model which is to be treated and shown in Fig. 2.3 consists of an
inner helix of radius a and pitch angle \pi which is coaxial with the outer
helix of radius 6 and pitch angle \j/2 . The sheath helix model will be
treated, wherein it is assumed that helices consist of infinitely thin sheaths
which allow for ciuTent flow- only in the direction of the pitch angle \p.
The components of the field in the region inside the inner helix, be-
tween the two helices and outside the outer helix can be written as
follows — inside the inner helix
H,, = BrIoM (1)
E., = B^hM (2)
H,, = j - BMyr) (3)
7
Hr, = ^^ BMyr) (4)
7
E,, = -j "^ BMyr) (5)
7
Er, = -^ BJ,(rr) (())
7
COUPLED HELICES 169
and between the two helices
H,, = BMrr) + BJuirr) ' (7)
E., = BJoiyr) + B^oiyr) (8)
H,, = ^~ [B,h(yr) - B^^(yr)] (9)
7
Hr, = -^ [53/1(7/0 - BJuiyr)] (10)
7
E,, = - J ^ [B^hiyr) - BJuiyr)] (11)
7
Er, = -^ [BMyr) - BJv,{yr)\ (12)
7
and outside the outer hehx
H.^ = B,Ko(yr) (13)
E,, = 58/vo(7r) (14)
^.s = -J- BsK,{yr) (15)
7
Hr, = ^^ 5,Ki(7r) (16)
7
^,, = i — BJuiyr) (17)
7
^r« = ^^ 58Ki(7r) (18)
7
With the sheath helix model of current flow only in the direction of wires
we can specify the usual boundary conditions that at the inner and outer
helix radius the tangential electric field must be continuous and per-
pendicular to the wires, whereas the tangential component of magnetic
field parallel to the current flow must be continuous. These can be written
as
E, sin t/' + E^ cos ^ = 0 (19)
' E, , E^ and (H, sin \f/ -f H^ cos \p) be equal on either side of the helix.
By applying these conditions to the two helices the following equations
are obtained for the various coefficients.
170 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
First, we will define a more simple set of parameters. We will denote
Io(ya) by /oi and h{yh) by /02 , etc.
Further let us use the notation introduced by Humphrey, Kite and
James" in his treatment of coaxial helices.
Poi ^ laiKoi P02 = ToiKa2 Rq = I01K02
Pn = InKn P12 = InKu Ri = /iii^i2
and define a common factor (C.F.) by the equation
r(/3oa cot hY p p (/3oa cot ^pif cot i/'z „ r,
\_ (yay {jay cot t^i
+ Ro' — PoiP
(20)
.,]
(21)
With all of this we can now write for the coefficients of equations 1
through 18:
y ju j8oa cot \pi 1 02
U iQoa cot 1^1 7oi/vi2 RiSoa cot i^i)
y M ""to C.F. L
^4 _ _ • / £_ /3oa cot 1^1 /pi/ii r(
B^~ -^ T M 7^ C.F. L" (7a)^
5
5
(7a)'^
(/3oa cot 1^2)^
cot 1A2 p
cot ;^i J
P12 — jPo2
■]
B5
B,
Bt
Ro
C.F.
Ro —
((Soa cot xl/iY cot 1/'
(7a^)
(/3oa cot 1^2)
cot l/'
;«']
(7a)^
12 — -P02
B7 _ • . /£ i3oa cot lAi 1 /oi r
5; ~ "^ y M 7a C.F. K12 L
Bs _ (|8oa cot i/'i)" cot 1/^2 /pi ""
B2 {yay coT^i C.F.Po
P02R1 —
P02R1 -
cot l/'2
cot i/'i
cot l//
cot \l/
2R0
- P12R0
(22)
(23)
(24)
(25)
(26)
(27)
(28)
The last equation necessary for the solution of our field problem is the
transcendental equation for the propagation constant, 7, which can be
COUPLED HELICES
171
written
Ro —
(i8o a cot \J/iY cot ^2 „
(yaY cot 4/1
[
= P02 -
(jSo a cot \p2) D
? Vi -^ 12
Poi -
(/3oa cot ^0"
(yay
_ (29)
11
The solutions of this equation are plotted in Fig. 4.1.
There it is seen that there are two values of 7, one, yt , denoting the
slow mode with transverse fields between helices and the other, yt ,
denoting the fast mode with longitudinal fields midway between the two
helices.
5.0
4.S
4.0
3.5
3.0
ra
2.6
2.0
1.5
1.0
0.5
4 = 1.25
//
/
COT 5^2
COT ^1
0.82
0.90
0.98
^
#■
/t
//
A
na
/
f
A
y
f
/
r
/
I
/
if
<
A
/
-<^^
^
•y
L
--
•=**^
0.5 1.0 1.6
2.0 2.5 3.0
/3o a COT yj
3.5 4.0 4.5 5.0
Fig. 4.1.1 —-The radial propagation constants associated with the transverse
and longitudinal modes on coupled coaxial sheath helices given as a function of
|3oa cot ^i-i for several values of hja = 1.25.
172 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
These equations can now be used to compute the power flow as defined
by
P = }4 Re j E XH'
which can be written in the form
dA
(30)
r^;^(o)T
L ^'p J
fo © ^^-' '''
(31)
where
[F{ya, yb)] =
((
W +
(i8oa cot i/'
{yar
^ /n^)
(In' - /oi/2i)(C.F.)-
- A'02' +
240 (C.F.)'
(i8oa cot 1/^1)'
(t«)'^
/or/n- r
(80a cot ;^iY
'
/Vl2" i^O -
ya
((Soft cot i^i)' cot \p2
(ya)'' cot i/'i
Rx
- ) (/02/22 — /12') 4" (/ii — /01/21)
, /p (/3oa cot 1A1)- cot \i/2 p Wp (^0^ ^'0^' "^2)'' p
(ya)'^ cot i/'i
(7a)^
( - ) i'lInKu + /02/V22 + /22X02) — (2/iiKii + /01K21 + /21/voi)
ot ^2)'^ p T
(32)
2 , (^ofl cot l/'i) J ■>
•'01 i- 7 r;; ^11
(l3oa cot
- I (K02K22 — K12 ) — (K01K21 — Kn)
.a,
+
(/3oa cot i^i)" A^
■ 2 , (/Soa cot i/'2)" J 2 J. 2
(7a)'^
cot 1/^2 p J.
I 02itl — -— r- i 12A0
cot 1^1
[/Vo2A'22 — /V12"]
In (32) we find the power in the transverse mode by using values of
COUPLED HELICES
173
5.0
0.5
2.0 2.5 3.0
/3o a COT y/
5.0
Fig. 4.1.2 — The radial propagation constants associated with the transverse
and longitudinal modes on coupled coaxial sheath helices given as a function of
^ofl cot \}/i when h/a — 1.50.
yt obtained from (29) and similarly the power in the longittidinal mode is
found by using values of yi .
II. FINDING r
When coaxial helices are used in a transverse field amplifier, only the
transverse field mode is of interest and it is important that the helix
parameters be adjusted such that there is no longitudinal field at some
radius, f, where the cylindrical electron beam will be located. This condi-
tion can be expressed by equating Ez to zero at r = f and from (8)
BMyr) + B^,{yf) = 0
(33)
174 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
which can be written with (25) and (26) as
(jSott cot ipiY cot \f/2
K(i2 Ri
[
02 ilO
(7a)- cot \{/i
= /oi
Ri
loM
(/3oa cot \l/2)-
■I 02 — 7 rr, rn
(34)
Koiyf)
This equation together with (29) enables one to evaluate f/a versus j8oa
cot \l/i for various ratios of b/a and cot i^2/cot xpi . The results of these
calculations are shown in Fig. 3.1.
5.0
4.5
4.0
3.5
3.0
7a
2.5
2,0
0.5
Fig. 4.1. .3 — The radial propagation constants associated with the transverse
and longitudinal modes on coupled coaxial sheath helices given as a finiclion of
0oa cot \{/i when b/a = 1.75.
i
COUPLED HELICES
175
5.0
7a
2.0 2.5 3.0
/Oo <3 COT ^,
3.5
4.0
4.5
5.0
Fig. 4.1.4 — The radial propagation constants associated with the transverse
and longitudinal modes on coupled coaxial sheath helices given as a function of
/3oa cot yp\ when 6/a = 2.0.
III. COMPLETE POWER TRANSFER
For coupled heli.x applications we require the coupled helix parame-
ters to be adjusted so that RF power fed into one helix alone will set up
the transverse and longitudinal modes equal in amplitude. For this
condition the power from the outer helix will transfer completely to the
inner helix. The total current density can be written as the sum of the
current in the longitudinal mode and the transverse mode. Thus for the
inner helix we have
-i&li
J a = Jate-'''' + Jate
.-J^<2
(35)
17G THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
7?, 2.5
Fig. 4.1.5 — The radial propagation constants associated with the transverse
and longitudinal modes on coupled coa.xial sheath helices given as a function of
/3oa cot i/-! when hi a = 3.0.
and for the outer helix
For complete power transfer we ask that
•J hi — J hi
when Jo is zero at the input {z = 0)
or
Jbt _ Jbt
J at J at
\
(36) \
(37)
COUPLED HELICES 177
Now J at is equal to the discontinuity in the tangential component of
magnetic field which can be written at r = a
J at = {H,z cos ^i — //^5 sin \pi) — (H,i cos i/'i - H^o sin \f/i)
\^'hich can be written as
Ja( = - (H,i - H,3)a((cot i/'i + tau xj/i) slu \Pi (38)
and similarily at r = h
Jb( = — (H^7 — H,s)b({cot \p2 + tan 4^2) sin i/'2 (39)
Equations (38) and (39) can be combined with (37) to give as the condi-
tion for complete power transfer
At = -At (40)
where
^ = V (yay / ni)
(T J^ _i- r V \( T? (/3oa cot <Ai)'^ cot 1^2 „ \
\ {yo,y cot i/'i /
In (40) At is obtained by substituting jt into (41) and At is obtained by
substituting 7 < into (41).
The value of cot i/'o/cot i/'i necessary to satisfy (40) is plotted in Fig.
2.8.
In addition to cot i/'o/cot i/'i it is necessary to determine the interference
wavelength on the helices and this can be readily evaluated by consider-
ing (36) which can now be written
or
/, = /,,.-«^'+^''-''^> cos ^ilJZ^ , (48)
and
J, = J.ce-'''^'^'^''"' cos M/3i^ (49)
where we have defined
iSfcO = {yta — jta) (50)
This value of /S^ is plotted versus /3oa cot i/'i in Fig. 2.4.
178 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
BIBLIOGRAPHY
1. J. R. Pierce, Traveling Wave Tubes, p. 44, Van Nostrand, 1950.
2. R. Kompfner, Experiments on Coupled Helices, A. E. R. E. Report No.
G/M98, Sept., 1951.
3. R. Kompfner, Coupled Helices, paper presented at I. R. E. Electron Tube
Conference, 1953, Stanford, Cal.
4. G. Wade and N. Rynn, Coupled Helices for Use in Traveling-Wave Tubes,
I.R.E. Trans, on Electron Devices, Vol. ED-2, p. 15, July, 1955.
5. S. E. Miller, Coupled Wave Theory and Waveguide Applications, B.S.T.J.,
33, pp. 677-693, 1954.
6. M. Chodorow and E. L. Chu, The Propagation Properties of Cross-Wound
Twin Helices Suitable for Traveling-Wave Tubes, paper presented at the
Electron Tube Res. Conf., Stanford Univ., June, 1953.
7. G. M. Branch, A New Slow Wave Structure for Traveling-Wave Tubes, paper
presented at the Electron Tube Res. Conf., Stanford Univ., June, 1953.
G. M. Branch, E.xperimental Observation of the Properties of Double Helix
Traveling-Wave Tubes, paper presented at the Electron Tube Res. Conf.,
Univ. of Maine, June, 1954.
8. J. S. Cook, Tapered Velocity Couplers, B.S.T.J. 34, p. 807, 1955.
9. A. G. Fox, Wave Coupling by Warped Normal Modes, B.S.T.J., 34, p. 823,
1955.
10. W. H. Louisell, Analysis of the Single Tapered Mode Coupler, B.S.T.J., 34,
p. 853.
11. B. L. Humphrey's, L. V. Kite, E. G. James, The Phase Velocity of Waves in a
Double Helix, Report No. 9507, Research Lab. of G.E.C., England, Sept.,
1948.
12. L. Stark, A Helical-Line Phase Shifter for Ultra-High Frequencies, Technical
Report No. 59, Lincoln Laboratory, M.LT., Feb., 1954.
13. P. D. Lacy, Helix Coupled Traveling-Wave Tube, Electronics, 27, No. 11,
Nov.. 1954.
Statistical Techniques for Reducing the
Experiment Time in Reliability Studies
By MILTON SOBEL
(Manuscript received September 19, 1955)
Given two or more processes, the units from which fail in accordance with
an exponential or delayed exponential law, the problem is to select the partic-
ular process with the smallest failure rate. It is assumed that there is a com-
mon guarantee period of zero or positive duration during which no failures
occur. This guarantee period may be known or unknown. It is desired to
accomplish the above goal in as short a time as possible without invalidating
certain predetermined probability specifications. Three statistical techniques
are considered for reducing the average experiment time needed to reach a
decision.
1 . One technique is to increase the initial number of units put on test.
This technique will substantially shorten the average experiment time. Its
effect on the probability of a correct selection is generally negligible and in
some cases there is no effect.
2. Another technique is to replace each failure immediately by a new
unit from the same process. This replacement technique adds to the book-
keeping of the test, but if any of the population variances is large (say in
comparison with the guarantee period) then this technique will result in a
substantial saving in the average experiment time.
3. A third technique is to use an appropriate sequential procedure. In
many problems the sequential procedure results in a smaller average experi-
ment time than the best non-sequential procedure regardless of the true
failure rates. The amount of saving depends principally on the ^'distance'"
between the smallest and second smallest failure rates.
For the special case of two processes, tables are given to show the proba-
bility of a correct selection and the average experiment time for each of three
types of procedures.
Numerical estimates of the relative efficiency of the procedures are given
by computing the ratio of the average experiment time for two procedures of
different type with the same initial sample size and satisfying the same
probability specification.
179
180 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
INTRODUCTION
This paper is concerned with a study of the advantages and disad-
vantages of three statistical techniques for reducing the average dura-
tion of hfe tests. These techniques are:
1. Increasing the initial number of units on test.
2. Using a replacement technique.
3. Using a sequential procedure.
To show the advantages of each of these techniques, we shall consider
the problem of deciding which of two processes has the smaller failure
rate. Three different types of procedures for making this decision will
be considered. They are:
Ri , A nonsequential, nonreplacement type of procedure
E,2 , A nonsequential, replacement type of procedure
Rs , A sequential, replacement type of procedure
Within each type wq will consider different values of n, the initial
number of units on test for each process. The effect of replacement is
shown by comparing the average experiment time for procedures of
type 1 and 2 with the same value of n and comparable probabilities of a
correct selection. The effect of using a sequential rule is shown by com-
paring the average experiment time for procedures of type 2 and 3 with
the same value of n and comparable probabilities of a correct selection.
ASSUMPTIONS
1. It is assumed that failure is clearly defined and that failures are
recognized without any chance of error.
2. The lifetime of individual units from either population is assumed
to follow an exponential density of the form
f{x; e,g) =\ e-^^-")/" iov x -^ g
f(x; e,g) = 0 iorx<g
where the location parameter g ^ 0 represents the common guarantee
period and the scale parameter 6 > 0 represents the unknown parameter
which distinguishes the two different processes. Let Ox ^ do denote the
ordered values of the unknown parameter 6 for the two processes; then
the ordered failure rates are given by
Xi = 1/(01 + {/) ^ Xo = 1/(02 -f g) (2)
3. It is not known which process has the parameter di and which has
the parameter dt .
REDUCING TIME IN RELIABILITY STUDIES 181
4. The parameter g is assumed to be the same for both processes. It
may be known or unknown.
5. The initial number n of units put on test is the same for both pro-
cesses.
6. All units have independent lifetimes, i.e., the test environment is
not such that the failure of one unit results in the failure of other units
on test.
7. Replacements used in the test are assumed to come from the same
population as the units they replace. If the replacement units have to
sit on a shelf before being used then it is assumed that the replacements
are not affected by shelf-aging.
CONCLUSIONS
1. Increasing the initial sample size n has at most a negligible effect
on the probability of a correct selection. It has a substantial effect on the
average experiment time for all three types of procedures. If the value of
n is doubled, then the average time is reduced to a value less than or
equal to half of its original value.
2. The technique of replacement always reduces the average experi-
ment time. This reduction is substantial when ^ = 0 or when the popu-
lation variance of either process is large compared to the value of g.
This decrease in average experiment time must always be weighed against
the disadvantage of an increase in bookkeeping and the necessity of
having the replacement units available for use.
3. The sequential procedure enables the experimenter to make rational
decisions as the evidence builds up without waiting for a predetermined
number of failures. It has a shorter average experiment time than non-
sequential procedures satisfying the same specification. This reduction
brought about by the sequential procedure increases as the ratio a of
the two failure rates increases. In addition the sequential procedure
always terminates with a decision that is clfearly convincing on the basis
of the observed results, i.e., the a posteriori probability of a correct
selection is always large at the termination of the experiment.
SPECIFICATION OF THE TEST
Each of the three types of procedures is set up so as to satisfy the
same specification described below. Let a denote the true value of the
ratio 61/62 which by definition must be greater than, or equal to, one.
It turns out that in each type of procedure the probability of a correct
selection depends on 6i and 62 only through their ratio a.
182 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1950
1. The experimenter is asked to specify the smallest value of a (say
it is a* > I) that is worth detecting. Then the interval (1, a*) represents
a zone of indifference such that if the true ratio a lies therein then we
would still like to make a correct selection, but the loss due to a wrong
selection in this case is negligible.
2. The experimenter is also asked to specify the minimum value P* >
\'2 that he desires for the probability of a correct selection whenever
a ^ a*. In each type of procedure the rules are set up so that the proba-
bility of a correct selection for a = a* is as close to P* as possible without
being less than P*.
The two constants a* > 1 and \2 < P* < 1 are the only quantities
specified by the experimenter. Together they make up the specification
of the test procedure.
EFFICIENCY
If two procedures of different type have the same value of n and satisfy
the same specification then we shall regard them as comparable and
their relative efficiency will be measured by the ratio of their average
experiment times. This ratio is a function of the true a but we shall
consider it only for selected values of a, namely, a = 1, a = a* and
a = CO .
PROCEDURES OF TYPE Ri — • NONSEQUENTIAL, NONREPLACEMENT
"The same number n of units are put on test for each of the two pro-
cesses. Experimentation is continued until either one of the two samples
produces a predetermined number r (r ^ n) of failures. Experimenta-
tion is then stopped and the process with fewer than r failures is chosen
to be the better one."
Table I — Probability of a Correct Selection — Procedure
Type Ri
(a = 2, any g '^ 0, to be used to obtain r for a* = 2)
n
r = 1
r = 2
r = 3
r = i
1
0.667
. — .
2
0.667
0.733
—
—
3
0.667
0.738
0.774
—
4
0.667
0.739
0.784
0.802
10
0.667
0.741
0.78!)
0.825
20
0.667
0.741
0 . 790
0.826
00
0.667
0.741
0.790
0.827
Note: The value for ?• = 0 is obviously 0.500 for any n.
REDUCING TIME IN RELIABILITY STUDIES 183
We shall assume that the number n of units put on test is determined
by non -statistical considerations such as the availability of units, the
availability of sockets, etc. Then the only unspecified number in the
above procedure is the integer r. This can be determined from a table
of probabilities of a correct selection to satisfy any given specification
(a*, P*). If, for example, a* = 2 then we can enter Table I. If n is
given to be 4 and we wish to meet the specification a* = 2, P* = 0.800
then we would enter Table I with n — 4 and select r = 4, it being the
smallest value for which P ^ P*.
The table above shows that for the given specification we would also
have selected r = 4 for any value of n. In fact, we note that the proba-
bility of a correct selection depends only slightly on n. The given value
of n and the selected value of r then determine a particular procedure
of type Ri , say, Ri(n, r).
The average experiment time for each of several procedures R\{n, r)
is given in Table II for the three critical values of the true ratio a,
namely, a = \, a = a* and a = oo . Each of the entries has to be multi-
plied by 6-1 , the smaller of the two d values, and added to the common
guarantee period g. For n = oo the entry should be zero (-\-g) but it
was found convenient to put in place of zero the leading term in the
asymptotic expansion of the expectation in powers of I/71. Hence the
entry for n = 00 can be used for any large n, say, n ^ 25 when r ^ 4.
We note in Table II the undesirable feature that for each procedure
the average experiment time increases with a for fixed 62 . For the se-
quential procedure we shall see later that the average experiment time
is greater at a = a* than at either a = 1 or a = 00 . This is intuitively
more desirable since it means that the procedure spends more time when
the choice is more difficult to make and less time when we are indifferent
or when the choice is easy to make.
PROCEDURES OF TYPE R2 — NONSEQUENTIAL, REPLACEMENT
"Such procedures are carried out exactly as for procedures oiRi except
that failures are immediately replaced by new units from the same
population."
To determine the appropriate value of r for the specification a* = 2,
P* = 0.800 when g = 0 we use the last row of Table I, i.e., the row
marked n = ^ , and select r = 4. The probability of a correct selection
for procedures of type Ro is exactly the same for all values of n and de-
pends only on r. Furthermore, it agrees wdth the probability for pro-
cedures of type Ri with n = co so that it is not necessary to prepare a
separate table.
PL,
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184
REDUCING TIME IN RELIABILITY STUDIES
185
Table III — Value of r Required to Meet the Specification
(a*, P*) FOR Procedures of Type R2 (g = 0)
a*
p*
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
0
1.45
0
1.50
2.00
2.50
0
3.00
0.50
0
0
0
0
0
0
0
0
0
0
0.55
14
4
2
2
1
1
1
1
1
1
1
1
1
0.60
55
15
7
5
3
3
2
2
2
1
1
1
1
0.65
126
33
16
10
7
5
4
3
3
3
1
1
1
0.70
232
61
29
17
12
9
7
6
5
4
2
1
1
0.75
383
101
47
28
19
14
11
9
7
6
3
2
1
0.80
596
157
73
43
29
21
17
13
11
9
4
2
2
0.85
903
238
111
65
44
32
25
20
16
14
5
3
3
0.90
1381
363
169
100
67
49
37
30
25
21
8
5
4
0.95
2274
597
278
164
110
80
61
49
40
34
12
7
5
0.99
4549
1193
556
327
219
160
122
98
80
68
24
14
10
It i.s also unnecessary to prepare a separate table for the average ex-
periment time for procedures of type R2 since for g = 0 the exact values
can be obtained by substituting the appropriate value of n in the ex-
pressions appearing in Table II in the row marked n = oo . For example,
for /( = 2, /• = 1 and a = 1 the exact value for ^ = 0 is 0.500 62/2 =
0.250 62 , and for n = 3, r = 4, a = 00 the exact value for g = 0 is
4.000 62/3 = 1.333 62 . It should be noted that for procedures of type R2
we need not restrict our attention to the cases r ^ n but can also con-
sider r > //.
Table III shows the value of r recjuired to meet the specilication
(a*, F*) with a procedure of type R2 for various selected values of a*
and P*.
procedures of type R3 — sequential, replacement
Let D{t) denote the absolute difference between the number of fail-
ures produced by the two processes at any time t. The sequential pro-
cedure is as follows:
"Stop the test as soon as the inequality
Dit) ^
In [P*/{1 - P*)]
In
a
(3)
is satisfied. Then select the population with the smaller number of fail-
ures as the better one."
To get the best results we will choose (a*, P*) so that the right hand
member of the inequality (3) is an integer. Otherwise we would be operat-
ing with a higher value of P* (or a smaller value of a*) than was specified.
186
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
Table IV — Average Experiment Time and Probability of a
Correct Selection — Procedure Type R3
(a* = 2, P* = 0.800, ^ = 0)
(Multiply each average time entry by d^)
n
a = 1
a = 2
a = 00
1
2.000
2.400
2.000
2
1.000
1.200
1.000
3
0.667
0.800
0.667
4
0.500
0.600
0.500
10
0.200
0.240
0.200
20
0.100
0.120
0.100
oc
2.000/w
2.400/n
2.000/n
Probability
0.500
0.800
1.000
For example, we might choose a* = 2 and P* = 0.800. For procedures
of type R3 the probability of a correct selection is again completely in-
dependent of n; here it depends only on the true value of the ratio a.
The average experiment time depends strongly on n and only to a limited
extent on the true value of the ratio a. Table IV gives these quantities
for a = 1, a = 2, and a = 00 for the particular specification a* = 2,
p* = 0.800 and for the particular value ^ = 0.
efficiency
We are now in a position to compare the efficiency of two different
types of procedures using the same value of n. The efficiency of Ri rela-
tive to R2 is the reciprocal of the ratio of their average experiment time.
This is given in Table V for a* = 2, P* = 0.800, r = 4 and n = 4, 10, 20
and 00 . By Table I the value P* = 0.800 is not attained for n < 4.
In comparing the sequential and the nonsequential procedures it was
found that the slight excesses in the last column of Table I over 0.800
Table V — Efficiency of Type Ri Relative to
Type R2
{a* = 2, P* = 0.800, r = 4:,g = 0)
{
n
a = 1
a = 2
a = 00
4
10
20
00
0.501
0.837
0.925
1.000
0.495
0.836
0.917
1.000
0.480
0.835
0.922
1.000
I
REDUCING TIME IN RELIABILITY STUDIES
187
Table VI
— Efficiency of
(«* = 2, P*
Adjusted Ri Relative To R^
= 0.800, ^ = 0)
n
a = 1
a = 2
a = 00
4
10
20
00
0.615
0.754
0.818
0.873
0.575
0.708
0.768
0.822
0.419
0.528
0.573
0.612
had an effect on the efficiency. To make the procedures more comparable
the values for r = 3 and r = 4 in Table I were averaged with values p
and 1 — p computed so as to give a probability of exactly 0.800 at a = a*.
The corresponding values for the average experiment time were then
averaged with the same values p and 1 — p. The nonsequential pro-
cedures so altered will be called "adjusted procedures." The efficiency
of the adjusted Ri relative to Rz is given in Table VI.
In Table VI the last row gives the efficiency of the adjusted procedure
7^2 relative to Rz . Thus we can separate out the advantage due to
the replacement feature and the advantage due to the sequential fea-
ture. Table VII gives these results in terms of percentage reduction of
average experiment time.
We note that the reduction due to the replacement feature alone is
greatest for small n and essentially constant with a while the reduction
Table VII — Per Cent Reduction in Average Experiment Time
DUE TO Statistical Techniques
(a* = 2,P* = 0.800, ^ = 0)
a
K
Reduction due to
Replacement
Feature Alone
Reduction due to
Sequential
Feature Alone
Reduction
due to both
Replacement
and Sequential
Features
1
4
10
20
00
29.5
13.7
6.3
0.0
12.7
12.7
12.7
12.7
38.5
24.6
18.2
12.7
2
4
10
20
00
30.1
13.9
6.6
0.0
17.8
17.8
17.8
17.8
42.5
29.2
23.2
17.8
cc
4
10
20
00
31.5
13.6
6.3
0.0
38.8
38.8
38.8
38.8
58.1
47.2
42.7
38.8
188 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
due to the sequential feature alone is greatest for large a and is inde-
pendent of n. Hence if the initial sample size per process n is large we
can disregard the replacement techniciue. On the other hand the true
value of a is not known and hence the advantage of sequential experi-
mentation should not be disregarded.
The formulas used to compute the accompanying tables are given in
Addendum 2.
ACKNOWLEDGEMENT
The author wishes to thank Miss Marilyn J. Huyett for considerable
help in computing the tables in this paper. Thanks are also due to
J. W. Tukey and other staff members for constructive criticism and
numerical errors they have pointed out.
Addendum 1
In this addendum we shall consider the more general problem of select-
ing the best of k exponential populations treated on a higher mathemati-
cal level. For k = 2 this reduces to the problem discussed above.
DEFINITIONS AND ASSUMPTIONS
There are given k populations H, (^ = 1, 2, • • • , k) such that the life-
times of units taken from any of these populations are independent
chance variables with the exponential density (1) with a common (known
or unknown) location parameter g ^ 0. The distributions for the k popu-
lations are identical except for the unknown scale parameter 6 > 0 which
may be different for the k different populations. We shall consider three
different cases with regard to g.
Case 1 : The parameter g has the value zero (g = 0).
Case 2: The parameter g has a positive, known value (g > 0).
Case 3: The parameter g is unknown (g ^ 0).
Let the ordered values of the k scale parameters be denoted by
di^ e.-^ ■■■ ^ dk (4)
where equal values may be regarded as ordered in any arbitrary manner.
At any time / each population has a certain number of failures associated
with it. Let the ordered values of these integers be denoted by ri = ri{t)
so that
I
ri g r2 ^ • • • ^ r-fc (5) ^
i
REDUCING TIME IN RELIABILITY STUDIES 189
For each unit the life beyond its guarantee period will be referred to
as its Poisson life. Let Li{t) denote the total amount of Poisson life
observed up to time t in the population with Vi failures (z = 1, 2, • • • , fc).
If two or more of the r^ are equal, say Vi = rj+i = • • • = r^+y , then we
shall assign r, and L; to the population with the largest Poisson life,
ri+i and L^+i to the population with the next largest, • • • , ri+_, and Lj+,-
to the population with the smallest Poisson life. If there are two or more
equal pairs (ri , Li) then these should be ordered by a random device
giving equal probability to each ordering. Then the subscripts in (5) as
well as those in (4) are in one-to-one correspondence with the k given
populations. It should be noted that Li(t) ^ 0 for all i and any time
t ^ 0. The complete set of quantities Li{t) {i = 1, 2, • • • , k) need not
be ordered. Let a = 61/62 so that, since the 6i are ordered, a ^ 1.
We shall further assume that :
1 . The initial number n of units put on test is the same and the start-
ing time is the same for each of the k populations.
2. Each replacement is assumed to be a new unit from the same popu-
lation as the failure that it replaces.
3. Failures are assumed to be clearly recognizable without any chance
of error.
SPECIFICATIONS FOR CASE 1 : gf = 0
Before experimentation starts the experimenter is asked to specify two
constants a* and P* such that a* > 1 and l'^ < P* < 1. The procedure
Ri = Rsin), which is defined in terms of the specified a* and P*, has
the property that it will correctly select the population with the largest
scale parameter with probability at least P* whenever a ^ a*. The initial
number n of units put on test may either be fixed by nonstatistical con-
siderations or may be determined by placing some restriction on the
average experiment time function.
Rule Rs :
"Continue experimentation with replacement until the inequality
k
^ ^*-(^.-a) ^ (1 _ p*)/p* (6)
i=2
is satisfied. Then stop and select the population with the smallest num-
ber of failures as the one having the largest scale parameter."
190
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
Remarks
1. Since P* > Y2 then (1 — P*)/P* < 1 and hence no two popula-
tions can have the same vahie ri at stopping time.
2. For A: = 2 the inequality (6) reduces to the inequalitj^ (3).
3. The procedure 7^3 terminates onl}^ at a failure time, never between
failures, since the left member of (G) depends on t only through the
quantities 7-i{t).
4. After experimentation is completed one can make, at the lOOP per
cent confidence level, the confidence statement
ds ^ di S a* 9, (or di/a""
^ ds S e,)
(7)
where 6s is the scale parameter of the selected population.
Numerical Illustrations
»l/4
Suppose the preassigned constants are P* = 0.95 and a* = 19'
2.088 so that (1 - P*)/P* = ^9- Then for A; = 2 the procedure is to
stop when r-i — ri ^ 4. For A; = 3 it is easy to check that the procedure
reduces to the simple form: "Stop when ?'2 — ri ^ 5". For A; > 3 either
calculations can be carried out as experimentation progresses or a table
of stopping values can be constructed before experimentation starts.
For A: = 4 and A; = 5 see Table VIII.
In the above form the proposed rule is to stop Avhen, for at least one
Table VIII — Sequential Rule for P* = 0.95, a* = 19
A: = 4 fc = 5
1/4
r2 — ri
rs — ri
n — ri
5
5
9
5
6
6
6
6
6
ri — ri
ra — ri
n — ci
Ti — n
5
5
9
10
5
5
10
10
5
6
6
8
5
6
7
7
5
7
7
7
6
6
6
6
* Starred rows can be omitted without affecting the test since every integer in
these rows is at least as great as the corresponding integer in the previous row.
They are shown here to ilhistrate a systematic method which insures that all the
necessary rows are included.
REDUCING TIME IN RELIABILITY STUDIES 191
row (say row j) in the table, the observed row vector (r^ — Vi ,
Ts — Ti , ■ ■ ■ , Vk — z'l) is such that each comyonent is at least as large as
the corresponding component of row j.
Properties of Rs for k = 2 and g = 0
For A- = 2 and ^ = 0 the procedure Rs is an example of a Sequential
Probability Ratio test as defined by A. Wald in his book.^ The Average
Sample Number (ASN) function and the Operating Characteristics (OC)
function for Rs can be obtained from the general formulae given by
Wald. Both of these functions depend on di and 0-2 only through their
ratio a. In our problem there is no excess over the boundary and hence
Wald's approximation formulas are exact. When our problem is put into
the Wald framework, the symmetry of our problem implies equal proba-
bilities of type 1 and type 2 errors. The OC function takes on comple-
mentary values for any point a = 61/62 and its reciprocal 62/61 . We shall
therefore compute it only for a ^ 1 and denote it by P{a). For a > 1
the quantity P(a) denotes the probability of a correct selection for the
true ratio a.
The equation determining Wald's h function is
1 + a 1 + a
for which the non-zero solution in h is easily computed to be
h{a) = }^ (9)
In
a
Hence we obtain from Wald's formula (3:43) in Reference 5
s
a
Pia) = -^^ (10)
where s is the smallest integer greater than or equal to
S = In [PV(1 - P*)]/ln a* (11)
In particular, for a = 1"^, a* and 00 we have
Pi^^) = 1/2, ^(«*) ^ P*, P(^) = 1 (12)
^\'e have written P(l"^) above for lim P{x) as x -^ 1 from the right. The
procedure becomes more efficient if we choose P and a* so that *S' is an
integer. Then s ^ S and P(a*) = P*.
Letting F denote the total number of observed failures required to
192 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
terminate the experiment we obtain for the ASN function
and, in particular, for a = 1, oo
E(F; 1) = s- and E{F; oo) = s (14)
It is interesting to note that for s = 1 we obtain
E{F; a) = 1 for all a ^ 1 (15)
and that this result is exact since for s = 1 the right-hand member S \
of (3) is at most one and hence the procedure terminates with certainty '
immediately after the first failure. '
As a result of the exponential assumption, the assumption of replace- ;
ment and the assumption that ^ = 0 it follows that the intervals between \
failures are independently and identically distributed. For a single popu- '
lation the time interval between failures is an exponential chance vari- ;
able. Hence, for two populations, the time interval is the minimum of j
two exponentials which is again exponential. Letting r denote the i
(chance) duration of a typical interval and letting T denote the (chance) j
total time needed to terminate the procedure, Ave have
E{T; a, 62) = E{F; a)E(r; a, d^) = E{F; a) (^^^ (f^) (16)
I
Hence Ave obtain from (13) and (14)
E{T; a, 02) = - -^ ^^^ for a > 1 (17)
n a — 1 a* + 1
E{T; 1, d,) = ^ and E{T; <^, 0,) = ^ (18>
For the numerical illustration treated above Avith k = 2 we have
na) = ^-^ (19) :
P(l+) = ^; P(2.088) = 0.95; P(oo) = 1 (20)
EiF-a) = 4^^4^ = 4^--+ Vy + '^ (21)
a— la*-f-l a*-t-l
E{F; 1) = 16.0; /iXF; 2.088) = 10.2; E{F; 00) = 4 (22),
REDUCING TIME IN RELIABILITY STUDIES 193
E(T; 1, ^2) = — ; E{T; 2.088, 6^ = — ;
n n (23)
n
For /.• > 2 the proposed procedure is an application of a general se-
quential rule for selecting the best of A- populations which is treated in
[1]. Proof that the probability specification is met and bounds on the
probability of a correct decision can be found there.
CASE 2: COMMON KNOWN ^ > 0
In order to obtain the properties of the sec^uential procedure R:>. for
this case it will be convenient to consider other sequential procedures.
Let (S = 1/6-2 — 1/^1 so that, since the di are ordered, jS ^ 0. Let us
assume that the experimenter can specify three constants a*, /3* and
P* such that a* > 1, /3* > 0 and ^ 2 < -P* < 1 ai^d a procedure is de-
sired which will select the population with the largest scale parameter
with probability at least P* whenever we have both
a ^ a* and i3 ^ /3*
The following procedure meets this specification.
Rule Rs':
"Continue experimentation with replacement until the inec^uality
fi «*-(^i-'-i>e-^*(^i-^i)^ (l_p*)/p* (24)
1=2
is satisfied. Then stop and select the population with the smallest nimiber
of failures as the one having the largest scale parameter. If, at stopping
time, two or more populations have the same value ri then select that
particular one of these with the largest Poisson life Li ."
Remarks
1 . For k = 2 the inequality reduces to
(r, - n) In a* + (Li - L2) 13* ^ In [P*/a - P*)] (25)
If <7 = 0 then Li = Li for all t and the procedure R/ reduces to R3 .
2. The procedure R/ may terminate not only at failures but also be-
tween failures.
194 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
3. The same inequality (24) can also be used if experimentation is
carried on without replacement, one advantage of the latter being that
there is less bookkeeping involved. In this case there is a possibility
that the units will all fail before the inequality is satisfied so that the
procedure is not yet completely defined for this case. One possibility
in such a situation is to continue experimentation with new units from
each population until the inequality is satisfied. Such a procedure will
terminate in a finite time with probability one, i.e., Prob{ T > To} -^0
as To — > 00, and the probability specification will be satisfied.
4. A procedure R3 (ni , n-z , ■ • • , rik , ti , t2 , • • • , tk) using the same
inequality (24) but based on dilTerent initial sample sizes and/or on
different starting times for the initial samples also satisfies the above
probability specification. In the case of different starting times it is
required that the experimenter wait at least g units of time after the last
initial sample is put on test before reaching any decision.
0. One disadvantage of R3 is that there is some (however remote)
possibility of terminating while ri = r2 . This can be avoided by adding
the condition r^ > n to (24) but, of course, the average experiment time
is increased. Another way of avoiding this is to use the procedure R3
which depends only on the number of failures; the effect of using R3
when g > 0 will be considered below.
6. The terms of the sum in (24) represent likelihood ratios. If at any
time each term is less than unity then we shall regard the decision to
select the population with n failures and Li units of Poisson life as opti-
mal. Since (1 — P*)/P* < 1 then each term must be less than unity at
termination.
Properties of Procedure Rz for k = 2 p
The OC and ASN functions for Rs will be approximated by comparing
R3' with another procedure R/ defined below. We shall assume that P*
is close to unity and that g is small enough (compared to d^) so that the
probability of obtaining two failures within g imits of time is small
enough to be negligible. Then we can write approximately at termination
Li^nT - r,g {i = 1, 2, • • • , A:) (26)
and
Li - Li ^ (r, - r,)g (i = 2, 3, • • • , A:) (27)
Substituting this in (24) and letting
5* = a* c^*" (28)
suggests a new rule, say R/' , which we now define.
REDUCING TIME IN RELIABILITY STUDIES 195
h'ule R/
"Continue experimentation with replacement until the inequality
k
X 6*-(^i-'-i) ^ (1 - P*)/P* (29)
is satisfied. Then stop and select the population with n failures as the
one with the largest scale parameter."
For rule Rz" the experimenter need only specify P* and the smallest
value 5* of the single parameter
8 = ^' e''''"''-''"''' = ae'^ (30)
62
that he desires to detect with probability at least P*.
We shall approximate the OC and ASX function of R/' for k = 2
by computing them under the assumption that (27) holds at termina-
tion. The results will be considered as an approximation for the OC and
ASN functions respectively of R/ for /,■ = 2. The similarity of (29)
and (6) immediately suggests that we might replace a* by 5* and a by
5 in the formulae for (6). To use the resulting expressions for R^ we
would compute 5* as a function of a* and /3* by (28) and 5 as a function
of a and /3 by (30).
The similarity of (29) and (6) shows that Z„ (defined in Reference 5,
page 170) under (27) with gr > 0 is the same function of 5* and 5 as it
is of a* and a when g = 0. To complete the justification of the above
result it is sufficient to show that the individual increment ^ of Z„ is the
same function of 5* and 8 under (27) with ^ > 0 as it is of a* and a
when ^ = 0. To keep the increments independent it is necessary to as-
sociate each failure with the Poisson life that follows rather than with
the Poisson life that precedes the failure. Neglecting the probability
that any two failures occur ^^•ithin g units of time we have two values for
z, namely
^ -(.nt-g)/ei -ntl$2
z = log^^^ = -log 5 (31)
and, interchanging 61 and ^2 , gives z — log 5. Moreover
196 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
r r - e-(— «)/«v"^^^^ dx dy
Jg Jg 6-1
Prob \z = -logSj
^2 -0[92(n-l)+9l"l/9lfl2 _i_ ^1 -H9in+Bi(n-l)]l9ie2,)
- e + - e /o9\
1 + 5
Thus the OC and ASN functions under (27) with g > 0 bear the same
relation to 5* and 5 as they do to a* and a when ^ = 0. Hence, letting
w denote the smallest integer greater than or equal to
^ In [P*/(l - P*)] ^ \n[P*/{l-P*)]
In 8* gl3* + In a* ^' '
we can write (omitting P* in the rule description) |
7^15; /?/ («*, /5*){ ^ P{5; /^.^"(S*)! ^ ^-^^^ (34)
<w. I ■ — - tor 5 > 1 {So)
^ \8 - l/\5"' +1/
w~ for 5=1
W'e can approximate the average time between failures by
I
and the average experiment time by «
E{T; /?/(«*, ^*)} ^ E{F; R,'(a*, 0*)\ [^.^ f^'^ _^ ^'^, (37)
n{Oi -T 02 -f- zg)
Since 5 ^ 1 then 5"(1 + 5") is an increasing function of w and by
(33) it is a non-increashig function of 5*. By (28) 5* ^ a* and hence,
if we disregard the approximation (34),
P{8; AV(«*)1 - ^!^{py^/_p.^y..n^* ^ P{S;R/m} (38)
Clearly the rules Ri{a*, P*) and R/ {a*, P*) are equivalent so that
for g > 0 we haA-e
P{8;R-s{a*)} ^ P{8;R/ia*)] (39)
REDUCING TIME IN RELIABILITY STUDIES 197
and hence, in particular, letting 8 = 8* in (38) we have
P{8*;R,(a*)} ^ P{8*;R,"(8*)] ^ P* (40)
since the right member of (34) reduces to P* when W is an integer and
5 = 5*. The error in the approximations above can be disregarded when
g is small compared to 02 . Thus we have shown that for small values of
g/d2 the probability specification based on (a*, ^*, P*) is satisfied in the
sense of (40) if we use the procedure Rsia*, P*), i.e., if we proceed as if
It would be desirable to show that w^e can proceed as if g = 0 for all
values of g and P*. It can be shown that for swfficiently large n the rule
Ri{a*, P*) meets it specification for all g. One effect of increasing n
is to decrease the average time E{t) between failures and to approach
the corresponding problem without replaceme^it since g/E{T) becomes
large. Hence we need only show that Ri{a*, P*) meets its specification
for the corresponding problem without replacement. If we disregard the
information furnished by Poisson life and rely solely on the counting of
failures then the problem reduces to testing in a single binomial whether
6 = di for population IIi and 6 = do for population 112 or vice versa. Let-
ting p denote the probability that the next failure arises from 111 then
we have formally
tia'-V = -. — ; — versus Hi-.p =
1 + a ^ 1 + a
For preassigned constants a* > I and P* (V2 < P* < 1) the appropri-
ate sequential likelihood test to meet the specification:
"Probability of a Correct Selection ^ P* whenever a ^ a*" (41)
then turns out to be precisely the procedure Rsia*, P*). Hence we may
proceed as if gr = 0 when n is sufficiently large.
The specifications of the problem may be given in a different form.
Suppose 01* > 02* are specified and it is desired to haxe a probability of a
correct selection of at least P* whenever ^1 ^ 0i* > 02* ^ 02 . Then we
can form the following sequential likelihood procedure R3* which is
more efficient than Rsia*, P*).
Rule /?3*.-
"Continue experimentation without replacement until a time t is
reached at which the inequality
198 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
is satisfied. Then stop and select the population with ri failures as the
population with d = di".
It can be easily shown that the greatest lower bound of the bracketed
quantity in (42) is 0i*/^2*. Hence for di*/d2* = a* and P* > i 2 the time
required by Rz*{6i*, 62*, P*) ivill always be less than the time required
by R,(a*,P*).
Another type of problem is one in which we are given that 6 = di*
for one population and d = 62* for the A; — 1 others where 6]* > 62* are
specified. The problem is to select the population with 6 = di*. Then
(42) can again be used. In this case the parameter space is discrete with
k points only one of which is correct. If Rule R3* is used then the
probability of selecting the correct point is at least P*.
Equilibrium Approach When Failures Are Replaced
9
Consider first the case in which all items on test are from the same
exponential population with parameters (6, g). Let Tnj denote the length
of the time interval between the j^^ and the j + 1^* failures, (j = 0,
1, • • • ), where n is the number of items on test and the 0*'' failure de-
notes the starting time. As time increases to infinity the expected number
of failures per unit time clearly approaches n/(0 + g) which is called the
equilibrium failure rate. The inverse of this is the expected time between
failures at equilibrium, say E{Tn^). The question as to how the quanti-
ties E{Tnj) approach E(Tn^) is of considerable interest in its own right.
The following results hold for any fixed integer 71 ^ 1 unless explicitly
stated otherwise. It is easy to see that
^^(^i) ^ E{TnJ ^ E(T„o) (43)
since the exact values are respectively
e /, e-^-^'^/^X ^ g+d ^ , d
<
^ 9+ - (44)
n — 1 \ n / n n
In fact, since all units are new at starting time and since at the time of
the first failure all units (except the replacement) have passed their
guarantee period with probability one then
^(^i) ^ E(Tnj) S E{Tn,) (j ^ 0) (45)
If we compare the case g > 0 with the special case g = 0 we obtain
E{2\j) ^ - (y= 1,2, •••) (46)
n
REDUCING TIME IN RELIABILITY STUDIES 199
and if we compare it with the non-replacement case {g/Q is large) we
obtain
^(n,) ^ -^. (i = 1, 2, • . • , n - 1). (47)
These comparisons show that the difference in (46) is small when g/0 is
small and for j < n the difference in (47) is small when g/d is large.
It is possible to compute E{Tnj) exactly for g ^ 0 but the computa-
tion is extremely tedious for j ^ 2. The results for j = 1 and 0 are given
in (44). Fori = 2
E(Tn2) =
n
(n + 2)(/i - 1) -(n-2)gie
1 - ' ' ': -e
n
+ Vl^iI g-(«-i)p/^ ri-2_ -un-i),ie I {n>2)
n — \ v?{n — 1)
and
2{n-l)glB
(48)
E{T,.^ = ^ - ^ [1 - ^e-'" + e-'"'\ (49)
For the case of two populations with a common guarantee period g
we can write similar inequalities. We shall use different symbols a, h for
the initial sample size from the populations with scale parameters Oi , O2
respectively even though our principal interest is in the case a = b = n
say. Let Ta,b.j denote the interval between the j^^ and j -f P* fail-
ures in this case and let X, = l/di (i = 1,2). We then have for all values
of a and b
[aXi + b\o]-' ^ E(TaXj) ^ E(Taxo)
= g + [aXi + b\,]-' (j = 0,1,2, ■■■, ^) (50)
J?(T ^ (gl + g){e2 + g) .riN
a{92 -h 9) + b{di + g)
The result for E(Ta,b.i) corresponding to that in (43) does not hold if
the ratio di/62 is too large; in particular it can be shown that
-0[(a-l)Xi+6X2l-l
E{T.,b..) = ^ "^^ ^' ^
aXi + 6X2/ \(a — l)Xi 4- 6X2
_ Xie
aXi + 6X2
+ / ^X2 Y 1 \r x^e-''^'^^''-''''-'-
(52)
,aXi -\- bX2/\aXi + (& — 1)^2 L 0X1 + ^^2
is larger than E{Ta,h.J for a = 6 = 1 when ^/^i = 0.01 and g/di = 0.10
200 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
SO that QilQi = 10. The expression (52) reduces to that in (44) if we set
di = 02 = 6 and replace a and h by n/2 in the resulting expression.
Corresponding exact expressions for E(Ta.b,j) for j > 1 are extremely
tedious to derive and unwieldy although the integrations involved are
elementary. If we let g —^ oo then we obtain expressions for the non-
replacement case which are relatively simple. They are best expressed
as a recursion formula.
E(.Ta,bj) = — , ,. ETa-\,b,}-l
+ m^ ^"— ^^ = '^
(53)
EiT.,b.d = "^^ ^
aXi + 6X2 (a — l)Xi + 6X2
I 0X2 1 ( h > ^^
"^ aXi + 6X2 aXi + (6 - 1)X2 ' =
(54)
E(Tafij) ^ g + di/a fori ^ a and j = 0 (55)
E{Ta,oJ = dr/(a -j) for 1 ^ i ^ a - 1 (56)
Results similar to (55) and (56) hold for the case a = 0. The above
results for gr = 00 provide useful approximations for E{Ta,b,j) when g
is large. Upper bounds are given by M
E{Ta,bj) ^ [aXi + (6 - i)X2r (i = 1, 2, • • • , h) (57)
E(Ta.bj+b) ^ [(a - j)Xr' (i = 1, 2, • . • , a - 1). (58)
Duration of the Experiment
For the sequential rule R^' with k = 2 we can now write down approxi-
mations as well as upper and lower bounds to the expected duration
E{T) of the experiment. From (50)
I
g + ..5^;^.\ s E(T) = E /?(r.,,)
c-l
n(Xi -f X2) ^ '''^ ' ~ § '^^^ "'"'^^ (59)
+ \FA¥; 5) - c]i!;(T„,„,.)
where c is the largest integer less than or equal to E{F\ 5). The right ex-
pression of (59) can be approximated by (53) and (54) if g is large. If
c < 2n then the upper bounds are given by (57) and (58). A simpler
j
REDUCING TIME IN RELIABILITY STUDIES 201
upper bound, which holds for all \'aliies of c is given by
E{T) ^ E{F- b)E{Tn,n..) = E{F; 8) (g + ^^ (60)
CASE 3: COMMON UNKNOWN LOCATION PARAMETER ^ ^ 0
In this case the more conservative procedure is to proceed under the
assumption that </ = 0. By the discussion above the probability require-
ment will in most problems be satisfied for all ^ ^ 0. The OC and ASN
functions, which are now functions of the true value of g, were already
obtained above. Of course, we need not consider values of g greater than
the smallest observed lifetime of all units tested to failure.
Addendum 2
For completeness it would be appropriate to state explicitly some of
the formulas used in computing the tables in the early part of the paper.
For the nonsequential, nonreplacement rule Ri with /c = 2 the proba-
bility of a correct selection is
P(a; R,) = [ [ Mu, OAfrix, 6,) dy dx (61)
where
fXx, e) = '- C(l - e^'"y-' e-^^"-^+^"^ (r ^ n) (62)
and C" is the usual combinatorial symbol. This can also be expressed in
the form
P{a; R,) = 1 - (rC:r Z ^~^^"'
;=i n - r -\-j (63)
C'-l{B[r, n-r+l+a(n-r+ j)]}-'
where B[x, y] is the complete Beta function. Eciuation (66) holds for
any g ^ 0.
For the rule Ri the expected duration of the experiment for k = 2
is given by
E{T) = r x{fr(x, d,)[l - Frix, 62)] + frix, d,)[l - Fr(x, ^i)] } dx (64)
•'0
where frix, 6) is the density in (62) and Fr{x, B) is its c.d.f. This can
202 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
also be expressed in the form
^iKC^ZZt (-1) c.-. c, .
plus another similar expression in which 6i , a are replaced by 62 , a~^
respectively. For ^ > 0 we need only add g to this result. This result
was used to compute E(T) in table lA f or a = 1 and a = 2. For a = oo
the expression simplifies to
E{T) = e^rC: ± erl ^~^^'^\ (66)
which can be shoAvn to be equivalent to
E{T) = e,f: ^— (67)
REFERENCES
1. Bechhofer, R. E., Kiefer, J. and Sobel, M., On a Type of Sequential Multiple
Decision Procedures for Certain Ranking and Identification Problems with
k Populations. To be published.
2. Birnbaum, A., Statistical methods for Poisson processes and exponential
populations, J. Am. Stat. Assoc, 49, pp. 254-266, 1954.
3. Birnbaum, A., Some procedures for comparing Poisson processes or popula-
tions, Biometrika, 40, pp. 447-49, 1953.
4. Girshick, M. A., Contributions to the theory of sequential analj'sis I, Annals
Math. Stat., 17, pp. 123-43, 1946.
5. Wald, A., Sequential Analysis, John Wiley and Sons, New York, 1947.
I
A Class of Binary Signaling Alphabets
By DAVID SLEPIAN
(Manuscript received September 27, 1955)
A class of binary signaling alphabets called "group alphabets" is de-
scribed. The alphabets are generalizations of Hamming^ s error correcting
codes and possess the following special features: {1) all letters are treated
alike in transmission; {2) the encoding is simple to instrument; (3) maxi-
mum likelihood detection is relatively simple to instrument; and (4) in
certain practical cases there exist no better alphabets. A compilation is given
of group alphabets of length equal to or less than 10 binary digits.
INTRODUCTION
This paper is concerned with a class of signahng alphabets, called
"group alphabets," for use on the symmetric binary channel. The class
in question is sufficiently broad to include the error correcting codes of
Hamming,^ the Reed-Muller codes," and all "systematic codes''.^ On
the other hand, because they constitute a rather small subclass of the
class of all binary alphabets, group alphabets possess many important
special features of practical interest.
In particular, (1) all letters of the alphabets are treated alike under
transmission; (2) the encoding scheme is particularly simple to instru-
ment; (3) the decoder — a maximum likelihood detector — is the best
I possible theoretically and is relatively easy to instrument; and (4) in
certain cases of practical interest the alphabets are the best possible
theoretically.
It has very recently been proved by Peter Elias^ that there exist group
alphabets which signal at a rate arbitarily close to the capacity, C, of
the symmetric binary channel with an arbitrarily small probability of
error. Elias' demonstration is an existence proof in that it does not
show explicitly how to construct a group alphabet signaling at a rate
greater than C — e with a probability of error less than 5 for arbitrary
positive 5 and e. Unfortunately, in this respect and in many others, our
understanding of group alphabets is still fragmentary.
In Part I, group alphabets are defined along with some related con-
203
204 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
cepts necessary for their understanding. The main results obtained up
to the present time are stated without proof. Examples of these concepts
are given and a compilation of the best group alphabets of small size
is presented and explained. This section is intended for the casual reader.
In Part II, proofs of the statements of Part I are given along with
such theory as is needed for these proofs.
The reader is assumed to be familiar with the paper of Hamming,
the basic papers of Shannon* and the most elementary notions of the
theory of finite groups.
Part I — Group Alphabets and Their Properties
1.1 INTRODUCTION
We shall be concerned in all that follows with communication over the
symmetric binary channel shown on Fig. 1. The channel can accept
either of the two symbols 0 or 1 . A transmitted 0 is received as a 0 with
probability q and is received as a 1 w'ith probability p — 1 — g : a trans-
mitted 1 is received as a 1 with probability q and is received as a 0 with
probability p. We assume 0 ^ p ^ ^^. The "noise" on the channel
operates independently on each symbol presented for transmission. The
capacity of this channel is
C = 1 + P log2P + q log29 bits/symbol (1)
By a K-leUer, n-place binary signaling alphabet we shall mean a collec-
tion of K distinct sequences of n binary digits. An individual sequence
of the collection will be referred to as a letter of the alphabet. The integer
K is called the size of the alphabet. A letter is transmitted over the
channel by presenting in order to the channel input the sequence of n
zeros and ones that comprise the letter. A detection scheme or detector for
INPUT X OUTPUT
Fig. 1 — The symmetric binary channel.
A CLASS OF BINARY SIGNALING ALPHABETS
205
a given /v-letter, n-place alphabet is a procedure for producing a sequence
of letters of the alphabet from the channel output.
Throughout this paper we shall assume that signaling is accomplished
with a given /i-letter, n-place alphabet by choosing the letters of the
alphabet for transmission independently with equal probability l/K.
Shannon^ has shown that for sufficiently large n, there exist K-letter,
n-place alphabets and detection schemes that signal over the symmetric
binary chaimel at a rate R > C — e for arbitrary £ > 0 and such that
the probability of error in the letters of the detector output is less than
any 5 > 0. Here C is given by (1) and is shown as a function of p in
Fig. 2. No algorithm is known (other than exhaustvie procedures) for
the construction of A'-letter, /i-place alphabets satisfying the above
inequalities for arbitrary positive 8 and e except in the trivial cases C — 0
and C = 1.
1.2 THE GROUP -S„
There are a totality of 2" different w-place binary sequences. It is fre-
quently convenient to consider these sequences as the vertices of a cube
of unit edge in a Euclidean space of n-dimensions. For example the 5-
place sequence 0, 1, 0, 0, 1 is associated with the point in 5-space whose
o.e
0.6
0.4
0.2
Fig. 2 — The capacity of the symmetric binary channel.
C = 1 + p log2 p + {I - p) log2 (1 - p)
206
THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
coordinates are (0, 1, 0, 0, 1). For convenience of notation we shall gen-
erally omit commas in writing a sequence. The above 5-place sequence
will be written, for example, 01001.
We define the product of two n-ylace hinarij sequences, aicii • • • a„ and
^1^2 • ■ • bn as the n-place binary sequence
fli + hi , a-i ■]- h-i , ■ ■ • , ttn + hn
Here the a's and 6's are zero or one and the + sign means addition
modulo 2. (That is 0 + 0=1 + 1 = 0, 0+1 = 1+0=1)
For example, (01101) (00111) = 01010. With this rule of multiplication
the 2" w-place binary sequences form an Abelian group of order 2".
The elements of the group, denoted by Ti , T'2 , • • • , Tin, say, are the
n-place binary sequences ; the identity element I is the sequence 000 • • • 0
and
IT, = Til = T. ■ T,Tj = TjTr, TiiTjT,) = iTiTj)Tk ;
the product of any number of elements is again an element; every ele-
ment is its own reciprocal, Ti = Tf^, TI = /. We denote this group
by Bn .
All subgroups of Bn are of order 2 where k is an integer from the set
0, 1, 2, • • • , n. There are exactly
N{n, k) =
(2" - 2") (2" - 2') (2" - 2') • • • (2" - 2'-')
(2^ - 2»)(2'^ - 20(2* - 22)
= N(n, n — k)
{2" - 2'-')
(2)
distinct subgroups of Bn of order 2 . Some values of N(n, k) are given in
Table I.
Table I — Some Values of A^(n, k), the Number of Subgroups
OF Bn OF Order 2''. N(n, k) = N{n, n — k)
n\k
0
1
2
3
4
5
2
3
1
3
7
7
1
4
15
35
15
1
5
31
155
155
31
1
6
63
651
1395
651
63
7
127
2667
IISU
11811
2667
8
255
10795
97155
200787
97155
9
511
43435
788035
3309747
3309747
10
1023
174251
6347715
53743987
109221651
000
000
000
000
000
000
000
100
100
100
010
010
001
no
010
001
oil
001
101
no
on
110
101
111
on
111
111
101
A CLASS OF BINARY SIGNALING ALPHABETS 207
1.3 GROUP ALPHABETS
An ?i-place group alphabet is a 7v-letter, n-place binary signaling alpha-
bet whose letters form a subgroup of Bn . Of necessity the size of an
n-place group alphabet is /v = 2 where k is an integer satisfying 0 ^
k ^ n. By an (n, k)-alphahet we shall mean an n-place group alphabet of
size 2^. Example: the N{3, 2) = 7 distinct (3, 2)-alphabets are given by
the seven columns
(i) (ii) (iii) (iv) (v) (vi) (vii)
(3)
1.4 STANDARD ARRAYS
Let the letters of a specific (n, /i:)-alphabet be Ai = / = 00 • • • 0,
Ao , As , • ■ ■ , A^ , where ju = 2 . The group Bn can be developed accord-
ing to this subgroup and its cosets:
/, A2, A3, ■■• ,A^
S2 , S2A2 , S2A3 , • • • , S2A^
Sz , S3A2 , S3A3 , • • • , SsA^
Bn = ; (4)
Sr f SyA2 , SpAz , • ' • , SfAfi
In this array every element of Bn appears once and only once. The col-
lection of elements in any row of this array is called a coset of the (n, k)-
alphabet. Here *S2 is any element of B„ not in the first row of the array,
S3 is any element of Bn not in the first two rows of the array, etc. The
elements S2 , S3 , • • • , Sy appearing under I in such an array will be
called the coset leaders.
If a coset leader is replaced by any element in the coset, the same coset
will result. That is to say the two collections of elements
Si , ^1^2 , SiSz ; ■ • ■ , SiA^
and
SiA,, , (SiAu)A2 , (SiAMs ,■■■ {SiAk)A,
are the same.
208 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 195G
We define the weight Wi = w{Ti) of an element, Ti , of Bn to be the
number of ones in the n-place binary sequence T,- .
Henceforth, unless otherwise stated, we agree in dealing with an ar-
ray such as (4) to adopt the following convention:
the leader of each coset shall be taken to be an . .
element of minimal weight in that coset.
Such a table will be called a standard array.
Example: Bi can be developed according to the (4, 2)-alphabet 0000,
1100, 0011, nil as follows
(6)
0000
1100
0011
nil
1010
Olio
1001
0101
1110
0010
1101
0001
1000
0100
1011
0111
)W"ever,
^^-e should
write.
for exan
0000
1100
0011
nil
1010
0110
1001
0101
0010
1110
0001
1101
1000
0100
1011
0111
(7)
The coset leader of the second coset of (6) can be taken as any element
of that row since all are of weight 2. The leader of the third coset, how-
ever, should be either 0010 or 0001 since these are of weight one. The
leader of the fourth coset should be either 1000 or 0100.
1.5 THE DETECTION SCHEME
Consider now communicating with an (n, fc) -alphabet over the sym-
metric binary channel. When any letter, say A,, of the alphabet is
transmitted, the received sequence can be of any element of B„ . We
agree to use the following detector:
if the received element of Bn lies in column i of the array (4), the
detector prints the letter Ai ,i = 1,2, • • • , ju. The array (4) is to (8)
be constructed according to the convention (5).
The following propositions and theorems can be proved concerning
signaling with an (n, /c)-alphabet and the detection scheme given by (8).
1.6 BEST DETECTOR AND SYMMETRIC SIGNALING
Define the probability /,• = ((Ti) of an element Ti of Bn to be A =
^wi^n-uf ^yYiere p and q are as in (1) and Wi is the weight of Ti . Let
A CLASS OF BINARY SIGNALING ALPHABETS 209
Qi , i = 1 , 2, • • • , jLi be the sum of the probabilities of the elements in
the iih. column of the standard array (4).
Proposition 1. The probability that any transmitted letter of the
(n, A;) -alphabet be produced correctly by the detector is Qi .
Proposition 2. The equivocation^ per symbol is
1 **
Hy{x) = — S Qi log2 Qi
n i=i
Theorem 1 . The detector (8) is a maximum likelihood detector. That
is, for the given alphabet no other detection scheme has a greater average
probability that a transmitted letter be produced correctly by the de-
tector.
Let us return to the geometrical picture of w-place binary sequences
as vertices of a unit cube in n-space. The choice of a i^-letter, n-place
alphabet corresponds to designating K particular vertices as letters.
Since the binary sequence corresponding to any vertex can be produced
by the channel output, any detector must consist of a set of rules that
associates various vertices of the cube with the vertices designated as
letters of the alphabet. We assume that every vertex is associated with
some letter. The vertices of the cube are divided then into disjoint sets,
Wi , Wi , • • • , Wk where Wi is the set of vertices associated with tth
letter of the signaling alphabet. A maximum likelihood detector is char-
acterized by the fact that every vertex in Wi is as close to or closer to
the iih. letter than to any other letter, i = 1,2, • • • , K. For group alpha-
bets and the detector (8), this means that no element in the iih. column
of array (4) is closer to any other A than it is to ^i , z = 1, 2, • • • , ;u.
Theorem 2. Associated with each {n, /(;)-alphabet considered as a point
configuration in Euclidean n-space, there is a group of n X n orthogonal
matrices which is transitive on the letters of the alphabet and which
leaves the unit cube invariant. The maximum likelihood sets 1^1 ,
W2 , • • • Wn are all geometrically similar.
Stated in loose terms, this theorem asserts that in an (n, A;)-alphabet
every letter is treated the same. Every two letters have the same number
of nearest neighbors associated with them, the same number of next
nearest neighbors, etc. The disposition of points in any two W regions
is the same.
1.7 GROUP ALPHABETS AND PARITY CHECKS
Theorem 3. Every group alphabet is a systematic^ code: every syste-
matic code is a group alphabet.
210 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
We prefer to use the word "alphabet" in place of "code" since the
latter has many meanings. In a systematic alphabet, the places in any
letter can be divided into two classes : the information places — A; in
number for an (n, /c)-alphabet — and the check positions. All letters
have the same information places and the same check places. If there
are k information places, these may be occupied by any of the 2 /v-place
binary sequences. The entries in the n — k check positions are fixed
linear (mod 2) combinations of the entries in the information positions.
The rules by which the entries in the check places are determined are
called parity checks. Examples: for the (4, 2)-alphabet of (6), namely
0000, 1100, 0011, nil, positions 2 and 3 can be regarded as the informa-
tion positions. If a letter of the alphabet is the sequence aia^a^ai , then
ai = a2 , tti = az are the parity checks determining the check places 1
and 4. For the (5, 3)-alphabet 00000, 10001, 01011, 00111, 11010, 10110,
01100, 11101 places 1, 2, and 3 (numbered from the left) can be taken
as the information places. If a general letter of the alphabet is aiazazaiai ,
then a4 = a2 -j- as , Ob = ai -j- a2 -|- ^3 .
Two group alphabets are called equivalent if one can be obtained from
the other by a permutation of places. Example: the 7 distinct (3, 2)-
alphabets given in (3) separate into three equivalence classes. Alpha-
bets (i), (ii), and (iv) are equivalent; alphabets (iii), (v), (vi), are equiva-
lent; (vii) is in a class by itself.
Proposition S. Equivalent (n, fc) -alphabets have the same probability
Qi of correct transmission for each letter.
Proposition 4- Every (n, /c) -alphabet is equivalent to an (n, k)-
alphabet whose first k places are information places and whose last n — k
places are determined by parity checks over the first k places.
Henceforth we shall be concerned only with (n. A;) -alphabets w^hose
first k places are information places. The parity check rules can then
be written
k
ai = S Tij-ay , t = /b -j- 1, • • • , n (9)
where the sums are of course mod 2. Here, as before, a typical letter of
the alphabet is the sequence aia^ • ■ - ttn . The jn are k(n — k) quantities,
zero or one, that serve to define the particular (n, A;)-alphabet in question.
1.8 MAXIMUM LIKELIHOOD DETECTION BY PARITY CHECKS
For any element, J\ of Bn we can form the sum given on the right of
(9). This sum maj^ or may not agree with the symbol in the ?'th place of
A CLASS OF BINARY SIGNALING ALPHABETS 211
T. If it does, we say T satisfies the tth-place parity check; otherwise T
fails the zth-place parity check. When a set of parity check rules (9) is
giN'cii, we can associate an (n — /i^-place binary sequence, R{T), with
each element T of 5„. We examine each check place of T in order starting
with the (k -\- 1 )-st place of T. We write a zero if a place of T satisfies
the parity check; we write a one if a place fails the parity check. The re-
sultant sequence of zeros and ones, written from left to right is R(T).
We call R(T) the parity check sequence of T. Example: with the parity
rules 04 = 02 -j- 03 , 05 = Oi -j- 02 -j- c^s used to define the (5, 3)-alphabet
in the examples of Theorem 3, we find i?(11000) = 10 since the sum of
the entries in the second and third places of 11001 is not the entry of
the fourth place and since the sum of Oi = 1, 02 = 1, and 03 = 0 is
0 = 05 .
Theorem 4- Let I, A2 , • • • ^^^ be an {n, /c)-alphabet. Let R{T) be the
parity check sequence of an element T of B„ formed in accordance with
the parity check rules of the (n, /c) -alphabet. Then R(Ti) = R(T2) if
and only if Ti and T2 lie in the same row of array (4). The coset leaders
can be ordered so that R{Si) is the binary symbol for the integer i — 1.
As an example of Theorem 4 consider the (4, 2)-alphabet shown with
its cosets below
0000
1011
0101
1110
0100
nil
0001
1010
0010
1001
0111
1100
1000
0011
1101
0110
The parity check rules for this alphabet are 03 = oi , 04 = Oi -j- ^2 •
Every element of the second row of this array satisfies the parity check
in the third place and fails the parity check in the 4th place. The parity
check sequence for the second row is 01. The parity check for the third
row is 10, and for the fourth row 11. Since every letter of the alphabet
satisfies the parity checks, the parity check sequence for the first row is
00. We therefore make the following association between parity check
sequences and coset leaders
00 -^ 0000 = Si
01 -^ 0100 = S2
10 -^ 0010 = S,
11 -^ 1000 = ^4
1.9 INSTRUMENTING A GROUP ALPHABET
Proposition 4 attests to the ease of the encoding operation involved
212 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
with the use of an (n, fc) -alphabet. If the original message is presented as
a long sequence of zeros and ones, the sequence is broken into blocks of
length k places. Each block is used as the first k places of a letter of
the signaling alphabet. The last n-k places of the letter are determined
by fixed parity checks over the first k places.
Theorem 4 demonstrates the relative ease of instrumenting the maxi-
mum hkelihood detector (8) for use with an (n. A:) -alphabet. When an
element T of Bn is received at the channel output, it is subjected to the
n-k parity checks of the alphabet being used. This results in a parity
check sequence R{T). R(T) serves to identify a unique coset leader, say
Si . The product SiT is then formed and produced as the detector out-
put. The probability that this be the correct letter of the alphabet is Qi .
1.10 BEST GROUP ALPHABETS
Two important questions regarding (n, fc)-alphabets naturally arise.
What is the maximum value of Qi possible for a given n and k and which
of the N(n, k) different subgroups give rise to this maximum Qi? The
answers to these questions for general n and k are not known. For many
special values of n and k the answers are known. They are presented in
Tables II, III and IV, which are explained below.
The probability Qi that a transmitted letter be produced correctly by
the detector is the sum, Qi = ^i f{Si) of the probabilities of the coset
leaders. This sum can be rewritten as Qi = 2Zi=o «« P^Q^~^ where a, is
the number of coset leaders of weight i. One has, of course, ^a, = v =
/ y) \ T? '
2^"'' for an (n, /(;)-alphabet. Also «> ^ ( . ) = -7-7 — '■ — n- ! since this is the
\t / tlin — t)
number of elements of Bn of weight i.
The (Xi have a special physical significance. Due to the noise on the
channel, a transmitted letter, A, , of an (n, /c)-alphabet will in general be
received at the channel output as some element T of Bn different from
Ai .li T differs from Ai in s places, i.e., if w{AiT) = s, we say that an
s-tuple error has occurred. For a given (n, fc)-alphabet, ai is the number
of i-tuple errors which can be corrected by the alphabet in question,
i = 0, 1,2, ■ • • , n.
Table II gives the a{ corresponding to the largest possible value of Qi
for a given k and ?i for k = 2,3, •••w— l,n = 4--- ,10 along with a
few other scattered values of n and k. For reference the binomial coeffi-
cients ( . ) are also listed. For example, we find from Table II that the
best group alphabet with 2 =16 letters that uses n = 10 places has a
A CLASS OF BINARY SIGNALING ALPHABETS 213
1 A Q C 'J ** Q
probability of correct transmission Qi = q + lOg p + 39g p" + l-Ag'p .
The alphabet corrects all 10 possible single errors. It corrects 39 of the
possible f .^ j = 45 double errors (second column of Table II) and in
addition corrects 14 of the 120 possible triple errors. By adding an addi-
tional place to the alphabet one obtains with the best (11, 4)-alphabet
an alphabet with 16 letters that corrects all 11 possible single errors and
all 55 possible double errors as well as 61 triple errors. Such an alphabet
might be useful in a computer representing decimal numbers in binary
form.
For each set of a's listed in Table II, there is in Table III a set of
parity check rules which determines an {n, A)-alphabet having the given
a's. The notation used in Table III is best explained by an example. A
(10, 4)-alphabet which realizes the a's discussed in the preceding para-
graph can be obtained as follows. Places 1, 2, 3, 4 carrj- the information.
Place 5 is determined to make the mod 2 sum of the entries in places
3, 4, and 5 ecjual to zero. Place 6 is determined by a similar parity check
on places 1, 2, 3, and 6; place 7 by a check on places 1, 2, 4, and 7, etc.
It is a surprising fact that for all cases investigated thus far an {n, k)-
alphabet best for a given value of p is uniformly best for all values of
p, 0 ^ p ^ 1 2. It is of course conjectured that this is true for all n and /,-.
It is a further (perhaps) surprising fact that the best {n, fc) -alphabets
are not necessarily those with greatest nearest neighbor distance be-
tween letters when the alphabets are regarded as point configurations on
the n-cube. For example, in the best (7, 3)-alphabet as listed in Table
III, each letter has two nearest neighbors distant 3 edges away. On the
other hand, in the (7, 3)-alphabet given by the parity check rules 413,
512, 623, 7123 each letter has its nearest neighbors 4 edges away. This
latter alphabet does not have as large a value of Qi , however, as does
the (7, 3)-alphabet listed on Table III.
The cases /.; = 0, 1, /? — 1, n have not been listed in Tables II and III.
The cases k = 0 and k = n are completely trivial. For k = 1, all n > 1
the best alphabet is obtained using the parity rule a> = 03= • • • =
a„ = oi . If n = '2j,
If n = 2j + 1, Qi = i: (^') pY-\
For k = n — 1, /; > 1. the maximum Qi is Qi = g"~ and a parity rule
for an alphabet realizing this Qi is o„ = oi .
If the a's of an (/<, A)-alphabet are of the form a, = ( . j , i = 0, 1,
214 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
Table II — Probability of No Error with Best
Alphabets, Qi = 2Z «»P*2"~'
(?)
k = 2
k = 3
k = 4
k = 5
k = 6
k = 7
k = 8
k = 9
* = 10
i
0
ai
(li
a
a,
ai
Oi
fli
ai
a;
n = 4
1
1
1
4
3
0
1
1
1
n = 5
1
2
0
5
10
1
5
2
1
3
1
1
71 = 6
1
2
6
15
6
9
6
1
3
0
1
1
1
1
1
n = 7
1
2
3
7
21
25
7
18
6
7
8
7
3
0
1
1
1
1
1
1
n = 8
1
2
3
8
28
56
8
28
27
8
20
3
8
7
7
3
0
1
1
1
1
1
1
1
1
9
9
9
9
9
7
3
n = 9
2
3
4
36
84
126
36
64
18
33
21
22
6
0
1
1
1
1
1
1
1
1
1
10
10
10
10
10
10
7
3
n = 10
2
3
4
45
120
210
45
110
90
45
64
8
39
14
21
5
0
1
1
1
1
1
1
1
1
1
11
11
11
11
11
11
7
3
n = 11
2
3
4
5
55
165
330
462
55
165
226
54
55
126
63
55
61
20
4
0
1
1
1
1
1
1
1
1
12
12
12
12
12
7
3
n = 12
2
3
4
5
66
220
495
792
66
220
425
300
66
200
233
19
3
A CLASS OF BINARY SIGNALIHG ALPHABETS 215
2, • • • , j, «j+i = f some integer, aj+o = ay+s = • • • = «„ = 0, then
there does not exist a 2 -letter, w-place alphabet of any sort better than
the given (n, A)-alphabet. It will be observed that many of the a's of
Table II are of this form. It can be shown that
Proposition 5 ii n -\- I „ /"t"! q 1^2"^* — 1 there exists
no 2'''-letter, n-place alphabet better than the best (n, /c) -alphabet.
When the inequality of proposition 5 holds the a's are either «o = 1,
""'' - 1, all other « = 0; or ao = 1, «i = (Vj , «2 = 2"~' - 1 -
, all other a = 0; or the trivial ao = 1 all other a = 0 which holds
uhen k = n. The region of the n — k plane for which it is known that
(n, A-)-alphabets cannot be excelled by any other is shown in Table IV.
1.11 A DETAILED EXAMPLE
As an example of the use of {n, A") -alphabets consider the not un-
realistic case of a channel with -p = 0.001, i.e., on the average one binary
digit per thousand is received incorrectly. Suppose we wish to transmit
messages using 32 different letters. If we encode the letters into the 32
5-place binary sequences and transmit these sequences without further
encoding, the probability that a received letter be in error is 1 —
(1 _ pf = 0.00449. If the best (10, 5)-alphabet as shown in Tables II
and III is used, the probability that a letter be wrong is 1 — Qi =
1 - r/" - lOgV - 21gy - 24/)' - 72p' + • • • = 0.000024. Thus
by reducing the signaling rate by ^^, a more than one hundredfold re-
duction in probability of error is accomplished.
A (10, 5)-alphabet to achieve these results is given in Table III. Let
a typical letter of the alphabet be the 10-place sequence of binary digits
aia2 ■ • • agttio . The symbols aia^Ozaia^ carry the information and can be
any of 32 different arrangements of zeros and ones. The remaining places
are determined by
06 = ai -j- a-i -j- a4 -j- ^5
a? = tti -j- oo -f a4 -j- as
as = ai -j- a2 + a.3 + Os
ag = Oi + 02 4- Qi -j- 0,4
Oio = Oi + a-i -j- 03 4- 04 4- «5
To design the detector for this alphabet, it is first necessary to deter-
mine the coset leaders for a standard array (4) formed for this alphabet.
•Jl
t-l
a
pa
<
M
Ph
<
cc
o
H
O
H
ti;
O
H
I— I
-<
Ph
P3
t^ 00
-f ^ cc
CC C^) !M
O t^ X
lO a; t^ oc
00 C2
^ ^ CC
CC (N C^l
t- GC
lO ic lO -r
-f -^ CC CT
CC C^ CM C^I
;C 1^ X c:
^
cc -+
-f -^ cc
-f -^ cc cc
-r -^ cc re cc
(M <N
CC C^ CM
CC CM CM CM
re T-l CM CM CM
ic :c I- y: —
i
re cc
CO
ce
C^l cc
CM cc re
re C^J CM CM
CM re re c^i
CM re re CM
^— .-H
.-H -— C^l
_ ,_ — ,-H
r— ^- T-H (M ,— .
T-^ CM ^ ^ CM -^
'^^ lo
•^ lO «
-* iC <£) t^
•^ lO CO t^ oc
"* >OCD t^OO C5
C^l
ex
re
C^l CM C^l
re-rocot^ ce-^iocot^oc
C^l C^l
' >o
re f lO CO
re T lO CO t^ oC'
iCi
CO
oc
210
1—1 1—1
^CM
1-H 1-H
cO'f -*
CM CM CO
1-1 1-l
T— 1 1-H 1-H
Ot-h
Oi-HCM
1—1 1—1
I-H 1-H 1-H
00
^cot-oo
^^iCiO
134
0 124
1 123
12351
0 123
1 124
2134
Ol ^
01 .—1 1—1
"^ 1-H 1-H 1-H
r^
t- t- t^
coco
CO CO lO
•^iO-*
^^10^-^
CO
"^^00 CO
"''^ CO CO CO
-* 't< jvj
^'*(N^
'^'* CM CM CM
CO(M^
«^^^
COCM^^^
^-^o
-^-^O-H
^'~' 0--HCM
GOO-J T-1
00 01 1-1 1—1
00 02 1-H 1-H 1-H
CO
CO iC
^-t
OCOCO^^
iOiO>Oj^
'^'^'^coco
-^-^^0^
'^'^^cacM
CO!M C^ ^
CO <M CM ^ ^
T— I 1-H T-H _^
1— 1 1 — 1 r— * -^
o
C "—1
t^ 00 o i-H
t^ 00 C5 1— 1 >— 1
iCi
'I*
lOiOiO'*^ j^
•r-^ c^cc ^
CO CM iM O) ^
CO t^ 00 02 ^
•*
^
CO
^co
CO^ ^ -*
CM
'^'cOCM
'f CM (M CO CO
CO ^ "* coco j^
1— H
CO T-H 1— 1 ^H C^l
0
1— 1 CM r-( CM .-< ^
1— 1
10 CO t^ 00 cr.
10 CO t^ 00 0 rH
1-H
CO
coco
CO CO
CM
(N (M
CO CM CM
CI CO CO
r— 1
coco CM
T—l
T~i
o*o*c<i^^^
1— 1 CM CO r- 1 .— 1
CM
0
1— (
CO CO CM 1-1 1—1 1—1
0
1-H
^ CM CO -1 1-H -H ^ ^ ^
^lOfOi^ccoi
•^ lO CO t^ 00 Ci
I— 1
1— 1
rflOCOt^OOOli-Hi-Hi-H
CM
C^ C^l
CM CM CM
CM (M
!M
T-H
1—1
1— t
t— 1 1 — I
1— 1 ^H I— 1 CM CM
1-H
T— t
0
r-i .-< i-H CM CM CM
1— t
0
1-H
^ ^ ^ ^ CM CM CM ^ ^ ^
CO 'tl lO CO t^ 00 05
>— 1
CO ■* 10 CO t> 00 Oi
i-H
r— (
CO-*lOCOt^00C2l-Hr-l^
0
I-l
CM
T— 1
1— (
1— t
II
II
II
e
e
e
217
218 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
Table IV — Region of the n-k Plane for Which it is Known
THAT [n, fc)-ALPHABETS CaNNOT Be EXCELLED
k
30
29
28 • • •
27 ....
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
\
0 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 22 24 26 28 30 n
This can be done by a \'ariety of special methods which considerably
reduce the obvious labor of making such an array. A set of best »S's along
with their parity check symbols is given in Table V.
A maximum likelihood detector for the (10, 5)-alphabet in question
forms from each received sequence 6162 • • • &10 the parity check symbol
C1C2C3C4C5 where
Ci = h 4- ^h 4- ^3 + Ih + ^5
C2 = 67 -(- 6i -]- h-i + hi \- Ih
Cs = &8 + ^^1 + h -j- Ih + ^5
Ci = bg + hi 4- h-i -i- h-.i -(- hi
C5 = />in + hi + />, + h, 4- hi 4- 65
According to Table V, if CiC-jCiAf'b contains less than three ones, the de-
tector should brint hih^kihih^ . The detector should piint (/m 4- 1)^2^3^4'':.
if the parity check sequence C1C2C3C4C5 is either 11111 oi- 11110; the dv-
A CLASS OF BINARY SIGNALING ALPHABETS
219
Table V — Coset Leaders and Parity Check Sequences
FOR (10, 5) -Alphabet
ClCiCsCiCb
^ s
CIC2C3C4C6
5
00000
0000000000
11100
0000100001
10000
0000010000
11010
0001000001
01000
0000001000
11001
0001000010
00100
0000000100
10110
0010000001
00010
0000000010
10101
0010000010
00001
0000000001
10011
OOIOOOOIOO
1 1000
0000011000
OHIO
0100000001
10100
0000010100
01101
0100000010
10010
0000010010
01011
0100000100
10001
0000010001
00111
0100001000
01100
0000001100
11110
1000000001
01010
0000001010
11101
OOOOIOOOOO
01001
0000001001
11011
OOOIOOOOOO
00110
0000000110
10111
0010000000
00101
0000000101
01111
0100000000
00011
0000000011
mil
1000000000
tector should print 61(62 -j- l)b3lhh^ if the parity check sequence is 01111,
00111, 01011, 01101, or OHIO; the detector should print hMb-i + 1)6465
if the parity check sequence is 10111, 10011, 10101, or 10110; the de-
tector should print 616263(64 -j- 1)65 if the parity check sequence is 11011,
11001, 11010; and finally the detector should print 61626364(65 -j- 1) if the
parity check sequence is 11101 or 11100.
Simpler rules of operation for the detector may possibly be obtained
by choice of a different set of S's in Table V. These quantities in general
are not unique. Also there may exist non-equivalent alphabets with
simpler detector rules that achieve the same probability of error as the
alphabet in question.
I'vrt II — Additional Theory and Proofs of Theorems of Part I
' 2.1 the abstract group Cn
It will be helpful here to say a few more words about Br, , the group
of n-place binary sequences under the operation of addition mod 2. This
j group is simply isomorphic with the abstract group Cn generated by n
\ commuting elements of order two, say ai, a-2 , ■ ■ ■ , a„ . Here a,:ay =
<i,ai and a/ = /, i, j = 1, 2, • • • , n, where / is the identity for the
group. The eight distinct elements of C3 are, for example, /, o-i , a-y ,
(h , (iici-, , aio-.i , a-itti , aia-ittz . The group C„ is easily seen to be isomorphic
I with the Ai-fold direct product of the group Ci with itself.
220 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
It is a considerable saving in notation in dealing with C„ to omit the
symbol "a" and write only the subscripts. In this notation for example,
the elements of d are 7, 1, 2, 3, 4, 12, 13, 14, 23, 24, 34, 123, 124, 134,
234, 1234. The product of two or more elements of C„ can readily be
written down. Its symbol consists of those numerals that occur an odd
number of times in the collection of numerals that comprise the sym-
bols of the factors. Thus, (12)(234)(123) = 24.
The isomorphism between Cn and Bn can be established in many ways.
The most convenient way, perhaps, is to associate with the element
iii-2H ■ ■ ■ ik of Cn the element of Bn that has ones in places ii ,1-2, • • • , ik
and zeros in the remaining n — k places. For example, one can associate
124 of C4 with 1101 of Bi ; 14 with 1001, etc. In fact, the numeral no-
tation afforded by this isomorphism is a much neater notation for Bn
than is afforded by the awkward strings of zeros and ones. There are,
of course, other ways in which elements of C„ can be paired with elements
of Bn so that group multiplication is preserved. The collection of all such
"pairings" makes up the group of automorphisms of C„ . This group of
automorphisms of Cn is isomorphic with the group of non-singular linear
homogenous transformations in a field of characteristic 2.
An element T of C„ is said to be dependent upon the set of elements
Ti , T2 , • • ■ , Tj oi Cn if T can be expressed as a product of some ele-
ments of the set Ti , T2 , • • • , Tj ; otherwise, T is said to be independent
of the set. A set of elements is said to be independent if no member can
be expressed solely in terms of the other members of the set. For example,
in Cs , 1, 2, 3, 4 form a set of independent elements as do likewise 2357,
12357, 14. However, 135 depends upon 145, 3457, 57 since 135 =
(145) (3457) (57). Clearly any set of n independent elements of Cn can
be taken as generators for the group. For example, all possible products
formed of 12, 123, and 23 yield the elements of C3 .
Any k independent elements of C„ serve as generators for a subgroup
of order 2*". The subgroup so generated is clearly isomorphic with Ck ■
All subgroups of C„ of order 2'' can be obtained in this way.
The number of ways in which k independent elements can be chosen
from the 2" elements of C„ is
F{n, k) - (2" - 2'')(2" - 2')(2" - 2') • • • (2" - 2'-')
For, the first element can be chosen in 2" — 1 ways (the identity cannot
be included in a non-trivial set of independent elements) and the second
element can be chosen in 2" — 2 ways. These two elements determine a
subgroup of order 2\ The third element can be chosen as any element of
the remaining 2" — 2" elements. The 3 elements chosen determine a
I
A CLASS OF BINARY SIGNALING ALPHABETS 221
subgroup of order 2l A fourth independent element can be chosen as
any of the remaining 2" — 2 elements, etc.
Each set of k independent elements serves to generate a subgroup of
order 2''. The quantity F{n, k) is not, however, the number of distinct
subgroups of C„ of this order, for, a given subgroup can be obtained
from many different sets of generators. Indeed, the number of different
sets of generators that can generate a given subgroup of order 2^ of C„
is just F{k, k) since any such subgroup is isomorphic with Ck . Therefore
the number of subgroups of Cn of order 2'' is N{n, k) = F(n, k)/F(k, k)
which is (2). A simple calculation gives N(n, k) = N(n, n — k).
2.2 PROOF OF PROPOSITIONS 1 AND 2
After an element A of 5„ has been presented for transmission over
a noisy binary channel, an element T of 5„ is produced at the channel
output. The element U = AT oi Bn serves as a record of the noise
during the transmission. U is an n-place binary sequence with a one at
each place altered in A by the noise. The channel output, T, is obtained
from the input A by multiplication by U: T = UA. For channels of the
sort under consideration here, the probability that U be any particular
element of Bn of w^eight w is p^'g"""'.
Consider now signaling with a particular (n, /b) -alphabet and consider
the standard array (4) of the alphabet. If the detection scheme (8) is
used, a transmitted letter A i will be produced without error if and only
if the received symbol is of the form SjAi . That is, there will be no
error only if the noise in the channel during the transmission of Ai is
represented by one of the coset leaders. (This applies (or i = 1,2, • • • ,
fi = 2 ). The probability of this event is Qi (Proposition 1, Section 1.6).
The convention (5) makes Qi as large as is possible for the given alpha-
bet.
Let X refer to transmitted letters and let Y refer to letters produced
by the detector. We use a vertical bar to denote conditions when writing
probabilities. The quantity to the right of the bar is the condition. We
suppose the letters of the alphabet to be chosen independently with
ec^ual probability 2" .
The equivocation h{X \ Y) obtained when using an (n, fc)-alphabet
with the detector (8) can most easily be computed from the formula
h(X I F) = h{X) - h(Y) + h(Y I X) (10)
The entropy of the source is /i(X) = k/n bits per symbol. The probability
that the detector produce Aj when Ai was sent is the probability that
the noise be represented by AiAjSt , ^ = 1,2, • • • , v. In symbols,
222 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
Pr{Y -. Ai I X -^ Ad = Z Pr{N -^ AiA.Sc) = QiA^A,)
where Q{Ai) is the sum of the prol)abiUties of the elements that are in
the same column as Ai in the standard array. Therefore
Pr{Y -> .4,) = E Pr{Y -> A, \ X -^ AdPr{X -^ A^ = ^ E QU,A,)
= 4, since E Q^A.A^ = E QUi) = 1.
This last follows from the group property of the alphabet. Therefore
/i(lO = -- E P>iy -^ A,) log Pr{Y -^ A,) = - bits/symbol.
n n
It follows then from (10) that
h{X I Y) = h(Y I X)
The computation of h(Y \ X) follows readily from its definition
h{Y I X) = E Prix -^ AdhiY \ X -^ Ai)
i
= -E Prix -> AdPriY -^ Aj \ X -> Ai)
log PHY -^Aj I X-^Ai)
= -^,1211 PriN ->AiScAj) log E PriN -> AiS„,Aj)
I
= -^,ZQiAiAj)'}ogQiAiAj)
Zi ij
= - EQU,)logQ(A,)
i
Each letter is n binary places. Proposition 2, then follows.
2.3 DISTANCE AND THE PROOF OF THEOREM 1
Let A and B be two elements of Bn ■ We define the distance, diA, B),
between A and B to be the weight of their product,
d{A, B) = w(AB) (11)
The distance between .4 and B is the number of places in which A and
B difTer and is jnsl the "Hamming distance." ^ In terms of the n-cube,
diA, B) is Ihe minimum mmiber of edges that must be traversed to go
A CLASS OF BINARY SIGNALING ALPHABETS 223
from vertex ^4 to vertex B. The distance so defined is a monotone fnne-
tion of the Euchdean distance between vertices.
It follows from (11) that if C is any element of B„ then
d{A,B) = cJ(A(\BC) (12)
This fact shows the detection scheme (8) to be a maximum likelihood
detector. By definition of a standard array, one has
d(Si , I) ^ d(S,Aj , I) for all i and j
The coset leaders were chosen to make this true. From (12),
d(S, , I) = d(SiA,„S,- , / .4„.^S,) = d(SiA,n , A,„)
d(SAj , /) - diS^AjSiAm , I SiAJ = diAjA,n , SiAr.)
= d{SiAm , A()
where Af = AjA^ . Substituting these expressions in the inecjuality
above yields
d(SiAm , A„,) ^ d(SiAm , At) for all i, m, I
This equation says that an arbitrary element in the array (4) is at least
as close to the element at the top of its column as it is to any other letter
of the alphabet. This is the maximum likelihood property.
2.4 PROOF OF THEOREM 2
Again consider an (n, /c) -alphabet as a set of vertices of the unit n-cube.
Consider also n mutually perpendicular hyperplanes through the cen-
troid of the cube parallel to the coordinate planes. We call these planes
"symmetr}^ planes of the cube" and suppose the planes numbered in
accordance with the corresponding parallel coordinate planes.
The reflection of the vertex with coordinates (ai , a^ , • • • , a^ , • • • , a,j)
in symmetry plane i yields the vertex of the cube whose coordinates
are (ai , oo , ■ • • , a, -j- 1, • • • , 0,0 . More generally, reflecting a given
vertex successively in symmetry planes i, j, k, ■ • ■ yields a new vertex
whose coordinates differ from the original vertex precisely in places
i, j, k ■ ■ ■ . Successive reflections in hyperplanes constitute a transfor-
mation that leaves distances between points unaltered and is therefore
a "rotation." The rotation obtained by reflecting successively in sym-
metry planes ?', j, k, etc. can be represented by an ?i-place symbol having
a one in places ?', j, k, etc. and a zero elsewhere.
We now regard a given {n, /j)-alphabet as generated by operating on
the vertex (0, 0, • • ■ , 0) of the cube with a certain collection of 2 ro-
224 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
tation operators. The symbols for these operators are identical with the
sequences of zeros and ones that form the coordinates of the 2 points.
It is readily seen that these rotation operators form a group which is
transitive on the letters of the alphabet and which leave the unit cube
invariant. Theorem 2 then follows.
Theorem 2 also follows readily from consideration of the array (4).
For example, the maximum likelihood region associated with / is the
set of points I, So , S3 , • • • , Sy . The maximum likelihood region asso-
ciated with A; is the set of points Ai , AiS^ , AiSs , ■ • ■ , AiSy . The
rotation (successive reflections in symmetry planes of the cube) whose
symbol is the same as the coordinate sequence of Ai sends the maximum
likelihood region of / into the maximum likelihood region oi Ai , i =
1, 2, • • • , M.
2.5 PROOF OF THEOREM 3
That every systematic alphabet is a group alphabet follows trivially
from the fact that the sum mod 2 of two letters satisfying parity checks
is again a letter satisfying the parity checks. The totality of letters satis-
fying given parity checks thus constitutes a finite group.
To prove that every group alphabet is a systematic code, consider
the letters of a given (w, /c) -alphabet listed in a column. One obtains in
this way a matrix with 2 rows and n columns whose entries are zeros
and ones. Because the rows are distinct and form a group isomorphic to
Ck , there are k linearly independent rows (mod 2) and no set of more
than h independent rows. The rank of the matrix is therefore h. The
matrix therefore possesses k linearly independent (mod 2) columns and
the remaining n — k columns are linear combinations of these A;. Main-
taining only these k linearly independent columns, we obtain a matrix of
k columns and 2*' rows with rank k. This matrix must, therefore, have k
linearly independent rows. The rows, however, form a group under mod
2 addition and hence, since k are linearly independent, all 2" rows must
be distinct. The matrix contains only zeros and ones as entries; it has 2
distinct rows of k entries each. The matrix must be a listing of the num-
bers from 0 to 2^^ — 1 in binary notation. The other n — k columns of
the original matrix considered are linear combinations of the columns of
this matrix. This completes the proof of Theorem 3 and Proposition 4.
2.6 PROOF OF THEOREM 4
To prove Theorem 4 we first note that the parity check sequence of
the product of two elements of Bn is the mod 2 sum of their separate
A CLASS OF BINARY SIGNALING ALPHABETS 225
parity check sequences. It follows then that all elements in a given coset
have the same parity check sequence. For, let the coset be Si , SiA2 ,
SiAz , ■ ■ • SiA^ . Since the elements I, A^ , A3, • • • , A^ all have parity
check sequence 00 • • • 0, all elements of the coset have parity check
R(Si).
In the array (4) there are 2" cosets. We observe that there are 2"~*
elements of Bn that have zeros in their first k places. These elements
have parity check symbols identical with the last n — k places of their
symbols. These elements therefore give rise to 2"~ different parity check
symbols. The elements must be distributed one per coset. This proves
Theorem 4.
2.7 PROOF OF PROPOSITION 5
If
n ^ 2"-' -
we can explicity exhibit group alphabets having the property mentioned
in the paragraph preceding Proposition 5. The notation of the demon-
stration is cumbersome, but the idea is relatively simple.
We shall use the notation of paragraph 2.1 for elements of Bn , i.e.,
an element of Bn will be given by a list of integers that specify what
places of the sequence for the element contain ones. It will be convenient
furthermore to designate the first k places of a sequence by the integers
1, 2, 3, • • • , k and the remaining n — k places by the "integers" 1', 2',
3', • • • , r, where ( = n — k. For example, if n = 8, /c = 5, we have
10111010^ 13452'
10000100^ 11'
00000101 ^ 1'3'
Consider the group generated by the elements 1', 2', 3', • • • , (' , i.e.
the 2' elements /, 1', 2', ■■■,(', 1'2', 1'3', • • • , 1'2'3' ■■■('. Suppose
these elements listed according to decreasing weight (say in decreasing
order when regarded as numbers in the decimal system) and numbered
consecutively. Let Bt be the zth element in the list. Example: if ( ^ 3,
Ih = 1'2'3', B2 = 2'3', B, = 1'3', B, = 1'2', B, - 3', B, = 2', B, - 1'.
Consider now the (n, /^-alphabet whose generators are
ISi , 2B, ,W,, ■■• , kBk
We assert that if
22G THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
>r% n—k
.. — 2 -
this alphabet is as good as any other alphabet of 2 letters and n places.
In the first place, we observe that every letter of this (n, A-)-alphabet
(except /) has unprimed numbers in its symbols. It follows that each of
the 2' letters /, 1', 2', • ■ • , (', V2', ■■■ , V2' ■■■ (' occurs in a different
coset of the given (n, A-)-alphabet. For, if two of these letters appeared
in the same coset, their product (which contains only primed numbers)
would have to be a letter of the (n, k) alphabet. This is impossible since
every letter of the (/i, A) alphabet has unprimed numbers in its symbol.
Since there are precisely 2 cosets we can designate a coset by the single
element of the list Bi , Bi , ■ • ■ , B-ii = I which appears in the coset.
We next observe that the condition
71 ^ 2 —
guarantees that J5a+i is of weight 3 or less. For, the given condition is
equivalent to
'-■-©-o-o-e
We treat several cases depending on the weight of Bu+i .
If Bk+\ is of weight 3, we note that for i = 1,2, • • • , A-, the coset con-
taining Bi also contains an element of weight one, namely the element
i obtained as the product of Bi with the letter iBi of the given (n, A;)-
alphabet. Of the remaining (2 — A') 5's, one is of weight zero, C are of
weight one, f j are of weight 2 and the remaining are of weight 3. We
have, then an = 1, ai = f + A- = n. Now every B of weight 4 occurs in'
the list of generators \Bi , 2B-2 , • • • , kBk . It follows that on multi-
plying this list of generators by any B of weight 3, at least one element
of weight two will result. (E.g., (l'2'3')(il'2'3'40 = j4') Thus every
coset with a B of weight 2 or 3 contains an element of weight 2 and
a2 = 2 — ao — cn] .
The argument in case Bk+i is of weight two or one is similar.
2.8 MODULAR REPRESENTATIONS OF C„
In order to explain one of the methods used to obtain the best (//, A)-
alphabets listed in Tal)les II and III, it is necessary to digress here lo
present additional theory.
I
A CLASS OF BINARY SINGALING ALPHABETS
227
It has been remarked that every (n, /v)-alphabet is isomorphic with
Ck . Let us suppose the elements of Ci, hsted in a column starting with /
and proceeding in order /, 1, 2, 3, • • • , /.', 12, 13, ■••,(/.•— 1)/,-, 123,
, 123 • • • k. The elements of a given (n, A-)-alphabet can be
paired off with these abstract elements so as to preserve group multipli-
cation. This can be done in many different ways. The result is a matrix
with elements zero and one with 7i columns and 2 rows, these latter
being labelled by the symbols /, 1,2, • • • etc. What can be said about
the columns of this matrix? How many different columns are possible
when all (n, A)-alphabets and all methods of establishing isomorphism
with Ck are considered?
In a given column, once the entries in rows 1,2, • • • , /,• are known, the
entire column is determined by the group property. There are therefore
only 2 possible different columns for such a matrix. A table showing
these 2 possible columns of zeros and ones will be called a modular repre-
senfafion table for Ck ■ An example of such a table is shown for /,• = 4 in
Table VI.
It is clear that the colunuis of a modular representation table can also
be labelled by the elements of Ck , and that group multiplication of these
column labels is isomorphic with mod 2 addition of the columns. The
table is a symmetric matrix. The element with row label A and column
label B is one if the symbols A and B have an odd number of different
numerals in common and is zero otherwise.
Every (n, /c)-alphabet can be made from a modular representation
table by choosing w columns of the table (with possible repetitions) at
least k of which form an independent set.
Table VI — Modular Representation Table for Group C4
I 12 3 4 12 13 14 23 24 34 123 124 134 234 1234
I
1
2
3
4
12
13
14
23
24
34
123
124
134
234
1234
0
0
0
0
0
0
0
0
0
0
0
0
0
0
n
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
()
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
1
u
228 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
We henceforth exclude consideration of the column / of a modular
representation table. Its inckision in an (n, /v)-alphabet is clearly a waste
of 1 binary digit.
It is easy to show that every column of a modular representation table
for Ch contains exactly 2 " ones. Since an (n, /v)-alphabet is made from
n such columns the alphabet contains a total of n2 '~ ones and we have
Proposition 6. The weights of an (n, /c)-alphabet form a partition of
n2''~^ into 2* — 1 non-zero parts, each part being an integer from the set
1,2, ■■■ ,n.
The identity element always has weight zero, of course.
It is readily established that the product of two elements of even
weight is again an element of even weight as is the product of two ele-
ments of odd weight. The product of an element of even weight with an
element of odd weight yields an element of odd weight.
The elements of even weight of an (n, A;) -alphabet form a subgroup
and the preceding argument shows that this subgroup must be of order
2*" or 2*""^ If the group of even elements is of order 2''~\ then the collec-
tion of even elements is a possible (n, k — l)-alphabet. This (n, k — 1)
alphabet may, however, contain the column / of the modular represen-
tation table of Ck-i ■ We therefore have
Proposition 7. The partition of Proposition 6 must be either into
2^ — 1 even parts or else into 2 " odd parts and 2^—1 even parts.
In the latter case, the even parts form a partition of a2 "" where a is
some integer of the set k — I, k, ■ • • , n and each of the parts is an in-
teger from the set 1, 2, • • • , n.
2.9 THE CHARACTERS OF Ck
Let us replace the elements of Bn (each of which is a sequence of zeros
and ones) by sequences of 4-1 's and — I's by means of the following
substitution
The multiplicative properties of elements of Bn can be preserved iti this
new notation if we define the product of two 4-1,-1 symbols to be the
symbol whose tth component is the ordinary product of the ?'th compo-
nents of the two factors. For example, 1011 and 01 10 become respectively
-11 -1 -1 and 1 -1 -11. We have
(-11 -1 -1)(1 -1 -11) = (-1 -11 -1)
1
0
0
0
0
1
0
0
0
0
-1
0
0
0
0
-1
A CLASS OF BINARY SIGNALING ALPHABETS 229
corresponding to the fact that
(1011) (0110) = (1101)
If the +1,-1 symbols are regarded as shorthand for diagonal matrices,
so that for example
-11 -1 -1
then group multiplication corresponds to matrix multiplication.
(While much of what follows here can be established in an elementary
way for the simple group at hand, it is convenient to fall back upon the
established general theory of group representations for several proposi-
tions.
The substitution (13) converts a modular representation table (col-
umn / included) into a square array of +l's and — I's. Each column (or
row) of this array is clearly an irreducible representation of Ck ■ Since Ck
is Abelian it has precisely 2 irreducible representations each of degree
one. These are furnished by the converted modular table. This table also
furnishes then the characters of the irreducible representations of Ck
and we refer to it henceforth as a character table.
Let x"(^) be the entry of the character table in the row labelled A and
column labelled a. The orthogonality relationship for characters gives
E x'{A)/{A) = 2'8.,
ACCk
Z x%A)x"(B) = 2'b
<xCCk
AB
where 8 is the usual Kronecker symbol. In particular
E xiA)x\A) = Z AA) = 0, ^^I
ACCk ACCk
Since each x (A) is +1 or — 1, these must occur in eciual numbers in any
column ^ 9^ I. This implies that each column except / of the modular
representation table contains 2 ~ ones, a fact used earlier.
Every matrix representation of Ck can be reduced to its irreducible
components. If the trace of the matrix representing the element A in an
arbitrary matrix representation of Ck is x{A), then this representation
contains the irreducible representation having label ^ in the character
table dp times where
230 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
(h = ^. E x{A)AA) (14)
2^-
A C Ck
Every (n, A)-alphabet furnishes iis with a matrix representation of Ck
by means of (13) and the procedure outUned below (13). The trace xi^.)
of the matrix representing the element A of C\ is related to the weight
of the letter by
x(A) = n - 2w(A) (15)
Equations (14) and (15) permit us to compute from the weights of an
(u, /,)-alphabet what irreducible representations are present in the alpha-
bet and how many times each is contained. It is assumed here that the
given alphabet has been made isomorphic to Ck and that the weights are
labelled by elements of Ck ■
Consider the converse problem. Given a set of mmibers ivi , Wn , • ■ ■ ,
W'lk that satisfy Propositions 6 and 7. From these we can compute
cjuantities %/ = n — 2wi as in (15). It is clear that the given ty's will
constitute the weights of an (/t, A)-alphabet if and only if the 2^ x» can
be labelled with elements of (\ so that the 2 sums (14) {fi ranges over
all elements of Ck) are non-negative integers. The integers d^ tell what
representations to choose to construct an in, A)-alphabet with the given
weights Wi .
2.10 CONSTRUCTION OF BEST ALPHABETS
A great many different techniques were used to construct the group
alphabets listed in Tables II and III and to show that for each n and k
there are no group alphabets with smaller probability of error. Space
prohibits the exhibition of proofs for all the alphabets listed. We content
ourseh'es here with a sample argument and treat the case n = 10, k =
4 in detail.
According to (2) there are A^(10, 4) = 53,743,987 different (10, 4)-
alphabets. We now show that none is better than the one given in Table
III. The letters of this alphabet and weights of the letters are
1 0
167 8 10 5
2 6 7 9 10 5
3 5 6 8 9 10 6
4 5 7 8 9 10 6
1289 4
13579 5
A CLASS OF BINARY SIGNALING ALPHABETS
231
14569
23578
24568
3 4 6 7
12 3 5 7 9
12 4 5 7 10
1 3 4 8 10
2 3 4 9 10
12 3 4 6 7 8 9
5
5
5
4
6
6
5
5
8
The notation is that of Section 2.1. By actually forming the standard
array of this alphabet, it is verified that
ao =1, Oil = 10,
«2
39,
a:i
14.
Table II shows ( .-> ) = ^5, whereas a-z = 39, so the given alphabet
does not correct all possible double errors. In the standard array for the
alphabet, 39 coset leaders are of weight 2. Of these 39 cosets, 33 have
only one element of weight 2; the remaining 6 cosets each contain two
elements of weight 2. This is due to the two elements of weight 4 in the
given group, namely 1289 and 3467. A portion of the standard array
that demonstrates these points is
1289
3467
12
89
•
18
29
•
19
28
.
34
67
36
47
37
46
]
•
In order to have a smaller probability of error than the exhibited
alphabet, it is necessary that a (10, 4)-alphabet have an a^ > 39. We
proceed to show that this is impossible by consideration of the weights
of the letters of possible (10, 4)-alphabets.
We first show that every (10, 4)-alphabet must have at least one ele-
ment (other than the identity, /) of weight less than 5. By Propositions
• ') and 7, Section 2.8, the weights must form a partition of 10-8 = 80 into
1 5 positive parts. If the weights are all even, at least two must be less
than 6 since 14-6 = 84 > 80. If eight of the weights are odd, we see from
8-5 + 7-() = 82 > 80 that at least one weight must be less than 5.
232 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
An alphabet with one or more elements of weight 1 must have an
«2 ^ 36, for there are nine elements of weight 2 which cannot possibly
be coset leaders. To see this, suppose (without loss of generality) that
the alphabet contains the letter 1. The elements 12, 13, 14, • • • 1 10 can-
not possibly be coset leaders since the product of any one of them with
the letter 1 yields an element of weight 1 .
An alphabet with one or more elements of weight 2 must have an
ai S 37. Suppose for example, the alphabet contained the letter 12.
Then 13 and 23 must be in the same coset, 14 and 24 must be in the
same coset, ■ • • , 1 10 and 2 10 must be in the same coset. There are at
least eight elements of weight two which are not coset leaders.
Each element of weight 3 in the alphabet prevents three elements of
weight 2 from being coset leaders. For example, if the alphabet contains
123, then 12, 13, and 23 cannot be coset leaders. We say that the three
elements of weight 2 are "blocked" by the letter of weight 3. Suppose an
alphabet contains at least three letters of weight three. There are several
cases: (A) if three letters have no numerals in common, e.g., 123, 456,
789, then nine distinct elements of weight 2 are blocked and a-2 S 36;
(B) if no two of the letters have more than a single numeral in common,
e.g., 123, 345, 789, then again nine elements of weight 2 are blocked and
a-2 ^ 36; and (C) if two of the letters of weight 3 have two numerals in
common, e.g., 123, 234, then their product is a letter of weight 2 and l)y
the preceding paragraph ao ^ 37. If an alphabet contains exactly two
elements of weight 3 and no elements of weight 2, the elements of weight
3 block six elements of weight 2 and 0:2 ^ 39.
The preceding argument shows that to be better than the exhibited
alphabet a (10, 4)-alphabet with letters of weight 3 must have just one
such letter. A similar argument (omitted here) shows that to be better
than the exhibited alphabet, a (10, 4)-alphabet cannot contain more
than one element of weight 4. Furthermore, it is easily seen that an
alphabet containing one element of weight 3 and one element of weight
4 must have an ao ^ 39.
The only new contenders for best (10, 4)-alphabet are, therefore,
alphabets with a single letter other than / of weight less than 5, and this
letter must have weight 3 or 4. Application of Propositions 6 and 7 show
that the only possible weights for alphabets of this sort are: 35 6 and
5 46' where 5' means seven letters of weight 5, etc. We next show that
there do not exist (10, 4)-alphabets having these weights.
Consider first the suggested alphabet with weights 35 6'. As explained
in Section 2.9, from such an alphabet we can construct a matrix repre-
sentation of ('4 having the character x(/) = 10, one matrix of trace 4,
A CLASS OF BINARY SIGNALING ALPHABETS 233
seven of trace 0 and seven of trace —2. The latter seven matrices cor-
respond to elements of even weight and together with / must represent
a subgroup of order 8. We associate them with the subgroup generated
by the elements 2, 3, and 4. We have therefore
x(/) = 10, x(2) = x(3) = x(4) = x(23)
= x(24) = x(34) = x(234) = -2.
Examination of the symmetries involved shows that it doesn't matter
how the remaining Xi ai"e associated with the remaining group elements.
We take, for example
x(l) = 4, x(12) = x(13) = x(14) = x(123)
= x(124) = x(134) = x(1234) = 0.
Now form the sum shown in equation (14) with /3 = 1234 (i.e., with the
character x^" obtained from column 1234 of the Table VI by means
of substitution (13). There results c?i234 = V-i which is impossible. There-
fore there does not exist a (10, 4) -alphabet with weights 35 6 .
The weights 5 46 correspond to a representation of d with character
x(/) = 10, 0^, 2, ( — 2)^ We take the subgroup of elements of even weight
to be generated by 2, 3, and 4. Except for the identity, it is clearly im-
material to w^hich of these elements we assign the character 2. We make
the following assignment: x(/) = 10, x(2) = 2, x(3) = x(4) = x(23) =
x(24) = x(34) = x(234) = -2, x(l) = x(12) = x(13) = x(14) =
x(123) = x(124) = x(134) = x(1234) = 0. The use of equation (14)
shows that ^2 = \'2 which is impossible.
It follows that of the 53,743,987 (10, 4)-alphabets, none is better than
the one listed on Table III.
Not all the entries of Table III were established in the manner just
demonstrated for the (10, 4)-alphabet. In many cases the search for a
l)est alphabet was narrowed down to a few alphabets by simple argu-
ments. The standard arrays for the alphabets were constructed and the
best alphabet chosen. For large n the labor in making such a table can
be considerable and the operations involved are highly liable to error
when performed by hand.
I am deeply indebted to V. M. Wolontis who programmed the IBM
CPC computer to determine the a's of a given alphabet and who pa-
tiently ran off many such alphabets in course of the construction of
Tables II and III. I am also indebted to Mrs. D. R. Fursdon who eval-
uated many of the smaller alphabets by hand.
234 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
REFERENCES
1. R. W. Hamming, B.S.T.J., 29, i)p. 147-160, 1950.
2. I. S. Reed, Transactions of tlie Piofossional (iroup on Information Tlieorv,
^ PGIT-4, PI). 3S-49, 1954.
3. See section 7 of R . W. Hamniinji's paper, loc. cit.
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8. F. D. Murnaghan, Theory of Group Representations, Johns Hopkins Press,
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Michigan, 1944.
I
Bell System Technical Papers Not
Published in This Journal
Allen, L. J., see Fewer, D. R.
Alllson, H. W., see Moore, G. E.
Baker, W. 0., see Winslow, F. H.
Barstow, J. M.^
Color TV How it Works, I.R.E. Student Quarterly, 2, pp. 11-16,
Sept., 1955.
Basseches, H.^ and ^McLean, D. A.
Gassing of Liquid Dielectrics Under Electrical Stress, Ind. c^- Engg.
Chem., 47, pp. 1782-1794, Sept., 1955.
Beck, A. C}
Measurement Techniques for Multimode Waveguides, Proc. I.R.E.,
MRI, 4, pp. 325-6, Oct. 1, 1955.
Becker, J. A.^
The Life History of Adsorbed Atoms, Ions, and Molecules, N. Y.
Acad. Sci. Ann., 58, pp. 723-740, Sept. 15, 1955.
Hlackwell, J. H., see Fewer, D. R.
BooRSE, H. A., see Smith, B.
HozoRTii, R. M.,' Getlin, B. B.,' Galt, J. K.,' Merritt, F. R.,' and-
^'ager, W. a.'
Frequency Dependence of Magnetocrystalline Anisotropy, Letter to
the Editor, Phys. Rev., 99, p. 1898, Sept. 15, 1955.
1. Bell Telephone Laboratories, Inc.
235
236 THE BELL SYSTEM TECHXICAL JOURNAL, JANUARY 1956
BozoRTH. R. M.\ TiLDEX, E. F..' and Williams, A. j/
Anisotropy and Magnetostriction of Some Ferrites, Phys. Rev., 99,
pp. 17S8-1798, Sept. 15, 1955.
Bridgers, H. E.,^ and Kolb, E. D.^
Rate-Grown Germanium Crystals for High-Frequency Transistors,
Letter to the Editor, J. Appl. Phys., 26, pp. 1188-1189, Sept., 1955. j
BULLIXGTOX, K.^
Characteristics of Beyond-the-Horizon Radio Transmission, Pioc.
I.R.E., 43, pp. 1175-1180, Oct., 1955.
BULLIXGTOX, K.^ IXKSTER, W. J.,^ and DVRKEE, A. L.^
Results of Propagation Tests at 505 Mc and 4,090 Mc on Beyond-
Horizon Paths, Proc. I.R.E., 43, pp. 1306-1316, Oct., 1955.
Calbick, C. J.'
Surface Studies with the Electron Microscope, X. Y. Acad. Sci. Ann.,
58, pp. 873-892, Sept. 15, 1955.
Cass, R. S., see Fewer, D. R.
DuRKEE, A. L., see Bullington, K.
Fewer, D. R..' Blackwell. J. H..' Allex. L. J..^ and Cass, R. S."
Audio-Frequency Circuit Model of the 1-Dimensional Schroedinger
Equation and Its Sources of Error, Canadian J. of Pins., 33, pp. 483-
491, Aug., 1955.
Francois, E. E., see Law, J. T.
Davis, J. L., see Suhl, H.
Galt, J. K., see Bozorth, R. "SI., and Yager, W. A.
Garn, p. D.,' and Hallixe, Mrs. E. W.'
Polarographic Determination of Phthalic and Anhydride Alkyd Res-
ins, Anal Cliem., 27, pp. 15()3-15G5, Oct., 1955.
1. Bell Telephone Laboratories, Inc.
4. University of Western Ontario, London, Canada
5. Bell Telephone Company of Canada, Montreal
TECHNICAL PAPERS 237
Getlin, B. B., see Bozorth, R. M.
GlANOLA, V. F}
Application of the Wiedemann Effect to the Magnetostrictive Coupling
of Crossed Coils, J. Appl. Phys., 26, pp. 1152-1157, Sept., 1955.
Goss, A. J., see Hassion, F. X.
Green, E. I.^
The Story of 0, American Scientist, 43: pp. 584-594, Oct., 1955.
Halline, Mrs. E. W., see Garn, P. D.
Harrower, G. A.^
Measurement of Electron Energies by Deflection in a Uniform Electric
Field, Rev. Sci. Instr., 26, pp. 850-854, Sept., 1955.
Hassion, F. X.,^ Goss, A. .1.,^ and Trumbore, F. A.^
The Germanium-Silicon Phase Diagram, J. Phys. Chem., 59, p. 1118,
Oct., 1955.
Hassion, F. X.,^ Thurmond, C. D.,^ and Trumbore, F. A.^
On the Melting Point of Germanium, J. Phys. Chem., 59, p. 1076,
Oct., 1955.
Hines, I\I. E.,' Hoffman, G. W.,' and Saloom, J. A.^
Positive-Ion Drainage in Magnetically Focused Electron Beams, J.
Appl. Phys., 26, pp. 1157-1162, Sept., 1955.
Hoffman, G. W., see Hines, M. E.
Inkster, W. J., see Bullington, K.
Kelly, M. J.'
Training Programs of Industry for Graduate Engineers, Elec. Engg.,
74, pp. 866-869, Oct., 1955.
KoLB, E. D., see Bridgers, H. E.
1. Bell Telephone Laboratories, Inc.
1
238 THE BELL SYSTEM TECHXICAL JOURXAL, JANUARY 1 9 of)
Law, J. T./ and Francois, E. E.'
Adsorption of Gasses and Vapors on Germanium, X. Y. Acad. Sci.
Ann., 58, pp. 925-936, Sept. 15, 1955.
LovELL, Miss L. C, see Pfann, W. G.
Matreyek, W., see Winslow, F. H.
McLean, D. A., see Basseches, H.
Merritt, F. R., see Bozorth, R. M., and Yager, W. A.
Meyer, F. T.'
An Improved Detached-Contact Type of Schematic Circuit Drawing,
A.LE.E. Commun. ct Electronics, 20, pp. 505-513, Sept., 1955.
Miller, B. T.'
Telephone Merchandising, Telephony, 149, pp. 116-117, Oct. 22,
1955.
Miller, S. L.^
Avalanche Breakdown in Germanium, Phys. Rev., 99, pp. 1234-1241,
Aug. 15, 1955.
Moore, G. E.,^ and Allison, H. W.^
Adsorption of Strontium and of Barium on Tungsten, J. Chem.
Phys., 23, pp. 1609-1621, Sept., 1955.
Neisser, W. R.,^
Liquid Nitrogen Coal Traps, Rev. Sci. Instr., 26, p. 305, Mar., 1955.
Ostergren, C. N."
Some Observations on Liberahzed Tax Depreciation, Telephony, 149,
pp. 16-23-37, Oct. 1, 1955.
Ostergren, G. N.
Depreciation and the New Law, Telephony, 149, pp. 96-100-104-108, ;
Oct. 22, 1955. I
Rape, N. R., see Winslow, F. H.
1. Bell Telephone Laboratories, Inc.
2. American Telephone and Telegraph Co.
\\
technical papers 239
Pedekskn, L.
Aluminum Die Castings for Carrier Telephone Systems, A.I.E.E.
Commun. & Electronics, 20, pp. 434-439, Sept., 1955.
Peters, H.^
Hard Rubber, Tnd. and Engg. Chem., Part II, pp. 2220-2222, Sept.
20, 1955.
Pfann, w. c;.'
Temperature-Gradient Zone-Melting, J. Metals, 7, p. 961, Sept., 1955.
Pfann, W. G.,' and Lovell, Miss L. C.^
Dislocation Densities in Intersecting Lineage Boundaries in Ger-
manium, Letter to the Editor, Acta. Met., 3, pp. 512-513, Sept., 1955.
Pierce, J. P.'
Orbital Radio Relays, Jet Propulsion, 25, pp. 153-157, Apr., 1955.
Poole, K. M.'
Emission from Hollow Cathodes, J. Appl. Phys., 26, pp. 1176-1179,
Sept., 1955.
Saloom, J. A., see Hines, M. E.
Slighter, W. P.^
Proton Magnetic Resonance in Polyamides, J. Appl. Phys., 26, pp.,
1099-1103, Sept., 1955.
Smith, B./ and Boorse, H. A.
Helium II Film Transport. II. The Role of Surface Finish, Phys. Rev.
99, pp. 346-357, July 15, 1955.
Smith, B.,^ and Boorse, H. A.
Helium II Film Transport. IV. The Role of Temperature, Phys. Rev.,
99, pp. 367-370, July lo, 1955.
SuHL, H.,^ Van Uitert, L. G.,^ and Davis, J. L.^
Ferromagnetic Resonance in Magnesium-Manganese Aluminum Fer-
rite Between 160 and 1900 Mc, Letter to the Editor, J. Appl. Phys.,
26, pp. 1181-1182, Sept., 1955.
1. Bell Telephone Laboratories, Inc.
6. Columbia University, New York City
240 THE EELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956
Thurmond, C. D., see Hassion, F. X.
TiDD, W. H/ I
Demonstration of Bandwidth Capabilities of Beyond -Horizon Tropo-
spheric Radio Propagation, Proc. I.R.E., 43, pp. 1297-1299, Oct., 1955.
Tien, P. K.,' and Walker, L. R.'
Large Signal Theory of Traveling -Wave Amplifiers, Proc. I.R.E., 43,
p. 1007, Aug., 1955.
TiLDEN, E. F., see Bozorth, R. M.
Trumbore, F. a., see Hassion, F. X.
IThlir, a., Jr.^
Micromachining with Virtual Electrodes, Rev. Sci., Instr., 26, pp.
965-968, Oct., 1955.
Ulrich, W., see Yokelson, B. J.
Van Uitert, L. G., see Siihl, H.
Walker, L. R., see Tien, P. K.
Weibel, E. S.'
Vowel Synthesis by Means of Resonant Circuits, J. Acous. Soc, 27,
pp. 858-865, Sept., 1955.
Williams, A. J., see Bozorth, R. M.
WiNSLow, F. H.,' Baker, W. O.,^ and Yager, W. A.^
Odd Electrons in Polymer Molecules, Am. Chem. Soc, 77, pp. 4751-
4756, Sept. 20, 1955.
WiNSLow, F. II.,' Baker, W. O.,' Rape, N. R.' and Matreyek, W.'
Formation and Properties of Polymer Carbon, J. Polymer Science, 16,
p. 101, Apr., 1955.
Yager, W. A., sec Bozorth, R. M.
1. Bell Tc;l(;i)li()ne liaboratorics, Inc.
TECHNICAL PAPERS 241
Yagkr, W. a./ Galt, J. K/ and Merritt, F. R.'
Ferromagnetic Resonance in Two-Nickel-Iron Ferrites, Phys. Rev.,
99, pp. 1203-1209, Aug. 15, 1955.
YoKELSON, B. J.,^ and Ulrich, W.^
Engineering Multistage Diode Logic Circuits, A.I.E.E. Commun. &
Electronics, 20, pp. -466-475, Sept., 1955.
1. Bell Telephone Laboratories, Inc.
Recent Monographs of Bell System Technical
Papers Not Published in This Journal*
Arnold, W. O., and Hoefle, R. R.
A System Plan for Air Traffic Control, ]\Ionograph 2483.
Beck, A. C.
Measurement Techniques for Multimode Waveguides, ]\Ioiiograph
2421.
Becker, J. A., and Brandes, R. G.
Adsorption of Oxygen on Tungsten as Revealed in Field Emission
Microscope, Alonogiaph 24U3.
Boyle, W. S., see Germer, L. H.
Brandes, R. G., see Becker, J. A.
Brattain, W. H., see Garrett, C. G. B.
Garrett, C. G. B., and Brattain, W. H.
Physical Theory of Semiconductor Surfaces, Monograph 2453.
Gerner, L. H., Boyle, W. S., and Kisliuk, P.
Discharges at Electrical Contacts — II, Monograph 2499.
Hoefle, R. R., see Arnold, W. 0.
KisLiuK, P., see Germer, L. H.
Linvill, J. G.
Nonsaturating Pulse Circuits Using Two Junction Transistors, Mono-
graph 2-17."). I
* Copies of these monographs may 1)0 ()l)l;tin(Ml on request to the Pul)licat ion
Department, Hell Telephone Laboratories, Iiie., 463 West Street, New York 14,
N. Y. The numbers of the monographs should be given in all requests.
242
MONOGRAPHS 243
Mason, W. P.
Relaxations in the Attenuation of Single Crystal Lead, Monograph
2454.
Mkykr, F. T.
An Improved Detached-Contact-Type of Schematic Circuit Drawing,
Monograph 2456.
VoGEL, F. L., Jr.
Dislocations in Low-Angle Boundaries in Germanium, Monograph
2455.
Walker, T.. R.
Generalizations of Brillouin Flow, Monograph 2432.
Warner, A. W.
Frequency Aging of High -Frequency Plated Crystal Units, Monograph
2474.
Weibel, E. S.
On Webster's Horn Equation, Monograph 2450.
Contributors to This Issue
A. C. Beck, E.E., Rensselaer Polytechnic Institute, 1927; Instructor,
Rensselaer Polytechnic Institute, 1927-1928; Bell Telephone Labora-
tories, 1928 -. With the Radio Research Department he was engaged
in the development and design of short-wave and microwave antennas.
During World War II he was chiefly concerned with radar antennas and
associated waveguide structures and components. For several years
after the war he worked on development of microwave radio repeater
systems. Later he worked on microwave transmission developments
for broadband communication. Recently he has concentrated on further
developments in the field of broadband communication using circular
waveguides and associated test equipment.
J. S. Cook, B.E.E., and M.S., Ohio State University, 1952; Bell
Telephone Laboratories, 1952 -. Mr. Cook is a member of the Research
in High-Frequency and Electronics Department at Murray Hill and
has been engaged principally in research on the traveling- wave tube.
Mr. Cook is a member of the Institute of Radio Engineers and belongs
to the Professional Group on Electron Devices.
0. E. DeLange, B.S. University of Utah, 1930; M.A. Columbia Uni-
versity, 1937; Bell Telephone Laboratories, 1930 — . His early work was
principally on the development of high-frequency transmitters and re-
ceivers. Later he worked on frequency modulation and during World
War II was concerned with the development of radar. Since that time
he has been involved in research using broadband systems including
microwa^'e and baseband. Mr. DeLange is a member of the Institute
of Radio Engineers.
R. KoMPFNER, Engineering Degree, Technische Hochschule, Vienna,
1933; Ph.D., Oxford, 1951; Bell Telephone Laboratories, 1951 -. Be-
tween 1941-1950 he did work for the British Admiralty at Birmingham
University and Oxford University in the Royal Naval Scientific Service.
He invented the traveling-wave tube and for this achievement Dr.
Kompfner i-eceived the 1955 Duddcll Medal, bestowed by the Physical
Society of England. In the Laboratoi'ies' Research in High Frequency
244
CONTRIBUTORS TO THIS ISSUE 245
and Electronics Department, he has continued his research on vacuum
tubes, particularly those used in the microwave region. He is a Fellow
of the Institute of Radio Engineers and of the Physical Society in
London.
Charles A. Lee, B.E.E., Rensselaer Polytechnic Institute, 1943;
Ph.D., Columbia University, 1953; Bell Telephone Laboratories, 1953-.
When Mr. Lee joined the Laboratories he became engaged in research
concerning solid state devices. In particular he has been developing
techniques to extend the frequency of operation of transistors into the
microwave range, including work on the diffused base transistor. During
World War II, as a member of the United States Signal Corps, he was
concerned with the determination and detection of enemy counter-
measures in connection with the use of proximity fuses by the Allies.
He is a member of the American Physical Society and the American
Institute of Physics. He is also a member of Sigma Xi, Tau Beta Pi
and Eta Kappa Nu.
John R. Pierce, B.S., M.S. and Ph.D., California Institute of Tech-
nology 1933, 1934 and 1936; Bell Telephone Laboratories, 1936-. Ap-
pointed Director of Research — Electrical Communications in August,
1955. Dr. Pierce has specialized in Development of Electron Tubes and
Microwave Research since joining the Laboratories. During World War
li II he concentrated on the development of electronic devices for the
[I Armed Forces. Since the war he has done research leading to the develop-
;j ment of the beam traveling- wave tube for which he was awarded the
h 1947 Morris Liebmann Memorial Prize of the Institute of Radio Engi-
[li neers. Dr. Pierce is author of two books: Theory and Design of Electron
Ij Beams, published in second edition last year, and Traveling Wave Tubes
il (1950). He was voted the ''Outstanding Young Electrical Engineer of
[| 1942" by Eta Kappa Nu. Fellow of the American Physical Society and
J the I.R.E. Member of the National Academy of Sciences, the A.I.E.E.,
I Tau Beta Pi, Sigma Xi, Eta Kappa Nu, the British Interplanetary So-
il ciety, and the Newcomen Society of North America.
C. F. QuATE, B.S., University of Utah 1944; Ph.D., Stanford Uni-
i versity 1950; Bell Laboratories 1950-. Dr. Quate has been engaged in
rj research on electron dynamics — the study of vacuum tubes in the
;| microwave frequency range. He is a member of I.R.E.
I David Slepian, University of Michigan, 1941-1943; M.A. and Ph.D.,
li Harvard LTniversity, 1946-1949; Bell Telephone Laboratories, 1950-. Dr.
24G THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1950
Slepian has been engaged in mathematical research in communication
theory, switching theory and theory of noise. Parker Fellow in physics.
Harvard University 1949-50. Member of I.R.E,, American Mathemati-
cal Society, the American Association for the Advancement of Science
and Sigma Xi.
Milton Sobel, B.S., City College of New York, 1940; M.A., 1946 and
Ph.D., 1951, Columbia University; U. S. Census Bureau, Statistician,
1940-41; U. S. Army War College, Statistician, 1942-44; Cohunbia Uni-
versity, Department of Mathematics, Assistant, 1946-48 and Research
Associate 1948-50; Wayne University, Assistant Professor of Mathe-
matics, 1950-52; Columbia University, Department of Mathematical
Statistics, Visiting Lecturer, 1952; Cornell University, fundamental re-
search in mathematical statistics, 1952-54; Bell Telephone Laboratories,
1954-. Dr. Sobel is engaged in fundamental research on life testing
reliability problems with special application to transistors and is a con-
sultant on many Laboratories projects. Member of Institute of Mathe-
matical Statistics, American Statistical Association and Sigma Xi.
Morris Tanenbaum, A.B., Johns Hopkins University, 1949; M.A.,
Princeton University, 1950; Ph.D. Princeton University, 1952; Bell
Telephone Laboratories, 1952-, Dr. Tanenbaum has been concerned
with the chemistry and semiconducting properties of intermetallic com-
pounds. At present he is exploring the semiconducting properties of
silicon and the feasibility of silicon semiconductor devices. Dr. Tanen-
baum is a member of the American Chemical Society and American
Physical Society. He is also a member of Phi Lambda LTpsilon, Phi Beta
Kappa and Sigma Xi.
Donald E. Thomas, B.S. in E.E., Pennsylvania State College, 1929;
M.A., Columbia University, 1932; Bell Telephone Laboratories, 1929-
1942, 1946-. His first assignment at the Laboratories was in submarine
cable development. Just prior to World War II he became engaged in
the development of sea and airborne radar and continued in this work I
until he left for military duty in 1942. During World War II he was made '
a member of the Joint and Combined Chiefs of Staff Committees on
Radio C-ountermeasures. Later he was a civilian memlior of the Depart-'
ment of Defense's Research and Development Board Panel on Electronic
Countermeasures. Upon rejoining the Laboratories in 1946, Mr. Thomas
was active in the development and installation of the first deep sea re-
peatered submarine telephone cable, hctwcen Key West and Havana,'
COXTIUBUTOKS TO THIS ISSUE 247
which went into service in 1950. Later he was engaged in the develop-
ment of transistor devices and circuits for special applications. At the
present time he is working on the evaluation and feasibility studies of
new types of semiconductors devices. He is a senior member of the I.R.E.
and a member of Tau Beta Pi and Phi Kappa Phi.
Laurence R. Walker, B.Sc. and Ph.D., McGill University, 1935
and 1939; LTniversity of California 1939-41; Radiation Laboratory,
Massachusetts Institute of Technology, 1941-45; Bell Telephone La-
boratories, 1945-. Dr. Walker has been primarily engaged in the develop-
ment of microwave oscillators and amplifiers. At present he is a member
of a physical research group concerned with the applied physics of solids.
Fellow of the American Physical Society.
IHE BELL SYSTEM
Jechnical journal
VOTED TO THE SC I E N T I FIC^^^ AND ENGINEERING
PECTS OF ELECTRICAL COMMUNICATION
LUME XXXV MARCH 1956 NUMBER 2
An Experimental Remote Controlled Line Concentrator \.f^ y
A^E. JOEL, JR. 249
Transistor Circuits for Analog and Digital Systems
F. H. BLECHER 295
Electrolytic Shaping of Germanium and Silicon a. uhlir, jr. 333
A Large Signal Theory of Traveling-Wave Amplifiers p. k. tibn 349
A Detailed Analysis of Beam Formation with Electron Guns of the
Pierce Type w. e. danielson, j. l. rosenfeld and j. a. saloom 375
Theories for Toll Traffic Engineering in the U.S.A. r. i, Wilkinson 421
Crosstalk on Open -Wire Lines
W, C, BABCOCK, ESTHER RENTROP AND C. S. THAELER 515
Bell System Technical Papers Not Published in This Journal 519
Recent Bell System Monographs 527
Contributors to This Issue 531
COPYRIGHT 1956 AMERICAN TELEPHONE AND TELEGRAPH COMPANY
THE BELL SYSTEM TECHNICAL JOURNAL
ADVISORY BOARD
F. K. K A P P E L, President Western Electric Company
M. J. KELLY, President, Bell Telephone Laboratories
E. J. McNEELY, Executive Vice President, American
Telephone and Telegraph Company
EDITORIAL COMMITTEE
B. MCMILLAN, Chairman
A. J. BUSCH H. R. HUNTLEY
A. C. DICKIBSON F. R. LACK
R. L. DIETZOLD J. R. PIERCE
K. E. GOULD H. V. SCHMIDT
E. I. GREEN C. ESCHOOLEY
R. K. HON AM AN G. N. THAYER
ED ITORI AL STAFF
J. D. TEBO, Editor
M. E. s T R I E B Y, Managing Editor
R. L. SHEPHERD, Production Editor
THE BELL SYSTEM TECHNICAL JOURNAL is published six times
a year by the American Telephone and Telegraph Company, 195 Broadway,
New York 7, N. Y. Qeo F. Craig, President; S. Whitney Landon, Secretary;
John J. Scanlon, Treasurer. Subscriptions are accepted at $3.00 per year.
Single copies are 75 cents each. The foreign postage is 65 cents per year or 11
cents per copy. Printed in U. S. A.
THE BELL SYSTEM
TECHNICAL JOURNAL
VOLUME XXXV MARCH 1956 number 2
Copyright 1958, American Telephone and Telegraph Company
An Experimental Remote Controlled
Line Concentrator
By. A. E. JOEL, JR.
(Manuscript received June 30, 1955)
Concentration, which is the process of connecting a number of telephone
lines to a smaller number of switching paths, has always been a funda?nental
function in switching systems. By performing this function remotely from
the central office, a new balance between outside plant and switching costs
may be obtained which shows promise of providing service more economi-
cally in some situations.
The broad concept of remote line concentrators is not new. However, its
solution with the new devices and techniques now available has made the
possibilities of decentralization of the means for switching telephone con-
nections very promising.
Three models of an experimental equipment have been designed and con-
structed for service. The models have included equipment to enable the evalua-
tion of new procedures required by the introduction of remote line concentra-
tors into the telephone plant. The paper discusses the philosophy, devices,
and techniques.
CONTENTS
1 . Introduction 250
2. Objectives 251
3. New Devices Emploj^ed 252
4. New Techniques Emploved 254
5. Switching Plan ". 257
249
250 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
6. Basic Circuits 261
a. Diode Gates 261
b. Transistor Bistable Circuit 262
c. Transistor Pulse Amplifier 263
d. Transistor Ring Counter 264
e. Crosspoint Operating Circuit 266
f . Crosspoint Relay Circuit 267
g. Pulse Signalling Circuit 268
h. Power Supply 269
7. Concentrator Operation 270
a.Line Scanning 270
b. Line Selection 272
c. Crosspoint Operation and Check 273
8. Central Office Circuits 274
a. Scanner Pulse Generator 279
b. Originating Call Detection and Line Number Registration 280
c. Line Selection 282
d. Trunk Selection and Identification 284
9. Field Trials 286
10. Miscellaneous Features of Trial Equipment 287
a. Traffic Recorder, b. Line Condition Tester 288
c. Simulator, d. Service Observing 290
e. Service Denial, f . Pulse Display Circuit 291
1. INTRODUCTION
The equipment which provides for the switching of telephone connec-
tions has ahvays been located in what have been commonly called "cen-
tral offices". These offices provide a means for the accumulation of all
switching equipment required to handle the telephone needs of a com-
munity or a section of the community. The telephone building in which
one or more central offices are located is sometimes referred to as the
"wire center" because, like the spokes of a wheel, the wires which serve
local telephones radiate in all directions to the telephones of the
community.
A new development, made possible largely by the application of de-
vices and techniques new to the telephone switching field, has recently
been tried out in the telephone plant and promises to change much of .
the present conception of "central" offices and "wire" centers. It is
known as a "line concentrator" and provides a means for reducing the
amount of outside plant cables, poles, etc., serving a telephone central
office by dispersing the switching equipment in the outside plant. It is
not a new concept to reduce outside plant by bringing the switching
equipment closer to the telephone customer but the technical difficulties
of maintaining complex switching equipment and the cost of controlling"
such equipment at a distance have in the past been formidable obstacles
to the development of line concentrators. With the invention of low
power, small-sized, long-life devices such as transistors, gas tubes, and
sealed relays, and their application to line concentrators, and with the
development of new local switching systems with greater flcxibilit}', it
has been possible to make the progress described herein.
REMOTE CONTROLLED LINE CONCENTRATOR 251
2. OBJECTIVES
Within the telephone offices the first switching equipment through
which dial lines originate calls concentrates the traffic to the remaining
equipment which is engineered to handle the peak busy hour load with
the appropriate grade of service.^ This concentration stage is different for
different switching systems. In the step-by-step system^ it is the line
' finder, and in the crossbar systems it is the primary line switch.^ Pro-
1 posals for the application of remote line concentrators in the step-by-
i step system date back over 50 years/ Continuing studies over the years
have not indicated that any appreciable savings could be realized when
such equipment is used within the local area served by a switching center.
When telephone customers move from one location to another within
a local service area, it is desirable to retain the same telephone numbers.
The step-by-step switching system in general is a unilateral arrangement
where each line has two appearances in the switching equipment, one
for originating call concentration (the line finder) and one for selection
of the line on terminating calls (the connector) . The connector fixes the
line number and telephone numbers cannot be readily reassigned when
moving these switching stages to out-of-office locations.
Common-control systems^ have been designed with flexibility so that
the line number assignments on the switching equipment are independ-
ent of the telephone numbers. Furthermore, the first switching stage
in the office is bilateral, handling both originating and terminating calls
through the same facilities. The most recent common-control switching
system in use in the Bell System, the No. 5 crossbar,^ has the further
advantage of universal control circuitry for handling originating and
terminating calls through the line switches. For these reasons, the No.
5 crossbar system was chosen for the first attempt to employ new tech-
niques of achieving an economical remote line concentrator.
A number of assumptions were made in setting the design require-
ments. Some of these are influenced by the characteristics of the No. 5
crossbar system. These assumptions are as follows:
1. No change in customer station apparatus. Standard dial telephones
to be used with present impedance levels, transmission characteristics,
dial pulsing, party identification, superimposed ac-dc ringing,^ and sig-
naling and talking ranges.
2. Individual and two-party (full or semi-selective ringing) stations
to be served but not coin or PBX lines.
3. Low cost could best be obtained by minimizing the per line
equipment in the central office. AMA^ charging facilities could be used
but to avoid per station equipment in the central office no message reg-
ister operation would be provided.
252 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
4. Each concentrator would serve up to 50 lines with the central office
control circuits common to a number of concentrators. (Experimental
equipment described herein was designed for 60 lines to provide addi-
tional facilities for field trial purposes.) No extensive change would be
made in central office equipment not associated with the line switches
nor should concentrator design decrease call carrying capacities of exist-
ing central office equipment.
5. To provide data to evaluate service performance, automatic traffic
recording facilities to be integrated with the design.
6. Remote equipment designed for pole or wall mounting as an addi-
tion to existing outside plant. Therefore, terminal distribution facilities
would not be provided in the same cabinet.
7. Power to be supplied from the central office to insure continuity
of telephone service in the event of a local power failure.
8. Concentrators to operate over existing types of exchange area fa-
cilities without change and with no decrease in station to central office
service range.
9. Maintenance effort to be facilitated by plug-in unit design using
the most reliable devices obtainable.
3. NEW DEVICES EMPLOYED
»!
I
Numerous products of research and development were available for
this new approach. Only those chosen will be described.
For the switching or "crosspoint" element itself, the sealed reed switch
was chosen, primarily because of its imperviousness to dirt.* A short coil
magnet with magnetic shield for increasing sensitivity of the reed
switches were used to form a relay per crosspoint (see Fig. 1).
A number of switching applications^ '^^ for crosspoint control using
small gas diodes have been proposed by E. Bruce of our Switching Re-
search Department. They are particularly advantageous when used in
an "end marking" arrangement with reed relay crosspoints. Also, these
diodes have long life and are low in cost. One gas diode is employed for
operating each crosspoint (see Fig. 6). Its breakdown voltage is 125v ±
lOv, A different tube is used in the concentrator for detecting marking
potentials when termination occurs. Its breakdown potential is lOOv ±
lOv. One of these tubes is used on each connection.
Signaling between the remote concentrator and the central office con-
trol circuits is performed on a sequential basis with pulses indicative of
the various line conditions being transmitted at a 500 cycle rate. This
frequency encounters relatively low attenuation on existing exchange
area wire facilities and j^et is high enough to transmit and receive in-
formation at a rate which will not decrease call carrjdng capacitj^ of the
REMOTE CONTROLLED LINE CONCENTRATOR
253
Fig. 1 — Reed switch relay.
central office equipment. To accomplish this signaling and to process the
information economically transistors appear most promising.
Germanium alloy junction transistors were chosen because of their
; improved characteristics, reliability, low power requirements, and mar-
gins, particularly when used to operate with relays.^^ Both N-P-N and
P-N-P transistors are used. High temperature characteristics are par-
ticularly important because of the ambient conditions which obtain on
pole mounted equipment. As the trials of this equipment have progressed,
254 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
Table I— Transistor Characteristics
Code No.
Type and Filling
Alpha
Max. Ico at 28V
and 65°C
Emitter Zener
Voltage at 20^=1
M1868
M1887
p-n-p Oxygen
n-p-n Vacuum
0.9-1.0
0.5- .75
150 Ma
100 Ma
>735
>735
considerable progress has been made in improving transistors of thi.s
type. Table I summarizes the characteristics of these transistors.
For directing and analyzing the pulses, the control employs semicon-
ductor diode gate circuits." The semiconductor diodes used in these
circuits are of the silicon alloy junction type,^^ Except for a few diode.s
operating in the gas tube circuits most diodes have a breakdown voltage
requirement of 27v, a minimum forward current of 15 ma at 2v and a
maximum reverse current at 22v of 2 X 10^^ amp.
4. new techniques employed
The concentrator represents the first field application in Bell System
telephone switching systems which departs from current practices and
techniques. These include:
Fig. 2 — Transistor packages, (a) Diode unit, (b) Transistor counter, (c)
Transistor amplifiers and bi-stable circuits, (d) Five trunk unit.
REMOTE CONTROLLED LINE CONCENTRATOR 255
1. High speed pulsing (500 pulses per second) of information between
switching units.
2. The use of plug-in packages employing printed wiring and encap-
sulation. (Fig. 2 shows a representative group of these units.)
3. Line scanning for supervision with a passive line circuit. In present
systems each line is equipped with a relay circuit for detecting call orig-
inations (service requests) and another relay (or switch magnet) for
indicating the busy or idle condition of the line, as shown in Fig. 3(a).
The line concentrator utilizes a circuit consisting of resistors and semi-
conductor diodes in pulse gates to provide these same indications. This
circuit is shown in Fig. 3(b). Its operation is described later. The pulses
for each line appear at a different time with respect to one another.
These pulses are said to represent "time slots." Thus a different line is
examined each .002 second for a total cycle time (for 60 lines) of .120
second. This process is known as "line scanning" and the portion of the
circuit which produces these pulses is known as the scanner. Each of the
circuits perform the same functions, viz., to indicate to the central office
equipment when the customer originates a call and for terminating calls
to indicate if the line is busy.
4. The lines are divided for control and identification purposes into
twelve groups of five lines each. Each group of five lines has a different
pattern of access to the trunks which connect to the central office. The
ten trunks to the central office are divided into two groups as shown in
Fig. 4. One trunk group, called the random access group, is arranged in
a random multiple fashion, so that each of these trunks is available to
approximately one-half of the lines. The other group, consisting of two
trunks, is available to all lines and is therefore called the full access
group. The control circuitry is arranged to first select a trunk of the
random access group which is idle and available to the particular line to
which a connection is to be made. If all of the trunks of this random ac-
cess group are busy to a line to which a connection is desired, an attempt
is then made to select a trunk of the full access group. The preference
order for selecting cross-points in the random access group is different
for each line group, as shown in the table on Fig. 4. By this means, each
trunk serves a number of lines on a different priority basis. Random ac-
cess is used to reduce by 40 per cent the number of individual reed relay
crosspoints which would otherwise be needed to maintain the quality
of service desired, as indicated by a theory presented some years ago.^^
5. Built-in magnetic tape means for recording usage data and making
call delay measurements. The gathering of this data is greatly facilitated
by the line scanning technique.
256
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
CROSSBAR CROSSPOINT
OR
SWITCH CONTACTS
-^
TO LINE
-^
TO OTHER
CENTRAL OFFICE
EQUIPMENT
9 9
r
^
LR
■^f-
CO
c
HI
"H
1_
(a)
■:l
LINE BUSY
SERVICE
REQUEST
I + 5V
CROSSPOINT
■^
TO LINE
-^
TO
CENTRAL
OFFICE
^4-
-X
-16V
-16 VOLTS -NORMAL
(RECEIVER ON HOOK)
-3 VOLTS -AWAITING SERVICE
(RECEIVER OFF HOOK)
-16 VOLTS -CROSSPOINT CLOSED
(RECEIVER OFF HOOK)
S\.
-¥^
-16 V
^
LINE BUSY
+ 15 VOLT
TIME SLOT PULSE
FROM SCANNER
GATE
SERVICE
REQUEST
Fig. 3 — (a) Relay line circuit, (b) Passive line circuit.
REMOTE CONTROLLED LINE CONCENTRATOR
257
5. SWITCHING PLAN
The plan for serving lines directly terminating in a No. 5 Crossbar office
is shown in Fig. 5(a). Each line has access through a primary line switch
to 10 line links. The line links couple the primary and secondary switches
together so that each line has access to all of the 100 junctors to the trunk
link switching stage. Each primary line switch group accommodates
from 19 to 59 lines (one line terminal being reserved for no-test calls).
A line link frame contains 10 groups of primary line switches.^*
. The remote concentrator plan merely extends these line links as trunks
to the remote location. However, an extra crossbar switching stage is
introduced in the central office to connect the links to the secondary line
switches with the concentrator trunks as shown in Fig. 5(b). Since each
line does not have full access to the trunks, the path chosen by the marker
to complete calls through the trunk link frame may then be independent
of the selection of a concentrator trunk with access to the line. This
arrangement minimizes call blocking, simplifies the selection of a matched
path by the marker, and the additional crossbar switch hold magnet
serves also as a supervisory relay to initiate the transmission of disconnect
signals over the trunk.
In addition to the 10 concentrator trunks used for talking paths, 2
additional cable pairs are provided from each concentrator to the central
office for signaling and power supply purposes. The use of these two pairs
of control conductors is described in detail in Section 6g.
The concentrator acts as a slave unit under complete control of the
central office. The line busy and service request signals originate at the
LINE
60 LINES
I
o.-»-o
0
5
9
7 '^
/ ^
/ ■v
/
p, ■^
i'
\.
^
V
•y
\
/ s
f
\
^
\
,• \
'^
^
1 >
f
< >
1 2 3
5 6
8 9 10 11
Fig 4. — Concentrator trunk
to line crosspoint pattern and
preference order
CONCENTRATOR
TRUNKS
9
9
9
9
9
9
9
9
9
9
9
9
8
8
8
8
8
8
8
8
8
8
8
8
6
0
5
4
7
5
3
1
4
7
2
1
7
3
1
5
2
0
6
4
6
5
0
3
1
7
2
3
6
2
4
0
0
6
3
5
0
4
6
2
3
7
1
6
2
4
1
7
1
5 6
8
VERTICAL GROUPS OF FIVE LINES EACH "
ORDER OF PREFERENCE
GAS TUBE REED -RELAY
CROSS POINTS
10 11
258
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
49
LINES
TEN GROUPS
OF LINES
49
LINES I
CENTRAL OFFICE
LINE LINK FRAME
LINE SW
1
CON-
NECTOR
1
1
1
—
-- 1
1
CON-
NECTOR
I
TO MARKER
TRUNK
LINK
FRAME
Fig. 5(a) — No. 5 crossbar system subscriber lines connected to line link frame.
60
LINES
60
LINES
60
0 <?
10
CONTROL
CE^4TRAL OFFICE
TEN CONCENTRATOR
, TRUNKS
I
JL
TWO CONTROL PAIRS
60
0 0
10
TEN POLE-
MOUNTED
^CONCENTRATOR
UNITS AT
DIFFERENT
LOCATIONS
CONTROL
TEN CONCENTRATOR
TRUNKS
TWO CONTROL PAIRS
CONCENTRATOR
TRUNK SW JUNCTOR
SW
10
9 C>
TRUNK
LINK
FRAME
TO MARKER
CONCENTRATOR LINE LINK
FRAME
Fig. 5(b) — No. 5 crossbar system subscriber lines connected to remote line
concentrators.
REMOTE CONTROLLED LINE CONCENTRATOR
259
Fig. 6 — Line unit construction.
concentrator only in response to a pulse in the associated time slot or
when a crosspoint operates (a line busy pulse is generated under this
condition as a crosspoint closure check). The control circuit in the
central office is designed to serve 10 remote line concentrators connected
to a single line link frame. In this way the marker deals with a concen-
trator line link frame as it would with a regular line link frame and the
marker modifications are minimized.
The traffic loading of the concentrator is accomplished by fixing the
260
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
Fig. 7(a) — Line unit.
number of trunks at 10 and equipping or reassigning lines as needed to
obtain the trunk loading for the desired grade of service. The six cross-
points, the passive line circuit and scanner gates individual to each line
are packaged in one plug-in unit to facilitate administration. The cross-
points are placed on a printed wiring board together with a comb of plug
contacts as shown in Fig. 6. The entire unit is then dipped in rubber and
encapsulated in epoxy resin, as shown in Fig. 7(a).
This portion of the unit is extremely reliable and therefore it may be
considered as expendable, should a rare case of trouble occur. The passive
line circuit and scanner gate circuit elements are mounted on a smaller
second printed wiring plate (known as the "line scanner" plate, see Fig.
7(b) which fits into a recess in the top of the encapsulated line unit. Cir-
Fig. 7(b) — Scanner plate of the line unit shown in Fig. 7 (a).
REMOTE CONTROLLED LINE CONCENTRATOR
261
cuit connection between printed wiring plates is through pins which ap-
pear in the recess and to which the smaller plate is soldered.
6. BASIC CIRCUITS
a. Diode Gates
All high speed signaling is on a pulse basis. Each pulse is positive and
approximately 15 volts in amplitude. There is one basic type of diode
gate circuit used in this equipment. By using the two resistors, one con-
denser and one silicon alloy junction diode in the gate configuration
shown in Fig. 8, the equivalents of opened or closed contacts in relay
circuits are obtained. These configurations are known respectively as
enabling and inhibiting gates and are shown with their relay equivalents
ill Figs. 8(a) and 8(b).
In the enabling gate the diode is normally back biased by more than
the pulse voltage. Therefore pulses are not transmitted. To enable or
INPUT
ENABLING GATE CIRCUIT
CI
OUTPUT
(a)
ENABLING GATE SYMBOL
INPUT
OUTPUT
CONTROL
EQUIVALENT RELAY CIRCUIT
OUTPUT
INPUT f
CONTROL
CHli^
INPUT
INHIBITING GATE CIRCUIT
Cl
OUTPUT
INHIBITING GATE SYMBOL
INPUT
OUTPUT
CONTROL
EQUIVALENT RELAY CIRCUIT
OUTPUT
DhUHl
Fig. 8 — Gates and relay equivalents.
262 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
open the gate the back bias is reduced to a small reverse voltage which is
more than overcome by the signal pulse amplitude of the pulse. The
pulse thus forward biases the diode and is transmitted to the output.
The inhibiting gate has its diode normally in the conducting state so
that a pulse is readily transmitted from input to output. When the bias
is changed the diode is heavily back biased so that the pulse amplitude
is insufficient to overcome this bias.
The elements of 12 gates are mounted on a single printed wiring board
w4th plug-in terminals and a metal enclosure as shown in Fig. 2(a). All
elements are mounted in one side of the board so that the opposite side
may be solder dipped. After soldering the entire unit (except the plug)
is dipped in a silicone varnish for moisture protection.
b. Transistor Bistable Circuit
Transistors are inherently well adapted to switching circuits using but
two states, on (saturated) or off.^^ In these circuits with a current gain
greater than unity a negative resistance collector characteristic can be
obtained which will enable the transistor to remain locked in its conduct-
ing state (high collector current flowing) until turned off (no collector
current) by an unlocking pulse. At the time the concentrator develop-
ment started only point contact transistors were available in quantity.
Point contact transistors have inherently high current gains (>1) but
the collector current flowing when in the normal or unlocked condition
(Ico) was so great that at high ambient temperatures a relay once op-
erated in the collector circuit would not release.
Junction transistors are capable of a much greater ratio of on to off
current in the collector circuit. Furthermore their characteristics are
amenable to theoretical design consideration.^^ However, the alpha of a
simple junction transitor is less than unity. To utilize them as one would |
a point contact transitor in a negative resistance switching circuit, a
combination of n-p-n and p-n-p junction transistors may be employed, i
see Fig. 9(b). Two transistors combined in this manner constitute a '
"hooked junction conjugate pairs." This form of bi-stable circuit was j
used because it requires fewer components and uses less power than an
Eccles-Jordan bistable circuit arrangement. It has the disadvantage of a
single output but this was not found to be a shortcoming in the design
of circuits employing pulse gates of the type described. In what follows
the electrodes of the transistor will be considered as their equivalents
shown in Fig. 9(b).
The basic bi-stable circuit employed is shown in Fig. 10. The set
REMOTE CONTROLLED LINE CONCENTRATOR
263
EMITTER
COLLECTOR
EMITTER
n-p-n
COLLECTOR
BASE
fa)
POINT CONTACT
TRANSISTOR
Ic
BASE
(b)
CONJUGATE PAIR
ALLOY JUNCTION
TRANSISTORS
C _
0C> 1
Fig. 9 — Point contact versus hooked conjugate pair.
pulse is fed into the emitter (of the pair) causing the emitter diode to
conduct. The base potential is increased thus increasing the current
flowing in the collector circuit. When the input pulse is turned off the
base is left at about —2 volts thus maintaining the emitter diode con-
( lucting and continuing the increased current flow in the collector circuit.
The diode in the collector circuit prevents the collector from going
positive and thereby limits the current in the collector circuit. To reset,
a positive pulse is fed into the base through a pulse gate. The driving of
tlie base positive returns the transistor pair to the off condition.
c. Transistor Pulse Amplifier
This circuit (Fig. 11) is formed by making a bi-stable self resetting
circuit. It is used to produce a pulse of fixed duration in response to a
TRANSISTORS
p-n-p
SET
RESET
I-5V
-I6V
F/F
Fig. 10 — Transistor bi-stable circuit.
264
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
pulse of variable width (within limits) on the input. Normally the emitter
is held slightly negative with respect to the base. The potential difference
determines the sensitivity of the amplifier. When a positive input pulse
is received, the emitter diode conducts causing an increase in collector
current. The change in bias of the diode in the emitter circuit permits
it to conduct and charge the condenser. With the removal of the input
pulse the discharge of the condenser holds the transistor pair on. The
time constant of the circuit determines the on time. When the emitter
potential falls below the base potential, the transistor pair is turned off.
The amplifiers and bi-stable circuits or flip-flops, >as they are called
more frequently, are mounted together in plug-in packages. Each pack-
age contains 8 basic circuits divided 7-1, 6-2, or 2-6, between amplifiers
and fhp-flops. Fig. 2(c) shows one of these packages. They are smaller
than the gate or line unit packages, having only 28 terminals instead of
42.
The transistors for the field trial model w^ere plugged into small hear-
ing aid sockets mounted on the printed wiring boards. For a production
model it w^ould be expected that the transistors w^ould be soldered in.
d. Transistor Ring Counter
By combining bi-stable transistor and diode pulse gate circuits to-
gether in the manner shown in Fig. 12 a ring counter may be made, with
INPUT
p-n-p
^w
^vW-"
I
+ 5V
OUTPUT
-16 V
INPUT
OUTPUT
Fig. 11 — Transistor pulse amplifier.
REMOTE CONTROLLED LINE CONCENTRATOR
265
COUNT
INPUT
lie
STAGE NUMBER
3
NOTE:
LEADS A-0 TO A-4
ARE OUTPUT LEADS
OF RESPECTIVE STAGES
1 I I \ r
s 's 's 's 's
Fig. 12 — Ring counter schematic.
a bi-stable circuit per stage. The enabling gate for a stage is controlled
by the preceding stage allowing it to be set by an input advance pulse.
The output signal from a stage is fed back to the preceding stage to turn
it off. An additional diode is connected to the base of each stage for re-
setting when returning the counter to a fixed reference stage.
A basic package of 5 ring counter stages is made up in the same frame-
work and with the same size plug as the flip-flop and amplifier packages,
see Fig. 2(b). A four stage ring counter is also used and is the same
package with the components for one stage omitted. The input and out-
put terminals of all stages are available on the plug terminals so that
the stages may be connected in any combination and form rings of more
than 5 stages. The reset lead is connected to all but the one stage which
is considered the first or normal stage.
Other transistor circuits such as binary counters and square wave
generators are used in small quantity in the central office equipment.
They will not be described.
266 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
CONCENTRATOR
LINE BUSY
CENTRAL OFFICE
TO ALL CROSSPOINTS
/ SERVED BY TRUNK
+ 130 V
VG
VF
I
L..1..
/
TO ALL CROSSPOINTS
FOR SAME LINE
SELECTION
FROM
" CENTRAL
OFFICE
i-65V
I + 100V
Fig. 13 — Crosspoint operating circuit.
e. Crosspoint Operating Circuit
The crosspoint consists of a reed relay with 4 reed switches and a gas
diode (Fig. 1). The selection of a crosspoint is accomplished by marking
with a negative potential ( — 65 volts) all crosspoints associated with a
line, and marking with a positive potential ( + 100 volts) all crosspoints
associated with a trunk (Fig. 13). The line is marked through a relay
circuit set by signals sent over the control pair from the central office.
The trunk is marked b}^ a simplex circuit connected through the break
contacts of the hold magnet of the crossbar switch associated with the
trunk in the central office. Only one crosspoint at a time is exposed to
165 volts which is necessary and sufficient to break down the gas diode
to its conducting state. The reed relay operates in series with the gas
diode. A contact on the relay shunts out the gas diode. When the marking-
potentials are removed the relay remains energized in a local 30-voll
circuit at the concentrator. The holding current is approximately 2.5 ma.
This circuit is designed so that ringing signals in the presence or ab-
sence of lino marks will not falsely fire a crosspoint diode. Furthonnoi'o,
REMOTE CONTROLLED LINE CONCENTRATOR
267
a line or trunk mark alone should not be able to fire a crosspoint diode
on a busy line or trunk.
When the crosspoint operates, a gate which has been inhibiting pulses
is forward biased by the —65 volt signal through the crosspoint relay
winding. The pulse which initiates the mark operations at the concentra-
tor then passes through the gate to return a line busy signal to the central
office over this control pairs which is interpreted as a crosspoint closure
check signal.
f. Crosspoint Release Circuit
The hold magnet of the central office crossbar switch operates, remov-
ing the +100- volt operate mark signal after the crosspoint check signal
is received. A slow release relay per trunk is operated directly by the
hold magnet. When the central office connection in the No. 5 crossbar
system releases, the hold magnet is released. As shown in Fig. 14, with the
hold magnet released and the slow release relay still operated, a — 130-
volt signal is applied in a simplex circuit to the trunk to break down a
gas tube provided in the trunk circuit at the concentrator. This tube in
CONCENTRATOR
CENTRAL OFFICE
TO ALL CROSSPOINTS
SERVED BY SAME TRUNK
130V I
Fig. 14 — Crosspoint release circuit.
268
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
breaking down shunts the local holding circuit of the crosspoint causing
it to release. The — 130-volt disconnect signal is applied during the
release time of the slow release relay which is long enough to insure the
release of the crosspoint relay at the concentrator.
The release circuit is individual to the trunk and independent of the
signal sent over the control pairs.
g. Pulse Signalling Circuits
To control the concentrator four distinct pulse signals are transmitted
from the central office. Two of these at times must be transmitted
simultaneously, bvit these and the other two are transmitted mutually
exclusively. In addition, service request and line busy signals are trans-
mitted from the concentrator to the central office. The two way trans-
mission of information is accomplished on each pair by sending signals in
each direction at different times and inhibiting the receipt of signals
when others are being transmitted.
To transmit four signals over two such pairs, both positive and nega-
CONTROL
PAIR NO. 1
VF
M
LB
D
SR
-16V
VG
CONTROL
PAIR NO. 2
16 V
M
CONCENTRATOR
AMPLIFIERS
I
CENTRAL OFFICE
AMPLIFIERS
PER CONCENTRATOR
Fig. 15. — Signal transmission circuit.
REMOTE CONTROLLED LINE CONCENTRATOR 269
tive pulses are employed. Diodes are placed in the legs of a center tapped
transformer, as shown in Fig. 15, to select the polarity of the trans-
mitted pulses. At the receiving end the desired polarity is detected by
taking the signal as a positive pulse from a properly poled winding of a
transformer. The amplifier, as described in Section 6c responds only to
positive pulses. If pulses of the same polarity are transmitted in the
other direction over the same pair, as for control pair No. 1, the outputs
of the receiving amplifier for the same polarity pulse are inhibited
whenever a pulse is transmitted.
As shown in Fig. 15, the service request and line busy signals are
transmitted from the concentrator to the central office over one pair of
conductors as positive and negative pulses respectivel3^ The trans-
mission of these pulses gates the outputs of two of the receiving ampli-
fiers at the concentrator to permit the receipt of the polarized signals
from the central office. This prevents the pulses from being used at the
sending end. A similar gating arrangement is used with respect to the
signals when sent over this control pair from the central office. The pulses
designated VG or RS never occur when a pulse designated SR or LB
is sent in the opposite direction. The transmission of the VF pulse over
control pair No. 2 is processed by the concentrator circuit and becomes
the SR or LB pulses. Li section 7 the purpose of these pulses is described.
The signaling range objective is 1,200 ohms over regular exchange
area cable including loaded facilities from sfation to central office.
h. Power Supply
Alternating current is supplied to the concentrator from a continuous
service bus in the central office. The power supply path is a phantom
circuit on the two control pairs as shown in Fig. 16. The power trans-
former has four secondary windings used for deriving from bridge
rectifiers four basic dc voltages. These voltages and their uses are as
fofiows: —16 volts (regulated) for transistor collector circuits and gate
biases, -|-5 volts (regulated) for transistor base biases, -|-30 volts (regu-
, lated) for crosspoints holding circuits and — 65 volts for the marking and
operating of the line crosspoints. For this latter function a reference to
the central office applied -flOO volt trunk mark is necessary. The refer-
ence ground for the concentrator is derived from ground applied to a
simplex circuit on the power supply phantom circuit. Series transistors
and shunt silicon diodes with fixed reference breakdown voltages are
I used to regulate dc voltages.
270 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
Total power consumption of the concentrator is between 5 and 8 watts
depending upon the number of connections being held.
7. CONCENTRATOR OPERATION
a. Line Scanning
The sixty lines are divided into 12 groups of 5 lines each. These group-
ings are designated VG and VF respectively corresponding to the
vertical group and file designations used in the No. 5 crossbar system.
Each concentrator corresponds to a horizontal group in that system.
To scan the lines two transistor ring counters, one of 12 stages and
one of 5 stages, are employed as shown in Fig. 17. These counters are
driven from pulses supplied from the central office control circuits and
only one stage in each is on at any one time. The steps and combinations
of these counters correspond to the group and file designation of a par-
ticular line. Each 0.002 second the five stage counter (VF) takes a
step and between the fifth and sixth pulse the r2-stage counter (VG)
is stepped. Thus the 5-stage counter receives 60 pulses or re-cycles 12
times in 120 milliseconds while the 12-stage counter cycles but once.
Each line is provided with a scanner gate. The collector output of each
each stage of the VG counter biases this gate to enable pulses which
are generated by the collector circuit of the 5-stage counter to pass on
-65V
+ 30V
+ SV
-I6V
115 V
AC
MOTOR
GENERATOR
TO
COMMERCIAL
AC
REGULATORS
Fig. 16 — Power supply transmission circuit.
REMOTE CONTROLLED LINE CONCENTRATOR
271
to the gate of the passive line circuit, Fig. 3(b). If the line is idle the
pulses are inhibited. If the receiver is off-hook requesting service (no
(•rosspoint closed) then the gate is enabled, the pulse passes to the service
request amplifier and back to the central office in the same time slot
as the pulse which stepped the VF counter. If the line has a receiver
off-hook and is connected to a trunk the pulse passes through a contact
of the crosspoint relay to the line busy amplifier and then to the central
office in the same time slot.
At the end of each complete cycle a reset pulse is sent from the central
office. This pulse instead of the VG pulse places the 12-stage counter in
its first position. It also repulses the 5 stage VF counter to its fifth stage
so that the next VF pulse will turn on its first stage to start the next
j cycle. The reset pulse insures that, in event of a lost pulse or defect in
a counter stage, the concentrator will attempt to give continuous ser-
\'ice without dependence on maintaining synchronism with the central
I office scanner pulse generator. Fig. 18(a) shows the normal sequence of
I line scanning pulses.
, When a service request pulse is generated, the central office circuits
t]
04
r
VF 5- STAGE
COUNTER
03
TO 10
INTERMEDIATE
GATES EACH
V
02
I
01
00
TO 5 GATES EACH
I
1 23456 789 10
I I I I I I I I I I
I I I I I I I I I I
VG 12-STAGE COUNTER
59\
58
57
56
55
GATE PER LINE
■ FEEDS PASSIVE
LINE CIRCUITS
/
VG
RESET
VF
FROM
CENTRAL
OFFICE
Fig. 17 — Diode matrix for scanning lines.
272 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
common to 10 concentrators interrupt the further transmission of the
vertical group pulse so that the line scanning is confined to the 5 lines
in the vertical group in which the call originated. In this way the cen-
tral office will receive a service request pulse at least every 0.010 sec as
a check that the call has not been abandoned while awaiting service.
Fig. 18(b) shows the detection of a call origination and the several
short scan cycles for abandoned call detection.
b. Line Selection
When the central office is ready to establish a connection at the con-
centrator a reset pulse is sent to return the counters to normal. In gen-
eral, the vertical group and vertical file pulses are sent simultaneously
to reduce holding time of the central office equipment and to minimize
marker delays caused by this operation. For this reason the VG and VF
pulses are each transmitted over different control pairs from the central
office. The same polarity is used.
On originating calls it is desirable to make one last check that the
call has not been abandoned, while on terminating calls it is necessary
L* 120MS >|
■M k-2MS I
PULSE '
012340123401234 0123401234
VF -
VG
LB
RS
J__l I I I I I I I I I I I I I I 1 I I I I 1 I L
1^ \1 ^
(a) REGULAR LINE SCANNING
VF
123401 23401 23401 2340123401
_l_l 1 I I I I I I I I I I I I I I I I I L_l I I I I
,5 ,6
VG 1 1 —
LB-
RS-
SR-
M-
(b) CALL ORIGINATION SERVICE REQUEST FROM LINE 6/3
12 3 0 1
I I I I I
VG-
LB
RS — 1>-
SR h
1° 1' 1^ |3 1^ 1^ 1^
jLi.
M -
H^-l^--
"7
RESULTS FROM CONC CONTROL RECEIVED 'OPERATE ""CROSSPOINT 'NORMAL SCANNING
CKT AT CENTRAL OFFICE ONLY IF CROSSPOINT CLOSURE IS RESUMED
RECEIVING FROM MKR VG , LINE 6/3 HAS INDICATION
VF, HG INFORMATION BECOME BUSY
(C) LINE SELECTION FOR LINE 6/3
Fig. 18 — Pulse sequences, (a) Regular, (b) Call origination, (c) Line selection.
REMOTE CONTROLLED LINE CONCENTRATOR 273
to determine if the line is busy or idle. These conditions are determined
in the same manner as described for line scanning since a service re-
quest condition would still prevail on the line if the call was not aban-
doned. If the line was busy, a line busy condition would be detected.
However to detect these conditions a VF pulse must be the last pulse
transmitted since the stepping of the VF counter generates the pulse
which is transmitted through an enabled line selection and passive
line circuit gates. Fig. 18(c) shows a typical line selection where the num-
ber of VF pulses is equal to or less than the number of VG pulses. In
all other cases there is no conflict and the sending of the last VF pulse
need not be delayed. On terminating calls, the line busy indication is
returned to the central office within 0.002 sec after the selection is com-
plete. During selections the central office circuits are gated to ignore
any extraneous service request or line busy pulses produced as a result
of steps of the VF counter prior to its last step.
c. Crosspoint Operation and Check
Associated with each concentrator transistor counter stage is a reed
relay. These relays are connected to the transistor collector circuits
through diodes of the counter stages when relay M operates. The con-
tacts of these reed relays are arranged in a selection circuit as shown
in Fig. 19 and apply the —65 volt mark potential to the crosspoint
relays of the selected line.
After a selection is made as described above a "mark" pulse is sent
from the central office. This pulse is transmitted as a pulse of a different
polarity over the same control pair as the VF pulses. The received
pulse after amplification actuates a transistor bistable circuit w^hich has
the M reed relay permanently connected in its collector circuit. The
bi-stable circuit holds the M relay operated during the crosspoint opera-
tion to maintain one VF and one VG relay operated, thereby applying
— 65 volts to mark and operate one of the 6 crosspoint relays of the
selected line as described in section 6e, and shown on Fig. 13.
The operation and locking of the crosspoint relay with the marking
potentials still applied enables a pulse gate associated with the holding
circuit of the crosspoint relays in each trunk circuit. The mark pulses
are sent out continuously. This does not affect the bi-stable transistor
circuit once it has triggered but the mark pulse is transmitted through
the enabled crosspoint closure check gate shown in Fig. 20 and back
to the central office as a line busy signal.
With the receipt of the crosspoint closure check signal the sending
274 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
of the mark pulses is stopped and a reset pulse is sent to the concentra-
tor to return the mark bi-stable circuit, counters and all operated selec-
tor relays to normal. The concentrator remains in this condition until
it is resynchronized with the regular line scanning cycle.
A complete functional schematic of the concentrator integrating the
circuits described above is shown in Fig. 21. Fig. 22(a) and (b) show an
experimental concentrator built for field tests.
8. CENTRAL OFFICE CIRCUITS
The central office circuits for controling one or more concentrators
are composed of wire spring relays as well as transistors, diode and reed
VG
RS
VF
M
-20V
-20 V
o-
VF-5 STAGE
COUNTER
r
-65V
n
04
03
02
00
6 RELAY I W-, wo w<- ,^, -o p
PACKAGE J '-|„p_„p_^_p-_-p-^Ui
TO CONTACTS OF 4
INTERMEDIATE RELAYS
6 RELAY
PACKAGE
TO CONTACTS OF 4 .
INTERMEDIATE RELAYS
n
L
59
n
58
i^
34 33 32 31 30 ,
29 28 27 26 25 I 5^
57 56 55
TO 4
INTERMEDIATE
RELAYS
' 0
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I I 2
b^'"
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8_
9
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cr
LU
h-
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RELAYS
P^ig. 19 — Line selection and marking.
I
REMOTE CONTROLLED LINE CONCENTRATOR
275
relay packages similar to those used in the concentrator. The reed
relays are energized by transistor bi-stable circuits in the same manner
as described in Section 7c. The reed relay contacts in turn operate wire
spring relays or send the dc signals directly to the regular No. 5 crossbar
marker and line link marker connector circuits.
Fig. 23 shows a block diagram of the central office circuits. A small
amount of circuitry is provided for each concentrator. It consists of the
following:
1. The trunk connecting crossbar switch and associated slow relays
for disconnect control.
2. The concentrator control triuik circuits and associated pulse ampli-
fiers.
3. An originating call detector to identify which concentrator among
the ten served by the frame is calling.
4. A multicontact relay to connect the circuits individual to each
concentrator with the common control circuits associated with the line
link frame and markers.
The circuits associated with more than one concentrator are blocked
out in the lower portion of Fig. 23. Much of this circuitry is similar to
the relay circuits now provided on regular line link frames in the No. 5
crossbar system.^ Only those portions of these blocks which employ the
new techniques will be covered in more detail. These portions consist
of the following:
1. The scanner pulse generator.
2. The originating line number register.
T
TO ALL TRUNK LINES
+ 30V
A/vV
U
j^Wv-
-65V
T
I
I
I
I
I
CONCENTRATOR
TRUNK
I
I
I
I
I
i
Fig. 20 — Crosspoint closure check.
aoidzio nvbiNBo oi
iinoaio ONnvNois via
276
Fig. 22(a) — Complete line concentrator unit.
r 5 -STAGE COUNTER
12 -STAGE COUNTER
-fO TRUNK CiftCUITS
AMPLIFIERS
RECTIFIERS
Fig. 22(b) — Identification of units within the line concentrator.
277
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REMOTE CONTROLLED LINE CONCENTRATOR
279
3. The line selection circuit.
4. The trunk identifier and selection relay circuits.
(For an understanding of how these frame circuits work through the line
(link marker connector and markers in the No. 5 system, the reader
should consult the references.)
The common central office circuits will be described first.
a. Scanner Pulse Generator
The scanner pulse generator, shown in Fig. 24, produces continuously
the combination of VG, VF and RS or reset pulses, described in connec-
tion with Fig. 18(a), required to drive the scanners for a number of
concentrators. The primary pulse source is a 1,000-cycle transistor
oscillator. This oscillator drives a transistor bi-stable circuit arranged
as a binary counter such that on each cycle of the oscillator output it
alternately assumes one of its states. Pulses produced by one state drive
a 5-stage counter. Pulses produced by the other state through gates
drive a 12-stage counter.
The pulses which drive the 5-stage counter are the same pulses which
are used for the VF pulses to drive scanners. Each time the first stage
of the 5-stage counter is on, a gate is opened to allow a pulse to drive
the 12-stage counter. The pulses which drive the 12-stage counter are
also the pulses used as the VG pulses for driving the scanners. They
are out of phase with the VF pulses.
When the last stage of the 12-stage counter is on, the gate which
r VFC
Fig. 24 — Scanner pulse generator.
280
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 195(5
transmits pulses to the 12-stage counter is closed and another gate is
opened which produces the reset pulse. The reset pulse is thereby trans-
mitted to the scanners in place of the first vertical group pulse. At the
same time the 5 and 12-stage counters in the scanner pulse generator
are reset to enable the starting of a new cycle.
In the central office control circuits, out of phase pulses on lead TP
similar to those which drive the VG counters at the concentrator are
used for various gating operations.
b. The Originating Call Detection and Line Number Registration
The originating call detector (Fig. 25) and the originating line num-
ber register (Fig. 26) together receive the information from the line
concentrator used to identify the number of the line making a service i
request. The receipt of the service request pulse from a concentrator i
in a particular time slot will set a transistor bi-stable circuit HGT of {
Fig. 25 associated with that concentrator if no other originating call is
being served by the frame circuits at* this time.
The originating line number register consists of a 5 and 12-stage
counter. These counters are normally driven through gates in syn-
chronism with the scanning counters at concentrators with pulses sup-
plied from the scanner pulse generator. When a service request pulse
is received from any of the concentrators served by a line link frame, a
pulse is sent to the originating line number register which operates a
bi-stable circuit over a lead RH in Fig. 26. This bi-stable circuit then
closes the gates through which the 5- and 12-stage counters are being
driven, and also closes a gate which prevents them from being reset.
TO TRAFFIC I
RECORDER I
TO ORIGINATING
CALL REGISTER
I TO CONCENTRATOR
I CONTROL TRUNK
Fig. 25 — Originating call detector.
EEMOTE CONTROLLED LINE CONCENTRATOR
281
In this way, the number of the line which originated a service request is
locked into these counters until the bi-stable circuit is restored to nor-
mal.
The HGT bi-stable circuit of Fig. 25 indicates which particular con-
centrator has originated a service request. A relay in the collector cir-
cuit has contacts which pass this information on to the other central
office control circuits to indicate the number of the concentrator on the
frame which is requesting service. This is the same as a horizontal group
on a regular line link frame and hence the horizontal group designation
is used to identify a concentrator.
With the operation of this relay, relays associated with the counters
of the originating line number register are operated. These relays indicate
to the other central office circuits the vertical file and vertical group
identification of the calling line. Contacts on the vertical group relays
are used to set a bi-stable circuit associated with lead RL of Fig. 25 each
time the scanner pulse generator generates a pulse corresponding to the
vertical file of the calling line number registered.
The operation of the HGT bi-stable circuit inhibits in the concentra-
tor control trunk circuit (Fig. 27) the transmission of further VG and
SRS
FROM
CONCENTRATOR
CONTROL
TRUNK CIRCUIT
RB
RH
RH
FROM
SCANNER
PULSE
GENERATOR
VF
VFO-4
VG
RS
1
*" 5-STAGE COUNTER ^
12-STAGE COUNTER
^ ^
Fig. 26 — Originating line number register.
282 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
reset pulses to the concentrator so that, as described in Section 7a,
only the VF counter continues to step once each 0.010 sec. So long as
the line continues to request service this service request pulse is gated
to reset the RL bi-stable circuit within the same time slot that it was
set. If, however, a request for service is abandoned the RL bi-stable cir-
cuit of Fig. 26 will remain on and permit a TP pulse from the scanner
pulse generator to reset the HGT bi-stable circuit which initiated the
service request action.
Whenever the RH bi-stable circuit of Fig. 26 is energized it closes a
gate over lead SRS for each concentrator to prevent any further service
request pulses from being recognized until the originating call which
has been registered is served. The resetting of the RH bi-stable circuit
occurs once the call has been served. When more than one line concen-
trator is being served it is possible that the HGT bi-stable circuit of
more than one concentrator will be set simultaneously as a result of
coincidence in service requests from correspondingly numbered lines in
these concentrators. The decision as to which concentrator is to be
served is left to the marker, as it would normally decide which horizontal
group to serve.
c. Line Selection
On all calls, originating and terminating, the marker transmits to the
frame circuits the complete identity of the line which it will serve. In
the case of originating calls it has received this information in the manner
described in Section 8b. In either case, it operates wire spring relays
VGO-U and VFO-4, which enable gates so that the information may be
stored in the 5- and 12-stage counters of the line selection circuit shown "
in Fig. 28.
The process of reading into the line selection counters starts when
selection information has been received by the actuation of the HGS
bi-stable circuit in the concentrator control trunk circuit of Fig. 27.
This action stops the regular transmission of scanner pulses if they
have not been stopped as a result of a call origination. At the same time
it enables gates for transmission of information from the line selection
circuit. Fig. 28.
The ST bi-stable circuit of the line selection circuit is also enabled
to start the process of setting the line selection counters. The next TP
pulse sets the Rl bi-stable circuit. This bi-stable circuit enables a gate
which permits the next TP pulse to set the counters and transmit a re-
set pulse to the concentrator through pulse amplifier RIA. At the same
time bi-stable circuit ST is reset to prevent the further read-in cr reset
\
REMOTE CONTROLLED LINE CONCENTRATOR
283
pulses and to permit pulses through amplifier OPA to start the out-
pulsing of line selections. These pulses pass to the VGP and VFP leads
as long as the VG and VF line selection counters have not reached
their first and last stages respectively. The output pulses to the con-
centrator are also fed into the drive leads of these counters so that, as
the counters in the concentrator are stepped up, the counters in the
central office line selection circuit are stepped down. When the first
stage of the VF counter goes on, the VF pulses are no longer transmitted
until the first stage of the VG counter goes on. This insures that a VF
pulse is the last to be transmitted. Also this pulse is not transmitted
until the other frame circuits have successfully completed selections of
an idle concentrator trunk. Then bi-stable circuit VFLD is energized,
TO ORIGINATING
CALL DETECTOR
I
VF-
FROM
VG U SCANNER
PULSE
GENERATOR
FROM LINE
[-SELECTION
CIRCUIT
Fig. 27 — Concentrator control trunk circuit.
284
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
producing, during its transition, the last VF pulse for transmission to
the concentrator.
d. Trunk Selection and. Identification
The process of selecting an idle concentrator trunk to which the line
has access utilizes familar relay circuit techniques.^^ This circuit, in
Fig. 29, will not be described in detail. One trunk selection relay, TS, is
operated indicating the preferred idle trunk serving a line in the particu-
lar vertical group being selected as indicated by the VG relay which
has been operated by the marker.
The TS4 and TS5 relays select trunks 8 and 9 which are available to
each line while the 4 trunks available to only half of the lines are selected
by relays TS0-TS3. The busy or idle condition of each trunk is indicated
by a contact on the hold magnet associated with each trunk through
TRUNK
SELECTION
COMPLETE T
VFLD
_l
O
cr
I-
z
Oh
^5
tr u
O cr
Z :
LU :
^!
o
o
o
t-
VFP
VGP_
RS
VFLI
VFL 2
0-1
5-STAGE COUNTER
VF4X -2V
VGO
y^
12-STAGE COUNTER
0-0
ST
OPA
R1A
ST
FROM SCANNER
PULSE GENERATOR I
TP
Fig. 28 — Line selection circuit.
REMOTE CONTROLLED LINE CONCENTRATOR
285
relay HG which operates on all originating and terminating calls to the
particular concentrator served by these trunks. The end chain relay
TC of the lockout trunk selection circuit^^ connects battery from the
SR relay windings of idle trunks to the windings of the TS relays to
permit one of the latter relays to operate and to steer circuits, not shown
on Fig. 29, to the hold magnet of the trunk and to the tip-and-ring con-
ductors of the trunk to apply the selection voltages shown on Figs. 13
and 14.
The path for operating the hold magnet originates in the marker.
The path looks like that which the marker uses on the line hold mag-
net when setting up a call on a regular line link frame. For this reason
and other similar reasons this concentrator line link frame concept has
been nicknamed the "fool-the-marker" scheme.
Should a hold magnet release while a new call is being served the
ground from the TC relaj^ normal or the TS relay winding holds relay
CONCENTRATOR TRUNK
SWITCH CROSSPOINTS
SR [
LINE LINK
NUMBER FROM
MARKER I
-48 V
Fig. 29 — Trunk selection and identification.
286 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
SR operated through its own contact until the new call has been set up.
This prevents interference of disconnect pulses applied to the trunk
when a selection is being made and insures that a disconnect pulse is
transmitted before the trunk is reused.
A characteristic of the No. 5 crossbar system is that the originating
connection to a call register including the line hold magnet is released
and a new connection, known as the "call back connection", is estab-
lished to connect the line to a trunk circuit after dialing is completed.
With concentrator operation the concentrator trunk switch connection
is released but the disconnect signal is not sent to the concentrator as
a result of holding the SR relay as described above. However, the marker
does not know to which trunk the call back connection is to be estab-
lished. For this reason the frame circuits include an identification proc-
ess for determining the number of the concentrator trunk to be used
on call back prior to the release of the originating register connection, i
Identification is accomplished by the marker transmitting to the
frame circuits the number of the link being used on the call. This in-
formation is already available in the No. 5 system. The link being used
is marked with —48 volts by a relay selecting tree^" to operate the TS
relay associated with the trunk to which the call back connection is to
be established. Relay CB (Fig. 29) is operated on this type of call in-
stead of relay HG. The circuits for reoperating the proper hold magnet
are already available on the TS relay which was operated, thereby rc-
selecting the trunk to which the customer is connected. The concen-
trator connection is not released when the hold magnet releases and
again the marker operates as it would on a regular line link frame call.
9. FIELD TRIALS
Three sets of the experimental equipment described here have been
constructed and placed in service in various locations. The equipment
for these trials is the forerunner of a design for production which will
incorporate device, circuit and equipment design changes based on the
trial experiences. Fig. 30 shows the cabinet mounted central office trial
equipment with the designation of appropriate parts.
For the field trials described, the line links on a particular horizontal
level of existing line link frames were extended to a separate cross-bar
switch provided for this purpose in the trial equipment. The regular line
link connector circuits were modified to work with the trial control
circuits whenever a call was originated or terminated on this level. N(i
lines were terminated in the regular primary line switches for this level.
REMOTE CONTROLLED LINE CONCENTRATOR
287
10. MISCELLANEOUS FEATURES OF TRIAL EQUIPMENT
There are a number of auxiliary circuits provided with the trial equip-
ment to aid in the solutions of problems brought about by the concepts
of concentrator service. One of the purposes of the trials was to deter-
mine the way in which the various traffic, plant and commercial ad-
CONCENTRATOR
TRUNK SWITCH
SERVICE OBSERVING
TEST CONTROL-]
SIMULATOR
TRUNK DISCONNECT
RELAYS
CONCENTRATOR
CONNECTOR RELAYS
FRAME RELAY
CIRCUITS
SERVICE DENIAL
FRAME ELECTRONIC
CIRCUITS
POWER SUPPLY
LINE CONDITION
TESTER
Fig. 30 — Trial central office equipment.
288 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
ministrative functions could be economically performed when concen-
trators become common telephone plant facilities. The more important
of these miscellaneous features are discussed under the following head-
ings :
a. Traffic Recording
J
To measure the amount and characteristics of the traffic handled by
the concentrator a magnetic tape recorder, Fig. 31, was provided for
each trial. The number of the lines and trunks in use each 15 seconds
during programmed periods of each day were recorded in coded form
with polarized pulses on the 3-track magnetic tape moving at a speed of
1}/2" per second. Combinations of these pulses designate trunks busy on
intra-concentrator connections and reverting calls.
The line busy indications were derived directly from the line busy
information received during regular scanning at the concentrator. Dur-
ing one cycle in each 15 seconds new service requests were delayed to
insure that a complete scan cycle would be recorded. Terminating calls
were not delayed since marker holding time is involved. Trunk condi-
tions are derived for a trunk scanner provided in the recorder.
In addition to recording the line and trunk usage, recordings were
made on the tape for each service request detected during a programmed
period to measure the speed with which each call received dial tone
and the manner in which the call was served. In this type of operation
the length of the recording for each request made at a tape speed of
only \i!' per second is a measure of service delay time.
As may be observed from Fig. 31 the traffic recorder equipment was
built with vacuum tubes and hence required a rather large power supply.
It is expected that a transistorized version of this traffic recorder serv-
ing all concentrators in a central office will be included in the standard
model of the line concentrator equipment. With this equipment, traffic
engineers will know more precisely the degree to which each concentra--
tor may be loaded and hence insure maximum utilization of the concen-
trator equipment.
b. Line Condition Tester
It has been a practice in more modern central office equipment to
include automatic line testing equipment.^^ An attempt has been made
to include similar features with the concentrator trial equipment. The
line condition tester (see Fig. 30) provides a means for automatically
connecting a test circuit to each line in turn once a test cycle has been
I
REMOTE CONTROLLED LINE CONCENTRATOR
289
! , P ] 'f
^ u
POWER SUPPLIES
AND
PROGRAMMER
I
Fig. 31 — Traffic recorder.
290 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
manually initiated. This test is set up on the basis of the known concen-
trator passive line circuit capabilities. Should a line fail to pass this
test, the test circuit stops its progress and brings in an alarm to summon
central office maintenance personnel. The facilities of the line tester are
also used to establish, under manual control, calls to individual lines as
required to carry out routine tests.
c. Simulator
As the central office sends out scanner control pulses either no signal,
a line busy or service request pulse is returned to the central office in
each time slot. The simulator test equipment, shown in Fig. 30, was
designed to place pulses in a specific time slot to simulate a line under
test at the concentrator.
In addition to transmitting the equivalent of concentrator output
pulses the simulator can receive the regular line selection pulses trans-
mitted to the concentrator for purposes of checking central office opera-
tions. It is possible by combined use of the line tester and simulator to
observe the operation of the concentrator and to determine the probable
cause when a fault occurs.
d. Service Observing
The removal of the line terminals from the central office poses a num-
ber of problems in conjunction with the administration of central office
equipment. One of these is service observing.
To maintain a check on the quality of service being rendered by the
telephone system, service observing taps are made periodically on tele-
phone lines. This is normally done by placing special connector shoes
on line terminations in the central office.
To place such shoes at the remote concentrator point would lead to
administrative difficulties and added expense. Therefore, a method was
devised to permit service observing equipment to be connected to con-
centrator trunks on calls from specific lines which were to be observed.
This mcithod consisted of manual switches on which were set the number
of the line to be observed in terms of vertical group and vertical file.
Whenever this line originated a call and the call could be placed over the
first preferred trunk, automatic connection was made to the service ob-
serving desk in the same manner as would occur for a line terminated
directly in the central office.
In addition, facilities were provided for trying a new service observ-
ing technique where calls originating over a particular concentrator
REMOTE CONTROLLED LINE CONCENTRATOR 291
trunk would be observed without knowledge of the originating line num-
ber. For this purpose a regular line observing shoe was connected to
one of the ten concentrator trunk switch verticals in the trial equipment
and from here connected to the service observing desk in the usual
manner.
The basic service observing requirements in connection with line
concentrator operation have not as yet been fully determined. How-
ever, it appears at this time that the trunk observing arrangement may
be preferable.
e. Service Denial
In most systems denial of originating service for non-payment of
telephone service charges, for trouble interception and for permanent
signals caused by cable failures or prolonged receiver-off-hook conditions
may be treated by the plant forces at the line terminals or by blocking
the line relay. To avoid concentrator visits and to enable the prompt
clearing of trouble conditions which tie up concentrator trunks, a ser-
vice denial feature has been included in the design of the central office
circuits.
This feature consists of a patch-panel with special gate cords which
respond to particular time slots and inhibit service request signals pro-
duced by a concentrator during this period. In this way service requests
can be ignored and prevent originating call service on particular lines
until a trouble locating or other administrative procedure has been
invoked.
f. Display Circuit
A special electronic switch was developed for an oscilloscope. This
arrangement permited the positioning of line busy and service request
pulses in fixed positions representing each of the 60 lines served. Line
busy pulses were shown as positive and service request pulses as negative.
This plug connected portable aid, see Fig. 32, was useful in tracing calls
and identifying lines to which service may be denied, due to the existence
of permanent signals.
Other circuits and features, too detailed to be covered in this paper,
have been designed and used in the field trials of remote line concen-
trators. Much has been learned from the construction and use of this
equipment which will aid in making the production design smaller,
lighter, economical, serviceable and reliable.
Results from the field trials have encouraged the prompt undertaking
292 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
Fig. 32 — Pulse display oscilloscope.
REMOTE CONTROLLED LINE CONCENTRATOR 293
of development of a remote line concentrator for quantity production.
The cost of remote line concentrator equipment will determine the ul-
timate demand. In the meantime, an effort is being made to take advan-
tage of the field trial experiences to reduce costs commensurate with
insuring reliable service.
The author wishes to express his appreciation to his many colleagues
at Bell Telephone Laboratories whose patience and hard work have
been responsible for this new adventure in exploratory switching de-
velopment. An article on line concentrators would not be complete
without mention of C. E. Brooks who has encouraged this development
and under whose direction the engineering studies were made.
BIBLIOGRAPHY
1. E. C. Molina, The Theory of Probabilities Applied to Telephone Trunking
Problems, B.S.T.J., 1, pp. 69-81, Nov., 1922.
2. Strowger Step-bv-Step System, Chapter 3, Vol. 3, Telephone Theory and
Practice by K.B. Miller. McGraw-Hill 1933.
3. F. A. Korn and J. G. Ferguson, Number 5 Crossbar Dial Telephone Switching
System, Elec. Engg., 69, pp. 679-684, Aug., 1950.
4. U.S. Patent 1,125,965.
5. O. Myers, Common Control Telephone Switching Systems, B.S.T.J., 31, pp.
1086-1120, Nov., 1952.
6. L. J. Stacy, Calling Subscribers to the Telephone, Bell Labs. Record, 8, pp.
113-119, Nov., 1929.
7. J. Meszar, Fundamentals of the Automatic Telephone Message Accounting
System, A. I. E. E. Trans., 69, pp. 255-268, (Part 1), 1950.
8. O. M. Hovgaard and G. E. Perreault, Development of Reed Switches and
Relays, B.S.T.J., 34, pp. 309-332, Mar., 1955.
9. W. A. Malthaner and H. E. Vaughan, Experimental Electronically Controlled
Automatic Switching System, B. S.T.J., 31, pp. 443-468, May, 1952.
10. S. T. Brewer and G. Hecht, A Telephone Switching Network and its Electronic
Controls, B.S.T.J., 34, pp. 361-402, Mar., 1955.
11. L. W. Hussey, Semiconductor Diode Gates, B.S.T.J., 32, pp. 1137-54, Sept.,
1953.
12. U. S. Patent 1,528,982.
13. J. J. EbersandS. L. Miller, Design of Alloyed Junction Germanium Transis-
tor for High-Speed Switching, B. S.T.J. , 34, pp. 761-781, July, 1955.
14. W. B. Graupner, Trunking Plan for No. 5 Crossbar System, Bell Labs. Record,
27, pp. 360 365, Oct., 1949.
15. G. L. Pearson and B. Sawyer, Silicon p-n Junction Alloy Diodes, I.R.E. Proc,
42, pp. 1348-1351, Nov." 1952.
16. A. E. Anderson, Transistors in Switching Circuits, B.S.T.J., 31, pp. 1207-
1249, Nov., 1952.
17. J. J. Ebers and J. L. Moll, Large-Signal Behavior of Junction Transistors,
I. R. E. Proc, 42, pp. 1761-1784, Dec, 1954.
18. J. J. Ebers, Four-Terminal p-n-p-n Transistors, I. R. E. Proc, 42, pp. 1361-
1364, Nov., 1952.
19. A. E. Joel, Relay Preference Lockout Circuits in Telephone Switching, Trans.
A. L E. E., 67, pp. 720-725, 1948.
20. S. H. Washburn, Relay "Trees" and Symmetric Circuits, Trans. A. I. E. E.,
68, pp. 571-597, 1949.
21. J. W. Dehn and R. W. Burns, Automatic Line Insulation Testing Equipment
for Local Crossbar Systems, B.S.T.J., 32, pp. 627-646, 1953.
Transistor Circuits for Analog and
Digital Systems*
By FRANKLIN H. BLECHER
(Manuscript received November 17, 1955)
This paper describes the application of junction transistors to precision
circuits for use in analog computers and the input and output circuits of
digital systems. The three basic circuits are a summing amplifier, an inte-
grator, and a voltage comparator. The transistor circuits are combined into
a voltage encoder for translating analog voltages into equivalent time inter-
vals.
1.0. INTRODUCTION
Transistors, because of their reliability, small power consumption,
and small size find a natural field of application in electronic computers
and data transmission systems. These advantages have already been
realized by using point contact transistors in high speed digital com-
puters. This paper describes the application of junction transistors to
precision circuits which are used in dc analog computers and in the
input and output circuits of digital systems. The three basic circuits
which are used in these applications are a summing amplifier, an inte-
grator, and a voltage comparator. A general procedure for designing
these transistor circuits is given with particular emphasis placed on new
design methods that are necessitated by the properties of junction
transistors. The design principles are illustrated by specific circuits.
The fundamental considerations in the design of transistor operational
amplifiers are discussed in Section 2.0. In Section 3.0 an illustrative
summing amplifier is described, which has a dc accuracy of better than
one part in 5,000 throughout an operating temperature range of 0 to
50°C. The feedback in this amplifier is maintained over a broad enough
frequency band so that full accuracy is attained in about 100 micro-
seconds.
The design of a specific transistor integrator is presented in Section
* Submitted in partial fulfillment of the requirements for the degree of Doctor
of Electrical Engineering at the Polytechnic Institute of Brooklyn.
295
296 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
I
4.0. The integrator can be used to generate a voltage ramp which is
linear to within one part in 8,000. By means of an automatic zero set
(AZS) circuit which uses a magnetic detector, the slope of the voltage
ramp is maintained constant to within one part in 8,000 throughout a
temperature range of 20°C to 40°C.
The voltage comparator, described in Section 5.0, is an electrical de-
vice which indicates the instant of time an input voltage waveform
passes through a predetermined reference level. By taking advantage
of the properties of semiconductor devices, the comparator can be de-
signed to have an accuracy of ±5 millivolts throughout a temperature
range of 20°C to 40°C.
In Section 6.0, the system application of the transistor circuits is
demonstrated by assembling the summing amplifier; the integrator, and
the voltage comparator into a voltage encoder. The encoder can be used J
to translate an analog input voltage into an equivalent time interval
with an accuracy of one part in 4,000. This accuracy is realized through-
out a temperature range of 20°C to 40°C for the particular circuits
described.
2.0. FUNDAMENTAL CONSIDERATIONS IN THE DESIGN OF OPERATIONAL
AMPLIFIERS
The basic active circuit used in dc analog computers is a direct coupled
negative feedback amplifier. With appropriate input and feedback net-
works, the amplifier can be used for multiplication by a constant coef-
ficient, addition, integration, or differentiation as shown in Figure 1
The accuracy of an operational amplifier depends only on the passive
components used in the input and feedback circuits provided that there
is sufficient negative feedback (usually greater than 60 db). The time
that is required for the amplifier to perform a calculation is an inverse
f miction of the bandwidth over which the feedback is maintained.
Thus a fundamental problem in the design of an operational amplifier
is the development of sufficient negative feedback over a reasonably
broad frequency range. The associated problem is the realization of
satisfactory stability margins. Finally there is the problem of reducing
the drift which is inherent in direct coupled amplifiers and particularly
troublesome for transistors because of the variation in their character-
istics with temperature.
The first step in the design is the blocking out of the configuration
for the forward gain circuit (designated A in Fig. 1). Three primary re-
quirements must be satisfied:
(1) Stages must be direct coupled.
TRANSISTOR CIRCUITS FOR ANALOG AND DIGITAL SYSTEMS
297
(2) Amplifier must provide one net phase reversal.
(3) Amplifier must have enough current gain to meet accuracy re-
quirements.
Three possible transistor connections are available: (a) the common
base connection which may be considered analogous to the common
grid vacuum tube connection; (b) the common emitter connection
which is analogous to the common cathode connection; and (c) the
common collector connection which is analogous to the cathode follower
connection. These three configurations together with their approximate
equivalent circuits are shown in Fig. 2. It has been shown^ that for
most junction transistors the circuit element a is given by the expression
a = sech
W
(1 + PTrn)
1/2
(1)^
where W is the thickness of the transistor base region, Lm is the diffusion
length and t„, the lifetime of minority charge carriers in the base region,
Rk
I — ^AV
E- "J
-^ Wvr
Eo
Rk A/3EL Rk ^
•=0" Rj (i-A/i)"^ Rj ^l
(a) MULTIPLICATION BY A
CONSTANT COEFFICIENT
E,
R.
E ^2
E3 ^^
Rk
I — vv\-
Eo = E
Rk A/bEj
p, Rj (i-A/3)
(b) ADDITION
N r- .
•RKEf:
c
§i — vw-
£[Eo]
A/3 £[el] sl[eQ
Eo
^N^^^^?|^-PH«[EJ
(d) DIFFERENTIATION
(l-A/3) pRC ~ pRC
(C) INTEGRATION
note; £[Eo] = LAPLACE TRANSFORM OF OUTPUT VOLTAGE
£[Ei1 = LAPLACE TRANSFORM OF INPUT VOLTAGE
p = jco
Fig. 1 — Summary of operational amplifiers.
* This expression assumes that the injection factor y and the collector efficiency
at are both unity. This is a good approximation for all alloy junction transistors
and most grown junction transistors.
298 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
and 7? — ju. At frequencies less than Ua/^ir, (1) can be approximated by
a =
1 + ^
(2)'
COa
where ao is the low frequency value of
a ^ 1
l/TT
2U.
and
2.4Z).
CCa =
w
(Dm is the diffusion constant for the minority charge carriers in the base
region). A readily measured parameter called alpha (a), the short
circuit current gain of a junction transistor in the common base connec-
SCHEMATIC
Zc =
EQUIVALENT CIRCUIT
s ^ —
*■ e/
(V
b
=^ V\V
aZcLe
Tb
(a) COMMON BASE
Lb
:
rb
Zed -a)
aZc'Lb
'X,
■re
(b) COMMON EMITTER
i^b rb
aZc
re
aZcLb
Zed -a)
(C) COMMON COLLECTOR
re
1 + prcCc
a
P
—
ao
i-hP
re = COLLECTOR RESISTANCE
Cc = COLLECTOR CAPACITANCE
ZTT
ALPHA-CUTOFF FREQUENCY
Fig. 2 — Basic transistor connections.
TRANSISTOR CIRCUITS FOR ANALOG AND DIGITAL SYSTEMS 299
tion, is related to a by the equation
aZe -{■ n /^x
Ze + n
For most junction transistors the base resistance, n , is much smaller
than the collector impedance | Zc |, at frequencies less than Wa/27r. There-
fore, a ^ a and Ua/^ir is very nearly equal to the alpha-cutoff frequency,
the frequency at which | a | is down by 3 db.
The transistor parameters r^ and n are actually frequency sensitive
and should be represented as impedances. However, good agreement
between theory and experiment is obtained at frequencies less than
Wa/27r with re and n assumed constant.
The choice of an appropriate transistor connection for a direct coupled,
negative feedback amplifier, is based on the following reasoning. The
common base connection may be ruled out immediately because this
connection does not provide current gain unless a transformer interstage
is used. The common emitter connection provides short circuit current
gain and a phase reversal for each stage. Thus if the amplifier is com-
posed of an odd number of common emitter stages, all three requirements
previously listed, are satisfied. A common emitter cascade has the addi-
tional practical advantage, that by alternating n-p-n and p-n-p types of
transistors, the stages can be direct coupled with practically zero inter-
stage loss.
The common collector connection provides short circuit current gain
but no phase reversal. Consequently, the dc amplifier cannot consist
entirely of common collector stages and operate as a negative feedback
amplifier. This paper will consider only the common emitter connection
since, in general, for the same number of transistor stages, the common
emitter cascade provides more current gain than a cascade composed of
both common collector and common emitter stages.
2.1 Evaluation of External Voltage Gain
Since the equivalent circuit of the junction transistor is current acti-
vated, it is convenient to treat feedback in a single loop transistor ampli-
fier as a loop current transmission (refer to Appendix I) instead of as a
loop voltage transmission which is commonly used for single loop vacuum
tube amplifiers.^ Fig. 3 shows a single loop feedback amplifier in which
a fraction of the output current is fed back to the input. A is defined as
the short circuit current gain of the amplifier without feedback, and jS is
defined as the fraction of the short circuit output current (or Norton
300
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
equivalent circuit current) fed back to the input summing node. With
these definitions,
he = A/in' (4)
la - 131.
sc
where /sc is the Norton equivalent short circuit current.
From Kirchhoff's first law
/in = /in + Iff
Combining relations (4) to (6) yields
'sc
A
(5)
(6)
(7)
/in 1 - A^
Expression (7) provides a convenient method for evaluating the external
^
[|N
I IN
>
^
Fig. 3 — Single loop feedback amplifier.
voltage gain of an operational amplifier. Fig. 4 shows a generalized op-
erational amplifier with N inputs. With this configuration,
IN
j=i L
TTT he r, I
Zj
(S)
where Ej , j = 1,2, • ■ • , N, are the N input voltages referred to the
ground node.
Zj,j— 1,2, • ■ ■ , N, are the A^ input impedances
ZiN is the input impedance of the amplifier measured at the
summing node with the feedback loop opened.
Eo
//i
sc
UT
'IN
la =
A
Eovr =
Zk
/sc ~ /
(3
Rl Zovt
(5>)
(10)
TRANSISTOR CIRCUITS FOR ANALOG AND DIGITAL SYSTEMS 301
where Zovr is the output impedance of the amplifier measured with the
feedback loop opened. The expression for the output voltage is obtained
by combining (7), (8), (9), and (10).
E,
OUT
N y
= zL ^i 7"
;=1 ^i
A^ +
3 = 1 ^1 _
(iir
where
A^ = A
1 -
'IN
\Ri
+
/OUT
1 _^ ^ + ^^^
Rl Zovr
IA/3 is equal to the current returned to the summing node when a unit
Ei
Z,
MN
1/3 Zk
I IN
Zn
Zls
J7
1/5 Zk
Equt
NORTON EQUIVALENT CIRCUIT
Fig. 4 — Generalized operational amplifier.
icurrent is placed into the base of the first transistor stage (/in = 1).
If I A^ 1 is much greater than ] Zj^'/Zr \ and
1 + L
'IN
then
N
Eqvt — ~ 2^ J^j nT
(12)
y=i
The accuracy of the operational amplifier depends on the magnitude of
AjS and the precision of the components used in the input and feedback
networks as can be seen from (11). There is negligible interaction between
the input voltages because the input impedance at the summing node is
equal to Zin' divided by (1 — A^)? This impedance is usually negligibly
tsmall compared to the impedances used in the input circuit.
* In general, E,- and Eout are the Laplace transforms of the input and output
fvoltages, respectively.
302
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
2.2. Methods Used to Shape the Loop Current Transmission
An essential consideration in the design of a feedback amplifier is the
provision of adequate margins against instability. In order to accomplish
this objective, it is necessary to choose a criterion of stability. In Ap-
pendix I it is shown that it is convenient and valid to base the stability
of single loop transistor feedback amplifiers on the loop current trans-
mission. In order to calculate the loop current transmission of the dc
amplifier, the feedback loop is opened at a convenient point in the cir-
cuit, usually at the base of one of the transistors, and a unit current is
injected into the base (refer to Fig. 24). The other side of the opened
loop is connected to ground through a resistance (r^ -j- r^) and voltage
Veli • In many instances, the voltage re/4 can be neglected. If | Zj? | and
3=1 Zj
I
are much greater than | Z
IN
then A/3 is very nearly equal to the loop
ciu'rent transmission. For absolute stability^ the amplitude of the loop
current transmission must be less than unity before the phase shift
(from the low frequency value) exceeds 180°. Consequently, this charac-
teristic must be controlled or properly shaped over a wide frequency
10
_J
LU
O
LU
Q
<
o
\-
z
LU
a.
o
40
U),
a;,'
Wa
^{\-\-S)u)^
\
ao
^"
■\
\,
\J
i
"^
\
30
1-
ao+cT
t- —
. ao
\
7~'
\
\
^
AM PL
ITUC
E
\
\
20
10
i-ao
+ 7_
AMPLITUDE'
(WITH LOCAL
FEEDBACK)
\
\
\
\
S
<
PHASE (WITH
LOCAL FEEDBACK)
phase\
\
y
\
>
\
\
ao
0
^'^
f'
\+S 1
-270°
X
— .
s
\
\
N
d
«/c
-10
20
30
40
"^
N
\
^
^
\
^
\
\
•180
-200
-220
•240
•260 uj
_l
2
<
-280
•300
LU
< I
I
Q-
-320
■340
,02 2 5 ,q3 2 ^ ,o4 •=; S ,q5 t S ,q6
5 ■/^4 2 5 ,„s 2 5 ,„6 2 5 ^q7 2 5 jq8
FREQUENCY IN CYCLES PER SECOND
Fig. 5 — Current transmission of a common emitter stage.
TRANSISTOR CIRCUITS FOR ANALOG AND DIGITAL SYSTEMS 303
band. In addition, it is desirable that the feedback fall off at a rate equal
to or less than 9 db per octave in order to insure that the dc aniplifier
has a satisfactory transient response.
Three methods of shaping are described in this paper; local feedback
shaping, interstage network shaping, and (3 circuit shaping. Local feed-
back shaping will be described first. The analysis starts by considering
the current transmission of a common emitter stage, ecjuivalent circuit
shown in Fig. 2(b). If the stage operates into a load resistance Rl , then
to a good approximation the current transmission is given by
where
Gr = r" = ^ ~ ^° +/ (13)^
^^ 1 + ^ + '^
wi a)aCOc(l — ao -\- 8)
RL+Te
8 =
COl =
(1 - ao + 8)
1 + 5,1
-^ ^ alpha-cutoff frequency
Ztt
1
Uc
(7?x, + re)Cc
It is apparent from expression (13) that if (1 — Oo + 8) is less than 0.1,
then the current gain of the common emitter stage falls off at a rate of
6 db per octave with a corner frequency at wi .f A second 6 db per octave
cutoff with a corner frequency at [co^ + (1 + 5)aJc] is introduced by the
p" term in the denominator of (13). A typical transmission characteristic
is shown in Fig. .5. The current gain of the common emitter stage is unity
at a frequency equal to
ao
1 +5 I 1
* Expressions (13) and (14) are poor approximations at frequencies above
' coo/27r.
' t Strictly speaking the corner frequency is equal to 01/2 tt. However, for sim-
plicity, corner frequencies will be expressed as radian frequencies.
304 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
Since the phase crossover of A|S* is usually placed below this frequency,
the principal effect of the second cutoff is to introduce excess phase. This
excess phase can be minimized by operating the stage into the smallest
load resistance possible, thus maximizing Wc . j
An undesirable property of the common emitter transmission charac-
teristic is that the corner frequency coi occurs at a relatively low fre-
quency. However, the corner frequency can be increased by using local
feedback as shown in Fig. 6(a). Shunt feedback is used in order to pro-
vide a low input impedance for the preceding stage to operate into. The
amplitude and phase of the current transmission is controlled prin-
cipally by the impedances Z\ and Z2 . If | A& \ is much greater than one,
and if /3 ;^ ^1/^2 , then from (7) the current transmission of the stage is
approximately equal to — Z2/Z1 . Because of the relatively small size of
A^ for a single stage, this approximation is only valid for a very limited
range of values of Zi and Z2 . If Zi and Zi are represented as resistances
R\ and Ri , then the current transmission of the circuit is given to a good
approximation by
tto
h. _ R2 1 — gp + 7
^^ = /i= ~{R2 + n)r_^p_^ v'
where
7 =
coi =
COc =
Co/ COaCOcCl — Oo + 7),
R\ + Te _,Rl + Te
R2 + ^6
I
(14)
(/?2 +
rb)rc
i22 + n
(1 +ao
+ ro
+ 7)
1 + 7
1
{R, -f re)Cc i
By comparing (14) with (13), it is evident that the negative feedback
has reduced the low-frequency current gain from ao/(l — ao) (5 may
usually be neglected) to
(
R2 \ I «0 \ _ , ^2
R2 + rj \1 - ao + 7/ ^1 + re
(if 7 > 1 - ao)
.-•!
* The phase crossover of A/3 is equal to the frequency at which the phase shift
of A/3 from its low-frequency value is 180°.
I
TRANSISTOR CIRCUITS FOR ANALOG AND DIGITAL SYSTEMS 305
The half power frequency, however, has been increased from
1— Oo , 1— Oo + 7
t:^ 1 + 7 , 1
as shown by the dashed curves in Fig. 5.*
The bandwidth of the common emitter stage can be increased without
reducing the current gain at dc and low-frequencies by representing Zi
by a resistance Ri , and Z2 by a resistance R2 in series with a condenser
C2 . If I/R2C2 is much smaller than co/, then the current transmission of
the stage is given by (14) multiplied by the factor
P
1 +
C04
P
(15)
where
602
Wi
H^^i
1 - cro +
Ri + re
C2(/?2 + r6)(l - ao + 7)
The current transmission for this case is plotted in Fig. 6(b). The con-
denser d introduces a rising 6 db per octave asymptote with a corner
frequency at wi . At dc the current gain is equal to
ao
1 — ao + 5
A second method of shaping the loop current transmission char-
acteristic of a feedback amplifier is by means of interstage networks.
These networks are usually used for reducing the loop current gain at
relatively low frequencies while introducing negligible phase lag near
the gainf and phase crossover frequencies. Interstage networks should
be designed to take advantage of the variable transistor input impedance.
The input impedance of a transistor in the common emitter connection
* In Figs. 5 and 6(b), the factor R^/iRi + n) is assumed equal to unity. This is
' a good approximation since in practice R2 is equal to several thousand ohms while
rt is equal to about 100 ohms.
t The gain crossover frequency is equal to the frequency at which the magni-
tude of Al3 is unity.
306
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
is given by the expression
'INP
UT = ?'6 + ^e(l — Gi)
(16)1
where Gj is the current transmission given by (13). If Gi at dc is much'
greater than 1, then the input impedance and the current transmission
of the common emitter stage fall off at about the same rate and with
approximately the same corner frequency (wi). The input impedance
finally reaches a limiting value equal to r^ + Vb .
A particularly useful interstage network is shown in Fig. 7(a). This
network is analyzed in Appendix II and Fig. 7(b) shoAvs a plot of the
60
50
40
30
20
Z
<
z
UJ
10
tr 0
cr
D
U
-10
-20
-30
(a:
EQUIVALENT CIRCUIT
\
\
(b)
\
AMPLITUDE
an
\
(WITHOUT LOCAL
\
FEEDBACK)
1-ao+d"
^ -
^"
\
■*•>
1
^
s
.AMPLITUDE
^4
^>CiL
^''
,^_
•— ^ ■
■~^
r"**^
cvz
r^
i
/
"^v
^
' 1
>^
/
V
\
\
\
X
V
^ ao
i-ao+
7 -
/
A
/ ^
\
s.
\
k
\
\
\
/
/
PH/
>s>
/
\
\
\
\
V
\
\
PHASE N
\
(WITHOUT LOCAL
\
s
FEEDBACK)
s
w
k.
-
^-.
■"••^^,
120
140
-160 10
UJ
m
cr
-180 liJ
Q
Z
-200 ^
z
<
-220 ,
10
2 5p2 5,2 5.2 5,2 5
-!•= in^ m^ in5
10'=
lO-^* 10^ 10=
FREQUENCY IN CYCLES PER SECOND
lO''
-240 '
260
- -280
10'
Fig. 6 — Negative feedback applied to a common emitter stage.
TRANSISTOR CIRCUITS FOR ANALOG AND DIGITAL SYSTEMS
307
resulting current transmission. The amplitude of the transmission falls
off at a rate of 6 db per octave with the corner frequency C05 determined
by C'3 and the low frequency value of the transistor input impedance.
The inductance L3 introduces a 12 db per octave rising asymptote with
a corner frequency at C03 = WLsCs . The corner frequencies C03 and C05
are selected in order to obtain a desirable loop current transmission
characteristic (specific transmission characteristics are presented in Sec-
tions 3.0 and 4.0). The half power frequency of the current transmission
of the transistor, wi , does not. appear directly in the transmission char-
acteristic of the circuit because of the variation in the transistor input
impedance with frequency.
The overall (3 circuit of the feedback amplifier can also be used for
i-ao+(J
I ^
s
LU
Q
z
I -
<l<
z
<
15
Z
UI
cc
D
u
Q
UJ
y
<
2
a
o
z
40
20
-20
-40
-60
-80
(b)
/
/
CU5
u
■^3/
y'
*
^^^
A^
^
^s^
1
\.
^N,
/
^s^
S^
/
\
\
AMPLITUDE
/
/
\
\^
/
\
\
\
\
\
>
X
X
V
1
1
/
/
/
1
1
1
1
1
_
\
\
\
\
\
s,.
/
cu,(rb+
' Te
\
\-do+l
W
\
.PHASE
^
Tb+le-l-Ra-K^iLa
^^
/
\.
*^..,
—
^**
X
— -
N
-
-135
10
LU
UJ
isog
z
<
-225 1}^
<
I
a.
-270
102 " "^ \0^ " = 10^ -^ = 105
FREQUENCY IN CYCLES PER SECOND
Fig. 7 — Interstage shaping network.
lO''
308 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
shaping the loop current transmission. If the feedback impedance Zk
(Fig. 4) consists of a resistance Rk and condenser Ck in parallel, then
the loop current transmission is modified by the factor
1 +
CO;
1 + ^
COS
(17)
where
C07 =
C08 =
RkCk
(Rl_±_Rk)
RlRkC K
Since Zk affects the external voltage gain of the operational amplifier,
(11), the corner frequency C07 must be located outside of the useful fre-
quency band. Usually it is placed near the gain crossover frequency in
order to improve the phase margin and the transient response of the
amplifier.
In Sections 3.0 and 4.0, the above shaping techniques are used in the
design of specific operational amplifiers.
3.0. THE SUMMING AMPLIFIER
3.1. Circuit Arrangement
The schematic diagram of a dc summing amplifier is shown in Fig. 8.
From the discussion in Section 2.0 it is apparent that each common
emitter stage will contribute more than 90 degrees of high-frequency
phase lag. Consequently, while the magnitude of the low-frequency :
feedback increases with the number of stages, this is at the expense of ,
the bandwidth over which the negative feedback can be maintained.
It is possible to develop 80 db of negative feedback at dc with three
common emitter stages. This corresponds to a dc accuracy of one part
in 10,000. In addition, the feedback can be maintained over a broad
enough band in order to permit full accuracy to be attained in about
100 microseconds. Thus it is evident that the choice of three stages repre-
sents a satisfactory compromise between accuracy and bandwidth ob-
jectives.
The output stage of the amplifier is designed for a maximum power
dissipation of 75 milliwats and maximum voltage swing of ±25 volts
I
TRANSISTOR CIRCUITS FOR ANALOG AND DIGITAL SYSTEMS
309
when operating into an external load resistance equal to or greater than
50,000 ohms. A p-n-p transistor is used in the second stage and n-p-n
transistors are used in the first and third stages. This circuit arrangement
makes it possible to connect the collector of one transistor directly to
the base of the following transistor without introducing appreciable
interstage loss. ''Shot" noise" and dc drift are minimized by operating
the first stage at the relatively low collector current of 0.25 milliamperes.
The 110,000-ohm resistor provides the collector current for the first
stage, and the 4,700-ohm resistor provides 3.8 milliamperes of collector
current for the second stage. The series 6,800-ohm resistor between the
xcond and third stages, reduces the collector to emitter potential of the
second stage to about 4.5 volts.
The loop current transmission is shaped by use of local feedback ap-
plied to the second stage, by an interstage network connected between
the second and third stages, and by the overall (3 circuit. The 200-ohm
resistor in the collector circuit of the second stage is, with reference to
Fig. 6(a), Zi . The impedance of the interstage network can be neglected
since it is small compared to 200 ohms at all frequencies for which the
local feedback is effective. The interstage network is connected between
the second and third stages in order to minimize the output noise voltage.
^^'ith this circuit arrangement, practically all of the output noise voltage
iE
250 K
IN
+ 33V
5MUf
Hf-
20on
n-p-n
250 K
2.4 K 200 n
0.01/U.F
p-n-p
■llOK
100 K POT.
MANUAL
ZERO SET
I
+ 33V
I
+ 4.5V
OUT
5>UH
-45V -27V +33V
Fig. 8 — ■ DC summing amplifier.
310 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
120
100
UJ
U 80
LU
o
z
" 60
<
<
IS
LU
a:
tr
D
U
Q.
o
o
_)
40
20
■20
-40
,-'
../>'
--T
.-'
—
364
LOCAL _
FEEDBACK"^-
^-'
.-1
41,000
-^
^
d 6
630
\,
. 12
N
\
?,000
--..,
s^->
^-.
'S
'-..
\
\
V
\
\
V
2ND •^^
STAGE ^
s
\
-..
"-.
^-.
1ST & 3RD
STAGES
N
\
0.5/ZF
^■-S;:-.-,
^
\,
\
\
>
\
10'
10-^
10-
10'
10'
FRFOUENCY IN CYCLES PER SECOND
Fig. 9 — Gain-frequency asymptotes for summing amplifier.
is generated in the first transistor stage. If the transistor in the first
stage has a noise figure less than 10 db at 1,000 cycles per second, then
the RMS output noise voltage is less than 0.5 millivolts.
Fig. 9 shows a plot of the gain-frequency asymptotes for the sum-
ming amplifier determined from (13), (14), (15), (17), and (A6) under
the assumption that the alphas and alpha-cutoff frequencies of the tran-
sistors are 0.985 and 3 mc, respectively. The corner frequencies intro-'
duced by the 0.5 microfarad condenser in the interstage network, thel
local feedback circuit, and the cutoff of the first and third stages are so
located that the current transmission falls off at an initial rate of about'
9 db per octave. This slope is joined to the final asymptote of the loop
transmission by means of a step-type of transition.^ The transition is
provided by 3 rising asymptotes due to the interstage shaping network,
and the overall /S circuit. An especially large phase margin is used in order
to insure a good transient performance.
Fig. 10 shows the amplitude and phase of the loop current trans-
mission. When the amplitude of the transmission is 0 db, the phase angle
is -292°, and when the phase angle is —360°, the amplitude is 27.5 db
TRANSISTOR CIRCUITS FOR ANALOG AND DIGITAL SYSTEMS
311
100
LU
m
u
LU
Q
<^
z
<
H
Z
UJ
a.
a.
D
o
Q.
O "
o
_l
80
60
40
20
20
-40
—
■~-^
^•"v
>
\
^
AM
PLITL
DE
\
1
\
\
\
s
>
\.
._
s
>^
^r
•—''
y^ "N phase
'PHASE 'nCROSSOVER
s
\
\
V
/ GAIN^-N^
CROSSOVER
N
-27.5 DB
95 = -360°
sv
■160
-200
to
LU
-240 ^
O
LU
Q
-280 7
•320
-360
-400
■440
10=
FREQUENCY IN CYCLES PER SECOND
10^
10'
Fig. 10 — Loop current transmission of the summing amplifier.
below 0 db. The amplifier has a 68° phase margin and 27.5 db gain margin.
In order to insure sufficient feedback at dc and adequate margins against
instability, the transistors used in the amplifier should have alphas in
the range 0.98 to 0.99 and alpha-cutoff frequencies equal to or greater
than 2.5 mc.
3.2. Automatic Zero Set of the dc Summing Amplifier
The application of germanium junction transistors to dc amplifiers
does not eliminate the problem of drift normally encountered in vacuum
tube circuits. In fact, drift is more severe due principally to the varia-
tion of the transistor parameters alpha and saturation current with
temperature variation. Even though the amplifier has 80 db of negative
feedback at dc, this feedback does not eliminate the drift introduced by
[the first transistor stage. Because of the large amount of dc feedback,
the collector current of the first stage is maintained relatively constant.
The collector current of the transistor is related to the base current by
the equation
Ic =
/c
+
a
I — a 1 — a
(18)
[The saturation current, Ico , of a germanium junction transistor doubles
(approximately for every 11°C increase in temperature. The factor
a/(l — a) increases by as much as 6 db for a 25°C increase in tempera-
312 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
ture. Consequently, the base current of the first stage, Ih , and the output
voltage of the amplifier must change with temperature in order to main- '
tain Ic constant. The drift due to the temperature variation in a can be
reduced by operating the first stage at a low value of collector current.
With a germanium junction transistor in the first stage operating at a
collector current of 0.25 milliamperes, the output voltage of the amplifier
drifts about ±1.5 volts over a temperature range of 0°C to 50°C. It is
possible to reduce the dc drift by using temperature sensitive elements
in the amplifier. • In general, temperature compensation of a transistor
dc amplifier requires careful selection of transistors and critical adjust-
ment of the dc biases. However, even with the best adjustments, tem-
perature compensation cannot reduce the drift in the amplifier to within
typical limits such as ±5 millivolts throughout a temperature range of i
0 to 50°C. In order to obtain the desired accuracy it is necessary to use
an automatic zero set (AZS) circuit. t
Fig. 11 shows a dc summing amplifier and a circuit arrangement fori
reducing any dc drift that may appear at the output of the amplifier.
The output voltage is equal to the negative of the sum of the input volt-
ages, where each input voltage is multiplied by the ratio of the feedback
resistor to its input resistor. In addition, an undesirable dc drift voltage ^
is also present in the ovitput voltage. The total output voltage is
^o.t = -i:^y|^ + Adrift (1!))^
In order to isolate the drift voltage, the A^ input voltages and the output
voltage are applied to a resistance summing network composed of re-
sistors Ro , Ri , R2 , • • • , Rn ■ The voltage across Rs is equal to
Es=^ Adrift (20)
if
R,«Ro,R/; j = 1,2, ■■' ,N
and
RoRj = RkR,'; j = 1,2, ■■■ ,N
The voltage E, is amplified in a relatively drift-free narrow band dc
amplifier and is returned as a drift correcting voltage to the input of the
dc summing amplifier. If the gain of the AZS circuit is large, the drift
voltage at the output of the summing amplifier can be made very small.
Fig. 12 shows the circuit diagram of a summing amplifier which uses
a mechanical chopper in the AZS circuit.^^ The AZS circuit consists of a
TRANSISTOR CIRCUITS FOR ANALOG AND DIGITAL SYSTEMS 313
resistance summing network, a 400-cycle synchronous chopper, and a
tuned 400-cycle amplifier. Any drift in the summing amplifier will pro-
duce a dc voltage Es at the output of the summing network. The chopper
converts the dc voltage into a 400 cycles per second waveform. The
fundamental frequency in the waveform is amplified by a factor of about
400,000 by the tuned amplifier. The synchronous chopper rectifies the
sinusoidal output voltage and preserves the original dc polarity of Eg .
The rectified voltage is filtered and fed back to the summing amplifier
as an additional input current. The loop voltage gain of the AZS circuit
at dc is about 54 db. Any dc or low-frequency drift in the summing
amplifier is reduced by a factor of about 500 by the AZS circuit. The
drift throughout a temperature range of 0 to 50°C is reduced to ±3
millivolts.
Since the drift in the summing amplifier changes at a relatively slow
rate, the loop voltage gain of the AZS circuit can be cutoff at a relatively
low frequency. In this particular case the loop voltage gain is zero db at
about 10 cycles per second.
4.0. THE INTEGRATOR
4.1. Basic Design Considerations
The design principles previously discussed are illustrated in this sec-
tion by the design of a transistor integrator for application in a voltage
VvV
-OUT
Fig. 11 — DC summing amplifier with automatic zero set.
314 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
TRANSISTOR CIRCUITS FOR ANALOG AND DIGITAL SYSTEMS 315
encoder. The integrator is required to generate a 15-volt ramp which is
linear and has a constant slope to within one part in 8,000. This ramp is
to have a slope of 5 millivolts per microsecond for an interval of 3,000
microseconds.
The first step in the design is to determine the bandwidth over which
the negative feedback must be maintained in order to realize the desired
output voltage linearity. The relationship between the output and input
voltage of the integrator can be obtained from expression (11) by sub-
stituting (1/pc) for Zk and R for Zj (refer to Fig. 1).
£l-C'outJ —
pRC
A/3 + Zr^'pC
1 - AjS +
-nN_
R
(21)
where ce[£'ouT] and JSiii'iN] are the Laplace transforms of the output and
input voltages, respectively. In order to generate the voltage ramp, a
step voltage of amplitude E is applied to the input of the integrator. The
term Zy^ jR is negligible compared to unity at all frequencies. Therefore,
£L-£'outJ —
E \ A&
+
EZ
IN
1
'^-RC Ll - A&\ pR \\ - A^_
It will be assumed that A/3 is given by the expression
-K
(22)
A^ =
V
)0 + ^T
(i + -M(i + ^
(23)
Expression (23) implies that A/3 falls off at a rate of 6 db per octave at
low frequencies and 12 db per octave at high frequencies. The output
\ voltage of the integrator, as a function of time, is readily evaluated by
substituting (23) into (22) and taking the inverse Laplace transform of
the results. A good approximation for the output voltage is
^OUT —
E
RC
+
2K
^-[(2w2+«l)(/2] ^;„ -x/W
sm
Vk>
OJo
■iC02M
ER
(24)^
IN
R
[1 _ e-(-i'W _!_ g-[(2<-2+.i)t/2i ^Qg ^Tkc.,!]
The linear voltage ramp is expressed by the term — (Et/RC) . The
additional terms introduce nonlinearities. The voltage ramp has a slope
of 5 millivolts per microsecond for E = —21 volts, R = 42,000 ohms,
* In evaluating jE'out it was assumed that Zm' was equal to a fixed resistance
Rin' , the low frequency input resistance to the first common emitter stage. A
complete analysis indicates that this assumption makes the design conservative.
31G
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
and C = 0.1 microfarads. For these circuit values, and K = 10,000
(corresponding to 80 db of feedback) the nonhnear terms are less than
1/8,000 of the linear term (evaluated when / = 4 X 10"^ seconds) if
/i ^ 30 cycles per second, J2 ^ 800 cycles per second, and if the first
1000 microseconds of the voltage ramp are not used. Consequently, 80
db of negative feedback must be maintained over a band extending from
30 to 800 cycles per second in order to realize the desired output voltage
linearity.
4.2. Detailed Circuit Arrangement
Fig. 13 shows the circuit diagram of the integrator. The method of
biasing is the same as is used in the summing amplifier. The 200,000-ohm
resistor provides approximately 0.5 milliamperes of collector current for
the first stage. The 40,000-ohm resistor provides approximately 0.9
milliamperes of collector current for the second stage. The output stage
is designed for a maximum power dissipation of 120 milliwatts and for
an output voltage swing between —5 and +24 volts when operating
into a load resistance equal to or greater than 40,000 ohms.
J+'08V
• + 108V
42 K
D2
44-
C
0.01>(/F o.l/iF
2.4K
270 K
I
+ I08V
1MEG
200n
\ — vw
2>U.F
200 K
rVWA/^An
j 100 K [
POT. I
I
OUT
-10.5V
+ 108V
+ 4.5V
•45V -10.5V
Fig. 13 — Integrator.
TRANSISTOR CIRCUITS FOR ANALOG AND DIGITAL SYSTEMS 317
1 !!3
{ LU
I 5
u
ai
a
1 z
<
140
120
N
100
.^^
\
AMPLITUDE
v.
80
^""^
\
\
\
\
N
\,
60
\
\
>
\
\
\
s
40
20
\
'^— --
,''
S
"-s
S,
PHASE
^
\
\
■\
PHASE
. CROSSOVER
0
-20
-40
GAIN-"
CROSSOVER
\
\
— ?n HR
95=-
360°
■80
-120
160
■200
■240
•280
UJ
_J
z
<
LU
lO
-320 <
I
Q.
-360
-400
■440
10
2 S .- 2 5 .^3 2 5 ,^^ 2 ^ 105 2 ^ ,0« ' ' 10^
lO'^
w
FREQUENCY IN CYCLES PER SECOND
Fig. 14 — - Loop current transmission of the integrator.
The negative feedback in the integrator has been shaped by means of
local feedback and interstage networks as described in Section 2.2. The
loop current transmission has been calculated from (13), (14), (15), and
(A6) and is plotted in Fig. 14. The transmission is determined under the
assumption that the alphas of the transistors are 0.985 and the alpha-
cutoff frequencies are three megacycles. Since the feedback above 800
cycles per second falls off at a rate of 9 db per octave, the analysis in
Section 4.1 using (23), is conservative. The integrator has a 44° phase
margin and a 20 db gain margin. In order to insure sufficient feedback
between 30 and 800 cycles per second and adequate margins against
instability, the transistors used in the integrator should have alphas in
the range 0.98 to 0.99 and alpha-cutoff frequencies equal to or greater
than 2.5 megacycles.
The silicon diodes Di and D2 are rec^uired in order to prevent the
integrator from overloading. For output voltages between —4.0 and 21
volts the diodes are reverse biased and represent very high resistances, of
the order of 10,000 megohms. If the output voltage does not lie in this
range, then one of the diodes is forward biased and has a low resistance,
of the order of 100 ohms. The integrator is then effectively a dc amplifier
with a voltage gain of approximately 0.1. The silicon diodes affect the
318
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
linearity of the voltage ramp slightly due to their finite reverse resistances
and variable shunt capacities. If the diodes have reverse resistances
greater than 1000 megohms, and if the maximum shunt capacity of each
diode is less than 10 micromicrofarads (capacity with minimum reverse
voltage), then the diodes introduce negligible error.
As stated earlier, the integrator generates a voltage ramp in response
to a voltage step. This step is applied through a transistor switch which
is actuated by a square wave generator capable of driving the transistor
well into current saturation. Such a switch is required because the
equivalent generator impedance of the applied step voltage must be very
small. A suitable circuit arrangement is shown in Fig. 15. For the par-
ticular application under discussion the switch *S is closed for 5,000
microseconds. During this time, the voltage E = —217 appears at the
input of the integrator. At the end of this time interval, the transistor
switch is opened and a reverse current is applied to the feedback con-
denser C, returning the output voltage to —4.0 volts in about 2500 micro-
seconds. An alternate way of specifying a low impedance switch is to say
that the voltage across it be close to zero. For the transistor switch, con-
nected as shown in Fig. 15, this means that its collector voltage be within
FIRST STAGE
OF DC
AMPLIFIER
10.5V
50 K 150 K
' — WV-HVW
RESIDUAL
VOLTAGE BALANCE
(TO AZS)
Fig. 15 — Input circuit arrangement of the integrator.
TRANSISTOR CIRCUITS FOR ANALOG AND DIGITAL SYSTEMS 319
one millivolt of ground potential during the time the transistor is in
saturation. Xow, it has been shown that when a junction transistor in
the common emitter connection is driven into current saturation, the
minimum voltage between collector and emitter is theoretically equal to
— in - (25)
q oci
where k is the Boltzmann constant, T is the absolute temperature, q is
the charge of an electron ((kT/q) = 26 millivolts at room temperature),
and ai is the inverse alpha of the transistor, i.e., the alpha with the
emitter and collector interchanged. There is an additional voltage drop
across the transistor due to the bulk resistance of the collector and
emitter regions (including the ohmic contacts). A symmetrical alloy
junction transistor with an alpha close to unity is an excellent switch
because both the collector to emitter voltage and the collector and emit-
ter resistances are very small.
At the present time, a reasonable value for the residual voltage* be-
tween the collector and emitter is 5 to 10 millivolts. This voltage can be
eliminated by returning the emitter of the transistor switch to a small
negative potential. This method of balancing is practical because the
voltage between the collector and emitter of the transistor does not
change by more than 1.0 millivolt over a temperature range of 0°C to
50°C.
4.3. Automatic Zero Set of the Integrator
A serious problem associated with the transistor integrator is drift.
The drift is introduced by two sources; variations in the base current of
the first transistor stage and variations in the base to emitter potential
of the first stage wdth temperature. In order to reduce the drift, the
input resistor R and the feedback condenser C must be dissociated from
the base current and base to emitter potential of the first transistor stage.
This is accomplished by placing a blocking condenser Cb between point
T and the base of the first transistor as shown in Fig. 15. An automatic
zero set circuit is required to maintain the voltage at point T equal to
zero volts. This AZS circuit uses a magnetic modulator known as a
"magnettor."^^
A block diagram of the AZS circuit is shown in Fig. 16. The dc drift
current at the input of the amplifier is applied to the magnettor. The
carrier current required by the magnettor is supplied by a local transistor
* The inverse alphas of the transistors used in this application were greater
than 0.95.
320
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
oscillator. The useful output of the magnettor is the second harmonic of
the carrier frequency. The amplitude of the second harmonic signal is
proportional to the magnitude of the dc input current and the phase of
the second harmonic signal is determined by the polarity of the dc input
current. The output voltage of the magnettor is applied to an active
filter which is tuned to the second harmonic frequency. The signal is
then amplified in a tuned amplifier and applied to a diode gating circuit.
Depending on the polarity of the dc input current, the gating circuit
passes either the positive or negative half cycle of the second harmonic
signal. In order to accomplish this, a square wave at a repetition rate
equal to that of the second harmonic signal is derived from the carrier
oscillator and actuates the gating circuit.
A circuit diagram of the AZS circuit is shown in Figs. 17(a) and 17(b).
The various sections of the circuit are identified with the blocks shown
in Fig. 16. The active filter is adjusted for a Q of about 300, and the gain
of the active filter and tuned amplifier is approximately 1000. The AZS
circuit provides ±1.0 volt of dc output voltage for ±0.05 microamperes
of dc input current. The maximum sensitivity of the circuit is limited
to ±0.005 microamperes because of residual second harmonic generation
in the magnettor with zero input current.
When the transistor integrator is used together with the magnettor
AZS circuit, the slope of the voltage ramp is maintained constant to
within one part in 8,000 over a temperature range of 20°C to 40°C.
5.0. The Voltage Comparator
The voltage comparator is one of the most important circuits used in
analog to digital converters. The comparator indicates the exact time
that an input waveform passes through a predetermined reference level.
It has been common practice to use a vacuum tube blocking oscillator
as a voltage comparator. ^^ Due to variations in the contact potential,
heater voltage, and transconductance of the vacuum tube, the maximum
DC
INPUT
AC
MAGNETTOR
ACTIVE
FILTER
\
GATING
CIRCUIT
^
A
■~
OSCILLATOR
GATING
PULSE
DC
OUTPUT
Fig. 16 — Block diagram of AZS circuit.
TRANSISTOR CIRCUITS FOR ANALOG AND DIGITAL SYSTEMS 321
accuracy of the circuit is limited to about ±100 millivolts. By taking
advantage of the properties of semiconductor devices, the transistor
blocking oscillator comparator can be designed to have an accuracy of
±5 millivolts throughout a temperature range of 20°C to 40°C.
5.1. General Descri'ption of the Voltage Comparator
Fig. 18 shows a simplified circuit diagram of the voltage comparator.
Except for the silicon junction diode D\ , this circuit is essentially a
transistor blocking oscillator. For the purpose of analysis, assume that
the reference voltage Vee is set equal to zero. When the input voltage V,
is large and negative, the silicon diode Di is an open circuit and the jiuic-
tion transistor has a collector current determined by Rb and Ebb [Expres-
sion (18)]. The base of the transistor resides at approximately —0.2
volts. As the input voltage Vi approaches zero, the reverse bias across
the diode Di decreases. At a critical value of Vi (a small positive poten-
tial), the dynamic resistance of the diode is small enough to permit the
circuit to become unstable. The positive feedback provided by trans-
1 former Ti forces the transistor to turn off rapidly, generating a sharp
I output pulse across the secondary of transformer T-z . When Vi is large
and positive, the diode Di is a low impedance and the transistor is main-
tained cutoff. In order to prevent the comparator from generating more
than one output pulse during the time that the circuit is unstable, the
natural period of the circuit as a blocking oscillator must be properly
chosen. Depending on this period, the input voltage waveform must
have a certain minimum slope when passing through the reference level
in order to prevent the circuit from misfiring.
I The comparator has a high input impedance except during the switch-
1 ing interval.* When Vi is negative with respect to the reference level, the
\ input impedance is equal to the impedance of the reverse biased silicon
i diode. When Vi is positive with respect to the reference level, the input
I impedance is equal to the impedance of the reverse biased emitter and
! collector junctions in parallel. This impedance is large if an alloy
; junction transistor is used. During the switching interval the input im-
■ pedance is equal to the impedance of a forward biased silicon diode in
series with the input impedance of a common emitter stage (approxi-
mately 1,000 ohms). This loading effect is not too serious since for the
circuit described, the switching interval is less than 0.5 microseconds.
The voltage comparator shown in Fig. 18 operates accurately on
voltage waveforms with positive slopes. The voltage comparator will
operate accurately on waveforms with negative slopes if the diode and
* The switching interval is the time required for the transistor to turn off.
322 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
note: all capacitors and inductors
IN tuned circuits have a
tolerance of ±0.1%
Fig. 17(a) — AZS circuit.
battery potentials are reversed and if an n-p-n junction transistor is
used.
5.2. Factors Determining the Accuracy of the Voltage Comparator
Fig. 19 shows the ac equivalent circuit of the voltage comparator. In
the equivalent circuit Ri is the dynamic resistance of the diode Di , Rg
is the source resistance of the input voltage, and R2 is the impedance of
TRANSISTOR CIRCUITS FOR ANALOG AND DIGITAL SYSTEMS
323
the load R^ as it appears at the primary of the transformer T2 . Ri is a
function of the dc voltage across the diode Z)i . At a prescribed value of
Ri , the comparator circuit becomes unstable and switches. The relation-
ship between this critical value of Ri and the transistor and circuit
parameters is obtained by evaluating the characteristic equation for the
circuit and by determining the relationship which the coefficients of the
equation must satisfy in order to have a root of the equation lie in the
right hand half of the complex frequency plane. To a good approxima-
tion, the critical value of Ri is given by the expression
R, -\-R„ + n =
Mao
RiCc -\-
(26)
N'^Rr
where M is the mutual inductance of transformer Ti and R2 — ly h^l
Since the transistor parameters which appear in expression (26) have only
a small variation with temperature, the critical value of Ri is independent
of temperature (to a first approximation).
It will now be shown that the comparator can be designed for an ac-
curacy of ±5 millivolts throughout a temperature range of 20°C to 40°C.
In order to establish this accuracy it will be assumed that the critical
value of 7^1 is equal to 30,000 ohms. This assumption is based on the
30/iF
TO LC FILTER
IN MAGNETTOR
NPUT CIRCUIT
4/iF
+33V
I+33V
Fig. 17(b), 900-cycle carrier oscillator.
324 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
data displayed in Fig. 20 which gives the volt-ampere characteristics of a
silicon diode measured at 20°C and 40°C. Throughout this temperature
range, the diode voltage corresponding to the critical resistance of
30,000 ohms changes by about 30 millivolts. Fortunately, part of this
voltage variation with temperature is compensated for by the variation
in voltage Vb-e between the base and emitter of the junction transistor.
From Fig. 18,
V, = Vo - Vb-e + Ve
(27)
For perfect compensation (Vi independent of temperature), Vb-e should
have the same temperature variation as the diode voltage Vd . Experi-
REFERENCE
I LEVEL
-I ADJUSTMENT i+
Fig. 18 — Simplified circuit diagram of voltage comparator.
Fig. 19 — Equivalent circuit of voltage comparator.
TRANSISTOR CIRCUITS FOR ANALOG AND DIGITAL SYSTEMS
325
0.7
_)
O
>
0.6
R, = 30,000 OHMS
20°C
>
u:o.5
<
I-
_l
o
>
o
0.3
2 3 4 5 6
DIODE CURRENT, Ip, IN MICROAMPERES
Fig. 20 — Volt-ampere characteristic of a silicon junction diode.
mentally it is found that Yh-e for germanium junction transistors varies
by about 20 millivolts throughout the temperature range of 20°C to
40°C. Consequently, the variation in Yi at which the circuit switches is
±5 millivolts.
It is apparent from Fig. 20 that the accuracy of the comparator in-
creases slightly for critical values of R\ greater than 30,000 ohms, but
decreases for smaller values. For example, the accuracy of the comparator
is ±10 millivolts for a critical value of U\ equal to 5,000 ohms. In gen-
eral, the critical value of R\ should be chosen between 5,000 and 100,000
ohms.
5.3. A Practical Yoltage Comparator
Fig. 21 shows the complete circuit diagram of a voltage comparator.
The circuit is designed to generate a sharp output pulse* when the input
voltage waveform passes through the reference level (set by Yee) with a
positive slope. The pulse is generated by the transistor switching from
the "on" state to the "off" state. To a first approximation the amplitude
of the output pulse is proportional to the transistor collector current
during the "on" state. When the input voltage waveform passes through
the reference level with a negative slope an undesirable negative pulse is
generated. This pulse is eliminated by the point contact diode D2 .
The voltage comparator is an unstable circuit and has the properties
* For the circuit values shown in Fig. 21, the output pulse has a peak amplitude
of about 6 volts, a rise time of 0.5 microseconds, and a pulse width of about 2.0
microseconds.
32G
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
of a free running blocking oscillator after the input voltage Vi passes
through the reference level. After a period of time the transistor will
return to the "on" state unless the voltage Vi is sufficiently large at this
time to prevent switching. In order to minimize the required slope of the
hiput waveform the time interval between the instant Vi passes through
the reference level and the instant the transistor would naturally switch
to the "on" state must be maximized. This time intei-val can be con-
trolled by connecting a diode D3 across the secondary winding of trans-
former Ti . When the transistor turns off, the current which was flowing
through the secondary of transformer Ti(Ic) continues to flow through
the diode D3 so that L2 and D3 form an inductive discharge circuit. The
point contact diode D3 has a forward dynamic resistance of less than 10
ohms and a forward voltage drop of 0.3 volt. If the small forward re-
sistance of the diode is neglected, the time required for the current in the
circuit to fall to zero is
T =
0.3
(28)
During the inductive transient, 0.3 volt is induced into the primary of
transformer Ti (since N = 1) maintaining the transistor cutoff. The
duration of the inductive transient can be made as long as desired by
increasing L2 . However, there is the practical limitation that increasing
L2 also increases the leakage inductance of transformer Ti , and in turn,
I
I
-4.5V
5.1K
250A
:iD2
>3K
A-l-
OUTPUT
PULSE
V-
INPUT
WAVEFORM
PULSE
AMPLITUDE^,
ADJUSTMENT^
•^
2.5 MEG POT.
I-
jr
ee'
Ij, = 4 MILS
L, = L2= 5 MILLIHENRIES
L', = L2= 5 MILLIHENRIES
COEFFICIENT OF
COUPLING = 0.99
REFERENCE
g^ LEVEL
''adjustment
MA 1
I
I
-46V
I
I
-t-1.5V
100 OHM
POT.
I
I
-1.5V
Fig. 21 — Voltage comparator.
TRANSISTOR CIRCUITS FOR ANALOG AND DIGITAL SYSTEMS
327
increases the switching time. The circuit shown in Figure 21 does not
misfire when used with voltage waveforms having slopes as small as 25
millivolts per microsecond, at the reference level.
6.0. A TRANSISTOR VOLTAGE ENCODER
6.1. Circuit Arrangement
The transistor circuits previously described can be assembled into a
voltage encoder for translating analog voltages into equivalent time
intervals. This encoder is especially useful for converting analog informa-
, tion (in the form of a dc potential) into the digital code for processing
in a digital system. Fig. 22 shows a simplified block diagram of the
encoder. The voltage I'amp generated by the integrator is applied to
amplitude selector number one and to one input of a summing amplifier.
The amplitude selector is a dc amplifier which amplifies the voltage ramp
in the vicinity of zero volts. Voltage comparator number one, which
follows the amplitude selector, generates a sharp output pulse at the
exact instant of time that the voltage ramp passes through zero volts.
The analog input voltage, which has a value between 0 and —15
volts,* is applied to the second input of the summing amplifier. The
output voltage of the summing amplifier is zero whenever the ramp
INTEGRATOR
N0.1
N0.1
3000^65
SUMMING
AMPLIFIER
AMPLITUDE
SELECTORS
VOLTAGE
COMPARATORS
ANALOG
INPUT VOLTAGE
0-^-16V
N0.2
N0.2
Fig. 22 — • Simplified block diagram of voltage encoder.
* If the analog input voltage does not lie in this range, then the voltage gain
of the summing amplifier must be set so that the analog voltage at the output of
the summing amplifier lies in the voltage range between 0 and +15 volts.
328
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
voltage is equal to the negative of the input analog voltage. At this
instant of time the second voltage comparator generates a sharp output
pulse. The time interval between the two output pulses is proportional
to the analog input voltage if the voltage ramp is linear and has a con-
stant slope at all times.
6.2. The Amplitude Selector i
The amplitude selector increases the slope of the input voltage wave-
form (in the vicinity of zero volts) sufficiently for proper operation of the
voltage comparator. The amplitude selector consists of a limiter and a
dc feedback amplifier as shown in Fig. 23. The two oppositely poled
silicon diodes Di and D2 , limit the input voltage of the dc amplifier to
about ±0.65 volts. The dc amplifier has a voltage gain of thirty, and so
the maximum output voltage of the amplitude selector is limited to
about ±19.5 volts. The net voltage gain between the input and output
of the amplitude selector is ten.
The principal requirement placed on the dc amplifier is that the input
current and the output voltage be zero when the input voltage is zero.
This is accomplished by placing a blocking condenser Cb between point
T and the base of the first transistor stage, and by using an AZS circuit
to maintain point T at zero volts. The dc and AZS amplifiers are identical
in configuration to the amplifiers shown in Fig. 12. The dc amplifier is
50 K
-VvV
50 K
:|N
D
1::
SILICON
DIODES
Dp
1.5 MEG
Cb
250 /ZF
500 K
I
OUT
I V^^ »— AAA^
50 K 1.5 MEG
-1
Fig. 23 — Block diagram of the amplitude selector.
TRANSISTOR CIRCUITS FOR ANALOG AND DIGITAL SYSTEMS 329
designed to have about 15.6 db less feedback than that shown in Fig. 10
since this amount is adequate for the present purpose.
The bandwidth of the dc ampHfier is only of secondary importance
because the phase shifts introduced by the two amplitude selectors in
the voltage encoder tend to compensate each other.
6.3. Experimental Results
The accuracy of the voltage encoder is determined by applying a
precisely measured voltage to the input of the summing amplifier and by
measuring the time interval between the two output pulses. The maxi-
mum error due to nonlinearities in the summing amplifier and the voltage
ramp is less than ±0.5 microseconds for a maximum encoding time of
3,000 microseconds. An additional error is introduced by the noise voltage
generated in the first transistor stage of the summing amplifier. The
! RMS noise voltage at the output of the summing amplifier is less than
0.5 millivolts. This noise voltage produces an RMS jitter of 0.25 micro-
I seconds in the position of the second voltage comparator output pulse.
; The over-all accuracy of the voltage encoder is one part in 4,000 through-
' out a temperature range of 20°C to 40°C.
1
I
i ACKNOWLEDGEMENTS
!
I The author wishes to express his appreciation to T. R. Finch for the
^ advice and encouragement received in the course of this work. D. W.
! Grant and W. B. Harris designed and constructed the magnettor used
' in the AZS circuit of the integrator.
I Appendix I
I RELATIONSHIP BETWEEN RETURN DIFFERENCE AND LOOP CURRENT
i TRANSMISSION
} In order to place the stability analysis of the transistor feedback ampli-
fier on a sound basis, it is desirable to use the concept of return differ-
ence. It will be shown that a measurable quantity, called the loop current
transmission, can be related to the return difference of aZc with reference
Ve .*• t In Fig. 24, N represents the complete transistor network exclusive
of the transistor under consideration. The feedback loop is broken at
the input to the transistor by connecting all of the feedback paths to
* In this appendix it is assumed that the transistor under consideration is in
the common emitter connection. The discussion can be readily extended to the
other transistor connections.
t This fact was pointed out by F. H. Tendick, Jr.
330
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
Te+rb
^6^4 ( 'V
-aZcLb
N
COMPLETE
AMPLIFIER
EXCLUSIVE
OF THE
TRANSISTOR
IN QUESTION
Fig. 24 — Measurement of loop current transmission.
ground through a resistance (/•<; + n) and a voltage r J4 • Using the
nomenclature given in Reference 8, the input of the complete circuit is
designated as the first mesh and the output of the complete circuit is
designated as the second mesh. The input and output meshes of the
transistor under consideration are designated 3 and 4, respectively. The
loop current transmission is equal to I3', the total returned current when
a unit input current is applied to the base of the transistor.
The return difference for reference Ve is equal to the algebraic differ-
ence* between the unit input current and the returned current h'. 1 3 is
evaluated by multiplying the open circuit voltage in mesh 4 (produced
by the unit base current) by the backward transmission from mesh 4 to
mesh 3 with zero forward transmission through the transistor under
consideration. The open circuit voltage in mesh 4 is equal to (re — aZc).
The backward transmission is determined with the element aZc , in the
fourth row, third column of the circuit determinant, set equal to Ve .
Hence, the return difference is expressed as
A43
Fr' = 1 + {aZc - re)
(Al)t
Fr' =
A''* + {aZc - r.)A
43
ir',
(A2)
Fr'.=
A^''
= 1+ Tr'
(A3)
The relative return ratio Tr', is equal to the negative of the loop current
transmission and can be measured as shown in Fig. 24. The voltage reh
takes into account the fact that the junction transistor is not perfectly
* The positive direction for the returned current is chosen so that if the original
circuit is restored, the returned current flows in the same direction as the input
current.
t A''« is the network determinant with the element aZc in the fourth row, third
column of the circuit determinant set equal to r, .
TRANSISTOR CIRCUITS FOR ANALOG AND DIGITAL SYSTEMS 331
unilateral. Fortunately, in many applications, this voltage can be neg-
lected even at the gain and phase crossover frequencies.
In the case of single loop feedback amplifiers. A""* will not have any
zeros in the right hand half of the complex frequency plane. A study of
the stability of the amplifier can then be based on F^-, or T^-, .
Appendix II
INTERSTAGE NETWORK SHAPING
This appendix presents the analysis of the circuit shown in Fig. 7(a).
The input impedance of the common emitter connected junction tran-
sistor is given by the expression
^iNPUT = n-\- re(l - Gl) (A4)
where Gi is the current transmission of the common emitter stage, ex-
pression (13). The current transmission A of the complete circuit is equal
to
A = ^ = ^
I\ Zz -\- ^ IN PUT
G,
(A5)
where Z3 = i?3 + V^ + (l/p<^3). Combining (13), (A4), and (A5) yields
ao
A =
1 — ao + 5
1 +
C03
+ V
\ W5/ I, Wl
(A6)
+ p^
W5 , CsOO^in + Te -\- R3)
_C0iC03-
+
PCO5
where
WaWc(l — tto -}- 6) J ' CO3^C0aC0c(l — ^Q "j- 6) j
^ ^ Rl + Te
COl =
Wc =
CO3
OJs =
(1 - ao + 5)
1 + 6 _^ 1
1
(R^ + r,)Co
1
1
~. . ^«
C
(1 - ao
+ 5)J^
332 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
Expression (A6) is valid if l/ws ^ 1/coi + RzCz . The denominator of the
expression indicates a falUng 6 db per octave asymptote with a corner,
frequency at ws . The second factor in the denominator can be approxi-
mated bj^ a falHng 6 db per octave asymptote with a corner frequency at
COl
1 ^^
n +
(1 - ao + 5)
]
n -\- Te -^ Rz -\- W1L3
pkis additional phase and amplitude contributions at higher f recjuencies
due to the y and p terms. If
COzCzRz
then the circuit has a rising 12 db per octave asymptote with a corner
frequency at C03 . Fig. 7(b) shows the amplitude and phase of the current
transmission.
REFERENCES
1. Felker, J. H., Regenerative Amplifier for Digital Computer Applications,
Proc. I.R.E., pp. 1584-1596, Nov., 1952.
2. Korn, G. A., and Korn, T. M., Electronic Analog Computers, McGraw-Hil
Book Company, pp. 9-19.
3. Wallace, R. L. and Pietenpol, W. J., Some Circuit Properties and Applications
of n-p-n Transistors, B. S.T.J. , 30, pp. 530-563, July, 1951.
4. Shockley, W., Sparks, M. and Teal, G. K., The p-n Junction Transistor,
Physical Review, 83, pp. 151-162, July, 1951.
5. Pritchard, R. L., Frequenc}' Variation of Current-Amplification for Junction
Transistors, Proc. I.R.E., pp. 1476-1481, Nov., 1952.
6. Early, J. M., Design Theory of Junction Transistors, B.S.T.J., 32, pp. 1271-
1312, Nov., 1953.
7. Sziklai, G. C, Symmetrical Properties of Transistors and Their Applications,
Proc. I.R.E., pp. 717-724, June, 1953.
8. Bode, H. W., Network Analysis and Feedback Amplifier Design, Van Nos-
trand Co., Inc., Chapter IV.
9. Bode, H. W., Op. Cit., pp. 66-69.
10. Bode, H. W., Op. Cit., pp. 162-164.
11. Bargellini, P. M. and Herscher, M. B., Investigation of Noise in Audio Fre-
quency Amplifiers Using Junction Transistors, Proc. I.R.E., pp. 217-226,'
Feb., 1955.
12. Bode, H. W., Op. Cit., pp. 464-468, and pp. 471-473.
13. Keonjian, E., Temperature Compensated DC Transistor Amplifier, Proc:
I.R.E., pp. 661-671, April, 1954.
14. Kretzmer, E. R., An Amplitude Stabilized Transistor Oscillator, Proc. I.R.E.,«
pp. 391-401, Feb., 1954. i
15. Goldberg, E. A., Stabilization of Wide-Band Direct-Current Amplifiers for
Zero and Gain, R.C.A. Review, June, 1950.
16. Ebers, J. J. and Moll, J. L., Large Signal Behavior of Junction Transistors.
Proc. I.R.E., pp. 1761-1772, Dec, 1954.
17. Manlej', J. M., Some General Properties of Magnetic Amplifiers, Proc. I.R.K.
March, 1951.
18. M.I.T., Waveforms, Volume 19 of the Radiation Laboratories Series. McGraw
Hill Book Company, pp. 342-344.
Electrolytic Shaping of Germanium
, and Silicon
^ By A. UHLIR, JR.
i (Manuscript received November 9, 1955)
Properties of electrolyte-semiconductor barriers are described, with em-
phasis on germanium. The use of these barriers in localizing electrolytic
! etching is discussed. Other localization techniques are mentioned. Electro-
lytes for etching germanium and silicon are given.
I
INTRODUCTION
I
I Mechanical shaping techniques, such as abrasive cutting, leave the
surface of a semiconductor in a damaged condition which adversely
affects the electrical properties of p-n junctions in or near the damaged
j material. Such damaged material may be removed by electrolytic etch-
ing. Alternatively, all of the shaping may be done electrolytically, so
that no damaged material is produced. Electrolytic shaping is particu-
[ larly well suited to making devices with small dimensions.
I A discussion of electrolytic etching can conveniently be divided into
[■ two topics — the choice of electrolyte and the method of localizing the
ji etching action to produce a desired shape. It is usually possible to find
1 an electrolyte in which the rate at which material is removed is accurately
proportional to the current. For semiconductors, just as for metals, the
I choice of electrolyte is a specific problem for each material ; satisfactory
j electrolytes for germanium and silicon will be described.
The principles of localization are the same, whatever the electrolyte
used. Electrolytic etching takes place where current flows from the
semiconductor to the electrolyte. Current flow may be concentrated at
I certain areas of the semiconductor-electrolyte interface by controlling
the flow of current in the electrolyte or in the semiconductor.
LOCALIZATION IN ELECTROLYTE
Localization techniques involving the electrolytic current are appli-
cable to both metals and semiconductors. In some of these techniques,
333
334 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
the localization is so effective that the barrier effects found with n-type
semiconductors can be ignored; if not, the barrier can be overcome by
light or heat, as will be described below.
If part of the work is coated with an insulating varnish, electrolytic
etching will take place only on the uncoated surfaces. This technique,
often called "masking," has the limitation that the etching undercuts
the masking if any considerable amount of material is removed. The i
same limitation applies to photoengraving, in which the insulating coat-
ing is formed by the action of light.
The cathode of the electrolytic cell may be limited in size and placed
close to the work (which is the anode). Then the etching rate will be
greatest at parts of the work that are nearest the cathode. Various
shapes can be produced by moving the cathode with respect to the I
work, or by using a shaped cathode. For example, a cathode in the form |
of a wire has been used to slice germanium.
Instead of a true metallic cathode, a "virtual cathode" may be used
to localize electrolysis.^ In this technique, the anode and true cathode
are separated from each other by a nonconducting partition, except for
a small opening in the partition. As far as localization of current to the
anode is concerned, the small opening acts like a cathode of equal size
and so is called a virtual cathode. The nonconducting partition may
include a glass tube drawn down to a tip as small as one micron diameter
but nevertheless open to the flow of electrolytic current. With such a
tip as a virtual cathode, micromachining can be conducted on a scale
comparable to the wavelength of visible light. A general advantage of
the virtual cathode technique is that the cathode reaction (usually
hydrogen evolution) does not interfere with the localizing action nor
with observation of the process. :|
In the jet-etching technique, a jet of electrolyte impinges on the
work.^'* The free streamlines that bound the flowing electrolyte are
governed primarily by momentum and energy considerations. In turn,
the shape of the electrolyte stream determines the localization of etch-
ing. A stream of electrolyte guided by wires has been used to etch semi-
conductor devices.^ Surface tension has an important influence on the
free streamlines in this case,
PROPERTIES OF ELECTROLYTE-SEMICONDUCTOR BARRIERS
The most distinctive feature of electrolytic etching of semiconductors
is the occurrence of rectifying barriers. Barrier effects for germanium
will be described; those for silicon are qualitatively similar.
The voltage-current curves for anodic n-type and p-type germanium
ELECTROLYTIC SHAPING OF GERMANIUM AND SILICON
335
[in 10 per cent KOH are shown in Fig. 1. Tlie concentration of KOH
[is not critical and other electrolytes give similar results. The voltage
'drop for the p-type specimen is small. For anodic n-type germanium,
! however, the barrier is in the reverse or blocking direction as evidenced
by a large voltage drop. The fact that n-type germanium differs from
p-type germanium only by very small amounts of impurities suggests
that the barrier is a semiconductor phenomenon and not an electro-
i chemical one. This is confirmed by the light sensitivity of the n-type
1 voltage-current characteristic. Fig. 2 is a schematic diagram of the
! arrangement for obtaining voltage-current curves. A mercury-mercuric
loxide-10 per cent KOH reference electrode was used at first, but a gold
(wire was found equally satisfactory. At zero current, a voltage Vo exists
j between the germanium and the reference electrode ; this voltage is not
[included in Fig. 1.
I The saturation current Is , measured for the n-type barrier at a
\moderate reverse voltage (see Fig. 1), is plotted as a function of tempera-
Iture in Fig. 3. The saturation current increases about 9 per cent per
[degree, just as for a germanium p-n junction, which indicates that the
I
40
35
30
^25
Lil
O 20
15
10
1
12 OHM-CM
n-TYPE
/
DAR\<.
1
/
/
1
1
1
1
1
/
1
1
1
1
1
WITH ;
LIGHT ^'
1
1
I
1
1
1
n
i
1
1
/
/ P-
FYPE
10 20 30 40 50 60
CURRENT FLOW IN MILLIAMPERES PER CM^
Fig. 1 — Anodic voltage-current characteristics of germanium.
336
THE BELL SYSTEM TECHXICAL JOURNAL, MARCH 1956
current is proportional to the equilibrium density of minority carriers
(holes). The same conclusion may be drawn from Fig. 4, which shows
that the saturation current is higher, the higher the resistivity of the
n-type germanium. But the breakdown voltages are variable and usu-
ally much lower than one would expect for planar p-n junctions made,
for example, by alloying indium into the same n-type germanium.
Breakdown in bulk junctions is attributed to an avalanche multipli-
cation of carriers in high fields.^ The same mechanism may be responsible
for breakdown of the germanium-electrolyte barrier; low and variable
breakdown voltages may be caused by the pits described below.
The electrolyte-germanium barrier exhibits a kind of current multi-
plication that differs from high-field multiplication in two respects: it
occurs at much lower reverse voltages and does not vary much with
voltage.^ This effect can be demonstrated very simply by comparison
with a metal-germanium barrier, on the assumption that the latter has
a current multiplication factor of unity. This assumption is supported
by experiments which indicate that current flows almost entirely by
hole flow, for good metal-germanium barriers.
The experimental arrangement is indicated in Fig. 5(a) and (b). The
voltage-current curves for an electrolyte barrier and a plated barrier on
the same slice of germanium are shown in Fig. 5(c).* The curves for the
REFERENCE
ELECTRODE
CATHODE
LIGHT
Fig. 2 — Arrangement for obtaining voltage current characteristics.
* In Fig. 5 the dark current for the phited barrier is much hirger than can be
exphained on the basis of hole current; it is even higher than the dark current for
the electrolyte barrier, which should be at least 1.4 times the hole current. This
excess dark current is believed to be leakage at the edges of the plated area and
probably does not affect the intrinsic current multiplication of the plated barrier
as a whole.
ELECTROLYTIC SHAPING OF GERMANIUM AND SILICON
337
10
2
o
a.
01
a.
to
Ui
oc
LU
Q.
5
<
_)
m
cc
tr
3
U
z
o
cc
3
(0
•> I
10"
/
{
-
/
-
1
/
7
/
/
/
-
/%
-
/
/
/
/
n/
^
y
i<:i
0 10 20 30 40 50 60
TEMPERATURE IN DEGREES CENTIGRADE
Fig. 3 — Temperature variation of the saturation current of a barrier between
5.5 ohm-cm n-type germanium and 10 per cent KOH solution.
illuminated condition were obtained by shining light on a dry face of a
slice while the barriers were on the other face. The difference between
the light and dark currents is larger for the electrolyte-germanium bar-
rier than for the metal-germanium barrier, by a factor of about 1.4.
The transport of holes through the slice is probably not very different
for the two barriers. Therefore, a current multiplication of 1.4 is indi-
cated for the electrolyte barrier. About the same value was found for
temperatures from 15°C to 60°C, KOH concentrations from 0.01 per
cent to 10 per cent, n-type resistivities of 0.2 ohm-cm to 6 ohm-cm,
light currents of 0.1 to 1.0 ma/cm^, and for O.IN indium sulfate.
Evidently the flow of holes to the electrolyte barrier is accompanied
by a proportionate return flow of electrons, which constitutes an addi-
tional electric current. Possible mechanisms for the creation of the
electrons will be discussed in a forthcoming article.
338 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
7
> 4
LU
o
>
I
0,5 1.0 1
CURRENT F
5 2.0 2.5 3.0 3.5 4.0
LOW IN MILLIAMPERES PER CM^
4.5
Fig. 4. — Anodic voltage -current curves for various resistivities of germanium.
SCRATCHES AND PITTING
The voltage- current curve of an electrolyte-germanium barrier is
very sensitive to scratches. The curves given in the illustrations were :
obtained on material previously etched smooth in CP-4, a chemical I
etch.* ''
If, instead, one starts with a lapped piece of n-type germanium, the
electrolyte-germanium barrier is essentially "ohmic;" that is, the voltage
drop is small and proportional to the current. A considerable reverse
voltage can be attained if lapped n-type germanium is electrolytically
etched long enough to remove most of the damaged germanium. How-
ever, a pitted surface results and the breakdown voltage achieved is
not as high as for a smooth chemically-etched surface.
The depth of damage introduced by typical abrasive sawing and
lapping was investigated by noting the voltage-current curve of the
Br2
Five parts HNO3 , 3 parts 48 per cent HF, 3 parts glacial acetic acid, ^0 P^-^t
ELECTROLYTIC SHAPING OF GERMANIUM AND SILICON
339
electrolyte-germanium barrier after various amounts of material had
been removed by chemical etching. After 20 to 50 microns had been re-
moved, further chemical etching produced no change in the barrier
characteristic. This amount of material had to be removed even if the
lapping was followed by polishing to a mirror finish. The voltage-current
curve of the electrolyte-germanium barrier will reveal localized damage.
On the other hand, the photomagnetoelectric (PME) measurement of
I
-< —
REFERENCE
ELECTRODE
CATHODE-
--
-^
■<
■y
GLASS TUBING
CEMENTED
TO Ge
E
LECTROLYT
z i
N-Ge
■^
1
1
1
1
<rri>
(a)
ELECTROPLATED
INDIUM
METAL TO N-Ge
CONTACT
ELECTROLYTE TO
N-Ge BARRIER
(c)
0 2 4 6
CURRENT, I, IN MILLIAMPERES
PER CM 2
Fig. 5 — Determination of the current multiplication of the barrier between
6 ohm-cm n-type germanium and an electrolyte.
340 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
Fig. 6 — Electrolytic etch pits on two sides of 0.02-inch slice of n-type germa-
nium. Half of the slice was in contact with the electrolyte.
surface recombination velocity gives an evaluation of the average con-
dition of the surface. A variation of the PME method has been used
to study the depth of abrasion damage; the damage revealed by this
method extends only to a depth comparable to the abrasive size.
A scratch is sufficient to start a pit that increases in size without limit
if anodic etching is prolonged. However, a scratch is not necessary. Pits
are formed even when one starts with a smooth surface produced by
chemical etching. A drop in the breakdown voltage of the barrier is
noticed when one or more pits form. The breakdown voltage can be
restored by masking the pits with polystyrene cement.
Evidence that the spontaneous pits are caused by some features of
the crystal, itself, was obtained from an experiment on single-crystal
n-type germanium made by an early version of the zone-leveling process.
A slice of this material was electrolytically etched on both sides, after
preliminary chemical etching. Photographs of the two sides of the slice
are shown in Fig. 6. Only half of the slice was immersed in the electro-
lyte. The electrolytic etch pits are concentrated in certain regions of
the slice — the same general regions on both sides of the slice. It is
interesting that radioautographs and resistivity measurements indicate
high donor concentrations in these regions. Improvements, including
more intensive stirring, were made in the zone-leveling process, and the
electrolytic etch pit distribution and the donor radioautographs have
been much more uniform for subsequent material.
Several pits on a (100) face are shown in Fig. 7. The pits grow most
rapidly in (100) directions and give the spiked effect seen in the illustra-
tion. Toiler prolonged etching, the spikes and their branches form a com-
plex network of caverns beneath the surface of the germanium.
High-field carrier generation may be responsible for pitting. A locally
ELECTROLYTIC SHAPING OF GERMAXIUM AND SILICON
341
Fig. 7 — Electrolytic etch pits on n-type germanium.
high donor concentration would favor breakdown, as would any con-
cavity of the germanium surface (which would cause a higher field for
a given voltage) . Very high fields must occur at the points of spikes such
jas those shown in Fig. 7. The continued growth of the spikes is thus
favored by their geometry.
Microscopic etch pits arising from chemical etching have been corre-
;lated with the edge dislocations of small-angle grain boundaries. A
I specimen of n-type germanium with chemical etch pits was photomicro-
graphed and then etched electrolytically. The etch pits produced elec-
trolytically could not be correlated with the chemical etch pits, most
of which were still visible and essentially unchanged in appearance.
Also, no correlation could be found between either kind of etch pit and
the locations at which copper crystallites formed upon immersion in a
copper sulfate solution. Microscopic electrolytic etch pits at dislocations
j in p-type germanium have been reported in a recent paper that also
I mentions the deep pits produced on n-type germanium.^*
y Electrolytic etch pits are observed on n-type and high-resistivity
silicon. These etch pits are more nearly round than those produced in
germanium.
In spite of the pitting phenomenon, electrolytic etching is success-
342
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
I
fully used in the fabrication of devices involving n-type semiconductors.
Pitting can be reduced relative to "normal" uniform etching by any
agency that increases the concentration of holes in the semiconductor.
Thus, elevated temperatures, flooding with light, and injection of holes
by an emitter all favor smooth etching.
SHAPING BY MEANS OF INJECTED CARRIERS
I
Hole-electron pairs are produced when light is absorbed by semi-
conductors. Light of short wavelength is absorbed in a short distance,
while long wavelength light causes generation at considerable depths.
The holes created by the light move by diffusion and drift and increase
the current flow through an anodic electrolyte-germanium barrier at
whatever point they happen to encounter the barrier. In general, more
holes will diffuse to a barrier, the nearer the barrier is to the point at
which the holes are created. For n-type semiconductors, the current
due to the light can be orders of magnitude greater than the dark cur-
rent, so that the shape resulting from etching is almost entirely deter-
mined by the light. As shown in Fig. 3, the dark current can be made
very small by lowering the temperature.
An example of the shaping that can be done with light is shown in
Fig. 8. A spot of light impinges on one side of a wafer of n-type germanium
or silicon. The semiconductor is made anodic with respect to an etching
electrolyte. Accurately concentric dimples are produced on both sides of
the wafer. Two mechanisms operate to transmit the effect to the oppo-
site side. One is that some of the light may penetrate deeply before
generating a hole-electron pair. The other is that a fraction of the car-
riers generated near the first surface will diffuse to the opposite side.
By varying the spectral content of the light and the depth within the \
\
-n-TYPE SEMICONDUCTOR
LIGHT
I I
Fig. 8 — Double dimpling with light.
ELECTROLYTIC SHAPING OF GERMANIUM AND SILICON
343
wafer at which the light is focused, one can produce dimples with a vari-
,'ety of shapes and relative sizes.
I It is obvious that the double-dimpled wafer of Fig. 8 is desirable for
{the production of p-n-p alloy transistors. For such use, one of the most
[important dimensions is the thickness remaining between the bottoms
of the two dimples. As has been mentioned in connection with the jet-
I etching process, a convenient way of monitoring this thickness to de-
Itermine the endpoint of etching is to note the transmission of light of
[suitable wavelength.^ There is, however, a control method that is itself
[automatic. It is based on the fact that at a reverse-biased p-n junction
[Or electrolyte-semiconductor barrier there is a space-charge region that
is practically free of carriers. When the specimen thickness is reduced
so that space-charge regions extend clear through it, current ceases to
flow and etching stops in the thin regions, as long as thermally or op-
tically generated carriers can be neglected. However, more pitting is to
be expected in this method than when etching is conducted in the pres-
ence of an excess of injected carriers.
A p-n junction is a means of injecting holes into n-type semiconduc-
tors and is the basis of another method of dimpling, shown in Fig. 9.
The p-n junction can be made by an alloying process such as bonding
an acceptor-doped gold wire to germanium. The ohmic contact can be
made by bonding a donor-doped gold wire and permits the injection of
a greater excess of holes than would be possible if the current through
the p-n junction were exactly equal to the etching current. Dimpling
without the ohmic contact has been reported.^
14
OHMIC CONTACT
p-n JUNCTION
Fig. 9 — Dimpling with carriers injected by a p-n junction.
344
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
CONTROL BY OHMIC CONDUCTION
The carrier-injection shaping techniques work very well for n-typei
material. It is also possible to inject a significant number of holes intos
rather high resistivity p-type material. But what can be done about:
p-type material in general, short of developing cathodic etches? ]
The ohmic resistivity of p-type material can be used as shown in Fig.!^
10. More etching currect flows through surfaces near the small contact
than through more remote surfaces. A substantial dimpling effect is
observed when the semiconductor resistivity is equal to the electrolyte
resistivity, but improved dimpling is obtained on higher resistivity
semiconductor. This result is just what one might expect. But the math-
ematical solution for ohmic flow from a point source some distance from
a planar boundary between semi-infinite materials of different conduc-
tivities shows that the current density distribution does not depend on
the conductivities. An important factor omitted in the mathematical
solution is the small but significant barrier voltage, consisting largely of
electrochemical polarization in the electrolyte. The barrier voltage is;
approximately proportional to the logarithm of the current density;
while the ohmic voltage drops are proportional to current density. Thus,-
high current favors localization.
ELECTROLYTES FOR ETCHING GERMANIUM AND SILICON »
The electrolyte usually has two functions in the electrolytic etching
of an oxidizable substance. First, it must conduct the current necessary
for the oxidation. Second, it must somehow effect removal of the oxida-
tion product from the surface of the material being etched.
The usefulness of an electrolytic etch depends upon one or both of:
ANY CONTACT,
PREFERABLY OHMIC
^//yyyy//y/y/y////////y////y/////yyyyyyyyyyy7^
Fig. 10 — Dimpling by ohmic conduction.
ELECTROLYTIC SHAPING OF GERMANIUM AND SILICON 345
the following situations — the electrolytic process accomplishes a reac-
tion that cannot be achieved as conveniently in any other way or it
permits greater control to be exercised over the reaction. Accordingly,
chemical attack by the chosen electrolyte must be slight relative to the
electrochemical etching.
A smooth surface is probably desirable in the neighborhood of a p-n
junction, to avoid field concentrations and lowering of breakdown
voltage. Therefore, a tentative requirement for an electrolyte is the
production of a smooth, shiny surface on the p-type semiconductor. Such
\ an electrolyte will give a shiny but possibly pitted surface on n-type
j specimens of the same semiconductor.
The effective valence of a material being electrolytically etched is
; defined as the number of electrons that traverse the circuit divided by
the number of atoms of material removed. (The amount of material
! removed was determined by weighing in the experiments to be described.)
If the effective valence turns out to be less than the valence one might
predict from the chemistry of stable compounds, the etching is sometimes
said to be "more than 100 per cent efficient." Since the anode reactions
in electrolytic etching may involve unstable intermediate compounds
and competing reactions, one need not be surprised at low or fractional
effective valences.
Germanium can be etched in many aqueous electrolytes. A valence of
almost exactly 4 is found. That is, 4 electrons flow through the circuit
for each atom of germanium removed. For accurate valence measure-
ments, it is advisable to exclude oxygen by using a nitrogen atmosphere.
Potassium hydroxide, indium sulfate, and sodium chloride solutions are
among those that have been used. Sulfuric acid solutions are prone to
) yield an orange-red deposit which may be a suboxide of germanium/*
I Similar orange deposits are infrequently encountered with potassium
I hydroxide.
Hydrochloric acid solutions are satisfactoiy electrolytes. The reaction
I product is removed in an unusual manner when the electrolyte is about
2N hydrochloric acid. Small droplets of a clear liquid fall from the etched
regions. These droplets may be germanium tetrachloride, which is denser
than the electrolyte. They turn brown after a few seconds, perhaps be-
cause of hydrolysis of the tetrachloride.
Etching of germanium in sixteen different aqueous electroplating
electrolytes has been mentioned. Germanium can also be etched in the
partly organic electrolytes described below for silicon.
One would expect that silicon could be etched by making it the anode
in a cell with an aqueous hydrofluoric acid electrolyte. The seemingly
346 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956 |
)
likely oxidation product, silicon dioxide, should react with the hydro-!
fluoric acid to give silicon tetrafluoride, which could escape as a gas. In
fact, a gas is formed at the anode and the silicon loses weight. But the
gas is hydrogen and an effective valence of 2.0 ± 0.2 (individual deter-
minations ranged from 1.3 to 2.7) was found instead of the value 4 that i
might have been expected. The quantity of hydrogen evolved is con-
sistent with the formal reaction
Si —> Si"*"'" + me (electrochemical oxidation)
Si+™ + (4-to)H+ -^ Si+' + Vz (4-m)H2 (chemical oxidation)
where m is about two. The experiments were done in 24 per cent to 48
per cent aqueous solutions of HF at current densities up to 0.5 amp/cm^.
The suggestion that the electrochemical oxidation precedes the chemi-
cal oxidation is supported by the appearance and behavior of the etched
surfaces. Instead of being shiny, the surfaces have a matte black, brown,
or red deposit.
At 40 X magnification, the deposit appears to consist of flakes of a;
resinous material, tentatively supposed to be a silicon suboxide. A re-
markable reaction can be demonstrated if the silicon is rinsed briefly in
water and alcohol after the electrolytic etch, dried, and stored in air for
as long as a year. Upon reimmersing this silicon in water, one can observe
the liberation of gas bubbles at its surface. This gas is presumed to be
hydrogen. To initiate the reaction it is sometimes necessary to dip the
specimen first in alcohol, as water may otherwise not wet it. The speci-
mens also liberate hydrogen from alcohol and even from toluene.
Thus, chemical oxidation can follow electrolytic oxidation. But
chemical oxidation does not proceed at a significant rate before thei
current is turned on.
Smooth, shiny electrolytic etching of p-type silicon has been obtained;
with mixtures of hydrofluoric acid and organic hydroxyl compounds,;
such as alcohols, glycols, and glycerine. These mixtures may be an-
hydrous or may contain as much as 90 per cent water. The organic
additives tend to minimize the chemical oxidation of the silicon. They;
also permit etching at temperatures below the freezing point of aqueous
solutions. They lower the conductivity of the electrolyte.
For a given electrolyte composition, there is a threshold current
density, usually between 0.01 and 0.1 amps/cm , for smooth etching.;
Lower current densities give black or red surfaces with the same hy-
drogen-liberating capabilities as those obtained in aqueous hydrofluoric
acid.
ELECTROLYTIC SHAPING OF GERMANIUM AND SILICON 347
In general, smooth etching of siHcon seems to result when the effective
valence is nearly 4 and there is little anodic evolution of gas. The elec-
I trical properties of the smooth surface appear to be equivalent to those
! of smooth silicon surfaces produced by chemical etching in mixtures of
i nitric and hydrofluoric acids. On the other hand, the reactive surface
[produced at a valence of about 2, with anodic hydrogen evolution, is
I capable of practically shorting-out a silicon p-n junction. The electrical
j properties of this surface tend to change upon standing in air.
ACKNOWLEDGEMENTS
Most of the experiments mentioned in this paper were carried out by
my wife, Ingeborg. An exception is the double-dimpling of germanium
by light, which was done by T. C. Hall. The dimpling procedures of
Figs. 9 and 10 are based on suggestions by J. M. Early. The effect of
light upon electrolytic etching was called to my attention by 0. Loosme.
W. G. Pfann provided the germanium crystals grown with different
degrees of stirring.
REFERENCES
1. J. F. Barry, I.R.E.-A.I.E.E. Semiconductor Device Research Conference,
Philadelphia, June, 1955.
2. A. Uhlir, Jr., Rev. Sci. Inst., 26, pp. 965-968, 1955.
3. W. E. Bailey, U. S. Patent No. 1,416, 929, May 23, 1922.
4. Bradley, et al. Proc. I.R.E., 24, pp. 1702-1720, 1953.
5. M. V. Sullivan and J. H. Eigler, to be published.
6. S. L. Miller, Phys. Rev. 99, p. 1234, 1955.
7. W. H. Brattain and C. G. B. Garrett, B.S.T.J., 34, pp. 129-176, 1955.
8. E. H. Borneman, R. F. Schwarz, and J. J. Stickler, J. Appl. Phvs., 26, pp.
1021-1029, 1955.
9. D. R. Turner, to be submitted to the Journal of the Electrochemical Society.
10. R. D. Heidenreich, U. S. Patent No. 2,619,414, Nov. 25, 1952.
11. T. S. Moss, L. Pincherle, A. M. Woodward, Proc. Phys. Soc. London, 66B,
p. 743, 1953.
12. T. M. Buck and F. S. McKim, Cincinnati Meeting of the Electrochemical
Society, Mav, 1955.
13. F. L. Vogel, W. G. Pfann, H. E. Corey, and E. E. Thomas, Phys. Rev., 90,
p. 489, 1953.
14. S. G. Ellis, Phys. Rev., 100, pp. 1140-1141, 1955.
15. Electronics, 27, No. 5, p. 194, May, 1954.
16. F. Jirsa, Z. f. Anorg. u. AUgemeine Chem., Bd. 268, p. 84, 1952.
\
A Large Signal Theory of Traveling
Wave Amplifiers
Including the Effects of Space Charge and Finite
Coupling Between the Beam and the Circuit
By PING KING TIEN
Manuscript received October 11, 1955)
The non-linear behavior of the traveling-wave amplifier is calculated in
this paper by numericalhj integrating the motion of the electrons in the
presence of the circuit and the space charge fields. The calculation extends
the earlier work by Nordsieck and the srnall-C theory by Tien, Walker and
Wolontis, to include the space charge repulsion between the electrons and
the effect of a finite coupling between the circuit and the electron beam. It
however differs from Poulter's and Rowers works in the methods of calcu-
lating the space charge and the effect of the backward wave.
The numerical work was done using 701 -type I.B.M. equipment. Re-
sults of calcidation covering QC from 0.1 to 0.4, b from 0.46 to 2.56 and k
from 1.25 to 2.50, indicate that the saturation efficiency varies between
23 per cent and 37 per cent for C equal to 0.1 and between 33 per cent and
Jf.0 per cent for C equal to 0.15. The voltage and the phase of the circuit wave,
the velocity spread of the electrons and the fundamental component of the
charge-density modidation are either tabulated or presented in curves. A
method of calculating the backward wave is provided and its effect fully
discussed.
1. INTRODUCTION
Theoretical evaluation of the maximum efficiency attainable in a
traveling-wave amplifier requires an understanding of the non-linear
behavior of the device at various working conditions. The problem has
been approached in many ways. Pierce/ and later Hess,^ and Birdsalf
and Caldwell investigated the efficiency or the output power, using cer-
tain specific assumptions about the highly bunched electron beam. They
either assume a beam in the form of short pulses of electrons, or, specify
349
350 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
an optimum ratio of the fundamental component of convection current
to the average or d-c current. The method, although an abstract one,
generally gives the right order of the magnitude. When the usual wave
concept fails for a beam in which overtaking of the electrons arises, we
may either overlook effects from overtaking, or, using the Boltzman's
transport equation search for solutions in series form. This attack has
been pursued by Parzen and Kiel, although their work is far from com-
plete. The most satisfying approach to date is Nordsieck's analysis.'
Nordsieck followed a typical set of "electrons" and calculated their
velocities and positions by numerically integrating a set of equations of
motion. Poulter has extended Nordsieck equations to include space
charge, finite C and circuit loss, although he has not perfectly taken into
account the space charge and the backward wave. Recently Tien,
Walker, and Wolontis have published a small C theory in which "elec-
trons" are considered in the form of uniformly charged discs and the
space charge field is calculated by computing the force exerted on one
disc by the others. Results extended to finite C, have been reported by
Rowe,^*^ and also by Tien and Walker.^^ Rowe, using a space charge
expression similar to Poulter's, computed the space charge field based on
the electron distribution in time instead of the distribution in space. This
may lead to appreciable error in his space charge term, although its
influence on the final results cannot be easily evaluated.
In the present analysis, we shall adopt the model described by Tien,
Walker and Wolontis, but wish to add to it the effect of a finite beam to
circuit coupling. A space charge expression is derived taking into account
the fact that the a-c velocities of the electrons are no longer small com-
pared with the average velocity. Equations are rewritten to retain terms
involving C. As the backward wave becomes appreciable when C in-
creases, a method of calculating the backward wave is provided and the
effect of the backward wave is studied. Finally, results of the calculation
covering useful ranges of design and operating parameters are presented
and analyzed.
2. ASSUMPTIONS
To recapitulate, the major assumptions which we have made are:
1. The problem is considered to be one dimensional, in the sense that
the transverse motions of the electrons are prohibited, and the current,
velocity, and fields, are functions only of the distance along the tube and
of the time.
2. Only the fundamental component of the current excites waves on
the circuit.
A LARGE SIGNAL THEORY OF TRAVELING-WAVE AMPLIFIERS 351
3. The space charge field is computed from a model in which the
helix is replaced by a conducting cylinder, and electrons are uniformly
charged discs. The discs are infinitely thin, concentric with the helix and
have a radius equal to the beam radius.
4. The circuit is lossfree.
These are just the assumptions of the Tien-Walker-Wolontis model.
In addition, we shall assume a small signal applied at the input end of a
long tube, where the beam entered unmodulated. What we are looking
for are therefore the characteristics of the tube beyond the point at which
the device begins to act non-linearly. Let us imagine a flow of electron
discs. The motions of the discs are computed from the circuit and the
space charge fields by the familiar Newton's force equation. The elec-
trons, in turn, excite waves on the circuit according to the circuit equa-
tion derived either from Brillouin's model^ or from Pierce's equivalent
circuit. The force equation, the circuit equation, and the equation of
conservation of charge in kinematics, are the three basic equations
from which the theory is derived.
3. FORWARD AND BACKWARD WAVES
In the traveling-wave amplifier, the beam excites forward and back-
ward waves on the circuit. (We mean by "forward" wave, the wave
which propagates in the direction of the electron flow, and by "back-
ward" wave, the wave which propagates in the opposite direction.)
Because of phase cancellation, the energy associated with the backward
wave is small, but increases with the beam to circuit coupling. It is there-
fore important to compute it accurately. In the first place, the waves on
the circuit must satisfy the circuit equation
dH^(z,t) 2d'V{z,t) „ d'p^iz, t) ,v
Here, V is the total voltage of the waves. Vo and Zo are respectively the
phase velocity and the impedance of the cold circuit, z is the distance
along the tube and t, the time, p^ is the fundamental component of the
linear charge density. V and p„ are functions of z and /. The complete
solution of (1) is in the form
Viz) = Cre'^'' + (726 "^"^
+ e —-y— J e " po,{^) dz ^2)
+ e " —^ j e p^{z) dz
352 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
where the common factor e^"' is omitted. To = j{co/vo), j = \/— 1 and w
is the angular frequency. Ci and C2 are arbitrary constants which will
be determined by the boundary conditions at the both ends of the beam.
The first two terms are the solutions of the homogeneous equation (or
the complementary functions) and are just the cold circuit waves. The
third and the fourth terms are functions of electron charge density and
are the particular solution of the equation.
Let us consider a long traveling-wave tube in which the beam starts
from z = 0 and ends at 2; = D. The motion of electrons observed at any
particular position is periodic in time, though it varies from point to
point along the beam. To simplify the picture, we may divide the beam
along the tube into small sections and consider each of them as a current
element uniform in z and periodic in time. Each section of beam, or each
current element excites on the circuit a pair of waves equal in ampli-
tudes, one propagating toward the right (i.e., forward) and the other,
toward the left. One may in fact imagine that these are trains of waves
supported by the periodic motion of the electrons in that section of the
beam. Obviously, a superposition of these waves excited by the whole
beam gives the actual electromagnetic field distribution on the circuit.
One may thus compute the forward traveling wave at z by summing all
the waves at z which come from the left. Stated more specifically, the
forward traveling energy at z is contributed by the waves excited by the
current elements at the left of the point z. Similarly the backward travel-
ing energy, (or the backward wave) at z is contributed by the waves
excited by the current elements at the right of the point z. It follows
obviously from this picture that there is no forward wave at 2 = 0
(except one corresponding to the input signal), and no backward wave
at 2 = D. (This implies that the output circuit is matched.) With these
boundary conditions, (1) is reduced to
z) = Finput e " + e ° — -— / e " po,{z)
Z Jo
dz
+ /-^J e-%.(.)
(3)
dz
Equations (2) and (3) have been obtained by Poulter.^ The first term of
(3) is the wave induced by the input signal. It propagates as though the ;
beam were not present. The second term is the voltage at z contributed
by the charges between 2 = 0 and 2 = 2. It is just the voltage of the
forward wave described earlier. Similarly the third term which is the
voltage at 2 contributed by the charges between z = z and 2 = D is the
voltage of the backward wave at the point 2. Denote F and B respec-
A LARGE SIGNAL THEORY OF TRAVELING-WAVE AMPLIFIERS 353
tively the voltages of the forward and the backward waves, we have
F{z) = Fi„put e-'"^ + e-^»^ ^« r e'^' p^z) dz (4)
Z Jo
Biz) = e^- ^° £ e-^-p„(e) dz (5)
It can be shown by direct substitution that F and B satisfy respectively
the differential equations
dz Vo dt 2 (9^
(6)
dB(z, t) 1 a5(2, 0 Zo ap„(2, 0
(92 1^0 di 2 dt
(7)
We put (4) and (5) in the form of (6) and (7) simply because the differ-
ential equations are easier to manipulate than the integral equations.
In fact, we should start the analysis from (6) and (7) if it were not for a
physical picture useful to the understanding of the problem. Equations
(6) and (7) have the advantage of not being restricted by the boundary
conditions at 2; = 0 and D, which we have just imposed to derive (4)
and (5). Actually, we can derive (6) and (7) directly from the Brillouin
model in the following manner. Suppose Y, I and Zo are respectively
the voltage, current and the characteristic impedance of a transmission
line system in the usual sense. (V + /Zo) must then be the forward wave
and {V — IZo) must be the backward wave. If we substituted F and B
in these forms into (1) of the Brillouin' s paper,^^ we should obtain exactly
(6) and (7).
It is obvious that the first and third terms of (2) are respectively the
complementary function and the particular solution of (6), and similarly
the second and the fourth terms of (2) are respectively the comple-
mentary function and the particular solution of (7). From now on, we
shall overlook the complementary functions which are far from syn-
chronism with the beam and are only useful in matching the boundary
conditions. It is the particular solutions which act directly on the elec-
tron motion. With these in mind, it is convenient to put F and B in the
form
Fiz, t) = -j~ [aiiij) cos <p - aiiy) sin ^] (8)
B{z, t) = -^ [hiiy) cos ip - h^iy) sin 9?] (9)
354 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
where ai(y), 02(2/), hi(y) and 62(2/) are functions of y. y and <p are inde-
pendent variables and have been used by Nordsieck to replace the vari-
ables, z and t, such as
y = C — Z
(f = w [ — — t ]
\Vo /
Here as defined earlier, I'o is the phase velocity of the cold circuit and Vq
the average velocity of the electrons. They are related by the parameter
h defined by Pierce as
Uo 1
vo (1 - hC)
C is the gain parameter also defined by Pierce,
^3 _ ZqIo
in which, Vo and 7o are respectively the beam voltage and current.
Adding (6) to (7), we obtain an important relation between F and B,
that is,
dFjz, t) _^ 1_ dF{z, t) ^ dBjz, t) _j_ l_ dBjz, t) ^^Q^
dz Vo dt dz Vo dt
Substituting (8) and (9) into (10) and carrying out some algebraic
manipulation, we obtain
'"'^^ = "2(1 + bC) I ^'^^'> + "'-^"^^
(11)
"'^^'^ = 2(1 + bC) ly '"'^^^ + '"^^^'
or
B{z, t) =
ZqIo C
dMy) + bM) ,„, ^ + diaM+ b.(,j)) ^.^ -
dy dy
[
For better understanding of the problem, we shall first solve (12a) ap-
proximately. Assuming for the moment that hiiy) and h^^y) are small
compared with ai{ij) and a^iy) and may be neglected in the right-hand
A LARGE SIGNAL THEORY OP TRAVELING-WAVE AMPLIFIERS 355
member of the equation, we obtain for the first order solution
iKz, t) ^
ZqIo I (^
sin <p + — ^^^ cos <p
40 \ 2(1 + bC) I dij ^ ' dy
(12b)
Of course, the solution (12b) is justified only when hi(y) and ?)2(?y) thus
obtained are small compared with ai(y) and aoiy). The exact solution
of B obtained by successive approximation reads
Biz, t)
+
ZqIo I c
4(7 V 2(1 + bC)
4(1 + hC)
It may be seen that the term involving
dai(y) . , da2(ij)
-^ sm <p + , cos
_ dy dy
■ ]
•]
'^^' cos<p + — f^sm^ +
(12c)
dy- dy-
4(1 + bcy
and the higher order terms are neglected in our approximate solution.
For C equal to few tenths, the difference between (r2b) and (12c) only
amounts to few per cent. We thus can calculate the backward wave by
(12b) or (12c) from the derivatives of the forward wave. To obtain the
complete solution of the backward wave, we should add to (12b) or
(12c) a solution of the homogeneous equation. We shall return to this
point later.
4. WORKING EQUATIONS
With this discussion of the backward wave, we are now in a position
to derive the working equations on which our calculations are based. In
Nordsieck's notation, each electron is identified by its initial phase.
Thus, (p(y, (fo) and Cuow(y, <po) are respectively the phase and the ac
velocity of the electron which has an initial phase (fo . It should be remem-
bered that y is equal to
and is used by Nordsieck as an independent variable to replace the vari-
al)le z. Let us consider an electron which is at Zo when /, = 0 and is at
z (or ?/) when t = /. Its initial phase is then
OiZo
<Po = —
356
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
and its phase at y is
<p(y,<po) = oj f- - tj
i
The velocity of the electron is expressed as
dz
dt
= Wo[l + Cw{ij, ip^)]
where Uo is the average velocity of the electrons, and, Cuow(y, tpo) as men-
tioned earlier, is the ac velocity of the electron when it is at the position
y. The electron charge density near an electron which has an initial phase
cpo and which is now at y, can be computed by the equation of conserva-
tion of charge, it is
p(y, <Po) = -
Wo
d(po
d(p{y, <po)
1
1 + Cw(y, ifo)
(13)
One should recall here that h is the dc beam current and has been de-
fined as a positive quantity. When several electrons with different initial
phases are present at y simultaneously, a summation of
d<po
of these electrons should be used in (13). From (13), the fundamental
component of the electron charge density is
pMt) = ---
sm
d<po
sin (fiy, <po)
1 + Cw{y, <pq)
r^" , cos <p{y, <po)
+ cos <p I d(po
Jo
(14)
1 + Cw(y, ifo)/
These are important relations given by Nordsieck and should be kept
in mind in connection with later work. In addition, we shall frequently
use the transformation
I = t s = ^"(' + ^'"(^-» 1^
which is written following the motion of the electron. Let us start from
the forward wave. It is computed by means of (6). After substituting
(8) and (14) into (6), we obtain by equating the sin <p and the cos v'
A LARGE SIGNAL THEORY OF TRAVELING-WAVE AMPLIFIERS 357
terms
dax{y) ^ _2 T^" ^ sin <p(y, cpo) .^.
dy IT h " 1 + Cwiv, (po)
da.Xy) 2 f^" cos<p{y,<po) ..^n
— 1 — = ~- / d(po , r (.lb;
dy IT Jo 1 + Cw{y, <po)
Next we shall calculate the electron motion. We express the acceleration
of an electron in the form
d'z „ /I I /o / ^^ dw{y, <po)
^ = Cuod + Cw{y, M -^^
and calculate the circuit field by differentiating F in (8) and B in (12c)
with respect to z. One thus obtains from Newton's law
2[1 + Cw{y, <po)] ^^'^J' ^°^ = (1 + hOMy) sin <p + a,{y) cos <p\
dy
+ ^-^ r^ «in ^ + ^^ cos J - -^ ^.
4(1 + 6C) L ^Z/- c?^^ J WomwC^
Here Eg is the space charge field, which will be discussed in detail later.
Finally a relation between w{y, (po) and <p{y, ^o) is obtained by means of
(13)
difiy, <po) _ ^ ^ ^^(y, <Po) QgN
dy 1 + Cw{y, <pq)
Equations (15), (16), (17) and (18) are the four working equations
which we have derived for finite C and including space charge.
Instead of writing the equations in the above form, Rowe, ignoring
the backward wave, derives (15) and (16) directly from the circuit
equation (1). He obtains an additional term
C d^tti
2 dy""
for (15) and another term
C d"ai
2df
for (16). It is apparent that the backward wave, though generally a
small quantity, does influence the terms involving C.
358
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
5. THE SPACE CHARGE EXPRESSION
We have mentioned earlier that the space charge field is computed
from the disc-model suggested by Tien, Walker and Wolontis. In their
calculation, the force excited on one disc by the other is approximated
by an exponential function
F. =
— [a(z'— z)/ro]
27rro-eo
Here ro is the radius of the disc or the beam, q is the charge carried by
each disc, and eo is the dielectric constant of the medium. The discs are
supposed to be respectively at z and z . a is a constant and is taken
equal to 2.
Consider two electrons which have their initial phases <pq and ^o and
which reach the position ij (or z) at times t and t' respectively. The time
difference,
* - / = 1
00
wt — — Z — [bit — — Z)
Vo \ Vq J
CO
multiplied by the velocity of the electron i<o[l + Cw(y, (po )] is obviously
the distance between the two electrons at the time t. Thus
(z - z)t=t = - y(y, <Po) - <p(y, <Po)]uo[l + Cw(y,ipo)] (19a)
In this equation, we are actually taking the first term of the Taylor's
expansion,
(z — z)t=t =
dzjij, cpo)
dt
t=t
(t _ /^ j_ ^ c?^2(y, <pq)
it - ty
t=t
(19b)
+
It is clear that the electrons at y may have widely different velocities
after having traveled a long distance from the input end, but changes in
their velocities, in the vicinity of y and in a time-period of around 2 tt,
are relatively small. This is why we must keep the first term of (19b)
and may neglect the higher order terms. From (19a) the space charge
field Es in (17) is
2e
Es =
/+00
-k]ip(.y ,<po+<t>)—<p(.U ,<Po) 1 li+Cw(y,(po+<t>)]
d(f> sgn (<p(<po -\- <p) - <t>iy, <po))
Here, e/m is the ratio of electron charge to mass, cop is the electron
A LARGE SIGNAL THEORY OF TRAVELING-WAVE AMPLIFIERS 359
angular plasma frequency for a beam of infinite extent, and k is
2
k =
a
0) CO
— ro — ro
Uo Wo
(20)
In the small C theory, th^e distribution of electrons in time or in time-
phase at z is approximately the same as the distribution in z (also ex-
pressed in the unit of time-phase) at the vicinity of z. This is, however,
not true when C becomes finite. The difference between the time and
space distributions is the difference between unity and the factor
(1 -}- Cw{y, <po )). We can show later that the error involved in con-
; sidering the time phase as the space phase can easily reach 50 per cent
or more, depending on the velocity spread of the electrons.
6. NUMERICAL CALCULATIONS
Although the process of carrying out numerical computations has
been discussed in Nordsieck's paper, it is desirable to recapitulate here
I a few essential points including the new feature added. Using the work-
ing equations (15), (16), (17) and (18),
dai da 2 dw , dcp
dy ' dy ' dy dy
\ are calculable from ai , a^ , w and <p. The distance is divided into equal
I intervals of A?/, and the forward integrations of Oi , ao , w and (p are per-
f formed by a central difference formula
ax{y + A?/) = ax{y) -f
dy
y+y2&y
■Ay
In addition.
d^ai
dy^
and
d 02
df
in (17) are computed from the second difference formula such that
d''ai
- At/
_ dtti da\
dy^ j/=j/ \_dy y+l/2i,y dy y-^/2^y_
We thus calculate the behavior along the tube by forward integration
j made in steps of Ay, starting from y = 0. At ?/ = 0 the initial condi-
tions are determined from Pierce's linearized theory. Because of its
complications in notation, this will be discussed in detail in Appendix I.
j Numerical calculations were carried out using the 701-type I.B.M.
Table I
a;
U
QC
k
c
6
Ml
MJ
ycsAT.)
<!
01!
H
•i
i
a.
1
1
0.1
2.5
0.05
0.455
m max.
0.795662
-0.748052
5.6
1.26
0.415
2
0.1
2.5
0.1
0.541
Ml max.
0.827175
-0.787624
5.2
1.24
0.482
3
0.1
2.5
0.1
1.145
0.941;ui max.
0.778535
-1.05370
5.6
1.31
0.820
4
0.1
2.5
0.1
1.851
0.66jui max.
0.550736
-1.37968
7.0
1.36
1.05
J
5
0.1
2.5
0.2
0.720
m max.
0.900312
-0.873606
4.8
1.02
0.726
6
0.2
1.25
0.1
0.875
jui max.
0.769795
-1.04078
5.9
1.22
0.570
7
0.2
1.25
0.1
1.422
0.951^1 max.
0.724527
-1.29469
6.0
1.30
0.803
8
0.2
1.25
0.1
2.072
0.666mi max.
0.512528
-1.60435
7.6
1.35
1.08
9
0.2
2.5
0.05
0.765
Ml max.
0.731493
-0.973376
6.2
1.30
0.412
10
0.2
2.5
0.1
0.875
Ml max.
0.769795
-1.04078
5.8
1.22
0.490
11
0.2
2.5
0.1
1.422
0.941mi max.
0.724527
-1.29469
6.0
1.26
0.720
12
0.2
2.5
0.1
2.072
0.666mi max.
0.512528
-1.60435
7.2
1.25
0.92
13
0.2
2.5
0.1
2.401
0.300mi max.
0.230930
-1.76243
12.4
1.24
1.36
j
U
0.2
2.5
0.15
0.976
Ml max.
0.812900
-1.10656
5.4
1.11
0.572
15
0.2
2.5
0.15
1.549
0.941mi max.
0.765101
-1.37540
5.8
1.14
1.03
16
0.2
2.5
0.15
2.2311
0.666mi max.
0.541234
-1.70180
7.0
1.12
1.22
17
0.2
2.5
0.15
2.575
0.300mi max.
0.243864
-1.86844
10.8
1.04
1.34
18
0.4
2.5
0.05
1.25
Ml max.
0.653014
-1.36746
7.6
1.26
0.315
19
0.4
2.5
0.1
1.38
Ml max.
0.701470
-1.47477
6.6
1.11
0.674
20
0.4
2.5
0.1
1.874
0.941mi max.
0.660223
-1.71341
7.8
1.19
1.05
21
0.4
2.5
0.1
2.458
0.666mi max.
0.467038
-1.99840
8.6
1.09
1.25
l>
360
A LARGE SIGNAL THEORY OF TRAVELING- WAVE AMPLIFIERS 361
equipment. The problem was programmed by Miss D. C. Legaus. The
cases computed are listed in Table I in which m and m2 are respectively
Pierce's .xi and iji , and A,(d — iny) and tj at saturation will be discussed
later. All the cases were computed with A^ = 0.2 using a model based
on 24 electron discs per electronic wavelength. To estimate the error
involved in the numerical work, Case (10) has been repeated for 48 elec-
trons and Cases (10) and (19) for Ay = 0.1. The results obtained by
using different numbers of electrons are almost identical and those ob-
tained by varying the inter\'al A// indicate a difference in A (y) less than
1 per cent for Case (10) and about 6 per cent for Case (19). As error
generally increases with QC and C the cases listed in this paper are
limited to QC = 0.4 and C = 0.15. For larger QC or C, a model of more
electrons or a smaller interval of integration, or both should be used.
7. POWER OUTPUT AND EFFICIENCY
Define
A(ij) = HVa,(yy + aM'
-0(y)=i^n-'^-^ + by ^^^^
aiiy)
We have then
F{z,t) = ^A{y) cos
^ -^t- e{y)
Uo
(22)
The power carried by the forward wave is therefore
2CA'hVo (23)
(f) =
\Z/o/ average
and the efficiency is
Eff. = ?£^^ = 2CA' or ^ = 2CA' (24)
In Table I, the values of A(y), 6{y) and y at the saturation level are
listed for every case computed. We mean by the saturation level, the
distance along the tube or the value of y at which the voltage of the
forward wave or the forward traveling power reaches its first peak.
The Eff./C at the saturation level is plotted in Fig. 1 versus QC, for
k = 2.5, h for maximum small-signal gain and C = small, 0.05, 0.1, 0.15
and 2. It is also plotted versus h in Fig. 2 for QC = 0.2, k = 2.5 and
C = small, 0.1 and0.15, and in Fig. 3 for QC = 0.2, C = 0.1 and k = 1.25
and 2.50. In Fig. 2 the dotted curves indicate the values of h at Avhich
1
362 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 195G
4.5
0.5
Fig. 1 — The saturation eff./C versus QC, for k = 2.5, h for maximum small-
signal gain and C = small, 0.1, 0.15 and 0.2.
ixx = Ml (max), 0.94 jui(max), 0.67 iui(max) and 0.3 /ii(niax), respectively.
It is seen that Eff./C decreases as C increases particularly when h is
large. It is almost constant between k = 1.25 and 2.50 and decreases
slowly for large values of C when QC increases.
The (Eff./C) at saturation is also plotted versus QC in Fig. 4(a) for
small C, and in Fig. 4(b) for C = 0.1. It should be noted that for C = 0.1
the values of Eff./C fall inside a very narrow region say between 2.5 to
3.5, whereas for small C they vary widely.
8, VELOCITY SPREAD
In a traveling-wave amplifier, when electrons are decelerated by the
circuit field, they contribute power to the circuit, and when electrons
are accelerated, they gain kinetic energy at the expense of the circuit
power. It is therefore of interest to plot the actual velocities of the fastest
and the slowest electrons at the saturation level and find how they vary
with the parameters QC, C, b and k. This is done in Fig. 5. These veloci-
ties are also plotted versus y for Case 10 in Fig. 6, in which, the A(y)
curve is added for reference.
9. THE BACKWARD WAVE AND THE FUNDAMENTAL COMPONENT OF THE
ELECTRON CHARGE DENSITY
Our calculation of efficiency has been based on the power carried by
the forward wave only. One may, however, ask about the actual power
A LARGE SIGNAL THEORY OF TRAVELING-WAVE AMPLIFIERS 363
6.0
5.5
5.0
4.5
4.0
3.5
EFFI.
C 3.0
(SAT.)
2.5
2.0
1 .5
1.0
0.5
1
QC = 0.2
1
1
A- —
K=2.5
\
SMALI "
*^r^
\
1
Sa
y^
1
1
\
_/^
I
Ji
A
1
/^
\
1
\
/
\
t
\
/
\
\
^
/
\
\
X
f
\
(
\
\
\
\
^ '
\
\
C = 0.1
'\
\
\
\
,
lyj
\
\
\
JT"^
\
\
V C=0.15
\
\
\
\
\
\
>"1 =
1
AX)
/"1=C
K 1 1
).94/Z.(MAX)
.at^
/ 1
\^
/t/i = 0.67//i(MAX)
\
//, = 0.3//i(MAX)
0.5
1.0
1.5
b
2.0
2.5
3.0
Fig. 2 — The saturation eff./C versus fe, for k = 2.5, QC = 0.2, and C = small,
0.1 and 0.15. The dotted curves indicate the values of h for m = \, 0.94, 0.67, and
0.3 of ;ui(max) respectively.
output in the presence of the backward wave. For simphcity, we shall
use the approximate solution (12b) which can be written in the form
B{z, t) ^ Real Component of
ZqIq c
4C 2(1 + hC)
dax(y)Y ^ (da,{y)\- j^^-v,.-,y+j^\ (12d)
with
tan ^ =
dij
(laiiyT
dy ,
dy
dchiyY
dy ,
As mentioned earlier that the complete solution of (6) is obtained by
adding to (12b) a complementary function such that
-yu 1+ r Qz
ZqIq
+
c
4C 2(1 + bC)
dy:) ^\dy ) '
-hy+ji
(25)
364 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
EFFI.
c
(SAT.) 3
QC = o.2
C = 0.1
J<_=K25.
3-
2.50
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
b
Fig. 3 — The saturation eff./C versus b, for QC = 0.2 C = 0.1 and k = 1.25
and 2.50.
If the output circuit is matched by cold measurements, the backward
wave must be zero at the output end, z = D. This determines Ci , that is,
„ ZqIq c
^1 = ~^rPT
or
Cie
jut+Toz
4C 2(1 + bC)
ZqIq C
//dai(t/)Y I /da2{y)Y ro(2+bc)D+ji
dai{y)V /da2{y)y
4C 2(1 + 6C) y \ dy )z=o \ dy Jz^d (26)
The backward wave therefore consists of two components. One compo-
o
7
(a)
C = SMALL
^-
Ml = 0.67
/U,(MAX)
D
5
^^;;:^
^^
EFFI.
C 4
/U, = 0.94//i(MAX)
^^^
1
(SAT.) ^
2
■"Zr^AtlC^AX)
"
0
(b)
C = o.i
= 0.94//, (MAX)
1
Xj
fea,^_^-VZi = 0.67 /Z, (MAX)
>U, = /i|(MAX)-
1 —===3
^^^
0.1
0.2
QC
0.3 0.4 0 0.1
0.2
QC
0.3 0.4
Fig. 4 — The saturation eff./C versus QC for h corresponding jui = 1, 0.94 and
0.67 of Mi(max), (a) for C = small, (b) for C = 0.1.
A LARGE SIGNAL THEORY OF TRAVELING- WAVE AMPLIFIERS 365
nent is coupled to the beam and has an amplitude equal to
Zolo C
IC 2(1 + bC)
VX^'Y +
K^y /
\dy)
which generally grows with the forward wave. It thus has a much larger
amplitude at the output end than at the input end. The other component
is a wave of constant amplitude, which travels in the direction opposite
to the electron flow with a phase velocity equal to that of the cold cir-
cuit. At the output end, 2 = Z), both components have the same ampli-
tude but are opposite in sign. One thus realizes that there exists a re-
flected wave of noticeable amplitude, in the form of (26), even though
the output circuit is properly matched by cold measurements. Under
j such circumstances, the voltage at the output end is the voltage of the
forward wave and the power output is the power carried by the forward
wave only. This is computed in (23).
Since (26) is a cold circuit wave it may be eliminated by properly ad-
c[-w],
■C[w],
5.0
4.5
4.0
3.5
5 3.0
2
o
9- 2.5
1.5
1.0
0.5
(a)
;
/
y
/
/
(
r'
,.---
(
L"1
.-'■
(b)
j^
V
/
/
/
y
1
Qw
'"--^
^-"^
(c)
J
i
/
/
^
/
/
,''^
1
/ (
f
r
1
1
1
1
<
f
0.1 0.2 0.3 0.4 0.5 1.0
QC
1.5 2.0 2.5 0
b
0.05 0.10 0.15 0.20
Fig. 5 — Cw(y, <po) of the fast and the slowest electrons at the saturation level,
(a) versus QC for k = 2.5, C = 0.1 and b for maximum small-signal gain; (b) versus
6 for A; = 2.50, C = 0.1 and QC = 0.2; and (c) versus C for A- = 2.50, QC = 0.2
and b for maximum small-signal gain.
366 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1950
3.5
3.0
2.5
2.0
9-
^1.5
U
1.0
0.5
>
r\
/
^
\
/
\
CASE 10
QC = 0.2
C = 0.1
b = 0.875
k = 2.5
MAXC(-W) /
,-'
''s
\
\
/A(y)
\
\
,
1
1
/
/\
S
//
y
/
X-
./
,^
"^AXCW
i
/
/
/
y
r
■7
/
/
A
y
^-'
^
^
:z=^
— ** —
^
1.4
1.2
1.0
0.8
ID
<
0.6
0.4
0.2
0
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5
y
Fig. 6 — Cw{y, (pa) of the fast and the slowest electrons versus y for Case
(10). A{y) is also plotted in dotted lines for reference.
justing the impedance of the output circuit. This may be necessary in
practice for the purpose of avoiding possible regenerative oscillation. In
doing so, the voltage at 2 = D is the sum of the voltage of the forward
wave and that of the particular solution of the backward wave. In every
case, the output power is always equal to the square of the net voltage
actually at the output end divided by the impedance of the output cir-
cuit.
We find from (14), (15) and (16) that the fundamental component of
electron charge density may be written as
f s. \ h ( . dai{y) . da2(y)\
= Real component of
1/0
dai{y)
dy ,
+
doM
dy
(26)
jo)—Toz—by+Ji
)
where —Io/uq is the dc electron charge density, po .
If (26) is compared with (12d) or (12c), it might seem surprising that
the particular solution of the backward wave is just equal to the funda-
A LARGE SIGNAL THEORY OF TRAVELING-WAVE AMPLIFIERS 367
1.6
t.5
1.4
1.3
1.2
1.1
1.0
Pq 0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
1.2
1.1
1.0
0.9
Pq 0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
CASES 2,
10,19
(a)
k = 2.5
- C = 0.1
b-»MAX n^
/'
\
r
\
J
'
^
r
\
r\
\
/
f
V
1]
s —
QC=o.i/
/
f
0.2
//
r
0.4
//
1
V
//
\
7
\
<^
L
/
\
A
\
^
^
CASES 9,
0,14
(c)
QC=0.2
- k=2.5
b-»MAX//|
rv
-\
1
u
\
r
C=o,s///
\
/ rf-o 10
\
///o.05
i
II
k
A
f
/
^
8 0
4
y
CASES 1C
,11,12
iH
r
V
r\
(b)
QC = o.2
C = o.i
k = 2.5
r
k\
(A
\
//
\ /
y
^
c
\
/
\f
A
\
\
/^, = >U,MAx/^
'
/
A
/
\
//
/
\
/
f
\
\
A
/
I
/
J
/09« /
11
y
/
\
\ .
//
/
/
11
/
\J
17
//
Ai.^i
^^
"w
1
/'
y
^^
.^^
-^
>^
'^1 = 0.3X/,MAX
1 1
7 8
y
10 11
12 13 14 15
Fig. 7(a) — p^/po versus ?/, (a) using QC as the parameter, for A; = 2.5, C = 0.1,
and 6 for maximum small-signal gain (Cases 2, 10, and 19) ; (b) using h as the param-
eter, for k = 2.50, C = 0.1 and QC = 0.2 (Cases 10, 11, 12 and 13); and (c) using
C as the parameter, for k = 2.50, QC = 0.2 and h for maximum small-signal gain
(Cases 9, 10 and 14).
368
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
mental component of the electron charge density of the beam multiplied
by a constant
/ Zq/o C 2uo
2wo\
h)
(27)
V 4C 2(1 + hC)
The ratio of the electron charge density to the average charge density,
P«(2)
Po
2319^21
5 17/^,1 9
^ +e
Fig. 8(a) — y versus <f - hrj for QC = 0.2, k = 2.5, b for mi = 0.67
C = small.
Ml (max) and
A LARGE SIGNAL THEORY OF TRAVELING-WAVE AMPLIFIERS 369
is plotted in Fig. 7 versus y, using QC, h and C, as the parameters. They
lare also the curves for the backward wave (the component which is
! coupled to the beam) when multiplied by the proportional constant given
in (27). It is interesting to see that the maximum values of p^/po are
between 1.0 and 1.2 for QC = 0.2 and decrease as QC increases. The
peaks of the curves do not occur at the saturation values of y.
10. y VERSUS ((p — by) diagrams
To study the effect of C, b, and QC on efficiency y versus (<p — by)
diagrams are plotted in Figs. 8(b), (c), (d) and (e) for Cases (21), (16),
(10) and (21), respectively. {<p — by) here is ($ + 6) in Nordsieck's nota-
tion. In these diagrams, the curves numbered from 1 to 24 correspond to
the 24 electrons used in the calculation with each curve for one electron.
Only odd numbered electrons are presented to avoid possible confusion
arisen from too many lines. The reciprocal of the slope of the curve as
-10 -9 -8
jo-by
Fig. 8(b) — y versus <p
C = 0.1 (Case 12).
bij for QC = 0.2, k = 2.5, b for mi = 0.67Mi(max) and
370
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
given by (18) is proportional to the ac displacement of electron per unit
of ij. (In small-C theorj^ it is proportional to the ac velocity of the elec-
tron.) Concentration of curves is obviously proportional to the charge-
density distribution of the beam. In the shaded regions, the axially di-
rected electric field of the circuit is negative and thus accelerates elec-
trons in the positive z direction. Electrons are decelerated in the un-
shaded regions where the circuit field is positive. The boundaries of these
regions are constant phase contours of the circuit wave. (They are con-
stant $ contours in Nordsieck's notation.)
These figures are actuallj' the "space-time" diagrams which unfold
the historj^ of every electron from the input to the output ends. The
effect of C can be clearly seen by comparing Figs. 8(a), (b) and (c).
These diagrams are plotted for QC = 0.2, A; = 2.5, h for jui = 0.67
jui(max) and for Fig. 8(a), C = small, for Fig. 8(b), C = 0.1, and for
Fig. 8(c), C = .15. It may be seen that because of the velocity spread of
the electrons, the saturation level in Fig. 8(a) is 9.3 whereas in Figs. 8(b)
and (c), it is 7.2 and 7.0, respectively. It is therefore not surprising that
Eff./C decreases as C increases.
The effects of h and QC may be observed by comparing Figs. 8(d) and
(b), and Figs. 8(b) and (e), respectively. The details will not be de-
scribed here. It is however suggested to study these diagrams with those
given in the small-C theory.
7.2
5
1
23 9
11
i'5
7 3
1719 21 13
23
15
1719 21
^"
^-^^ ?ny
J^
V
^v:\
S
\|
A
\-
I
SATURATION
6.8
6.4
6.0
5.6
6.2
.«,^
^
*tf
LEVEL
"
vK
sL-
^
^N
^
V
\
^
■I
^
^
L^
i
^
^
y
r
\
rt
'a
[ \
1
rt
^VL
/
1
V
«x
t
/
<
$
^W
I /
/
-^
\
\
\
w
t
ll 1
'— T
^
kU\
4.4
4.0
3.6
3.2
2.8
2.4
?0
'^
t
^
\\\^
\ \ V
\
I 1
/
\\
1
- 1
\ \
1 \
1 \
r-
1
/,
1
\
\\\
IS _H
1 1
li
V-'
\ \
\
'
%
1
■ 1
1 1
1 1
i 1
> 1
1
\
\
1
j
i
r
1
ll
i i
i5!r
1
ti23l
11 1
,3
_
-1
9 in
L. J
3 15 17 ig/sii
1 i i
23
-10 -9
-8 -7
-4 -3
0 1
10
Fig. 8(c) — y versus <p — by for QC = 0.2, k — 2.5, b for^i = 0.67^1 (max) and ,
C = 0.15 (Case 16).
A LARGE SIGNAL THEORY OF TRAVELING-WAVE AMPLIFIERS 371
11. A QUALITATIVE PICTURE AND CONCULSIONS
We have exhibited in the previous sections the most important non-
linear characteristics of the traveling wave ampUfier. Xumerical compu-
tations based on a model of 24 electrons have been carried out for more
than twenty cases covering useful ranges of design and operating parame-
ters. The results obtained for the saturation Eff./C may be summarized
as follows:
(1) It decreases with C particularly at large values of QC.
(2) For C = 0.1, it varies roughly from 3.7 for QC = 0.1 to 2.3 for
i}C = 0.4, and only varies slightl}^ with h.
(3) For C = 0.15, it varies from 2.7 to 2.5 for QC from 0.1 to 0.2 and
\i corresponding to the maximum small-signal gain. It varies slightly
with h for QC = 0.2.
(4) It is almost constant between k — 1.25 and 2.50.
In order to understand the traveling-wave tube better, it is important
to have a simplified qualitative picture of its operation. It is obvious that
to obtain higher amplification, more electrons must travel in the region
where the circuit field is positive, that is, in the region where electrons
6.8
6.4
6.0
17
3
51 9i7
13 15
11
23 21
7
J 19
13
5
11
O^
N
N
cl.
\
vV
\
vn
^
. ^^vV ^
\
Vv
\
\
^A
TURAT
lOM
^
v^§^
\
\
\j
l\
LEVEL
5.6
5.2
4.8
4.4
4.0
3.6
3.2
2.8
2.4
*
3" -
.
/
^
\
\
N
/
/
/
/
'V
\\
\
K
l\
\
1
1
1
1
/
/
1
/i^
\\
-^A
"^
\
\
t
/
/
1
r
1
■ /A\\\
f
f
fX
V
v
1
1
\
1
I
1
/
N
\\v
\\ \
/
t
/
1
\
^
\° 1
I
i
/
f
\\\
f
1
/
\ \
\ \
f
1
1
(
1
r
f
//
\\
1
1
1
\\
/
\ \
11«13»
151 17
1 3
5
]
g\ inisl 15
7
19
21/ 2
3
?n
1 1
1
1 \ li\
1 i
t J iJ
-1
SP-by
Fig. 8(d) — V versus <p — by for QC = 0.2, k = 2.5, b for m = mi (max) and
'' = 0.1 (Case 10).
372
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
8.8
11
5 3 15 9
7 21
17?
23
1
15
21
23
^-~
-^
R
StiC^ 1
^^
/
/'
1-
SATURATION
8.4
8.0
7.6
7.2
6.8
6.4
6.0
6.6
5.2
4.8
4.4
4.0
3.6
3.2
2.8
2.4
?,0
IQ**
:^
^
■" LEVEL
~ -
1
r4-
■~3
N, ,
/
\
\
\
\,
7H
1
"^^
d
\
/
^v.-— ^.-.
""^
\
\
t
y-
[V\
fe
\
^
\
>^
\ — p
\ \
\ \
v\
I
::
''^:
N\
"t
^
:\
\
\
-^^
K\l
1
H.
'■.-■;
1
1
1
Ui
y
V
t
1
J.
1 ^W
^\
/
/
))
r
i
t
l-^i
\V
d
\
r
//
1
(
1
i :
1
\\
;
1
/
i
w
\\
, :'
■,J;
W
I
1
1
1
— p-
rl -
1 \
/
]
\
-— -
1
1
1
1
\\\
1
%
1
1 1
1 1
1
1
t
n
,
9 1
1
1
15;
f
,'21 123
/ !l
V'
3 15 17 jl9
21 23
-1
0 -
9 -
8 -
7 -
6 -
5 -
4 -
3 -
2 -
1
0
1 :
3
3
-
i 5
6
7
3 9
y-by
Fig. 8(e) — y versus <p — by for QC = 0.4, k = 2.5, b for in = 0.67ui(max) and
C = 0.1 (Case 21).
are decelerated by the circuit field. At the input end of the tube, elec-
trons are uniformly distributed both in the accelerating and decelerating
field regions. Bunching takes place when the accelerated electrons push
forward and the decelerated ones press backward. The center of a bunch
of electrons is located well inside the decelerating field region because
the circuit wave travels slower than the electrons on the average (6 is
positive). The effectiveness of the amplification, or more specifically the !
saturation efficiency, therefore depends on (1), how tight the bunching :'
is, and (2), how long a bunch travels inside the decelerating field region
before its center crosses the boundary between the accelerating and
decelerating fields.
For small-C, the ac velocities of the electrons are small compared with
the dc velocity. The electron bunch stays longer with the decelerating
circuit field before reaching the saturation level when h or QC is larger.
On the other hand, the space charge force, or large QC or k tends to dis-
tort the bunching. As the consequence, the saturation efficiency increases ,
with h, and decreases as k or QC increases. When C becomes finite how-
A LARGE SIGNAL THEORY OF TRAVELING-WAVE AMPLIFIERS 373
ever, the ac velocities of the electrons are no longer small as compared
I with their average speed. The velocity spread of the electrons becomes
, an important factor in determining the efficiency. Its effect is to loosen
the bunching, and consequently it lowers the saturation level and re-
duces the limiting efficiency. It is seen from Figs. 5 and 6 that the
. velocity spread increases sharply with C and also steadily with b and QC.
\ This explains the fact that in the present calculation the saturation
Eff./C decreases with C and is almost constant with h whereas in the
1 1 small-C theory it is constant with C and increases steadily with b.
12. ACKNOWLEDGEMENTS
The writer wishes to thank J. R. Pierce for his guidance during the
course of this research, and L. R. Walker for many interesting discus-
sions concerning the working equations and the method of calculating
I the backward wave. The writer is particularly grateful to Miss D. C.
Leagus who, under the guidance of V. M. Wolontis, has carried out the
^ numerical work presented with endless effort and enthusiasm.
APPENDIX
The initial conditions at i/ = 0 are computed from Pierce's linearized
theory. For small-signal, we have
ai(?/) = 4A(y) cos (6 -f ^2)2/ (A-1)
«2(2/) = -4A(y) sin (6 + ju2)y (A-2)
A(y) = ee"'' (A-3)
Here e is taken equal to 0.03, a value which has been used in Tien-Walker-
' Wolontis' paper. Define
; ^ = wiy, <po) (A-4) 'X = pe-^'" + p*e^'^'> (A-5)
dy
where p* is the conjugate of p. After substituting (A-1) to (A-5) into the
working equations (15) to (18) and carrying out considerable algebraic
work, we obtain exactly Pierce's equation.
2 (1 + jC/i)(l + bC) innn \ ah \^ r\ r\
(j - >iCfi -h j}/ibC)(ti + jb)
provided that
+ CO
—k\((>(.y ,<po+<t>)—<p(.y ,Vo)l['^+Cw(.y ,ipo+(t>)]
0
(A-7)
• di^ sgn (^(?/, .i?o + «/)) - 9?(^, <Po)) = 8eQC
(1 -f 3Cy){ii ^ jb) I e''" cos (arg [(1 -f jCm)(m + jb)] + my - ^0)
374
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
Here ^ = Mi + JM2 or Pierce's rri + jiji . From (A-7) the value of Up is
determined for a given QC. The ac velocities of the electrons are derived
from (A-4), such as,
= -26
M
M + jb
1 + jcn
e"^" cos ( arg
M
M + jb
rvi+iCM/j
+ M22/ — <Po
(A-8)
(A-1), (A-2), (A-7) and (A-8) are the expressions used to calculate the
initial conditions at y = 0, Avhen fn and jU2 are solved from Pierce's equa-
tion (A-6).
From (12c), the particular solution of the backward wave at small-
signal is found to be
j^, . ., -2iC(l+iC/x)(M+ib)
^Ml!/
2j — CfjL -\- icb
r [-2jC{\ -
cos
+ iCM)(M+i6)'
Cn + jcb
+ M2y — ^0
which agrees with Pierce's analysis
17
3.
4.
REFERENCES
1. J. R. Pierce, Traveling-Wave Tubes, D. Van Nostrand Co., N.Y., 1950, p. 160.
2. R. L. Hess, Some Results in the Large-Signal Analysis of Traveling-Wave
Tubes, Technical Report Series No. 60, Issue No. 131, Electronic Research
Laboratory, University of California, Berkeley, California.
C. K. Birdsall, unpublished work.
J. J. Caldwell, unpublished work.
5. P. Parzen, Nonlinear Effects in Traveling-Wave Amplifiers, TR/AF-4, Radia-
tion Laboratory, The Johns Hopkins University, April 27, 1954.
6. A. Kiel and P. Parzen, Non-linear Wave Propagation in Traveling-Wave
Amplifiers, TR/AF-13, Radiation Laboratory, The Johns Hopkins Univer-
sity, March, 1955.
7. A. Nordsieck, Theory of the Large-Signal Behavior of Traveling-Wave Ampli-
fiers, Proc. I.R.E., 41, pp. 630-637, May, 1953.
H. C. Poulter, Large Signal Theory of the Traveling-Wave Tube, Tech. Re-
port No. 73, Electronics Research Laboratory, Stanford University, Cali-
fornia, Jan., 1954.
P. K. Tien, L. R. Walker and V. M. Wolontis, A Large Signal Theory of Trav-
eling-Wave Amplifiers, Proc. LR.E., 43, pp. 260-277 March, 1955.
J. E. Rowe, A Large Signal Analysis of the Traveling-Wave Amplifier, Tech.
Report No. 19, Electron Tube Laboratory, University of Michigan, Ann
Arbor, April, 1955.
11. P. K. Tien and L. R. Walker, Correspondence Section, Proc. I.R.E., 43,
p. 1007, Aug., 1955.
Nordsieck, op. cit., equation (1).
L. Brillouin, The Traveling-Wave Tube (Discussion of Waves for Large
Amplitudes), J. Appl. Phys., 20, p. 1197, Dec, 1949.
Pierce, op. cit., p. 9.
Nordsieck, op. cit., equation (4).
Pierce, op. cit., equation (7.13).
17. J. R. Pierce, Theory of Traveling-Wave Tube, Appendix A, Proc. I.R.E.
35, p. 121, Feb., 1947.
8.
10
12
13
14
15
16
A Detailed Analysis of Beam Formation
with Electron Guns of the Pierce Type
By W. E. DANIELSON, J. L. ROSENFELD,* and J. A. SALOOM
(Manuscript received November 10, 1955)
The theory of Cutler and Hines is extended in this paper to permit an
analysis of heam-spreading in electron guns of high convergence. A lens
correction for the finite size of the anode aperture is also included. The Cutler
and Hines theory was not applicable to cases where the effects of thermal
velocities are large compared with those of space charge and it did not include
a lens correction. Gun design charts are presented which include all of these
effects. These charts may he conveniently used in choosing design parameters
to produce a prescribed beam.
CONTENTS
1 . Introduction 377
2. Present Status of Gun Design; Limitations 378
3. Treatment of the Anode Lens Problem 379
A. Superposition Approach 379
B. Use of a False Cathode 382
C. Calculation of Anode Lens Strength by the Two Methods 383
4. Treatment of Beam Spreading, Including the Effect of Thermal Electrons 388
A. The Gun Region 388
B. The Drift Region 392
5. Numerical Data for Electron Gun and Beam Design 402
A. Choice of Variables 402
B. Tabular Data 402
C. Graphical Data, Including Design Charts and Beam Profiles 402
D. Examples of Gun Design Using Design Charts 403
6. Comparison of Theory with Experiment 413
A. Measurement of Current Densities in the Beam 413
B. Comparison of the Experimentally Measured Spreading of a Beam with
that Predicted Theoretically 416
C. Comparison of Experimental and Theoretical Current Density Distri-
butions where the Minimum Beam Diameter is Reached 418
D. Variation of Beam Profile with T 418
7. Some Additional Remarks on Gun Design 418
* Mr. Rosenfeld participated in this work while on assignment to the Labora-
tories as part of the M.I.T. Cooperative Program.
375
376 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
GLOSSARY OF SYMBOLS
Ai , 2 anode designations
B, C anode potentials
Ci , 2 functions used in evaluating cr+'
dA increment of area
dl, dz increments of length
e . electronic charge, base of natural logarithms
En electric field normal to electron path
F modified focal length of the anode lens
Fd focal length of the anode lens as given by Davisson^
Fn force acting normal to an electronic path
Fr , a fraction of the total current which would flow through
a circle of radius r, a
/, Id total beam current
It beam current within a radius, r, of the center
J current density
k Boltzman's constant
K - a quantity proportional to gun perveance
m electronic mass
P gun perveance
P{r) probability that a thermal electron has a radial posi-
tion between r and r -\- dr
r radial distance from beam axis
Va , c anode, cathode radii
r^ distance from beam axis to path of an electron emitted
with zero velocity at the edge of the cathode
rgs radius of circle through which 95% of the beam cur-
rent would pass
f distance from center of curvature of cathode; hence,
fc is the cathode radius of curvature and (fc — fa)
is the distance from cathode to anode
re+' slope of edge nonthermal electron path on drift side of
enode lens
Te-' slope of edge nonthermal electron path on gun side of
anode lens
R a dummy integration variable
t time
T cathode temperature in degrees K
u longitudinal electron velocity
Vc , X , y transverse electron velocities
V, Va , f , X beam voltages with cathode taken as ground
BEAM FORMATION WITH ELECTRON GUNS 377
V(f, /■), Vc.(f, potential distributions used in the anode lens study
r), etc.
V' voltage gradient
z distance along the beam from the anode lens
2n,in distance to the point where rgs is a minimum
( — a) Langmuir potential parameter for spherical cathode-
anode gun geometry
7 slope of an electron's path after coming into a space
charge free region just beyond the anode lens
r the factor which divides Fd to give the modified anode
focal length
5 dimensionless radius parameter
€o dielectric constant of free space
f dimensionless voltage parameter
6 slope of an electron's path in the gun region
r} charge to mass ratio for the electron
fx normalized radial position in a beam
a the radial position of an electron which left the cathode
center with "normal" transverse velocity
(T+' slope of o--electron on drift side of anode lens
a J slope of (T-electron on gun side of anode lens
^ electric flux
1. INTRODUCTION
During the past few years there have been several additions to the
family of microwave tubes rec}uiring long electron beams of small diame-
ter and high current density. Due to the limited electron current which
can be "drawn from unit area of a cathode surface with some assurance
of long cathode operating life, high density electron beams have been
produced largely through the use of convergent electron guns which
increase markedly the current density in the beam over that at the
cathode surface.
An elegant approach to the design of convergent electron guns was
provided by J. R. Pierce^ in 1940. Electron guns designed by this method
are known as Pierce guns and have found extensive use in the produc-
tion of long, high density beams for microwave tubes.
]\Iore recent studies, reviewed in Section 2, have led to a better under-
standing of the influence on the electron beam of (a) the finite velocities
with which electrons are emitted from the cathode surface, and (b) the
defocusing electric fields associated with the transition from the ac-
celerating region of the gun to the drift region beyond. Although these
two effects have heretofore been treated separately, it is in many cases
378 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
necessary to produce electron beams under circumstances where both
effects are important and so must be dealt with simultaneously and more
precisely than has until now been possible. It is the purpose of this paper
to provide a simple design procedure for typical Pierce guns which in-
cludes both effects. Satisfactory agreement has been obtained between
measured l^eam contours and those predicted for several guns having
per\'eances (i.e., ratios of beam current to the ^^ power of the anode
voltage) from 0.07 X 10-« to 0.7 X 10"^ amp (volt)-3/2.
2. PRESENT STATUS OF GUN DESIGN — LIMITATIONS
Gun design techniques of the type originally suggested by J. R. Pierce
were enlarged in papers by SamueP and by Field^ in 1945 and 1946.
Samuel's work did not consider the effect of thermal velocities on beam
shape and, although Field pointed out the importance of thermal veloci-
ties in limiting the theoretically attainable current density, no method
for predicting beam size and shape by including thermal effects was
suggested. The problem of the divergent effect of the anode lens was
treated in terms of the Davisson"* electrostatic lens formula, and no
corrections were applied.*
More recently. Cutler and Hines^ and also Cutler and Saloom^ have
presented theoretical and experimental work which shows the pro-
nounced effects of the thermal velocity distribution on the size and shape
of beams produced by Pierce guns. Cutler and Saloom also point to the
critical role of the beam-forming electrode in minimizing beam distor-
tion due to improper fields in the region where the cathode and the
beam-forming electrode would ideally meet. With regard to the anode
lens effect, these authors also show experimental data which strongly
suggest a more divergent lens than given by the Davisson formula. The
Hines and Cutler thermal velocity calculations have been used"' "^ to
predict departures in current density from that which should prevail in
ideal beams where thermal electrons are absent. Their theory is limited,
however, by the assumption that the beam-spreading caused by thermal
velocities is small compared to the nominal beam size.
In reviewing the various successes of the above mentioned papers in
affording valuable tools for electron beam design, it appeared to the
present authors that significant improvement could be made, in two
respects, by extensions of existing theories. First, a more thorough in-
* It is in fact erroneously statoci in Reference 5 that the lens action of an actual
structure must be somewhat weaker than i)re(licted by the Davisson formula so
that the beam on leaving the anode hole is more convergent than would be calcu-
lated by llie Davisson method. This cjuestion is discussed further in Section 3.
BEAM FORMATION WITH ELECTRON GUNS 379
vestigation of the anode lens effect was called for; and second, there was
a need to extend thermal velocity calculations to include cases where
the percentage increase in beam size due to thermal electrons was as
large as 100 per cent or 200 per cent. Some suggestions toward meeting
this second need have been included in a paper by M. E. Hines.* They
have been applied to two-dimensional beams by R. L. Schrag.^ The
particular assumptions and methods of the present paper as applied to
the two needs cited above are somewhat different from those of Refer-
ences 8 and 9, and are fully treated in the sections which follow.
3. TREATMENT OF THE ANODE LENS PROBLEM
Using thermal velocity calculations of the type made in Reference 6,
it can easily be shown that at the anode plane of a typical moderate
perveance Pierce type electron gun, the average spread in radial posi-
tion of those electrons which originate from the same point of the cathode
is several times smaller than the beam diameter. For guns of this type,
then, we may look for the effect of the anode aperture on an electron
beam for the idealized case in which thermal velocities are absent and
confidently apply the correction to the anode lens formula so obtained
to the case of a real beam.
Several authors have been concerned with the diverging effect of a
hole in an accelerating electrode where the field drops to zero in the
space beyond, ^° but these treatments do not include space charge effects
except as given by the Davisson formula for the focal length, Fd , of
the lens:
F. = -^ (1)
where V would be the magnitude of the electric field at the aperture if
it were gridded, and V would be the voltage there.
In attempting to describe the effect of the anode hole with more ac-
curacy than (1) affords, we have combined analytical methods with
electrolytic tank measurements in two i-ather different ways. The first
method to be given is more rigorous than the second, hut a modification
of the second method is much easier to use and gives essentially the
same result.
A. Siipcrposition Approach to the Anode Lens Problem
Special techniques are required for finding electron trajectories in a
space charge limited Pierce gun having a non-gridded anode. M. E.
380 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
Hines has suggested* that a fairly accurate description of the potential
distribution in such guns can be obtained by a superposition method as
follows:
By the usual tank methods, find suitable beam forming electrode and
anode shapes for conical space charge limited flow in a diode having!
cathode and anode radii of curvature given by fc and f„i , respectively,
as shown in Fig. 1(a). Using the electrolytic tank with an insulator along
the line which represents the beam edge, trace out an equipotential
which intersects the insulator at a distance fa2 from the cathode center
of curvature. Let the cathode be at ground potential and let the voltage
on anode Ai be called B. Suppose, now, that we are interested in electron
trajectories in a non-gridded gun where the edge of the anode hole is a
distance fai from the center of curvature of the cathode. Let the voltage,
C, for this anode be chosen the same as the value of the equipotential
traced out above for the case of cathode at ground potential and A\
at potential B. If we consider the space charge limited flow from a
cathode which is followed by the apertured anode, Ai , and the full
anode, Ai , at potentials C and B, respectively, it is clear that a conical
flow of the type which would exist between concentric spheres will re-
sult. The flow for such cases was treated by Langmuir,^ and the associ-
ated potentials are commonly called the "Langmuir potentials."
If we operate both Ai and A2 at potential C, however, the electrons
will pass through the aperture in anode A2 into a nearly field-free region. .
If the distance, fa2 — Tai , from A2 to Ai is greater than the diameter of
the aperture in A2 , the flow will depend very little on the shape of Ai
and the electron trajectories and associated equipotentials will be of the
type we wish to consider except in a small region near Ai . We will shortly
make use of the fact that the space charge between cathode and A 2 is
not changed much when the voltage on Ai is changed from B to C, but
first we will define a set of potential functions which will be needed.
In order to obtain the potential at arbitrary points in any axially sym-
metric gun when space charge is not neglected, w^e may superpose po-
tential solutions to 3 separate problems where, in each case, the boundary
condition that each electrode be an equipotential is satisfied. We will
follow the usual notation in using f for the distance of a general point
from the cathode center of curvature, and r for its radial distance from
the axis of symmetry. Let Vdr, r), Vh(r, >') and Vsdr, r) be the three
potential solutions where: (1) Vaif, r) is the solution for the case of no
space charge with Ai and cathode at zero potential and A 2 at potential
C, (2) Vb{r^ r) is the solution for the case of no space charge with A2
* Verbal disclosure.
BEAM FORMATION WITH ELECTRON GUNS
381
and cathode at zero potential and Ai at potential B, and (3) Vsc(f, r) is
the soUition when space charge is present but when Ax , A^ , and cathode
are all grounded.
If the configuration of charge which contributes to Vs<-(f, r) is that
corresponding to ideal Pierce type flow, then we can use the principle
of superposition to give the Langmuir potential, VL(r, r):
VUr, r) = Vcif, r) + V,{f, r) + V..{f, r)
(2)
Furthermore, the potential configuration for the case where ^i and A2
are at potentical C can be written
V =V.-\-^V, + F(.c)'
(3)
where the functional notation has been dropped and F(sc)' is the po
icntial due to the new space charge when Ai and A2 are grounded.
We are now ready to use the fact that F(sc)' may be well approximated
1)3' Fsc which is easily obtained from (2). This substitution may be
justified by noting that the space charge distribution in a gun using a
\'oltage C for Ai does not differ significanth^ from the corresponding dis-
tribution when Ai is at voltage B except in the region near and beyond
A-i where the charge density is small anyway (because of the high electron
velocities there). Substituting Fsc as given by (2) for F(sc)' in (3) then
gives
V
Vi
1
B,
V,
(4)
We have thus obtained an expression, (4), for the potential at an arbi-
ANODE A2
v=c
ANODE A,
V = B
CATHODE
Fig. 1(a) — ■ Electrode configuration for anode lens evaluation in Section 2>A.
382 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
■i
trary point in our gun in terms of the well known solution for space
charge limited flow between two concentric spheres, Vl , and a potential
distribution, Vb , which does not depend on space charge and can there-
fore be obtained in the electrolytic tank. Once the potential distribution
is found, electron trajectories may be calculated, and an equivalent lens
sj^stem found. Equation (4) is used in this way in Part C as one basis for
estimating a correction to the Davisson equation. (It will be noted that i
(4) predicts a small but finite negative field at the cathode. This is be-
cause the space charge density associated with Fsc is slightly greater
near the cathode than that associated with F(sc)' , and it is this latter
space charge which will make the field zero at the cathode under real
space charge limited operation. Equation (4), as applied in Part C of this
section, is used to give the voltage as a function of position at all points
except near the cathode where the voltage curves are extended smoothly
to make the field at the cathode vanish.)
B. Use of a False Cathode in Treating the Anode Lens Problem
Before evaluating the lens effect by use of (4), it will be useful to de-
velop another approach which is a little simpler. The evaluation of the
lens effect predicted by both methods will then be pursued in Part C
where the separate results are compared.
In Part A we noted that no serious error is made in neglecting the dif-
ference between the two space charge configurations considered there
because these differences were mainly in the very low space charge
region near and beyond A2 . It similarly follows that we can, with only 1
a small decrease in accuracy, ignore the space charge in the region near
and beyond A2 so long as we properly account for the effect of the high
space charge regions closer to the cathode. To place the foregoing obser-
vations on a more quantitative basis, we may graph the Langmuir po-
tential (for space charge limited flow between concentric spheres) versus
the distance from cathode toward anode, and then superpose a plot of
the potential from LaPlace's equation (concentric spheres; no space
charge) which will have the same value and slope at the anode. The La-
Place curve will depart significantly from the Langmuir in the region of
the cathode, but will adequately represent it farther out." Our experi-
ence has shown that the representation is "adequate" until the difference
between the two potentials exceeds about 2 per cent of the anode voltage.
Then, since space charge is not important in the region near the anode
for the case of a gridded Pierce gun, corresponding to space charge
limited flow between concentric spheres, it can be expected to be similarly
unimportant for cases where the grid is replaced by an aperture. Let us
I
BEAM FORMATION WITH ELECTRON GUNS
383
therefore consider a case where electrons are emitted perpendicularly
and with finite velocity from what would be an appropriate spherical
equipotential between cathode and anode in a Pierce type gun. So long
as (a) there is good agreement between the LaPlace and Langmuir curves
at this artificial cathode and (b) the distance from this artificial cathode
to the anode hole is somewhat greater than the hole diameter, we will
liiid that the divergent effect of the anode hole will be very nearly the
same in this concocted space charge free case as in the actual case where
space charge is present. (The quantitative support for this last state-
ment comes largely from the agreement between calculations based on
this method and calculations by method A.) The electrode configura-
tion is shown in Fig. 1(b), and the potential distribution in this space
charge free anode region can now be easily obtained in the electrolytic
j tank. This potential distribution will be used in the next section to pro-
^•ide a second basis for estimating a correction to the Davisson equation.
C. Calculation of Anode Lens Strength by the Two Methods
The Davisson equation, (1), may be derived by assuming that none
of the electric field lines which originate on charges in the cathode-anode
region leave the beam before reaching the ideal anode plane where the
voltage is F, and that all of these field lines leave the beam symmetrically
and radially in the immediate neighborhood of the anode. Electrons
I are thus considered to travel in a straight line from cathode to anode,
and then to receive a sudden radial impulse as they cross radially diverg-
ing electric field lines at the anode plane. A discontinuous change in
CATHODE
ANODE A2
V = C
ANODE A,
v = c
(b)
^ FALSE
CATHODE
Fig. 1(b) — The introduction of a false cathode at the appropriate potential
lUows the effect of space charge on the potential near the anode hole to be satis-
:ictorily approximated as discussed in Section 3i?.
384 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
slope is therefore produced as is common to all thin lens approximations.
The diverging effect of electric field lines which originate on charges
which have passed the anode plane is then normally accounted for by
the universal beam spread curve/" In our attempt to evaluate the lens
effect more accurately, we will still depend upon using the universal
beam spread curve in the region following the lens and on treating the ;
equivalent anode lens as thin. Consequently our improved accuracy
must come from a mathematical treatment which allows the electric
field lines originating in the cathode-anode region to leave the beam grad-
ually, rather than a treatment where all of these flux lines leave the beam ,
at the anode plane. In practice the measured perveances, P(= I/V^'^),
of active guns of the type considered here have averaged within 1 or 2
per cent of those predicted for corresponding gridded Pierce guns. There-
fore the total space charge between cathode and anode is much the
same with and without the use of a grid, even though the charge dis-
tribution is not the same in the two cases. The total flux which must
leave our beam is therefore the same as that which will leave the cor- ,
responding idealized beam and we may write
yp = I EndA = TT/VFidea/ (5)
w^here En is the electric field normal to the edge of the beam, ra = rdfa/fc)
is the beam radius at the anode lens, and Videai is the magnitude of the
field at the corresponding gridded Pierce gun anode.
To find the appropriate thin lens focal length we will now find the
total integrated transverse impulse which would be given to an elec-
tron which follows a straight-line path on both sides of the lens (see Fig.
2), and we will equate this impulse to wAw where An is the transverse
velocity given to the electron as it passes through the equivalent thin
lens. In this connection we will restrict our attention to paraxial elec-
trons and evaluate the transverse electric fields from (4) and from the
tank plot outlined in Section B, respectively. The total transverse im-
pulse experienced by an electron can be written
f Fn dt = e [ —dl (())
J Path J Path U
where u is the velocity along the path and Fn is the force normal to the
path.
We will usually find that the correction to (1) is less than about 20
per cent. It will therefore be worthwhile to put (6) in a form which in
effect allows us to calculate deviaiions from Fu as given by (1) instead
BEAM FORMATION WITH ELECTRON GUNS
385
1 of deriving a completely new expression for F. In accomplishing this piir-
f pose, it will be helpful to define a dimensionless function of radius, 6, by
- = 1 + 5,
r
and a dimensionless function of voltage, f, by
(7a)
(7b)
where Ta is the radius at the anode lens when the lens is considered thin,
and T^'x is a constant voltage to be specified later. (Note that the quan-
tities 5 and f are not necessarily small compared to 1.) Using u = \/2r]V,
and substituting for -y/V from (7b) we obtain
f En dl 4 r ,
= 7~7tW / ^"^1 + r + 5 + rs) ^z
(8)
where use has also been made of (7a) in the form 1 = r(l + d)/ra . Now,
as outlined above, we equate this impulse to 771 An, and we obtain
^» = WW. (/ ''■'' '' + / ''"'■'^ + ' + ^'' 'i
(9)
CATHODE
Fig. 2 — The heavy line represents an electron's path when the effect of the
.•mode hole may be represented by a thin lens, and when space charge forces are
iihsent in the region following the anode aperture. For paraxial electrons, the
(negative) focal length is related to the indicated angles by (y = 0 + Ta/F).
386
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
CENTER OF
~~ CURVATURE
OF CATHODE
SURFACE
Fig. 3 — The gun parameters used in Section SC for comparing two methods of
evaluating the effect of the anode lens.
The first integral can be obtained from (5) ; hence, if we are able to choose
Vx so that the second integral vanishes, we may write:
Au =
raV'2riVx
The reciprocal of the thin lens focal length is therefore
i _ ^ _ ^'
F ~ ~raUf ^ ~^VWf
(10)
where w/ and F/ are the final velocity and voltage of the electron after
it leaves the lens region.
The real task, then, is to use the potential distribution in the gun as
obtained by the methods of Part A or Part B above to find the value of
V X which causes the last integral in (9) to vanish : To compare the two
focal lengths obtained by the methods of Part A and B respectively, a
specific tank design of the type indicated in Fig. 1 was carried out. The
relevant gun parameters are indicated in Fig. 3. Approximate voltages
on and near the beam axis were obtained as indicated in Parts A and B,
above, with the exception that in the superposition method, A, special
techniques were used to subtract the effect of the space charge lying in
the post-anode region (because the effect of this space charge is accounted
for separately as a divergent force in the drift region*). From these data,
* See Section 4B.
BEAM FOKMATION WITH ELECTRON GUNS
387
800 805 810 815 820 825 830 835 840 845 850 855 860
Fig. 4 — Curves for finding the value of Fx to be used in equation (10) for the
set of gun parameters of Fig. 3.
l)oth the direction and magnitude of the total electric field near the
beam axis were (with much labor) determined. Once these data had
been obtained, a trial value was selected for Vx , and the corresponding
local length was calculated by (10). This enabled the electron's path
through the associated thin lens to be specified so that, at this point in
the procedure, both r and V were known functions of ^, and the quan-
tities 8 and f were then obtained as functions of € from (7). Finally the
second integral in (9) was evaluated for the particular Vx chosen, and
then the process was repeated for other values of Vx . Fig. 4 shows curves
whose ordinates are proportional to this second integral and whose
abscissae are trial values for Vx . As noted above, the appropriate value
for Vx is that value which makes the ordinate vanish, so that we obtain
T'c = 813 and 839 for methods A and B, respectively. The percentage
difference in the focal lengths obtained by the two methods is thus only
1 .6 per cent, and the reasonableness of making calculations as outlined
in Part B is thus put on a more quantitative basis.
Even calculations based on the method of Part B are tedious, and we
naturally look for simpler methods of estimating the lens effect. In this
fonnection we have found that Vx is usually well approximated by the
\alue of the potential at the point of intersection between the beam axis
and the ideal anode sphere. The specific values of the potential at this
point as obtained by the methods of Parts A and B were 814 and 827,
respectively. It will be noted that these values agree remarkably well
with the values obtained above. Furthermore, very little extra effort is
required to obtain the potential at this intersection in the false cathode
case:
I
388 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
Electrolytic tank measurements are normally made in the cathode-
anode region to give the potential variation along the outside edge of
the electron beam (for comparison with the Langmuir potential) ; hence,
by tracing out a suitable equipotential line, the shape of the false cathode
can easily be obtained. With the false cathode in place and at the proper
potential, the approximate value for Vx is then obtained by a direct tank
measurement of the potential at an axial point whose distance from the
true cathode center is (fc — fa) as outlined above. Although finite elec-
tron emission velocities typically do not much influence the trajectory
of an electron at the anode, they do nevertheless significantly alter the
beam in the region beyond. It is in this affected region where experi-
mental data can be conveniently taken. We must, therefore, postpone a
comparison of lens theory with experiment until the effect of thermal
velocities has been treated. At that time theoretical predictions com-
bining the effects of both thermal velocities and the anode lens can be
made and compared with experiment. Such a comparison is made in
Section 6.
4. TREATMENT OF BEAM SPREADING, INCLUDING THE EFFECT OF THERMAL
ELECTRONS
Jn Section 2 the desirability of having an approach to the thermal
spreading of a beam which would be applicable under a wide variety of
conditions was stressed. In particular, there was a need to extend ther-
mal velocity calculations to include the effects of thermal velocities even
when electrons with high average transverse velocities perturb the beam
size by as much as 100 or 200 per cent. Furthermore, a realistic mathe-
matical description which would allow electrons to cross the axis seemed
essential. The method described below is intended adequately to answer
these requirements.
A. The Gun Region
The Hines-Cutler method of including the effect of thermal velocities
on beam size and shape leads one to conclude that, for usual anode
voltages and gun perveance, the beam density profile in the plane of
the anode hole is not appreciably altered by thermal velocities of emis-
sion. (This statement will be verified and put on a more quantitative
basis below.) Under these conditions, the beam at the anode is ade-
quately described by the Hines-Cutler treatment. We will therefore find
it convenient to adopt their notation where possible, and it will be
worthwhile to review their approach to the thermal problem.
BEAM FORMATION WITH ELECTRON GUNS 389
It is assumed that electrons are emitted from the cathode of a therm-
ionic gun with a IMaxwelhan distribution of transverse velocities
ZTTfC 1
where Jc is the cathode current density in the z direction, T is the cath-
jode temperature, and v^: and Vy are transverse velocities. The number
iof electrons emitted per second with radially directed voltages between
V and V + dV is then
-(.Ve/kT)
(S)
^J. = /.e— -^^^(^^j (12)
Now in the accelerating region of an ideal Pierce gun (and more generally
I in any beam exhibiting laminar flow and having constant current density
()\'er its cross section) the electric field component perpendicular to the
axis of symmetry must vary linearly with radius. Conseciuently Hines
and Cutler measure radial position in the electron beam as a fraction,
^, of the outer beam radius (re) at the same longitudinal position,
r = fire (13)
The laminar flow assumption for constant current densities and small
beam angles implies a radius of curvature for laminar electrons which
so varies linearly with radius at any given cross section so that
a
Substituting for r from (13), (14) becomes
rfV , /2 dre\ dfj.
d^^VcTt)dt=^ ^^^^
where Ve and dr /dt can be easily obtained from the ideal Langmuir
solution. Since the eciuation is linear in /x, we are assured that the radial
position of a non-ideal electron that is emitted with finite transverse
velocity from the cathode center (where ^ = 0) will, at any axial point,
be proportional to dii/dt at the cathode.
Let us now define a quantity "o-" such that n = a/re is the solution
to (15) with the boundary conditions /Xr = 0 and
_ 1
where the subscript c denotes evaluation at the cathode surface, k is
390 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
Boltzman's constant, T is the cathode temperature in degrees Kelvin,
and m is mass of the electron. For the case ixc = 0, but with arbitrary
initial transverse velocity, we will then have
/^\
^^nl_ /kf ^^^'^
Tc y m
Plence we can express a in terms of the thermal electron's radial po-
sition (r), and its initial transverse velocity, Vc ,
y m _ y
. . - . /kT
dt } f
The quantity a can now be related to the radial spread of thermal
electrons (emitted from a given point on the cathode) with respect to
an electron with no initial velocity: By (11) we see that the number
of electrons leaving the cathode with dji/dt = Vc/ve is proportional to Vc
exp —Vcm/2kT. Suppose many experiments were conducted where all
electrons except one at the cathode center had zero emission velocity,
and suppose the number of times the initial transverse velocity of the
single thermal electron were chosen as Vc , is proportional to Vc exp
— Vcm/2kT. Then the probability, P{r), that the thermal electron
would have a radial position between r and r -\- dr when it arrived at the
transverse plane of interest would be proportional to Vc exp —Vc^(m/2kT).
Here Vc is the proper transverse velocity to cause arrival at radius r, and
by (17) we have
a y m
so that the probability becomes
Pir) = J.e-^^'''-'^ d (^Q (18)
We therefore identify cr with the standard deviation in a normal or
Gaussian distribution of points in two dimensions. At the real cathod(\
thermal electrons are simultaneously being emitted from the cathode
surface with a range of transverse velocities. However, if a as definml
above is small in comparison with r,. , the forces experienced by a ther-
mal electron when other thermal electrons are present will be very nearly
BEAM FORMATION WITH ELECTRON GUNS
391
2.0
1.8
1.6
> 1.4
t 1.2
\%y
1.0
0.8
0.6
0.4
1.0
1.2
1.4
1.6
1.8 2.0 2.2 2.4
2.6
2.8 3.0 3.2 3.4 3.6 3.8 4.0
Fig. 5 — Curves useful in finding the transverse displacement of electron tra-
i jectories at the anode of Pierce-type guns.
i
tlie same as the forces involved in the equations above. Thus if o- <3C J'e ,
(18) may be taken as the distribution, in a transverse plane, of those
electrons which were simultaneously emitted at the cathode center.
I Furthermore, the nature of the Pierce gun region is such that electrons
emitted from any other point on the cathode will be similarly distributed
\\ ith respect to the path of an electron emitted from this other point
w ith zero transverse velocity (so long as they stay within the confines
, of the ideal beam). Hines and Cutler have integrated (15) with n^ = 0
' and {dn/dt)c = 1 to give g/ {fc\/kT/'2eV^ at the anode as a function of
; /", /fo . This relationship is included here in graphical form as Fig. 5.
, For a large class of magnetically shielded Pierce-type electron guns,
including all that are now used in our traveling wave tubes, Ve/a at the
anode is indeed found to be greater than 5 (in most cases, greater than
10) so that evaluation of a at the anode of such guns can be made with
considerable accuracy by the methods outlined above. One source of
error lies in the assumption that electrons which are emitted from a
point at the cathode edge become normally distributed about the cor-
responding non-thermal (no transverse velocity of emission) electron's
path, and with the same standard deviation as calculated for electrons
from the cathode center. In the gun region where Ve/a tends to be large
this difference between representative a- values for the peripheral and
central parts of the beam is unimportant, but it must be re-examined in
tlie drift region following the anode.
392 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
We have already investigated the region of the anode hole in some
detail in Section 3 and have found it worth while to modify the ideal
Davisson expression for focal length of an equivalent anode lens. In
particular, let us define a quantity F by
F = focal length = Fd/T (19)
where Fd is the Davisson focal length. Thus T represents a corrective
factor to be applied to Fd to give a more accurate value for the focal
length. In so far as any thin lens is capable of describing the effects of
diverging fields in the anode region, we may then use the appropriate
optical formulas to transfer our knowledge of the electron trajectories
(calculated in the anode region as outlined above) to the start of the drift
region. In particular,
-f (20)
where {dr/dz)i and {dr/dz)^ are the slopes of the path just before and
just after the lens, and r is the distance from the axis to the point where
the ideal path crosses the lens plane.
B. The Drift Region
Although Te/a- was found to be large at the anode plane for most guns
of interest, this ratio often shrinks to 1 or less at an axial distance of
only a few beam diameters from the lens. Therefore, the assumption that
electron trajectories may be found by using the space charge forces
which would exist in the absence of thermal velocities of emission (i.e.,
forces consistant with the universal beam spread curve) may lead to very
appreciable error. For example, if ecjual normal (Gaussian) distributions
of points about a central point are superposed so that the central points
are equally dense throughout a circle of radius Te , and if the standard de-
viation for each of the normal distributions is cr = r^ , the relative density
of points in the center of the circle is only about 39 per cent of what it
would be Avith a < (re/5).
In order to minimize errors of this type we have modified the Hines-
Cutler treatment of the drift space in two ways: (1) The forces influenc-
ing the trajectories of the non- thermal electrons are calculated from a
progressive estimation of the actual space charge configuration as modi-
fied by the presence of thermal electrons. (2) Some account is taken of
the fact that, as the space charge density in the beam becomes less uni-
form as a function of radius, the spread of electrons near the center of
the beam increases more rapidly than does the corresponding spread
BEAM FORMATION WITH ELECTRON GUNS 393
farther out. Since item (1) is influenced by item (2), the specific as-
sumptions involved in the latter case will be treated first.
When current density is uniform across the beam and its cross section
changes slowly with distance, considerations of the type outlined above
for the gun region show that those thermal electrons which remain
within the beam will continue to have a Gaussian distribution with re-
spect to a non-thermal electron emitted from the same cathode point.
When current density is not uniform over the cross section, we would
still like to preserve the mathematical simplicity of obtaining the current
density as a function of beam radius merely by superposing Gaussian
distributions which can be associated with each non-thermal electron.
To lessen the error involved in this simplified approach, we will arrive
at a value for the standard deviation, a (which specifies the Gaussian
distribution), in a rather special way. In particular, a at any axial po-
sition, z, will be taken as the radial coordinate of an electron emitted
from the center of the cathode with a transverse velocity of emission
given by,
ve = y-
— (21)
m
It is clear from (17) that for such an electron, r = o- in the gun region.
From (18), the fraction of the electrons from a common point on the
cathode which will have r ^ a in the gun region is
2
fraction = [ e'^'-'"-''^ d ^= I - e'"' = 0.393 (22)
If re denotes the radial position of the outermost non-thermal electron
and if 0- > /■,, , the "a--electron" will be moving in a region where the
space charge density is significantly lower than at the axis. We could,
of course, have followed the path of an electron with initial velocity
equal to say 0.1 or 10 times that given in (21) and called the correspond-
nig radius O.lcr or lOo-. The reason for preferring (21) is that about 0.4
or nearly half of the thermal electrons emitted from a common cathode
point will have wandered a distance less than a from the path of a non-
thermal electron emitted from the same cathode point, while other
thermal electrons will ha\'e wandered farther from this path; conse-
quently, the current density in the region of the o--electron is expected
to be a reasonable average on which beam spreading due to thermal
\elocities may be based. With this understanding of how a is to be cal-
culated, we can proceed to the calculation of non-thermal electron
trajectories as suggested in item (1).
394 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
The non-thermal paths remain essentially laminar, and with r^ de-
noting the radial coordinate of the outermost non-thermal electron, we
will make little error in assuming that the current density of non-ther-
mal electrons is constant for r < Ve . Consequently, if equal numbers of
thermal electrons are assumed to be normally distributed about the cor-
responding non-thermal paths, the longitudinal current density as a
function of radius can be found in a straightforward way by using (18).
The result is
J ^ ^_(..,,..) n" R ^-(«^/2.^)^^ frR\ ^ /R\ ^23)
Jd Jo a \a^/ \(t/
where /o is the zero order modified Bessel function and the total current
is Id = TTVe Jd ' Equation (23) was integrated to give a plot of Jr/Jo
versus r/a, with re/a as a parameter and is given as Fig. 6 in Reference
6. It is reproduced here as Fig. 6. Since the only forces acting on elec-
trons in the drift region are due to space charge, we may write the equa-
tion of motion as
where Er is the radial electrical field acting on an electron with radial
coordinate r. Since the beam is long and narrow, all electric lines of force
may be considered to leave the beam radially so that Er is simpl}^ ob-
tained from Gauss' law. Equation (24) therefore becomes
-— = --^— / 2irp dr = -— ! — / ■ Iirr dr
dt^ zireor Jo Zireor Jo \/2t]V a.
(25)
2irenr Jo
27reor
From (23) we note that the fraction of the total current within any
radius depends only on fe/o- and j'/ct:
:il
dr
^ / J0')2irr ar / xo ,/o
r = - = H-) f
'- r.J(r)2.rdr ^''''° (2«) '
Jo
■•r I a
C
'^dV^]^Fr-j-
\(X a t
\
BEAM FORMATION WITH ELECTRON GUNS
395
Fig. 6 — Curves showing the current density variation with radius in a beam
I which has been dispersed by thermal velocities. Here r« is the nominal beam radius,
I r is the radius variable, and <t is the standard deviation defined in equation 17.
A family of curves with this ratio, Fr , as parameter has been reproduced
: from the Hines-Cutler paper and appears here as Fig. 7. Using this no-
tation, (25) becomes
dV ^ Vr,/{2V.) j^ Fr
di^ 27reo r
or
d r
dz^
jn_ lo Fr^ Fr
27r€0 (27,7a)3/2 J. J.
(27)
where we have made use of the dc electron drift velocity to make dis-
tance the independent variable instead of time, and have defined a
quantity K which is proportional to gun perveance. We can now apply
(27) to the motion of both the outer (edge) non-thermal electron and
the cr-electron. From (26) we see that Fr, and Fg depend only on re/a]
396 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
12
11
10
a
LLI
<
u
B 1
z
z
o
<
o ^
/^
,/;^
^
//
P>
^
Fr =
0.995/
^
^
/^
^
^
^
/^
/
rz
^
/ >>
/
^
z:^
^
:^
/
y.
^
/y
'A
%:
^
;^
^
Xy
'^.
^^
^^
^^
w
i^
/^
oao^
^
1^
^-
oo^
=
^^
10
re/0-
Fig. 7 — Curves showing the fraction, Fr , of the total beam current to be found
within any given radius in a beam dispersed by thermal velocities as in Fig. 6.
consequently the continuous solution for r^ and r„ (= a) as one moves
axially along the drifting beam involves the simultaneous solution of two
equations :
(fve
d~a
d^
KFr./re
KFJa
(28)
BEAM FORMATION WITH ELECTRON GUNS
397
0.36
0.32
0.28
0.24
0.16
0.12
0.08
0.04
0
\
\
1
\
\
\
\
V
V.
---
—
■
8
10
12
14
16
I Fig. 8 — A curve showing the effect of a quantity related to the space charge
• force (in the drift region) on a thermal electron with standard deviation a. (See
'equation 28.)
which are related by the mutual dependence of Fr^ and Fa on re/a. F„
and Frjve are plotted in Figs. 8 and 9.
We may summarize the treatment of the drift region, then, as follows:
1 (a) The input values of r^ and rgJ at the entrance to the anode lens
jare obtained from the Pierce gun parameters r^ and 6, while the value
of a and aJ at the lens entrance can be obtained as mentioned above
by integrating (15) from the cathode, where Mc = 0 and (dfx/dt)c = 1,
to the anode plane. (The minus subscripts on r' and a' indicate that
these slopes are being evaluated on the gun side of the lens; a plus sub-
script will be used to indicate evaluation on the drift region side of the
lens.) The values of Ve and a on leaving the lens will of course be their
entrance values in the drift region, and the effect of the lens on r/ and
a' is simply found in terms of the anode lens correction factor T by use
of (20). The value of a at the anode can be obtained from (17) if n is
known there. In this regard, (15) can be integrated once to give
= 1_/M dt
" " r\dt)c{r,/r,y
(29)
398
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
LL
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
. —
—
■-^
\
X
^
\
I
/
\
\ J
\ /
/
A
7 \
/ \
/ \
\
\
\
\
\
\
\
f.,/(reA)
\
\
\
s
^,
>
"-.
'"-..
^-*^^
■•—.^
1/
1
0.38
0.36
0.34
0.32
0.30
0.28
0.26
0.24
0.22
0.20
0.18 1?
0.1 6
0.14
0.12
0.10
0.08
0.06
0.04
0.02
6 7 8 9
10
11 12 13
14
Fig. 9 — Showing quantities related to the effect of the space charge force in
the drift region on the outermost non-thermal electron. (See equation 28.)
i
We can now substitute for transit time in terms of distance and Lang-
muir's well known potential function/^ —a. The value of this parameter,
for the case of spherical cathode-anode geometry in which we are in-
terested, depends only on the ratio fe/f which is equal to Vc/rg . (Because
of their frerjuent use in gun design, certain functions of —a are included
here as Table I.) In terms of —a, then, the potential in the gun region
BEAM FORMATION WITH ELECTRON GUNS
399
Fable I
Table of Functions of —a Often Used in Electron
Gun Design
fc/f
(-«)2
(- a)V3
(- a)2/3
difc/r)
1.0
0.0000
0.0000
0.0000
0.0000
1.025
0.0006
0.0074
1.05
0.0024
0.0179
0.134
1.075
0.0052
0.0306
0.173
1.10
0.0096
0.0452
0.212
1.392
0.590
1.15
0.0213
0.0768
0.277
1.20
0.0372
0.1114
0.334
1.767
0.716
1.25
0.0571
0.1483
0.385
1.30
0.0809
0.1870
0.432
2.031
0.790
1.35
0.1084
0.2273
0.476
1.40
0.1396
0.2691
0.519
2.243
0.874
1.45
0.1740
0.3117
0.558
1.50
0.2118
0.3553
0.596
2.423
0.886
1.60
0.2968
0.4450
0.667
2.583
0.915
1.70
0.394
0.5374
0.733
2.725
0.939
1.80
0.502
0.6316
0.795
2.855
0.954
1.90
0.621
0.7279
0.853
2.975
0.970
2.00
0.750
0.8255
0.908
3.087
0.982
2.10
0.888
0.9239
0.961
3.192
0.993
2.20
1.036
1.024
1.012
3.292
1.003
2.30
1.193
1.125
1.061
3.388
1.012
2.40
1.358
1.226
1.107
3.481
1.020
2.50
1.531
1.328
1.152
3.570
1.028
2.60
1.712
1.431
1.196
3.655
1.034
2.70
1.901
1.535
1.239
3.738
1.039
2.80
2.098
1.639
1.280
3.817
1.044
2.90
2.302
1.743
1.320
3.894
1.048
3.00
2.512
1.848
1.359
3.968
1.052
3.1
2.729
1.953
1.397
4.040
1.056
3.2
2.954
2.059
1.435
4.111
1.059
3.3
3.185
2.164
1.471
4.180
1.062
3.4
3.421
2.270
1.507
4.247
1.064
3.5
3.664
2.376
1.541
4.315
1.066
3.6
3.913
2.483
1.576
4.377
1.068
3.7
4.168
2.590
1.609
4.441
1.070
3.8
4.429
2.697
1.642
4.501
1.072
3.9
4.696
2.804
1.674
4.563
1.074
4.0
4.968
2.912
1.706
4.621
1.076
400
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
may be written
df df i-aaY'^
dt
'V2nV a/2;^ {-a)
2/3
(30)
(31)
(32)
so that upon substitution from (29) and (31), (17) becomes
Fig. 5, which has been referred to above, shows
O-a . /2eVa
'fcV 'kf-
as a function of {fc/fa) as obtained from (32), and allows o-„ to be de-
termined easily. Using (20), the value of re+' is given by
/ Tea ,
F
-,.= -^^_,. = ,/_g-l) (33)
where dg is the half-angle of the cathode (and hence the initial angle
which the path of a non-thermal edge electron makes with the axis).
We may write for 1/Fd
1 V fe /d(-aY"\
Fo 4F 4(-aa)^/VV\rf(fc/r-) 7a
(34)
In Fig. 10 we plot —falFr, as a function of fjfa for easy evaluation of
re+' in (33). Taking the first derivative of (32) with respect to ^, we ob-
tain an expression for aJ. Using this in conjunction with (20) and (34)
we find
0-+ =
Y (r<^i + C2)
I
(35)
where
cira
d{fc/f)
/3
and
^-i/f. ft -(-''"/
(-a)2/3_
!
Ci and C2 are plotted as functions of fc/fa in Fig. 11.
(b) After choosing a specific value for r and evaluating K = rj/c/ .
BEAM FORMATION WITH ELECTRON GUNS
401
Q
LL
lU
I.O
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0
\
\
V
\
\
~~~-
■---
1.0 12 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 40
rcAa
Fig. 10 — Curve used in finding ?•«+', the direction of a nonthermal edge elec-
tron as it enters the drift region. (See equation 33.)
(27r€o(277 Fa) ''), (28) is integrated numerically using the BTL analog com-
puter to obtain a and r^ as functions of axial distance along the beam,
(c) Knowing a and Ve , other beam parameters such as current dis-
tribution and the radius of the circle which would encompass a given
percentage of the total current can be found from Figs. 6 and 7.
X
tvi
U
20
15
10
5
0
-5
-10
-15
-20
-25
-30
POLYNOMIAL REPRESENTATION
(ACCURATE WITHIN 2°/o)
-OR
c, &
C2
,''''
C, = 4.13 fc/ra + 2.67
C2 = 0.635(r^/faf-13.56 rc/fa + 19-33
, ,-'
.' '
.-'''
.'-'
,'-'
\
^^
-'
^^-'
<
^v
■^
X
,.-'
^**
,^-'
''H
'^
"^
^
^
^^
\>
^
20
18
16
14
12
rO
O
10 X
(J
8
2
0
10 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0
tc/fa
Fig. 11 — Curves used in evaluating o-+', the slope of the trajectory of a thermal
electron with standard deviation a as it enters the drift region. (See equation 35.)
402 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
5. NUMERICAL DATA FOR ELECTRON GUN AND BEAM DESIGN
A. Choice of Variables
Except for a scaling parameter, the electrical characteristics of an
ideal Pierce electron gun are completely determined when three param-
eters are specified, e.g., fc/fa , perveance, and Va/T. Also, for the simp-
lest case r is equal to 1 so that (since K depends only on gun perveance)
in this case no additional parameter is needed. This implies that nor-
malized values of ?-/, a, a', and K at the drift side of the anode lens are
not independent. If, however, the value of F at the anode lens is taken
as an additional variable, four parameters plus simple scaling are re-
quired before complete predictions of beam characteristics can be made.
In assembling analog computer data which would adequately cover
values of fc/fa , perveance, and Va/T which are likely to be of interest
to us in designing future guns, we chose to present the major part of
our data with T fixed at 1.1. This has seemed to be a rather typical value
for r, and by choosing a specific value we decrease the total number of
significant variables from 4 to 3. (The effect of variations in T on the
minimum radius which contains 95 per cent of the beam is, however,
included in Fig. 16 for particular values of Va/T and perveance.) Al-
though the boundary conditions for our mathematical description of the
beam in a drift space are simplest when expressed in terms of Vg , r/, a
and ct', we have attempted to make the results more usable by express-
ing all derived parameters in terms of fc/fa , s/Va/T, and the perveance,
P.
B. Tabular Data
The rather extensive data obtained from the analog computer for the
r = 1.1 case and for practical ranges in perveance, Ve/T, and fc/fa
are summarized in Tables IIA to E where the parameters r^ and a which
specify the beam cross section are given as functions of axial distance
from the anode plane. Some feeling for the decrease in accuracy to be
expected as the distance from the anode plane increases can be obtained
by reference to Section 6B where experiment and theory are compared
over a range of this axial distance parameter.
C. Graphical Data, Including Design Charts and Beam Profdes
In typical cases, the designer of Pierce electron guns is much more
concerned with the beam radius at the axial position where it is smallest
(and in the axial position of this minimum) than he is in the general
BEAM FORMATION WITH ELECTRON GUNS 403
jspreadiug of the beam with distance. This is true because, in microwave
beam tubes, the beam from a magnetically shielded Pierce gun normally
enters a strong axial magnetic field near a point where the radius is a
minimum, so that magnetic focusing forces largely determine the beam's
subsequent behavior. The analog computer data has therefore been re-
processed to stress the dependence of the beam's minimum diameter and
the corresponding axial position of the minimum on the basic design
iparameters fdfa , perveance, and s/Va/T. As a first step in this direc-
tion, the radius, rgs , of a circle which includes 95 per cent of the beam
: I current is obtained as a function of axial position along the beam. Such
idata are shown graphically in Fig. 12. Finally, the curves of Fig. 12 are
. lused in conjunction with the tabular data to obtain the "Design Curves"
of Fig. 13 where all of the pertinent information relating to the beam
at its minimum diameter is presented.
\D. Example of Gun Design Using Design Charts
Assume that we desire an electron gun with the following properties :
anode voltage Va = 1,080 volts, cathode current Ip = 7.1 ma, and mini-
mum beam diameter 2(r95)min = 0.015 inches. Let us further assume a
cathode temperature T = 1080° Kelvin, an available cathode emission
density of 190 ma per square cm, and an anode lens correction factor
of r = 1.1. From these data we find -x/Va/T = 1.0, perveance P =
0.2 X 10"^ amps/(volts)^''" and (r95)min/''c = 0.174. Reference to the de-
sign chart, Fig. 13, now gives us the proper value for fc/fa : using the
upper set of curves in the column for y/Va/T =1.0 we note the point
of intersection between the horizontal line for {rgr^^i^/rc = 0.174 and
the perveance line P = 0.2, and read the value of fc/fa (= 2.8) as the
corresponding abscissa. The convergence angle of the gun, de , is now
simply determined fi'om the equation^^
de = cos-^ {\ - t|^ X 10^) (37)
{Qe is found to be 13.7° in this example) and the potential distribution
in the region of the cathode can be obtained from (30).
When this point has been reached, the gun design is complete except
for the shapes of the beam forming electrode and the anode, which are
determined with the aid of an electrolytic tank in the usual way. The
radius of the anode hole which will give a specified transmission can be
found by obtaining (re/a)a through the use of Fig. 5, and then choosing
the anode radius from Fig. 7. In practical cases where (rf/a)a > 3.0,
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BEAM FORMATION WITH ELECTRON GUNS 413
we find less than 1 per cent anode interception if
anode hole radius = 0.93 r^a + 2o-a (38)
Additional information about the axial position of (r95)min and the cur-
rent density distribution in the corresponding transverse plane is con-
tained in Fig. 13. The second set of curves in the \/Va/T = 1 column
gives Zm\n/Tc — 2.42 for this example, so that we would predict
Zmin = distance from anode to (r95)inin = 0.104''
The remaining 3''^ and 4*^^ sets of curves in the ■\/Va/T = 1 column
allow us to find o- and re/a- at ^min . In particular we obtain a = 0.0029"
and I'e/o = 0.8, and use Fig. 6 to give the current density distribution at
2min .* Section VI contains experimental data which indicate a some-
what larger value for 2m in than that obtained here. However the pa-
rameter of greatest importance, (r95)niin , is predicted with embarrassing
precision.
For those cases in which additional information is required about the
beam shape at axial points other than ZnVin , the curves of Fig. 12 or the
data of Table II may be used.
6. COMPARISON OF THEORY WITH EXPERIMENT
In order to check the general suitability of the foregoing theory and
the usefulness of the design charts obtained, several scaled-up versions
of Pierce type electron guns, including the gun described in Section 5D,
were assembled and placed in the double-aperture beam analyzer de-
scribed in Reference 7.
A. Measurement of Current Densities in the Beam
Measurements of the current density distributions in several trans-
verse planes near Smin were easily obtained with the aid of the beam
analyzer. The resulting curve of relative current density versus radius
at the experimental 2min is given in Fig. 14 for the gun of Section 52).
(This curve is further discussed in Part C below.) For this case, as well
as for all others, special precautions were taken to see that the gun was
functioning properly : In addition to careful measurement of the size and
position of all gun parts, these included the determination that the dis-
tribution of transverse velocities at the center of the beam was smooth
* When j'c/o- < 0.5, the current density distribution depends almost entirely on
a, and, in only a minor way, on the ratio Te/a- so that in such cases this ratio need
not be accurately known.
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415
416
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
12
11
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01 23456789
RADIUS IN MILS
Fig. 14 — Current density distribution in a transverse plane located where the
95 per cent radius is a minimum. The predicted and measured curves are normal-
ized to contain the same total current. (The corresponding prediction from the
universal beam spread curve would show a step function with a constant relative
current density of 64.2 for r < 1.2 mils and zero beyond.) The gun parameters are
given in Section 5D.
and generally Gaussian in form, thereby indicating uniform cathode
emission and proper boundary conditions at the edge of the beam near
the cathode. The ejffect of positive ions on the beam shape was in every I
case reduced to negligible proportions, either by using special pulse
techniques, or by applying a small voltage gradient along the axis of
the beam.
B. Comparison of the Experiinentally Measured Spreading of a Beam with
that Predicted Theoretically
From the experimentally obtained plots of current density versus
radius at several axial positions along the beam, we have obtained at
each position (by integrating to find the total current within any radius)
a value for the radius, rgs , of that circle which encompasses 95 per cent
of the beam. For brevity, we call the resulting plots of rgs versus axial
distance, "beam profiles". The experimental profile for the giui de-
scribed in Section 5D is shown as curve A in Fig. 15(a). Curve B shows
the profile as predicted by the methods of this paper and obtained from
Fig. 12. Curve C is the corresponding profile which one obtains by the
Hines-Cutler method, and Curve D represents Tq^ as obtained from the
BEAM FORMATION WITH ELECTRON GUNS
417
CO
20
18
16
14
12
t- 8
2
0
I
50
45
40
35
if) 30
Z 25
l? 20
15
10
(a)
GUN PARAMETERS:
fc/fa=2.8
s
/
^
\,
(C)j
/
1
/
e = i3.7°
VVa/T-i.o
\
^>
k
/
/
/
[B]/
r
rc = 0.043"
(A) EXPERIMENT
(B) METHODS OF
THIS PAPER
(C) HINES-CUTLER
METHOD
(D) UNIVERSAL BEAM
SPREAD CURVE
\
^^
V
/
/
/
/
/
\
N
s.
<;
>^
^
'4
/
^
<.
\
\,
"^
^>3e
\
\,
y
/(D)
\
\
y
y
"~~-
^^
^
40
80 120 160 200 240
Z, DISTANCE FROM IDEAL ANODE IN MILS
280
320
(b)
i
/(C)
y
GUN PARAMETERS:
f c/fa = 2.5
1
1
1
/
/
e =
8°
1.0
/
1
*
y
^B)
^/V, /T-
\
x^
V a/
rc = 0.150"
/
/
/
f
y
/^
V
^
V
^
^***^^
•■
•
•
}
\
X
X
"^
, -»
-^
<^
— ■^
(A)
\
^^
.^
y
^--
^^
^
(D)
100 200 300 400 500 600
Z, DISTANCE FROM IDEAL ANODE IN MILS
700
800
Fig. 15 — Beam profiles (using an anode lens correction of r = 1.1 and the gun
parameters indicated) as obtained (A) from experiment, (B) bj^ the methods of this
paper, (C) Hines-Cutler method, (D) by use of the universal beam spread curve.
universal l^eam spread curve'" (i.e., under the assumption of laminar
flow and gradual variations of beam radius with distance) . Note that in
each case a value of 1.1 has been used for the correction factor, r, repre-
senting the excess divergence of the anode lens. The agreement in
(/'95)min as obtaiucd from Curves A and B is remarkably good, but the
axial position of (r95)min in Curve A definitely lies beyond the correspond-
418 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
ing inininumi position in Curve B. Fortunately, in the gun design stage,
one is usually more concerned with the value of (r95)min than with its
exact axial location. The principal need for knowing the axial location of
the minimum is to enable the axial magnetic field to build up suddenly
in this neighborhood. However, since this field is normally adjusted ex-
perimentally to produce best focusing, an approximate knowledge of
2m in is usually adequate.
In Fig. 15b we show a similar set of experimental and theoretical beam
profiles for another gun. The relative profiles are much the same as in
Fig 15a, and all of several other guns measured yield experimental
points similarly situated with respect to curves of Type B.
C. Comparison of Experimental and Theoretical Current Density Dis-
tributions where the Minimum Beam Diameter is Reached
In Fig. 14 we have plotted the current density distribution we would
have predicted in a transverse plane at ^min for the example introduced
in Section 5Z). Here the experimental and theoretical curves are nor-
malized to include the same total currents in their respective beams.
The noticeable difference in predicted and measured current densities
at the center of the beam does not appreciably alter the properties such
a beam would have on entering a magnetic field because so little total
current is actually represented by this central peak.
D. Variation of Beam Profile with T
All of the design charts have been based on a value of T = 1.1, which
is typical of the values obtained by the methods of Section 3. When
appreciably different values of F are appropriate, we can get some feel-
ing for the errors involved, in using curves based on T = 1.1, by refer-
ence to Fig. 16. Here we show beam profiles as obtained by the methods
of this paper for three values of F. The calculations are again based on
the gun of Section 5D, and a value of just over 1.1 for F gives the ex-
perimentally obtained value for (r95)min .
7. SOME ADDITIONAL REMARKS ON GUN DESIGN
In previous sections we have not differentiated between the voltage
on the accelerating anode of the gun and the final beam voltage. It is
important, howovei', that the separate functions of these two voltages
be kept clearly in mind: The accelerating anode determines the total
current drawn and largely controls the shaping of the beam; the final
beam voltage is, on the other hand, chosen to give maximum interaction
between the electron beam and the electromagnetic waves traveling
along the slow wave circuit. As a consequence of this separation of func- ,
BEAM FORMATION WITH ELECTRON GUNS
419
0.006
0.02
0.18
0.20
0.22
0.04 0.06 0.08 0.10 0.12 0.14 0.16
Z, DISTANCE FROM IDEAL ANODE IN INCHES
Fig. 16 — Beam profiles as obtained by the methods of this paper for the gun
parameters given in Section bD. Curves are shown for three values of the anode
lens correction, viz. T = 1.0, 1.1, and 1.2.
tions, it is fouiicl that some beams which are difficult or impossible to
obtain with a single Pierce-gun acceleration to final beam voltage may
be obtained more easily by using a lower voltage on the gun anode. The
acceleration to final beam voltage is then accomplished after the beam
has entered a region of axial magnetic field.
Suppose, for example, that one wishes to produce a 2-ma, 4-kv beam
with (rgs/rc) = 0.25. If the cathode temperature is 1000°K, and the gun
anode is placed at a final beam voltage of 4 kv, we have \^Va/T = 2
and P = 0.008. From the top set of curves under \^Va/T = 2 in Fig.
13, we find (by using a fairly crude extrapolation from the curves shown)
that a ratio of fc/fa'^ 3.5 is required to produce such a beam. The value
of {ve/o-) at Zmin IS therefore less than about 0.2 so that there is little
x'mblance of laminar flow here. On the other hand we might choose
r, = 250 volts so that a/fT^ = 0.5 and P = 0.51. From Fig. 13*
we than obtain fc/fa = 2.6 and (re/o-)min = 0.8 for the same ratio of
'■'joAc(= 0.25). While the flow could still hardly be called laminar, it is
(•(jnsiderably more ordered than in the preceding case. Here we have in-
cluded no correction for the (convergent) lens effect associated with the
post-anode acceleration to the final beam voltage, F = 4 kv.
Calculations of the Hines-Cutler type will always predict, for a given
set of gun parameters and a specified anode lens correction, a minimum
beam size which is larger than that predicted by the methods of this
])aper. Nevertheless, in many cases the difference between the minimum
sizes predicted by the two theories is negligible so long as the same anode
lens correction is used. The extent to which the two theories agree ob-
420 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
viously depends on the magnitude of Velo. When rel(T as calculated by
the Hines-Cutler method (with a lens correction added) remains greater
than about 2 throughout the range of interest, the difference between
the corresponding values obtained for rgs will be only a few per cent.
For these cases where rja does not get too small, the principal advan-
tages of this paper are in the inclusion of a correction to the anode lens
formula and in the comparative ease with which design parameters may
be obtained. In other cases r^la may become less than 1, and the theory
presented in this paper has extended the basic Hines-Cutler approach
so that one may make realistic predictions even under these less ideal
conditions where the departure from a laminar-type flow is quite severe.
ACKNOWLEDGMENT
We wish to thank members of the Mathematical Department at
B.T.L., particularly H. T. O'Neil and Mrs. L. R. Lee, for their help in
programming the problem on the analog computer and in obtaining the
large amount of computer data involved. In addition, we wish to thank
J. C. Irwin for his help in the electrolytic tank work and both Mr. Irwin
and W. A. L. Warne for their work on the beam analyzer.
REFERENCES
1. Pierce, J. R., Rectilinear Flow in Beams, J. App. Phys., 11, pp. 548-554, Aug.,
1940.
2. Samuel, A. L., Some Notes on the Design of Electron Guns, Proc. I.R.E., 33,
pp. 233-241, April, 1945.
3. Field, L. M., High Current Electron Guns, Rev. Mod. Phys., 18, pp. 353-361,
July, 1946.
4. Davisson, C. J., and Calbick, C. J., Electron Lenses, Phys. Rev., 42, p. 580,
Nov., 1932.
5. Helm, R., Spangenburg, K., and Field, L. M., Cathode-Design Procedure for
Electron Beam Tubes, Elec. Coram., 24, pp. 101-107, March, 1947.
6. Cutler, C. C, and Hines, M. E., Thermal Velocity Effects in Electron Guns,
Proc. I.R.E., 43, pp. 307-314, March, 1955.
7. Cutler, C. C, and Saloom, J. A., Pin-hole Camera Investigation of Electron
Beams, Proc. I.R.E., 43, pp. 299-306, March, 1955.
8. Hines, M. E., Manuscript in preparation.
9. Private communication.
10. See for example, Zworykin, V. K., et al.. Electron Optics and the Electron
Microscope, Chapter 13, Wiley and Sons, 1945, or Klemperer, O., Electron
Optics, Chapter 4, Cambridge Univ. Press, 1953.
11. Brown, K. L., and Siisskind, C., The Effect of the Anode Aperature on Po-
tential Distribution in a "Pierce" Electron Gun, Proc. I.R.E., 42, p. 598,
March, 1954.
12. See, for example, Pierce, J. R., Theory and Design of Electron Beams, p. 147,
Van Nostrand Co., 1949.
13. See Reference 6, p. 5.
14. Langmuir, I. L., and Blodgett, K., Currents Limited by Space Charge Be-
tween Concentric Spheres, Phys. Rev., 24, p. 53, July, 1924.
15. See Reference 12, p. 177.
16. See Reference 12, Chap. X.
Theories for Toll Traffic Engineering in
the U.S.A.*
By ROGER I. WILKINSON
(Manuscript received June 2, 1955)
Present toll trunk traffic engineering practices in the United States are
reviewed, and various congestion formulas compared with data obtained on
long distance traffic. Customer habits upon meeting busy channels are noted
and a theory developed describing the probable result of permitting subscribers
to have direct dialing access to high delay toll trunk groups.
Continent-wide automatic alternate routing plans are described briefly,
in which near no-delay service will permit direct customer dialing. The
presence of non-random overflow traffic from high usage groups co7nplicates
the estimation of correct quantities of alternate paths. Present methods of
solving graded multiple problems are reviewed and found unadaptable to the
variety of trunking arrangements occurring in the toll plan.
Evidence is given that the principal fluctuation characteristics of overflow-
type of non-random traffic are described by their mean and variance. An
approximate probability distribution of simultaneous calls for this kind of
non-random traffic is developed, and found to agree satisfactorily with theo-
retical overflow distributions and those seen in traffic simidations.
A method is devised using ^^ equivalent random''^ traffic, which has good
loss predictive ability under the "lost calls cleared" assumption, for a diverse
field of alternate route trunking arrangements. Loss comparisons are made
with traffic simulation residts and with observations in exchanges.
Working curves are presented by which midti-alternate route trunking
systems can be laid out to meet economic and grade of service criteria. Exam-
ples of their application are given.
Table of Contents
1 . Introduction 422
2. Present Toll Traffic Engineering Practice 423
* Presented at the First International Congress on the Application of the
Theory of Probability in Telephone Engineering and Administration, Copen-
hagen, June 21, 1955.
421
422 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
3. Customers Dialing on Groups with Considerable Delay 431
3.1. Comparison of Some Formulas for Estimating Customers' NC Service
on Congested Groups 434
4. Service Requirements for Direct Distance Dialing by Customers 436
5. Economics of Toll Alternate Routing 437
6. New Problems in the Engineering and Administration of Intertoll Groups
Resulting from Alternate Routing 441
7. Load-Service Relationships in Alternate Route Systems 442
7.1. The "Peaked" Character of Overflow Traffic 443
7.2. Approximate Description of the Character of Overflow Traffic 446
7.2.1. A Probability Distribution for Overflow Traffic 452
7.2.2. A Probability Distribution for Combined Overflow Traffic Loads 457
7.3. Equivalent Random Theory for Prediction of Amount of Traffic Over-
flowing a Single Stage Alternate Route, and Its Character, with Lost
Calls Cleared 461
7.3.L Throwdown Comparisons with Equivalent Random Theory on
Simple Alternate Routing Arrangements with Lost Calls
Cleared 468
7.3.2. Comparison of Equivalent Random Theory with Field Results
on Simple Alternate Routing Arrangements 470
7.4. Prediction of Traffic Passing Through a Multi-Stage Alternate Route
Network 475
7.4.1. Correlation of Loss with Peakedness of Components of Non-
Random Offered Traffic 481
7.5. Expected Loss on First Routed Traffic Offered to Final Route 482
7.6. Load on Each Trunk, Particularly the Last Trunk, in a Non-Slipped
Alternate Route 486
8. Practical Methods for Alternate Route Engineering 487
8.1. Determination of Final Group Size with First Routed Traffic Offered
Directly to Final Group 490
8.2. Provision of Trunks Individual to First Routed Traffic to Equalize
Service 491
8.3. Area in Which Significant Savings in Final Route Trunks are Real-
ized by Allowing for the Preferred Service Given a First Routed
Traffic Parcel 494
8.4. Character of Traffic Carried on Non-Final Routes 495
8.5. Solution of a Typical Toll Multi-Alternate Route Trunking Arrange-
ment : Bloomsburg, Pa 500
9. Conclusion 505
Acknowledgements 506
References 506
Abridged Bibliography of Articles on Toll Alternate Routing 507
Appendix I: Derivation of Moments of Overflow Traffic 507
Appendix II: Character of Overflow when Non-Random Traffic is Offered
to a group of Trunks 511
1. INTRODUCTION
It has long been the stated aim of the Bell System to make it easily
and economically possible for any telephone customer in the United
States to reach any other telephone in the world. The principal effort
in this direction by the American Telephone and Telegraph Company
and its associated operating companies is, of course, confined to inter-
connecting the telephones in the United States, and to providing com-
munication channels between North America and the other countries of
the world. Since the United States is some 1500 miles from north to
fSOuth and 3000 miles from east to west, to realize even the aim of fast
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 423
and economical service between customers is a problem of great magni-
tude; it has engaged our planning engineers for many years.
There are now 52 million telephones in the United States, over 80 per
cent of which are equipped with dials. Until quite recently most telephone
users were limited in their direct dialing to the local or immediately sur-
rounding areas and long distance operators were obliged to build up a
circuit with the aid of a "through" operator at each switching point.
Both speed and economy dictated the automatic build-up of long toll
circuits without the intervention of more than the originating toll oper-
ator. The development of the No. 4-type toll crossbar switching system
with its ability to accept, translate, and pass on the necessary digits (or
lujuivalent information) to the distant office made this method of oper-
ation possible and feasible. It was introduced during World War II, and
now by means of it and allied equipment, 55 per cent of all long distance
calls (over 25 miles) are completed by the originating operator.
As more elaborate switching and charge-recording arrangements were
developed, particularly in metropolitan areas, the distances which cus-
tomers themselves might dial measurably increased. This expansion of
the local dialing area was found to be both economical and pleasing to
the users. It was then not too great an effort to visualize customers
dialing to all other telephones in the United States and neighboring
countries, and perhaps ultimately across the sea.
The physical accomplishment of nationwide direct distance dialing
which is now gradually being introduced has involved, as may well be
imagined, an immense amount of advance study and fundamental plan-
ning. Adequate transmission and signalling with up to eight intertoll
trunks in tandem, a nationwide uniform numbering plan simple enough
to be used accurately and easily by the ordinary telephone caller, pro-
^ ision for automatic recording of who called whom and how long he
talked, with subsequent automatic message accounting, are a few of
man}^ problems which have required solution. How they are being met is
a romantic story beyond the scope of the present paper. The references
given in the bibliography at the end contain much of the history as well
as the plans for the future. •
2. PRESENT TOLL TRAFFIC ENGINEERING PRACTICE
There are today approximately 116,000 intertoll trunks (over 25 miles
in length) in the Bell System, apportioned among some 13,000 trunk
groups. A small segment of the 2,600 toll centers which they interconnect
is shown in Fig. 1. Most of these intertoll groups are presently traffic
engineered to operate according to one of several so-called T-schedules:
T-8, T-15, T-30, T-60, or T-120. The number following T (T for Toll) is
424 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
KEY
O TOLL CENTERS
INTERTOLL TRUNK GROUPS
Fig. 1 — Principal intertoll trunk groups in Minnesota and Wisconsin.
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 425
4 5 6 7 8 9 10
NUMBER OF TRUNKS
30 40 50
Fig. 2 — Permitted intertoU trunk occupancy for a 6.5-minute usage time
per message.
the expected, or average, delay in seconds for calls to obtain an idle
trunk in that group during the average Busy Season Busy Hour. In 1954
the system "average trunk speed" was approximately 30 seconds, re-
sulting from operating the majority of the groups at a busy-hour trunk-
ling efficiency of 75 to 85 per cent in the busy season.
The T-engineering tables show permissible call minutes of use for a
426 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
wide range of group sizes, and several selections of message holding
times. They were constructed following summarization of many obser-
vations of load and resultant average delays on ringdown (non-dial)
intertoll trunks.^ Fig. 2 shows the permissible occupancy (efficiency) of
various trunk group sizes for 6.5 minutes of use per message, for a va-
riety of T-schedules. It is perhaps of somfe interest that the best fitting
curves relating average delay and load were found to be the well-known
Pollaczek-Crommelin delay curves for constant holding time — this in
spite of the fact that the circuit holding times were far indeed from
having a constant value.
A second, and probably not uncorrected, observation was that the
per cent "No-Circuit" (NC) reported on the operators' tickets showed
consistently lower values than were measured on group-busy timing de-
vices. Although not thoroughly documented, this disparity has generally
been attributed to the reluctance of an operator to admit immediately
the presence of an NC condition. She exhibits a certain tolerance (very
difficult to measure) before actually recording a delay which would
recjuire her to adopt a prescribed procedure for the subsequent handling
of the call.* There are then two measures of the No-Circuit condition
which are of some interest, the "NC encountered" by operators, and the
"NC existing" as measured by timing devices.
It has long been observed that the distribution of numbers n of simul-
taneous calls found on T-engineered ringdown intertoll groups is in re-
markable agreement with the individual probability terms of the Erlang
"lost calls" formula,
f n — a '
a e
fin) = ^-^^ (1)
e
E-
n=o n!
where c = number of paths in the group,
a' = an enhanced average load submitted such that
a'[l — Ei^c(a')] = L, the actual load carried, and
Ei^cid') = fie) = Erlang loss probability (commonly called Er-
lang B in America).
An example of the agreement of observations with (1) is shown in Fig.
3, where the results of switch counts made some years ago on many
ringdown circuit groups of size 3 are summarized. A wide range of "sub-
* Upon finding No-Circuit, an operator is instructed to try again in 30 seconds
and GO seconds (before giving an NC report to the customer), followed by addi-
tional attempts 5 minutes and 10 minutes later if necessary.
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 427
0.10 0.2 0.5 1.0 2
AVERAGE "submitted" LOAD IN ERLANIGS
Fig. 3 — Distributions of simultaneous calls on three-trunk toll groups at
.\lbany and Buffalo.
I nit ted" loads a' to produce the observed carried loads is required. On
Fig. 4 are shown the corresponding comparisons of theory and obser-
vations for the proportions of time all paths are busy ("NC Existing")
for 2-, 4-, 5-, 7-, and 9-circuit groups. Good agreement has also been ob-
served for circuit groups up to 20 trunks. This has been found to be a
stable relationship, in spite of the considerable variation in the actual
practices in ringdown operation on the resubmission of delayed calls.
Since the estimation of traffic loads and the subsequent administration
of ringdown toll trunks has been performed principally by means of
Group Busy Timers (which cumulate the duration of NC time), the
Erlang relationship just described has been of great importance.
428
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
With the recent rapid increase in operator dialed intertoll groups, it
might be expected that the above discrepancy between " % NC encoun-
tered" and "% NC existing" would disappear — for an operator now
initiates each call unaware of the momentary state of the load on any
particular intertoll group. By the use of peg count meters (which count
calls offered) and overflow call counters, this change has in fact been
observed to occiu'. ]\Ioreo^'er, since the initial re-trial intervals are com-
monly fairly short (30 seconds) subsequent attempts tend to find some
of the previous congestion still existing, so that the ratio of overflow to
peg count readings now exceeds slightly the "% NC existing." This
situation is illustrated in Fig. 5, which shows data taken on an operator-
1.0
AVERAGE SUBMITTED LOAD
Fig. 4 — Observed proportions of time all trunks were busy on Albany and
Buffalo groups of 2, 4, 5, 7, and 9 trunks,
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 429
u
z
o
z
I-
UJ
HI
5
ul
_i
_i
<
o
U-
o
z
o
(-
cc
o
a.
o
tr
a.
0.001
12 14
L = LOAD CARRIED IN ERLANGS
18
Fig. 5 — Comparison of NC data on a 16-trunk T-engineered toll group with
various load versus NC theories.
dialed T-engineered group of 16 trunks between Newark, N. J., and
Akron, Ohio. Curve A shows the empirically determined "NC encoun-
tered" relationship described above for ringdown operation; Curve B
gives the corresponding theoretical "NC existing" values. Lines C and D
give the operator-dialing results, for morning and afternoon busy hours.
The observed points are now seen generally to be significantly above
Curve B.*
At the same time as this change in the "NC encountered" was occur-
ring, due to the introduction of operator toll dialing, there seems to have
l)een little disturbance to the traditional relationship between load
* The observed point at 11 erlangs which is clearly far out of agreement with
the remainder of the data was produced by a combination of high-trend hours
and an hour in which an operator apparently made many re-t^rials in rapid suc-
cession.
430
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
u.
10
z
o
o
5
o
m
rvj
ti
_r
<
(-
z
LU
z
o
z
o
i
tr
UJ
I/)
§
o
«--- LIMIT OF
OBSERVED
DATA
i
[
oiT
/
/
/
/
/
/
/
/
/
/
/
y
/
/
/'
^•^
/^
^
^
««-
^
^
Tt^^
^•^^
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8
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SBIONII^ 1- a3AO SidlAjaiiV dO iN3D«3d
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 431
carried and " % NC existing." C. J. Truitt of the A.T. & T. Co. studied
i a number of operator-dialed T-engineered groups at Newark, New Jersey,
in 1954 with a traffic usage recorder (TUR) and group-busy timers, and
found the relationship of equation (1) still good. (This analysis has not
been published.)
A study by Dr. L. Kosten has provided an estimate of the probability
that when an NC condition has been found, it will also appear at a time
T later." When this modification is made, the expected load-versus-NC
relationship is shown by Curve E on Fig. 5. (The re-trial time here was
taken as the operators' nominal 30 seconds; with 150-second circuit-use
time the return is 0.2 holding time.) The observed NC's are seen to lie
slightly above the E-curve. This could be explained either on the basis
that Kosten's analysis is a lower limit, or that the operators did not
strictly observe the 30-second return schedule, or, more probably, a
combination of both.
3. CUSTOMERS DIALING ON GROUPS WITH CONSIDERABLE DELAY
It is not to be expected that customers could generally be persuaded to
wait a designated constant or minimum re-trial time on their calls which
meet the NC condition. Little actual experience has been accumulated
on customers dialing long distance calls on high-delay circuits. However,
it is plausible that they would follow the re-trial time distributions of
customers making local calls, who encounter paths-busy or line-busy
signals (between which they apparently do not usually distinguish).
Some information on re-trial times was assembled in 1944 by C. Clos by
observing the action of customers who received the busy signal on 1,100
local calls in the City of New York. As seen in Fig. 6, the return times,
after meeting "busy," exhibit a marked tendency toward the exponential
distribution, after allowance for a minimum interval required for re-
dialing.
An exponential distribution with average of 250 seconds has been
I fitted by eye on Fig. 6, to the earlier ■ — and more critical — customer re-
turn times. This may seem an unexpectedly long wait in the light of indi-
vidual experience; however it is probably a fair estimate, especially
since, following the collection of the above data, it has become common
practice for American operating companies in their instructional lit-
erature to advise customers receiving the busy signal to "hang up, wait
a few minutes, and try again."
The mathematical representation of the situation assuming exponen-
I tial return times is easily formulated. Let there be .r actual trunks, and
432 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
imagine y waiting positions, whore y is so large that few calls are re-
jected.* Assume that the offered load is a erlangs, and that the calls have
exponential conversation holding times of unit average duration. Finally \
let the average return time for calls which have advanced to the waiting >
positions, be 1/s times that of the unit conversation time. The statistical j
equilibrium equation can then be written for the probability j\m, n) (j
that m calls are in progress on the x trunks and n calls are waiting on
the y storage positions: ■
/(w, n) = aj{m — 1, n) dt + s(w + l)/(m — 1, n + 1) dt ''■)
+ (m + \)J{m + 1, n) dt + a/(.r, n - 1) dH^ (2)
+ [1 - (a*** + sn**) dt - m dt]f(m, n) ^
where 0 ^ m ^ .-r, 0 ^ w ^ //, and the special limiting situations are
recognized by:
■* Include term only when m — x
**■ Omit sn when m = x
*** Omit a when m = x and n = y
Equation (2) reduces to
(a*** + snifif + m)f{m; n) = af{m — 1, n) 1
+ s(n + l)/(m - 1, w + 1) (3)
+ (m + l)/(w + 1, n) + af(x, n - !)•,
Solution of (3) is most easily effected for moderate values of x and y
by first setting f(x, ?/) = 1 .000000 and solving for all other /(/?? , ?? ) in
X y
terms of /(o:, ?/). Normahzing through zl 11f(m, n) = 1.0, then gives
m=0 n=0
the entire f(m, n) array.
The proportion of time "NC exists," will, of course be
Z Six, n) (4)
n=0
and the load carried is
L = Xl X wi/(m, n) (5)
The proportion of call attempts meeting NC, including all re-trials
* The quant itjr y can also be chosen so that some calls are rejected, thus roughly
describing those calls abandoned after the first attempt.
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A, 433
will be
W{x, a, s) =
Expected overflow calls per unit time
Expected calls offered per unit time
Z (a + sn)jXx, n) - , ./ ^ ^^^
sn -\- af{x, y)
n=0
X y
S 2 (« + sn)f(m, n)
a -{- sn
m=0 71=0
X y
in which n = ^ 2^ nf(7n, n). And when y is chosen so large that/(.r, y)
7H = 0 71=0
is negligible, as we shall use it here,
L = a
W(x, a, s) =
sn
a -\- sn
(5')
(6')
1^ 0.5
<
"^O 0.4
ilZ
Oo
ZZ 0.3
Ol-
pllJ
o5 0.2
Q.
o
? 0.1
6 TRUNKS
/ // APOISSON
' ^1 P(C,L)
5=0.6
2 4 6 8
L=LOAD CARRIED IN ERLANGS
APOISSON
P(C,L)
fly >^-
f I6j _,
8 10 12 14
L = LOAD CARRIED IN ERLANGS
Fig. 7 — ■ Comparison of trunking formulas.
434 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
I
This formula provides a means for estimating the grade of service
which customers might he expected to receive if asked to dial their calls
over moderate-delay or high-delay trunk groups. For a circuit use length
of 150 seconds, and an average return time of 250 seconds (as on Fig. 6),
both exponential, the load-versus-proportion-NC curves for 6 and IG
trunks are given as curves (3) on Fig. 7. For example with an offered
(= carried) load of a = 4.15 erlangs on 6 trunks we should expect to find
27.5 per cent of the total attempts resulting in failure.
For comparison with a fixed return time of NC-calls, the IF-formula
curves for exponential returns of 30 seconds (s = 5) and 250 seconds
(s = 0.6) averages are shown on Fig. 5. The first is far too severe an
assumption for operator performance, giving NC's nearly double those
actually observed (and those given by theory for a 30-second constant
return time). The 250-second average return, however, lies only slightly
above the 30-second constant return curve and is in good agreement with
the data. Although not logically an adequate formula for interpreting
Peg Count and Overflow registrations on T-engineered groups under
operator dialing conditions, the IF-formula apparently could be used for
this purpose with suitable s-values determined empirically.
3.1. Comparison of Some Formulas for Estimating Customers' NC Service
on Congested Groups
, 1
As has been previously observed, a large proportion of customers who
receive a busy signal, return within a few minutes (on Fig. 6, 75 per cent
of the customers returned within 10 minutes). It is well known too, that
under adverse service conditions subscriber attempts (to reach a par-
ticular distant office for example) tend to produce an inflated estimate
of the true offered load. A count of calls carried (or a direct measurement
of load carried) will commonly be a closer estimate of the offered load
than a count of attempts. An exception may occur when a large propor-
tion of attempts is lost, indicating an offered load possibly in excess even
of the number of paths provided. Under the latter condition it is diffi-
cult to estimate the true offered load by any method, since not all the
attempts can be expected to return repeatedly until served; instead, a
significant number will be abandoned somewhere through the trials. In
most other circumstances, however, the carried load will prove a reason-
ably good estimate of the true offered load in systems not provided with
alternate paths.
This is a matter of especial interest for both toll and local operation
in America since principal future reliance for load measurement is ex-
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 435
pected to be placed on automatically processed TUR data, and as the
TUR is a switch counting device the results will be in terms of load
carried. Moreover, the quantity now obtained in many local exchanges
is load carried.* Visual switch counting of line finders and selectors off-
normal is widely practiced in step-by-step and panel offices; a variety of
electromechanical switch counting devices is also to be found in crossbar
offices. It is common to take load-carried figures as equal to load-offered
when using conventional trunking tables to ascertain the proper pro-
vision of trunks or switches. Fig. 7 compares the NC predictions made by
a number of the available load-loss formulas when load carried is used as
the entry variable.
The lowest curves (1) on Fig. 7 are from the Erlang lost calls formula
El (or B) with load carried L used as the offered load a. At low losses,
say 0.01 or less, either L or a = L/[l — Ei(a)] can be used indiscrimi-
nately as the entry in the Ei formula. If however considerably larger
losses are encountered and calls are not in reality "cleared" upon meet-
ing NC, it will no longer be satisfactory to substitute L for a. In this
circumstance it is common to calculate a fictitious load a' to submit to
the c paths such that the load carried, a'[I — Ei^dd')], equals the desired
L. (This was the process used in Section 2 to obtain " % NC existing.")
The curves (2) on Fig. 7 show this relation ; physically it corresponds to
an initially offered load of L erlangs (or L call arrivals per average hold-
ing time), whose overflow calls return again and again until successful
but without disturbing the randomness of the input. Thus if the loss
from this enhanced random traffic is E, then the total trials seen per
holding time will be L(l + ^ + ^' -f • • •) = L/(l - E) = a', the ap-
parent arrival rate of new calls, but actually of new calls plus return
attempts.
The random resubmission of calls may provide a reasonable descrip-
tion of operation under certain circumstances, presumably when re-trials
are not excessive. Kosten^ has discussed the dangers here and provided
upper and lowxr limit formulas and curves for estimating the proportions
of NC's to be expected when re-trials are made at any specified fixed
leturn time. His lower bounds (lower bound because the change in con-
gestion character caused by the returning calls is ignored) are shown by
open dots on Fig. 7 for return times of 1.67 holding times. They lie above
curves (2) (although only very slightly because of the relatively long
return time) since they allo\\- for the fact that a call shortly returning
* In fact, it is difficult to see how any estimate of offered load, other than carried
load, can be obtained with useful reliability.
436 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
after meeting a busy signal will have a higher probability of again find-
ing all paths busy, than would a randomly originated call.
The curves (3) show the TF-formula previously developed in this sec-
tion, which contemplates exponential return times on all NC attempts.
The average return time here is also taken as 1 .67 holding times. These
curves lie higher than Kosten's values for two reasons. First, the altered
congestion due to return calls is allowed for; and second, with exponential
returns nearly two-thirds of the return times are shorter than the aver-
age, and of these, the shortest ones will have a relatively high probability
of failure upon re-trying. If the customers were to return with exponen-
tial times after waiting an average of only 0.2 holding time (e.g., 30
seconds wait for 150-second calls) the TT^-curves would rise markedly to
the positions shown by (4).
Curves (5) and (6) give the proportions of time that all paths are busy
(equation 4) under the T'F-formula assumptions corresponding to NC
curves (3) and (4) respectively; their upward displacement from the
random return curves (2) reflects the disturbance to the group congestion
produced by the non-random return of the delayed calls. (The limiting
position for these curves is, of course, given by Erlang's E2 (or C) delay
formula.) As would be expected, curve (6) is above (5) since the former
contemplates exponential returns with average of 0.2 holding time, as
against 1.67 for curve (5). Neither the (5)-curves nor the open dots of
constant 30-second return times show a marked increase over curves (2).
This appears to explain why the relationship of load carried versus "NC
existing" (as charted in Figs. 3 and 4) was found so insensitive to vari-
able operating procedures in handling subsequent attempts in toll ring-
down operation, and again, why it did not appreciably change under
operator dialing.
Finally, through the two fields of curves on Fig. 7 is indicated the
Poisson summation P{c, L) with load carried L used as the entering
variable. The fact that these values approach closely the (2) and (3) sets
of curves over a considerable range of NC's should reassure those who
have been concerned that the Poisson engineering tables were not useful
for losses larger than a few per cent.*
4. SERVICE REQUIREMENTS FOR DIRECT DISTANCE DIALING BY CUSTOMERS
As shown by the TF-curves (3) on Fig. 7, the attempt failures by cus-
tomers resulting from their tendency to re-try shortly following an NC
* Reference may be made also to a throwdown by C. Clos (Ref. 3) using the
return times of Fig. 6; his "% NC" results agreed closely with tlie Poisson pre-
dictions.
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 437
would be expected to exceed slightly the values for completely random
re-trials. These particular curves are based on a re-trial interval of 1.67
times the average circuit-use time. Such moderation on the part of the
customer is probably attainable through instructional literature and
other means if the customer believes the "NC" or "busy" to be caused
by the called party's actually using his telephone (the usual case in local
practice). It would be considerably more difficult, however, to dissuade
the customer from re-trying at a more rapid rate if the circuit NC's
should generally approach or exceed actual called-party busies, a con-
dition of which he would sooner or later become aware. His attempts
might then be more nearly described by the (4) curves on Fig. 7 cor-
responding to an average exponential return of only 0.2 holding time — or
e\en higher. Such a result would not only displease the user, but also
result in the requirement of increased switching control equipment to
handle many more wasted attempts.
If subscribers are to be given satisfactory direct dialing access to the
iiitertoll trunk network, it appears then that the probability of finding
XC even in the busy hours must be kept to a low figure. The following
engineering objective has tentatively been selected: The calls offered to
the ^'final" group of trunks in an alternate route system should receive no
more than 3 per cent NC(P.03) during the network busy season busy hour.
(If there are no alternate routes, the direct group is the "final" route.)
Since in the nationwide plan there will be a final route between each
of some 2,600 toll centers and its next higher center, and the majority
of calls offered to high usage trunks will be carried without trying
their final route (or routes), the over-all point-to-point service, while
not easy to estimate, will apparently be quite satisfactory for cus-
tomer dialing.
5. ECONOMICS OF TOLL ALTERNATE ROUTING
In a general study of the economics of a nationwide toll switching plan,
made some years ago by engineers of the American Telephone and Tele-
graph Company, it was concluded that a toll line plant sufficient to give
ihe then average level of service (about T-40) with ordinary single-route
procedures could, if operated on a multi-alternate route basis, give the
desired P.03 service on final routes with little, if any, increase in toll line
investment.* On the other hand to attain a similar P.03 grade of service
by liberalizing a typical intertoll group of 10 trunks working presently
* This, of course, does not reflect the added costs of the No. 4 switching equip-
I nient.
438 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
at a T-40 grade of service and an occupancy of 0.81 would recjuire an
increase of 43 per cent (to 14.3 trunks), with a corresponding decrease
in occupancy to 0.57. The possible savings in toll lines with alternate
routing are therefore considerable in a system which must pro\'ide a
service level satisfactory for customer dialing.
In order to take fullest advantage of the economies of alternate rout-
ing, present plans call for five classes of toll offices. There will be a large
number of so-called End Offices, a smaller number of Toll Centers, and
progressively fewer Primary Centers (about 150), Sectional Centers
(about 40) and Regional Centers (9), one of which will be the National
Center, to be used as the "home" switching point of the other eight
Regional Centers.* Primary and higher centers will be arranged to per-
form automatic alternate routing and are called Control Switching
Points (CSP's). Each class of office will "home" on a higher class of
office (not necessarily the next higher one) ; the toll paths between them
are called "final routes." As described in Section 4, these final routes will
be provided to give low delays, so that between each principal toll point
and ever}' other one there will be available a succession of approximatelj'
P.03 engineered trunk groups. Thus if the more direct and heavily loaded
interconnecting paths commonly provided are busj- there will still be a
good chance of making immediate connection over final routes.
Fig. 8 illustrates the manner in which automatic alternate routing will
operate in comparison with present-day operator routing. On a call from
Syracuse, X. Y., to Miami, Florida, (a distance of some 1,250 miles),
under present-day operation, the Syracuse operator signals Albany, and
requests a trunk to Miami. With T-schedule operation the Syracuse-
Miami traffic might be expected to encounter as much as 25 per cent NC
during the busy hour, and approximately 4 per cent NC for the whole
day, producing perhaps a two-minute over-all speed of serA-ice in the
busy season.
With the proposed automatic alternate routing plan, all points on the
chart will have automatic switching systems. f The customer (or the
operator until customer dialing arrangements are completed) will dial a
ten-digit code (three-digit area code 305 for Florida plus the listed
Miami seven-digit telephone number) into the Jiiachine at Syracuse.
The various routes which then might conceivably be tried automatically
* Sec the hihlio^rajjliy ( i);irticulMily Pilliod and Truitt) for details of tlie
general trunkinji plan.
t The notation uscmI on the diagram of Fig. 8 is: Opon firclo — Primary Center
(Syracuse, Miamij; Triangle — Sectional Center (All)an\-, Jacksonville); Sqviare
— Regional Center (White Plains, Atlanta, St. Louis; St. Louis is also the Na-
tional Center).
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 439
PRESENT OPERATOR
ROUTING '^^
AUTOMATIC ALTERNATE
ROUTING
white Plains
N. Y.)
Miami
Miami
Fig. 8 — Present and proposed methods of handling a call from Syracuse, N. Y.,
to Miami, Florida.
are shown on the diagram numbered in the order of trial; in this par-
ticular layout shown, a maximum of eleven circuit groups could be tested
for an idle path if each high usage group should be found NC. Dotted
lines show the high usage roiites, which if found busy will overflow to the
final groups represented by solid lines. The switching ecjuipment at each
point upon finding an idle circuit passes on the required digits to the
next machine.
While the routing possibilities shown are factual, only in rare instances
would a call be completed over the final route via St. Louis. Even in the
busy season busy hour just a small portion of the calls would be expected
to be switched as many as three times. And only a fraction of one per
cent of all calls in the busy hour should encounter NC. As a result the
service will be fast. When calls are handled by a toll operator, the cus-
440
THE BELL SYSTEM TECHNICAL JOURNAL; MARCH 1956
tomer will not ordinarily need to hang up when NC is obtained. When
he himself dials, a second trial after a short wait following NC should
have a high probability of success.
Not many situations will be as complex as shown in Fig. 8; commonly
several of the links between centers will be missing, the particular ones
retained having been chosen from suitable economic studies. A large
number of switching arrangements Avill be no more involved than the
illustrative one shown in Fig. 9(a), centering on the Toll Center of
Bloomsburg, Pennsylvania. The dashed lines indicate high usage groups
from Bloomsburg to surrounding toll centers; since Bloomsburg "homes"
on Scranton this is a final route as denoted by the solid line. As an exam-
ple of the operation, consider a call at Bloomsburg destined for Williams-
port. Upon finding all direct trunks busy, a second trial is made via
Harrisburg; and should no paths in the Harrisburg group be available,
a third and final trial is made through the Scranton group.
In considering the traffic flow of a network such as illustrated at
Bloomsburg it is convenient to employ the conventional form of a two-
stage graded multiple having "legs" of varying sizes and traffic loads
individual to each, as shown in Fig. 9(b). Here only the circuits im-
mediately outgoing from the toll center are shown; the parcels of traffic
(a) GEOGRAPHICAL LAYOUT
WILLIAMSPORT I
SCRANTON
BLOOMSBURG
HARRISBURG PA.
(b) GRADED MULTIPLE SCHEMATIC
FRACKVILLE
HAZLETON
WILKES-
BARRE
PHILADELPHIA
FINAL GROUP TO SCRANTON
H.U. GROUP TO HARRISBURG
.1 M t
I
NO. TRUNKS IN H.U. GROUPS I [T] [jF] [^ [A] [T] [28 1 rsl m
LOAD TO AND FROM ^^^ .^. ^^ ^
DISTANT OFFICE (CCS) "^^^ '^' ^^ ^'^^ ^^' '^0 '^3 836 228 154
DISTANT OFFICE SCRN HBG PTVL SHKN SNBY WMPT FKVL HZN WKSB PHLA
Fig. 9
liiirg, Pa.
Aulonialic ;ilU'riiaie routing for direct distance dialing at Blooms-
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 441
calculated for each further connecting route will be recorded as part of
the offered load for consideration when the next higher switching center
is engineered. It is implicitly assumed that a call which has selected one
of the alternate route paths will be successful in finding the necessary
paths available from the distant switching point onward. This is not
quite true but is believed generally to be close enough for engineering
piu'poses, and permits ignoring the return attempt problem.
6. NEW PROBLEMS IN THE ENGINEERING AND ADMINISTRATION OF INTER-
TOLL GROUPS RESULTING FROM ALTERNATE ROUTING
With the greatly increased teamwork among groups of intertoll trunks
which supply overflow calls to an alternate route, an unexpected increase
or flurry in the offered load to any one can adversely affect the service to
all. The high efficiency of the alternate route networks also reduces their
overload carrying ability. Conversely, the influence of an underprovision
of paths in the final alternate route may be felt by many groups which
overflow to it. With non-alternate route arrangements only the single
groups having these flurries would be affected.
Administratively, an alternate route trunk layout may well prove
easier to monitor day by day than a large number of separate and in-
dependent intertoll groups, since a close check on the service given on
the final routes only may be sufficient to insure that all customers are
being served satisfactorily. When rearrangements are indicated, how-
SIMPLE PROGRESSIVE
GRADED MULTIPLE GRADED MULTIPLE
(a) (b)
t t t t t t tt t t tl
ILLUSTRATIVE INTERLOCAL AND INTERTOLL
ALTERNATE ROUTE TRUNKING ARRANGEMENT;
(c) (d)
t t t t t = ,-"" ^
tttl It ttl 1 t
Fig. 10 — Graded multi])los .•nid altornaic route trunking nrrangeinoiits.
I
442 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
ever, the determination of the proper place to take action, and the de
sirable extent, may sometimes be difficult to determine. Suitable traffic
measuring devices must be provided with these latter problems in mind
For engineering purposes, it will be highly desirable:
(1) To be able to estimate the load-service relationships with any
specified loads offered to a particular intertoll alternate routing network;
and
(2) To know the day-to-day busy hour variations in the various
groups' offered loads during the busy season, so that the general grade of
service given to customers can be estimated.
The balance of this paper will review the studies which have been made
in the Bell System toward a practicable method for predicting the grade
of service given in an alternate route network under any given loads.
Analyses of the day-to-day load variations and their effects on customer
dialing service are currently being made, and will be reported upon later.
?;
7. LOAD-SERVICE RELATIONSHIPS IN ALTERNATE ROUTE SYSTEMS
In their simplest form, alternate route systems appear as symmetrical
graded multiples, as shown in Fig. 10(a) and 10(b). Patterns such as
these have long been used in local automatic systems to partially over-
come the trunking efficiency limitations imposed by limited access
switches. The traffic capacity of these arrangements has been the sub-
ject of much study by theory and "throwdowns" (simulated traffic
studies) both in the United States and abroad. Field trials have sub-
stantiated the essential accuracy of the trunking tables which have
resulted.
In toll alternate route systems as contemplated in America, however,
there will seldom be the symmetry of pattern found in local graded
multiples, nor does maximum switch size generally produce serious
limitation on the access. The ''legs" or first-choice trunk groups will vary
widely in size; likewise the number of such groups overflowing calls
jointly to an alternate route may cover a considerable range. In all cases
a given group, whether or not a link of an alternate route, will have one
or more parcels of traffic for which it is the first-choice route. [See the
right-hand parcel of offered traffic on Fig. 10(c).] Often this first routed
traffic will Ijc the bulk of the load offered to the group, which also serves
as an alternate I'oute for other traffic.
The simplest of the approximate formulas developed for solving the
local graded multiple problems are hopelessly unwieldy when applied
to such arrangements as shown in Fig. 10(d). Likewise it is impracticable i
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 443
to solve more than a few of the infinite variety of arrangements by means
of "throwdowns."
However, for both engineering (planning for future trunk provisions)
I and administration (current operating) of trunks in these multi-alternate
routing systems, a rapid, simple, but reasonably accurate method is
(required. The basis for the method which has been evolved for Bell
System use will be described in the following pages.
7.1. The "Peaked" Character of Overflow Traffic
The difficulty in predicting the load-service relationship in alternate
route systems has lain in the non-random character of the traffic over-
flowing a first set of paths to which calls may have been randomly
offered. This non-randomness is a well appreciated phenomenon among
traffic engineers. If adecjuate trunks are provided for accommodating
the momentary traffic peaks, the time-call level diagram may appear
as in Fig. 11(a), (average level of 9.5 erlangs). If however a more limited
j number of trunks, say a: = 12, is provided, the peaks of Fig. 11(a) will be
Ichpped, and the overflow calls will either be "lost" or they may be
j handled on a subsequent set of paths y. The momentary loads seen on 2/
then appear as in Fig. 11(b). It will readily be seen that a given average
i load on the y trunks will have quite different fluctuation characteristics
i than if it had been found on the x trunks. There will be more occurrences
of large numbers of calls, and also longer intervals when few or no calls
are present. This gives rise to the expression that overflow traffic is
"peaked."
Peaked traffic requires more paths than does random traffic to operate
at a specified grade of delayed or lost calls service. And the increase in
paths required will depend upon the degree of peakedness of the traffic
involved. A measure of peakedness of overflow traffic is then required
which can be easily determined from a knowledge of the load offered and
the number of trunks in the group immediately available.
In 1923, G. W. Kendrick, then with the American Telephone and
I Telegraph Company, undertook to solve the graded multiple problem
■through an application of Erlang's statistical eciuilibrium method. His
i principal contribution (in an unpublished memorandum) was to set up
I the equations for describing the existence of calls on a full access group
\oi X -{- y paths, arranged so that arriving calls always seek service first
iu the .T-group, and then in the ^/-group when the x are all busy.
Let f{m, n) be the probability that at a random instant m calls exist
j on the x paths and n calls on the y paths, when an average Poisson load
444
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
of a erlangs is submitted to the x -\- y paths. The general state equation
for all possible call arrangements, is
(a* + m + n)f{m, n) = (w + l)/(m + 1, n)
+ (n + l)/(m, w + 1) + ajim — 1, n) + aj{x, n — 1)%
(7)
in which the term marked {%) is to be included only when m = x, and
* indicates that the a in this term is to be omitted when in -\- n = x -{- y.
m and n may take values only in the intervals, 0 -^ m ^ x;Q -^ n -^ y.
As written, the equation represents the "lost calls cleared" situation.
(a) RANDOM TRAFFIC
10 00 AM
< I
if) Q.
a.
2
to
10 00 A M
10 30
TIME OF DAY
(b) PEAKED OVERFLOW TRAFFIC
PI
-^
10 30
TIME OF DAY
Fig. 11 — Production of peakedness in overflow traffic.
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 445
By choosing x -]- y large compared with the submitted load a a "lost
calls held" situation or infinite-overflow-trunks result can be approached
as closely as desired.
Kendrick suggested solving the series of simultaneous equations (7) by
determinants, and also by a method of continued fractions. However
little of this numerical work was actually undertaken until several years
later.
Early in 1935 Miss E. V. Wyckoff of Bell Telephone Laboratories be-
came interested in the solution of the (x -\- 1)(^/ + 1) lost calls cleared
simultaneous equations leading to all terms in the /(m, n) distribution.
She devised an order of substituting one equation in the next which pro-
vided an entirely practical and relatively rapid means for the numerical
solution of almost any set of these equations. By this method a con-
siderable number of /(m, n) distributions on x, y type multiples with
varying load levels were calculated.
From the complete m, n matrix of probabilities, one easily obtains the
distribution 9m{n) of overflow calls when exactly m are present on the
lower group of x trunks; or by summing on m, the d{n) distribution with-
out regard to m, is realized. A number of other procedures for obtaining
the/(m, n) values have been proposed. All involve lengthy computations,
very tedious for solution by desk calculating machines, and most do not
have the ready checks of the WyckofT-method available at regular points
through the calculations.
In 1937 Kosten^ gave the following expression for /(m, n) :
/(», n) = (- l)V.fe) i (i) M^- "f^'l., (8)
i=0
(Pi^l{x)ipi(x)
where
(po{x) =
x^—a
a e
xl
; and for i > 0,
;=o \ J / (.^• - J)i
These equations, too, are laborious to calculate if the load and num-
1 K^rs of trunks are not small. It would, of course, be possible to program a
modern automatic computer to do this work with considerable rapidity.
The corresponding application of the statistical equilibrium equations
to the graded multiple problem was visualized by Kendrick who, how-
ever, went only so far as to write out the equation for the three-trunk
446 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
case consisting of two subgroups of one trunk each and one common
overflow trunk.
Instead of solving the enormously elaborate system of equations de-
scribing all the calls which could simultaneously be present in a large
multiple, several ingenious methods of convoluting the
X
6(n) = Z/(w, n)
overflow distributions from the individual legs of a graded multiple have
been devised. For example, for the multiple of Fig. 10(a), the probability
of loss Pi as seen by a call entering subgroup number i, is approximately,
Pi = 2 £ e.Ar)-rl^{z -r) +J: d.Ar) (9)
r=0 z=y T—y
in which \l/{z — r) is the probability of exactly z — r overflow calls being
present, or wanting to be present, on the alternate route from all the
subgroups except the zth, and with no regard for the numbers of calls
present in these subgroups. The ^x,i(^) = jiixi , r) term, of course, con-
templates all paths in the particular originating call's subgroup being
occupied, forcing the new call arriving in subgroup i to advance to the
alternate route. This corresponds to the method of solving graded mul-
tiples developed by E. C. Molina^ but has the advantage of overcoming
the artificial "no holes in the multiple" assumption which he made.
Similar calculating procedures have been suggested by Kosten.* These
computational methods doubtless yield useful estimates of the resulting
service, and for the limited numbers of multiple arrangements which
might occur in within-office switching trains (particularly ones of a sym-
metrical variety) such procedures might be practicable. But it would be
far too laborious to obtain the individual overflow distributions Q{n),
and then convolute them for the large variety of loads and multiple
arrangements expected to be met in toll alternate routing.
7.2. Approximate Description of the Character of Overflow Traffic
It was natural that various approximate procedures should be tried in
the attempt to obtain solutions to the general loss formula sufficiently
accurate for engineering and study purposes. The most ol^vious of these
is to calculate the lower moments or semi-invariants of the loads over-
flowing th(; sul)groups, and from them construct approximate fitting
* Kosten gives the above approximation (9), which he calls Wb^, Jis an upper
limit to the blocking. He also gives a lower limit , Wr, in which z = // throughout
(References 4, 5).
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 447
I distributions for 6{n) mid dx(;n). Since each such overflow is independent
I of the others, they may be combined additively (or convokited), to ob-
[tain the corresponchng total distribution of calls appearing before the
, I alternate route (or common group) . It may further be possible to obtain
I [an approximate fitting distribution to the sum-distribution of the over-
flow calls.
The ordinary moments about the 0 point of the subgroup overflow
distribution, when m of the x paths are busy, are found by
V
ta'im) = 2 njim, n) (10)
When an infinite number of |/-paths is assumed, the resulting expres-
sions for the mean and variance are found to be:*
Number of x-paths busy unspecified :'\
Mean = a = a-Ei,^{a) (11)
Variance = v = a[l — a -{- a{x -\- I -\- a — a)'^] (12)
All x-paths occupiedi
Mean = a^^ = a[x - a + 1 -\- aEiMf^ (13)
Variance = v^ = ax[l — ax + 2a(x + 2 + a^ — a)~^] (14)
Equations (11) and (12) have been calculated for considerable ranges
1 of offered load a and paths x. Figs. 12 and 13 are graphs of these results.
i For example when a load of 4 erlangs is submitted to 5 paths, the aver-
I age overflow load is seen to be a = 0.80 erlang, the same value, of
I course, as determined through a direct application of the Erlang Ei
formula. During the time that all x paths are busy, however, the over-
flow load wdll tend to exceed this general level as indicated by the value
of ax = 1.41 erlangs calculated from (13). Similarly the variance of the
overflow load will tend to increase when the x-paths are fully occupied,
* The derivation of these equations is given in Appendix I.
t The skewness factor may also be of interest :
ilz
l^i:
3/2
^" + "-"^"' +a^ (15)
x+1 +a- a \x + 2\{x-a)'^^-2{x-a) + x + 2 + {x^-2-a)a
+ 3(1 -a) I + a(l - a)(l - 2a)
o
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452 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
as shown by ?; = 1.30, and Vx = 1.95. In all cases the variances v and Vx
will exceed the variance of corresponding Poisson traffic (which would
have variances of a and ax respectively).
7.2.1. A Prohahility Distribution for Overflow Traffic
It would be of interest to be able, given the first several descriptive
parameters of any traffic load (such as the mean and variance and skew-
ness factors of the overflow from a group of trunks), to construct an
approximate probability distribution d{n) which would closely describe
the true momentary distribution of simultaneous calls. Any proposed
fitting distribution for the overflow from random traffic offered to x
trunks, can, of course, be compared with . ^
X
determined from (7) or (8).
Suitable fitting curves should give probabilities for all possitive in-
tegral values of the variable (including zero) , and have sufficient unspeci-
fied constants to accommodate the parameters selected for describing
the distribution. Moreover, the higher moments of a fitting distribution
should not diverge too radically from those of the true distribution ; that
is, the "natural shapes" of fitting and true distributions should be simi-
lar. Particularly desirable would be a fitting distribution form derived
with some attention to the physical circumstances causing the ebb and
flow of calls in an overflow situation. The following argument and der-
ivation undertake to achieve these desiderata.*
A Poisson distribution of offered traffic is produced by a random arrival
of calls. The assumption is made or implied that the probability of a new
arrival in the next instant of time is quite independent of the number
currently present in the system. When this randomness (and correspond-
ing independence) are disturbed the resulting distribution will no longer
be Poisson. The first important deviation from the Poisson would be
expected to appear in a change from variance = mean, to variance ^
* A two-parameter function which has the ability to fit quite well a wide variety
of true overflow distributions, has the form
t(n) = Kin + l)''e-^(''+i)
in which K is the normalizing constant. The distribution is displaced one unit
from the usual discrete generalized exponential form, so that ^(0) 9^ 0. The ex-
pression, however, has little rationale for being selected a priori as a suitable
fitting function.
I
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 453
mean. Corresponding changes in the higher moments would also be
expected.
WTiat would be the physical description of a cause system with a vari-
ance smaller or larger than the Poisson? If the variance is smaller, there
must be forces at work which retard the call arrival rate as the number
of calls recently offered exceeds a normal, or average, figure, and which
increase the arrival rate when the number recently arrived falls below
the normal level. Conversely, the variance will exceed the Poisson's
.should the tendencies of the forces be reversed.* This last is, in fact, a
rough description of the incidence rates for calls overflowing a group of
trunks.
Since holding times are attached to and extend from the call arrival
instants, calls are enabled to project their influence into the future; that
is, the presence of a considerable number of calls in a system at any in-
stant reflects their having arrived in recent earlier time, and now can be
used to modify the current rate of call arrival.
Let the probability of a call originating in a short interval of time dt be
Po.n = [a + (n — a)co(n)] dt
where n = number of calls present in the system at time t,
a = base or average arrival rate of calls per unit time, and
w(n) = an arbitrary function which regulates the modification in
call origination rate as the number of calls rises above
or falls below a.
Correspondingly, let the probability that one of n calls will end in the
short interval of time dt be
which will be satisfied in the case of exponential call holding times, with
mean unity. Following the usual Erlang procedure, the general statistical
equilibrium equation is
(16)
Jin) = /(n)[(l - Po.n){l - Pe,n)\ + /(« " l)Po,n-l(l " Pe.n-l)
-Vj{n+ 1)(1 - Po.„+i)P,,„+i
which gives
(Po,„ + P.,„)/(n) = Po,«-i/(n - 1) + Pe,n+xKn + 1)
i ignoring terms of order higher than the first in dt.
* The same thinking lias been used by Vaiilot^ for decreasing the call arrival
I rate according to the number momentaril}^ present; and by Lundquist^ for both
increasing and decreasing the arrival rate.
454 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
(17)
Or,
[a + (n — a)w(?i) + ??.]/(n)
= [a + (n -a- l)co(n - l)]/(/^ - 1) + (n + l)/(7i + 1)
The choice of aj(n) will determine the solution of (17). Most simply,
co(n) = k, making the variation from the average call arrival rate directly-
proportional to the deviation in numbers of calls present from their
average number. In this case, the solution for an unlimited trunk group
becomes, with a' = a{l — k),
a (a + k) -■■ [a + {n - 1)A;]
fin) =
n!
^^ , , a' (a' + k) , a' (a' + k)(a' + 2k) ,
1 + « H ^t; H ^ TT, +
(18)
2! ' 3!
which may also be written after setting a" = a'/k = a(l — k)/k, as
a'ia' + 1) • • • [a" + (n - 1)]A;"
fin) =
n!
(19);
(1 - k)-
The generating function (g.f.) of (19) is
Z/(n)r =
(1 - kT)-""
n=0 (1 - k)--"
which is recognized as that for the negative binomial, as distinguished
from the g.f.,
P
(i + ? tX
(1/g)^
for the positive binomial.
The first four descriptive parameters of /(w) are:
Order
Moment about Mean
Descriptive Parameter
1
Ml
= 0
Mean = n = a
(20)
2
M2
= variance, v = a/(l — k)
Std Devn, <r = [a/(l - fc)]'/2
(21)
3
f^a
a(l + k)
(1 - fc)^
Skewness, \/sT — — , ,
(22)
4
M4
3a2(l - A0 + a(fc2+4A; + l)
M4 A;2 + 4fc + 1
Kurtosis, /3., = - = 3 + —7^ ry-
o-* a(l — k)
(23)
(1 - fc)3
I
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 455
Since only two constants, a and k, need specification in (18) or (19),
the mean and variance are sufficient to fix the distribution. That is, with
the mean /7 and variance v known,
a = ,7 or a' = n(l - k) = if/v, or a" = n(l - k)/k (24)
A: = 1 - a/y = 1 - n/v. (25)
The probability density distribution f(n) is readily calculated from
(19); the cumulative distribution G(^n) also may be found through use
of the Incomplete Beta Function tables since
G(^n) = hi7i - l,a")
(26)
= h(n - l,a(l - k)/k)
The goodness with which the negative binomial of (19) fits actual dis-
tributions of overflow calls requires some investigation. Perhaps a more
elaborate expression for co(n) than a constant k in (17) is required. Three
comparisons appear possible: (1), comparison with a variety of 0«(n)
distributions with exactly m calls on the x trunks, or d{n) with m unspeci-
fied, (obtained by solving the statistical equilibrium equations (7) for a
divided group) ; (2), comparison with simulation or "throwdown" results;
and (3), comparison with call distributions seen on actual trunk groups.
These are most easily performed in the order listed.*
Co7nparison of Negative Binomial with True Overflow Distributions
Figs. 14 to 17 show various comparisons of the negative binomial dis-
tribution with true overflow distributions. Fig. 14 gives in cumulative
form the cases of 5 erlangs offered to 1, 2, 5, and 10 trunks. The true
j = n
distributions (shown as solid lines) are obtained by solving the difference
equations (7) in the manner described in Section 7.1. The negative bi-
nomial distributions (shown dashed) are chosen to have the same mean
and variance as the several F{^n) cases fitted. The dots shown on
* Comparison could also be made after equating means and variances respec-
tively, between the higher moments of the overflow traffic beyond x trunks and
the corresponding negative binomial moments: e.g., the skewness given by (15)
can be compared with the negative binomial skewness of (22). The difficulty here
is that one is unable to judge whether the disparity between the two distribution
functions as described by differences in their higher parameters is significant or
not for traffic engineering purposes.
456
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
the figure are for random (Poisson) traffic having the same mean values
as the /'' distributions. The negative binomial provides excellent fits
down to cumulated probabilities of 0.01, with a tendency thereafter to
give somewhat larger values than the true ones. The Poisson agreement
is good only for the overflow from a single trunk, as might have been
anticipated, the divergence rapidly increasing thereafter.
Fig. 15 corresponds with the cases of Fig. 14 except that the true over-
flow Fxi^n) distributions for the conditional situation of all .r-paths
busy, are fitted. Again the negative binomial is seen to give a good agree-
ment down to 0.01 probability, with somewhat too-high estimates for
larger values of the simultaneous overflow calls n.
Fig. 16 shows additional comparisons of overflow and negative bi-
nomial distributions. As before, the agreement is quite satisfactory to
0.01 probability, the negative binomial thereafter tending to give some-
what high values.
On Fig. 17 are compared the individual 6(n) density distributions for
several cases. The agreement of the negative binomial with the true
distribution is seen to be uniformly good. The dots indicate the random
(Poisson) individual term distribution corresponding to the a = 9.6 case-
1.0
"T*^
;J-^
—
TRUE DISTRIBUTION
\
^^^^^\-
_
NEGATIVE BINOMIAL
\
<^
•
\
FITTING DISTRIBUTION
CORRESPONDING
RANDOM TRAFFIC
0.1
-\
\
>
v
\
_ \
• \
•\
\
n)
\
\ ^
\
» \\ \
\ •
\
^ V \
0.01
-
\
V5
• v\
\s:=io
\\
\\ \
.
^
V \> V
• \
•
\ ^^ \ n^
0.001
_J M \ i 1 \ l> \V 1 1
0 t 2 3 4 5 6 7 8 9 10 11 12 13 14 15
n = NUMBER OF SIMULTANEOUS CALLS
Fig. 14 — Probability distributions of overflow traffic with 5 erlangs offered to
1, 2, 5, and 10 trunks, fitted by negative binomial.
I
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 457
the agreement, of course, is poor since the non-randomness of the over-
flow here is marked, having an average of 1.88 and a variance of 3.84.
Comparison of Negative Binomial with Overflow Distributions Observed
hi/ llirowdoivns and on Actual Trunk Groups
Fig. 18 shows a comparison of the negative binomial with the over-
How distributions from four direct groups as seen in throwdown studies,
'ilie agreement over the range of group sizes from one to fifteen trunks is
seen to be excellent. The assumption of randomness (Poisson) as shown
by the dot values is clearly unsatisfactory for overflows beyond more
than two or three trunks.
A number of switch counts made on the final group of an operating
toll alternate routing system at Newark, New Jersey, during periods
when few calls were lost, have also shown good agreement with the neg-
ative binomial distribution.
7.2.2. A Probability Distribution for Combined Overflow Traffic Loads
It has been shown in Section 7.2.1 that, at least for load ranges of wide
interest, the negative binomial with but two parameters, chosen to agree
Fx(§n)
0.01
0.001
TION
OMIAL
BUTION
0 I 2 3 4 5 6 7 8 9 10 11 12 13 14 15
n= NUMBER OF SIMULTANEOUS CALLS
Fig. 15 — Probability distributions of overflow traffic with 5 erlangs offered to
1, 2, 5, and 10 trunivs, when all trunks are busy; fitted by negative binomial.
458
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
with mean and variance, gives a satisfactory jfit to the distribution of
traffic overflowing a group of trunks. It is now possible, of course, to
convohite the various overflows from any number of groups of varying
sizes, to obtain a combined overflow distribution. This procedure, how-
ever, would be very clumsy and laborious since at each switching point
in the toll alternate route system an entirely difl"erent layout of loads and
high usage groups would require solution; it would be unfeasible for
practical working.
We return again to the method of moments. Since the overflows of
the several high usage groups will, in general, be independent of one
another, the iih semi-invariants Xi of the individual overflows can be
combined to give the corresponding semi-invariants A, of their total,
Ai — iXi + 2X1 +
(27)
Or, in terms of the overflow means and variances, the corresponding
parameters of the combined loads are
Average = A' = ai -{- az + ■ ■ ■ (28)
Variance = V = vi + V2 + • • - (29)
TRUE DISTRIBUTION
NEGATIVE BINOMIAL
FITTING DISTRIBUTION
0.001
2 3 4 5 6 7 8 9 10 II 12 13 14 15
n = NUMBER OF SIMULTANEOUS CALLS
Fig. 16 — Probability distributions of overflow traffic: 3 erlangs offered to 2
trunks, and 9.6 erlangs offered to 10 trunks.
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 459
With the mean and variance of the combined overflows now deter-
mined, the negative binomial can again be employed to give an approxi-
mate description of the distribution of the simultaneous calls (p{z) offered
to the common, or alternate, group.
The acceptability of this procedure can be tested in various ways. One
way is to examine whether the convolution of several negative binomials
(representing overflows from individual groups) is sufficiently well fitted
by another negative binomial with appropriate mean and variance, as
found above.
It can easily be shown that the convolution of several negative bi-
nomials all with the same over-dispersion (variance-to-mean ratio) but
not necessarily the same mean, is again a negative binomial. Shown in
Table I are the distribution components and their parameters of two
examples in which the over-dispersion parameters are not identical. The
third and fourth semi-invariants of the fitted and fitting distributions, are
seen to diverge considerably, as do the Pearsonian skewness and kurtosis
factors. The test of acceptability for traffic fluctuation description comes
in comparing the fitted and fitting distributions which are shown on
Fig. 19. Here it is seen that, despite what might appear alarming dis-
0(n)
0.01
O.OOI
TRUE DISTRIBUTION
NEGATIVE BINOMIAL
FITTING DISTRIBUTION
• RANDOM TRAFFIC, 8=1.9
a = 9.6
= 3.84
I 2 3 4 5 6 7 8 9 10 II 12
n = NUMBER OF SIMULTANEOUS CALLS
Fig. 17 — Probability density distributions of overflow traffic from 10 trunks,
fitted by negative binomial.
460
THE BELL SYSTEM TECHNICAL JOUENAL, MARCH 1956
parities in the higher semi-invariants, the agreement for practical traffic
purposes is very good indeed.
Numerous throwdown checks confirm that the negative binomial em-
ploying the calculated sum-overflow mean and variance has a wide range
over which the fit is quite satisfactory for traffic description purposes.
Fig. 20 shows three such trunking arrangements selected from a con-
siderable number which have been studied by the simulation method.
Approximate!}^ 5,000, 3,500, and 580 calls were run through in the three
examples, respective!}' . Tlie overflow parameters obtained !)y experiment
are seen to agree reasonably well with the theoretical ones from (28)
and (29) when the numbers of calls processed is considered.
On Fig. 21 are sliown, for the first arrangement of Fig. 20, distributions
of simultaneous offered calls in each subgroup of trunks compared with
the corresponding Poisson; the agreement is satisfactory as was to be
expected. The sum distribution of the overflows from the eight subgroups
is given at the foot of the figure. The superposed Poisson, of course, is a
poor fit; the negative binomial, on the other hand, appears quite accept-
able as a fitting curve.
1.0
0.8
0.6
P 2n
1 TRUNK- a = \.22
3 TRUNKS- a = 2.24
0.4 -
0.2 ■
1.0
0.8 -
0.6
0.4
0.2
234501 234
n=NUMBER OF SIMULTANEOUS CALLS
THEORY
OBSD
V\
( )
( )
AVG 0.67
0.63
VAR 0.77
0.60
i • RANDOM TRAFFIC
\, a = 0.67
THEORY OBSD
c- ) ( — 1
u
AVG 0.55
0.51
VAR 0.77
0.63
\\
• RANDOM
TRAFFIC
a=
D.55
v^^
P^n
1.0
15 TRUNKS- a
\ THEORY
= 11.46
OBSD '-O
.\ ( H
( )
0.8
*\ AVG 0.81
0.80 '-'•®
'A VAR 1.88
1.42
0.6
"\\, • RANDOM TRAFFIC °-^
\l a=o.8i
0.4
0.4
0.2
0.2
0
• ^'^v,.^^^^
_ , n
9 TRUNKS- a = 6.21
THEORY OBSD
( -) ( )
AVG 0.52 0.46
VAR 1.00 1.48
. RANDOM TRAFFIC
a = 0.52
4 68 10 024 68
n=NUMBER OF SIMULTANEOUS CALLS
10
12
Fifj;. 18 — Ovorflow (li.-<t ril)utioiis from diroct interoffice trunk groups; negative
binomial theory versus thrgwclowji observations.
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 461
Table I — Comparison of Parameters of a Fitting
Negative Binomial to the Convolution of
Three Negative Binomials
Example No. 1
Example No. 2
Component
Component
parameters
Component
dist'n No.
Component parameters
dist'n No.
Mean
Variance
Mean
Variance
1
5
5
1
1
1
2
2
4
2
2
3
3
1
3
3
2
6
8
12
5
10
Semi-Invariants A, Skewness \/pi , and Kurtosis ^2 , of Sum Distributions
Parameter
E.xact
Fitting
Parameter
Exact
Fitting
Ai
8
8
Ai
5
5
Ao
12
12
A2
10
10
As
32
24
As
37
30
A4
168
66
A4
239.5
130
VFi
0.770
0.577
V/3i
1.170
0.949
/32
4.167
3.458
/32
5.395
4.300
Fig. 22 shows the corresponding comparisons of the overflow loads in
the other two trunk arrangements of Fig. 20. Again good agreement
with the negative binomial is seen.
7.3. Equivalent Random Theory for Prediction of Amount of Traffic Over-
flowing a Single Stage Alternate Route, and Its Character, with Lost
Calls Cleared
As discussed in Section 7.2, when random traffic is offered to a limited
number of trunks x, the overflow traffic is well described (at least for
traffic engineering purposes) by the two parameters, mean a and variance
V. The result can readily be applied to a group divided (in one's mind)
two or more times as in Fig. 23.
Employing the a and v curves of Figs. 12 and 13, and the appropriate
numbers of trunks a;i , Xi + 0:2 , and Xi + X2 + x^ , the pairs of descrip-
tive parameters, ai , vi , ao , vo and a-s , v-a can be read at once. It is clear
then that if at some point in a straight multiple a traffic with parameters
ai , Vi is seen, and it is offered to .r2 paths, the overflow therefrom will
have the characteristics 012 , vo . To estimate the particular values of a-y
and v-i , one would first determine the values of the equivalent random
462
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
P5n
P^n
CONVOLUTION OF 3 NEGATIVE BINOMIAL
VARIABLES WITH PARAMETERS:
AVG WR
1 I
2 3
2 6
, -FITTING NEGATIVE BINOMIAL
6 8 10 12
n= NUMBER OF CALLS PRESENT
I
-I I l_^
14
16
Fig. 19 — Fitting sums of negative binomial variables with a negative binomial.
traffic a and trunks .Ti which would have produced ai and Vi . Then pro-
ceeding in the forward direction, using a and Xi + X2 , one consults the
a and v charts to find txi and Vz . Thus, within the limitations of straight
group traffic flow, the character (mean and variance) of any overflow
load from x trunks can be predicted if the character (mean and variance)
of the load submitted to them is known.
Curves could be constructed in the manner just described by which the
overflow's a' and v' are estimated from a load, a and v, offered to x trunks.
An illustrative fragment of such curves is shown in Appendix II, with an
example of their application in the calculation of a straight trunk group
loss by considering the successive overflows from each trunk as the
offered loads to the next.
Enough, perhaps, has been shown in Section 7.2 of the generally ex-
cellent descriptions of a variety of non-random traffic loads obtainable
by the use of only the two parameters a and v, to make one strongly
suspect that most of the fluctuation information needed for traffic engi-
neering purposes is contained in those two values. If this is, in fact, the
case, we should then be able to predict the overflow a', v' from x trunks
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 463
\\ith an offered load a, v which has arisen in any manner of overflow from
earlier high usage groups, as illustrated in Fig. 24.
This is found to be the case, as will be illustrated in several studies de-
scribed in the balance of this section. In the determination of the charac-
teristics of the overflow traffic a', v' in the cases of non-full-access groups,
such as Figs. 24(b) and 24(c), the equivalent straight group is visualized
[Fig. 24(a)], and the Eciuivalent Random load A and trunks S are found.*
I Using A, and *S + C, to enter the a and v curves of Figs. 12 and 13, a
, and v' are readily determined. To facilitate the reading of .1 and S, Fig.
25 1 and Fig. 26 f (which latter enlarges the lower left corner of Fig. 25)
have been drawn. Since, in general, a and v will not have come from a
simple straight group, as in Fig. 24(a), it is not to be expected that *S,
OVERFLOW THEORY OBSD
AVERAGE 5.76 5.98
VARIANCE 12.37 14.89
= = _ = OST N0.1
t t
13.16 1024
f
1024
t t
10.18 9.22
t t
7.63 7.48
0.76 ERLANGS
OVERFLOW
AVERAGE
VARIANCE
THEORY
5.02
9.95
OBSD
5.06
7.90
^^
~ ^
—
OST N0.6
t t t t t t t
OFFER 10.66 3.24 2.44 11.46 9.81 9.59 1.42 ERLANGS
OVERFLOW THEORY OBSD
AVERAGE 2.83 2.87
VARIANCE 3.35 3.34
OST N0.14
t t t t 1 1 t
OFFER 2.52 1.08 0.94 0.94 0.59 1.13 0.85 ERLANGS
Fig. 20 — Comparison of joint-overflow parameters; theory versus throwdown.
* A somewhat similar method, commonly identified with the British Post
Office, which uses one parameter, has been employed for solving symmetrical
graded multiples (Ref. 9).
t Figs. 25 and 26 will be found in the envelope on the inside back cover.
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
GROUP N0.1
17 TRUNKS, a = 13.t6
GROUP NO. 2
14 TRUNKS, a:
10 15 20 0 5 10 15
r = NUMBER OF SIMULTANEOUS CALLS OFFERED TO THE DIRECT TRUNKS
0.15
0.10
f(r)
ao5
I-
z
ui
BC
a.
Ill
S
1-
z
o
o
o
a.
a.
10
GROUP NO. 3
13 TRUNKS, a = 10.24
q:
<
1- A GROUP NO. 5
A\^^ 12 TRUNKS, a= 9.22
10 0.10
11 f(r)
O 0.05
//v.
c
y^ ^x^\_^
a 0
20
0.20
r GROUP NO. 7
/\ 10 TRUNKS, a = 748
0.15
/7X\
f(r) 0.10
/ nk
0.05
yy \v
0
---^r ^^^^^C::^— -^
GROUP N0.4 '
14 TRUNKS,;
GROUP N0.6
10 TRUNKS, i
8 10 12 14 16 18
0.15 r
0.10
F(n)
0.05
DISTRIBUTION OF OVERFLOW CALLS FROM 8 DIR
GROUPS OFFERED TO 1ST ALTERNATE ROUTE
THEORY
OBSD
AVG 5.76
5.98
VAR 12.4
14.9
THROWDOWN OBSNS
NEGATIVE BINOMIAL
-^^^^l!!^^^^^>^
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
n = NUMBER OF SIMULTANEOUS CALLS OFFERED TO THE ALTERNATE ROUTE
17
Fig. 21 — Comparison of theoretical and throwdown dis(ril)utions of simul-
taneous calls offered to direct groups and to tlieir first alternate route (OST No. 1).
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 465
read from Fig. 25, will be an integer. This causes no trouble and S should
be carried along fractionally to the extent of the accuracy of result de-
sired. Reading *S' to one-tenth of a trunk will usually be found sufficient
for traffic engineering purposes.
Example 1: Suppose a simple graded multiple has three trunks in each
of two subgroups, which overflow to C common trunks, where C = 1,
P^n
OST NO. 6
THEORY OBSD
AVG 5.02 5.06
VAR 9.95 7.90
• RANDOM TRAFFIC, a = 5.0
-OBSD
-NEGATIVE BINOMIAL
2 4 6 8 10 12 14 16 18
n = NUMBER OF SIMULTANEOUS CALLS
P?n
--OBSD
OST N0.14
THEORY OBSD
( ) ( )
AVG 2.83 2.87
VAR 3.35 3,34
RANDOM TRAFFIC, a = 2.8
-NEGATIVE BINOMIAL
2 4 6 8 10 12 14 16 18
n = NUMBER OF SIMULTANEOUS CALLS
Fig. 22 — Combined overflow loads off'ered to alternate-route OST trunks from
lirect interoffice trunks; negative binomial theory vs throwdown observations.
t«3.
V,
ta2,y
2y^2
f a,,i
Fig. 23 — A full access group divided at several points to examine the traffic
character at each point.
466
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
2 or 3. A load of a erlangs is submitted to each subgroup, a having the
values 1, 2, 3, 4 or 5. What grade of service will be given?
Solution: The load overflowing each subgroup, when a = 1 for example,
has the characteristics a = 0.0625 and y = 0.0790. Then A' = 2a = 0.125
and V — 2v = 0.158. Reading on Fig. 26 gives the Ecjuivalent Random
values oi A = 1.04 erlangs, S = 2.55 trunks. Reading on Fig. 12.1 with
C + *S = 3.55 when C = 1, and A = 1.04, we find a' = 0.0350 and
oi' liflx + a-^ = 0.0175. We construct Table II in which loss values pre-
dicted by the Equivalent Random (ER) Theory are given in columns
(3), (5) and (7). For comparison, the corresponding exact values given
by Neovius* are sho\vn in columns (2), (4) and (6). (Less exact loss
s
(OR X)
(a)
ta,v
(b)
fa'.v
ta,v
(c)
fa'.V
|A fa, f;
la, faafaa 134*35* J
Fig. 24 — Various high usage trunk group arrangements producing the same
total overflow a, v.
figures were given previously by Conny Palm^°. The agreement is seen
to be excellent for engineering needs for all values in the table.
Example 2: Suppose in Fig. 24(b) the random offered loads and paths
are as given in Table III; we desire the proportion of overflow and the
overflow load characteristics from an alternate route of 5 trunks.
Solution: The individual overflows ai , vi ; a^ , v-i ; and as , Vz are read
from Figs. 12 and 13 and recorded in columns (4) and (5) of the table.
The a and v columns are totalled to obtain the sum-overflow average A'
and variance V . The Equivalent Random load A which, if submitted to
S trunks would produce overflow A', V , is found from Fig. 26. Finally,
with A submitted io S -\- C trunks the characteristics a' and y', of the
load overflowing the C trunks are found. The numerical values obtained
* Artificial Traffic Trials Using Digital Computers, a paper presented by G.
Neovius at the First International Congress on the Application of the Theory of
Probability on Telephone Engineering and Administration, Copenhagen, June,
1955.
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 467
Table II^ — Calculation of Loss in a Simple Graded Multiple
g = 2, Xi = X2 = S, ai = a2 = a = 1 to 5, C = 1 to 3
T nafl Submitted to each
Proportion of Each Subgroup Load which Overflows
= a'/(.ai + ai)
Subgroup in Erlangs
a
C = 1
C = 2
C = 3
True
ER
True
ER
True
ER
(1)
1
2
3
5
5
(2)
0.01737
0.11548
0.24566
0.35935
0.44920
(3)
0.0175
0.115
0.246
0.363
0.445
(4)
0.00396
0.05630
0.16399
0.27705
0.37336
(5)
0.0045
0.057
0.163
0.279
0.370
(6)
0.00077
0.02438
0.10212
0.20535
0.30308
(7)
0.00088
0.024
0.103
0.210
0.305
for this example are shown in the lower section of Table III. As before,
of course, the "lost" calls are assumed cleared, and do not reappear in
the system.
Example 3: A load of 18 erlangs is offered through four groups of
10-point selector switches to twenty- two trunks which have been desig-
nated as "high usage" paths in an alternate route plan. Which of the
trunk arrangements shown in Fig. 27 is to be preferred, and to what
extent?
Solution: By successive applications of the Equivalent Random
method the overflow percentages for each of the three trunk arrange-
ments are determined. The results are shown in column 2 of Table IV.
The difference in percentage overflow between the three trunk plans is
small; however, plan 2 is slightly superior followed by plans 3 and 1 in
Table III — Calculation of Overflows from a Simple
Alternate Route Trunk Arrangement
Subgroup
Number
Offered Load in
Erlangs
a
Number of Trunks
X
Overflow Loads
a
V
1
2
3
3.5
5.7
6.0
15.2
3
6
9
1.41
1.39
0.45
3.25
1.98
2.40
0.85
5.23
Description of load offered to alternate route: A' = 3.25, V = 5.23.
]'"quivalent straight multiple: S = 5.8 trunks, A = 8.00 erlangs (from Fig. 26).
Overflow from C = 5 alternate route trunks (enter Figs. 12 and 13 with A =
8.0 and S + C = 10.8: a' = 0.72, v' = 1.48.
Proportion of load to commons which overflows = 0.72/3.25 = 0.22.
Proportion of offered load which overflows = 0.72/15.2 = 0.0475.
468
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
PROPORTION OVERFLOWING
N0.1 E.R THEORY NEOVIUS THROWDOWNS
f — ^- • • • •
—m- • . • .
A = 18 <^
l^ — •- • • • »
[ 1
BESK PUNCHED
1 CARDS
■ ■
»
-*- 0.123 0.118 0.114
NO. 2
A = 18 <
fr: : : 1 1 1
l~: : : n I
■
1
-^0.113 0.110 0.110
N0.3
f"*' ■ 1 1 n 1 1
-»-0.118 0.113 0.111
l::::imii
'
Fig. 27 — Comparison of losses on three graded arrangements of 22 trunks.
that order. The results of extensive simulations made by Neovius on the
three trunk plans are available for comparison.* The values so obtained
are seen to be very close to the ER theoretical ones ; moreover the same
order of preference among the three plans is indicated and with closely
similar loss differentials between them.
7.3.1. Throwdown Comparisons with Equivalent Random Theonj on
Simple Alternate Routing Arrangements with Lost Calls Cleared
Results of manuallj' run throwdowns on a considerable number of
non-symmetrical single-stage alternate route arrangements are available.
Some of these were shown in Fig. 20; they represent part of a projected
multi-alternate route layout (to be described later) for outgoing calls
from the local No. 1 crossbar Murray Hill-6 office in New York to all
other offices in the metropolitan area. The paths hunted over initially are
called direct trunks; they overflow calls to Office Selector Tandem (GST)
groups, numbered from 1 to 17, which are located in widely dispersed
central office buildings in the Greater New York area.
* Loc. cit.
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 469
Table IV — Loss Comparison of Graded Arrangements
Estimates of Percentage of Load Overflowing
Plan Number
ER Theory
Neovius Throwdowns
BESK Computer
(262144 calls)
Punched Cards
(10,000 calls)
(1)
1
2
3
(2)
12.3
11.3
11.8
(3)
11.81
10.98
11.25
(4)
11.4
11.0
11.1
Table V — Comparison of Theory and Throwdowns for the
Parameters of Loads Overflowing the Common Trunks
in Single-Stage Graded Multiples
OST (Alternate)
Route Group
No. of
Groups of
Total No.
of Trunks
Total Load Offered to
Direct Trunks
Total Overflow
Load from OST
Group
No. of
trunks
Direct
Trunks
in Direct
Groups
Erlangs
Approximate
No. of Calls
Theory
Throwdown
no.
(in 2.7 hours)
a'
v'
a'
v'
1
6
8
91
68.91
4950
2.00
5.50
2.36
6.52
2
3
3
45
37.49
2690
2.10
5.60
2.05
6.36
3
6
6
80
60.62
4355
1.50
4.00
1.30
5.67
4
3
6
52
38.49
2765
2.30
5.20
2.08
6.43
5
3
3
17
12.51
900
0.45
0.83
0.49
1.02
6
4
7
64
48.62
3490
2.50
5.90
2.36
4.88
7
8
12
78
57.42
4125
2.20
5.60
1.71
4.08
8
6
9
16
12.96
930
0.82
1.63
0.81
1.11
9
1
2
22
16.96
1220
1.30
2.60
1.02
1.73
10
5
6
10
9.52
685
0.78
1.40
1.05
2.07
11
8
13
16
16.43
1180
1.90
3.80
2.77
7.29
12
8
9
2
6.88
495
0.70
1.30
0.81
1.83
13
5
15
33
21.42
1540
1.75
3.30
1.16
2.01
14
2
7
11
8.05
580
1.46
2.20
1.63
2.14
15
9
15
8
11.97
860
1.60
3.25
1.55
4.12
16
11
22
34
27.46
1970
1.75
4.00
1.34
2.26
17
3
7
4
5.81
420
1.53
2.31
1.43
1.80
26.64
58.42
25.92
61.32
In Table V are given certain descriptive data for the 17 OST trunk
arrangements showing numbers of legs of direct trunks, total direct
trunks, the offered erlangs and calls, and the mean and variance of the
alternate routes' overfiovvs, as obtained by the ER theory and by
throwdowns.* The throwdown a' and v' values of the OST overflow
* Additional details of this simulation study are given in Section 7.4.
470
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
i.a
^O 0.2
EQUIVALENT
RANDOM THEORY
ERLANG THEORY-
1 2 3 4 5 6 7 8 9 10 It 12 13 14 15 16 17
ALTERNATE ROUTE (OST) NUMBER
Fig. 28 — Comparison of theoretical and throwdown overflows from a number
of first alternate routes.
were obtained by 36-second switch counts of those calls from each OST
group which had come to rest on subsequent alternate routes.
On Fig. 28 is shown a summary of the observed and calculated pro-
portions of "lost" to "offered" traffic at each OST alternate route group.
As may be seen from the figure and the last four columns of Table V,
the general agreement is quite good ; the individual group variations are
probably no more than to be expected in a simulation of this magnitude.
An assumption of randomness (which has sometimes been argued as
returning when several overflows are combined) for the load offered to
the OST's gives the Erlang Ei loss curve on Fig. 28. This, as was to be
expected, rather consistently understates the loss.
Since "switch-counts" were made on the calls overflowing each OST,
the distributions of these overflows may be compared with those esti-
mated by the Negative Binomial theory having the mean and variance
predicted abo\'e for the overflow. Fig. 29 shows the individual and cumu-
lative probability distributions of the overflow simultaneous calls from
the first two OST alternate routes. As will be seen, the agreement is
quite good even though this is traffic which has been twice "non-ran-
domized." Comparison of the observed and calculated overflow means
and variances in Table V indicates that similar agreement between
observed and theoretical fitting distributions for most of the other OST's
would be found.
7.3.2. Comparison of Equivalent Random Theory with Field Results on
Simple Alternate Routing Arrangements _
Data were made available to the author from certain measurements
made in 1941 by his colleague C. Clos on the automatic alternate routing
trunk arrangement in operation in the Murray Hill-2 central office in
New York. Mr. Clos observed for one busy hour the load carried on
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 471
several of its OST alternate rovite groups (similar to those shown in
Table V for the Murray Hill-6 office, but not identical) by means of an
electromechanical switch-counter having a six-second cycle. During
each hour's observation, numbers of calls offered and overflowing were
also recorded.
Although the loads offered to the corresponding direct trunks which
()^'erflowed to the OST group under observation were not simultaneously
measured, such measiu'ements had been made previously for several
hours so that the relative contribution from each direct group was
closely known. In this way the loads offered to each direct group which
produced the total arriving before each OST group could be estimated
with considerable assurance. From these direct group loads the character
(mean and variance) of the traffic offered to and overflowing the OST's
was predicted. The observed proportion of offered traffic which over-
flowed is shown on Fig. 30 along with the Equivalent Random theory
prediction. The general agreement is again seen to be fairly good al-
though with some tendency for the ER theory to predict higher than
observed losses in the lower loss ranges; perhaps the disparity on in-
(n)
0.5
0.4
0.3
0.2
0.1
0
OST N0.1
THEORY OBSD
AVG
VAR
2.00 2.36
5.50 6.52
RANDOM TRAFFIC
^--NEGATIVE BINOMIAL
-THROWDOWN
OST NO. 2
THEORY OBSD
AVG
VAR
2.10
5.60
2.05
6.36
>RAND0M TRAFFIC
THROWDOWN
-NEGATIVE BINOMIAL
10 15 0 5
n = NUMBER OF SIMULTANEOUS CALLS
15
p^n
-NEGATIVE BINOMIAL
-THROWDOWN
-NEGATIVE BINOMIAL
THROWDOWN
10 15 0 5
n = NUMBER OF SIMULTANEOUS CALLS
15
Fig. 29 — Distributions of loads overflowing from first alternate (OST) groups;
negative binomial theory versus throwdown observations.
472
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 195G
dividual OST groups is within the limits one might expect for data
based on single-hour observations and for which the magnitudes of the
direct group offered loads required some estimation. The assumption of
random traffic offered to the OST gives, as anticipated, loss predictions
(Erlang £"1) consistently below those observed.
More recently extensive field tests have been conducted on a working
toll automatic alternate route system at Newark, New Jersey. High
usage groups to seven distant large cities o\'erflowed calls to the New-
ark-Pittsburgh alternate (final) route. Data describing the high usage
groups and typical system busy hoiu- loads are given in Table ^T. (The
loads, of course, varied considerably from day to day.) The size of the
Pittsburgh route varied over the six weeks of the 1955 tests from 64 to
71 trunks. Altogether the system comprised some 255 intertoll trunks.
Observations were made at the Newark end of the groups by means
of a Traffic Usage Recorder — making switch counts every 100 seconds
— and by peg count and o^'erflow registers. Register readings were photo-
graphically recorded by half-hourly, or more frequent, intervals. To
^-
<a
uz
^^
zz
05
1-0
(T-l
°^
1.0
0.5
0.2
2 0.1
0.05
0.02
0.01
-
-
-
Z'
-
^,^!^ 1^ f^-^^
U^ — - "^
Jft
NON-RANDOM (ER) //''
THEORY "^xX /'
y^ Jrf -OBSERVED
X ^-i^sM '
_
X ^____— --sss:^*^^'^^^ /
-
/j^ ' ^^ ^'^-RANDOM THEORY
^ 1 yJ
1
/
J
^
•
•
11
(\j
—
^
ro
tn
n
—
—
^
d
0
0
d
d
0
0
0
0
TANDEM
z
Z
Z
z
z
z
Z
Z
Z
OFFICE
0
<£>
r^
t:
0
0
ro
0
CI
(^
m
O)
ro
Q
Q
n
LU
UJ
UJ
LU
LU
CD
LU
(D
03
NO. TRUNKS
13
12
8
7
3
8
3
4
3
OFFERED JavG
7.55
7.19
5.22
3.81
2.06
7.79
2.36
4.09
2.4
LOAD |vAR 13.58 15.66 6.59 7.30 2.51 18.54 2.77 4.59 5.90
Fig. 30 — -Observed tandem ovciflow.s in nlicriKilc
llill-2 (New York) 1940-1941.
loulc study at Murray
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 473
Table VI — High Usage Groups and Typical System
Busy Hour Loads
High Usage Group,
Newark to:
Length of Direct Route
(Air Miles)
Nominal Size of Group
(Number of Trunks)
Typical Offered Load
(erlangs)
Baltimore
170
560
395
1375
470
1100
1170
18
42
27
33
37
26
5
19
Cincinnati
Cleveland
Dallas
Detroit
Kansas City
New Orleans
43
26
34
36
23
4
compare theory with the observed overflow from the final route, esti-
mates of the offered load A' and its ^-ariance V are required. In the
present case, the total load offered to the final route in each hour was
estimated as
A' = Average of Offered Load
Peg Count of Calls Offered
to Pittsburgh Group
(Peg Count of Offered Calls)
— (Peg Count of Overflow Calls)
X Average Load Carried
by Pittsburgh Group
The variance V of the total load offered to the final route was estimated
for each hour as
V' = Variance of Offered Load
7 7
= A' — 2 «i + 2 Vi
i=l
where «» and Vi are, respectively, the average and variance of the load
overflowing from the tth high usage group. (The expression. A' —
7
^ «i , is an estimate of the average — and, therefore of the variance
1=1
— of the first-routed traffic offered directly to the final route. Thus the
total variance, V, is taken as the sum of the direct and overflow com-
ponents.) Using A', V and the actual number, C, of final route trunks in
service, the proportion of offered calls expected to overfloAv was calcu-
lated for the traffic and trunk conditions seen for 25 system busy hours
from February 17 to April 1, 1955 on the Pittsburgh route. The results
are displayed on Fig. 31, where certain traffic data on each hour are
given in the lower part of the figure. The hours are ordered — for con-
venience in plotting and viewing — by ascending proportions of calls
overflowing the group; observed results are shown by the double line
474 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
0.001
3 5 7 9 11 13 15 17 19 21 23 25
NO. P'BGH TRKS 71 70 65 71 65 71 65 69 64 64 70 65 64 71 68 65 64 65 64 70 65 65 65 65 65
HOURS BY AMT.
OF OBS'D loss
EST'd LOAD fAVG. 50 54 55 56 55 63 55 58 54 54 68 60 63 74 76 74 76 83 91 102 109105 101 115124
OFFERED War. 82 95 85 89 98 101 84 98 97 89110 10588125 121140114 141 175182 170 176 179 199197
Fig. 31 — Final route (Newark-Pittsburgh) overflows in 1955 toll alternate^
route study. I
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 475
curve. The superposed single line is the corresponding estimate by EE,
theory of the hour-to-hour call losses. As may be seen, theory and ob-
servation are in good agreement both point by point and on the average
over the range of losses from 0.01 to 0.50. The dashed line shows the
prediction of final route loss for each hour on the assumption that the
offered traffic A' was random. Such an assumption gives consistently low
estimates of the existing true loss.
As of interest, a series of heavy dots is included on Fig. 31. These are
the result of calculating the Poisson Summation, P{C,L), where L is the
average load carried on, rather than offered to, the C trunks. It is inter-
esting that just as in earlier studies in this paper on straight groups of
intertoll trunks (for example as seen on Fig. 7), the Poisson Summation
with load carried taken as the load offered parameter, gives loss values
surprisingly close to those observed. Also, as before, this summation has
a tendency to give too-great losses at light loadings of a group and too-
small losses at the heavier loadings.
; 7.4 Prediction of Traffic Passing Through a Midti-Stage Alternate Route
Network
I In the contemplated American automatic toll switching plan, wide
I advantage is expected to be taken of the efficiency gains available in
i multi-alternate routing. Thus any procedure for traffic analysis and
prediction needs to be adaptable for the . more complex multi-stage
arrangements as well as the simpler single-stage ones so far examined.
Extension of the Equivalent Random theory to successive overflows is
easily done since the characterizing parameters, average and variance,
of the load overflowing a group of paths are ahvays available.
Since few cases of more than single-stage automatic alternate routing
are yet in operation in the American toll plant, it is not readily possible
to check an extension of the theoiy with actual field data. Moreover col-
lecting and analyzing observations on a large operating multi-alternate
route system would be a comparatively formidable experiment.
However, in New York city's local interoffice trunking there is a very
considerable development of multi-alternate routing made possible by
the flexibility of the marker arrangements in the No. 1 crossbar switching
system. None of these overflow arrangements has been observed as a
whole, simultaneously and in detail. The Murray Hill-2 data in OST
groups reviewed in Section 7.3.2 were among the partial studies which
have been made.
In connection with studies made just prior to World War II on these
476 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
Table VII — Sum of Direct Group Overflow Loads,
Offered to OST's
Average.
Variance
Theory
86.06
129.5
Observed
87.12
127.4
local multi -alternate route systems, a throwdown was made in 1941 on a
proposed trunk plan for the Murray Hill-6 office. The arrangement of :
trunks is shown on Fig. 32. Three successive alternate routes, Office
Selector Tandems (OST), Crossbar Tandem (XBT), and Suburban:
Tandem (ST), are available to the large majority of the 123 direct trunk
groups leading outward to 169 distant offices. (The remaining 46 parcels
of traffic did not have direct trunks to distant offices but, as indicated
on the diagram, offered their loads directly to a tandem group.) A total
of 726 trunks is involved, carrying 475 erlangs of traffic.
A throwdown of 34,001 offered calls corresponding to 2.7 hours of
traffic was run. Calls had approximate exponential holding times, averag-
ing 135 seconds. Records were kept of numbers of calls and the load from
the traffic parcels offered to each direct group, as they were carried or
passed beyond the groups of paths to which they had access. Loads car-
ried by each trunk in the system were also observed by means of a 36-
second "switch-count." (The results on the 17 OST groups reported in
Section 7.3.1 were part of this study.)
Comparisons of observation and theory which are of interest include
the combined loads to and overflowing the 17 OST's. Observed versus
calculated parameters (starting with theory from the original direct
group submitted loads) are given in Table VII. The agreement is seen
to be very good.
The corresponding comparison of total load from all the OST's is
given in Table VIII. Again the agreement is highly satisfactory.
Not all of the overflow from the OST's was offered to the 22 crossbar
tandem trunks; for economic reasons certain parcels by-passed XBT andf
were sent directly to Suburban Tandem.* This posed the problem of
breaking off certain portions of the overflow from the OST's, to be added"'
again to the overflow from XBT. An estimate was needed of the contri
bution made by each parcel of direct group traffic to any OST's over
flow. These were taken as proportional to the loads offered the OST by
each direct group (this assumes that each parcel suffers the same over-
* In the toll alternate route system by -passing of this sort will not occur.
Tt
U'lnntuunu u L
\'^\\\\\\\'' \va
p^^^^^
\\nii\^
S
m
T^
m:
Tr±
7 J '''.': ; ,
±±±
^PP
tf+Ff-
4^
:«
tn
^
'/V//'/-'//./'/''///;^:
fl
NO. 16
NO. 17
SPECIAL
TANDEM
tt inttttiiittttMitiftt ttinit tit t tttttttttt ttttt
(V OJ ^O ^^»*^u-^^OsO r- u-^Ty fv^ O OJ fVOJ O^ rNvO TO-* -t OJ C^ V\vO (V-*fV<HrH OI^C^ »H -tTOTO _*(^-*«) -*CJtO <-ITOnO C*- -*
^O r^ O -* J- -*rj r^ -j-joj rj rH O OO 0«> C^OiJ^<*\<*\fH TO^OC^OJU^r^ ^ -^ i/n f^ OtO to r^*rfc"~'-*r^r^rsi CT^^OJi-tiH
OO -* r^ i-H ^ O rH ^ rH.-H .-H rH rH rHrH O O O OO O O O rH (-1 ^ O O O O r^rH O O OOOOOOOOOO OOOOO
27.46 5.81 5.44 0.31 5.99 1.96
tOvO -JvO rH fV f'^0^_JO>JD O^ r^rH (Vr- ifNvO »A(NJryNO -*fV (NiTO Of^Of^O^ -* ^ ^ -* (N* ONf^ "^tO C^ t*^C^ <^ *'^ C^CM^^TO
>-i t£) E-« cr: tn CO ,_j ti3 < <i<i: tH w kJ »Jo- J i-H w hJ> a. i*; M <ow»H'J<-< mo:-* > M<fHO-<>JM*s<:w mmooo
crossbar office.
FINAL ,0
TANDEM
TRUNKS
5
INTERMEDIATE
TANDEM
TRUNKS 10
FIRST
ALTERNATE 5 ■
nUTE(OST)
TRUNKS
SUBURBAN TANDEM
N0.1 N0.2 N0.3 N0.4 N0.5 N0.6
NO. 7
N0.8 N0.9 NO.IO
N0.11
N0.12
N0.I3
N0.14
DIRECT
INTEROFFICE
TRUNKS
15 r.
10rzE
5:E:
1 ---
m ill ]M \M\ Vw timii ttimlmtt tiitifti! ti flmi tttitttttiiit tttitttft tmmmntti tiiittt tmiitittittit tmtmitmitmtni imttt tii i ititnttit ftitt
Y I k.ni.L' IMnu ■-! fv IV iH r>j >0 J t^ i-t^.H p^tov>r^s>r^ O (v rt o (N to mr^pj O cvj ^ -tto ''^-4 O rsi tT>C'tJ't~-t^C^NO&''">-i -* (m lAi-i r\ O O- r~ f^ 'O
[ERLAN6S) f|JOOO£>r-t^O 'OcvtJ. rHC'O'OO-Ov i^-0~0,0'0 J ■/■OO Ot^fv-^Cr'ovrH O<0 t^i-^f^r^rufOcjpHu^ pJc-j^^^^^OcJ (>
68.91 37.49 60.62 38.49 12.51 48.62
57.42
DESTINATION *Cr^-*t^r>^,^ r.^>r
OFFICES S£S253S£ gS?
~-»f«Ot- Jr"
mff-tO toO^iT
^rHrHO rH p- ^ -i f-i rt -J r4 -^ ,H ^d O -4 rH r4 O O O O O O «/^ (V cJ .-* O O O -- r+^ f"* O OO O (VrHodcHO ^ddOrHOOOOOOOOOO
12.96 16.96 9.52 16.43 6.88 21.42 8.05 11.97 27.46 5.81 5.44 0.31 5.99 1.
T Q Ita. tfc< C3 O Z OW < f)
Fig. 32. — Multi-alternate route trunking arrangcinenl at Murray Hill — 6 (New York) local No. 1 crossbar office.
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A.
477
flow probability). The variance of this overflow portion by-passing XBT
was estimated by assigning to it the same variance-to-average ratio as
was found for the total load overflowing the OST. Subtracting the means
and variances so estimated for all items by-passing XBT, left an approxi-
mate load for XBT from each OST. Combining these corrected overflows
gave mean and variance values for offered load to XBT, Observed values
Table VIII -
-Sum of Loads Overflowing OST's
Theory
Observed
Avftraere
26.64
58.42
25.92
Variance
61.32
Table IX — Load Offered to Crossbar Tandem
I Average.
Variance
Theory
25.18
47.67
Observed
25.51
56.10
0.10 r
-RANDOM TRAFFIC
-THROWDOWN
,--NEGATIVE BINOMIAL
to 20 30 40 50
n = NUMBER OF SIMULTANEOUS CALLS
P^n
THEORY
OBSD
1.0
I — - — -^
.^^^ ( )
( )
^X AVG 25.18
25.51
0.8
^V VAR 47.67
56.10
0.6
VS.
0.4
0.2
0
,
,
10 20 30 40 50
n = NUMBER OF SIMULTANEOUS CALLS
Fig. 33 — Distribution of load offered to crossbar tandem trunks; negative bi-
nomial theory versus throwdown observations.
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 477
flow probability). The variance of this overflow portion by-passing XBT
was estimated by assigning to it the same variance-to-average ratio as
was found for the total load overflowing the OST. Subtracting the means
' and variances so estimated for all items by-passing XBT, left an approxi-
mate load for XBT from each OST. Combining these corrected overflows
gave mean and variance values for offered load to XBT, Observed values
Table VIII -
- Sum OF Loa
Ds Overflowing OST's
Theory
Observed
Average
Variance
26.64
58.42
25.92
61.32
Table IX
. — Load Offered to Crossbar Tandem
Theory
Observed
Average
25.18
47.67
25.51
Variance
56.10
0.10 r
^-.--RANDOM TRAFFIC
-THROWDOWN
--NEGATIVE BINOMIAL
10 20 30 40 50
n = NUMBER OF SIMULTANEOUS CALLS
THEORY OBSD
( ) ( )
AVG 25.18 25.51
VAR 47.67 56.10
Pin
10 20 30 40 50
n = NUMBER OF SIMULTANEOUS CALLS
Fig. 33 — Distribution of load offered to crossbar tandem trunks; negative bi-
nomial theory versus throwdown observations.
478 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
Table X — Load Overflowing Crossbar Tandem
Average.
Variance ,
Observed
6.47
33.48
and those calculated (in the above manner) are given in Table IX.
Fig. 33 shows the distribution of XBT offered loads, observed and calcu-
lated. The agreement is very satisfactory. The random traffic (Poisson)
distribution, is of course, considerably too narrow.
In a manner exactly similar to previous cases, the Ecjuivalent Random
load method was applied to the XBT group to obtain estimated param-
eters of the traffic overflowing. Comparison of observation and theory
at this point is given in Table X.
Fig. 34 shows the corresponding observed and calculated distributions
0.15
0.10
f(n)
0.05
)RANDOM TRAFFIC
THEORY OBSD
AVG 6.55 6.47
VAR 23.80 33.48
^'NEGATIVE BINOMIAL
0 5 10 15 20 25 30 35
n=NUMBER OF SIMULTANEOUS CALLS
P^n
_^^RANDOM TRAFFIC
--NEGATIVE BINOMIAL
THROWDOWN
0 5 10 15 20 25 30 35
n = NUMBER OF SIMULTANEOUS CALLS
Fig. 34 — Distribution of calls from crossbar tandem trunks; negative binomial
theory versus throwdown observations.
!
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A.
479
of siniiiltaneoiis calls. The agreement again is reasonably good, in spite
of the considerable disparity in variances.
The overflow from XBT and the load which by-passed it, as well as
some other miscellaneous parcels of traffic, were now combined for final
offer to the Suburban Tandem group of 17 trunks. The comparison of
parameters here is again available in Table XI. On Fig. 35 are shown
the observed and calculated distributions of simultaneous calls for the
load offered to the ST trunks. The agreement is once again seen to be
very satisfactory.
We now estimate the loss from the ST trunks for comparison with the
actual 'proportion of calls which failed to find an idle path, and finally
Table XI — Load Offered to Suburban Tandem
Average. .
Variance .
Theory
15.38
42.06
Observed
14.52
48.53
THEORY OBSD
f(n)
P^n
10 20 30 40
n = NUMBER OF SIMULTANEOUS CALLS
I.O
^ ^
\
0.8
"
^
, --NEGATIVE
BINOMIAL
0.6
V ^-THROWDOWN
\ \
0.4
0.2
x^^^
0
1
" -r-^
10 20 30 40
n^NUMBER OF SIMULTANEOUS CALLS
50
Fig. 35 — Distribution of load offered to suburban tandem trunks; negative
linomial theory versus throwdown observations.
480
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
Table XII -
— Grade of Service on ST Group
Theory
Obser-
vation
Observation
Load submitted (erlangs)
Load overflowing (er-
langs)
Proportion load over-
flowing
15.38
3.20
0.209
14.52
2.63
0.181
Number of calls sub-
mitted 1057
Number of calls over-
flowing 200
Proportion of calls over-
flowing 0.189
Table XIII — Grade of Service on the System
Total load submitted
Total load overflowing
Proportion of load not served
Theory
Observed
475 erlangs
3.20 erlangs
0.00674
34,001 calls
200 calls
0.00588
compare the proportions of all traffic offered the system which failed to
find a trunk immediately. See Tables XII and XIII.
After these several and varied combinations of offered and overflowed
loads to a system of one direct and three alternate routes it is seen that 'i
the final prediction of amount of load finally lost beyond the ST trunks
is gratifyingly close to that actually observed in the throwdown. The
prediction of the system grade of service is, of course, correspondingly
good.
It is interesting in this connection to examine also the proportions I
overflowing the ST group when summarized by parcels contributed from
the several OST groups. The individual losses are shown on Fig. 36; they
appear well in line with the variation one would expect from group to
group with the moderate numbers of calls which progressed this far
through the multiple.
0.4
0.3
octr
o^ 0.2
So
a ^0.1
,-THEORY =0.21
._>.
• •
--AVG OBSD = 0.19
12 4 6 8 10 12 14 16 18 20
OST GROUP NUMBER
Fig. 36 — Overflow calls on third alternate (ST) route.
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A.
481
7.4.1 Correlation of Loss with Peakedness of Components of Non-Ran-
dom Offered Traffic
Common sense suggests that if several non-random parcels of traffic
are combined, and their joint proportion of overflow from a trunk group
is P, the parcels which contain the more peaked traffic should experience
overflow proportions larger than P, and the smoother traffic an overflow
proportion smaller than P. It is by no means clear however, a priori, the
extent to which this would occur. One might conjecture that if any one
parcel's contribution to the total combined load is small, its loss would
be caused principally by the aggregate of calls from the other parcels,
and consequently its own loss would be at about the general average loss
P, and hence not very much determined by its own peakedness. The
Murray Hill-6 throwdowai results may be examined in this respect. The
mean and variance of each OST-parcel of traffic, for example, arriving
at the final ST route was recorded, together with, as noted before, its
own proportion of overflow from the ST trunks. The variance/mean over-
dispersion ratio, used as a measure of peakedness, is plotted for each
parcel of traffic against its proportion of loss on Fig. 37. There is an un-
doubted, but only moderate, increase in proportion of overflow with
increased peakedness in the offered loads.
It is quite possible, however, that by recognizing the differences be-
tween the service given various parcels of traffic, significant savings in
final route trunks can be effected for certain combinations of loads and
trunking arrangements. Of particular interest is the service given to a
parcel of random traffic offered directly to the final route when compared
04
o
oc_l 0.3
UJUJ
>u
°%
°ia2|-
zo
o<
OO0.1
o
a.
• • •
0.5 1.0 1.5 2.0 2.5 3.0 3.5
V/a OF EACH OST PARCEL REACHING ST TRUNKS
Fig. 37 — Effect of peakedness on overflow of a parcel of traffic reaching an
ilternate route.
482 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
with that received by non-random parcels overflowing to it from high
usage groups.
7.5 Expected Loss on First Routed Traffic Offered to Final Route
The congestion experienced by the first-routed traffic offered to the
final group in a complex alternate route arrangement [such as the right
hand parcels in Figs. 10(c) and (d)] \vill be the same as encountered in a
series of random tests of the final route by an independent observer,
that is, it will be the proportion of time that all of the final trunks are
busy. As noted before, the distribution of simultaneous calls n (and hence
the congestion) on the C final trunks produced by some specific arrange-
ment of offered load and high usage trunks can be closely simulated by
that due to a single Equivalent Random load offered to a straight group
of aS -f C trunks. Then the proportion of time that the C trunks are
busy in such an equivalent system provides an estimate of the corres-
ponding time in the real system ; and this proportion should be approxi-
mately the desired grade of service given the first routed traffic.
Brockmeyer has given an expression (his equation 36) for the pro-
portion of time, Rx , in a simple S -\- C system with random offer A,
and "lost calls cleared," that all C trunks are busy, independent of the
condition of the *S-trunks:
R, = f{S,C,A)
= Ii,x,s+cKA) — —
where
m=o \ m / (S — m
However, (rdS) is usually calculated more readily step-by-step using
the formula
<Tc{S) = aciS - 1) -f CTc-liS) ,
starting with
crc(O) = 1 and ao(S) = A^Sl
The average load carried on the C paths is clearly
Lc = A[Ei,sU) - Ei,s+c{A)], (31)
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 483
and the variance of the carried load can be shown to be*
Vc = ALc ^ - ACEx,s+c{A) + Lc- L\ (32)
On Fig. 38, Ri values are shown in solid line curves for several com-
binations of A and C over a small range of S trunks. The corresponding
losses Ri for all traffic offered the final group, where R^ = oc'/A', are
shown as broken curves on the same figure. The R2 values are always
above Ri , agreeing with the common sense conclusion that a random
component of traffic will receive better service than more peaked non-
random components.
However, there are evidently considerable areas where the loss differ-
ence between the two Z^'s will not be large. In the loss range of principal
interest, 0.01 to 0.10, there is less proportionate difference between the
R's, as the A = C paired values increase on Fig. 38. For example, at
/?2 = 0.05, and A = C = 10, R./Ri = 0.050/0.034 = 1.47; while for
A = C = 30, i?2/Ri = 0.050/0.044 = 1.13. Similarly for A = 2C, the
R2/R1 ratios are given in Table XIV. Again the rapid decrease in the
R2/R1 ratio is notable as A and C increase.
F. I. Tange of the Swedish Telephone Administration has performed
elaborate simulation studies on a variety of semi-symmetrical alternate
route arrangements, to test the disparity between the Ri and R2 types
of losses on the final route. f For example if g high-usage groups of 8
paths each, jointly overflow 2.0 erlangs to a final route which also serves
2.0 erlangs of first routed traffic, Tange found the differences in losses
between the two 2-erlang parcels, i?high usage (h.u.) —Ri, shown in
column 9 of Table XV. The corresponding ER calculations are performed
in columns 2 to 8, the last of which is comparable with the throwdown
\alues of column 9. The agreement is not unreasonable considering the
sensitiveness of determining the difference between two small prob-
abilities of loss. A quite similar agreement was found for a variety of
other loads and trunk arrangements.
* In terms of the first two factorial moments of n : Vc is given by
Vc = M(2) + M(i) - M(i)*, where Mw = Lc
(leneral expressions Mu) for the factorial moments of n are derived in an unpub-
lished memorandum by J. Riordan.
t Optimal Use of Both-Way Circuits in Cases of Unlimited Availability, a
paper by F. I. T&nge, presented at the First International Congress on the Appli-
cation of the Theory of Probability in Telephone Engineering and Administration,
June 1955, Copenhagen.
484 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
D
O
a.
_(
0.1
<
z
0.09
0.08
II
z
o
0.07
0.06
U1
in
0.05
o
_i
0.04
II
o
7-
0.03
O
(-
a.
o
0.02
n
o
a
a.
ru
a.
0.01
a
0.009
z
0.008
<
0.007
cr
0.006
0.005
0.004
0.003
0.002
0.001
^•>_^
^^
;-.^
V
'*^^>v
•^
'N^
Y^x.
X
\
V
vv
\ \
\ \
\ \
\ \
A = 30
C = 15
s
\s\^
\
.' ^
\\v
\
n, -^ ^
f- \
>■
\
\
\ \
"S^ \
V
\ \
\ \
\
[a
\ ""')
\ \
\
^
\X' ^"'
o\
\ \
\ \
\
\ A?T
iO \
\ \
\ \
R, \'C-.
\ \
I A = 20^
rc = io^^
V \
\ \
\ \
\
\
\ \
\ \ \
\
\
\ \ \
\
\
\
\ ^ \
\
\
\
\
\
\
\
' \^
\
\
\
\
\
A \
\
V
A = 10,^
C = io \
\
\
\
\
10
15
20 25
S = *equivalent"number of paths
30
35
Fig. 38 — Comparison of Ri and R2 losses under various load and trunk con-
ditions.
Table XIV— The R2/R1 Ratios for A = 2C
A
C
Ri/Ri when R2 = 0.05
10
20
30
5
10
15
10.6
3.25
2.44
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A.
485
Table XV — Comparison of E.R. Theory and Throwdowns on
Disparity of Loss Between High Usage Overflow and
Random Offer to a Final Group
(8 trunks in each high usage group; 9 final trunks serving 2.0 erlangs
high usage overflow and 2.0 erlangs first routed traffic.)
Number of
Groups of
8 High Usage
Trunks
ER Theory {A' = 4.0)
Tange
V
A
5
R2=a7A'
i?i
Rh.u, ~
2R-L- Ri
Rh.u.—Rl=
2{R2 - Ry)
Throwdown
Rh.u. - Ri
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
1
5.77
7.51
4.17
0.0375
0.0251
0.0499
0.0248
0.0180
2
5.80
7.50
4.25
0.0383
0.0255
0.0511
0.0256
0.0247
3
5.74
7.44
4.08
0.0369
0.0248
0.0490
0.0242
0.0286
4
5.68
7.30
3.91
0.0362
0.0247
0.0477
0.0230
0.0276
5
5.64
7.20
3.80
0.0355
0.0242
0.0468
0.0226
0.0245
6
5.58
7.06
3.64
0.0350
0.0240
0.0460
0.0220
0.0221
7
5.55
7.00
3.56
0.0345
0.0238
0.0452
0.0204
0.0202
8
5.51
6.91
3.45
0.0335
0.0236
0.0434
0.0198
0.0188
9
5.47
6.81
3.34
0.0325
0.0231
0.0419
0.0188
0.0177
10
5.45
6.76
3.29
0.0312
0.0225
0.0399
0.0174
0.0166
Limited data are available showing the disparity of Ri and Ro in
actual operation in a range of load and trunk values well beyond those
for which Ri values have been calculated. Special peg count and over-
flow registers were installed for a time on the final route during the 1955
Newark alternate route tests. These gave separate readings for the calls
from high usage groups, and for the first routed Newark to Pittsburgh
calls. Comparative losses for 17 hours of operation over a wide range of
loadings are shown on Fig. 39. The numbers at each pair of points give
the per cent of final route offered traffic which was first routed (random).
In general, approximately equal amounts of the two types of traffic were
offered.
In 6 of the hours almost identical loss ratios were observed, in 7 hours
the overflow-from-high-usage calls showed higher losses, and in 4 hours
lower losses, than the corresponding first routed calls. The non-random
calls clearly enjoyed practically as good service as the random calls. This
result is not in disagreement with what one might expect from theory.
To compare directly with the Newark-Pittsburgh case we should need
curves on Fig. 38 expanded to correspond to A', V values of (50, 85)
to (120, 200). Examining the mid-range case of C = 65, A' = 70, V =
120, we find A = 123, >S = 54. Here A is approximately 2C; extrapolat-
ing the A = 2C curves of Fig. 38 to these much higher values of A and C
suggests that R2/R1 w^ould be but little different from unity.
486 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
It is clear from the above theory, throwdowns, and actual observa-
tion that there are certain areas where the service differences given first
routed and high usage trunk overflow parcels of traffic are significant.
In Section 8, where practical engineering methods are discussed, curves
are presented which permit recognition of this fact in the determination
of final trunk requirements.
7.6 Load on Each Trunk, Particularly the Last Trunk, in a Non-Slipped
Alternate Route
In the engineering of alternate route systems it is necessary to deter-
mine the point at which to limit a high usage group of trunks and send
the overflow traffic via an alternate route. This is an economic problem
whose solution requires an estimate of the load which will be carried on
1.0
0.5
z
o
il' 0.05
a.
UJ
>
o
z
o
I-
cc
o
a.
O
a.
a- O.OiO
0.005
0.00)0
6 64
56 8'
57
61(
OL 65^ 69,
40
56
o
50
,58
41
58
69
8
64
52
s
38
6
66
49
8
52
O FIRST ROUTED TRAFFIC (NUMBERS INDICATE PER
CENT OF TOTAL WHICH IS FIRST ROUTED)
• OVERFLOW TRAFFIC FROM 7 HIGH USAGE GROUPS
60 70 80 90 100 110 120
A'= ESTIMATED OFFERED LOAD TO PITTSBURGH IN ERLANGS (INCLUDING RETRIALS)
Fig. 39 — Comparison of losses on final route (Newark to Pittsburgh) for high
usage overflow and first routed traffic.
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 487
the last trunk of a straight high usage group of any specified size, carry-
ing either first or higher choice traffic or a mixture thereof.*
The Equivalent Random theory readily supplies estimates of the loads
carried by any trunk in an alternate routing network. After having found
the Equivalent Random load A offered to *S + C trunks which corresponds
to the given parameters of the traffic offered to the C trunks, it is a simple
matter to calculate the expected load i on any one of the C trunks if
they are not slipped or reversed. The load on the ith trunk in a simple
straight multiple (or the S + jth. in a divided multiple of *S lower and C
upper trunks), is
A- = Is+j = A[E^,s+j-M) - Ex,s+j{A)] (33)
where Ei,n(A) is the Erlang loss formula. A moderate range of values of
■Ci versus load A is given on Figure 40. f
Using this method, selected comparisons of theoretical versus observed
loads carried on particular trunks at various points in the Murray-
Hill-6 throwdown are shown in Fig. 41 ; these include the loads on each
of the trunks of the first two OST groups of Fig. 32, and on the second
and third alternate routes, crossbar and suburban tandem, respectively.
The agreement is seen to be fairly good, although at the tail end of the
latter two groups the observed values drop aw^ay somewhat from the
theoretical ones. There seems no explanation for this beyond the possi-
bility that the throwdown load samples here are becoming small and
might by chance have deviated this far from the true values (or the
arbitrary breakdown of OST overflows into parcels offered to and by-
passing XBT may well have introduced errors of sufficient amount to
account for this disparity). As is well known, (33) gives good estimates
of the loads carried by each trunk in a high usage group to which random
(Poisson) traffic is offered; this relationship has long been used for the
purpose in Bell System trunk engineering.
8. PRACTICAL METHODS FOR ALTERNATE ROUTE ENGINEERING
To reduce to practical use the theory so far presented for analysis of
alternate route systems, working curves are needed incorporating the
* The proper selection point will be where the circuit annual charge per erlang
of traffic carried on the last trunk, is just equal to the annual charge per erlang
of traffic carried by the longer (usually) alternate route enlarged to handle the
overflow traffic.
t A comprehensive table of /< is given by A. Jensen as Table IV in his book
"Moe's Principle," Copenhagen, 1950; coverage is for / ^ 0.001 erlang, z = 1(1)140;
A = 0.1(0.1)10, 10(1)50, 50(4)100. Note that n + 1, in Jensen's notation, equals i
here.
488 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
6
<0
6
ID
6 6 6
soNvibB Ni viNnai Hi-n 3hi no agiaavD avon
= '-Tf
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A.
489
pertinent load-loss relationships. The methods so far discussed, and
proposed for use, will be briefly reviewed.
The dimensioning of each high usage group of trunks is expected to be
performed in the manner currently in use, as described in Section 7.6.
The critical figure in this method is the load carried on the last high
usage trunk, and is chosen so as to yield an economic division of the
offered load between high usage and alternate route trunks. Fig. 40 is
one form of load-on-each-trunk presentation suitable for choosing eco-
nomic high usage group size once the permitted load on the last trunk
is established.
The character (average a and variance v) of the traffic overflowing
each high usage group is easily found from Figs. 12 and 13 (or equivalent
- OST GROUP NO. 2
1.U
OST GROUP NO.l
0.5
-
^
0
4 5 6
TRUNK NUMBER
CROSSBAR TANDEM GROUP
Z 0
O
2 4
6 8 10 12 14 16 18 20 22
TRUNK NUMBER
SUBURBAN TANDEM GROUP
12 4 6 8 10 12 14 16
TRUNK NUMBER
Fig. 41 — Comparison of load carried by each alternate route trunk; theory
versus throwdowns.
490
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
tables). The respective sums of the overflow a's and v^s, give A' and V
by (28) and (29); they provide the necessary statistical description of
traffic offered to the alternate route.
According to the Equivalent Random method for estimating the alter-
nate route trunks required to provide a specified grade of service to the
overflow traffic A', one next determines a random load A which when
submitted to S trunks will yield an overflow with the same character
{A', V) as that derived from the complex system's high usage groups.
An alternate route of C trunks beyond these S trunks is then imagined.
The erlang overflow a', with random offer A, to S + C trunks is found
from standard i^i-formula tables or curves (such as Fig. 12).
The ratio R2 = a! I A' is a first estimate of the grade of service given to
each parcel of traffic offered to the alternate route. As discussed in Sec-
tion 7.5, this service estimate, under certain conditions of load and
trunk arrangement, may be significantly pessimistic when applied to a
first routed parcel of traffic offered directly to the alternate route. An
improved estimate of the overflow probability for such first routed
traffic was found to be R\ as given by (30).
8,1 Determination of Final Group Size with First Routed Traffic Offered
Directly to the Final Group
When first routed traffic is offered directly to the final group, its
service Ri will nearly always be poorer than the overall service given to
those other traffic parcels enjoying high usage groups. The first routed
traffic's service will then be controlling in determining the final group
size. Since Ri is a function of *S, C and A in the Equivalent Random
solution (30), and there is a one-to-one correspondence of pairs of A and
S values with A' and V values, engineering charts can be constructed at
selected service levels Ri which shoAv the final route trunks C required,
for any given values of A' and V. Figs. 42 to 45 show this relation at
service levels of Ri = 0.01, 0.03, 0.05 and 0.10, respectively.*
* On Fig. 42 (and also Figs. 46-49) the low numbered curves assume, atjfirst
sight, surprising shapes, indicating that a load with given average and variance
would require fewer trunks if the average were increased. This arises from the
sensitivity of the tails of the distribution of offered calls, to the V'/A' peaked-
ness ratio which, of course, decreases with increases in A'. For example, with C
= 4 trunks and fixed V = 0.52, the loss rapidly decreases with increasing A':
A'
V'/A'
A
S
a'
a' /A'
0.28
0.33
0.40
0.52
1.86
1.58
1.30
1.00
6.1
3.0
1.42
0.52
10.
5.0
2.03
0
0.0155
0.0081
0.0036
0.0008
0.055
0.025
0.009
0.002
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 491
These four Ri levels would appear to cover the most used engineering
range. For example, if the traffic offered to the final route (including the
first routed traffic) has parameters A' = 12 and V ^ 20, reading on
Fig. 43 indicates that to give P = 0.03 "lost calls cleared" service to
the first routed traffic, C = 19 final route trunks should be provided.
(For random traffic (F' = A' = 12), 17.8 trunks would be required.)
Other charts, of course, might be constructed from which Ri could be
read for specific values of A', V and C. They would become voluminous,
however, if a wide range of all three variables were required.
8.2 Provision of Trunks Individual to First Routed Traffic to Equalize
Service
If the difference between the service Ri given the first routed parcel of
traffic and the service given all of the other parcels, is material, it may be
desirable to take measures to diminish these inequities. This may readily
be accomplished by setting aside a number of the otherwise full access
final route trunks, for exclusive and first choice use of the first routed
traffic. High usage groups are now provided for all parcels of traffic. The
alternate route then services their combined overflow. The overall grade
of service given the ith. parcel of offered traffic in a single stage alter-
nate route system will then be approximately
'*
Pi = Ei,Xi{ai)R2 = EiXiia.)^, (34)
Thus the service will tend to be uniform among the offered parcels when
all send substantially identical proportions of their offered loads to the
alternate route. And the natural provision of "individual" trunks for the
exclusive use of the first routed traffic would be such that the same pro-
portion should overflow as occurs in the associated high \isage groups.
This procedure cannot be followed literally since high usage group
size is fixed b}^ economic considerations rather than any predetermined
overflow value. The resultant overflow proportions will commonly vary
over a considerable range. In this circumstance it would appear reason-
able to estimate the objective overflow proportion to be used in estab-
lishing the individual group for the first routed traffic, as some weighted
average h of the overflow proportions of the several high usage groups.
Thus with weights g and overflow proportions h,
h = ^'^' + ^'^' + • ' • (35)
^1 + ^2+ • • •
* Although not exact, this equation can probably be accepted for most engi-
neering purposes where high usage trunks are provided for each parcel of traffic.
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494 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
A choice of all weights g equal to unity will often be satisfactory for the
present purpose. The desired high usage group size for the first routed
traffic is then found from standard £'i-tables showing trunks x required,
as a function of offered traffic a and proportion overflow b.
Since the different parcels of traffic have varying proportions h of their '
loads overflowing to the final route, by equation (34) the parcel with
the largest proportion will determine the permitted value of R2 . Thus '
R2 = P/&max (36)
where P is the specified poorest overall service (say 0.03) for any parcel.
It may be noted that on occasion some one parcel, perhaps a small one,
may provide an outstandingly large bmax value, which will tend to give
a considerably better than required service to all the major traffic
parcels. Some compromise with a literal application of a fixed poorest
service criterion may be indicated in such cases.
An alternative and somewhat simpler procedure here is to use an
average value b in (36) instead of ^max , with a compensating modifica- ,
tion of F, so that substantially the same R2 is obtained as before. The
allowance in P will be influenced by the choice of weights g in (35). It
will commonly be found in practice that overflow proportions to final
groups for large parcels of traffic are lower than for small parcels. Choos-
ing all weights, as unity, as opposed to weighting by traffic volumes for :
example, tends to insert a small element of service protection for those ,
traffic parcels (often the smaller ones) with the higher prportionate high .
usage group overflows.
Having determined R2 , a ready means is needed for estimating the
required number of final route trunks. Curves for this purpose are pro-
vided on Figs. 46 to 49, within whose range, R2 = 0.01 to 0.10, it will
usually be sufficiently accurate to interpolate for trunk engineering
purposes. These F2-curves exactly parallel the i?i-curves for use when
first routed traffic is offered directly to the final group without benefit
of individual high usage trunks. If R2 is well, outside the charted range
a run-through of the ER calculations may be required.
8.3 Area in Which Significant Savings in Final Route Trunks are Realized
by Allowing for the Preferred Service Given a First Routed Traffic Parcel
Considerable effort has been expended by alternate route research
workers in various countries to discover and evaluate those areas where
first routed (random) traffic ofl'ered to a final route enjoj^s a substantial
service advantage over competing parcels of traffic which have over-
,
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 495
flowed from high usage groups. A comparison of Figs. 42 to 45, (which
indicate trunk provision for meeting a first routed traffic criterion Ri)
with Figs. 46 to 49 (which indicate trunk provision for meeting a com-
posite-load-offered-to-the-final-route criterion R2) gives a means for de-
ciding under what conditions in practice it is important to distinguish
between the two criteria. Fig. 50 shows the borders of areas, defined in
terms of A' and V, the characterizing parameters of the total load
offered to the final route, where a 2 and 5 per cent overprovision of final
trunks would occur using R2 for Ri as the loss measure for first routed
traffic. Thus in the alternate route examples displayed in Table XV,
where x = S, g = 2 to 10, A' = 4.0 and V varies from 5.80 to 5.45,
Fig. 50 shows that by failing to allow for the preferred position of the 2
erlang first routed parcel, we should at R = 0.02 engineered loss, provide
a little over 5 per cent more final trunks than necessary. (Actually 10.2
and 9.9 versus 9.6 and 9.4 trunks f or gr = 2 and 10; respectively.)
The curves of Fig. 50 for final route loads larger than a few erlangs,
are almost straight lines. At an objective engineering base of i? = 0.03,
for example, the 2 and 5 per cent trunk overprovision areas through
using i?2 instead of Ri are outlined closely by:
2 per cent overprovision occurs at Fy(A' — 1) = 1.4
5 per cent overprovision occurs at V'/(A' — 1) = 1.8.
Thus in the range of loads covered by Fig. 50, one might conclude that
useful and determinable savings in final trunks can be achieved by use
of the specialized /?i-curves instead of the more general 7?2-curves, when
the ratio V'/(A' — 1) exceeds some figure in the 1.4 to 1.8 range, say 1.6.
(In the examples just cited the V'/{A' — 1) ratio is approximately 1.9.)
8.4. Character of Traffic Carried on Non-Final Routes
Telephone traffic which is carried by a non-final route will ordinarily
be subjected to a peak clipping process which will depress the variance
of the carried portion below that of the offered load. If this traffic ter-
minates at the distant end of the route, its character, while conceivably
affecting the toll and local switching trains in that office, will not require
further consideration for intertoll trunk engineering. If, however, some
or all of the route's load is to be carried on toll facilities to a more distant
point (the common situation), the character of such parcels of traffic will
l)e of interest in providing suitable subsequent paths. For this purpose
it will be desirable to have etimates of the mean and variance of these
carried parcels.
When a random traffic of "a" erlangs is offered to a group of "c" paths
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497
498 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
2 4 6 8 10 12 14 16 18 20 22 24 26
A' == AVERAGE LOAD OFFERED TO FINAL ROUTE IN ERLANGS
28
Fig. 50 — Overprovision of final route trunks when R2 is used instead of Ri
as service to first routed traffic.
and overflowing calls do not return, the variance of the carried load is
Fed = a[l - Er, , (a)] fl + aE^, , (a) - aEi, , _i(a)]* (37)
and the ratio of variance to average of the carried load is
V
cd
= 1 - a [£-1,0-1 (a) - Ei,c(a)]*
= 1 - /c
(38)
These particular forms are due to P. J. Burke.
THEORIES FOR TOLL TRAFFIC EXGINEERIXG IX THE U. S. A. 499
From (38) it is easy to see that
Fed = L{1 - Q
= (Load carried by the group) (1 — load on last trunk) (39)
This is a convenient relationship since for high usage trunk study work,
both the loads carried (in eriangs) on the group and on the last trunk
will ordinarily be at hand.
If the high usage group's load is to be split in various directions at
the distant point for re-offer to other groups, it would appear not un-
reasonable to assign a variance to each portion so as to maintain the
ratio expressed in eciuation (38). That is, if a carried load L is divided
into parts Xi , X2 • • • where L = Xi -f X2 • • • , then the associated
variances 71 , 72 . . • would be
71 = Xi (1 - fc)
y, = Xo (1 - fc) (40)
If, however, the load offered to the group is non-random (e.g., the
group is an intermediate route in a multi-alternate route system), the
procedure is not quite so simple as in the random case just discussed.
Equation (32) expresses the variance Vc of the carried load on a group
of C paths whose 'offered traffic consists of the overflow from a first
group of S paths to which a random load of A eriangs has been offered.
Vc could of course be expressed in terms of A', V and C, and curves or
tables constructed for working purposes. However, such are not avail-
able, and in any case might be unwieldy for practical use.
A simple alternative procedure can be used which jdelds a conserva-
tive (too large) estimate of carried load variance. With random load
offered to a divided two stage multiple of x paths followed by tj paths, a
positive correlation exists between the numbers m and n of calls present
simultaneously on the x and y paths, respectively. Then the variance
V-n+n of the m -\- n distribution is greater than the sum of the individual
variances of m and n,
y m-\-n ^ ' m l~ ' n
or
Vm < y^n - Vn (41)
Now n can be chosen arbitrarily, and if made very large, Vm+n becomes
the offered load variance, and F„ the overflow load variance. Both of
these are usually (or can be made) available. Their difference then,
according to (41) gives an upper limit to F,„ , the desired carried load
500 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
Table XVI — Approximate Determination of the Variance
OF Carried Loads;
X lower paths, 8 upper paths; offer to upper paths = 3 erlangs
Lower Paths, x
Upper Paths, y
No.
Lower
Paths
X
Random
offered
load
A (= V)
Variance
of
overflow
Vn
Estimated
variance
of carried
load
V -Vn
True
variance of
carried load
Eq (37)
Variance
of offer
V (= Vn)
(Col 3)
Variance of
overflow
V"
Estimated
variance
of cd load
V - V"
True
variance
of cd load
(Brocli-
meyer)
(1)
0
3
6
12
(2)
3.00
5.399
7.856
12.882
(3)
3.00
4.05
4.98
6.22
(4)
0
1.35
2.88
6.66
(5)
0
0.60
1.418
3.538
(6)
3.00
4.05
4.95
6.22
(7)
0.035
0.121
0.236
0.520
(8)
2.97
3.93
4.74
5.70
(9)
2.853
3.664
4.175
4.790
variance- Corresponding reasoning yields the same conclusion when the
offered load before the x paths is non-random.
A numerical example by Brockmeyer" while clearly insufficient iu
establish the degree of the inequality (41), indicates something as to the
discrepancy introduced by this approximate procedure. Comparison with
the true values is shown in Table XVI.
In the case of random offer to the 0, 3, 6, 12 "lower paths," the ap-
proximate method of equation (41) overestimates the variance of the
carried load by nearly two to one (columns 4 and 5 of Table XVI). The
exact procedure of (37) is then clearly desirable when it is applicable,
that is when random traffic is being offered. For the 8 upper paths to
which non-random load is offered (the non-randomness is suggested by
comparing the variance of column 6 in Table XVI with the average
offered load of 3 erlangs), the approximate formula (41) gives a not too
extravagant overestimate of the true carried load variance. Until curves
or tables are computed from equation (32), it would appear useful to
follow the above procedure for estimating the carried load variance
when non-random load is offered.
8.5. Solution of a Typical Toll Multi- Alternate Route TrunJcing Arrange-
ment: Bloomsburg, Pa.
In Fig. 9 a typical, moderately complex, toll alternate route layout
was illustrated. It is centered on the toll office at Bloomsburg, Pa. The
loads to be carried between Bloomsburg and the ten surrounding cities
are indicated in CCS (hundred call seconds per hour of traffic; 36 CCS =
1 erlang). The numbers of direct high usage trunks shown are assumed
to have been determined by an economic study; we are asked to find
I
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 501
the number of trunks which should be installed on the Bloomsburg-
Harrisburg route, so that the last trunk will carry approximately 18
CCS (0.50 erlang). Following this determination, (a) the number of final
trunks from Bloomsburg to Scranton is desired so that the poorest
service given to any of the original parcels of traffic will be no more than
3 calls in 100 meeting NC. Also (6) the modified Bloomsburg-Scranton
trunk arrangement is to be determined when a high usage group is pro-
vided for the first routed traffic.
Solution (a): First Routed Traffic Offered Directly to Final Group
The offered loads in CCS to each distant point are shown in column
(2) of Table XVII; the corresponding erlang values are in column (3).
Consulting Figs. 12 and 13, the direct group overflow load parameters,
average and variance, are read and entered in columns (5) and (6) re-
spectively for the four groups overflowing to Harrisburg, and in columns
(7) and (8) for the four groups directly overflowing to Scranton. The
variance for the direct Bloomsburg-Harrisburg traffic equals its average ;
likewise for the direct Bloomsburg-Scranton traffic. They are so entered
in the table. The parameters of the total load on the Harrisburg group
are found by totalhng, giving A' = 11.19, and V = 19.90.
The required size Ci of the Harrisburg group is now determined by
the Equivalent Random theory. Entering Fig. 25 with A' and V just
determined, the ER values of trunks and load found are Si = 13.55,
and Ai = 23.75. Ci is to be selected so that on a straight group of Si +
Ci trunks with offered load A, the last trunk will carry 0.50 erlang.
Reading from Fig. 40, the load carried by the 26th trunk approximates
this figure. Hence Ci = 26 — *Si = 12.45 trunks; or choose 12 trunks.
The overflow load's mean and variance from the Harrisburg group
v/ith 12 trunks, is now read from Figs. 12 and 13, entering with load
Ai = 23.75 and Ci -\- Si = 25.55 trunks. The overflow values (a' =
2.50 and v' = 7.50) are entered in columns (7) and (8) of the table.
The total offered load to Scranton is now obtained by totalling columns
(7) and (8), giving A" = 16.27 and V" = 25.60.
We desire now to know the number of trunks C2 for the Scranton
group which will provide NC 3 per cent of the time to the poorest service
parcel of traffic, i.e., the first routed Bloomsburg-Scranton parcel. The
Ri = 0.03 and R2 = 0.03 solutions are available, the former of course
being more closely applicable. A check reference to Fig. 50 shows a
difference of approximately 4 per cent in trunk provision would result
from the two methods. Entering Figs. 43 and 47 with A" = 16.27 and
502
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
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THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 503
I Y" = 25.60, we obtain the trunk requirements:
! Rx Method 23.8 trunks
i?2 Method 24.8 trunks
Thus the more precise method of sokition here yields a reduction of 1 .0
in 25 trunks, a saving of 4 per cent, as had been predicted.
The above calculation is on a Lost Calls Cleared basis. Since the over-
flow direct traffic calls will return to this group to obtain service, to as-
sure their receiving no more than 3 per cent 'NC, the provision of the
final route would theoretically need to be slightly more liberal. An esti-
mate of the allowance required here may be made by adding the ex-
pected erlangs loss A for the direct traffic (most of the final route over-
flow calls which come from high usage routes will be carried by their
respective groups on the next retrial) to both the A" and Y" values
previously obtained, and recalculating the trunks required from that
point onward. (In fact this could have been included in the initial com-
putation.) Thus:
A = 0.03 X 10.14 = 0.30 erlang
A'" = 16.27 + 0.30 = 16.57 erlangs
V" = 25.60 + 0.30 = 25.90 erlangs
Again consulting Figs. 43 and 47 gives the corresponding final trunk
values
Ri Method 24.1 trunks
R2 Method 25.1 trunks
Of the above four figures for the number of trunks in the Scranton
route, the i?i-Method with retrials, i.e., 24.1 trunks, would appear to
give the best estimate of the required trunks to give 0.03 service to the
poorest service parcel.
Solution (h) : With High Usage Group Provided for First Routed Traffic
Following the procedure outlined in Section 8.2, we obtain an average
of the proportions overflowing to the final route for all offered load par-
cels. The individual parcel overflow proportion estimates are shown in
the last column of Table XVII; their unweighted average is 0.112. With
a first routed offer to Scranton of 10.14 erlangs, a provision of 12 high
usage trunks will result in an overflow of a = 1.26 erlangs, or a propor-
tion, of 0.125 which is the value most closely attainable to the objective
0.112. With 12 trunks the overflow variance is found to be 2.80.
504 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
Replacing 10.14 in columns 7 and 8 of Table XVII with 1.26 and 2.80,
respectively, gives new estimates characterizing the offer to the final
route. A" = 7.39 and V" — 18.26. We now proceed to insure that the
poorest service parcel obtains 0.03 service. This occurs on the Phila-
delphia and Harrisburg groups, which overflow to the final group ap-
proximately 0.224 of their original offered loads. The final group must
then, according to equation (34) be engineered for
R2 = 0.03/0.224 = 0.134 service.
This value lies above the highest R2 engineering chart (Fig. 49, R2 =
0.10), so an ER calculation is indicated.
The Equivalent Random average is 28.6 erlangs, and S = 23.5
trunks. We determine the total trunks S -\- R which, with 28.6 erlangs
offered, will overflow 0.134(7.39) = 0.99 erlang. From Fig. 12.2, 35.6
trunks are required. Then the final route provision should be C = 35.6 —
23.5 = 12.1 trunks; and a total of 12 + 12.1 or 24.1 Scranton trunks
is indicated.
Simplified Alternative Solution: In Section 8.2 a simplified approxi-
mate procedure was described using a modified probability P' for the
average overall service for all parcels of traffic, instead of P for the poor-
est service parcel. Suppose P' = 0.01 is chosen as being acceptable.
Then
P' 0 01
«' = T = am = oo^"
Interpolating between the R2 = 0.05 and 0.10 curves (Figs. 48 and 49)
gives with A" = 7.39 and F" = 18.26, C = 13.4, the number of final
trunks required. Again the same result could have been obtained by
making the suitable ER computation. It may be noted that if P' had
been chosen as 0.015 (one-half of P), R2 would have become 0.134,
exactly the same value found in the poorest-service-parcel method. The
final trunk provision, of course, would have again l)een 12.1 trunks.
Disscussion
In the first solution above, 24.1 full access final trunks from Blooms-
burg to Scranton were refiuired. The service on the first routed traffic
was 0.03; however, the service enjoyed by the offered traffic as a whole
was markedly better than 0.03. The corresponding ER calculation
shows (.4 = 28.3, .S -\- C = 12.3 + 24.1) a total overflow of a" = 0.72
erlangs, or an overall service of 0.72/91.21 = 0.008.
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 505
In the second solution, 12 high usage and 12.1 common final, or a total
of 24.1, trunks were again required, to give 0.03 service to the poorest
service parcels of offered load. The overall service here, however, was
0.99/91.21 .= 0.011. Thus, with the same number of paths provided,
in the second solution (high usage arrangement) the overall call loss was
40 pes cent larger than in the first solution,* However, it may well be
desirable to accept such an average service penalty since by providing
high usage trunks for the first routed traffic, the latter's service cannot
be degraded nearly so readily should heavy overloads occur momentarily
in the other parcels of traffic.
9. CONCLUSION
As direct distance dialing increases, it will be necessary to provide
intertoll paths so that substantially no-delay service is given at all times.
To do this economically, automatic multi-alternate routing will replace
the present single route operation. Traffic engineering of these compli-
cated trunking arrangements will be more difficult than with simple
intertoll groups.
One of the new problems is to describe adequately the non-random
character of overflow traffic. In the present paper this is proposed to be
done by employing both mean and variance values to describe each par-
cel of traffic, instead of only the mean as used heretofore. Numerous
comparisons are made with simulation results which indicate that ade-
quate predictive reliability is obtained by this method for most traffic
engineering and administrative purposes. Working curves are provided
by which trunking arrangements of considerable complexity can readily
j be solved.
A second problem requiring further review is the day-to-day variation
i among the primary loads and their effect on the alternate route system's
I grade of service. A thorough study of these variations will permit a re-
I evaluation of the service criteria which have tentatively been adopted.
j A closely allied problem is that of providing the necessary kind and
[ amounts of traffic measuring devices at suitable points in the toll alter-
! nate route systems. Requisite to the solution of both of these problems
! is an understanding of traffic flow character in a complex overflow-type
I * The actual loss difference may be slightly greater than estimated here since
i in the first solution (complete access final trunks), an allowance was included for
i j return attempts to the final route by first routed calls meeting an 0.03 loss, while
1 in the second solution (high usage group for first routed traffic) no return at-
i| tempts to the final route were considered. These would presumably be small since
I I only 1 per cent of all calls would overflow and most of these upon retrial would be
ij handled on their respective high usage groups.
506 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
of trunking plan, and a method for estimating quantitatively the essential
fluctuation parameters at each point in such a system. The present paper
has undertaken to shed some light on the former, and to provide an
approximate j^et sufficiently accurate method by which the latter can
be accomplished. It may be expected then that these studies, as they are
developed, will provide the basis for assuring an adequate direct dis-
tance dialing service at all times with a minimum investment in intertoll
trunk facilities.
ACKNOWLEDGEMENTS
The author wishes to acknowledge the technical and mathematical as-
sistance of his associates, Mrs. Sallie P. Mead, P. J. Burke, W. J. Hall,
and W. S. Hayward, in the preparation of this paper. Dr. Hall provided
the material on the convolution of negative binomials leading to Fig. 19.
Mr. Hayward extended Kosten's curve E on Fig. 5 to higher losses by a
calculating method involving the progressive squaring of a probability
matrix. The author's thanks are also due J. Riordan who has summarized |
some of the earlier mathematical work of H. Nyquist and E. C. INIolina,
as well as his own, in the study of overflow load characteristics; this
appears as Appendix I.
The extensive calculations and chart constructions are principally
the work of Miss C. A. Lennon.
REFERENCES
1. Rappleye, S. C, A Study of the Delays Encountered bj'^ Toll Operators in Ob-
taining an Idle Trunk, B. S.T.J. , 25, p. 539, Oct., 1946.
2. Kosten, L., Over de Invloed van Herhaalde Oproepen in de Theorie der Blok-
keringskausen, De Ingenieur, 59, j). 1'j123, Nov. 21, 1947.
3. Clos, C, An Aspect of the Dialing Behavior of Subscribers and Its Effect on
the Trunk Plant, B. S.T.J. , 27, p. 424, July, 1948.
4. Kosten, L., Uber Sperrungswahrscheinlichkeiten bei Staffelschaltungen,
E.N.T., 14, p. 5, Jan., 1937.
5. Kosten, L., Over Blokkeerings-en Wachti)rol>lemen, Thesis, Delft, 1942.
6. Molina, E. C, Appendix to: Interconnection of Telephone Systems — Graded
Multiples (R. I. Wilkinson), B.S.T.J., 10, p. 531, Oct., 1931.
7. Vaulot, A. E., Application du Calcul des Probabilites a I'Exploitation Tele-
phonique. Revue Gen. de I'Electricite, 16, p. 411, Sept. 13, 1924.
8. Lundcpiist, K., General Theorv for Telephone Traffic, Ericsson Technics, 9,
p. Ill, 1953.
9. Berkeley, G. S., Traffic and Trunking Principles in Automatic Telei)hony, 2nd
revised edition, 1949, Ernest Benn, Ltd., London, Chapter V.
10. Pahu, C., Calcul I']xact de la Perte dans les Groupes de Circuits Echelonn^s,
lOricsson Technics, 3, ]). 41, 1936.
11. Brockmever, 1']., The Simph> Overflow Problem in the Theory of Telephone
Traffic! Teleteknik, 5, ji. 361, December, 1954.
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 507
ABRIDGED BIBLIOGRAPHY OF ARTICLES ON TOLL ALTERNATE ROUTING
Clark, A. B., and Osborne, H. S., Automatic Switching for Nationwide Telephone
Service, A.I.E.E., Trans., 71, Part I, p. 245, 1952. (Also B.S.T.J., 31, p. 823,
Sept., 1952.)
Pilliod, J. J., Fundamental Plans for Toll Telephone Plant, A.I.E.E. Trans., 71,
Part I, p. 248, 1952. (Also B.S.T.J., 31, p. 832, Sept., 1952.)
Nunn, W. H., Nationwide Numbering Plan, A.I.E.E. Trans., 71, Part I, p. 257,
1952. (Also B.S.T.J., 31, p. 851, Sept., 1952.)
Clark, A. B., The Development of Telephony in the United States, A.I.E.E.
Trans., 71, Part I, p. 348, 1952.
Shiplev, F. F., Automatic Toll Switching Systems, A.I.E.E. Trans., 71, Part I,
p. '261, 1952. (Also B.S.T.J., 31, p. 860, Sept., 1952.)
Myers, O., The 4A Crossbar Toll System for Nationwide Dialing, Bell Lab.
Record, 31, p. 369, Oct., 1953.
Clos, C, Automatic Alternate Routing of Telephone Traffic, Bell Lab. Record,
32, p. 51, Feb., 1954.
Truitt, C. J., Traffic Engineering Techniques for Determining Trunk Require-
ments in Alternate Routing Trunk Networks, B.S.T.J., 33, p. 277, March,
1954.
Molnar, I., Some Recent Advances in the Economy of Routing Calls in Nation-
wide Dialing, A.E. Tech. Jl., 4, p. 1, Dec, 1954.
Jacobitti, E., Automatic Alternate Routing in the 4A Crossbar System, Bell Lab.
Record, 33, p. 141, April, 1955.
Appendix I*
DERIVATION OF MOMENTS OF OVERFLOW TRAFFIC
This appendix gives a derivation of certain factorial moments of the
c(iuilibrium probabilities of congestion in a di^dded full-access multiple
used as a basis for the calculations in the text. These moments were de-
rived independently in unpublished memoranda (1941) by E. C. Molina
(the first four) and by H. Nyquist; curiously, the method of derivation
here, which uses factorial moment generating functions, employs auxili-
ary relations from both Molina and Nyquist. Although these factorial
moments may be obtained at a glance from the probability expressions
given by Kosten in 1937, if it is remembered that
pw = |:(-i)'-'(';)^, (1.1)
where p{x) is a discrete probability and M (k) is the A;th factorial moment
of its distribution, Kosten does not so identify the moments and it may
1)0 interesting to have a direct derivation.
Starting from the equilibrium formulas of the text for f(;ni, n), the
l)robability of m trunks busy in the specific group of x trunks, and n in
Prepared by J. Riordan.
508 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
the (unlimited) common group, namely
{a -{- m -\- n)f(m, n) — (w + l)f(m + 1, n)
— (n + l)/(m, n + 1) — af(in — 1, n) = 0
(1-2) «
(a -{- X -{- n)j{x, n) — af{x, n — 1) \
- (n -\- l)f(x, n + 1) - af(x - 1, n) = 0
and
/(m, n) = 0, m < 0 or n < 0 or m > x,
factorial moment generating function recurrences may be found and
solved.
With m fixed, factorial moments of n are defined by
M(fc)(m) = E {n)kf{m, n) (1.3)
n=0
or alternatively by the factorial moment exponential generating function
M{m, 0 = Z MUm)t'/k\ = £ (1 + 07K n) (1.4) ]
fc=0 n=0 I
In (1.3), {n)k = n{n — 1) • • • (n — /c + 1) is the usual notation for a \
falling factorial.
Using (1.4) in equations (1.2), and for brevity D = d/dt, it is found
that
a^ m ^- tD)M{in, t) - (m + l)M{m + 1, t)
- aM(m - l,t) = 0 (1.5)
(x - at -\- tD)M{x, t) - aM{x - \,t) = 0
which correspond (by equating powers of t) to the factorial moment re-
currences
{a-\- m^ k)M^kM) - (m + l)Ma)(w + 1)
- ailf (fc)(m - 1) = 0 (1.6)
(x + k)M(k)(x) - akM^k-i)ix) - aMik)(x - 1) = 0
Notice that the first of (1.6) is a recurrence in m, which suggests (fol-
lowing Molina) introducing a new generating function defined by
Gdu) = T.M^k){m)u'^ (1.7)
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 509
Using this in (1.5), it is found that
(a -h k - au + (u - l)~\ GM = 0 (1.8)
Hence
1 dGM^^^J^ ^j_g^
Gk(u) du I — u
and, by easy integrations,
Gk{u) = ce"" (1 - ur\ (1.10)
with c an arbitrary constant, which is clearly identical with Gk(0) =
M(.)(0).
Expansion of the right-hand side of (1.10) shows that
il/a,(m) = Ma)(0) Z "^ •^. , "" ■„ = Ma,(0)a-.(m), (1.11)
j=o \ J / {m - j)l
if
<jo{m) = a'/ml and, a,(w) = ^ ( •^- ~ ) y-^ ^ri (1-12)
The notation ak(m) is copied from Xyquist; the functions are closely
related to the ^^^"^ used by Kosten; indeed akim) = e'ipm'''' ■ They have
the generating function
00
Qkiu) = 53 (TkMu" = e""(l — u)~'' (1.13)
from which a number of recurrences are found readily. Thus
Qkiu) = (1 - u)gk+Xu)
u -^ — = augkiu) + kugk+i(u)
du
= -agk-iiu) + (a - k)gk(u) + kgk-i(u)
(the last by use of the first) imply
ckim) = ak+iim) — (Tk+iim — 1)
m(Tk(m) = ackim — 1) + k<jk+i(m — 1)
= - a<jk-i{m) + (a - k)<Tk{m) + k<Xk+i(ni)
510 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
The first of these leads to
cr/^(0) + (7,(1) + • • • + cr,(x) = ak+i(x) (1.14) J
and the last is useful in the form j
kak+i{m) = {m + k - a)ak{m) + 0(rt_i(m) (1.15) ■-
Also, the first along with ao(m) = a" /m\ leads to a simple calculation ;
procedure, as Kosten has noticed.
By (1.11) the factorial moments are now completely determined ex-
cept for il/(A-)(0). To determine the latter, the second of (1.6) and the
normalizing equation
X
E M,{m) = 1 (1.16)
are available.
Thus from the second of (1 .6)
[(:r + k)<r,{x) - mu{x - l)].^/(A-)(0) = a/v(r,_i(.c)M(,_i)(0) (1.17)
Also
{x + k)ak{x) — acTkix — 1)
= (x -\- k - a)ak(x) + a[(Xk{x) - (Tk(.x — 1)]
= (x -\- k - a)(Tk{x) + a<Tk-i{x)
= /t'o-fc+i^r),
the last step by (1.15). Hence
(Tk-l{x)
MaM = a "-^=^ Ma-iM (1.18)
<rk+i{x)
and by iteration
^k (7i(x)(roix)
MaAO) = a' "^7" "7, Mo(0) (1.19)
From (l.ll) and (1.16), and in the last step (1.14),
t.M,(m) = i: il/o(0)cro(7n) = ilfo(0)cri(a;) = 1 (1.20)
Hence finally
Ma)(m) = Ma-M<rk{ni)
, a,(x)ak(m) (1.21)
= a
(Tki.i{.r)<^k{x)
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 511
^""^ Ma) = Z Ma,{m) = a'ao{x)/a,(x) (1.22)
m=0
Ordinary moments are found from the factorial moments by linear
relations; thus if Wt is the A;th ordinary moment (about the origin)
mo = M^o) nil = M^) m-i = il/(2) + il/(i)
mz = il/(3) + 3Af (2) + il/(i)
Thus
mo(m) = (ro(m)/ai(x)
mi(m) = aai(m)(To(x) / (Ti(x)(T2(x)
vi-iim) = aa2{m)(TQ{x) / (r'2{x)(7z{x) + a(Ji{;m)<Ta{x) / <ti{x)(T2{x)
and, in particular, using notation of the text
mo{x) = (ro{x)/ax{x) = Ei,xia)
mi(x) (Tiix) a
(Xx = — ^r = a
mo{x) <T.(x) .T - a + 1 + aEi,,{a) (1.23)
ni2{x) 2 aaiix) , 2
Vx = — 7-r — (Xx = ir-^ + OCx — ax , ^
mo{x) csix) (1,24)
= ax[l — ax + 2a(x + 2 -\- ax - a)~^]
X
Finally the sum moments: nik = ^ mk{m) are
0
Wo = 1
mi = a = a(To{x)/(yi{x) = aEi_x{a)
rrh = aaQ{x)/a2{x) -\- mi = mi[a{x -\- I -\- nii — a)~ +1]
(1.25)
(1.26)
y = m2 — mi = mi[l — vh + a(.^' + 1 + nii — a) ]
In these, Ei,x(a) = (ro(:c)/(ri(.T) is the familiar Erlang loss function.
Appendix II — character of overflow load when non-random
TRAFFIC IS offered TO A GROUP OF TRUNKS
It has long been recognized that it would be useful to have a method
by which the character of the overflow traffic could be determined when
non-random traffic is offered to a group of trunks. Excellent agreement
has been found in both throwdown and field observation over ranges of
considerable interest with the "equivalent random" method of describ-
to
z
<
LJJ
in
z
D
h-
X
o
en
Q
<
o
3
LL
cr
LU
>
o
LL
o
LLI
<
LJJ
II
0.04f/ AQ--
0.02
TRUN
10 .1 0:3
TRUNKS
.1 0.3 1.0 3
a,= AVERAGE
IN
10 .1 0.3
TRUN
10 .1 0.3 1.0 3
OF OFFERED TRAFFIC
ERLANGS
Fig. 51 — Mean and variance of overHovv load when non-random traffic is
offered to a group of trunks.
512
THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 513
ing the character of non-random traffic. An approximate solution of the
problem is offered based on this method.
Suppose a random traffic a is offered to a straight multiple which is
divided into a lower Xi portion and an upper X2 portion, as follows:
T «2 , V2
X2.
] OCl,Vi
u
From Nyquist's and Molina's work we know the mean and variance
of the two overflows to be:
ai = a-Ei^xiia) = a
a"»
•ril
Vi = ai\ 1 — ai -\ ■ — -
L Xi — a + ai + IJ
a2 = a-Ei,xi+x2(0')
V2 = aol I — a2 -\ j j : — r
L xi + a;2 - a + 0:2 4- IJ
Since ai and vi completely determine a and Xi , and these in turn, with
X2 , determine 02 and Vo , we may express 02 and V2 in terms of only ai ,
Vi , and X2 . The overflow characteristics (0:2 and V2), are then given for a
non-random load (ai and Vi) offered to x trunks as was desired.
Fig. 51 of this Appendix has been constructed by the Equivalent Ran-
dom method. The charts show the expected values of 0:2 and I'o when
ai , Vi (or vi/ai), and X2 , are given. The range of ai is only 0 to 5 er-
langs, and v/a is given only from the Poisson unity relation to a peaked-
ness value of 2.5. Extended and more definitive curves or tables could
readily, of course, be constructed.
The use of the curves can perhaps best be illustrated by the solution
of a familiar example.
Example: A load of 4.5 erlangs is submitted to 10 trunks; on the "lost
calls cleared" basis; what is the average load passing to overflow?
Solution: Compute the load characteristics from the first trunk when
4.5 erlangs of random traffic are submitted to it. These values are found
to be a\ = 3.G8, vi = 4.15. Now using ai and vi (or vi/ai = 4.15/3.68 =
1.13) as the offered load to the second trunk, read on the chart the param-
eters of the overflow from the second trunk, and so on. The successive
overflow values are given in Table XVIII.
514
THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
The proportion of load overflowing the group is then 0.0472/4.50 =
0.0105, which agrees, of course, with the Erlang £^i,io(4.5) value. The
successive overflow values are shown on the chart by the row of dots
along the a2 and V2 1-trunk curves.
Instead of considering successive single-trunk overflows as in the ex-
ample above, other numbers of trunks may be chosen and their over-
flows determined. For example suppose the 10 trunks are subdivided
into 2 + 3 + 2-1-3 trunks. The loads overflowing these groups are
given in Table XIX.
Again the overflow is 0.0472 erlang, or a proportion lost of 0.0105,
which is, as it should be, the same as found in the previous example.
The values read in this example are indicated by the row of dots marked
1, 3, 6, 8 on the 2-trunk and 3-trunk curves.
The above procedure and curves should be of use in obtaining an esti-
mate of the character of the overflow traffic when a non-random load
is offered to a group of paths.
I
Table XVIII — Successive Non-Random Overflows
Characteristics of Load Offered to Trunk No. i
(same as overflow from previous trunk)
Trunk Number
i
Average
Variance
Ratio of variance to
average
1
4.50
4.50
1.00 (Random)
2
3.68
4.15
1.13
3
2.92
3.68
1.26
4
2.22
3.11
1.40
5
1.61
2.46
1.53
6
1.09
1.80
1.64
7
0.694
1.19
1.72
8
0.406
0.709
1.75
9
0.217
0.377
1.74
10
0.106
0.180
1.70
Overflow
0.0472
0.077
1.64
Table XIX — Sucessive Non-Random Overflows
Trunlc Number
No. Trunks in
Next Bundle
Offered Load Cliaracteristics
(same as overflow from previous trunk)
i
Average
Variance
Ratio of variance to
average
1
3
6
8
Overflow
2
3
2
3
4.50
2.92
1.09
0.406
0.0472
4.50
3.68
1.80
0.709
0.077
1.00 (Random)
1.26
1.64
1.75
1.64
Crosstalk on Open-Wire Lines
By W. C. BABCOCK, ESTHER RENTROP, and C. S. THAELER
(Manuscript received September 29, 1955)
Crosstalk on open-wire lines results from cross-induction between the
circuits due to the electric and magnetic fields surrounding the wires.
The limitation of crosstalk couplings to tolerable magnitudes is achieved
by systematically turning over or transposing the conductors that
comprise the circuits. The fundamental theory underlying the engineer-
ing of such transposition arrangements was presented by A. G. Chapman
in a paper entitled Open-Wire Crosstalk published in the Bell System
Technical Journal in January and April, 1934.
There is now available a Monograph (No. 2520) supplementing Mr.
Chapman's paper which reflects a considerable amount of experience re-
sulting from the application of these techniques and provides a basis for
the engineering of open-wire plant. The scope of the material is indi-
cated by the following:
TRANSPOSITION PATTERNS
This describes the basic transposition types which define the number
and locations of transpositions applied to the individual open-wire
circuits.
TYPES OF CROSSTALK COUPLING
Crosstalk occurs both within incremental segments of line and be-
tween such segments. Furthermore, the coupling may result from cross-
induction directly from a disturbing to a disturbed circuit or indirectly
by way of an intervening tertiary circuit. On the disturbed circuit the
crosstalk is propagated both toward the source of the original signal
and toward the distant terminal. A knowledge of the relative importance
of the various types of coupling is valuable in establishing certain time-
saving approximations which facilitate the analysis of the total cross-
talk picture.
515
516 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
TYPE UNBALANCE CROSSTALK
Crosstalk is measured in terms of a current ratio between the disturb-
ing and disturbed circuits at the point of observation. Crosstalk between
open-wire circuits is also generally computed in terms of a current ratio
(cu) but it is also convenient to refer to it in terms of a coupling loss
(db). The coupling in crosstalk units (cu) is the product of three terms:
a coefficient dependent on wire configuration; a type unbalance depend-
ent on transposition patterns; and frequency. The coefficient represents
the coupling between relatively untransposed circuits of a specified
length (1 mile) at a specific frequency (1 kc). The type unbalance is a
measure of the inability to completely cancel out crosstalk by intro-
ducing transpositions because of interaction effects between the two
halves of the exposure and because of propagation effects, primarily
phase shift. Type unbalance is expressed in terms of a residual unbalance
in miles and the frequency is expressed in kilocycles.
The coefficients applicable to lines built in accordance with certain
standardized specifications are available in tabular form. When it is
desired to obtain coefficients for other types of line, it is possible to
compute approximate values which may be modified by correction
factors to indicate the relationship between the computed values and
measurements on carefully constructed lines.
Expressions for near-end type unbalance for certain simple types of
exposures are developed and the formulas for all types of exposures are
given. In addition, the values for near-end type unbalance are tabulated
at 30° line angle intervals for lines where the propagation angle is iu
2,880° or less.
The principal component of far-end crosstalk between well transposed
circuits results from compound couplings involving tertiary circuits.
Again the expressions are developed for some of the exposures involving
a few transpositions and the procedure for obtaining the formulas for
any type of exposure is shown. Formulas are included for the types of
exposures encountered in normal practice and the numerical values of
far-end type unbalance are given at 30° intervals for line angles up to
2,880°.
SUMMATION OF CROSSTALK
The procedures referred to thus far evaluate the crosstalk occurring
within a limited length of line known as a transposition section. In
practice, however, a line is transposed as a series of sections. It is neces-
sary, therefore, to determine how the crosstalk arising within the several
CROSSTALK ON OPEN- WIRE LINES 517
sections and that arising from interactions between the sections tend to
combine. In a series of like transposition sections there is a tendency
for the crosstalk to increase systematically, sometimes reaching in-
tolerable magnitudes. This tendency can be controlled to a degree by
introducing transpositions at the junctions between the sections, thus
cancelling out some of the major components of the crosstalk. Complete
cancellation is impossible because of interaction and propagation effects.
ABSORPTION
Since very significant couplings exist by way of tertiary circuits, it is
possible for crosstalk to reappear on the disturbing circuit and thus
strengthen or attenuate the original signal. This gives rise to the ap-
pearance of high attenuation known as absorption peaks in the line
loss characteristic at certain critical frequencies. The evaluation of such
pair-to-self coupling requires the use of coefficients which differ from
those between different pairs and these are given for standard configura-
tions.
STRUCTURAL IRREGULARITIES
It is impracticable to maintain absolute uniformity in the spacing
between wires and in the spacing of transpositions. Thus there are un-
avoidable variations in the couplings between pairs from one transposi-
tion interval to the next. This in turn reduces the effectiveness of the
measures to control the systematic or type unbalance crosstalk and
produces what is known as irregularity crosstalk. Since the occurrence
of structural irregularities tends to follow a random distribution, it is
possible to evaluate it statistically and procedures for doing so are in-
cluded. In addition to this direct effect of structural irregularities, there
is a component of crosstalk resulting from the combination of systematic
and random unbalances. A method is developed for estimating the
magnitude of this important component of crosstalk.
EXAMPLES
In order to demonstrate how the procedures and data are used in
solving practical problems, there is included the development of a
transposition system to satisfy certain assumed conditions. This is
carried through to the selection of transposition types for one transposi-
tion section and the selection of suitable junction transpositions.
Additional examples of transposition engineering are given in the form
518 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
of several transposition systems which have been widely used in the Bell
System. These include:
Exposed Line — for voice frequency service.
CI — for voice frequency and carrier service up to 30 kc.
J5 — for voice frequency and carrier operation up to 143 kc.
01 ■ — for voice frequency and compandored carrier operation up to
156 kc.
RIC — suitable for exchange lines with a limited number of carrier
assignments.
Altogether, the theory, explanatory material, formulas and compre-
hensive data included in the Monograph make it possible to estimate
open-wire crosstalk couplings and provide the necessary background for
the development of new transposition systems.
P
I
Bell System Technical Papers Not
Published in This Journal
Alsberg, D. A.^
6-KMC Sweep Oscillator, I.R.E. Trans., PGI-4, pp. 32-39, Oct., 1955.
Anderson, J. R.,i Brady, G. W.,^ Merz, W. J.,^ and Remeika, J. P.^
Effects of Ambient Atmosphere on the Stability of Barium Titanate,
J. Appl. Phys., Letter to the Editor, 26, pp. 1387-1388, Nov., 1955.
Anderson, 0. L.,^ and Andreatch, P.^
stress Relaxation in Gold Wire, J. Appl. Phys., 26, pp. 1518-1519,
Dec, 1955.
Anderson, P. W.,^ and Hasegawa, H.^
Considerations on Double Exchange, Phys. Rev., 100, pp. 675-681,
Oct. 15, 1955.
Anderson, P. W.^
Electromagnetic Theory of Cyclotron Resonance in Metals, Phys.
Rev., Letter to the Editor, 100, pp. 749-750, Oct. 15, 1955.
Andreatch, P., see Anderson, 0. L.
Augustine, C. F., see Slocum, A.
Barstow, J. M.*
The ABC's of Color Television, Proc. I.R.E., 43, pp. 1574-1579,
Nov., 1955.
Bartlett, C. A.2
Closed-Circuit Television in the Bell System, Elec. Engg., 75, pp.
34-37, Jan., 1956.
1. Bell Telephone Laboratories, Inc.
2. American Telephone and Telegraph Company.
5. University of Tokyo, Japan.
519
520 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
Becker, J. A.^
Adsorption on Metal Surfaces and Its Bearing on Catalysis, Advances
in Catalysis, 1955, Nov., 1955.
Bommel, H. E.i
Ultrasonic Attenuation in Superconducting and Normal-Conducting
Tin at Low Temperatures, Phys. Rev., Letter to the Editor, 100, pp.
758-759, Oct. 15, 1955.
Bemski, G.^
Lifetime of Electrons in p-Type Silicon, Phys. Rev., 100, pp. 523-524,
Oct. 15, 1955.
Bennett, W. R.^
Steady State Transmission Through Networks Containing Periodi-
cally Operated Switches, Trans. I.R.E., PGC.T., 2, pp. 17-21, Mar.,
1955.
Bommel, H. E.,i Mason, W. P.,* and Warner, A. W., Jr.'
Experimental Evidence for Dislocation in Crystalline Quartz, Phys.
Rev., Letter to the Editor, 99, pp. 1895-1896, Sept. 15, 1955.
Bradley, W. W., see Compton, K. G.
Brattain, W. H., see Buck, T. M., and Pearson, G. L.
Brady, G. W., see Anderson, J. R.
Brown, W. L.'
Surface Potential and Surface Charge Distribution from Semicon-
ductor Field Effect Measurements, Phys. Rev., 100, pp. 590-591,
Oct. 15, 1955.
Buck, T. M.,' and Brattain, W. H.'
Investigations of Surface Recombination Velocities on Germanium by
the Photoelectric Magnetic Method, J. Electrochem. Soc, 102, pp.
636-640, Nov., 1955.
Cetlin, B. B., see Gait, J. K.
Charnes, a., see Jacobson, M. J.
1. Bell Telephone Laboratories, Inc.
I
TECHNICAL PAPERS
521
CoMPTON, K. G.,^ Mendizza, a./ and Bradley, W. W.'
Atmospheric Galvanic Couple Corrosion, Corrosion, 11, pp. 35-44,
Sept., 1955.
CoRENzwiT, E., see Matthias, B. T.
Dail, H. W., Jr., see Gait, J. K.
Dillon, J. F., Jr.,^ Geschwind, S.,^ and Jaccarino, V.^
Ferromagnetic Resonance in Single Crystals of Manganese Ferrite,
Phys. Rev., Letter to the Editor, 100, pp. 750-752, Oct. 15, 1955.
Dodge, H. F.^
Chain Sampling Inspection Plan, Ind. Quality Control, 11, pp. 10-13,
Jan., 1955.
Dodge, H. F.^
Skip-lot Sampling Plan, Ind. Quality Control, 11, pp. 3-5, Feb., 1955.
Fagen, R. E.,^ and Riordan, J.^
Queueing Systems for Single and Multiple Operation, J. S. Ind. Appl.
Math., 3, pp. 73-79, June, 1955.
Fine, M. E.^
Erratum: Elastic Constants of Germanium Between 1.7° and 80°K
J. Appl. Phys., Letter to the Editor, 26, p. 1389, Nov., 1955.
1 Flaschen, S. S.^
A Barium Titanate Synthesis from Titanium Esters, J. Am. Chem.
Soc, 77, p. 6194, Dec, 1955.
Fletcher, R. C.,^ Yager, W. A.,* and Merritt, F. R.^
Observation of Quantum Effects in Cyclotron Resonance, Phys. Rev.,
Letter to the Editor, 100, pp. 747-748, Oct. 15, 1955.
Franke, H. C.i
Noise Measurement on Telephone Circuits, Tele-Tech., 14, pp. 85-97,
Mar., 1955.
1. Bell Telephone Laboratories, Inc.
522 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
Galt, J. K.,1 Yager, W. A./ Merritt, F. R./ Cetlin, B. B.,» and
Bail, H. W., .Tr.^
Cyclotron Resonance in Metals: Bismuth, Phys. Rev., Letter to the
Editor, 100, pp. 748-749, Oct. 15, 1955.
Geller, S.,^ and Thurmond, C. D.'
On the Question of a Crystalline SiO, Am. Chem. Soc. J., 77, pp.
5285-5287, Oct. 20, 1955.
Geschwind, S., see Dillon, J. F.
Harker, K. J.^
Periodic Focusing of Beams from Partially Shielded Cathodes, I.R.E.
Trans., ED-2, pp. 13-19, Oct., 1955.
Hasegawa, H., see Anderson, P. W.
Haynes, J. R.,^ and Hornbeck, J. A.^
Trapping of Minority Carriers in Silicon II: n-type Silicon, Phys.
Rev., 100, pp. 606-615, Oct. 15, 1955.
Hornbeck, J. A., see Haynes, J. R.
Israel, J. 0.,^ Mechline, E. B.,^ and Merrill, F. F.^
A Portable Frequency Standard for Navigation, I.R.E. Trans., PGI-4,
pp. 116-127, Oct., 1955.
Jaccarino, v., see Dillon, J. F.
Jacobson, M. J.,' Charnes, A., and Saibel, E.^
The Complete Journal Bearing With Circumferential Oil Inlet, Trans.
A.S.M.E., 77, pp. 1179-1183, Nov., 1955.
James, D. B., see Neilson, G. C.
KoHN, W.,^ and Scheciiter, D.^
Theory of Acceptor Levels in Germanium, Phys. Rev., Letter to the
Editor, 99, pp. 1903-1904, Sept. 15, 1955.
1. Bell Telephone Laboratories, Inc.
4. Carnegie Institute.
TECHNICAL PAPERS 523
Law, J. T.,1 and Meigs, P. S.^
The Effect of Water Vapor on Grown Germanium and Silicon n-p
Junction Units, J. Appl. Phys., 26, pp. 1265-1273, Oct., 1955.
Leavis, H. W.i
Search for the Hall Effect in a Superconductor: II — Theory, Phys.
Rev., 100, pp. 641-645, Oct. 15, 1955.
LiNViLL, J. G.,^ and Mattson, R. H.^
Junction Transistor Blocking Oscillators, Proc. I.R.E., 43, pp. 1632-
1639, Nov., 1955.
Logan, R. A.^
Precipitation of Copper in Germanium, Phys. Rev., 100, pp. 615-617,
Oct. 15, 1955.
Logan, R. A.,^ and Schwartz, M.^
Restoration of Resistivity and Lifetime in Heat Treated Germanium,
J. Appl. Phys., 26, pp. 1287-1289, Nov., 1955.
McCall, D. W., see Shulman, R. G.
Mason, W. P., see Bommel, H, E.
Matthias, B. T.,^ and Corenzwit, E.^
Superconductivity of Zirconium Alloys, Phys. Rev., 100, pp. 626-627,
Oct. 15, 1955.
Mattson, R. H., see Linvill, J. G.
Mays, J. M., see Shulman, R. G.
Mechline, E. B., see Israel, J. 0.
Meigs, P. S., see Law, J. T.
Mendizza, a., see Compton, K. G.
Merrill, F. F., see Israel, J. 0.
' Merritt, F. R., see Fletcher, R. C., and Gait, J. K.
Merz, W. J., see Anderson, J. R.
1. Bell Telephone Laboratories, Inc.
524 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
Moll, J. L.^
Junction Transistor Electronics, Proc. I.R.E., 43, pp. 1807-1818,
Dec, 1955. J
MuMFORD, W. W.,^ and Schafersman^, R. L.^ ^
Data on Temperature Dependence of X-Band Fluorescent Lamp Noise
Sources, I.R.E. Trans., PGI-4, pp. 40-46, Oct., 1955.
Neilson, G. C.,^ and James, D. B.^
Time of Flight Spectrometer for Fast Neutrons, Rev. Sci. Instr., 26,
pp. 1018-1023, Nov., 1955.
Nesbitt, E. A.,^ and Williams, H. J.^
New Facts Concerning the Permanent Magnet Alloy, Alnico 5, Conf .
on Magnetism and Magnetic Materials, T-78, pp. 205-209, Oct., 1955.
Nesbitt, E. A.,^ and Williams, H. J.^
Shape and Crystal Anisotropy of Alnico 5, J. Appl. Phys., 26, pp.
1217-1221, Oct., 1955.
OWNES, C. D.i
Stability of Molybdenum Permalloy Powder Cores, Conf. on Mag- J
netism and Magnetic Materials, T-78, pp. 334-339, Oct., 1955.
Pearson, G. L.,^ and Brattain, W. H.^
History of Semiconductor Research, Proc. I.R.E., 43, pp. 1794-1806,
Dec, 1955.
Pederson, L.^
Aluminum Die Castings in Carrier Telephone Systems, Modern
Metals, 11, pp. 65, 68, 70, Sept., 1955.
Prince, M. B.^
High-Freauency Silicon Aluminum Alloy Junction Diode, Trans.
I.R.E., ED-2, pp. 8-9, Oct., 1955.
Remeika, J. P., see Anderson, J. R.
RiORDAN, J., see Fagen, R. E.
1. Bell Telephone Laboratories, Inc.
6. University of British Columbia, Vancouver, Canada.
TECHNICAL PAPERS 525
Saibel, E., see Jacobson, M. J.
ScHAFERSMAN, R. L., See Mumford, W. W.
Schechter, D., see Kohn, W.
Schelkunoff, S. A.^
On Representation of Electromagnetic Fields in Cavities in Terms of
Natural Modes of Oscillation, J. Appl. Phys., 26, pp. 1231-1234, Oct.,
1955.
Schwartz, M., see Logan, R. A.
Shulman, R. G.,1 Mays, J. M.,i and McCall, D. W.^
Nuclear Magnetic Resonance in Semiconductors: I — ^ Exchange
Broadening in InSb and GaSb, Phys, Rev., 100, pp. 692-699, Oct.
15, 1955.
Slocum, A.,^ and Augustine, C. F.^
6-KMC Phase Measurement System For Traveling Wave Tube,
Trans. I.R.E., PGI-4, pp. 145-149, Oct., 1955.
Thurmond, C. D., see Geller, S.
Uhlir, a., Jr.^
Micromachining with Virtual Electrodes, Rev. Sci. Instr., 26, pp.
965-968, Oct., 1955.
Ulrich, W., see Yokelson, B, J,
Van Uitert, L. G.^
DC Resistivity in the Nickel and Nickel Zinc Ferrite System, J. Chem.
Phys., 23, pp. 1883-1887, Oct., 1955.
Van Uitert, L. G.^
Low Magnetic Saturation Ferrites for Microwave Applications, J.
Appl. Phys., 26, pp. 1289-1290, Nov., 1955.
Wannier, G. H.^
Possibility of a Zener Effect, Phys. Rev., Letter to the Editor, 100,
p. 1227, Nov., 15, 1955.
1. Bell Telephone Laboratories, Inc.
526 the bell system technical journal, march 1956
Wannier, G. H.^
Threshold Law for Multiple Ionization, Phys. Rev., 100, pp. 1180,
Nov. 15, 1955.
Warner, A. W., Jr., see Bommel, H. E.
Williams, H. J., see Nesbitt, E. A. i
Yager, W. A., see Fletcher, R. C, and Gait, J. K.
YoKELSON, B. J.,^ and Ulrich, W.^
Engineering Multistage Diode Logic Circuits, Elec. Engg., 74, p. 1079,
Dec, 1955.
1. Bell Telephone Laboratories, Inc.
Recent Monographs of Bell System Technical
I Papers Not Published in This Journal*
Allison, H. W., see Moore, G. E.
Baker, W. 0., see Winslow, F. H.
Basseches, H., and McLean, D. A.
Gassing of Liquid Dielectrics Under Electrical Stress, Monograph
2448.
BozoRTH, R. M., TiLDEN, E. F., and Willlams, A. J.
Anistropy and Magnetostriction of Some Ferrites, Monograph 2513.
Bradley, W. W., see Compton, K. G.
CoMPTON, K. G., Mendizza, a., and Bradley, W. W.
Atmospheric Galvanic Couple Corrosion, Monograph 2470.
Davis, J. L., see Suhl, H.
Fagen, R. E., and Riordan, John
Queueing Systems for Single and Multiple Operation, Monograph
2506.
Fine, M. E.
Elastic Constants of Germanium Between 1.7° and 80°K, Monograph
2479.
FoRSTER, J. H., see Miller, L. E.
Galt, J. K., see Yager, W. A.
II' Geballe, T. H., see Morin, F. J.
* Copies of these monographs may l)e obtained on request to the Publication
Department, Bell Telephone Laboratories, Inc., 463 West Street, New York 14,
N. Y. The numbers of the monographs should be given in all requests.
527
528 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
GlANOLA, U. F.
Use of Wiedemann Effect for Magnetostrictive Coupling of Crossed
Coils, Monograph 2492.
Green, E. I.
The Story of Q, Monograph 2491.
GuLDNER, W. G., see Wooten, L. A.
Harrower, G. a.
Measurement of Electron Energies by Deflection in a Uniform Electric
Field, Monograph 2495.
Haus, H. a., and Robinson, F. N. H.
The Minimum Noise Figure of Microwave Beam Amplifiers, Mono-
graph 2468.
Hines, M. E., Hoffman, G. W., and Saloom, J. A.
Positive-ion Drainage in Magnetically Focused Electron Beams,
Monograph 2481.
Hoffman, G. W., see Hines, M. E.
Kelly, M. J.
Training Programs of Industry for Graduate Engineers, Monograph
2512.
Law, J. T., and Meigs, P. S.
Water Vapor on Grown Germanium and Silicon n-p Junction Units,
Monograph 2500.
McAfee, K. B., Jr.
Attachment Coefficient and Mobility of Negative Ions by a Pulse
Techniaue, Monograph 2471.
McLean, D. A., see Basseches, H.
Meigs, P. S., see Law, J. T.
Mendizza, a., see Compton, K. G.
Merritt, F. R., see Yager, W. A.
MONOGRAPHS 529
Miller, L. E., and Forster, J. H.
Accelerated Power Aging with Lithium-Doped Point Contact Transis-
tors, Monograph 2482.
Miller, S. L.
Avalanche Breakdown in Germanium, Monograph 2477.
Moore, CI. E., see Wooten, L. A.
Moore, G. E., and Allison, H. W.
Adsorption of Strontium and of Barium on Tungsten, Monograph
2498.
MoRiN, F. J., and Geballe, T. H.
Electrical Conductivity and Seebeck Effect in Nio.so Fe2.2o04 , Mono-
graph 2514.
Morrison, J., see Wooten, L. A.
Nesbitt, E. a., and Williams, H. J.
Shape and Crystal Anisotropy of Alnico 5, Monograph 2502.
Olmstead, p. S.
Quality Control and Operations Research, Monograph 2530.
Pearson, G. L., see Read, W. T., Jr.
Pfann, W. G.
Temperature Gradient Zone Melting, Monograph 2451.
Poole, K. M.
Emission from Hollow Cathodes, Monograph 2480.
Read, W. T., Jr., and Pearson, G. L.
^ The Electrical Effects of Dislocations in Germanium, Monograph
! 2511.
RiORDAN, John, see Fagen, R. E.
Robinson, F. N. H., see Haus, H. A.
Saloom, J. A., see Hines, M. E.
530 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
SCHELKUNOFF, S. A.
Electromagnetic Fields in Cavities in Terms of Natural Modes of
Oscillation, INlonograph 2505.
Sears, R. W.
A Regenerative Binary Storage Tube, jNIonograph 2527. '<
Slighter, W. P.
Proton Magnetic Resonance in Polyamides, Monograph 2490.
SuHL, H., Van Uitert, L. G., and Davis, J. L.
Ferromagnetic Resonance in Magnesium-Manganese Aluminum
Ferrite Between 160 and 1900 mc, Monograph 2472.
Tilden, E. F., see Bozorth, R. M.
Treuting, R. G.
Some Aspects of Slip in Germanium, Monograph 2485.
Uhlir, A., Jr.
Micromachining with Virtual Electrodes, Monograph 2515.
Van Uitert, L. G., see Suhl, H.
Walker, L. R.
Power Flow in Electron Beams, Monograph 2469.
Williams, A. J., see Bozorth, R. M.
Williams, H. J., see Nesbitt, E. A.
WiNSLOW, F. H., Baker, W. O., Yager, W. A.
Odd Electrons in Polymer Molecules, Monograph 2486.
WooTEN, L. A., Moore, G. E., Guldner, W. G., and Morrison, J.
Excess Barium in Oxide-Coated Cathodes, Monograph 2497.
Yager, W. A., see Winslow, F. H.
Yager, W. A., Galt, J. K., and Merritt, F. R.
Ferromagnetic Resonance in Two Nickel-Iron Ferrites, Monograph
2478.
Contributors to This Issue
Armand 0. Adam,* New York Telephone Company, 1917-1920; West-
ern Electric Company, 1920-24; Bell Telephone Laboratories; 1925-.
Mr. Adam tested local dial switching systems before turning to design
j on the No. 1 and toll crossbar systems. From 1942 to 1945 he was as-
sociated with the Bell Laboratories School For War Training. Since
then he has been concerned with the design and development of the
marker for the No. 5 crossbar system. Currently he is supervising a group
I doing common control circuit development work for the crossbar tandem
I switching system.
i Wallace C. Babcock, A.B., Harvard University, 1919; S.B., Harvard
University, 1922. U.S. Army, 1917-1919. American Telephone and Tele-
i graph Company, 1922-1934; Bell Telephone Laboratories, 1934-. Mr.
Babcock was engaged in crosstalk studies until World War IL Afterward
, he was concerned with radio countermeasure problems for the N.D.R.C.
' Since then he has been working on antenna development for mobile
radio and point-to-point radio telephone systems and military projects.
I Member of I.R.E. and Harvard Engineering Society,
, Franklin H. Blecher, B.E.E., 1949, M.E.E., 1950 and D.E.E.,
, 1955, Brooklyn Polytechnic Institute; Polytechnic Research and De-
' velopment Company, June, 1950 to July, 1952; Bell Telephone Labora-
I tories 1952-. Dr. Blecher has been engaged in transistor network de-
I velopment. His principal interest has been the application of junction
[ transistors to feedback amplifiers used in analog and digital computers.
He is a member of Tau Beta Pi, Eta Kappa Nu and Sigma Xi and is an
associate member of the I.R.E.
W. E. Danielson, B.S., 1949, M.S., 1950, Ph.D, 1952, California
Institute of Technology; Bell Laboratories 1952-. Dr. Danielson has been
j engaged in microwave noise studies with application to traveling-wave
[ tubes and he has been in charge of development of traveling-wave tubes
* Inadvertently, Mr. Adam's biography was omitted from the January issue of
the Journal in which his article, "Crossbar Tandem as a Long Distance Switch-
ing Equipment," appeared.
531
532 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
for use at 11,000 megacycles since June of 1954. He is the author of
articles published by the Journal of Applied Physics, Proceedings of the
I.R.E., and the B.S.T.J., and he is a Member of the American Physical
Society, Tau Beta Pi, and Sigma Xi.
Amos E. Joel, Jr., B.S., Massachusetts Institute of Technology,
1940; M.S., 1942; Bell Telephone Laboratories, 1940-. IMr. Joel's first
assignment was in relay engineering. He then worked in the crossbar
test laboratory and later conducted fundamental development studies.
During World War II, he made studies of communications projects
and from 1944 to 1945 designed circuits for a relay computer. Later he
prepared text and taught a course in switching design. The next two
years were spent designing AM A computer circuits, and since 1949
Mr. Joel has been engaged in making fundamental engineering studies
and directing exploratory development of electronic switching systems.
He was appointed Switching Systems Development Engineer in 1954.
Member of A.I.E.E., I.R.E., Association for Computing Machinery, and
Sigma Xi.
Esther M. Rentrop, B.S., 1926, Louisiana State Normal College.
Miss Rentrop joined the transmission group of the Development and
Research Department of the American Telephone and Telegraph Com-
pany in 1928, and transferred to Bell Laboratories in 1934. In both com-
panies she has been concerned principally wdth control of crosstalk, both
in field studies and transposition design work. During World War II,
she assisted in problems of the Wire Section, Eatontown Signal Corps
Laboratory at Fort Monmouth, and later she worked on other military
projects at the Laboratories for the duration of the war. Miss Rentrop is
presently a member of the noise and crosstalk studies group of the Out-
side Plant Engineering Department and is engaged in studies of inter-
ference prevention.
Jack L. Rosenfeld is a student in electrical engineering at the Mas-
sachusetts Institute of Technology. He will receive the S.M. and S.B.
degrees in 1957. He has been with Bell Telephone Laboratories on co-
operative assignments in microwave tube development and electronic
central office during 1954 and 1955. He is a student member of the I.R.E.
and a member of Tau Beta Pi and Eta Kappa Nu.
Joseph A. Saloom, Jr., B.S., 1948, M.S., 1949, and Ph.D., 1951, all
in Electrical Engineering, University of Illinois. He joined Bell Labora-
tories in 1951. Mr. Saloom worked on electron tube development at'
CONTRIBUTORS TO THIS ISSUE 533
Murray Hill until 1955 with particular emphasis on electron beam
studies. He is now at the Allentown, Pa., laboratory where he is en-
gaged in the development of microwave oscillators. Member of the
Institute of Radio Engineers, Sigma Xi, Eta Kappa Nu, Pi Mu Epsilon.
Charles S. Thaeler, Moravian College, 1923-25, Lehigh University
1925-28, E.E., 1928. During the summer of 1927 he was employed by the
Bell Telephone Company of Pennsylvania, returning there after gradua-
tion, where he was concerned with transmission engineering and the
Toll Fundamental Plan. In 1943 he was on loan to the Operating and
Engineering Department of the A.T.&T. Co., working on toll transmis-
sion studies. From 1944 to the present he has been with the Operating
and Engineering Department and is currently engaged in toll circuit
noise and crosstalk problems on open wire and cable systems. Mr.
Thaeler is an Associate Member of A.I.E.E., and member of Phi Beta
I Kappa, Tau Beta Pi, and Eta Kappa Nu.
Ping King Tien, B. S., National Central University, China, 1942;
M.S., 1948, Ph.D., 1951, Stanford University; Stanford Microwave
]>aboratory, 1949-50; Stanford Electronics Research Laboratory, 1950-
52; Bell Telephone Laboratories, 1952-. Since joining the Laboratories,
' Dr. Tien has been concerned with microwave tube research, particularly
t raveling- wave tubes. In the course of this research he has engaged in
studies of space charge wave amplifiers, helix propagation, electron beam
focusing, and noise. He is a member of Sigma Xi.
Arthur Uhlir, Jr., B.S., M.S. in Ch.E., Illinois Institute of Tech-
jnology, 1945, 1948; S.M. and Ph.D. in Physics, University of Chicago,
' 1950, 1952. Dr. Uhlir has been engaged in many phases of transistor
development since joining the Laboratories in 1951, including electro-
I chemical techniques and semiconductor device theory. Since 1952 he
has participated in the Laboratories' Communications Development
I'laining Program, giving instruction in semiconductors. Member of
American Physical Society, Sigma Xi, Gamma Alpha, and the Institute
' of Radio Engineers.
Roger I. Wilkinson, B.S. in E.E., 1924, Prof. E.E., 1950, Iowa State
College; Northwestern Bell Telephone Company, 1920-21; American
Telephone and Telegraph Company, 1924-34; Bell Telephone Labora-
tories, 1934-. As a member of the Development and Research Depart-
iinent of the A.T.&T. Co., Mr. Wilkinson specialized in the applica-
tions of the mathematical theory of probability to telephone problems.
534 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956
Since transferring to Bell Telephone Laboratories in 1934, he has con-
tinued in the same field of activity and is at present Traffic Studies
Engineer responsible for probability studies and traffic research. For two
years during World War II, in a civilian capacity, he engaged in opera-
tions analysis studies for the Far East Air Forces in the South Pacific,
for which he received the Medal for Merit. He has also served as a con-
sultant to the Air Force, the Navy and the Air Navigation Delevopment
Board. Mr. Wilkinson is a member of A.I.E.E., American Society for
Engineering Education, American Statistical Association, Institute of
Mathematical Statistics, Operations Research Society of America, Amer-
ican Society for Quality Control, Eta Kappa Nu, Tau Beta Pi, Phi
Kappa Phi and Pi ]\Iu Epislon.
I
I
i
1 p
1 cr
FIG. 25 EQUIVALENT RANDOM LOAD A AND TRUNKS S, FROM NON-RANDOM LOAD A',V'
8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
A=AVERAGE RANDOM LOAD IN ERLANGS
»
Copyright 1955 by Bel] Telephone Laboratories, Incorporated
Fig. 25 - Equivalent random load A and number of trunks S, from non-random load A', V - random loads 0 to 50 erlangs
FIG. 26 EQUIVALENT RANDOM LOAD A AND TRUNKS S, FROM NON-RANDOM LOAD A'V
3 4 5 6 7
A = AVERAGE RANDOM LOAD IN ERLANGS
10
Copyright 1955 by Bell Telephone Laboratories, Incorporated
Fig 26 - Equivalent random load A and number of trunks S. from non-nuidom load A'. V - random loads 0 to 10 erlangs
[HE BELL SYSTEM
Jechnical journal
fIvOTED TO THE SC I E N T I FIC^W^ AND ENGINEERING
[PECTS OF ELECTRICAL COMMUNICATION
KANSAS C"^ MO'
t*M— IM I III I
(ILUME XXXV MAY 1956 NUMBERS
Chemical Interactions Among Defects in Germanium and Silicon
H. REISS, C. S. FULLER AND F. J. MORIN 535
Single Crystals of Exceptional Perfection and Uniformity by Zone
Leveling D. c, bennett and b, sawyer 637
Diffused p-n Junction Silicon Rectifiers M. b. prince 661
The Forward Characteristic of the PIN Diode d. a. kleinman 685
A Laboratory Model Magnetic Drum Translator for Toll Switch-
ing Offices F. J. buhrendorf, h. a. henning and o. j. murphy 707
Tables of Phase of a Semi-Infinite Unit Attenuation Slope
D. E. THOMAS 747
Bell System Technical Papers Not Published in This Journal 751
Recent Bell System Monographs 759
Contributors to This Issue 762
COPYRIGHT 195< AMERICAN TELEPHONE AND TELEGRAPH COMPANY
THE BELL SYSTEM TECHNICAL JOURNAL
ADVISORY BOARD
F. R. KAPPEL, President, Western Electric Company
M. J. KELLY, President, Bell Telephone Laboratories
E. J. McNBELY, ExecutivB Vice President, American
Telephone and Telegraph Company
EDITORIAL COMMITTEE
B. MCMILLAN, Chairman
A. J. BUSCH
A. C. DICKIESON
B. L. DIETZOLD
K. E. GOULD
E. I. GREEN
R. E. HONAMAN
H. R. HUNTLEY
F. R. LACK
J. R. PIERCE
H. V. SCHMIDT
G. N. THAYER
EDITORIAL STAFF
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M . E. 8TRIEBY, Managing Editor
R. L. SHEPHERD, Prodvction Editor
THE BELL SYSTEM TECHNICAL JOURNAL is pubUshed six timea a year
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THE BELL SYSTEM
TECHNICAL JOURNAL
VOLUME XXXV MAY 1956 number 3
Copyright 1956, American Telephone and Telegraph Company
Chemical Interactions Among Defects in
Germanium and Silicon
By HOWARD REISS, C. S. FULLER, and F. J. MORIN
Interactio7is among dejects in germanium and silicon have been investi-
gated. The solid solutions involved hear a strong resemblance to aqueous
solutions insofar as they represent media for chemical reactions. Such
phenomena as acid-base neutralization, complex ion formation, andion pair-
ing, all take place. These phenomena, besides being of interest in themselves,
are uscfid in studying the properties of the semiconductors in which they
occur. The following article is a blend of theory ami experime7it, and de-
scribes developments in this field during the past few years.
CONTENTS
I . Introduction 536
IL Electrons and Holes as Chemical Entities 537
in. Application of the Mass Action Principle 546
IV. Further Applications of the Mass Action Principle 550
V. Complex Ion Formation 557
VI. Ion Pairing 565
VII. Theories of Ion Pairing 567
VIII. Phenomena Associated with Ion Pairing in Semiconductors 575
IX. Pairing Calculations 578
X. Theory of Relaxation 582
XI. Investigation of Ion Pairing by Diffusion 591
535
536 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
XII. Investigation of Ion Pairing by Its Effect on Carrier Mobility 601
XIII. Relaxation Studies 607
XIV. The Effect of Ion Pairing on Energy Levels 610
XV. Research Possibilities 611
Acknowledgements 613
Appendix A — The Effect of Ion Pairing on Solubility 613
Appendix B — Concentration Dependence of Diffusivity in the Pres-
ence of Ion Pairing 617
Appendix C — Solution of Boundary Value Problem for Relaxation. . 619
Appendix D —Minimization of the Diffusion Potential 623
Appendix E — Calculation of Diffusivities from Conductances of
Diffusion Layers 626
Glossary of Symbols 630
References 634
I. INTRODUCTION
The effort of Wagner' and his school to bring defects in solids into the
domain of chemical reactants has provided a framework within which •
various abstruse statistical phenomena can be viewed in terms of the
intuitive principle of mass action.^ Most of the work to date in this field '
has been performed on oxide and sulfide semiconductors or on ionic com- '[
pounds such as silver chloride. In these materials the control of defects ■
(impurities are to be regarded as defects) is not all that might be desired, i
and so with a few exceptions, experiments have been either semiquanti- .
tative or even qualitative. i
With the emergence of widespread interest in semi-conductors, cul- :
minating in the perfection of the transistor, quantities of extremely pure ,
single crystal germanium and silicon have become available. In addition
the physical properties, and even the quantum mechanical theory of the
behavior of these substances have been widely investigated, so that a
great deal of information concerning them exists. Coupled with the fact
that defects in them, especially impurities, are particularly susceptible
to control, these circumstances render germanium and silicon ideal sub-
stances in which to test many of the concepts associated with defect I
interactions.
This view was adopted at Bell Telephone Laboratories a few years ago
when experimental work was first undertaken. Not only has it been
possible to demonstrate quantitatively the validity of the mass action
principle applied to defects, but new kinds of interactions have been
discovered and studied. Furthermore new techniques of measurement
have been developed which we feel open the way for broader investiga-
tion of a still largely unexplored field.
In fact solids (particularly semiconductors like germanium and silicon)
CHEMICAL INTERACTIONS AMONG DEFECTS IN Gg AND Si 537
appear in every respect to provide a medium for chemical reactivity
similar to liquids, particularly water. Such pehnomena as acid-base reac-
tions, complex ion formation, and electrolyte phenomena such as Debye
Hiickel effects, ion pairing, etc., all seem to take place.
Besides the experiments theoretical work has been done in an attempt
to define the limits of validity of the mass action principle, to furnish
more refined electrolyte theories, and most importantly, to provide firm
theoretical bases for entirely new phenomena such as ion pair relaxation
processes.
The consequence is that the field of diamond lattice^ semiconductors
which has previously engaged the special interests of physicists threatens
to become important to chemists. Semiconductor crystals are of interest,
not only because of the specific chemical processes occurring in these
substances, but also because they serve as proving grounds for certain
ideas current among chemists, such as electrolyte theory. On the other
hand renewed interest is induced on the part of physicists because chem-
ical effects like ion pairing engender new physical effects.
The purpose of this paper is to present the field of defect interaction
as it now stands, in a manner intelligible to both physicists and chem-
ists. However, this is not a review paper. Most of the experimental re-
sults, and particularly the theories which are fully derived in the text or
the appendices are entirely new. Some allusion will be made to published
work, particularly to descriptions of the results of some previous theories,
in order to round out the development.
The governing theme of the article lies in the analogy between
semiconductors and aqueous solutions. This analogy is useful not so
j much for what it explains, but for the experiments which it suggests.
: More than once it has stimulated us to new investigations.
1 In our work we have made extensive use of lithium as an impurity.
This is so because lithium can be employed with special ease to demon-
strate most of the concepts we have in mind. This specialization should
not obscure the fact that other impurities although not well suited to
the performance of accurate measurements, will exhibit much of the
same behavior.
II. ELECTRONS AND HOLES AS CHEMICAL ENTITIES
Since electrons and holes'* are obvious occupants of semiconductors
I like germanium and silicon, and are intimately associated with the pres-
[ence of donor and acceptor impurities,^ it is fitting to inciuire into the
f roles they may play in chemical interactions between donors and ac-
538 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
ceptors. This question has been discussed in two papers,^- ® and only its
principle aspects will be considered.
To gain perspective it is convenient to consider a system representing
the prototype of most systems to be discussed here. Consider a single
crystal of silicon containing substitutional boron atoms. Boron, a group
III element, is an acceptor, and being substitutional cannot readily dif-
fuse^ at temperatures much below the melting point of silicon. If this
crystal is immersed in a solution containing lithium, e.g., a solution of
lithium in molten tin, lithium will diffuse into it and behave as a donor.
Evidence suggests that lithium dissolves interstitially in silicon, thereby
accounting for the fact that it possesses a high diffusivity^ at a tempera-
ture where boron is immobile, for example, below 300°C. When the
lithium is uniformly distributed throughout the silicon its solubility in
relation to the external phase can be determined. Throughout this process
boron remains fixed in the lattice.
If both lithium and boron were inert impurities the solubility of the
former would not be expected to depend on the presence or absence of
the latter, for the level of solubility is low enough to render (under
ordinary circumstances) the solid solution ideal.* On the other hand the
impurities exhibit donor and acceptor behaviors respectively, and some
unusual effects might exist. We shall first speculate on the simplest possi-
bility in this direction, with the assistance of the set of equilibrium reac-
tions diagrammed below.* ,
Li{Sn) «=± Li{Si) t± Li+ + e~
+
B{Si) :f±B- + e+ (2.1)
Ti
eV
At the left lithium in tin is shown as Li(Sn). It is in reversible equilib-
rium with Li(Si), un-ionized lithium dissolved in silicon. The latter, in
turn, ionizes to yield a positive Li'^ ion and a conduction electron, e~.
Boron, confined to the silicon lattice as B(Si) ionizes as an acceptor to
give B" and a positive hole, e"*". The conduction electron, e~, may fall
into a valence band hole, e"*", to form a recombined hole-electron pair,
e"^e~. This process and its reverse are indicated by the vertical equilibrium
at the right.
All of the reactions in (2.1), occuring within the silicon crystal are
describable in terms of tansitions between states in the energy band dia-
A glossary of symbols is given at the end of this article.
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 539
gram of silicon, exhibited in Fig. 1. The conduction band, the valence
band, and the forbidden gap are shown. Lithium and boron both intro-
duce localized energy states in the range of forbidden energies. The state
for lithium lies just below the bottom of the conduction band while that
for boron lies just over the top of the valence band. The separations in
energy between most donors or acceptors and their nearest bands are of
the order of hundredths of an electron volt while the breadths of the for-
bidden gaps in germanium or silicon are of the order of one electron volt.
Process 1 in Fig. 1 involving a transition between the donor level and
conduction band corresponds to the ionization of lithium in (2.1). Proc-
ess 2 is the ionization of boron while process 3 represents hole-electron
recombination and generation. The various energies of transition are the
heats of reaction of the chemical-like changes in (2.1).
Proceeding in the chemists fashion one might argue as follows concern-
ing (2.1). If e'^e' is a stable compound, as it is at fairly low temperatures,
then its formation should exliaust the solution of electrons, forcing the
set of lithium equilibria to the right. In this way the presence of boron,
supplying holes toward the formation of e'^e", increases the solubility of
lithium. In fact if e"*" is regarded as the solid state analogue of the hydro-
gen ion in aqueous solution, and e~ as the counterpart of the hydroxyl
ion, then the donor, lithium, may be considered a base while boron, may
be considered an acid. Furthermore e'*"e~ must correspond to water.
Thus the scheme in (2.1) is analogous to a neutralization reaction in
which the weakly ionized substance is e'*"e~.
If the immobile boron atoms were replaced by immobile donors, e.g.,
I phosphorus atoms, a reduction, rather than an increase, in the solubility
IT
BORON LEVELS (ACCEPTORS)
x : ;w>/.-v v.^;i::-.:-:VX;^;;;v valence band v.
DISTANCE
Fig. 1 — Energy band diagram showing the chemical equilibria of (2.1).
540 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
of lithium might be expected on the basis of an oversupply of electrons
(i.e., by the common ion effect^"). In that case we would have a base
displacing another base from solution.
The intimate comparison between this kind of solution and an aqueous
solution is worth emphasizing not so much for what it adds to one's
understanding of the situation but rather for the further effects it sug-
gests along the lines of analogy. These additional phenomena have been
looked for and found, and Mill be discussed later in this article.
The scheme shown in (2.1) should be applicable, in principle, to other
donors and acceptors and to germanium and other semiconductors as
well as silicon. Furthermore the external phase may be any one of a suit-
al)le variety, and need not even be liquid. Other systems, however, are
not as convenient, especially in regard to the ease of equilibration of an
impurity over the parts of an heterogeneous system. The lengths to which
one can go in comparing electrolytes and semiconductors are discussed
in a recent paper."
In order to quantify the scheme of (2.1) it seems natural to invoke the
law of mass action. Treatments in which holes and electrons are in-
volved in mass action expressions are not new, although systems forming
such perfect analogies to aqueous solutions do not seem to have been
discussed in the past. For example, in connection with the oxidation of
copper Wagner " writes
4Cu -f O2 ^ 2CU2O -f 40" + 4e+ (2.2)
in which D ~ is a negatively charged cation vacancy in the CU2O lattice,
and e"^ is a hole. Wagner proceeds to invoke the law of mass action in
order to compute the oxygen pressure dependence in this system.
In another example Baumbach and Wagner^^ and others have investi-
gated oxygen pressure over non-stoichiometric zinc oxide. They consider
the possible reactions
2ZnO ;=± 2Zn + O2 t\
u
2Z?i+ i^ 2Zn++ -f 2e" (2.3)
+
2e-
and apply the law of mass action. In (2.3) the various states of Zii are
presumably interstitial.
Kroger and Vink have recently considered the problem in oxides and
sulfides in a rathcM- general way. However in none of the oxide-sulfidc
systems has it been possible to achieve really quantitative results. In
CHEMICAL INTEKACTIONS AMONG DEFECTS IN Ge AND Si 541
contrast silicon and germanium offer possibilities of an entirely new order.
The advent of the transistor has not only provided large supplies of pure
single crystal material, but it has also made available a store of funda-
mental information concerning the physical properties of these sub-
stances. For example, data exists on their energy band diagrams includ-
ing impuritj^ states — also on resistivity — impurity density curves,
diffusivities of impurities, etc. Furthermore, the amount of ionizable
impurities can be controlled within narrow limits, and can be changed
at will and measured accurately. Consequently it is reasonable to assume
that experiments on germanium and silicon will be more successful than
similar investigations using other materials.
A t this point it is in order to examine whether or not the treatment of
electrons and holes as normal chemical entities satisfying the law of
mass action is altogether simple and straightforward. This problem has
been investigated by Reiss who found the treatment permissible only
as long as the statistics satisfied by holes and electrons remain classical.
The validity of this contention can be seen in a very simple manner.
Consider a system like that in (2.1). Let the total concentration of donor
(ionized and un-ionized) be No , the concentration of ionized donor be
D"*", the concentration of conduction electrons be n, and that of valence
band holes be p. Let A''^ and A~ denote the concentrations of total ac-
ceptor and acceptor ions respectively. Finally, let a be the thermody-
namic activity'^ of the donor (lithium in (2.1)) in the external phase.
Then, corresponding to the heterogeneous equilibrium in which lith-
ium distributes itself between the two phases we can write
^» - ^" = K, (2.4)
a
in which Ko depends on temperature, but not on composition. This as-
sumes the semiconductor to be dilute enough in donor so that the ac-
tivity of un-ionized donor can be replaced by its concentration. No — D^.
For the ionization of the donor we can write the mass action relation,
Z)+
n
and for the acceptor.
Nd - D+
A~p
= Kd (2.5)
= Ka (2.6)
iVx - A-
while for the electron-hole recombination equilibrium
np = Ki (2.7)
542 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
In (2.5), (2.6), and (2.7) all the i^'s are independent of composition. To
these equations is added the charge neutrality condition,
D+ + p = A~ + 7i (2.8)
Equations (2.4) through (2.8) are enough to determine No in its de-
pendence on Na , «, and the various K's. Together they represent the
mass action approach. To demonstrate their validity it is necessary to
appeal to statistical considerations.
Thus Nd — D^, the concentration of un-ionized donor is really the
density of electrons in the donor level of the energy diagram for the semi-
conductor. According to Fermi statistics this density is given by
No- D+ = No/{l + M exp \{Eu - F)/kT]} . (2.9)
in which Ed is the energy of the donor level, F is the Fermi level, k,
the Boltzmann constant, and T, the temperature. Furthermore, accord-
ing to Fermi statistics, n, the total density of electrons in the conduction
band is
n
= E ^y {1 + exp [{Ei - F)/kT]} (2.10)
where Qi is the density of levels of energy, Ei , in the conduction band,
and the sum extends over all states in that band. Similar expressions are
available for the occupation of the acceptor level and the valence band.
F is usually determined by summing over all expressions like (2.9) and
(2.10) and equating the result to the total number of electrons in the
system. This operation corresponds exactly to applying the conserva-
tion condition, (2.8). It is obvious from the manner of its determina-
tion that F depends upon No — D^y n, etc.
If we now form the expression on the left of (2.5) by substituting for
each factor in it from (2.9) and (2.10), it is obvious that the result de-
pends in a very complicated fashion upon F, and so cannot be the con-
stant, Kd , independent of composition, since in the last paragraph F
was shown to depend on composition. On the other hand if attention is
confined to the limit in which classical statistics apply^ the unities in
the denominators of (2.9) and (2.10) can be disregarded in comparison
to the exponentials, and those equations become
1
No - /)+ = 2Noe''"\-'''"'' (2.11);
and
n = e
I
^"'' Z 9ie~"'"" (2.12)
I
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 543
respectively. Moreover, from (2.11)
i)+ ^ Nn[l - 2e"'^e-^'"'^] = Nu (2.13)
where the second term in brackets is ignored for the same reason as unity
in the denominators of (2.9) and (2.10). Substituting (2.11) through
(2.13) into (2.5) yields
D^n _ ?^-- (2.14)
in which the right side is truly independent of composition, since F has
cancelled out of the expression. Similar arguments hold for (2.6) and
(2.7). Therefore in the classical limit the law of mass action is valid, at
least insofar as internal equilibria are concerned.
We have next to examine the validity of (2.4) which is really the law
of mass action applied to the heterogeneous equilibrium between phases.
Substitution of (2.11) into (2.4) leads to the prediction
a = ^"^^ {e"''}No = K{e"''}Nu (2.15)
in the classical case, if (2.4) is valid. In order to confirm (2.15) it is neces-
sary to evaluate the chemical potentials of the donor in the external
phase and in the semiconductor, and equate the two. The resulting ex-
pression should be equivalent to (2.15).
Since a is the activity of the donor in the external phase its chemical
potential in that phase is, by definition,
M = fl'iT, p) + kT in a (2.16)
where /i°, the chemical potential in the standard state, may depend on
temperature and pressure, but not on composition. To compute the chem-
ical potential in the semiconductor statistical methods must once more
be invoked. Thus, according to (2.13), donor atoms are nearly totally
ionized in the classical case, so that the addition of a donor atom to the
semiconductor amounts to addition of two separate particles, the donor
ion and the electron. The chemical potential of the added atom is there-
fore the sum of the potentials of the ion and the electron separately.
Since the ions are supposedly present in low concentration the latter
can serve as an activity, ^^ and in analogy to (2.16) we obtain for the
ionic chemical potential
MD+ = hd+\T, p) -f kT (n Z)+ (2.17)
544 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
Furthermore, it is well established'" that the Fermi level plays the role
of chemical potential, ju* , for the electron
ile = F (2.18)
Thus the chemical potential for the donor atom is
y^D^ + M. = MB+' + kTfnD^ + F
(2.19)
= Mz)+° + kT inNn + F = /x/>+" + kT In [e''"'^]Nn
where (2.13) has been used to replace D'^ by Nd . We note that the ac-|
tivity of the donor atom must be
{e^^'^\Nn (2.20)1
with e^""^ playing the role of an activity coefficient."
Equating ixd given by (2.19) to n in (2.16) results in the equation
a = exp[(M.>+° - ix')/kT]{e'^"]Nu (2.21)|
which can be made identical to (2.15) by identifying
exp[(Mz.+° - n')/kT]
with K of that expression. Thus in the classical case the law of mass]
action is applicable to the heterogeneous equilibrium.
When classical statistics no longer apply it is still possible to evaluatei
Nd — D'^, using the full expression (2.9). Therefore the solubility Nd J
of the donor can still be determined if (2.4) remains valid. To decidef
this question it is necessary to evaluate hd , the chemical potential of j
the donor in the semiconductor under non-classical conditions. Thisl
problem is not as simple as those treated above, but it can be solved,™
and the detailed arguments can be found in Reference 5. Here we shall
be content with quoting the results. However, before doing this the non-
classical counterpart of (2.15) will be written by combining (2.9) with!
(2.4). The result is
a = [K,/{1 + yi exp[(^„ - F)/kT\\]ND (2.22),
and if (2.4) is valid (2.22) should be derivable by equating n to the|
proper value of (Xd .
Since in the non-classical case a finite portion of the donor states are''
occupied by electrons, the introduction of an additional average donoi
atom is no longer equivalent to adding two independent particles whose
chemical potentials can be summed. In the statistical derivation of ni
it is therefore necessary to evaluate the total free energy of the semi-
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 545
j conductor phase, and to differentiate this with respect to No , keeping
I temperature and pressure fixed.* The result is
' ^^ = juz,+° + kT in Nd
(2 23)
j + F - kT In [1 + 2 Qx\^[- {Ed- F)/kT]]
I in which it has been assumed that the concentration of impurity is
j sufficiently low so that the solution would be ideal if the impurity could
not ionize. In the classical case the exponential in the logarithm is small
t compared to unity and (2.23) becomes identical with (2.19), as it should.
1 In the totally degenerate case the exponential dominates the unity and
we have
^^ = {^^+0 -{- Ed - kTin2] + kT (uNd
I (2.24)
= fil -{- kTin Nd
' which is the chemical potential of an un-ionized component of a dilute
j * An interesting by-product of this derivation (discussed in Reference 5) is the
I fact that the Fermi level, F, is hardly ever the Gibbs free energy per electron for
the electron assembly, although it is always the electronic chemical potential, in
1 the sense that it measures the direction of flow of electrons. This arises because
I the Gibbs free energy is not alwa3-s a homogeneous function^^ of the first degree in
; the mole numbers (electron numbers). Thus if the number of electrons in the as-
sembly is N, the Gibbs free energy, G, is given by
G =^ NF + kT Z
1
T.N
In ■-
hi
where the sum is over all energy levels, j, referred to an invariant standard level.
' V is the volume of the system, w/ is the total number of states at thejth level, and
, hj is the number of unoccupied states (holes) at the yth level. For F to be the free
! energy per electron the term involving the sum must vanish so that
But this can only happen when
N
CO; = KjV
where K^ is independent of V. This requirement is formally met in the case of the
free electron gas where the electrons have been treated as independent particles
in a box so that
CO,- = [8mo"' TT E dE/2h^V
where mo is the electron mass, and h, Plank's constant. Since this is the case most
frequently dealt with in thermodynamic problems it has been customary to think
of F as the free energy per electron, although even here the truth of the contention
depends on the assumption of particle in the box behavior.
At the other extreme, it is obvious that co, for a level corresponding to the deep
closed shell states of the atoms forming a solid cannot depend at all on the ex-
ternal volume since they are essentially localized. In computing the free energy
of the semiconductor phase it is necessary to understand carefully subtleties of
this nature.
546 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
solution, as it should be for the degenerate case in which ionization is
suppressed. Equating iid in (2.23) to n in (2.16) yields
_ jH exp [(>■„/ - M° + Bo)/kT]\ .
" - \ 1 + J/, exp [(£ - FVATJ / ^" ('-^S'
which is identical Avith (2.22) if A'o is taken to be
}i exp[(Mz>+° - M° + Eo)/kT] (2.26)
Thus one arrives at the conclusion that the law of mass action remains
valid for the heterogeneous equilibrium even when it fails for the homo-
geneous internal equilibria.
This is a fairly important result since it implies that solubilities can
give information on the behavior of the Fermi level and hence on the
distribution of electronic energy levels, even under conditions of de-
generacy.
The chemical potential specified by (2.23) is of course important in
itself, for treating any equilibrium (external or internal) in which the
donor may participate.
One last remark is in order. This concerns the treatment of heterogene-
ous equilibria involving some external phase, and the surface^^ rather than
the body of a semiconductor. In such treatments it has been customary
to compute the chemical potential of an ionizable adsorbed atom by
summing the ion chemical potential and the Fermi level, as in (2.19).
This is no more possible if the statistics of the surface states are non-
classical, then it is possible when considering non-classical situations
involving the body of the crystal. Care must therefore be exercised also
in the treatment of surface equilibria.
The above discussion has shown that there are extensive ranges of
conditions under which holes and electrons obey the law of mass action,
and behave like chemical entities. In the next section some of the con-
sequences of this fact will be developed.
III. APPLICATION OF THE MASS ACTION PRINCIPLE
Equations (2.4) through (2.8) will now be used to determine how, in
the classical case, the solubility. No , of lithium in (2.1) depends upon
Na the concentration of boron in silicon. In the experiments to be de-
scribed, the systems are classical, and the donors and acceptors there-
fore so thoroughly ionized that No can be replaced by D and Na by
A~. Insertion of (2.4) into (2.5) yields
D+n = aKoKo = K* (3.1)
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 547
since a is maintained constant. Furthermore (2.7) can be written as
np = /vi = ni (3.2)
where Wj is obviously the concentration of holes or electrons under the
condition that the two are equal. It is called the intrinsic concentration
of holes or electrons. The values of rii in germanium and silicon have been
determined by Morin.^^' ^® Fig. 2 gives plots of the logarithms of n,- in
germanium and silicon versus the reciprocals of temperature. These re-
sults are necessary for subsequent calculations.
Since A''^ and A" are assumed equal, we may dispense with (2.6).
The one remaining equation is then (2.8) which we adopt unchanged.
These three relations, (3.1), (3.2), and (2.8) are sufficient to determine
D^ or Nd as a function of A" or Na • The only undetermined parameter
in the set is K* and this can be evaluated by measuring the solubility,
D"^, in the absence of acceptor, i.e., under the condition that A~ is zero.
The symbol Do^ is used to designate this value of D'^. In Reference 6 it
is shown that
Z)/ = K*/(K* + n^y
or
K* = (Doy/2 + {{Doy/4: + ni'iDoy}'" (3.3)
Eliminating K* by the use of this relation it is further shown in Ref-
erence 6 that
A- '
1 + VI + (2n,/i)o+)^ ,^^,
V/2 (^-4)
D+ =
+
_1 + Vl + {2ni/Do+y_
+\2\
+ (Do")
which is the required relation between donor solubility and acceptor
concentration.
Examination of (3.4) reveals several simple features, the more import-
ant of which we list below:
(1) When A~ (the acceptor doping) is sufficiently large so that
{Do^Y in the second term can be ignored relative to the term in A~,
(3.4) reduces to that of a straight line with slope
Knowledge of this slope is equivalent to knowledge of Do .
(2) Wlicre the straight lino portion of the D^ \'ersus A~ curve is in-
548
THE BELL SYSTEM TECHNICAL JOURNAL, AL\Y 1956
volved, the temperature dependence of the solubiHty, D'^, enters only
through the ratio, ni/Do^ . If this ratio is very small, then
D^ ^ A~ (3.6)
and the solubility is independent of temperature. In this condition Z)"^
may approximate A~ by being either slightly less or slightly greater than
the latter. Details are given in Reference 6.
(3) Whereas D^ at small values of doping may be an increasing func-
tion of temperature, it may, depending on the system, be a decreasing
function of temperature at high dopings. Thus doping may change the
sign of the temperature coefficient of solubility. Because of this, doping
sometimes may prevent precipitation of a donor when a semiconductor
is cooled, since the latter becomes an undersaturated rather than a
supersaturated solution of impurity. Details are given in Reference 6.
(4) It is also shown in Reference 6 that for the acceptor to have any
effect on the solubility of the donor the concentration of A~ should satisfy
the following criterion
A- > (Do"*" or m) (3.7)
Do or Hi being used depending on which is greater. Obviously at high
10 '9
10
10'
18
5 '0'^
O
lO'S
10'
10
13
10
12
\
\
\
\
\
GERMA
NIUM
^
V
\
5IL
jcon\
\
\
\
i
0.001 0.002 0.003 0-004
i/TEMPERATURE in degrees KELVIN
Fig. 2 — Temperature dependences of intrinsic carrier concentrations in ger-,
manium and silicon. "ft
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 549
temperatures when rii achieves a very large value it may not be possible
to have A~ exceed n, , and no effect due to the acceptor will be observable.
This is simply a mathematical reflection of the fact that the hypothetical
compound e'^e~ in (2.1) is highly dissociated at high temperatures so that
the holes contributed by the acceptor cannot cause the exhaustion of
electrons in the solution.
In Reference 6 the system described in (2.1) was investigated for the
purpose of testing (3.4). The concentrations, Z)"*" and A~, of lithium and
boron respectively were determined by measuring the electrical resis-
tivities of the crystal specimens before and after immersion in molten
tin contaning lithium. Some typical results of these experiments are
shown in Fig. 3 which contains three Z)"*" versus A~ isotherms for the
temperatures 249°, 310°, and 404°C. For the case shown the tin phase
contained 0.18 per cent lithium by weight.
The points in the figure represent experimental findings, while the
drawn curves are based on theory. The agreement between theory and
Ij experiment is very good, in fact the overall accuracy appears to be bet-
ter than 1 per cent. These isotherms are only a few of a large group ob-
tained at different temperatures and with differently proportioned ex-
ternal phases. The accuracy in all of these is of the same order.
I Various of the features of (3.4) listed above are apparent in the curves
of Fig. 3. For example at large values of ^~ the curves are straight lines,
thus validating (3.5). Also, the inversion of the temperature coefficient
of solubility with doping is apparent for the curves cross one another,
md whereas, at low dopings (low A~) the solubility is an increasing func-
on of temperature, at high dopings it decreases with increasing tempera-
ture. Finally we note that D'^ remains more or less independent of A~
until A~ exceeds n,- , confirming (3.7). Values of n,- appear in the Figure.
The possible increases in solubility above Do^ are really quite large.
For example in Fig. 3 the largest increase is of the order of a factor of
10^ However in some experiments increases of 10 have been observed.
These effects truly represent profound interactions between impurities
which are present in highly attenuated form. Thus the number of atoms
per cubic centimeter in crystal silicon is of the order of 5 X 10 cm" .
Interactions at doping levels as low as 10^* cm~^, as appear in Fig. 3,
therefore take place at atom fraction levels of about 2 X 10 .
In Fig. 4 we show a curve of lithium solubility at room temperature
in gallium-doped germanium. The curve is wholly experimental; no
attempt has been made to apply theory. The symbols D and A~ are
once more used for the donor and acceptor. In this case the curve again
exhibits some of the general features required by (3.4). The measure-
/
550
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
10
18
17
10
r<5
o
a. io'®
UJ
Q.
+
10
,15
to''
10
,13
POINTS
-EXPERIMENTAL
THEORY
LUTE BATH
"C nL=6.16Xl0'4
Dl_
D 249
J
i
A 404 "C nL = 2.06X 10'6
J
"^
^
^
^
— ff
^
/
_
— D
y^
10"
10'
15
10"
10
,17
10^
,18
A" PER CM3
Fig. 3 — Isotherms showing the solubility of lithium Z)+, in silicon as a func-
tion of boron doping A~, for an external phase of tin containing 0.18 per cent
lithium.
ments were made by saturating gallium-doped germanium crystals with
lithium by alloying lithium to the germanium surface at a high tempera-
ture, and letting it diffuse in. Following this the crystals were cooled
and lithium was allowed to precipitate to equilibrium. In this case the
external solution is the precipitate and is of unknown composition.
If the straight line portion of the curve is used to determine D^/A~
appearing in (3.5), the value of Do"*" associated with the precipitate as an
external phase can be computed by using the value of n, obtained from
Fig. 2 for 25°C. The latter is 3 X lO'' cm"', and the measured D^/A"
is 0.85. Application of (3.5) then leads to a value of Dq'^ of 6.6 X 10^'
+
cm at 25°C. Since the highest value of D measured in Fig. 4 is 5.5 X
10 cm
, the solubility increase here shows a factor of 10 . Interaction
is already apparent at values of A~ as low as 10^ cm~*, and since there
are 4.4 X 10 cm~ atoms per cubic centimeter in pure germanium this
represents interaction at levels of atom fraction as low as 2 X 10~ .
IV. FURTHER APPLICATIONS OF THE MASS ACTION PRINCIPLE
In the last section the possibility was mentioned of inverting the sign
of the temperature coefficient of solubility, and so preventing impurity
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 551
10
19
10"
10"
5
10'-
to''
o
/
y
V
/
/
/
Y
/
A
_^
10
13
10''
10'S
10
16
10
17
10
t&
to'
|19
GALLIUM CONCENTRATION IN CM"
Fig. 4 — Room temperature isotherm showing the solubility of lithium in
germanium as a function of gallium doping, the external phase being an alloy of
lithium and germanium. The curve merely shows locus of experimental points.
precipitation which might normally occur upon cooling a crystal speci-
men. An experiment demonstrating this effect is described in Reference 6.
Two specimens of germanium, one without added acceptor, and the other
containing gallium at an estimated concentration of 1.3 X 10 cm" ,
were saturated with lithium. Table I compares the changes in lithium
content observed in these samples with the passage of time. After 25
days no apparent precipitation had occurred in the gallium doped speci-
men, while precipitation was almost complete in the other.
This result suggests a practical scheme for measuring the concentra-
tion of lithium along the solidus curve of the lithium-germanium phase
diagram, i.e., the solubility of lithium in solid germanium when the ex-
ternal phase is also composed of germanium and lithiimi, and probably
represents the liquidus phase. This measurement, though desirable, has
not been performed before because lithium, diffused into germanium at
an elevated temperature, precipitates when the specimen is cooled.
552
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
Table I
Ga Cone, (cm-s)
Li Cone, after saturation
(cm-3)
Li Cone, after 4 days
at room Temp. (cm"3)
Li Cone, after 25 days
at room Temp, (cm"')
0
1.3 X lO's
1.4 X 10i«
8.0 X 1018
9.0 X 1015
8.0 X 1018
1.1 X 1016
8.0 X 1018
Resistivities then measure only the dissolved lithium although the true
solubility at the temperature of saturation includes the precipitated
material.
However, we have seen that germanium suitably doped with gallium
will not lose lithium by precipitation. Therefore the experiment might
be performed in doped germanium. The only difficulty with this sugges-
tion lies in the fact that doping chayiges the solubility. This objection can
be overcome through use of (3.4). In terms of that equation D'^ would
be measured in the presence of gallium whereas Do"^, the solubility in
undoped germanium, is required. But according to (3.4) if Z) , n, , and
A~ (gallium concentration) are known Do"*" can be computed. In fact
solving (3.4) for Do yields
^+
D^(D-^ - A-)
+
Do"- =
/
D^iD"- - A-)
+ (Dyn,'
V'
rii +
D^{D^ - A~)
+
/
Z)^(D^ - A-)
-\ 2
(4.1) i
+\2 2
+ aryn^
The plan is therefore self-evident. Samples of germanium of known !
suitable gallium contents A~ are to be saturated with lithium at various \
temperatures. If a judicious choice of gallium content is made the lith-
ium will not precipitate when the specimen is cooled. Therefore the value *
of D^ characteristic of the saturation temperature can be determined '
through resistivity measurements performed at room temperature.
Taking nj from Fig. 2 it then becomes possible to calculate Do using
(4.1). I
The crystal specimens employed were cut in the form of small rec-l
tangular wafers of dimensions, approximately 1 cm X 0.4 cm X 0.1 cm. "
On the surfaces of these, small filings of lithium were distributed densely
enough so that their average separation was less than the half thickness
of the specimen's smallest dimension. The filings Avere alloyed to the
germanium specimen by heating in dry helium for 30 seconds at 530°C. ■
Then the crystals w^ere permitted to saturate with lithium by diffusion
from the alloy at some chosen lower temperature. After the period of
saturation which ranged from one half hour to as long as 1G8 days, de-
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 553
Table II
T°C.
po ohm cm
A- (cm-3)
p ohm (cm)
Z>+cm-3
I»o+ (cm-')
25
6.6 X 10"
100
0.0523
2.2 X 10''
0.0735
.9 X 10i«
2.5 X 10'^
200
0.44
1.3 X 10i«
0.90
7.8 X 1015
4.6 X lOK*
250
0.1494
4.7 X 1016
0 652
3.9 X 10>6
2.6 X 1016
300
0.042
2.9 X 10''
O.IOS
2.15 X 10"
7.3 X 1016
500
0.00614
4.5 X lO's
0.0340
4.13 X lO's
1 7 X 1018
608
0.00577
5.0 X IQis
0.049
4.78 X 10i«
2.8 X 1018
650
0.00584
4.3 X W
0.0178
3.75 X lO's
2.4 X lO's
pending on the temperature, the specimen surface was lapped smooth
with carborundum paper. Resistivities were then measured by means of
a two point probe.
Table II collects the data showing T, the temperature of saturation
in degrees centigrade, po the resistivity before saturation, .4" the gallium
concentration computed from po, p the resistivity after saturation, and
D^ the lithium concentration computed from p. The final column shows
Do"^ computed using (4.1) and Fig. 2.
In Table II the 25°C value of Dq^ has been taken as the value com-
puted in section III in connection with Fig. 4. It might be thought (in
view of a later section in this paper) that the 25° and 100°C values of
Do are not as reliable as the others because at the low temperatures
involved the solubility of lithium may be influenced by ion pairing as
well as electron-hole equilibria. However, Appendix A shows that the
possible error is small.
In Fig. 5 Dq^ is plotted against temperature using these data. The plot
is the curve labeled GaT = 0, and the open circles were obtained by in-
serting the measured D^ values (crosses) into (4.1). We notice that the
curve has a maximum in the neighborhood of 600°C. The occurrence of
a maximum, is a necessity if Dq^ is to pass to zero, as it must at the
melting point of germanium. It is also worth noticing that Do"*" near
room temperature lies in the range of order 10^^ cm~^, but that its meas-
urement has been effected at concentrations as high as 10^^ cm~^ This
! illustrates another application of the electron-hole equilibrium, namely
in the determination of solubilities.
\18
and 10 cm
This
3
With Do in our possession it is interesting to return to (3.4) and to
calculate D^ as a function of temperature for various levels of A
has been done for values of A" equal to 10^^ 10^ ^ 10^^,
The curves so obtained appear in Fig. 5, labeled Ga" = 10'", 10'°, 10
1 10 cm" , respectively. Their most striking common feature is the mini-
I mum which appears below 200°C. This minimum introduces a new prob-
<i&
17
554
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
16
lem in preparing samples without precipitate. Thus consider the A~ =
curve. Suppose the specimen is saturated at 200°C. Then
D^ after satura-
However, as the sample is cooled it will tend,
at first, to become supersaturated. For example it will achieve its maxi
mum supersaturation at about 140°C. where the minimum of the 10
~^ - Thereafter it will return to its undersaturated state.
could be supported,
lithium atoms.
Some of these may have precipitated as the cooling process passed
through the minimum, so that sufficient time must be provided for the
process of re-solution.
If the original saturation had taken place at 250°C, the concentration
inl6 -3
1 0 cm
according to Fig. 5, if A" for the specimen is 10 cm~
tion will be 7 X 10 cm"
cm curve appears.
In fact at 25°C a concentration of 9.3 X 10^^ cm"^
whereas the solution contains no more than 7 X 10 cm"
10
19
10
n
I
u
2 10'
18
17
Z
o
<
cr
(-
z
LU
u
z
o
o
10
16
10
15
10
H
10
,13
Ga IN
;
X
< 1
X
CM-3 =
io'«
•^
^^
-^
X
to'^
^
/
/
\
<
^J
V
X
■"^ — ^
/
io'6
«/
^
//
X \
10'^
1
J
x\
J
/
0./
if
T\ \ F
CRY
/
CAL
FOR
1
CULAT "
Ga =
1
ED
1
■
100
200 300 400 500
TEMPERATURE IN ° C
600 700
Fig. 5 — Solubility of lithium in germanium as a function of temperature for
various gallium dopings. The external phase is an alloy of lithium and germanium.
The broken line is the locus of the points (circles) calculated from equation (4.1)
for zero gallium concentration. The values of A' and Z)+, used in applying (4.1),^
correspond to the points shown by X iu the illustration. See Table II.
CHEMICAL INTERACTIONS AMONG DEFECTS IN Gg AND Si 555
of lithium would have been 2.4 X 10 cm~^. Since this exceeds the 9.3 X
10^^ cm" supportable at 25°C, such a sample would have contained some
precipitate. It was important to avoid these various pitfalls in preparing
the specimens used in the above study. Care was taken to insure that this
was the case.
We now turn to another application of the electron-hole equilibrium.
It has been emphasized that just as a fixed acceptor will increase the
solubility of lithium in silicon, a fixed donor should decrease it. In fact
in a crystal containing a p-n junction" the solubility should be above nor-
mal on the p side and below normal on the n side. The built-in field^^
which exists at the junction is a reflection of this difference in solubility,
for if it M^ere not present the concentration gradient created by the dis-
parity in solubilities would cause the lithium to diffuse from the p to the
n side until its concentration was uniform throughout the crystal. Ob-
viously this field is in such a direction as to cause lithium ions to move
back to the p side.*
Now in both silicon and germanium the oxide layers on the surface
can react readily with dissolved lithium. As a result the surface behaves
as a sink, and at temperatures as low as room temperature lithium is lost
to the surface from the body of the crystal. At higher temperatures the
body of the crystal can be exhausted of lithium in a few minutes. There
are many experiments which one would like to perform in which the
crystal must be maintained without loss of lithium at an elevated tem-
perature for long periods of time.
The application now to be discussed involves utilization of the built-in
field at a p-n junction to prevent lithium from reaching the surface where
* The distribution of lithium in the space charge region of a p-n junction cannot
be computed by the methods advanced thus far. This is because the charge neu-
trality condition (2.8) is no longer valid. Instead the concentration of lithium is
determined by Boltzmann's law,-' and is given by
D+ = D^+exp [- qV/kT]
where q is the charge on a lithium ion, V is the local electrostatic potential, and
D^:'*' is the concentration where V is zero.
V itself must be determined from Poisson's equation^"
V^V =
K
where p is the local charge density and k is the dielectric constant of the medium.
In semiconductors p is given in terms of V by'^
P = q[H + D+ - 2ni sinh (qV/kT)]
= q[H + D^+ exp [- qV/kT] - 2ni sinh (qV/kT)]
where H is the local density of fixed donors less the local density of fixed acceptors.
556
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
it can attack the oxide. Two specimens of 0.34 ohm cm p-type silicon
doped with boron were cut from adjacent parts of a crystal. Each
specimen w^as about 1 cm long, 0.2 cm wide, and 0.15-cm thick. The
samples were lapped on No. 400 silicon carbide paper, etched in HF and
HNO3 and sealed in helium-flushed evacuated quartz tubes, one con-
taining a small grain of P2O5 . The tubes were then heated at 1,200°C.
for 24 hours. This treatment introduced an n-type layer, highly doped
with phosphorus and about 0.001-cm thick, into the surface regions of
the specimen in the tube containing P2O5 . Upon removal from the tube
this specimen was lapped on the end to remove the n-skin. Complete
removal was determined by testing with a thermal probe.
Small cubes of lithium (0.038 cm on a side) were placed on the ends of
both samples (the lapped end of phosphorus-doped one) and alloyed to
the silicon for 30 seconds at 650°C in an atmosphere of dry helium. After
this treatment the various junction contours should have looked like
those in Fig. 6, in which the bottom crystal is shown with the phosphorus-
doped skin (cross hatched). During the alloying process a small amount
of spherical diffusion of lithium occurs so that small hemispherical
n-regions form with the alloy beads as origins. These are shown in Fig. 6.
Next the specimens were heated in vacuum for about six hours at
400°C. Diffusion of lithium into the body of the crystal should occur
during this period. However in the sample not protected by the n-type
skin lithium should leak to the oxide sink on the surface so that the
n-type region due to the lithium should have the pear-shaped contour
shown in the upper part of Fig. 7. If the built-in field at the p-n junction
Fig. 6 — Initial stage following alloying in the diffusion experiment to demon , S
strate the impermeability to lithium of a heavily doped n-type skin on silicon.
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 557
formed by the phosphorus layer prevents lithium from reaching the sur-
face, diffusion in the sample with the skin should be plane parallel with a
straight front (except at the rear where the skin has been lapped off and
lithium can leak out) as the p-n junction contour in the lower part of
Fig. 7 indicates.
An acid staining technique " which reveals the junction contours should
then develop a picture resembling Fig. 7. The two specimens were cut
along their long axes and the stain applied to the newly exposed sur-
faces. The result has been photographed and is shown in Fig. 8 where
the crystal on the right has the n-skin. The p-regions show up dark and
the n, light. The result agrees wdth Fig. 7.
In another experiment a crystal completely enclosed in a phosphorus
skin was immersed in the tin bath described in Section III. It was dis-
covered that lithium entered the crystal with no evident difficulty, just
as though the skin were absent, but once in, could not be driven out by
removal of the external source and continued heating. The implication is
clear. The built-in field has a rectifying action permitting the lithium to
enter the crystal but not to leave. In this sense it performs the same func-
tion for the mobile lithium ions as it does for holes in a p-n junction
diode.''
V. COMPLEX ION FORMATION
In the previous text processes involving the interaction of electrons
and holes have been considered. In this section attention will be drawn,
JoCn>o<xxx><^0<><>^6^^^\:SX\\«^
Fig. 7 — Distribution of lithium after an extended period of diffusion at a
temperature lower than the alloying temperature — showing leakage out of the
crystal in the one case (no-skin) and conservation in the other.
558
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
Fig. 8 — Photograph of experimental situation described schematically in
Fig. 7.
to the possibility of interactions between the donor and acceptor ions
themselves. For example, in (2.1) direct interaction of Li^ and B" above
600°C may be possible, especially in view of the mobility of Li^ . Such
a reaction was indicated in the work of Reiss, Fuller, and Pietruszkie-
34
wicz.
Fig. 9 is of assistance in understanding the nature of these observa-
tions. In it are shown plots of the solubility of lithium in silicon. In this
case the situation is similar to that involved in the germanium curves
of Fig. 5 because the external phase is composed of silicon and lithium
and is probably of the liquidus composition. It is formed by simply
alloying lithium to the silicon surface. In Fig. 9, Curve A, illustrates
how solubility depends on temperature when the silicon is undoped.
Curve B, unlike A, is not an experimental plot, i.e., it is not supposed
to represent the locus of the points through which it seems to pass. In-
stead it has been calculated from the theory expounded below. The points
themselves are experimental and represent solubility measurements on
silicon doped with boron to the level 1.9 X 10 cm"
I
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 559
Curve A possesses a maximum (just as the Dq^ curve of Fig. 5) in the
neighborhood of 650°C. A marked disparity is apparent between solu-
bihties in undoped and doped sihcon, the sohibiHty in the latter bemg
greater. Below 500°C this disparity is easily understood. It stems from
the electron-hole equilibrium considered previously. However the high
solubility in doped silicon at high temperatures is not explicable on this
basis since the crystal becomes intrinsic, and e'^e~ is mostly dissociated.
To account for this phenomenon Reiss, Fuller, and Pietruszkiewicz
invoked the idea of interaction between Li'^ and B". They presented
the following argument.
At low temperatures lithium ions occupy the interstices of the silicon
• 1 EXPERIMENTAL
/\
/•••^
p
9
B
7 / \\
^ v\
1
/
\\
7
L
r
\ \
11
\\
t
6
11
h
V \
^ / /
I \
b//
\
/
/A
•
3
/
/
\
/
1
\
/ i
1
° \
y
•
^
/
o
O
c
) 1
1
1
1
1
\
\
\
\
\
•
•
1/
•
\
9
J
\
•
i
\
\
8
7
/
/
I
\
/
\
/
\
/
/
^
/
r
\
t
1
\
•\
2
200
400 600 800 1000
TEMPERATURE IN DEGREES CENTIGRADE
1200
Fig. 0 — Plots showing the soluliilitj' of lithium in silicon us a function of tem-
perature. The external phase is an alloy of lithium and silicon. Curve A is for un-
doped silicon. The locus of the points in B is for silicon doped with about 1.9 X 10^*
cm~^ boron.
560
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
lattice as in Fig. 10. In an interstitial position lithium can approach an
oppositely charged boron, but the interaction will be, at the most,
coulombic so that an ion pair will form (see later sections). A covalent
bond is unable to appear not only because there are no electrons avail-
able for it, but also because the lithium ion cannot move to a position
where it can satisfy the tetrahedral symmetry inherent in sp^ hybridiza-
tion. Calculations (of the sort appearing in the later sections of this
paper) show that at high temperatures, at the ion densities involved,
ion pairs of the kind depicted in Fig. 10 are completely dissociated.
Suppose, however, that as temperature is raised vacancies dissolve
in the silicon lattice, and that one such vacancy occupies a position near
Fig. 10 — Schematic diagram of a silicon lattice showing a lithium ion in an
interstitial position near a substitutional boron ion, as it occurs in an ion pair.
a boron ion, as in Fig. 11, a slight modification of Fig. 10 in which the
dots represent electrons (dangling bonds). Unpaired electrons such as
these might capture an electron from the valence band of silicon so that
the vacancy acquires a negative charge and behaves like an acceptor.
It is reasonable to suppose that the positive lithium ion will move into
this negative vacancy, in the tetrahedral position, and form a covalent
bond as in Fig. 11. The lithium-boron complex so formed retains a nega-
tive charge and is thus a complex ion. If the specimen were extrinsic at
these high temperatures, there would still appear to be as many net
acceptors as before the addition of lithium.*
If the LiB~ compound is stable enough (a question to which we shall
* It is possible that rapid cooling may quench some of these LiB acceptors into
the crystal at room temperature. If this is so it should be possible to investigate
the associated energy level by Hall measurements in the interval of time before '
the complexes anneal out. Similar phenomena might be observed in germanium.
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 561
return below) to hold the lithium atom, the solubility of lithium will be
determined principally by the density of boron atoms. At low tempera-
tures, \-a(*an('ies are reabsorbed and the lithium atoms return to their
interstitial positions, at quenched-in densities corresponding to the tem-
peratures of equilibration. However, boron acceptors now appear to be
compensated since interstitial lithium behaves as a donor. This renders
it feasible to measure the concentration of lithium by the determination
of resistivity.
The overall reaction may be written in the form
w^ + B^ + n + t" -
= LiB~ (5.1)
in which D represents a vacancy. This equilibrium can be grafted onto
(2.1) so that the latter becomes (ignoring un-
ionized lithium and boron)
Li (external) <r^ Li^ +
e~
+
+
B- -f
e-^
+
' *
D
eV (5.2)
+
e
T
LiB~
The original vertical equilibrium involving holes and electrons loses its
significance at high temperatures, and the new vertical reaction becomes
important, for both D and e~ appear in increased concentrations. In this
way a certain amount of symmetry, insofar as temperature is concerned,
is introduced into the problem, i.e., as one equilibrium ceases to dominate
SL SL SL SL SL SL
v\/ \/\.
B Sl B SL
• • \ ::! / \ •
SL LL"^ □ SL SL LL ^SL
. . / -e \ . .
SL SL SL SL
SL St SL SL SL
Fig. 11- — Schematic diagram illustrating the reaction in (5.1). The square
nqjresents the center of a vacancj^ and the dots, electrons left unpaired by the oc-
currence of the vacancy.
562 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
the system the other begins to take effect. This symmetry, of course, is
necessary for explaining the symmetrical locus of the points around Curve
B in Fig. 9.
The scheme (5.2) can be treated quantitatively by applying the mass
action principle, but now the symbol D^ can not be used for the solu-
bility of lithium since the totality of dissolved lithium is distributed
between LiE~ and Li^, and the symbol only applies to the latter. We
therefore denote the total concentration of lithium by No , and the con-
centration of LiB" by C. Then
No = D^ + C (5.3)
The same argument applies to boron, so that its total concentration will
be designated by
Na = A- + C (5.4)
The problem then reduces to specifying No as a function of Na • To
accomplish this, to (3.1) and (3.2) is added the mass action expression
going with (5.1)
""^ = ^e-w-) = ^ (5,5)
D+A-n
where 7 and jS are constants. It has been assumed that the vacancy con-
centration follows a temperature law of the form 7* exp[ — ^*/T] where ^
7* and ;S* like 7 and ^ are constants. This permits the equilibrium con-
stant when multiplied by the vacancy concentration to assume the form
7 exp[ — /S/r] shown in (5.5). In place of (2.8) a new conservation condi-
tion,
D^-\-p = C+A- + n (5.6)
is introduced. The combination (3.1), (3.2), (5.3), (5.4), (5.5) and (5.6)
can be solved so that No , the lithium solubility appears as a function of
the total boron concentration A^^ . Thus
^" - 1 + Vl + (2n,/No^y + y {1 + Vl + (2n,/iV.o) j + ^^^""^'
^_ TNANpyjl + Vl + {2n~/N7)']
2 -I- wiNo'fil + Vl + (27ii/No'y\
In this equation No like Do in (3.4) is the solubility of lithium in un-
doped silicon, i.e., in silicon from which boron is absent.
All the parameters in (5.7) are independently measurable save x
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 563
which can be known for all temperatures when 7 and jS have been deter-
mined. Reiss, Fuller, and Pietruszkiewicz used two of the points near
Curve B in Fig. 9, above 1,000°C, to define values of No for use in (5.7).
Then t was computed from (5.7) at these two temperatures. From these
values of t, 7 and (3 were determined, and from these, in turn, w was
calculated for all temperatures down to 200°C. Using t, Nd was computed
from (5.7) over the entire experimental range of temperature. The result
is Curve B of Fig. 9 which fits the experimental points very well.
Another check on the validity of the theory (which has not yet been
accomplished) would be the following. At high temperatures (5.7) re-
duces to
^. = i^.« + |^^^^f4L+^ (5.8)
l2 + TiN^yil + Vl + (2n,/A^z,o)2]J
i.e., Nd is a linear function of Na with the slope (in brackets) depending
upon X. Measurement of this slope at one temperature would thus pro-
vide an independent evaluation of tt.
A little thought concerning the scheme outlined in (5.2) leads one to
wonder why the introduction of boron really increases the solubility of
lithium because the same mechanism could be applied to the case in
which boron is absent, i.e., to Curve A of Fig. 9. Thus, if B~ is replaced
by a silicon atom in Figs. 10 and 11, the entire scheme can be adopted
unchanged, except that Si replaces B~. Thus
Li (external) <=± Li"^ -{- e~
^ + +
Si + e+
+ Ti
D eV (5.9)
-f
e
u
LiSi
and one wonders why LiB~ should be more stable than Li Si. A possible
answer is the following:
The tetrahedral covalent radius of boron is 0.88 A. This is to be con-
trasted with the tetrahedral radius of silicon which is 1.17 A. When
boron is substituted in the silicon lattice it therefore produces consider-
able local compressive strain. This strain is partially relieved when a
\ acancy is formed adjacent to the boron. Thus the energy required to
form a vacancy near a boron ion in silicon is less than is required for its
564 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
formation near a silicon atom. Hence the endothermal heat of formation
of LiB" in (5.2) is reduced substantially (by the amount of the released
energy of elastic strain) below the heat of formation of LiSi. This ac-
counts for the greater stability of the former.
The compressive strain around a substitutional boron in germanium
is also illustrated by ion pairing studies to be described later in Section
XII. Its action in that case keeps the ions which form a pair from ap-
proaching each other as closely as they otherwise might. Although really
quantitative studies of pairing have not yet been performed in silicon,
the lattice parameters of germanium and silicon are sufficiently close to
render it fairly certain that the same strain exists in the latter as in the
former. This lends support to the previous argument.
Before closing this section there is another related topic which is worth
mentioning. This concerns part of the explanation of the retrograde solu-
bility observable in the curves of Figs. 5 and 9, i.e., the occurrence of the
maxima. The solubilities along these curves are given by (3.3) in the form
Suppose that at low temperatures K* is an increasing function of tem-
perature and considerably larger than Ui . Then we have the approxima-
tion
A"" = (K*f' (5.10)
in which the solubility Do^ must increase with temperature. If Ui in-
creases more rapidly than K* with temperature, a point will be reached
at which nf in the denominator of the (3.3) in its special form above,
exceeds K* by so much that the latter can be ignored. When this is so
another approximation holds,
J. K*
Do"- = — (5.11)
rii
in which Do"*" decreases with temperature since rii increases more rapidly
than K*. Since (5.10) predicts an increase in solubility with temperatmc
at low temperatures and (5.11) a decrease at higher temperatures a
maximum occurs somewhere between. The maximum may not be due to
this cause alone, however. For example K* contains the activity, a, in
the external phase, and this may vary with temperature in an erratic
manner.
In any event the influence of the electron-hole equilibrium on Z)o^ in
both'silicon and germanium cannot be ignored. The fact that the distri-
bution coefficients of donors and acceptors in silicon are usually some
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 565
ten-fold greater than in germanium may be due to the smaller width of
the forbidden gap in the latter. This makes for greater values of n,- and
according to (3.3) smaller values of Do^.
VI. ION PAIRING
The preceding text drew an analogy between semiconductors and
aqueous solutions — phenomena such as neutralization, common ion ef-
fects, and complex formation have been discussed. Another feature of
"wet" chemistry which has appealed to chemists concerns the influence
of coulomb forces among ions on the properties of solutions. This subject
is of peculiar interest because such forces are well understood, and con-
siderable progress can be made in the quantitative prediction of their
effects.
The first really successful theoretical treatment of coulomb forces in
solution is the Debye-Hiickel theory.^'' This treatment recognizes the
long range character of coulomb forces, and endeavors to account for
their effects in terms of a communal interaction involving all of the ions
in solution. The theory has now been shown to include certain statistical
inconsistencies^^ which, however, are of small consequence in dilute solu-
tions where theory and experiment are in excellent agreement.
The central feature of the Debye-Hiickel theory is the concept of the
ionic atmosphere, i.e., the time average excess concentration of ions of
opposite sign which accumulates in the neighborhood of a particular ion.
The radius of this atmosphere is measured (order of magnitude-wise) by
the now famous Debye length.
" ys7q
87rgW
(6.1)
ill which K is the dielectric constant of the medium, q is the charge on an
ion, and N is the (in this case identical) concentration of both positive
and negative ions. As k decreases or N increases, L becomes smaller so
that the atmosphere is more tightly gathered in. As this process continues
a stage is reached in which the atmospheres of some of the ions may
be best thought of as being fully constituted by a single ion of opposite
sign, i.e., an ion pair forms. This pair-wise interaction is so intense rela-
tive to the communal interaction mentioned above, that insofar as the
paired ions are concerned it may be regarded as the only interaction in-
fluencing the distribution of the pairs themselves. Unpaired ions may still
be treated by the communal Debye-Hiickel theory but their concentra-
tion must be considered as the true concentration of ions reduced by the
566 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
concentration of pairs since tlie latter possess effectively no fields. In any
event when pairing occurs the Debye-Hiickel effects are relatively second
order, since, even normally, they represent quite small deviations from
ideal solution behavior. Under pairing conditions it is desirable, in the
first approximation, to focus one's attention on the pairing interaction.
While developing the aqueous solution analogy inherent in our semi-
conductor model it is natural to inquire whether or not a system like
(2.1), in which at least one of the ions can move, will show effects due to
coulomb interaction. A preliminary calculation using (6.1) indicates
that if coulomb effects are to be observed they are likely to be of the ion
pairing variety rather than of the Debye-Huckel type because the dielec-
tric constants of semiconductors are low relative to that of water, e.g.,
12 for silicon^^ and 16 for germanium^'' as against 80 for water .^^ The
dominance of ion pairing stems, as it will become clear later, from still
another feature peculiar to semiconductors. This is the closeness with
which two ions of opposite sign can approach one another in semicon-
ductors. In any event experiments are not yet at the stage of sensitivity
necessary for the accurate measurement of the small Debye-Hiickel
effects so that we are virtually compelled to ignore such phenomena.
Fig. 10 is a picture of an ion pair in boron-doped silicon. Corresponding
to this process one may sketch in another vertical equilibrium in (2.1)
to yield (ignoring un-ionized Li)
Li (external) ^ Li'^ + e~
+ +
B- + e"^ (6.2)
u u
[Li-^B-] eV
where [Li'^B~] stands for the ion pair in which the individual ions main-
tain their polar identities and the binding energy is coulombic. The ion
pair is a compound in a statistical sense since as will be seen later the dis
tance between the ions of a pair is distributed over a range of values. The ■
interaction between Li'^ and B~ is to be distinguished from that sho\\ii
in (5.2). The latter occurs at high temperatures whereas the former is
presumably limited to low temperatures, below 300°C.
The quantitative aspects of ion pairing were first considered by Bjer- _
rum and later by Fuoss^^ who placed Bjerrum's theory on a somewhat
more acceptable basis. Fuoss's theory, however, suffers from some of the
same limitations as Bjerrum's. Nevertheless the Bjerrum-Fuoss theory is
capable of satisfying experimental data over broad ranges of conditions.
In the next section w^e present a brief resume of this theory together with
relevant criticism and its relation to a more refined theory due to Reiss.
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 567
VII. THEORIES OF ION PAIRING
Fuoss begins by considering a solution of dielectric constant k, con-
taining equal concentrations, A'', of ions of opposite sign. When equilib-
rium has been achieved each negative ion will have another ion (most
probably positive) as a nearest neighbor, a distance r away from it.
Fuoss discounts the possibility that the nearest neighbor will be another
negative ion, and proceeds to calculate what fraction of such nearest
neighbors lies in spherical shells of volumes, ixr^ dr, having the negative
ions at their origins. If this fraction is denoted by g{r) dr, it may be evalu-
ated as follows.
In order for the nearest neighbor to be located in the volume, Airr" dr,
two events must take place simultaneously. First the volume, 47rr /3,
enclosed by the spherical shell must be devoid of ions, or else the ion in
the shell would 7iot be the nearest neighbor. Since g(x)dx is the proba-
bility that a nearest neighbor lies in the shell, ^TX^dx, the probability
that a nearest neighbor does not lie in this shell is 1 — g(x)dx. From this
it is easily seen that the chance that the volume 47rrV3 is empty is
E(r) = I - f gix) dx (7.1)
where a is the distance separating the centers of the two ions of opposite
sign when they have approached each other as closely as possible.
The second event which must take place is the occupation of the shell
;: 47rr^ dr by any positive ion. The chance of this event depends on the time
average concentration of positive ions at r. This concentration is bound
to exceed the normal concentration A^ by an amount depending on r,
because of the attractive effect of the negative ion at the origin. It may
be designated by c{r). The probability in question is then
47rr'c(r) dr (7.2)
The chance g{r) dr that the nearest neighbor lies in the shell A-wr dr is
therefore the product of (7.1) by (7.2), i.e., the product of the proba-
bilities of the two events required to occur simultaneously. This leads
to the relation
g{r) = (l - £ gix) dA ^^^Mr) (7.3)
an integral equation whose solution is
g(r) = exp — 47r / x^cix) dx 4Trr^c(r) (7.4)
Ja
568
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
4.S
40
3.5
3.0
X10^
j^
— -v
/
N
\
/
\
/
\
B2.5
1
\
f
Y
Z
g2.0
en
\
\
1.6
— s
k
1.0
0.5
7
\
/
\.
0
^
^
'
05 1.0 1.5 20 2.5 3.0 3.5 4.0
r IN CENTIMETERS
4.5
5.0
5.5
6.0
X10~^
Fig. 12 — Distribution of nearest neighbors in a random assembly of particles
for a concentration of 10^^ cm~^.
That (7.4) solves (7.3) is easily demonstrated by substitution of the
latter into the former.
If there were no forces of attraction between ions then c{r) would
equal N, and if a is take equal to zero (7.4) reduces to
g{r) = 47rr'A^exp(-47rr'A^/3) (7.5)
This function is plotted in Fig. 12 for the case N = 10^^ cm~^ Note that
the position of the maximum, the most probable distance of location of a
nearest neighbor, occurs near the value of r equal to (3/47rA^)^'^ This is
the radius of the average volume per particle when the concentration is
N, i.e. the volume, 1/A^.
In order to write g{r) for the case of coulombic interaction it is neces-
sary to compute c(r) under these conditions. Fuoss (after Bjerrum) rea-
soned as follows. If a theory can be constructed which depends only upon
the characteristics of near nearest neighbors (nearest neighbors at small
values of r) then the force of interaction experienced by the nearest
neighbor can be assumed to originate completely in the coulomb field of
the negative ion at the origin. This is predicated on the argument that
both positive and negative ions develop atmospheres of opposite sign
which are superposed when the two ions are close to one another. The
result is a cancellation of the net atmosphere leaving nothing for the two
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 569
ions to interact with but themselves. Thus the potential energy of inter-
action, for near nearest neighbors will be
- - (7.6)
KV
For small values of r, therefore, c(r) can be derived from Boltzmann's
law and is given by
c(r) = hexp[q-/KkTr] (7.7)
where his a constant. Guided by the requirement that c(r) should equal
A^ at infinite distance from the central negative ion, h was set equal to
N giving, finally,
c{r) = N exp [g'/KkTr] (7.8)
The assumption that a theory could be developed depending only on
near nearest neighbors proved reasonable, but the choice of /t = A'' in
(7.8) leads to certain logical diflEiculties. Thus the average volume domi-
nated by a given negative ion is evidently 1/A^. If (7.8) is summed over
this volume the result, representing the number of positive ions in 1/A'',
should be unity since there are equal numbers of positive and negative
ions. Unfortunately, the i-esult exceeds unity by very large amounts ex-
cept for very small values of iV, i.e., for veiy dilute solutions. We shall
return to this point later.
If (7.8) is inserted into (7.4) the resulting g{r) has the form typified
by Fig. 13. First, there is an exponential maximum occurring at r = a,
followed bj^ a long low minimum, and this by another maximum which
like the one in Fig. 12 occurs, not far from r = (3/47rA'')*'^, if N is not
too large. For small values of N the minimum occurs at
r = h = q/2KkT (7.9)
The function g{r) is actually normalized in (7.4) so that the area under
the curve is unity. The second maximum corresponds to the most proba-
ble position for a nearest neighbor in a random assembly, i.e., to the maxi-
mum in Fig. 12. Essentially the first maximum has been grafted onto
Fig. 12 by the interaction at close range which makes it probable that
short range neighbors will exist. At high values of N the region under the
first maximum becomes so great that enough area is drained (by the con-
dition of normalization) from the second maximum to make it disappear
entirely. At this point the minimum is replaced by a point of inflection.
More will be said concerning this phenomenon later.
Fuoss chooses to define all sets of nearest neighbors inside the mini-
570
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
Fig. 13 — Schematic distribution of neighbors in an assembl}- of particles when
forces of interaction are present. Repulsive forces are reflected in the appearance
of a distance a, of closest approach of two particles, attractive forces b}- the ex-
ponential ma.ximum at a .
mum, i.e., inside 6 = 5 /2k/cT', as ion pairs, and the rest as unpaired. Noj
thought is given to the small fraction of nearest neighbors which involvesi
ions of like sign, as it must be small inside r = h. Nor is any thought
given to the possibility that a given positive nearest neighbor may be the
nearest neighbor of two negative ions simultaneously. Such a coincidence
would be very improbable at a distance short enough to be within r = b.
Thus if the entire theory can be made to depend on what happens inside
b, its foundations are reasonable, except for the choice oi h = N.
To obviate this difficulty Fuoss had further to devise a means of per-
forming all calculations under conditions where the choice of /i = iVi
was not inconsistent. He assumed (following Bjerrum) that paired and
unpaired ions were in dynamic equilibrium and that the law of mass ac-
tion could be applied to this equilibrium. Thus if P represents the con-|
centration of pairs, N — P denotes the concentration of unpaired ions of;
one sign and the mass action expression is
P
(N - py
= fi
(7.10)1
where Q, is an equilibrium constant independent of concentration. At
infinite dilution, where the assignment h = N is valid, U should be the'
same as at higher concentrations. Therefore (7.4) can be used to evalu-'
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 571
ate 12 at infinite dilution, and the value so obtained employed at higher
concentrations.
Besides the inconsistency of the choice, h = N, the form (7.4) contains
another objectionable feature. This is revealed by a more rigorous treat-
ment devised recently by Reiss, and has to do with the factor,
exp [— 47r / x^c(r) dx],
Ja
in (7.4). It can be shown that this factor is inconsistent with the suppo-
sition that the nearest neighbor to a given negative ion interacts only
with that ion and no other. Fortunately, in Fuoss's scheme g(r) given by
(7.4) needs to be used only at infinite dilution, and then only for such
values of r as lie inside h. Under this condition and in this range the ex-
ponential factor in question can be replaced by unity from which it de-
viates only slightly. Thus the form of g(r) used eventually is
g(r) = Awf^N exp [q^KkTr-] (7.11)
U is computed as follows. At infinite dilution P tends toward zero so
that (7.10) becomes
^ = fiA^ (7.12)
But P/N is the fraction of ions paired which by definition is the fraction
of nearest neighbors lying inside r ^ h. From the definition of g{r),
P/N is evidently given by
^ = I g(r) dr = 4.tN [ r' exp [q^KkTr] dr (7.13)
iV Ja "a
which upon substitution in (7.12) yields
j^ = 47r f r' exp [q'/KkTr] dr (7.14)
The evaluation of 0 in this way permits one to base the entire theory on
the distribution of near nearest neighbors, so that all the assumptions
\\hich demand this procedure are validated.
Using the computed 12 in (7.10) P can be evaluated, and also N — P
which as the concentration of free ions of one species measures the ther-
modynamic activity of that species. In this manner it is possible to calcu-
late the equilibrium effects of coulomb interaction insofar as solution
properties are concerned. To treat transport phenomena such as ionic
mobility in an applied electric field Fuoss assumes that paired ions repre-
572 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
senting neutral complexes are unable to respond to the applied field and
so do not contribute to the overall mobility. The mobility of unpaired
ions is assumed to be no , the mobility observable at infinite dilution. The
apparent mobility n at any finite concentration is then no reduced by
the fraction P/N of ions paired. Thus
M = [1 - iP/N)U (7.15)
The Bjerrum-Fuoss theory when applied to real systems reproduces
the experimental data very well, although the parameter a, the distance
of closest approach, needs to be determined from the data itself. :
The concept of a pair defined in terms of the minimum occurring at b,
becomes rather vague when that minimum vanishes in favor of a point
of inflection. At this stage triplets and other higher order clusters form;
and the situation becomes very complicated.
In Reference 44, Reiss has developed a more refined theory of pairing.
Instead of avoiding the use of an inconsistent g(r) by introduction of the
mass action principle, an attempt is made to provide a rigorous form for
g(r), which proves to be the following
g(r) = exp [-47rr^A^/3] 47rr\ exp [q^/KkTr] (7.16)
in which
!
h = I / j exp [- 47rr'i\r/3] 4xr' exp [q'/KkTr] dr (7.17) i
It is also shown that the activity of an ionic species, measured by A^ — P
in the Bjerrum-Fuoss theory, is measured by y/hN in the more rigorous ,
theory. The distribution (7.16) suffers neither from an inability to con-d
serve charge in the volume 1/N (as does (7.4)) nor from any inconsistency
involving the interaction of a nearest neighbor with other ions than the
one to which it is nearest neighbor [as does (7.4)].
When -s/hN computed by (7.17) is compared with {N — P) computed
according to (7.10) and (7.14), for arbitrary values of /c, a, T, and N,
the results are almost identical. This shows the virtue of the Bjerrum-
Fuoss theory, and in fact, suggests that in most cases it should be used
for calculation rather than the more refined theory, for the latter involves
rather complicated numerical procedures.
The refined theory can also be adapted to the treatment of transport
phenomena. Thus in place of g{r) it is possible to write a distribution
function r(r), specifying the fraction of nearest neighbors lying in the \o\-
ume element dr, in a system in the steady state rather than at equilib-
rium. In the presence of an applied field the distribution loses its spheri-
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 573
cal symmetry and it must be defined in terms of the volume elment df,
lying at the vector distance r, rather than in terms of the spherical shell
of volume, 47rr dr. In reference (44) it is shown that
T{r) = exp [-4Tr'N/3]c{r)
(7.18)
where 6(7) is the density function in the non-equilibrium case, and is
determined by the equation
IcT
Vc + cV" t// + Vc • Vi/' = 0
(7.19)
after suitable boundary conditions have been appended. The quantity
^, designates the local electrostatic potential, determined by the ions as
well as the applied field. These equations are restricted specifically to
the semiconductor case in w^hich the negative ion is unable to move.
The current carried by nearest neighbors in the volume element dr
in unit volume of solution is
Jir) = -exp[-47rrW/3]c(?)/xoV[i/' + (kT/q) tn c(f)] (7.20)
Using these equations it proves possible in reference 45 to provide a
more refined version of (7.15) in which the mobility of nearest neighbors
inside r = h need not be considered zero, nor those outside r = 6 be con-
sidered perfectly free and possessed of the mobility )Uo . In fact the aver-
age mobility of a nearest neighbor separated by a distance r from its
immobile partner proves to be
^ 2(1 - F) \L3r2 ^ 3r ^ _
exp (- e/r) + 2F
.3r
- 1
where
and
£ = q/KkT
F = (7^+§ + l)exp(-£/a)
,2
,2a2 a
I'or values of ?■ greater than e (7.21) can be approximated by
p. 1 / £" , 4£ ^
i"0
2 V3r2
+ - + 2 exp (- e/r)
(7.21)
(7.22)
(7.23)
(7.24)
and is therefore a function of e/r. Fuoss's b corresponds to r = £/2 or to
r/r = 2. Fig. 14 contains a plot of jl/no versus r for T = 400°K, a =
cm, 5 = 4.77 X 10"^" statcoulombs, and k = 16. Note that
-*.5 X 10"
574 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
1.0
0.8
0.6
o
li
0.4
0.2
'n
2e
}
/
/
T = 400° K
K = 16
0 = 2.5x10-8 CM
J
10 20 30 40
r IN CM X (08
50
60
Fig. 14 — Average mobility (calculated from the refined theory of pairing) of
a mobile ion in a pair as a function of the distance from its immobile neighbor.
The example shown corresponds to a substance having a = 2.5 X 10~* cm k = 16
at a temperature of 400°K.
at r = £/2 = 6, ju/juo is near 0.5 which is the average value of Fuoss's
/i/)Uo for ions taken from either side of r = h. Therefore a certain sym-
metry with respect to r = 6 does exist, tending to justify Fuoss's model.
According to (7.24) ju/juo is 0.8 by the time r = 3£/2 = 36, independent
of the value of a. In other words an ion located a short distance beyond
h does have practically complete mobility as the Bjerrum-Fuoss theory
assumes.
The refinement of (7.15) which occurs can be written as follows
+ 2f(^ - A exp (£/r)
(7.25)
exp (- 4t/N/3) dr\
Mo
Comparison of ju/mo computed from (7.25) with 1 — (P/N) appearing
in (7.15) over wide ranges of conditions again reveals an excellent cor-
respondence and further substantiates the Bjerrum-Fuoss theory. Since
calculations employing the latter are so much simpler it is expedient to
regard the cruder theory as an accurate approximation to the more re-
fined one. This practice will be followed from now on.
CHEMICAL INTERACTIONS AMONG DEFECTS IN Gc AND Si 575
VIII. PHENOMENA ASSOCIATED WITH ION PAIRING IN SEMICONDUCTORS
In this section we shall discuss some of the phenomena which are to
be expected in semiconductors when ion pairing takes place. At the time
of writing several of these phenomena have been investigated quantita-
tively in germanium and casually in silicon. A report on these studies
will be given in the later sections of this paper.
In the meantime it is fitting to inquire into the peculiarities which arise
because a semiconducting medium rather than a dielectric liquid is in-
volved. The possible means of detecting and measuring ion pairing in
semiconductors are numerous, and many of them do not have counter-
parts in aqueous solution. This implies that a host of new phenomena are
to be expected, many of which are peculiar to semiconductors.
Some distinctions between semiconductors and liquids are apparent
at once. Thus ions are not always mobile in semiconductors at tempera-
tures where ion pairing is pronounced. Lithium is exceptional in this
respect, being mobile in germanium and silicon down to very low tem-
peratures. In fact ion pairing has been observed in germanium containing
lithium down to dry ice temperatures, and even below. Another difference
is the low dielectric constant of semiconductors as compared with water.
I^'urthermore, in semiconductors, charge balance need not be maintained
l)y the ions themselves, but may be effected by the presence of holes or
electrons. Although charged the latter entities need not be considered in
pairing processes since, as particles, they possess effective radii of the
order of their thermal wavelengths which may exceed 20 Angstroms at
the temperatures involved. At these distances very little coulomb binding
energy would be available. Under certain rare conditions the screening
effect of these mobile carriers may make some contribution. This may be
particularly the case when relaxation processes (to be discussed later) are
carried out in poorly compensated specimens of semiconductor, since
such processes involve phenomena between ions separated by large dis-
tances.
A very obvious distinction is the fact that ions in a semiconductor
Dccupy a lattice, and cannot therefore move through a continuum of
positions, as in the case of liquid solutions. Furthermore the lattice may
introduce elastic strain energy into the binding energy of a pair. This
influence will alter the value of a, the distance of closest approach, when
the latter is chosen so as to achieve the best fit between theory and ex-
periment. As the extent of pairing is extremely sensitive to the magnitude
of a, its measurement provides a useful tool for exploring the state of
telrain in the neighborhood of an isolated impurity. We shall demonstrate
576 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
this application later in connection with the strain in the neighborhood
of a substitutional boron in germanium.
Aside from its bearing on the minimum distance a, the existence of the
lattice will be ignored in the following considerations.
The values of a, typical of semiconductors, are generally of the order
of 2 Angstroms as against 6 to 8 Angstroms for ions in liquids. This re-
sults from the fact that liquid ions are generally solvated. The conse-
quence to be expected, and indeed found, is that ion pairing will be far
more pronounced in semiconductors than in liquids of comparable di-
electric constant.
The fact that ions have limited mobilities in semiconductors can be
turned to advantage by choosing a system such as lithium and boron in
silicon in which only one species of ion, in the case mentioned, lithium, is
mobile. Under these conditions it is possible to obviate the clustering
phenomenon, mentioned previously, which appears in liquids at high ion
concentrations. Clustering is prevented because the immobile ions are
uniformly distributed in a random manner, having been grown into the
crystals at high temperature where pairing and related processes are un-
important. The obvious complications attending cluster formation can
therefore be avoided.
Of course, mobility, being limited to a single species of ion is also an
advantage in the theory of the transport phenomena, in such systems.
It is convenient to list some of the effects due to pairing Avhich are to
be expected in semiconductors. We do so in the following compilation.
{A) Equilihrium Phase Relations
From (6.2) it is apparent that the pairing equilibrium should affect
the solubility of lithium in silicon. The same must be true for germanium
doped with an acceptor. Although such effects probably occur, they are
accompanied by influences arising from the other possible equilibria. As
a result the situation is somewhat complex and it is not easy (see Ap-
pendix A) to produce experimental conditions under which pairing will
be evident. For this reason quantitative investigations along these lines
have not yet been attempted.
(B) Variation of Energy Levels
When an ion pair is formed of a donor and acceptor, both the donor
and acceptor levels are altered. Thus the proximity of the negative ac-
ceptor ion increases the difficulty of return to the donor state for an
electron, (i.e. the donor level is raised). Likewise the acceptor level is
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 577
lowered. In ion pairs it is in fact to be expected that the donor level will
be moved up into the conduction band and the aceptor level down into
the valence band.* This change in energy level structure should be ap-
parent in Hall coefficient measurements at low temperature. Experiments
of this sort have been conducted and are reported in this paper. Under
certain conditions this phenomenon may be useful for the elimination of
trapping"*^ levels from the forbidden gap.
(C) Change of Carrier Mohilitij
Ion pairs possess dipolar fields, and consequently, scattering cross-sec-
tions very much smaller than those of point charges. The addition of
hthium to a sample under such conditions that more than half the added
lithium becomes paired should therefore increase rather than decrease
the mobility of holes. The latter effect is the one to be expected in the
absence of pairing. In other words not only carriers but also the scat-
terers are removed by compensating the acceptor with donor. Experi-
ments of this sort have been performed. They are described later in this
paper. Since they allow us to measure the degree of pairing with good
accuracy they have been very valuable in validating the theory, and also
in exploring the nature of the potential function in the neighborhood of
an isolated acceptor.
(D) Relaxation Times
A semiconductor containing unpaired donors and acceptors at one
temperature can be cooled to a lower temperature, and the impurities
should then pair. If the temperature is lowered sufficiently, the pairing
process will be slow enough to be followed, kinetically, by observing any
parameter (such as carrier mobility) sensitive to pairing. Experiments of
this sort have been performed and will be described later.
The process of pairing can be characterized by a calculable relaxation
time, which depends on the acceptor concentration, the diffusivity of
the mobile donor, the dielectric constant, and the charges on the ions
among other things. The measured time can therefore be used as a means
of determining any one of these parameters.
(E) Diffusion
It is evident that pairing should reduce the diffusivity of a mobile
donor. Studies of diffusion in the presence of an immobile acceptor should
* A rough calculation indicates that about 0.5 e.v. would be required to place
an additional electron on an ion pair.
578 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
therefore reveal the action of pairing. Experiments of this sort have been
performed and will also be described in this paper.
The reduction in the diffusivity of a donor such as lithium may be
desirable in certain places.
(F) Direct Transport
Diffusion studies suffer from the. defect that ion pairing produces a
concentration dependent diffusivity. (See Appendix B). For this resaon
a very desirable measurement would involve determining the amount of
a mobile donor like lithium transported by an electric field through a
uniformly saturated specimen of semiconductor. This flux, together with
information concerning the level of saturation, should provide a direct
measure of the mobility of lithium under homogeneous conditions.
Formula (7.15) or its refinement (7.25) could then be applied directly
to the results.
The above list is by no means complete, for there are still other tech-
niques available for measurement, for example nuclear and paramagnetic
resonance. Enough has been given however to indicate the ^^dde range
of phenomena which ion pairing in solids can affect. In liquids, only A
and F are of any consequence. It is important to realize that not only do
these phenomena serve as tools for the study of ion pairing, but that ion
pairing, when properly understood, can serve as a tool for the study of
the phenomena themselves.
IX. PAIRING CALCULATIONS
The evaluation of fi according to (7.14) presents somewhat of a prob-
lem because the integral must be arrived at numerically. Fortunately,
the literature contains tables of the integral in what amounts to di-
mensionless form. The transformation
^ = q'/KkTr (9.1)
is introduced and then fi is shown to be given by
U = 4Tr[q^/KkTf Q(a) (9.2)
where
a = q-/KkTa (9.3)
and logio Q((x) is tabulated in Table III.
In a specimen in which the numbers of donors and acceptors are im-
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 579
Table III
a
logio Q{a)
a
logio Q(oc)
2.0
— CO
18.0
2.92
2.5
-0.728
20.0
3.59
3.0
-0.489
25.0
5.35
4.0
-0.260
30.0
7.19
5.0
-0.124
35.0
9.08
6.0
0.016
40.0
11.01
7.0
0.152
45.0
12.99
8.0
0.300
50.0
14.96
9.0
0.470
55.0
16.95
10.0
0.655
60.0
18.98
12.0
1.125
65.0
21.02
14.0
1.680
70.0
23.05
16.0
2.275
75.0
25.01
80.0
27.15
equal* (7.10) may be written as
(iVx - P){Nr> - P)
= fi
(9.4)
where Na and No are, respectively, the total densities of acceptors and
donors.
This equation has the following solution for P/Nd , the fraction of
donors paired.
P_
No
1
= o 1 +
1 , Na'
nNo Nd,
/i
1 +
1
N,
mo + ¥j-k ^'-'^
Inspection of (9.5) reveals that for given A^^ and 0, P/Nd is a decreasing
function of increasing No .
Very often, P/Nd is measured in an experiment, and from this it is
desired to calculate a, the distance of closest approach. For such pur-
poses the form (9.5) is not very convenient. In fact an entirely different
procedure is to be preferred. Suppose P/Nd is denoted by 6, and 6 is
substituted into (9.4), into which (9.2) has been inserted. We obtain
logio Q{(x) = logio
d
{Na - eND)(i - e)
]
(9.6)
A knowledge of 6 thus suffices to determine logic Q(a), from which, in
turn, a can be determined by interpolation in Table III. Then (9.3) can
be used for the evaluation of a.
* This is a situation which cannot arise in liquids, since there, charge balance
-.must be maintained by the ions themselves. It can occur when the ions are of
Idifferent charge, but then things are complicated by the formation of triplets,
etc., in addition to pairs.
580
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
Table IV
r°K
Q (cm')
r°K
n (cm3)
too
2.2 X 102
400
2.3 X 10-"
150
6.45 X 10-7
500
1.54 X 10-18
200
3.42 X 10-1'
600
3.0 X 10-19
225
1.28 X 10-12
700
1.03 X 10-19
250
8.79 X 10-"
800
4.7 X 10-2"
300
1.61 X 10-16
Experiments which will be described later indicate that in germanium,
gallium and lithium can approach as close as 1.7 X 10 cm, Usmg this
value of a, and k = 16, g = 4.77 X 10~^ statcoulombs, the values of Q
appearing in Table IV were computed from (9.2)
With these values, P/Nd , the fraction of donors paired can be com-
puted from (9.5) as a function of temperature and N a for the simplest
case, i.e., the one for which A''^ = No . Fig. 15 contains plots showing
these dependences. It must be remembered that all other things remain-
ing the same P/Nd will be greater than the values shown in Fig. 15
when Nd < Na '
A rather important integral to which reference shall be made later is
x^ exp {q/KkTx)
• 1
dx
(9.7)
The integral appearing in (7.14) is a special case of (9.7) with ri = a, and
Ti = h. I(r2 , n) has been evaluated over a considerable range. To facili-
tate matters the transformation
X = (q^'/KkT) X
(9.8)
has been employed. In this notation n and ro transform to pi and p2 , and
I{r, , n) = {g'/KkTY r X' exp (1/X) dX = {q/KkTYHp^ , pi) (9.9)
•'pi
Figs. 16 and 17 contain plots of i{p2 , 0.05) out to p2 = 5. The choice
of pi equal to 0.05 was rather unfortunate since for k = 16, and T =
300°K it corresponds to pi = 2.5 X 10~^ cm. Since acceptors like gallium
possess values in respect to lithium as low as 1.7 X 10~ cm i(p2 , 0.05)
is not much use in these cases. The choice 0.05 was made before the ex-
perimental data on gallium was available. Below we shall describe a
method for extending t(p2 , pi) to cases where n is less than 2.5 X 10
cm.
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 581
Ga IN Ge
a = i.7 X to'^CM
q=4.77 xio"'° e.s.u.
1 0
100°K
0.9
150°H
/
^
^
/
y^
/
/
/
/
/
/
/
/
200°K.
/
/
/
/
/
//
0.8
/
/
/
/
f
/ /
/
/
1
i
1
' /
Q
^ 0.7
1
1
f
1
/
/
1
//
/
/
250 /
/
/
/
//
|o.a
o
<
q: 0.5
LL
0.4
0.3
0.2
O.t
1
/
/
/
/
/
/ /
/
/
/
300/
1
/
//
/
/
1
/
/
/
r
400/
500/
7,
,-6 00
/
/
1
/
/
/
//
700°K
/
/
/
/
/,
//
1
/
/
/
/
J
7
/
/
y
f
/
/
J
//
0
y
y
•^
\y
^
/
■^
y
i/
10
10
10" 10
12
10'^ 10'
10
15
10
16
10
17
10
18
N IN CM"^
10'9 10'
Fig. 15 — Fraction of ions paired, assuming equal densities of positive and
negative ions, calculated as a function of temperature and concentration from
equation (9.5). The situation illustrated might apply to gallium and lithium in
germanium in view of the choice of a and /c.
Fig. 16 covers the range from pi = 0.05 to 0.08 and involves a
logarithmic scale because of the sharp variation of i in this range. (This
points up the sensitivity of the degree of pairing to the magnitude of a.)
Fig. 17 extends the curve to pi = 5. When pi exceeds 5, i{pi. , 0.05) can
be obtamed from the formula
i{pi , 0.05) = 3865 + ^' + ^'
(9.10)
In order to determine i{pi , pi) when pi ^ 0.05, the following formula
may be used.
i(p2 , Pi) = i(p2 , 0.05) - 2(pi , 0.05) (9.11)
582
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
Finally for cases in which pi < 0.05, Table III can be used. Thus
^(P2 , pi) = Qil/pi) - Q(20) + t(p2 , 0.05) (9.12)
where 1/pi , and 20 are a values in Table III.
X. THEORY OF RELAXATION
In Section VIII attention was drawn to the fact that ion pairing in
semiconductors can be made to occur slowly enough so that its kinetics
can be followed. It is possible to characterize these kinetics by a relaxa-
tion time r, which we shall endeavor to calculate in the present section.
4000
2000
1000
800
600
500
400
300
In
o
d
<5.
100
80
60
50
40
30
20
10
^ ^
0.050
0.055
0.060
0.065
Pa
0.070
0.075
0.080
Fig. 16 — Plot, for small values of P2 of i(p2 , 0.05) from (9.9).
CHEMICAL INTEKACTIONS AMONG DEFECTS IN Ge AND Si 583
3920
3900
^^3880
O
c£^3860
3840
3820
3800
/
y
^
y
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Fig. 17 — Plot, for larger values of p-i , of i(p2 , 0.05) from (9.9).
Suppose a system is first maintained at a temperature high enough to
prevent pairing, and then, at an instant designated as zero time, is
suddenly chilled to a temperature at which pairing takes place. One
thereby has a system which would normally contain pairs but which
finds itself with donors and acceptors which are uniformly and randomly
distributed. Since the donors are assumed mobile, a process ensues
whereby they drift toward acceptors until an equilibrium is established
in which each acceptor develops an atmosphere of donors with density
c(r), given by (7.7).
This final state in which the atmosphere is fully developed is the paired
state characteristic of the lower temperature. The relaxation time to be
defined must measure the interval required for the near completion of
the above process.
In order to acquire physical feeling for the phenomenon, we begin with
some simple considerations. In particular a system will be dealt with
containing equal numbers of positive and negative ions. This restriction
can be lifted later.
Now, to a first approximation the pairing phenomenon may be re-
garded as a trapping process in which mobile, positive donor atoms are
captured by the negative acceptors. Thus, suppose each acceptor is imag-
ined to possess a sphere of influence of radius R, beyond which its force
field may be considered negligible, and inside which a positive ion is to be
regarded as captured. This picture immediately emphasizes certain sub-
tleties which require discussion before further progress can be made.
In the crudest sense one might reason that the probability of an en-
counter between a positive ion and a negative trap would depend on the
584 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
product of the densities of both. These densities must be equal because
when a positive ion is trapped the resulting ion pair is neutral so that a
trap is eliminated simultaneously. If these equal densities are designated
by n, we arrive at the second order rate law
- f = '^^^ (^°-'>
where /ca is a suitable constant, and t is time.
This law would be perfectly valid if the mean free path of a mobile
positive ion were large compared to the distance between ions and the
probability of sticking on a first encounter were small. The trapping
cross-section rather than the movement prior to trapping would de-
termine the trapping rate. In this case the rate would certainly depend
on the concentrations of both the traps and the ions being trapped.
On the other hand, in our case, not only is the mean free path of a
positive ion much smaller than the distance between ions, but the
sticking probability is high. A given ion must diffuse or make many ran-
dom jumps before encountering a trap and upon doing so is immediately
captured. Therefore, the rate of reaction is diffusion controlled.
Because of the random jump process a given mobile ion is most likely
to be captured by its nearest neighbor during the first half of relaxation,
and relative to the degree of advancement of the trapping process, the
density of traps may be considered constant. This leads to first order
kinetics rather than second,* i.e., to
- ^ = /cin (10.2)
at
where n is the density of untrapped ions.
By definition ki is the fraction of ions captured in unit time, i.e., the
probability that one ion will be captured per unit time. Its reciprocal
must be the average lifetime of an ion. This lifetime
r = I (10.3)
ki
shall be defined as the relaxation time for ion pairing. A rough calculation
of T can be made quickly. Thus, suppose that the initial concentrations
of donors and acceptors are equally A^. About each fixed acceptor can be
described a sphere of volume, 1/A^. On the average this sphere should be
occupied by one donor which according to what has been said above, will
eventually be captured by the acceptor at the center. In the mind, all
* The phenomenon stems from the fact that first and second order processes are
almost indistinguishable during the first half of the reaction, but also from the
fact that the diffusion control prevents the process from being a ti-ue second or-
der one, although its departure from second order may be small.
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 585
the spheres can be superposed so that an assembly of donors A'' in num-
ber is contained in the volume 1/A^, at the density A'^ . The problem of
relaxation is then the problem of diffusion of these donors to the sink of
radius R, at the center of the volume. The bounding shell of the sphere
may be considered impermeable, thus enforcing the condition that each
donor shall be trapped by its nearest neighbor. Since the diffusion prob-
lem has spherical symmetry the radius, r, originating at the center of
the sink at the origin may be chosen as the position coordinate. At r =
R, the density, p, of diffusant may be considered zero. The radius, L, of
the volume, 1/A^, is so large compared to R, that in the initial stages of
diffusion L may be regarded as infinite.
In spherical diffusion to a sink from an infinite field, a true steady
state is possible, and this steady state is quickly arrived at when the
radius, R, of the sink is small. Under this condition concentration is
described by
p = A -- (10.4)
r
where A and B are constants. Furthermore at early times n is still N,
the initial concentration at r = L ^ oo , so that
p(oo) = AT' (10.5)
In addition we know that
p(R) = 0 (10.6)
These boundary conditions suffice to determine A and B in (10.4), and
yield
P = N'
1-^
r
(10.7)
Now the rate of capture (—(dn/dt) in (10.2)) is obviously measured
by the flux of ions into the spherical shell of area, 4tR', which marks the
boundary of the sink. This flux is given according to Fick's law by
4.^R'D, (^-^) = - ^ (10.8)
where Do is the diffusivity of the donor. Substituting (10.7) into (10.8)
yields
r2 r- - C?n
4:tN'RDo = - 4^ (10.9)
dt
During the initial stages of trapping the right side of (10.2) may be
586 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
written as ^lA'', i.e.,
hN^-'^ (10.10)
Equating the left sides of (10.9) and (10.10) gives
A;i = 4:7rNRDo
or
^ = r = A A^r. (10-11)
It now remains to choose a value for the capture radius, R. A reason-
able guess may be made as follows: Around each acceptor there is a
coulomb potential well of depth
V = -(IIkt . (10.12)
Since the average thermal energy is kT, it seems reasonable to regard an
ion as trapped when it falls to a depth kT in this well. Thus, inserting kT
on the left of (10.12) and R for r on the right leads to
R = qlKkT (10.13)
and upon substitution in (10.11) we obtain
KkT
(10.14)
4xgWZ)o
This result, obtained by crude reasoning, is actually quite close to the
more rigorous value derived below. Furthermore, the above derivation
is useful in providing insight into the physical meaning of the relaxation
time.
The chief difficulty with the preceding lies in the arbitrary choice of
72, and is a direct consequence of the long range nature of coulomb forces.
Another difficulty arises because the distribution of donors about ac-
ceptors is eventually specified by (7.7) so that at r = i^ = q/KkT
Be
Since this slope has a negative value the trap exhibits some aspects of a
source rather than a sink which could only produce a positive concen-
tration gradient. This last objection will not be serious when h is very
small since, then the final value of c{r) beyond r = q/KkT = R will be
effectively zero, as would be required for a perfect sink.
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 587
The last point raises still another question: What happens when the
sink is not perfect, i.e. where the equilibrium state does not involve
complete pairing?
All these difficulties can be removed by a more sophisticated treatment
of the diffusion problem. Thus, retain the sphere of volume, 1/A^, en-
closing A^ donors at the density N^. However, the equations of motion of
these donors are altered to account for the fact that besides diffusing
they drift in the field of the acceptor at the origin. Thus the flux density
of donors will be given by
/*(r,o = -z).|^^+l^
(10.16)
where R has been substituted for q/KkT. Equation (10.16) is obtained
by adding to the diffusion component,
— Lfo —
dr
of the flux density, the drift component,
Mog
where hq is the mobility of a donor ion and —q/nr' is the field due the
acceptor at the origin. The Einstein relation^"
Mo - qD,/hT (10.17)
has also been used to replace mo with Do .
The spherical shell bounding the volume, 1/iV, of radius
L = {^y (10.18)
is regarded as impermeable, so we obtain the boundary condition
J*{L, t) = 0. (10.19)
Furthermore an arbitrary inner boundary, r = i?, is no longer defined
but use is made of the real boundary, r = a, i.e., the distance of closest
approach, at which is applied the condition
J*ia, 0-0 (10.20)
As before, the initial condition may be expressed as
p = N- t = 0 a < r < L (10.21)
588 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
51
The continuity equation, in spherical coordinates takes the form
r^ dr dt
Substitution of (10.16) into (10.22) gives, finally,
L I h 1^ + 7^ A = 1 % (10.23)
r^dr\ dr '^ j Do dt
Equations (10.23), (10.21), (10.20) and (10.19) form a set defining a
boundary value problem, the solution of which is p(7\ t), from which, in
turn, J*(r, t) can be computed. It then remains to compute (dn/dt) in
(10.2) from J*. The former is not simply AttR^J* (as in (10.8)) because
now J* is not defined unambiguously, being a function of r. J*{R, t)
might be employed but then the method is no less arbitrary than the
simple one described above.
Fortunately, nature eliminates the dilemma. It is a peculiarity of
spherical diffusion, when the sink radius is much smaller than the radius
of the diffusion field, that after a brief transient period, 47rr'J*(r), except
near the boundaries of the field, becomes practically independent of r,
and depends only on t. This feature is elaborated in Appendix C. Since
in our case the radius of the field is of order, L, and the effective radius of
the sink is of order, R, and L » R, it may be expected that this phe-
nomenon will be observed. In fact its existence has been assumed previ-
ously in the derivation of (10.4).
Under such conditions it does not matter how the radius of the sink
is defined so long as 4:irR^ is multiplied by J*{R) and not the value of
J* at some other location.
The boundary value problem, (10.23), (10.21), (10.20), (10.19) is
solved in Appendix C, and it is shown there that the value of 47rr"J*(?')
obtained after the transient has passed is closely approximated by
4xrV*(r) = -^C^° e-"' (10.24)
with
where
M
^ .kTiN-M) ,^)
47r5W2/)o
= l/47r [ r exp [q/KkTr] dr (10.26)
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 589
The close connection between M defined by (10.26) and h defined by
(7.17) is apparent. Thus in (7.17) when r = L, exp[-47rrW/3] is e~\
and for larger values of r this exponential quickly forces the convergence
of the integral. Therefore the values of h and M will be almost equal.
This is not surprising since they are meant to be the same thing, i.e.,
the average concentration, c(oo), of donors at infinite distance in the
equilibrium atmosphere of an acceptor. Both quantities are computed
so as to conserve charge in this atmosphere.
At large values of N, M proves to be much smaller than A^ so that
(10.25) reduces to (10.14), validating the crude treatment, for r in (10.24)
is obviously the relaxation time. This is easily seen by writing
-^ = -4,rrV*(r) = ^^« .""^ (10.27)
at kkT
from which one derives by integration
n = M + (AT - M)e~"'' (10.28)
According to (10.28) at ^ = 0, n = A", the correct initial density for
unpaired ions. At ^ = 00,72 = M, also the correct density, i.e., the
density at large values of ?-, when equilibrium is achieved. Obviously r
plays the role of the relaxation time, since by differentiation of (10.28)
din - M) _{n- M) ^^^^9)
dt T
which is to be compared with (10.2) and (10.3).
Values oiM can be computed using formulas (9.10), (9.11), and (9.12)
and Figs. 16 and 17 since the integral in (10.26) is one of the i integrals
I'lg. 18 shows some values of M, computed in this way for the tempera-
tures 206°, 225°, 250°, and 300°K, for a semiconductor where the value
of a = 2.5 X 10~^ cm, k = 16, and q = 4.77 X 10"^" statcoulombs. The
plots are of M versus N. Note that the values of M are generally much
less than A", the disparity increasing with lower temperatures and larger
A.
It is also possible to calculate t for the above system in its dependence
upon A" and T. To do this the value of Z)o must be known as a function
of temperature. Fuller and Severiens have measured the diffusivities of
lithium in germanium and silicon down to about 500°K. These data plot
logarithmically against \/T as excellent straight lines. In Fig. 19, we
show an extrapolation of the line for lithium in germanium down to the
neighborhood of 200°K. From this figure it is possible to read values of
590
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
10"
300° K
a = 2.5X10"8 CM
>f=16
^
^
4^16
/^
/
X'
,^
/
250
1
5
LJ J /-lis
/v
U ^Ql5
/
^
z
225
2
^
J ,^14
20 6° K
1015
10'
10
16
10"
N IN CM"3
10''
10
19
Fig. 18 — Dependence of constant M defined by (10.26) on temperature and
concentration, for particular values of a and k.
Do for germanium to which the system of Fig. 18 refers, since k has been
chosen at 16.
Using Figs. 18 and 19, Fig. 20 was computed. It shows t plotted in
seconds versus A^ for the same temperatures appearing in Fig. 18. These
curves show that at values of N as low as 10 cm" relaxation times are
short enough to be observable down to 200°K, being at the most some
50 hours in extent. The value of N makes a big difference.' For example
at 200°K the relaxation time is only 4 minutes with A'' = 10^^ cm~^
Presumably, at 10 cm~ , relaxation could be observed down to much
lower temperatures.
It is interesting to note that insofar as M hardly appears in r, the
latter is independent of the distance of closest approach, a. Since a is to
some extent empirical this is a fortunate circumstance, and the measure-
ment of T may provide an accurate means of determining, A^, Do , k, or
q, whichever parameter is regarded as unknown. Furthermore k as a
macroscopic parameter has real meaning in r since the forces involved
may be regarded as being applied over the many lattice parameters
separating the di-ifting donor from its acceptor.
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 591
This section will be closed by indicating how the restriction to systems
containing equal numbers of donors and acceptors might be lifted. Thus,
suppose Na exceeds No • Then there will be Na — Nd mobile holes main-
taining charge neutrality. To a first approximation these will screen the
N^ — Nd uncompensated acceptor ions so that the No donors will see
effectively only A''!, acceptors. Thus in first approximation r can be com-
puted for this system by replacing N in the preceding formulas by Nd •
Of course it is possible that there will be a further effect. Thus the
mobile holes will probably shield some of the compensated acceptors as
well. This Avill lead to a further (probably small) reduction in t, over and
above that obtained by replacing N by Nd - We shall not go into this
in the present paper, because in most of the experiments performed Nd
was near Na - In the few^ exceptions the crude correction, suggested
above, can be used.
XI. INVESTIGATION OF ION PAIRING BY DIFFUSION
Most of the theoretical tools required for the study of ion pairing have
now been provided, and attention will be turned to experiments which
10'
- 7
iO
10-8
Q
0,0-9
JJ
UJ
CL
10-
5 ,n-ii
10"
o 10'
Q
■12
10"
10"
10-'5
o.oot
TEMPERATURE IN DEGREES KELVIN
600 500 400 350 300 250
200
0.002 0.003 0.004 0.005
t/TEMPERATURE IN DEGREES KELVIN
Fig. 19 — Diffusivitj' of lithium in germanium extrapolated from the data of
Fuller and Severiens.
592
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
have been performed in this field. A fairly large group of these exist, and
it remains to describe them in detail. We shall begin with the study of
the diffusion of lithium in p-type germanium.
At the outset a matter having to do with the diffusion 'potential de-
mands attention. This is the potential which arises, for example, in
p-type material, because the mobility of a hole is so much greater than
the mobility of a lithium ion. In consequence, holes diffuse into regions
containing high concentrations of lithium more rapidly than lithium ions
can diffuse out to maintain space charge neutrality. As a result such re-
o
2
O
o
ai
in
105
\
\
\
s.
3 = 2.5X10-8 CM
/C=16
10^
\
\
\
N
\
>
\
V,
\
s.
103
\
s
\
206°K
^
\
\
\
\
<''
1
\
102
N
\
\
\,
\
\
s
\
250°K
\
10
\
■\
N
\
^
\,,
^
00°K
n-'
\
\
10'5
N IN CM-3
10'
Fig. 20 — Relaxation time as a function of temperature and concentration com-
puted from equation (10.25) using the data of Figs. 18 and 19.
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 593
gions develop positive potentials and a field exists tending to expel
lithium. This causes the lithium to drift as well as diffuse so that Fick's
laW^ is no longer valid.
The most that can be done toward the elimination of diffusion poten-
tials is to minimize them so that no local space charge exists. At equilib-
rium, this corresponds to the condition^^
Nd - Na = 2ni smh(qV/kT) (11.1)
where V is the local electrostatic potential. It is always permissible to
assume that fast moving electrons and holes are in equilibrium relative
to diffusing ions. If a material which is p-type everywhere is being con-
sidered, (11.1) can be simplified to
Na - Nj, = Ui exp [-qV/kT] (11.2)
In Appendix D it is proved that (11.2) will be valid everywhere within
a region where N a is constant and greater than Nd , provided that No
does not fluctuate through ranges of the order Na in a distance less than
(11.3)
Under most conditions of experiment I will be of the order of 10~ cm.
Unfortunately many of the experiments described in this section (par-
ticularly those performed at 25°C.) involve diffusion layers as thin as
10"^ cm. As a result space charge will exist and the diffusion potential
will not always be minimized. Even if it is minimized so that (11.2) is
satisfied the residual field will still aid diffusion and lead to higher ap-
parent diffusivities. Therefore the effect cannot be ignored even when
minimization has been achieved.
In the absence of space charge the drift component of flux density
due to the field is easily computed. It will be given by
-M ^ No (11.4)
dx
According to (11.2)
_dV _ kT dNp
dx ~ q{NA - Nd) dx
so that (11.4) becomes
nkT / Nd \ ONd ^ _fiokT / _ _P \ / Nd \ dNp
^'a - No) dx q \ Nd) \Na - Nd) dx
Nd \ dNp
- Nd) dx
(11.5)
(ii.rO
594 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
where (7.15) and the Emstein relation have been used, and Do is the
diffusivity in the absence of pairing.
P/Nd in (11.6) can be evaluated using (9.5) so that the coefficient pre-
ceding (dNo/dx) contains No as the only variable.
In Appendix B it is shown that ion pairing itself leads to severe de-
partures from Fick's law.*^ In fact the diffusion flux density in the pres-
ence of pairing is given by
-2 l^" - ^- + 5)
l/i(^° - iV. - i) +
'-f° (11.7)
dx
Here again the diffusivity is specified by the factors preceding (dNo/dx)
and, though variable, depends only on No , the local concentration of
diffusant. Adding the two coefficients appearing in (11.6) and (11.7) the
value of the diffusivity, D, in the presence of both pairing and diffusion
potential is obtained. Thus
D-^\l +
(11.8)
It is obvious from (11.8) that even in the absence of space charge D is
an extremely complicated function of Nd , and will be much more com-
plex if space charge needs to be considered. When Nd « A^.i (11.8) re-
duces to
Comparison with equation (B15) shows that when (11.8) is true (i.e.,
in the absence of space charge) the diffusion potential may be ignored
for Nd <3C Na • Comparison of (B14) with (B15) shows how much D can
vary with Nd when ion pairing occurs.
The proper study of diffusion in the presence of ion pairing should be
augmented by a mathematical analysis, accounting for the concentra-
tion dependent diffusivity. Since this dependence is complicated the
resulting boundary value problem must be solved numerically, and this
CHEMICAL INTEKACTIONS AMONG DEFECTS IN Ge AND Si 595
represents a formidable task. Although work along these lines is being
done we shall content ourselves, in this article, with a less quantitative
approach. The following plan has been followed.
A rectangular wafer of semiconductor uniformly doped with ac-
ceptor to the level, Na , is uniformly saturated with lithium to a level,
Nd , slightly less than Na • Thus, the resulting specimen is well compen-
sated but not converted to n-type. Lithium is then allowed to diffuse
out of the specimen, and because of the thinness of the wafer, this
process may be regarded as plane-parallel diffusion normal to its large
surfaces. Low resistivity p-type layers therefore develop near the sur-
faces. If the thin ends of the wafer are put in contact with a source of
current, current will flow parallel to its axis, so that the equipotential
surfaces will be planes normal to this axis. The flow of current will be
one dimensional because the inhomogeneity in lithium distribution oc-
curs in the direction normal to its flow (see Fig. 21).
If two probe points are placed at a fixed distance apart on the broad
surface of the wafer (see Fig. 21), then the conductance measured be-
tween them is a reflection of the total number of carriers in the low
resistivity layers, i.e., a measure of the total amount of lithium which
has diffused out. A more detailed connection between this conductance
and diffusivity is derived in Appendix E. For the moment, however,
attention will be confined to the description of the general plan of ex-
periment.
According to the formulas derived in the early parts of this section,
and also to (B14) and (B15), the diffusivity is something like Do/2 in the
CURRENT
CURRENT,
(I)
Fig. 21 — Diagram illustrating measurement of dependence of diffusivity on
ion pairing (see Section XI).
596 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
bulk of the wafer where Nd almost equals Na , but is as low as Do/(l +
^Na) near the surface where Nd « A''^ . If Q,Na is very much larger
than unity as it will be under conditions where appreciable pairing oc-
curs, the diffusivity will, therefore, be much smaller near the surface
than at the high end of the diffusion cui-ve, deeper within the specimen.
The surface will then offer resistance to diffusion, and it may be expected
that the measured value of the diffusivity Avill correspond more closely
to the slow process near the surface rather than to the faster process
occurring deeper in the semiconductor. Of course this cannot be entirely
true because the resistance at the surface coupled with the lack of re-
sistance inside the wafer will tend to steepen the concentration gradient
near the surface. This wdll give the impression of a diffusivity somewhat
higher than the one corresponding to the surface.
If the current flowing in the wafer under the conditions of measure-
ment is I, and the potential measured between the points is V, then the
conductance between the points is
S = I/V. (11.10)
In Appendix E it is shown (under the assumption that D is constant)
that
S/S. = 1 + ?:?«|v^ (1^) V^ (lUl)
where So is the conductance after the specimen is saturated with
lithium, but before any lithium has diffused out, and S^ is the con-
ductance before lithium has been added. Na is the uniform concentration
of acceptor, and Nd° is the initial uniform concentration of lithium, while
d is the thickness of the wafer. ?? is a correction factor which arises be-
cause the mobility of holes varies from point to point in the wafer, as
the density of lithium varies. There are two extreme types of variation.
The first takes place in a specimen in which, at room temperature
(where the conductance measurement is made) ion pairing is complete.
Then the local density of impurity scatterers will be A''^ — Nd ■ At
the other extreme no ion pairing occurs, and the density of scatterers is
Na + Nd.
The nature of t> depends on how much pairing is involved. In Fig. 22 d^
has been evaluated in its dependence on Nd° for the extreme cases men-
tioned. Furthermore it has been assumed then that Nd is given by a
Fick's law solution of the diffusion problem, and that diffusion begins in
a nearly compensated specimen.
The first thing to notice is that ?? is not very different from unity in
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 597
1.7
1.6
.5 -
1.4
1.3
1.2
1. 1
1.0
0.9
0.8
0.7
10
16
y-00
-r r I
Fr
t Ai
1 yUI,IMCIl^S;v.ii^>3^.'>,
t Jo
//(n)/ erf c i di
^0
y
/
^
y
^
y
^
^^AIRIN
G
-"^
NON PAIklNfc.
^
^
10
17
5 6
10
18
Nd in cm'
Fig. 22 — Plots of correction factor ??, required to compensate for the depend-
ence of hole mobility on the density of scattering centers along a diffusion curve.
I? is plotted against the initial density of donor and is shown for the two extreme
cases of pairing and no pairing.
either extreme, and therefore closer to unity in some intermediate situ-
ation. In any event the correct value of ?? can be read from Fig. 22 if the
experiments involve either extreme at the measurement temperature.
This has, in fact, been approximately the case in our experiments, in
which pairing is almost complete at the temperature where conduc-
tances have been measured.
According to (11.11) a plot of S/2o against 's/l should be a straight
line of slope
2.256^V^/2«>A^D°\
S =
d
\:eoNa
(11.12)
f Measurement of S therefore affords a measure oi D. Of course the ap-
! parent D obtained in this manner can never represent anything beyond
' some average quantity having the general significance of a diffusi\-ity.
This follows from the previous discussion concerning the non-constancy
598 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
of D. The only exception to this statement occurs in connection with high
temperature experiments (above 200°C.) where both pairing and the
diffusion potential are of little consequence. The mere fact that 2/2o
plots as a straight line against -s/t is not evidence for the constancy of
D. In Appendix E it is shown that a straight line will result, even when
ion pairing is important, provided that the diffusion potential is based
on the no-space- charge condition, i.e. provided that D varies only
through its dependence on Nd •
On the other hand, the last statement implies that the existence of a
straight line relationship is evidence that the diffusion potential has at
least been minimized.
The most careful experiments were performed in germanium doped to
various levels with gallium, indium, and zinc as acceptors. The ger-
manium specimens were cut in the form of rectangular wafers of ap-
proximate dimensions (1.25 cm X 0.40 cm X 0.15 cm). Fresh lithium
filings, were evenly and densely spread on one surface of the wafer, and
alloyed to the germanium by heating for 30 seconds at 530°C in an at-
mosphere of dry flowing helium. Then the other surface was subjected
to similar treatment.
After this the specimen was sealed in an evacuated pyrex tube and
heated at a predetermined temperature for a predetermined period of
time. The temperature was chosen, according to Fig. 5, so that the
saturated specimen would still be p-type and just barely short of being
fully compensated. Also attention was paid to the problem of avoiding
precipitation on cooling. The time of saturation was determined from an
extrapolation of the known lithium diffusion data, in germanium, of
Fuller and Severiens^^ which is plotted in Figure 19 for the range ex-
tending from about 0° to 300°C.
After saturation the sealed tube was dropped into water and cooled, t
It was opened and the wafer ground on both sides, first with No. 600 '
Aloxite paper, and then with M 303)^ American Optical corundum
abrasive paper. The final thicknesses of the specimens ranged from 0.025 '
to 0.075 cm, the thinnest samples being used for the runs at the lowest
temperature.
If the specimen is quite thin and highly compensated it is possible in
principle to measure very small diffusivities (as low as 10~ cm /sec) i
within a period of several hours. This is so because the low resistivity
layer formed near the surface, although thin, will carry a finite share of
the current in thin compensated specimens. On the other hand, additional
o
difficulties arise. Diffusion layers as small as 100 A may be involved. If
the surface is microscopically rough, diffusion will not be plane-parallel;
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 599
and the measured diffusivity will appear larger than the real diffusivity.
This condition can be partially corrected by etching the surface chemi-
cally until it is fairly smooth.
When dealing with such thin layers, the no-space-charge assumption
becomes invalid and the diffusion potential ought really to be considered.
Considering all the difficulties, i.e., concentration dependence of diffusion
coefficient, possible existence of space charge, and roughness of surface,
it is apparent that only qualitative effects are to be looked for in the dif-
fusivities which have been measured.
The most that can be predicted is that for specimens containing a
given amount of acceptor, the measured D (some average quantity)
should be less than Do , the disparity increasing with decreasing tem-
perature. At high temperatures D should converge on Do . Furthermore,
at a given temperature D should decrease with an increase in concen-
tration of acceptor. These tendencies are in line with the idea that reduc-
tion of temperature or increase of doping leads to an increase in pairing.
Runs Avere carried out on specimens etched with Superoxol^^ at the
temperatures 25°, 100°, and 200°C. In the 25°C run the wafer was allowed
to remain in the measuring apparatus under the two probe points in air,
and S was measured from time to time. At 100°C the specimen was
immersed in glycerine containing a few drops of HCl, the temperature
of the bath being controlled. Periodic removal from the bath facilitated
the measurement of 2. At 200°C glycerine was again used as a sink for
lithium, the sample being removed periodically for measurement.
Fig. 23 illustrates some typical plots of 2/So versus \/t. They are
all satisfactorily straight. Fig. 24 shows a plot of log Do against \/T,
extrapolated from the data of Fuller and Severiens.^^ In this illustration,
Aalues of log D (obtained from the above measurements by determining
the slopes S and employing (11.12)) are also plotted at the temperatures
of diffusion. For ■& the case of complete pairing was assumed.
The first thing to note is that the points for log D all lie below log Do
except at 200°C and satisfy the qualitative requirement outlined above.*
Moreover they drop further below log Do as the temperature is reduced,
^\■hile at 200°C they have almost converged on log Do .
The results for zinc are particularly interesting. Zinc is supposed to
have a double negative charge in germanium. Hence we would expect
very intense pairing to occur. This is indicated in the difi'usion data
where the sample containing zinc at the rather low level, A^^ = 2.7
* The long range nature of the interaction forces becomes evident when one
considers that the diffusivities are being altered by impurity (acceptor) concen-
trations of the order of 1 part per million.
I
600
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
UJ
D
O
o
o
tr
o
4.5
4.0
3.5
3.0
2.5
MM
2.0
1.5
1.0
/
/
/
/
/
/
/
/
200° c/
/
/
/
/
/
/
A
/
f
/
/
/
/
/zb" c
/
/
/
7
/
/
//
/
/
1.14
1.12
1.10
1.08
1.06
>
a.
D
O
o
LL
WW
1.04
1.02
1.00
10 15 20 25 30 35
1(/t IN SECONDS
40 45
50
55
Fig. 23 — Curves illustrating the observed linear dependence of S/2o on the \/~t.
X 10^^ cm~', shows a large reduction in diffusivity even at temperatures
as high as 200°C.
The difficulties discussed in this section serve to emphasize the im-
portance of a direct transport experiment in which lithium atoms nni-
jormlij distributed throughout germanium or silicon, uniformly doped
with acceptor, are caused to migrate by an electric field, and their
mobilities measured. Because of the uniform dispersion of solutes the
mobility will be constant everywhere. Furthermore no diffusion poten-
tial will be involved, and also the refined formula (7.25) can be applied.
There are, however, many difficulties associated with the performance
of this type of measurement.
In closing it may be mentioned that a few much less careful experi-
ments of the kind described here have been performed in boron-doped
silicon. The results indicate ion pairing in a qualitative way but more
definite experiments are needed.
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 601
XII. INVESTIGATION OF ION PAIRING BY ITS EFFECT ON CARRIER MOBILITY
II In Section VIII attention was called to the fact that ion pairing should
influence the mobility of holes, because each pair formed, reduces the
number of charged impurities by two. Thus, a specimen previously doped
with acceptor, might, if sufficient lithium is added, exhibit an increase in
hole mobility, even though the addition of lithium implies the addition
of more impurities. This effect has been observed in connection with the
Hall mobility of holes in germanium.
Two specimens of germanium were cut from adjacent positions in a
single crystal doped with gallium to the level 3 X 10^^ cm~l One of these
iwas saturated with lithium through application of the same procedure
TEMPERATURE IN °C
200 100
25
r
1.4
1.6
1.8 2.0
2.2 2.4 2.6 2.S 3.0 3.2
Y X 10^
^3.4
Fig. 24 — Plot of diffusivity of lithium in undoped germanium as a function
of temperature — also showing points for apparent diffusivities of lithium in
variously doped specimens.
602
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
employed in section V. Hall mobilities of the two specimens were meas-
ured^^ down to below 10°K. Cooling was carried out slowly to permit as
much relaxation into the paired state as possible (see Section X). Li
Fig. 25 plots of the Hall mobilities versus temperature of both specimens
are presented. Curve A is for the sample containing 2.8 X lO" cm~*
lithium. It therefore contained about 5.8 X 10^^ cm~^ total impurities
as compared to the control sample whose curve is shown as B in Figin-e
25 and which contained only 3 X 10 cm" impurities.
The lithium doped bridge exhibits by far the higher Hall mobility for
holes (except at very low temperatures where poorly understood phe-
nomena occur). In fact at 40°K the sample containing lithium shows a
hole mobility 16 times greater than that of the control at the correspond-
ing temperature. Rough analysis of the relative mobilities at T = 100°K
indicate '^2 X 10 cm scattermg centers in the control sample and 5
X 10 cm" scattering centers in the sample containing pairs.
This experiment has been repeated with other specimens doped to
different levels with gallium and even with other acceptors, and leaves
no doubt that a mechanism which is most reasonably assumed to be
pairing, is removing charged impurities from the crystal.
The phenomenon we have just described suggests an excellent method
for testing the ion pairing formula derived in Sections VII and XI, for it
10'
Q
Z
o
u
o
>
DC
liJ
a
cvj
5 10
u
CD
O
5
<
X
10'
-
i
r
'^'^-^
■v.^
- 1
^^
^^
- 1
\.
X
s_
/
^
-^
_^
^
N)
r
/
"*"
"^
/
/
:
40 80 120 160 200 240 280
TEMPERATURE IN DEGREES KELVIN
320
Fig. 25 — Plot of Hall mobility as a function of temperature for germanium
containing 3 X 10^' cm"' gallium. Curve A is for a sample containing 2.8 X 10'''
cm~^ lithium.
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 603
enables us to determine at what temperature, at given values of Na
and Nd , P/Nd is exactly 0.5. Thus consider the fact that, all other things
being equal, the control bridge and the one containing added lithium
will exhibit equal Hall mobilities at a given temperature when the con-
centrations of charged impurities are identical in both of them. Now the
concentration of such impurities in the control is simply Na • The con-
centration in the bridge containing lithium is
Na + No- 2P (12.1)
The quantity 2P is removed from Na + Nd , because each time a pair
forms two charged scatterers are eliminated. The condition that the
; .scattering densities in both bridges be equal is then simply
I Na = NA-\-Nn-2P
or
■^ = 0.5 (12.2)
N D
i Therefore if plots of Hall mobilities versus temperature such as those
I appearing in Figure 25 are continued until they cross, the temperature
I of crossing marks the point at which P/Nd is 0.5.
In Fig. 26 typical crossings of this kind are shown. They are for two
I ••17
! different gallium doped germanium crystals, one containing 3 X 10
cm~^ gallium and the other 9 X 10^^ cm~^. The curves for the controls
and lithium saturated samples in each case are shown as plots of the
logarithm of Hall mobility against logarithm of absolute temperature.
: The lines plotted in this manner are straight. The lithium content of
1he bridge containing 9 X 10^^ cm~^ gallium was 6.1 X 10 cm~ while
that in the bridge with 3 X 10^^ cm"^ gallium was 2.8 X 10^^ cm~l All
, of these concentrations were obtained from Hall coefficient measurements
< m the controls and the lithium doped specimens.
As the temperature is increased the mobilities of the samples with
lithium are reduced and approach the mobilities of the controls. This
happens because pairs dissociate and more charged impurities appear.
1 inally when P/Nd is exactly 0.5 the curves cross. In Fig. 27 we notice
that mobility measurements were not performed right up to the cross
point, but that the straight lines have been extrapolated. This procedure
was adopted of necessity, because of the high diffusivity of lithium. Thus,
Inference to Fig. 5 shows that the solubility in doped germanium de-
i (leases to a minimum as the temperature is raised from room tempera-
t ure, and there is danger of precipitation. For this reason the measure-
604
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
a
z
o
o
Ud
I/)
I
o
>
a.
Ill
a.
2
o
ffl
o
5
Ga
CONTROL \
= 9X10'^CM-A
k
2600
^^
i
a, CALCULATED
\
^ CROSS POINT
A =1.73X10-8CM
2000
\
\L '
\
\
1500
\ V
\ \
\
1000
CONTROL ^
Ga = 3x 10"CM"
\
\
\
\
A
900
H
w \
\ \
800
700
600
\ \
V
V
A
\
a, = 1.71xlO-8CM--A.
500
1 w
100
150 ?00 250 300 400
TEMPERATURE IN DEGREES KELVIN
500 600
Fig. 26 — Illustration of cross over phenomenon for germanium samples con-
taining gallium. Sample 314 contains 9 X 10^* cm"^ gallium and sample 302 con-
tains 3 X 10'^ cm"^ Samples 316 and 301 are the corresponding samples to which
lithium has been added.
ments were not carried to high temperatures.* In addition the value
of the Hall coefficient was carefully checked at each temperature to see
if it had changed. Since the reciprocal of the Hall coefficient measures
the carrier density any reduction in its value would have implied loss of
compensation, or precipitation of lithium.
Over the measured points no appreciable variation of Hall coefficient
was noted. Fortunately, the pairing relaxation time is quite small (less
than a second) at the high temperatures involved so that it wasn't
necessaiy to hold the samples at these temperatures for long periods in
order to achieve pairing equilibrium. The times involved were too short
for the occurrence of phase equilibrium characterized by precipitation.
The above discussion points up some of the care that must be taken
to obtain reliable measurements. Another factor which enters the pic-
ture is the possible existence of a precipitate in the lithium doped bridge.
* In boron-doped germanium the cross-over was actually observed — no extra-
polation having been necessary, because the temperature of intersection was suffi-
ciently low.
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 605
During the course of our experiments it was discovered that precipitates
have a profound effect on carrier mobility, reducing it so severely, that
the mobility of the lithium doped bridge may never even rise above that
of the control. Great care must be exercised in the preparation of suitable
bridges to avoid the presence of precipitated lithium. Thus it may be
necessary to saturate the bridge at a very low temperature (see Section
IV, Figure 5) so that it is somewhat undersaturated at room tempera-
ture. This means that diffusion periods of weeks may be involved.
In Fig. 26 the sample with Na = 9 X lO'' cm~^ and No = 6.1 X lO'*
cm~^ has P/Nd = 0.5 at 348°K, while the sample with AT^ = 3 x lO"
cm"* and No = 2.8 X 10^^ cm~* is half-paired at 440°K. This is to be
expected, the more heavily doped specimen remaining paired up to
higher temperatures. Using (9.6) and (9.3) it is possible to calculate a,
the distance of closest approach of a gallium and lithium ion, from each
of the measured cross points.
Thus in (9.6) we set 6 = 0.5, and Na , No and T to correspond to each
of the cases described. Having logio Q((x), a can be determined by in-
terpolation in Table III and a then determined from (9.3). Of course k
is taken to be 16. Carrying through this procedure in connection with
Fig. 26 leads to the satisfying result that a = 1.71 X 10~^ cm for the
heavily doped sample and 1.73 X 10"* cm for the lightly doped one.
The values of Q, appearing in Table IV based on a = 1.7 X 10" cm there-
fore correspond to gallium.
Not only is this result satisfying because the two a's agree so well
even though the samples involved were so different in constitution, but
also because it is expected on the basis of the addition of known particle
radii. Thus according to Pauling^^ the tetrahedral covalent radius of
gallium is 1.26 X 10~* cm while the ionic radius of lithium is 0.6 X 10"
cm. Since gallium is presumably substitutional in a tetrahedral lattice
we use its tetrahedral covalent radius, and since lithium is probably in-
terstitial we use the ionic radius. The sum of the two is 1.86 X 10 cm
which compares very favorably with the values of a quoted above.
This result constitutes good evidence that lithium is interstitial, for if
it were somehow substitutional we might expect a to be something like
a germanium-germanium bond length which is 2.46 X 10" cm. Such a
value of a would lead to profoundly different crossing temperatures (of
the order of 100° lower) so that it is not very likely.
One further point needs mention. This is the fact that as the two ions
approach very closely, the concept of the uniform macroscopic dielectric
constant, k, loses its meaning. In fact, the binding energy should be in-
creased (as though K were reduced). Crude estimates of the magnitude
606
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
of this effect based on a dielectric cavity model show it to be of the order
of some 10 or 15 percent of the energy computed on the assumption of
the dielectric continuum, the increased binding energy showing up as a
reduced value of a. This may account for the fact that the observed a,
at 1.7 X 10" cm is less than the theoretical value, 1.86 X 10" cm.
The above example shows the ion pairing phenomenon in action as a
structural tool, useful in investigating isolated impurities. In particular
the demonstration that lithium is interstitial is interesting. The values
of a have much more meaning as independent parameters in solids than
they have in liquids, where a given ion may be surrounded by a sheath of
solvating solvent molecules. Under the latter conditions the value of (i
can only be determined through application of the ion pairing theor}-
itself.
Of course, certain unusual situations arise in solids also, and values of
a (determined from ion pairing) are valuable indications of structural
peculiarities.
Similar experiments have been performed on specimens doped with
indium and boron. The results of all our investigations on the cross-over
phenomenon are tabulated in Table V. In the table the first column
lists the acceptor involved, and the second and third the appropriate
concentrations of impurities. The fourth column contains the cross-over
temperature, while the fifth, the measured value of a determined from
it. The last column lists the values of a to be expected on the basis of the
addition of tetrahedral covalent radii to the ionic radius of lithium — all
of which appear in Pauling.
The reliability of the measurements are in the order gallium, alumi-
num, boron, and indium. The principal reason for this is that the indium
crystal was not grown specially for this work and was somewhat non-
uniform. Of the two values obtained for a we tend to place more confi-
Table V
Acceptor
Acceptor
cone.
Lithium
cone.
Cross-over
Temp.
Measured
a
Pauling a
(cm-3)
(cm-3)
(°C.)
(cm)
(.cm;
B
7.0 X 1016
5.9 X 10i«
338
2.05 X 10-8
1.48 X 10-8
B
7.0 X 10i«
5.54 X 10"
320
2.27 X 10-8
1.48 X 10-8
B
7.0 X 10'«
5.85 X 10"
330
2.16 X 10-8
1.48 X 10-8
Al
9.5 X 10"
9.0 X 10"
350
1.68 X 10-8
1.86 X 10-8
Ga
3.0 X 101^
2.8 X 10"
440
1.71 X 10-8
1.86 X 10-8
Ga
9.0 X 10"
6.1 X 10"
348
1.73 X 10-8
1.86 X 10-8
In
8.3 X 10'7
1.9 X 10"
476
1.61 X 10-8
2.04 X 10-8
In
3.3 X 10"
2.68 X 10"
426
1.83 X 10-8
2.04 X 10-8
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 607
dence in 1.83 X 10~^ than in 1.61 X 10~^ cm. More work is necessary,
however, before a real decision can be made.
A feature of Table V is the fact that gallium, aluminum, and indium
exhibit orthodox behavior, i.e., the measured a's are in both cases slightly
less than those expected on the basis of the addition of radii. The in-
ternal consistency of the theory gains support from the fact that gal-
lium and aluminum behave similarly as the Pauling a's tabulated in
Table V predict. In fact if 1.83 X 10~ cm is taken as the more reliable
indium value the three cases fail to match the Pauling radii by about the
same amount, a result which implies that the disparity is due to the same
cause, i.e., failure of the dielectric continuum concept.
Another feature of Table V is the fact that boron is out of line to the
extent that the measured a exceeds the Pauling a by 50 per cent. A pos-
sible explanation is the following. The tetrahedral radii of boron and
o o
germanium are poorly matched (0.88 A and 1.26 A, respectively). The
strain in the boron-germanium bond may appear as a distortion of the
germanium atom in such a way as to increase the effective size of the
boron ion. This strain was mentioned before in Section V where it was
invoked to explain the stability of LiB~ complex in silicon.
XIII, RELAXATION STUDIES
The relaxation time discussed in Section X has been studied experi-
mentally. The following procedure was used. A specimen was warmed
to 350°K where a considerable amount of pair dissociation occurred, and
then cooled quickly by plunging into liquid nitrogen. It was then rapidly
transferred to a constant temperature bath, held at a temperature where
pair formation took place at a reasonable rate, and the change in sample
conductivity (as pairing took place) was measured as a function of time.
The principle upon which this measurement is based is the following.
At a given temperature the occurrence of pairing does not change the
carrier concentration, only the carrier mobility. As a result the measure-
ment of conductivity is effectively a measurement of relative mobility.
During relaxation the densities of charged impurities are changed, at the
most, by amounts of the order of 50 per cent. Over this range, the mobil-
ity may be considered a linear function of scatterer density. The depend-
ence of conductivity on time, as pairing takes place, must be of the form
c ^ a„-^ e-"' (13.1)
where cr^ is the conductivity when ^ = co , and r is the relaxation time de-
fined in section X while $ is some unknown constant, depending among
608
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
other things on the initial state of the system. Equation (13.1) is based
on the assumption that the number of charged scatterers decays as a
first order process, and that cr is a linear function of this number, relative
to the exponential dependence on time.
The first order character of pairing is fortunate for it renders the
measurement of r independent of a knowledge of $, i.e. independent of
the initial state of the system. This is not only fortunate from the point
of view of calculation but from experiment, since it is almost impossible
to prepare a specimen in a well defined initial state.
The unimportance of <l> is best seen by plotting the logarithm of
(T„ — (T against time. According to (13.1) this plot is specified by
log (o-« - cr) = log * + -
T
(13.1)
Thus the reciprocal of its slope measures r, and $ is not involved. Fig.
27 illustrates the data for a typical run plotted in this manner. The sam-
ple is one containing about 9 X lO'^ cm~^ gallium and the experiment
was performed at 195°K (dry ice temperature). Notice that the curve is
absolutely straight out to 3500 minutes, demonstrating beyond a doubt
that the process is first order. The relaxation time computed from its
slope is 1.51 X 10 seconds as against a value calculated by the methods
1
I
I
o
l.Or-:
0.6
0.4
0.2
0.1
1
"V,^^
\
TEm
Go
T =
T =
P = 195°
= lO'^CM"
1.66 X 10^
1.51 X 10^
3
SEC (mE/C
SEC (CAL
vSURED)
culated)
\
^\
'.!•
500 1000 1500 2000
TIME IN MINUTES
2500
3000
3500
Fig. 27 — Plot of log (o-„ — <r) as a function of time showing first order kinetics
of pairing.
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 609
10^
10=
10'
10-
102
10
/
/
THEC
)RY FC
R lO'^GALLIL
/
/
f
/
^
/
f
r
/
/
•
'theo
RY FOR 7XK
)16 BORON
i
1
0.0030
0.0035 0.0040 0.0046 0.0050
l/TEMPERATURE IN DEGREES KELVIN
0.0055
Fig. 28 — Plots of logarithm of relaxation time versus reciprocal temperature
showing agreement between theory and experiment.
of section X of 1.66 X 10 seconds. The result is in good agreement with
iiieoiy.
Studies of the kind ilkistrated in Fig. 27 have been carried out in
samples doped to various levels and also at various temperatures.
Boron and indium have been used as doping agents, as well as galHum.
Relaxation times have been measured over the range extending from
about a second to hundreds of thousands of seconds. In each case straight
line plots were obtained and the agreement between calculated and
measured r's has been as good as in the example illustrated by Fig. 28.
Relaxation connected with dissociation has also been measured with
equally satisfactory results.
Some of these data are shown in Fig. 29 where log r is plotted as a
function of reciprocal temperature for gallium and boron at two different
values of doping. The drawn curves are theoretical obtained from Fig. 20
while the points shown are experimental. It is seen that agreement is
nearly perfect. The relaxation time, true to the demands of theory, does
not seem to depend on the kind of acceptor used for doping, i.e., it is
independent of a, the distance of closest approach.
The data in Fig. 28 actually can be used to measure the diffusivity of
610 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
lithium. As must be the case from the above mentioned agreement, the
values of Do computed from them agree with the diffusion data of Fuller
and Severiens almost perfectly. This is a very quick and sensitive
method (also probably exceedingly accurate) for determining diffusivi-
ties. For example the work already completed, in effect, represents the
determination of diffusivities of the order of 10~^^ cm^/sec within a
matter of an hour, and, no doubt, smaller diffusivities could be deter-
mined by doping more heavily with acceptor.
XIV. THE EFFECT OF ION PAIRING ON ENERGY LEVELS
It was predicted in Section VIII that ion pairing would drive the
electronic energy states of donors and acceptors from the forbidden
energy region. In this section it will be demonstrated by low temperature
Hall effect measurements that the addition of lithium to gallium-doped
germanium does indeed result in the removal of states from the forbidden
gap rather than in the simple compensation which occurs when a non-
mobile donor such as antimony is added.
At low temperatures where carrier concentration, p, is less than the
donor concentration, it can be expressed in the form^^
Na - N,
V =
. {^_]^Y exp [-EJkT] (14.1)
where Na and No are the concentrations of acceptor and donor states,
respectively, irip , the effective mass of free holes, h, Plank's constant,
and Ea the ionization energy of the acceptor. The values of nip and Ea
are known for the group III acceptors.
Lithium was added to a specimen of germanium known to contain
1.0 X 10 cm~ gallium atoms and a negligible amount of ordinary
donors. Carrier concentrations for this specimen were determined from
Hall coefficient measurements. The logarithm of this concentration is
shown in Fig. 29 plotted against reciprocal temperature. The high
temperature limit of this plot fixes N a — Nd at 1.15 X 10 cm~^.
At low temperatures the curve exhibits an extended linear portion to
which (14.1) should apply. Evaluating (14.1) with p = 4.0 X 10^^ cm"' at
1/T = 0.06 deg~' and A^^ - A^^ = 1.15 x lO'' cm~^ we find that Nd =
2.6 X 10'* cm"' and A^^ = 1.4 X lO'' cm~l
Therefore, the density of apparent acceptor states has been decreased
by 1.0 X 10'® - 1.4 X 10'' = 8.6 X 10^^ cm"l The added concentration
of lithium was 1.0 X 10^^ cm"' - 1.15 X 10^^ cm"' = 8.85 X lO'^cm"',
almost identical with the loss in concentration of acceptor states. This im-
plies (as would be expected) that the lithium is almost totallj^ paired.
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 611
8
5
V
z
o
<
a:
O
I
10'
10
13
Na-Nd
TRUE Na=10'6cM"3
APPARENT Na = 1.4X10'ScM-3
-
^^^
V,
-
\
-
N
V
-
\
\
\
s.
-
\
-
\
-
\
-
_ Na-Nd f27rmpkTA^/2j'EA\ ,
P~ Nd I h2 P'UtJ'
\
\
\
0.1
0.2 0.3 0.4 0.5 0.6
1/ TEMPERATURE IN DEGREES KELVIN
0.7
0.8
Fig. 29 — Plot of hole concentration as a function of reciprocal temperature for
a sample containing ion pairs.
An even more striking result appears. From the above results the
density of lithium atoms involved in pairs is 8.85 X 10^^ cm~^ — 2.6 X
10 cm~ = 8.6 X 10 cm~ , the same number by which the density of
acceptors has been decreased! There can be little question that ion pairing
is the mechanism responsible for the removal of states.
In closing it is worth pointing out that the density of unpaned lithiums
2.6 X 10 cm~ , is certainly not characteristic of the low temperatures
at which the above Hall measurements were performed. Obviously a
density characteristic of some higher temperature has been quenched
into the specimen. At the low temperature involved the unpaired density
would be effectively zero.
XV. RESEARCH POSSIBILITIES
The fields described in the preceding text have been hardly touched,
even by this long paper, and it does not seem fitting to close without
some speculation concerning the possibilities of future work.
In the first place, there are other donors and acceptors besides lithium
which are reasonably mobile in germanium or silicon, e.g. copper, iron,
612 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
zinc or gold. To some extent the methods of this paper can be appHed
to these. Furthermore, returning to Hthium, there are impurities both
mobile and immobile which introduce more than one energy state into
the forbidden gap. The phase relations of lithium in the presence of these
should be extremely interesting since the corresponding mass action
equations are more complicated. Analogues of dibasic*^ acids and bases
should exist.
In the case of ion pairing doubly charged acceptors like zinc in ger-
manium^^ should be extremely interesting, since large amounts of pairing
should persist up to very high temperatures. In fact such studies repre-
sent excellent means of testing for the existence of doubly charged ions.
There is also the question of what happens to the two energy levels when
an acceptor like zinc pairs with a single lithium ion. Are both levels
driven from the forbidden gap or do they split under the perturbation?
Then there is the problem of ion triplets — a possibility with impuri-
ties hke zinc ■ — which is unexplored both theoretically and experiment-
ally. Also, very strange diffusion effects must occur in the presence of
doubly charged ions, to say nothing of the effect which uncompensated
mobile holes might have on relaxation processes.
The field of ion pairing in silicon is relatively unexplored.
All of the phenomena discussed in this paper must occur in the group
III-V compounds, more or less complicated by additional effects.
The question of the formation of the LiB~ complex in both germanium
and silicon needs further study. It should behave as an acceptor and its
electronic energy state might be revealed by suitable quenching
techniques.
Non ionic reactions between group V donors and group III acceptors
very likely occur, i.e., a real III-V covalent bond may be formed be-
tween such atoms dissolved in germanium or silicon at high tempera-
tures. This possibility could be investigated by looking for changes in
carrier mobility or impurity energy levels upon extended heating — in
much the same way that ion pairing has been studied. If found, the
phenomenon may provide an excellent technique for measuring the dif-
fusitivities of all classes of impurities even at fairly low temperatures.
Such compounds may possess strange energy levels and be responsible
for unexplained traps and recombination centers.
The effect of stress on the extent of ion pairing may well be profound
since there will be a tendency for such stress to concentrate at imperfec-
tions. Stress studies on ion pairing may therefore be useful for further
investigating the strain about an isolated impurity.
Ion pairing between lithium ions and acceptor centers located in
dislocations or vacancies should occur. In the first case the dislocation
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 613
would be the analogue of the polyelectrolyte molecule in the aqueous
solution.
An interesting question, in the diffusion of substitutional acceptors,
concerns whether the ion or the neutral atom is responsible for diffusion.
It is possible that the neutral atom, less securely bonded to the lattice,
is the chief agent. This might be determined by changing the ratio of
neutral atoms to ions by suitably doping with other donors or acceptors.
Doping apparently affects the concentration of vacancies which have
acceptor properties and therefore the rate of diffusion.'"'' '^^
Other interesting effects concerning the distribution of an impurity
between two different kinds sites in the lattice^^ are also possible.
These and many other fascinating fields still require exploration. We
hope to investigate some of them in the near future.
ACKNOWLEDGMENTS
The authors are greatly indebted to A. J. Pietruszkiewicz, Jr., for as-
sistance in carrying out experimental work relating to solubility and
diffusion and to J. P. Malta for help with experimental work on Hall
effect and an ion-pair relaxation. Thanks are due N. B. Hannay for many
helpful comments during the course of the work and during preparation
of the manuscript. Thanks are also due Miss M. C. Gray for the evalua-
tion of the integrals in Section VII and to F. G. Foster for the photograph
of Fig. 8. Finally the authors would like to thank the editors of the
Bell System Technical Journal for providing space so that all of the im-
portant features of our subject could be treated in one article.
Appendix A
THE EFFECT OF ION PAIRING ON SOLUBILITY
In Section VHI attention was called to the fact that ion pairing should
have some effect on lithium solubility but that it would be difficult to
achieve conditions under which the effect would be observable. Now, this
point will be enlarged upon. Consider an equilibrium like (2.1) except
imagine it to take place in germanium with gallium as the immobile ac-
ceptor. (This because germanium with gallium has been studied in ion
pairing investigations.)
Li (external) ^ Li"*" + e~
+ +
Ga~ -1- e+ (Al)
Ti U
[Li+Ga"] eV
614 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
where [Li"'"Ga~] represents an ion pair, whose concentration we denote
by P. Na and No will be the total densities of acceptor and donor re-
spectively and A" and D'^ the densities of acceptor and donor ions in the
unpaired state.
As in the main text, n and p will represent the concentrations of holes
and electrons. The following relations are then to be expected on the
basis of definition, mass action, and charge balance.
Na = A- + P (A2)
AT^ = £)+ + P (A3)
D^n = K* (A4)
np = n/ (A5)
^ = n (A6)
A+D-
D'^ + p = A~ -j- n (A7)
Equations (A4), (A5), and (A7) are just reproductions of (3.1), (3.2),
(2.8), while (A6) is the same as (9.4). The problem is to express the solu-
bility of lithium, Nd , as a function of Na ■ Manipulation of the pre-
ceding set of equations gives this result as
N. = (^^ - ^")(1 + "^") (AS)
with A~ given by the solution of
Na - A~ A-
QA-
A-
2
(A9)
+n2
/i+d
i + ^/i + i|-;^'
+ (Do*)
where Do^ is defined by (3.3). Equation (A9) generally needs to be solved
numerically for A~. •
To see what these relations predict in a special case consider the
solubility of lithium in gallium-doped germanium at 300°K. At this
temperature the values of Ui and Do^ and 12 are
rii = 2.8 X 10^' cm~^
2)/ = 7 X 10'' cm"' (AlO)
fi = l.Gl X 10^'cm"l
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 615
Table AI —
Temperature =
300°K
Na (cm-3)
Nd (cm-3)
Nd* (cm-3)
P = Na - A- (cm-3)
IQi*
1015
1016
101'
1018
1.25 X 10'*
0.94 X 10'5
0.985 X 1016
0.990 X IQi'
0.995 X 1018
1.25 X IQi*
0.875 X 10'5
0.875 X 1016
0.875 X 101'
0.875 X 10'8
0.15 X 101*
0.44 X 1015
0.77 X 1016
0.92 X 101'
0.97 X 1018
The value of Ui is taken from Figure 2, of Do'^, from Figure 5, and of fi,
from Table IV. Using (AlO) together with (A9) and (A8) leads to the
results tabulated in Table AI. In this table, Nd* represents the solu-
bility for the case 0 = 0, i.e., the solubility if there were no ion pairing.
The main feature to be obtained from the Table is that Nd is not very
much larger than Nd*, no matter how large the value of A^^ . This is
true in spite of the fact that the last column which lists P shows that at
Na = 10^^ cm~^ P is about 98 % of A''^ so that pairing of the donor is
virtually complete.
The result is not limited to the special conditions of doping and tem-
perature chosen in compiling Table AI, but must be quite general. One
can arrive at this conclusion in the following way.
By subtracting (A3) from (A2) we obtain
Na- Nd = A~ - Z)+.
(All)
^+
The quantities A~ and D appear in equations (A4) and (A7), while n
and p, appearing in (A4) and (A7) are related by (A5) . These three equa-
tions are sufficient for the determination oi D^ in its dependence on A".
' That this is the case is immediately obvious when (A4), (A5), and (A7)
are recognized as reproductions of (3.1), (3.2) and (2.8). In fact this
means that the desired relationship between D^ and A~ is nothing more
than equation (3.4) which itself is predicated on (3.1), (3.2), and (2.8).
Hut then it is known according to (3.6), that D'^ can at the most be
slightly greater than A~, although most likely less. This assumes of course
that we deal with dopings sufficiently high so that (3.5) applies. On
the other hand at low dopings (3.4) tells us that Z)"^ will be Do^. There-
fore if we work with a system in which in the absence of pairing the elec-
1 ion-hole equilibrium has driven the value of Nd close to Na (as it has
ill this system — see Nd*) the introduction of pairing cannot drive it
much higher, since according to (All) if D^ cannot get higher than A~,
\'d cannot exceed Na • This is evident in Table AI where Nd comes very
I close to Na but never exceeds it.
When A''^ is very small so that D"*" equals Do'^ and does exceed A~ by
616
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
a large amount, there can be no visible increment in solubility as a result
of pairing because P can never exceed N a which by definition is small.
The physical reason for these limitations is the following. Suppose Nd
is driven close to A''^ by the hole-electron equilibrium so that in terms of
carriers (holes and electrons) the specimen is very closely compensated.
Then if by the formation of pairs, additional donors are caused to enter
the crystal, the electrons they donate cannot be absorbed by holes be-
cause very few of the latter are present. Thus the following two sketched
equilibria will oppose each other
Li (external)
Li+
+
Ga~
Ti
[Li+Ga"]
+
(A12)
the one involving electrons attempting to drive lithium out of solution
because of the build-up of electron concentration, and the pairing equi-
librium attempting to bring lithium into solution in order to form pairs.
Thus the pairing process will not be as efficient a solubilizer as might
be thought at first.
This point can be illustrated by considering a situation in which the
germanium crystal not only contains gallium to the level, A''^ but also
an immobile donor, to the level A'^ — 0.99 N a . Thus, the crystal is almost
compensated before any lithium has been added. Nevertheless, there are
still Na gallium ions so that even though the hole-electron equilibrium,
working on the differential, 0.01 Na , cannot increase the solubility of
lithium, the pairing process might. To investigate this situation equations
(A2) to (A7) can be adopted with the simple change that (A~ — N) re-
places A~ in (A7).
Taking the situation covered by (AlO) at 300°K, Table All was com-
piled. Here again Nd* is the solubility for 12 = 0.
If only the hole-electron effect were operative, then we could not ex
pect to drive Nd much beyond Na — N. In the 10^^ case Na — A" is 10
cm"^ and in the lO" case it is 10^^ cm"'. The values of Nd* in Table All
thus confirm this argument. Furthermore, Nd is in neither case much
greater than No* showing that despite the fact that there were, respec-
14
Table AH — Temperature 300°K
Na (cm->)
N (cm-«)
Nd (cm-»)
Nd* (cm-»)
P (cm-»)
10i«
10"
0.99 X 10"
0.99 X 1017
3.2 X 101*
1.6 X 10"
1.26 X 10'*
0.88 X 10"
3 X 101* .
1.6 X 10"
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 617
lively, 10^^ and 10^^ cm~^ gallium ions available for pairing, the pairing
process did \'ery little to increase the solubility.
If the constant 9, is exceedingly large as is probably the case for a
multiply charged acceptor, it is possible that ion paring will have a meas-
urable effect on solubility.
Appendix B
concentration dependence of diffusivity in the presence of ion
PAIRING
In Section VIII it was mentioned that the diffusivity of a mobile donor
like lithium is concentration dependent when the donor participates in a
pairing equilibrium with an immobile acceptor. In this appendix we
propose to investigate the nature of the dependence.
Consider a semiconductor, uniformly doped to the level, Na , with
acceptor. Let the local density of mobile donor be Noix), x being the
position coordinate. If P(x) is the local pair concentration, then the local
density of free diffusible ions is {No — P). The flux of these diffusing
ions then depends upon the gradient (assuming Fick's law^^) of {N d —
P). Thus, if Do is the diffusivity of free donor, i.e. the diffusivity in the
absence of pairing, then the flux density is
/=-D.£(^[^) (Bl)
dX
If we apply (9.4) to the present case we can write
O = ^ ^ - {No - P) + .V.
{Na - P){Nu - P) [{Na - No) + (A^;, - P)]{No -P) ^ ^^
ifrom which it is possible to solve for {No — P). Thus
Substitution of (B3) into (Bl) yields
Do
^=-2
\[Nn-NA +
1 +
0/
/I
dNi
dx
(B4)
llf ion pairing was not thought of, the flux density would have been writ-
ten in terms of the gradient of the total concentration. No ■
f= -D^-p^ (B5)
dx
618
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
where D is the diffusivity. Comparison of (B5) with (B4) leads to the
relation
D =
Do
1 +
K^^-
N^ +
i/l(^«-
(B6)
so that D depends on the local concentration, No , of diffusant.
It is interesting to explore the limiting forms of D when No « Na and
when Nd = Na . In the latter case (B6) reduces to
1 +
^
-f
y 4fi2 ^ 12 _
(B7)
while (B3) becomes
N,
^20 y 402 ^ j2
(B8)
Substituting the left side of (B8) for the denominator involving the
radical in (B7) leads to
- = T°
1 +
2(Na - P)0 + IJ
But according to (B2), when Na = Nd ,
P
(Na - P)0 =
N,
(B9)
(BIO)
so that (B9) becomes
« = l"
1 +
2P
N.
+ 1
(B12)
Now in case the degree of pairing is high (which is, of course, the case
we are interested in) P will be almost equal to Na so that
2P
Na- P
(B13)
will be a very large number. If this is so the second term in brackets in
(B12) can be set equal to zero and we have
D,
D =
(B14)
CHEMICAL INTERACTIONS AMONG DEFECTS IN Gg AND Si 619
In the other extreme with No « Na (B6) becomes
-f
1 +
«-^^
4/laWJ
Do
1 + ^Na
(B15)
Since Q Na can exceed unity by a large amount it is evident that the re-
lation in (B15) predicts a large reduction in diffusivity towards the
front end of a diffusion curve where Nd « A^^ , and (B14) a smaller re-
duction in Do where Np may be close to Na . That part of the medium
near the front of the diffusion curve acts therefore like a region of high
resistance, confining the diffusant to the back end where the resistance
is low.
Appendix C
solution of boundary value problem for relaxation
In Section X equations (10.23), (10.21), (10.20), and (10.19) defined
a boundary value problem which we reproduce here, except that (10.20)
and (10.19) have been written more completely with the aid of (10.16).
Thus
r^ dr \ dr .
Do dt
dp , R n T
r- + ^P=0, r = L,
dr r^
r = a
p = N\ t == 0,
a <r < L
(CI)
(C2)
(C3)
In principle this problem is soluble by separation of variables.^^ Thus we
define
pir, t) = Gir) S(t) (C4)
which upon substitution into (CI), yields the two ordinary differential
equations
d
dr
2 dG , r,^
r -T- + RG
dr
+ 77'(? = 0
d (n S 2r, A
-^ + ^Z)o = 0
(C5)
(C6)
where 77 is an arbitrary positive parameter.
The allowable values of -q are determined by (C2) which can now be
620 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
replaced by
^ + ^ (? = 0, r = L, r = a (C7)
dr r^
Equation (C6) can be solved immediately to give
S,{t) = e-'''">' (C8) I
and if we assign the subscript 77 to the G going with r? the most general
solution of (CI) and (C2) will be
P = Z A,Gr,(r)e-"'''°' (C9)
where the A,, are arbitrary constants so determined that (C3) is satisfied.
Equation (C9) shows that in reality there exists, for this problem, a
spectrum of relaxation times, I/t^'Do . After a brief transient period many
of the higher order terms will decay away and eventually only the first
two terms will have to be considered. Finally when equilibrium is at-
tained only the first term Avill survive.
The last statement implies that 77 = 0, is an allowable eigenvalue, i.e.,
that the first term is independent of time. That this is so can be proved
by solving (C5) for 17 = 0, and substituting the result in (C7). Thus
Go(r) = exp (f^^ (CIO)
and this does satisfy (C7). p can then be approximated after the transient
by
p = Ao exp (j^ + ^1 Gi(r)e-''i-^'" (Cll)
from which it is obvious that the relaxation time dealt with in section X
is
T = -hr (C12)
In principle it should be possible to evaluate Gi by the straightforward
solution of (C5) and determination of the second eigenvalue through
substitution of this solution in (C7). In fact this represents a rather un-
pleasant task since G is a confluent hypergeometric function. Therefore
we shall follow an alternative route based on the assumption that by the
time (Cll) applies the flux 4xr"J*(r), where J* is given by (10. IG), is
almost independent of r. The reader is referred to some related papers '
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 621
for the justification of this view. Briefly it is permissible, after a short
transient period, in spherical diffusion, whenever the dimensions of the
diffusion field are large compared to the dimension of the sink. This re-
sults from the fact that in spherical diffusion from an infinite field a
real steady state is reached after a brief transient period. In contrast, in
plane-parallel diffusion to a sink from an infinite field, a steady state is
never reached.
Substituting (Cll) into (10.16) then yields
J* == -AAie-'"'''"' ("^ + ^ G^ (C13)
\dr r^ /
Multiplying J* by 47rr" and demanding that the product be independent
of r, leads to the relation
r'^+RG^ = 8 (C14)
dr
where 8 is constant. The solution of (C14) is
G, = exp g) + I (C15)
This is a sufficient approximation for Gi .
1 The constants r]i , Ao , Ai , and 5 must now be determined. To accom-
'plish this we note that (C2) which specifies that the boundaries at r = a
,and r = L, are impermeable is equivalent to the condition that ions be
'conserved with the interval (a, L), or that
47r ( r'p dr = N (C16)
Ja
\
\fter infinite time p is specified by the first term of (Cll) and when this
is inserted into (CI 6) the result is
Ao = NM (C17)
|,vhere M is defined by (10.26).
': Substitution of (C17) and (CIS) into (Cll) gives
p = NM exp (R/r) + (ai exp (R/r) + ^ j e""^'"'"' (C18)
Now (C3) applied to (C18) demands
NM + Ai = 0 (C19)
^ ^ N' (C20)
R
622 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
Of course this presumes that the approximation contained in (C18) is
valid down to very small values of time. This assumption is well founded
as the transient does vanish after a rather short time.
Inserting (C19) and (C20) in (C18) then gives us
p = NM exp {R/r) + N[N - M exp iR/r)]e-'"''">' (C21)
in which only 771 remains to be determined.
Substitution of (C21) into (C16), recalling the definitions of M and L,
shows that it already satisfies (C16) for any time, t. Thus (C16) cannot
be used for determining 771 .
On the other hand we note from (C21) that as soon as r becomes of
order, R, p becomes almost independent of r, being given
p = N{N + (N - M)e-'"'''''} (C22)
Since L is of the order lOR or greater, this means that throughout most
of the volume, l/N (in fact throughout 0.999 1/A^) p is independent
of r. Effectively, the entire volume 1/iV has been drained of ions, i.e.,
they have been trapped. The total ion content at time t, may then be
taken as the product of p, given by (C22), with 1/iV, that is,
N + (N - M)e-'""'''' (C23) :
The time rate of change of this content must be given by the flux Airr J*.
^[Ar+ (iV - M)e-''^'^°']
, , (C24)l
= -mDo(N - M)e-'"^°' = 47rrV*(r, t)
= -AwRN^D^e-''"''''
in which (C21) has been substituted into (10.16) to pass from the third
to the fourth expression. Comparing the second and fourth term of (C24)
reveals
or
1 KkTjN - M)
"" ~ 771'Do ~ Wn'Do
the value quoted in (10.25).
(C26)
chemical interactions among defects in ge and si 623
Appendix D
minimization of the diffusion potential
In Section V the statement was made that equation (11.2) was a valid
approximation everywhere within a p type region, provided that No
did not fluctuate through ranges of order A^^ in shorter distances than
= 4/^ (Dl)
This statement will now be proved.
The electrostatic potential is determined by the space charge equation
31
dx^
where we assume that the material is everywhere p-type so that the elec-
tron density, n, does not enter the right side of (D2). Furthermore, the
mobility of holes is so much greater than that of donor ions that the for-
mer may be considered to always be at equilibrium with respect to the
distribution of the latter. Boltzmann's law^^ may then be applied to p.
The result is
p = Na exp [-qV/kT] (D3)
where the potential is taken to be zero when p = A^^ .
Choose an arbitrary point, Xo , where the potential is Vo and investi-
gate (D2) in its neighborhood. We wish to determine the conditions under
which the right side of (D2) may be approximated by zero, i.e., the "no-
space-charge condition," in this neighborhood. The limits of the neigh-
borhood will be defined such that
\V - Vol = \n\ ^ kT/2q (D4)
so that, in it, the exponential in (D3) can be linearized
p = Na exp [- gVo/kT] (l - ||) (D5)
jThen (D2) becomes
i~ = ^ Ina [1 - exp (- qVo/kT)] - Noix)
+
w ^^p ^~ ^^°/^^^
u\
(D6)
624 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
The no space charge condition in the defined region is therefore
^ ^ Arexp(,yoAT)\ ^, ^ ,kT\ exp(-gFoAr)-l
\ q^A / \q/ exp {- qVo/kT)
To simplify notation define
expi-qVo/kT] = 70 (D8)
Next expand both No and u in Fourier series i
00
Nd = ^ As sin sx + Bs cos sx (D9)
s=0
00
u
= 2Z «3 sin s-x + jSa cos sa: (DIO)
»=o
Substitution of (D9) and (DIO) into (D6) and equating coefficients of
like terms leads to the set of relations
/3o = 4^ [^^(-^0 - 1) + ^J (1^11)
K \1 + (s2/V47r-7o)/
Now the wavelength of the sth component in (D9) is
X. = 27r/s (D14)'
If N'd contains no important components of wavelength shorter than
Vto
(D15)
the Bk for such components may be set equal to zero. But then the only-
terms which appear in (D12) and (D13) are terms where the denomina-
tors which (with the aid of (D14)) may be written as
may be set equal to k. Thus we have in place of (D12) and (D13)
a, = ^As= 4^ As (D17)
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 625
^. = 5-i 5, = -P- B, (D18)
KIT qJS AlO
The requirement that No contain no Fourier terms of wavelength shorter
than (D15) is obviously the condition that No never pass from its
maximum to its minimum value in a distance shorter than D(15). Since
we are assuming that Nd may at places be of order Na , and at others,
of order zero, this amounts to the condition that No does not fluctuate
over ranges comparable with A^^ in distances shorter than (D15).
The use of (Dll), (D17), and (D18) in (DIO) yields
kT
u
qNaJo
NAiyo — I) + '^ (As sin sx + B^ cos sx)
«=o J ,
(D19)
^ kT (70 - 1) ,kT_ND
q (to) qyo Na
which by reference to the definition (D8) for 70 proves to be identical
with (D7), the no-space- charge condition.
Equation (D19) is only true when No does not fluctuate through
ranges of order, Na , in distances smaller than //\/7o . This distance de-
pends on 7o and thus on the point where V = Vo , whose neighborhood
is being explored. Thus, we may say that there will be no space charge
at all points whose Vo is such as to fix 70 at a value such that
70 > .-2- (D20)
Amin
where Xmin is the minimum wavelength which needs to be considered in
the Fourier expansion of Nd . In terms of the definition of 70 this means
Vo <—in^ ■ (D21)
q (?■
Thus, at all points where Fo is less than the right side of (D21) the no
space charge approximation will hold. (D21) shows, that in the limit
when Xmin goes toward zero, i.e. when the infinite series must be used
for N n , the right side of (D21) will approach — 00 and Fo will satisfy
(D21) hardly anywhere. Thus space charge will exist almost eveiy where.
I In most diffusion problems the extremes of potential will occur in re-
Igions where there is no space charge. Thus in one extreme N d may equal
jO.9 N A and in the other it may equal zero. If there is no space charge in
(these extremes we may write for them
NA-Nn = V = Na exp i-qV/kT) (D22)
in which (D3) has been used. Setting N d equal to zero in one extreme
626 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
yields F = 0. In the other extreme No = 0.9 A'' a so that we get
l-T
7 = ^ ^n 10 (D23)
Q
This therefore is the largest value which Vo may assume in our case.
Inserting the expression in D21 in place of Vo we end with the relation
10 < ^ (D24)
Thus provided that in the distribution being considered
Xmin > 3.5^ (D25)
there will be no space charge anywhere.
At high temperatures 0.1 Na may be less than rii . Under these condi-
tions (D24) should be replaced by
12a. ^ Amrn ^j^26)
rii P
and in the limit that rii becomes very large it is obvious that (D26) will
always be satisfied. The rule to be enunciated for the cases we shall be
interested in is the one given in section XI, i.e. that no space charge will
exist provided that X min is no less than order, /.
Appendix E
calculation of diffusivities from conductances of diffusion
LAYERS
In this appendix equation (11.12) will be derived. In the first place
we note that the dependence of Nd on position x, and time t, will be of
the form Nc{x/\/t) at any stage of the diffusion process. This results
from a theorem due to Boltzmann^^ that when the dependence of D upon
X and t is of the form D(Nd), i.e., the dependence is through Nd , and a
semi-infinite region extending from x = 0 to a: = oo is being considered,
then, in the case of plane parallel diffusion, the only variable in the prob-
lem will be x/\/}.
Although the wafers considered in Section XI are of finite thickness d,
the stages of diffusion investigated are such that the two regions of loss
near the surfaces have not contacted each other. As a result the system
behaves like two semi-infinite regions backed against one another, and
the preceding arguments hold. The conductance 2, defined in section
XI will be proportional to the integral of the product of the local carrier
1
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 627
density by the local mobility. Thus
S = CO / ix(x, t)[NA - ND{x,t)]dx
(El)
where co is a proportionality constant and n(x, t) is the local mobility.
An upper limit of d/2 rather than d is used because of symmetry. The
local mobility will vary because No , and therefore the local density of
charged impurity scatterers, varies. Let No be the initial uniform den-
sity (before any diffusion out) of donors, and write (El) as
pan
S = CO n(x, t)[NA - No + No° - Nn(x, t)] dx
''0
= CO / IX{X, t)[NA. - Nd] dx + CO / li{x, t)[ND
Jo Jo
(E2)
- NdCxjOj^x
The second integral on the right of (E2) is given the upper limit co ,
because in the experiments we wish to perform No — No becomes zero
long before x reaches d/2.
Now in the first integral on the right of (E2) we may set fjL(x, t) equal
to the constant value no , which it assumes in the bulk of the wafer, be-
cause the breadth of the depletion layer near the surface (in which
(i(x, t) departs from juo) is small compared to d/2. The same thing can-
not be done in the second integral since the integrand vanishes beyond
the depletion layer and the total contribution comes from that layer.
We thus obtain
2 = com''(N^ - Nz,°) d/2
+ C0
X
"VV?,
.^"° - ^° ivi)] ""
(E3)
In the integral in (E3) both /x and No are represented as functions of
x/-\/i, the latter because of what has been said above, and the former,
because it is a function of the latter. Defining
V = x/2\/Dt (E4)
in which D is constant, and substituting in (E3) gives finally
2 = co/Xo(N^ - N/)f//2 + 2o^\/Di f m('')[Nz,° - Nx,(^)]rf^ (E5)
Jo
628 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
Since the definite integral is a constant (E5) shows that S is a Hnear
function of s/t^ a fact mentioned in section XL
In order to make use of the measured dependence of 2 on -sfi to
determine diffusivities, the functions y.{y) and A^d(v) must be specified.
For the latter we shall assume the Fick's law solution "
Ar„ = AT^" erf v (E6)
going with constant Z), and "N d = 0 as a boundary condition at a; = 0
at the surface. (In section XI the limitations of this assumption in the
presence of ion pairing and diffusion potential are discussed.) The v
dependence of \x is more complicated. In general, we shall be concerned
with electrical measurements in two extreme cases. In the first case
ion pairing, under the condition of measurement, is everywhere com-
plete so that the local density of scatterers will be given by
l^A - NM (E7)
In the other case ion pairing will be entirely absent, so that the local
scatterer density, will be specified by
N^ + NoM (E8)
In all experiments A^^ will be only slightly greater than Nd so that it
may be replaced by this quantity. Doing this, and substituting (E6)
into (E8) and (E9) gives
No' erfc V = N{v) (E9)
for the scattering density in the ion pairing case, and
Nn'a + erf v) = N(v) (ElO)
for the no pairing case.
Since almost all our experiments have been in germanium we now
specialize our attention to that substance. However, the procedure in-
voked below can be applied to silicon as well.
The dependence of hole mobility, n, on scattering density, A^, for ger-
manium at room temperature is shown in Fig. 30 taken from Prince's
data.^^ The integral in (E5) assumes the form
Nz," [ fxCNiv)) eric vdv. (Ell)
Jo
Choosing N{v) as either (E9) or (ElO) and using Fig. 30 together with a
tabic of error functions makes the numerical evaluation of (Ell) possible.
Since N(v) given by (E9) or (ElO) depends on No, so will the integral.
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 629
Q
Z
y <;uuu
in
> (600
Lll
^^
^^
N
s.
5 (200
z
\
\,
\
in
lU
d 800
I
u.
\
V.
\
V
O
>
\
t 400
_)
CD
O
5
h- 0
X
o
10'
10'^ (0'^ (0'° (0'
CONCENTRATION OF IONIZED IMPURITIES IN CM"^
(0"
Fig. 30 — Plot of hole-drift mobility in germanium as a function of ionized
impurity concentration after Prince.
The numerical evaluation has been performed for a range of Nd^ in
both the pairing and non-pairing cases. In this manner it has been pos-
sible to evaluate the "correction factor" t^ defined by the following equa-
tion
/ niv) erfc V dv = t?M«> / erfc v
Jq Jo
= t?Moc(0.563)
dv
(E12)
where /i^ is the mobility in the presence of A^^ scatterers. Fig. 22 contains
plots (for germanium) of i}(ND°) versus A^d" for both the pairing and non-
pairing cases. It is seen that t> is never much different from unity.
Equation (E5) can now be written as
2 = a;Mo(A^^ - ND°)d/2 + COM [i .l2St}N ^W D]\/t (E13)
Defining
2o = coMoCN^ - ^z>°)d/2
^00 — X
(E14)
(E15)
it is obvious that So is the conductance before any donor has diffused
630 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
out and S^ after all the donor has been diffused out. With these defini-
tions (E16) becomes
./..., ?-^ (^^-N^,) V. (-) =
Calling the slope of this curve S leads to the result
I
or using (E14) and (E15)
)
D = ( _^^iAZ£_ ) (E19)
This is equivalent to equation (11.12).
Glossary of Symbols
a distance of closest approach of two ions of opposite sign
A constant in expression for p in section on relaxation theory,'
A~ concentration of ionized acceptors
^0 Ar, going with t? = 0
Ai Ar, going with rji
Aj, constant preceding the Tjth eigenfunction in solution of the!
relaxation problem
A, coefficient of sin sx in Fourier expression for No
h q^/2KkT, position of minimum in g(r)
B constant in expression for p in section on relaxation theory
B~ boron ion \
B(Si) un-ionized boron in silicon ;
Bs coefficient of cos sx in Fourier expression for No
c(r) concentration of positive ions in atmosphere of a negative
ion
C concentration of LiB~
d thickness of wafer in diffusion experiment
D diffusivity of donor ion in the most general sense
Do diffusivity of donor ion m the absence of pairing
D"*" concentration of ionized donors
Do"*" value of D^ in the absence of acceptor
D*^ concentration of mobile donor ions where V = 0
e~ conduction band electron
valence band hole
.+
CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 631
, e^e" recombined hole-electron pair
E energy level in electron gas
Ed ionization energy of a donor
I Ea ionization energy of an acceptor
Ei energy level in conduction band
j E{r) chance that volume 47rr /3 will not contain an ion
I / flux density
t F Fermi level — also constant in equation (7.21)
! Qi density of states of energy Ei in conduction band
' g{r) nearest neighbor distribution function at equilibrium
I G Gibbs free energy of electron assembly
GaT gallium ion in germanium
(?„ space dependent part of relaxation eigenfunction
; Go G, for 77 = 0
Gi Gr, for r? = 171
h Plank's constant — also used for normalizing constant in
c(r)
hj number of holes in the jth energy level
H net local density of fixed donors
i{p2 , pi) £^/(r2 , n)
I field current in diffusion measurement
I(r2 , ri) integral for ion pairing calculations taken between ri and rz
J(r) current in the atmosphere of a nearest neighbor
J* flux density of ions being trapped
k Boltzmann's constant
fci first order rate constant in relaxation theory
^2 second order rate constant in relaxation theory
Ko distribution coefficient of donor between semiconductor and
external phase
Ki electron-hole recombination equilibrium constant
Ka ionization constant of acceptor
Kd ionization constant of donor
Kj constant relating wy to volume, V
K* product oi Kd , Ko, and a
I screening length for diffusion potential
L Debye length — also used for radius of volume, 1/A^
Li^ lithium ion
Li(Sn) lithium in molten tin
Li{Si) un-ionized lithium in silicon
LiSi lithium-silicon complex
LiB un-ionized LiB~
632 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
IAB~ lithium-boron complex ion in semiconductor
[Li^BT] lithium-boron ion pair
[Li^GaT] lithium-gallium ion pair
mo normal mass of electron
mp effective mass of a hole
M normalizing constant in relaxation theory
n concentration of conduction electrons — also used for density
of untrapped ions in relaxation
rii intrinsic concentration of electrons
N A total acceptor concentration
Nd total donor concentration
Nd total solubility of donor in undoped semiconductor — also used
for initial density of donors in diffusion experiments
N ion concentration in an electrolyte solution — also used for initial
value of n in relaxation — also used for concentration of im-
mobile donors in Appendix A
Nd* solubility of donor in absence of ion pairing in Appendix A
p concentration of holes
P concentration of ion pairs
q charge on an ion
Q{a) tabulated integral for computing 9,
r distance between positive and negative ions in a pair
ri a particular value of r
rt a particular value of r
R capture radius of an ion in relaxation
S slope of 2/So versus -\/f curve
S^ time dependent part of relaxation eigenfunction belonging
to eigenvalue t]
t time
T temperature
u V -Vo
V electrostatic potential — also used for volume — also used
for potential difference between probe points — also used for]
potential energy of a positive in neighborhood of negative
ion
Vo electrostatic potential where x = Xq
X variable of integration - — same as r also rectangular position
coordinate
Xo special value of a:.
1
CHEMICAL INTEEACTIONS AMONG DEFECTS IN Ge AND Si 633
zja — also used for thermodynamic activity of donor in external
phase
coefficient of sin sx in Fourier expression for u
constant in exponential in LiB~ equilibrium constant
constant in exponential in expression for vacancy concentra-
tion
/3s for s = 0
coefficient of cos 8X in fourier expression for u
pre-exponential factor in LiB~ equilibrium constant
pre-exponential factor in expression for vacancy concentra-
tion
exp[-gFoAT]
non-equilibrium nearest neighbor distribution function
constant appearing in Appendix C
eigenvalue in relaxation problem
second eigenvalue in set of q
fraction of donor paired
correction factor for variable carrier mobility
dielectric constant
xje
2ir/s, wavelength of sth component of fourier series
wavelength of component of fourier series for No , having
minimum wavelength
chemical potential of donor in an external phase — also used
for mobility of donor ion — also used for local carrier mo-
bility
chemical potential of donor in external phase in standard state
chemical potential of donor ion
chemical potential of donor ion in the standard state
chemical potential of an electron
chemical potential of donor atom in semiconductor
chemical potential of donor atom in standard state
mobility of donor atom at infinite dilution — also used for
carrier mobility in diffusion experiments before diffusion
carrier mobility in diffusion experiments after all diffusant
has diffused out
x/2VDt
e/r.
LiBT equilibrium constant
resistivity of gallium-doped germanium after saturation with
634 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
lithium — also used for local charge density in Poisson's
equation — also used for density of diffusing positive ions in
relaxation
Po resistivity of gallium-doped germanium before saturation
with lithium . J
Pi n/e I
a conductivity during relaxation |
a^ conductivity in relaxed state
S conductance between probe points
So conductance before diffusion begins in diffusion experiments;
S„ conductance after diffusion is over in diffusion experiments
T relaxation time
$ constant in relaxation formula for conductivity
"^ local electrostatic potential in ionic atmosphere
w proportionality constant connecting conductance between
probe points with integral over carrier concentration
CO; number of states in jih. level of electronic energy diagram
0 ion pairing equilibrium constant
D vacant lattice site in covalent crystal
n~ negatively charged cation vacancy
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CHEMICAL INTERACTIONS AMONG DEFECTS IN Ge AND Si 635
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636 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
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I
Single Crystals of Exceptional Perfection
and Uniformity by Zone Leveling
By D. C. BENNETT and B. SAWYER
(Manuscript received January 23, 1956)
The zone-leveling process has been developed into a simple and effective
tool, capable of growing large single crystals having high lattice perfection
and containing an essentially uniform distribution of one or more desired
impurities. Experimental work with germanium is discussed, and the possi-
bility of broad application of the principles involved is indicated.
IXTRODUCTION
The first publication describing the concept of zone melting appeared
about four j^ears ago.^ As there defined, the term zone melting designates
a class of solidification techniques, all of which involve the movement of
one or more liquid zones through an elongated charge of meltable ma-
terial. This simple concept has opened a whole new field of possibilities
for utilizing the principles of melting and solidification.
The first zone melting technique to gain widespread usage was one for
zone refining germanium by the passage of a number of liquid zones in
succession through a germanium charge. This process may be quite prop-
erly compared to distillation, the essential difference being that the
change in phase is from solid to liquid and back, instead of from liquid
to vapor and back. The zone refining technique has been eminently suc-
cessful in the purification of germanium. Harmful impurity concentra-
tions are of the order of one part in 10^". This is mainly because all the
impurities whose segregation behavior in freezing germanium has
been measured have segregation coefficients (see equation 1) differing
from 1 by an order of magnitude or more.^ During the zone refining
; operation, these impurities collect in the liquid zones and are swept
with them to the ends of the charge, which may be later removed.
1 Pfann, W. G., Trans. A.I.M.E., 194, p. 747, 1952.
^ Burton, J. A., Impurity centers in Germanium and Silicon, Physica, 20, p.
845, 1954.
637
638 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
This paper deals with a second zone melting process, zone leveling,^' ^
which has gained usage somewhat more slowly than zone refining, but
which has proved to be a highly effective tool for distributing desired
impurities uniformly throughout a charge. For this process, only one
liquid zone is used and its composition is adjusted to produce the desired
impurity concentration in the material which is solidified from the liq-
uid zone. Appropriate precautions are taken to insure the production of
single crystals, if the material is desired in this form.
Since the invention of zone leveling, the process has been developed
into a precision tool and as such it has become a preferred practical
method for growing germanium single crystals of uniform donor or ac-
ceptor content. It is the purpose of this paper to discuss the technical
development of this process, which has had two chief objectives: (1) the
attainment of the greatest possible uniformity of donor and/or acceptor
impurity distribution in the crystal ; and (2) the attainment of a germa-
nium crystal lattice with a minimum of imperfections of all kinds. The
presentation will cover the principles involved, the means developed
and results achieved toward these objectives in that order.
The first applications of the principles of zone melting have been in
the field of semiconductor materials processing, chiefly because there are
tio other known refining techniques capable of meeting the extremely
stringent purity requirements necessary for material to be used in semi-
conductor devices. Nevertheless, it is clear that these relatively simple
and very effective zone melting techniques are beginning to find a wide
variety of useful applications throughout the general fields of metallurgy
and chemical engineering.
BASIC PRINCIPLES
The basic concept, theory and experimental confirmation of zone level-
ing have been well covered in previous publications.'- ' Accordingly, the
intention here is only to repeat the salient points of the theory with a
special emphasis on the assumptions involved since it will be necessary
to refer to them.
Fig. 1 is a schematic drawing of a zone leveling operation showing a
liquid zone of constant volume containing a solute whose concentration
is Cl . As the zone moves a distance Ax an increment of germanium is
melted at the right end, and another is frozen at the left end. The
concentration of solute in the newly frozen Ax of solid solution is Cs •
The distribution coefficient k is now conveniently defined as the ratio
» Pfann, W. G., and Olsen, K. M., Physical Review, 89, p. 322, 1953.
SINGLE CRYSTAL BY ZONE LEVELING
of these solute concentrations:
k =
639
(1)
When A- < 1 , the freezing interface may be regarded as a filter permit-
ting only a fraction A: of the solute concentration in the liquid to pass into
the growing solid and rejecting the rest to remain in the liquid. If the
unmelted charge of solvent is pure — ■ that is, if no solute passes into the
zone at the melting interface it is readily seen that the liquid zone will be
: gradually depleted of its solute impurity content during passage through
the charge.
An expression for the solute concentration in the solid, Cs , deposited
there by the passage of one zone, for the case of "starting charge into
' pure solvent" has been derivec^ based on the following assumptions:
(1) The liquid volume is constant (both cross section of charge and
zone length I are constant).
(2) k is constant.
! (3) Mixing in the liquid is complete (i.e. concentration in the liquid is
uniform).
(4) Diffusion in the solid is negligible.
I The expression is
i Cs = kCo e-'"'" (2)
where Clq is the initial concentration of impurities in the liquid, I is the
zone length, and x is the distance moved by the solidifying interface. A
set of Cs versus x/l curves is shown in Fig. 2 for various k's. From this
' figure it is readily seen that when k is small the decay of Cs is slow (i.e.,
I the depletion of Cl is slight).
Largely because of this consideration, most of the practical work re-
I ported in this paper has utilized solutes in germanium having low segre-
MOVING HEATER
■ *■
cs^
'///////////,
/
/
liquid zone
"and impurity
y
SEED
r3-_^L^F
SOLID Ge CHARGE
^W%M.
AX-*
«--£—>
Fig. 1 — Schematic of zone leveling operation.
640
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
gation coefficients (usually antimony, whose k = 0.003 as donor, and
indium whose k = 0.001 as acceptor). However, the principles of zone
leveling are broad and capable of application to any solvent-solute sys-
tem within the range of solubilities of its solid and liquid phases. The
general method of attack' is first to find that composition of the liquid
zone which will deposit the desired solid solution. Secondly, if one or
more of the segregation coefficients involved is not small, the liquid zone
must be maintained at its proper composition by admixing to the solid
charge the same solutes that the zone will deposit in its product. Thus
the solutes that are removed from the liquid zone at the freezing end
will be replenished at the melting end.
The above mathematical treatment leads one to expect an essentially
uniform solute distribution throughout a zone leveled crystal for the case
under discussion in which k is small and the zone moves through a charge
of pure solvent as indicated in Fig. 2. Irregular variations of Cs along
the length or over the cross-section of the ingot are not predicted. The
CO
= 1.0
m 0.8
!< 0.6
_J
UJ
°' 0.4
z
in
O
z"
o
^
cr
(-
z
UJ
o
z
o
u
0.2
o.to
0.08
0.06
0.04
0.02
0.01
-
Cs =
kC, .
p-Wi
I
Clq=i except for k = o.oi
1
^l
^
sK
-r
\
1
\
^
\.
.^k=o
.01, Cl
0='° .
-" T-
^
NT
- \
N
Sr-*
_ai
- 1
\
\
v
...,___^
- '
1
\
0.
^\
\,
k=5.o\
\
\
\
ZONE -LENGTHS SOLIDIFIED, X/£
10
Fig. 2 — Solute concentration curves predicted for zone leveling with a start-
ing charge of solute into pure solvent.
SINGLE CRYSTAL BY ZONE LEVELING 641
treatment is not concerned with lattice imperfections in the ingot such
as dislocations, lineage, or grain boundaries. The predictions the theory
does make have been well verified by experiment insofar as it has been
possible to meet the assumptions enumerated above. However, as with
most assumptions, their validity is sensitive to the experimental condi-
tions, particularly in the cases of the first three. Much of the develop-
ment effort, especially that toward improving resistivity^ uniformity,
has been directed toward controlling the process so that these assump-
tions will be as nearly valid as possible.
Early experiments in zone leveling yielded crystals good enough to
meet device reciuirements of that time. However, as semiconductor de-
vices were designed to meet tighter design requirements, the demands
on the germanium material grew" more critical. Under these circum-
stances, it became necessary to examine the requirements on the product
of the process and what precautions would be necessary to insure that its
operation was under sufficient control. Accordingly, we shall chscuss first
the requirements on semiconductor material and then those critical as-
pects of the leveling operation which must be controlled to insure quality
of the final product.
liEQUIREMENTS ON GERMANIUM FOR SEMICONDUCTOR USES
The basic electrical bulk property of a germanium crystal is its con-
ductivity or the reciprocal of that quantity, its resistivity. For a great
majority of semiconductor uses, an extrinsic conductivity* is required in
addition to the 3^o ohm"~^ cm~' intrinsic conductivity that results at
room temperature from thermal excitation of electron-hole pairs in pure
•iermanium. An extrinsic conductivity may be either n-type or p-type.
Both of these may be produced by trace impurities distributed through-
out the crystal, the n-type by donor impurities and the p-type by accep-
tor impurities. At room temperature donors give rise to conduction elec-
trons and the acceptors to conduction holes which are free to move
within the germanium crystal. If both donors and acceptors are present
in the same crystal, the resulting electrons and holes recombine, leaving
essentially the extrinsic conductivity contributed by the excess of one
over the other, that is by | No — A''^ i .
The fundamental requirement is, then, to control the net donor and
1lie acceptor balance, | No — A^4 I , tea predetermined value throughout
the crystal. For most applications, the conductivity is to be increased
by one or two orders of magnitude above the 27°C intrinsic value. An
idea of the donor or acceptor concentrations involved may be acquired
* Shockley, W., Electrons and Holes in Semiconductors.
642 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
from noting that a conductivity of H ohm"^ cm""^ (that is, a conductivity
increased by one order of magnitude) corresponds to a No — Na concen-
tration of 7 parts per biUion.
The next most commonly measured bulk property of germanium is
the lifetime of minority carriers,^ i.e., the time constant for decay by
recombination of a surplus population of minority carriers artificially
introduced into the crystal. Minority carriers are holes in n-type ger-
manium or electrons in p-type germanium. This time constant may be
regarded reasonably as a figure of merit for the crystal, being an indica-
tion of its freedom both from certain chemical impurities and from crys-
tal faults, since these act as catalysts to the electron-hole recombination
reaction. Normally, the highest possible lifetime is desired. Thus it be-
comes important to take extreme precautions during handling and proc-
essing of the germanium to avoid contamination, particularly by such
known recombination center elements as nickel and copper and it is
also important to avoid crystal lattice faults such as dislocations, line-
age, and grain boundaries.
Another observable c^uantity has recently been gaining acceptance as
a more definite indication of mechanical crystal perfection than the mi-
nority carrier lifetime measurement. This is the etch pit density count,
€, (see Fig. 3) which is observed microscopically on an oriented (111)
surface of a Ge crystal that has been etched three minutes in an
agitated CP-4 etch (20 parts by volume concentrated HNO3 , 12 parts
concentrated HF, 12 parts concentrated acetic acid, and 3^^ part Br2).
There is strong evidence that the etch pits are formed at the intersections
of dislocations with the surface of the crystal. While an etch pit count
probably indicates only certain edge dislocations which intersect the sur-
face of the crystal, it is at least a relative indication of the total dis-
location density, and thus appears to be a highly useful index of crystal
lattice perfection.
In the last year, evidence of a strong correlation has been observed
between certain electrical properties of alloy junctions, especially the
l)reakdown voltage, and the etch pit density of the material on which
the alloy junction is made. Accordingly, material to be used for alloy
junction transistors is now selected on the basis of its maximum etch
pit count and its freedom from lineage, twin, and grain boundaries.
The usual device test requirements on n- or p-type Ge material vary
5 Valdes, L. B., Proc. I.R.E., 40, p. 1420, 1952.
« Vogel, F. L., Read W. T., and Lovell, L. C, Phys. Rev., 94, ]). 1791, 1954.
' Vogel, F. L., Pfann, W. G., Corey, H. E., Thomas, E. E., Physical Review,
90, p. 489, 1953.
* Zuk, P., and Westberg, R. W., private communication.
SINGLE CRYSTAL BY ZONE LEVELING
643
Fig. 3. — Microphotograph of Typical Etch Pits on (111) Plane.
from device to device, but may be summarized as follows:
(1) Composition — The donor-acceptor balance No — Na must be
accurately controlled so that the resistivity, p, of the crystal is uniform
and falls within acceptable tolerance limits.
(2) Macro Perfection — The crystal shall contain no grain boundaries,
lineage, or twinning.
(3) Micro Perfection — The etch pit density, e, must be lower than
a certain empirically determined maximum.
(4) Lifetime of Minority Carriers ■ — r, must usually be above a certain
minimum, although in many cases this minimum may be as low as a
few microseconds.
Assuming macro perfection a consideration of these requirements
leads directly to the two general objectives mentioned in the intro-
duction of this paper: composition uniformity and control, and crystal
lattice perfection. A third objective, high chemical purity, might also be
inferred from the lifetime requirement, but the results obtained by zone
refining raw material and by fairly standard laboratory techniques of
cleaning and baking of furnace parts at high temperature have been
.-satisfactory. Hence this objective has required little development effort.
We proceed to a discussion of critical aspects of zone leveling in the light
of the two major development objectives.
COMPOSITION UNIFORMITY AND CONTROL
The experimental development work described in this paper has been
•oncerned with the distribution of two trace impurities, indium and anti-
G44 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
mony, in a pure element, germanium. The traces are generally desired
in concentrations varying from 1 to 100 parts per billion, (p = 35 to
0.35 cocm). These amounts are too small to be detected by chemical or
spectrographic means, but are readily detectable by electrical resistiv-
ity measurements. Although this application of zone leveling is very
specific, it should be possible, as we have already suggested, to apply the
experimental results to be described to more general systems. The sub-
ject of uniformity is conveniently discussed in two sections: (a) longi-
tudinal resistivity uniformity, and (b) cross-sectional uniformity.
(a) Longitudinal Composition Uniformity
It has already been shown, by (2), that if the k is small, the variation
in Cs over four or five zone lengths should be slight. This should be true
either if a charge of pure germanium is used, or if a charge containing
the same impurity present in the liquid zone is used, provided that the
charge concentration of this impurity is of the same order of magnitude
as that sought in the product. Where the solute has a small k, the leveling
action of the zone is strong and the large C'l, that is required is relatively
unaffected by variations of the order of Cs ■
The primary cause of observed variations in the longitudinal resistiv-
ity is fluctuation of the volume of the liquid zone. If this volume increases
for any reason, the solute dissolved in it will be diluted. On the other
hand, if the volume decreases, which can occur only when some of the
liquid freezes and if k is small, most of the zone's solute will be concen-
trated in the smaller volume. Thus for small A;'s the concentration of
solute in the liquid zone, Cl , varies inversely with the zone's volume.
If Cl is to be constant, the volume must be constant, i.e. assumption (1)
must be valid.
Unfortunately, the zone volume is directly affected by many variables,
namely temperature fluctuation and drift, fluctuation in growth rate,
variation in the cross-section of the unmelted charge, variation in the
inert gas flow, and even cracks in the unmelted charge. For optimum
control of longitudinal resistivity uniformity, it is, therefore, necessary to
control all of these variables. The remainder of this section will consider
their control.
Toward minimizing the effect of temperature variation on the zone
volume, it is important to consider both the means of overall temperature
control and the design of the temperature field which melts the liquid
zone. It is clear that variation of the temperature field as a whole will
directly affect the length of the liquid zone. Accordingly, it will be im-
portant to use a precision temperature controller in order to maintain a
SINGLE CRYSTAL BY ZONE LEVELING 645
constant zone length. The controller used here is a servo system that
cycles the power on and off about ten times a second, adjusting the on
fraction of the cycle according to the demands of a control thermo-
couple. The sensitivity of the controller is ±0.2°C at 940°C. With a
liquid zone about 4 centimeters long and a temperature gradient of
about 10°C per centimeter at the solidification interface, this degree of
control should introduce longitudinal resistivity variations no greater
than ±0.3 per cent.
When other requirements permit, it is possible to design a temperature
contour to minimize the effects of control fluctuations. When the tem-
perature gradients at the ends of the liquid zone are small, a slight change
in the general temperature of the system will cause a relatively large
change in the position of the solid-liquid interface. On the other hand,
when the gradient is steep, the shift in position of the interface will be
small. It is with this consideration in mind that a temperature gradient
of about 130°C/cm is provided at the melting end of the liquid zone
(Fig. 4). A steep gradient has the added advantage that it provides a
large heat flux which is capable of supplying or removing the heat of
solidification even at relatively fast leveling rates. Thus, a steep temper-
ature gradient serves effectively to localize a solid-liquid interface. Other
considerations, soon to be discussed, dictate that a small temperature
ti;radient (about 10°C/cm) must be used at the freezing end of the zone.
Accordingly, high precision of temperature control is required to properly
stabilize the position of this solid-liquid interface.
Variation in the cross-section of the liquid zone may be controlled by
using a boat with uniform cross-section, and by using as charge material
which has been cast into a mold of controlled cross-section. Less precise
control is obtained by using ingots from the zone refining process which
were produced in a boat matched to the zone leveler boat. Even when
care is used to maintain a uniform height of the zone refined ingot, the
control is less precise than in a casting.
A constant and uniform growth rate is important toward obtaining
uniform longitudinal resistivity because segregation coefficients vary
with growth rate.^" This is especially true in the case of the/c forantimony.
Under steady state conditions, the growth rate is the rate at which the
boat is pulled through the heater. A stiff pulling mechanism is required
in order that the slow motion be steady. In the apparatus described here,
a syncronous motor, operating through a gear reduction to drive a lead
■ screw, has served to pull the boat smoothly over polished quartz rods.
"Pfann, W. G., J. Metals, 5, p. 1441, 1953.
" Burton, J. A., Kolb, E. D., Slichter, W. P., Struthers, J. D., J. Chem. Phys.,
21, p. 1991, Nov., 1953.
646
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
a;
a
>
o
o
>
o
bC
SINGLE CRYSTAL BY ZONE LEVELING 647
The true growth rate may be affected by factors that cause variations
from steady state growth such as temperature and gas flow fluctuations.
The need to control these variables has already been mentioned because
of their effect on zone volume; their effect on growth rate is thus a second
reason for their control.
Cracks or similar discontinuities in the unmelted charge act as barriers
to heat flow. Thus they cause a local rise in temperature and lengthening
of the liquid zone as the crack approaches the zone, until it is closed by
melting. The resulting transient increase in liquid volume (and in p of
the product) may be of the order of 10 per cent.
(b) Cross-Sectional Com'position Uniformity
Difficulty may be expected in controlling the cross-sectional uniform-
ity of the zone leveled ingot chiefly when the third assumption is invalid,
i.e., when Cl throughout the liquid is non-uniform. As shown in the next
paragraph, the true Cl must always rise locally near the solidifying inter-
face due to the solute diffusion which is necessary when k < \. However,
it is possible to improve the validity of assumption 3 both by slowing
Ihe groAvth rate and by stirring the liquid zone.
One can form an estimate of a theoretically reasonable growth rate
in terms of the rate of diffusion of impurities in liquid germanium. It
should be noted that movement of a liquid zone containing a solute
whose segregation coefficient is small implies a general movement by
diffusion of essentially all the solute atoms away from the solidifying
interface at a speed ecjual to the rate of motion of the zone. Even slow
zone motion corresponds to a high diffusion flux of the solute through
the Uquid. As a consequence, the solute concentration must rise in front
of the advancing solidification interface to a concentration Cl' (see Fig. 5)
until a concentration gradient is reached sufficient to provide a diffusion
flux equal to the growth rate. Fick's Law of diffusion is useful here to
calculate the extent of the rise in C/,/ at the growth interface, assuming
the liquid to be at rest. The ratio of the maximum concentration to the
bulk concentration may be taken from Fig. 5. If the maximum is to
l)c no greater than 10 per cent above the mean, a maximum growth
rate of 2 X 10~^ mils per second or 7 X 10"^ inches/hour would be
r(3(juired. Clearly, this rate is far too slow to provide an economical
means of growing single crystals. For a practical process, it will be neces-
sary to use non-equilibrium conditions at growth rates that must result
HI appreciable concentration differences within the liquid zone. Of course,
the slower the growth rate the smaller will be the diffusion gradient and
the higher will be the expected cross-sectional uniformity.
648
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
SOLID
Cs=k(x)CL=kCo)CL
fV n LIQUID
^*''*>*..,,_^^^^^ Cl (AVERAGE)-^
tQUILIBRIUM
DISTRIBUTION COEFFICIENT
~ Cu (AVERAGE)
*• MOTION OF INTERFACE
1
FOR GROWTH RATE = X
Cs= k(0)CL(AVERAGE)
..EQUILIBRIUM
DISTANCE, X
k(x) =
Cs
(7L(ave)
(3)
In practice, however, the situation is complicated by the existence of
convection currents in the liquid zone. It is true that these currents tend
to stir the liciuid zone and thereby to minimize the concentration gradient
within it. However, the currents are not uniform over the growing inter-
face and they carry liquid of varying concentrations past the interface,
causing fluctuations in Cs • Since these convection currents cannot be
eliminated, one turns to the alternative of using forced stirring of the
liquid zone. Such a forced stirring is readily available when RF induc-
tion heating is used by allowing the RF field to couple directly with the
Fig. 5 — Solute concentration in solid and liquid at equilibrium and at finite
growth rates.
If the liquid were static, that is, without any currents, it should be I;
possible to obtain a uniform, controlled solute concentration in the solid
even at appreciable growth rates, merely by adjusting the average con-
centration in the liquid to arrange that the Cl obtained at the growing
interface will be the desired one. Instead of working with the equilibrium
distribution coefficient ko , one works with an effective distribution co-
efficient k(x) for the given growth rate, x:
SINGLE CRYSTAL BY ZONE LEVELING
649
liquid zone." The resulting stirring currents are shown schematically
in Fig. 6. It is seen that the liquid is mo\'ed from the center of the zone
along its axis toward both ends. There it passes radially outward across
the interface and returns along the outside of the zone to its center.
These stirring currents are faster than convection currents and tend to
minimize the rise of Cl at the solidification interface and to improve the
uniformity of Cl and of crystal growth conditions in general over the
freezing interface.
CRYSTAL LATTICE PERFECTION
A single edge dislocation in germanium may be regarded as a line of
free valence bonds. The dislocation line is believed to have about -i X lO"
potential acceptor centers per centimeter, producing a space charge in
the neighboring germanium and strongly modifying its semiconductor
properties. A lineage boundary (a term found useful to designate a low
angle grain boundary) is a set of regularly spaced dislocations, and may
I be regarded as a surface of p-type material. Since the basic electrical
properties of a semiconductor, resistivity (and also minority carrier life-
time) are drastically out of control at dislocations and arrays of disloca-
I tions, it is easy to understand why these lattice imperfections are un-
' desirable in crystals to be used for most semiconductor purposes.
The attainment of high perfection in germanium lattices may conven-
iently be discussed in two parts: first, the growth of a single crystal of
i high perfection and, second, the preservation of the crystal's perfection
(luring its cooling to room temperature.
; The problem of growing a single crystal in the zone leveler is basically
one of arranging conditions so that the liquid germanium solidifies only
Fig. 6 — Stirring currents in liquid induced by RF induction heater.
" Brockmeir, K., Aluminium, 28, p. 391, 1952.
12 Read, W. T., Phil. Mag. 45, p. 775, 1954.
650
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
i 1
z
o
SLOW GROWTH
UJ<
11
Cj.
Oiu
(/)U
z
o
o
T GRADIENT
NO. 2
REGION OF \ ^
< CONSTITUTIONAL > \^
SUPER COOLING ^^^"^
LIQUIDUS
DISTANCE, X
DISTANCE, X
Fig. 7 — Schematic solute concentration and temperature curves in liquid, .
near freezing interface, illustrating constitutional supercooling. The left edge
of each diagram represents the solid-liquid interface.
on the single crystal germanium seed. In order to achieve this situation,
it is essential that no stable nuclei form. Thus, not only must the tem-
perature of the liquid zone be above its freezing point everywhere except
at the interface, but the liquid must also be free of foreign bodies that can
ct as nuclei. Furthermore, temperature fluctuations are to be avoided.
The requirement that the liquid temperature be above its freezing
point necessitates a slow growth rate because of what has been termed
"constitutional supercooling."^^ This phenomenon can best be described
with the aid of Fig. 7. The freezing point of a liquid is depressed by in-
creasing concentration of solutes having /c's less than unity. Because
of the rise in Cl near the solidifying interface, the freezing point is more
depressed in this region than that in the bulk of the liquid zone as shown
in Fig. 7.
It has also been shown^^ for crystals growing in one dimension that the
temperature gradient in the liquid decreases for increasing growth rates.
The temperature gradients for two growth rates are plotted on Fig. 7.
It can be seen that where the growth rate is slow and the temperatin-e
" Chalmers, B., J. Metals, 6, No. 5, Section 1, May, 1954.
" Burton, J. A., and Slichter, W. P., private communication.
SINGLE CRYSTAL BY ZONE LEVELING 651
gradient is steep, the temperature of the liquid is above its liquidus
(freezing point curve) throughout the Hqiiid, and no stable nuclei can
form. However, increasing the growth rate decreases the temperature
gradient, while it depresses the liquidus. If the temperature gradient
is reduced to that indicated for fast grow^th, a region of constitutional
supercooling will exist in front of the solidifying interface where nuclei
can form and grow. The freezing of such a crystallite onto the growing
crystal marks the end of single crystal growth.
A foreign body may also initiate polycrystalline growth. A natural site
for nucleation by foreign bodies is the wall of the boat, close to the growth
interface. Here the liquid germanium is in contact with foreign matter
at temperatures approaching its freezing point. It was found by D. Dorsi
that germanium single crystals could be grown satisfactorily in a smoked
quartz boat, at growth rates up to 2 mils per second. However, uniform-
ity considerations mentioned previously make it desirable to zone level
at much slower rates.
It is believed that scattered dislocations may be produced in a single
crystal germanium lattice by three chief mechanisms. They may be prop-
agated from a seed into the new lattice as it grows; they may result
from various possible growth faults; but probably the most important
mechanism in this work is plastic deformation of the solid crystal. The
lirst cause may be minimized by selecting the most nearly perfect seeds
available, the second by using slow growth rates, and the third by mini-
mizing stresses in the crystal.
The first hint that plastic deformation in the crystal might be an im-
portant source of dislocations came from the study of crystals pulled
from the melt by the Teal-Little technique. Frequently when sections of
crystals grown in the [111] direction were etched in CPi the pits were
arrayed in a star pattern, Fig. 8(a), in which the pits appeared on lines —
not randomly distributed. This coherent pattern suggested strongly that
the lines were caused by dislocations in slip planes which had been ac-
tive in plastic deformation of the crystal. The slip system of germanium
has been determined to be the <110> directions on {111} planes.^^
If the periphery of the crystal is assumed to be in tension, it is possible
to calculate the relative shear stress pattern in each slip system of the 3
{111 { planes which intersect the (111) section plane. The results of these
calculations are summarized in Fig. 8(b) which shows a polar plot of
the largest resolved shear stresses for these planes and also their traces
in the section plane. The agreement with the observed star pattern is
striking.
15 Treuting, R. G. Journal of Metals, 7, p. 1027, Sept., 1955.
652
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
Fig. 8 (a)-
from melt).
Star Pattern on (111) plane (etched cross-section of crystal pulled
The peripheral tension assumed in the above paragraph may be seen
to be quahtatively reasonable upon consideration of the heat flow pat-
tern of the crystal during growth. Heat must enter the crystal by
conduction through its hottest surface, the gro^\^ng interface, which
is a 940°C isotherm. It must leave through all the other surfaces by
radiation and conduction. Therefore, these surfaces must be cooler
than their adjacent interiors, and cross-sections of the crystal must
have cooler peripheries than cores because of the heat escaping from
the peripheral surfaces. Due to thermal contraction the cooler periphery
must be in tension and the core in compression.
In zone leveled crystals the distribution of etch pits on a (111) section
was not dense or symmetric enough to display a star pattern. However,
it was reasoned that since thermal contraction stresses appeared to play
a major role in the production of dislocations in pulled crystals through
plastic deformation in the available slip systems, the same mechanism
might be playing a significant role in zone leveled crystals.
.' "-.The only stresses in a zone leveled ingot other than those due to the
weight of the crystal itself must be those due to non-uniformities in
SINGLE CRYSTAL BY ZONE LEVELING
653
thermal contraction. Consider a small increment of the length of a newly
formed zone leveled crystal as heat flows through it from its hotter to its
colder ends while the crystal moves slowly through the apparatus. Heat
flows in by conduction from the higher temperature germanium adjacent
to it. Heat leaves not only by conduction out the other end, but also by
conduction and radiation from the ingot surface. Because of this latter
heat loss, there is a radial component as well as a longitudinal component
to the temperature gradient. The cooler surface contracts resulting, as
above, in peripheral tension and internal compression. Clearly if the
radial component of heat flow could be eliminated, there would be no
peripheral contraction. Accordingly, the most desirable temperature dis-
tribution is one whose radial heat flow is zero, i.e., a case of purely axial
or one dimensional heat flow, which implies a uniform temperature
gradient along the axis of the ingot. In practice, it is difficult to obtain
a uniform axial temperature gradient except for the special case of a
very small one. This may be obtained fairly easily by the use of an ap-
/ / / ffr
/ / / ^—
TRACE OF (ill)
-TRACE OF (Tll)
r /
/ /
7 / /
' ^^^N
— 7 ' / / / *
///'// \ , _,
N / / / /trace of (iii)
'', / / /
[oTi]
resolved s
STRESS (u
stress (Tm)-
STRESS (lTl) - -"
IT)- / / \\\\////
" ^' \\v///
\\v/
\v/
Fig. 8(b) — Resolved shear stress and slip-plane traces on (111) Plane.
u.
I-
<:
H
C,
<
654
SINGLE CRYSTAL BY ZONE LEVELING 655
propriate heater. The heater designed for this purpose is called an after-
heater and is shown in Figs. 4 and 9.
The after-heater reduces the heat loss by radiation and radial conduc-
tion from the crystal maintaining the entire crystal at a temperature
only slightly below its melting point throughout its growth. After
zone leveling has been completed, the entire ingot is cooled slowly and
uniformly. Of course, a finite temperature gradient must exist at the
liquid-solid interface. The gradient at the interface of the leveler shown
in Figs. 4 and 9 is about 10°C per centimeter and the maximum gradient,
about yi inch into the solid, is 30°C per centimeter. The gradient de-
creases slowly to nearly zero within the after-heater, as can be seen in
the measured temperature curve of Fig. 4.
A ZONE LEVELING APPARATUS AND TECHNIQUE FOR GERMANUIM
The apparatus required for zone leveling is basically simple. A single
crystal seed, the desired impurities, and a germanium charge, are held
in a suitable container in an inert atmosphere. Provision is supplied for
either moving a heater along the charge or the charge container through
a heater. The heater may be either an electric resistance type or a radio
frequency induction type. The resistance heater offers the advantage of
economy while the induction heating offers the advantage of direct in-
ductive stirring of the melted zone by the RF field, which, as mentioned
previously, is helpful in attaining uniformity of impurity distribution,
and is therefore to be preferred for critical work.
Schematic drawings of an RF powered zone leveler following in general
the original design by K. M. Olsen are shown in Fig. 9 in two useful
configurations. The outer clear quartz tube serves to support the inner
members of the apparatus and also to contain the inert atmosphere for
which nitrogen, hydrogen, helium, or argon, can serve. For this appara-
tus, a quartz boat is used to contain the germanium, since it permits
inductive stirring of the liquid germanium by the RF field. The auxiliary
fore and after heaters, which are made of graphite, have special purposes
discussed in the two preceding sections. A typical boat used in this ap-
paratus is about 16" long, is smoked on the inside, and is made of thin-
walled clear quartz of V I.D. and of semi-circular cross-section. A normal
charge of zone refined Ge and seed is about 12 inches long and weighs
about 500 gm. A photograph of the assembled apparatus appears in
Fig. 10.
For the best results in crystal perfection and resistivity uniformity,
the apparatus is run with the full length after-heater and at a slow pull
rate, 0.09 mils per second (approximately 1" in three hours). For some-
what less critical demands a pull rate 10 times faster is used, with a short-
ened after-heater or none at all.
If it is desired to reproduce a resistivity obtained in the zone leveler,
it is very convenient to reuse the solidified zone containing the impurity
addition that yielded the desired resistivity. This solid zone, if undam-
aged (when cut from the finished ingot), will contain all of the sohite
that was not deposited during the ingot run. When it is remelted next
to a seed the solute will redissolve into the liquid to yield very nearly
SINGLE CRYSTAL BY ZONE LEVELING 657
Fig. 11. — Photograph of zone leveled single crystal ingot.
the same Cl , provided that the zone vokime is accurately reproduced.
In this way it is readily possible to resume leveling as before and hence
virtually to reproduce a desired resistivity. For the small k solutes,
In and Sb , discussed in this paper the loss of d in one leveling run is so
small as to be insignificant compared to other sources of error in this
quantity.
' PILOT PRODUCTION RESULTS
The capabilities of the zone leveling equipment and techniques just
I described may be evaluated with reasonably good accuracy on the basis
1 of the measurement results obtained from more than 300 single crystal
1 ingots so produced. Over 200 of these crystals were grown in the after-
heater at the "slow" growth rate of 0.09 mils per second. The rest were
I grown with a short after-heater or none at all at a growth rate about ten
times greater.
The ingots to be measured (see Fig. 11) were usually 4-6 inches long
after removing seeds and solidified zones (i.e., 2-3 zone lengths), and
were cut into 1 inch lengths. The p, r, and e measurements were taken
^ on the flat ends of these segments. The results of the observations will
' be summarized and discussed in terms of the four device test require-
ments described earlier.
(1) Compositional Uniformity
The resistivity measurements were taken with a calibrated 4-point
probe technique at five locations on each ingot cross-section (center, top,
bottom and each side). The spacing between adjacent points of the probe
was 50 mils. Accordingly, these measurements would be insensitive to p
fluctuations in the material of this order or smaller. However, an investi-
gation by potential probing techniques, of Ge filaments cut from zone
leveled ingots indicates that p fluctuations in zone leveled material are
'6 L. B. Valdes, Proc. I.R.E., 42, p. 420, 1954.
" Erhart, D. L., private communication.
G58 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
Table I — Average Resistivity Variations
(A) Along length axis. Grand Length Average ± 10%.
Growth Rate
Mils per Second
0.9
0.8
0.09
n-Type
±%
9.9
7.6
9.0
No. of Ingots
27
12
108
p-Type
±%
10.9
17.4
9.3
No. of Ingots
33
16
137
Average
± /o
10.4
13.2
9.2
(B) Over Cross-Section
Growth Rate
n-Type
p-Type
Average
Mils per Second
±%
No. of Ingots
±%
No. of Ingots
±%
0.9
0.8
0.09
9.5
8.3
4.3
22
12
93
8.5
6.9
2.3
30
14
122
8.9
7.5
3.2
generally coarse — • changing over distances 2 to 5 times larger in dimen-
sion than the 50 mil dimension in question. Thus the p data summarized
here should give a reasonably valid representation of the true p variations
in the ingots measured.
Table I summarizes the resistivity variations recorded as percentages
of the mean resistivity of each ingot. These variations are separated into
those observed (a) along the length axis and (b) over the cross-section,
for the different growth conditions and resistivity types.
It is readily seen that the average variation along the length, about
±10 per cent, is larger than the average cross-sectional variation. The
variations are not systematic along the length of the ingot and are
chiefly due to fluctuation in the length of the liquid zone. An appreciable
part of this variation is due to the effect, mentioned earlier, of discon-
tinuities in the unmelted charges between 1 inch lengths of crystals
that were being releveled. A smaller length variation of p, about ±7
per cent, was observed in those ingots grown from continuous charges.
Part B of the table shows that the variation of p over the cross-section
is sensitive to the growth rate in the range covered. For slow growth, it
is small, and one would reasonably expect that if further improvement
in p variation were required, it should first be sought by improving the
control of the zone length.
(2) Macro Perfection
Macro perfection of the pilot production product is extremely high.
There were essentially no cases of polycrystallinity, or twinning, except
SINGLE CRYSTAL BY ZONE LEVELING
659
300
200
100
600
400
200
100
5 80
Z 60
tu 40
I- 400
LU
LL
_l
200
<
liJ 100
< 80
60
40
20
10
FAST p
(a) NO AFTER-HEATER
FAST n
1
SLOW n + p
in
Q
z
o
o
LU
10
o
cc
u
(b) 5" AFTER -HEATER
^ — ^
^^
.-'-"''
^— — "^
':^
^"
"slow p
" ^^ t
/
.^--^
^^Low n
(C) 12"
AFTER-h
HEATER
^^ — — "^
-•'''
^t
,-""
^^^00""''''''''^
^
x'
^.^
SLOW Pj
-' >
^^
y'^
^/^Low n
y
■v
''V
/
2 3 4 5
DISTANCE FROM SEED IN INCHES
Fig. 12 — Average minority carrier lifetime plotted against distance from seed
for 2-8 ohm cm crystals grown with 12", 5" and no after-heaters.
for clearly attributable causes such as power or equipment failure. There
were few cases of lineage in the short after-heater and virtually none in
the full after-heater, while lineage is not uncommon in ingots grown with
no after-heater.
(3) Micro Perfectio7i
Table II summarizes the etch pit density, e, measurement results. In
general, it can be seen that with the after-heater one can expect etch
pit counts of the order of 1,500 pits per cm- which is lower than results
without an after-heater by about an order of magnitude (and lower than
Table II — Average Etch Pit Densities, e
Growth Rate
Mils per Second
« Ave
a
No. of Ingots
(12" after-heater)
(5" after-heater)
No after-heater
0.09
0.09
0.9
0.9
1560
3800
7000
11000
770
1600
1900
6600
39
3
3
6
G60 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
e's of pulled Ge crystals by about two orders of magnitude) . The lowest
average count that has been observed is 40 pits per cm^ This crystal
was found to have the smallest X-Ray rocking-curve widths observed in
germanium at Bell Telephone Laboratories — very nearly the the-
oretically ideal mdths. The perfection indicated is exceptional — com-
parable to that of selected quartz crystals.
(4) Lifetime of Minority Carriers
T data are summarized in Fig. 12 in which are plotted averages of the
r measurements on the ingot sections against distance from the seed.
One sees a systematic rise in t along the length axis of an ingot grown
slowly in the after-heater. This is interpreted to indicate that the ingot is
being slowly contaminated with chemical recombination centers during
its long wait inside the after-heater at high temperatures. If improvement
were needed in lifetime, it should be sought first by increasing the chemi-
cal cleanliness precautions, which were nonetheless strict in this work.
SUMMARY
A zone leveler has been developed to provide growth conditions suit-
able for the production of quality germanium single crystals. The crys-
tals are nearly uniform and have exceptionally high lattice perfection, jri
Similar levelers are in use in production. ''
The apparatus developed has been used to supply germanium single
crystals for experiments and for the pilot production of a variety of point
contact, alloy, and diffusion transistors. The machine operating at slow
growth rate with an after-heater can produce one 6-inch 250-gm crystal
per day. For less critical demands, it can produce several longer crystals
per day.
Evaluation of the product indicates that resistivity variation on a
cross-section of the ingot can be ±3 per cent and that along the length
axis it can be controlled to ±7 per cent if a continuous charge is used.
Furthermore, the crystals contain no grain boundaries or lineage and
the scattered etch pit densities average about 1,500 per cm-. Thus, the
zone leveling process has proved to be simple, efficient, and capable of
more than meeting the present specifications for quality germanium
single crystals.
ACKNOWLEDGMENTS
i
The authors arc indebted for the help and cooperation of many people,
especially that of L. P. Adda and D. L. Erhart who guided the evaluation
of zone leveled material summarized above, and that of F. W. Bergwall
through whose patient effort and suggestions the machine worked.
Diffused p-n Junction Silicon Rectifiers
By M. B. PRINCE
(Manuscript received December 12, 1955)
Diffused p-n junction silicon rectifiers incoryorating the feature of con-
ductivity modulation are being developed. These rectifiers are made by the
liiffusion of impurities into thin wafers of high-resistivity silicon. Three
\ development models with attractive electrical characteristics are described
irhich have current ratings from 0 to 100 amperes with inverse peak voltages
qreater than 200 volts. These devices are attractive from an engineering stand-
point since their behavior is predictable, one process permits the fabrication
of an entire class of rectifiers, and large enough elements can be processed
so that power dissipation is limited only by the packaging and mounting
■of the unit.
l.n INTRODUCTION
1.1 The earliest solid state power rectifier, the copper oxide rectifier,
was introduced in the 1920's. It found some applications where effi-
ciency, space, and weight requirements were not important. In 1940
the selenium rectifier was introduced commercially and overcame to a
great extent the limitations of the copper oxide rectifier. As a result,
the selenium rectifier has found wide usage. In early 1952 a large area
licrmanium^ junction diode was announced which showed further im-
' provements in efficiency, size, and weight. In addition it shows promise
of greater reliability and life as compared to the earlier devices. How-
ever, all of these devices have one drawback in that they cannot operate
111 ambient temperatures greater than about 100°C.
Also in 1952, the silicon alloy^ junction diode was announced and was
shown to be capable of operating at temperatures over 200°C. However
it was a small area device and could not handle the large power that the
other devices could rectify. During the past three years development
has been carried on by several laboratories in improving the size and
power capabilities of these alloy diodes. In early 1954 the gaseous diffu-
' Hall, R. N., Proc. I.R.E., 40, p. 1512, 1952.
2 Pearson, G. L., and Sawyer, B., Proc. I.R.E., 40, p. 1348, 1952.
661
662
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
(a)
FORWARD
REVERSE
a:
a:
D
U
(b)
/rs
y^^
Vb
v„
VOLTAGE
Fig. 1 — (a). Ideal rectifier, (b). Semiconductor rectifier.
sion technique^ for producing large area junctions in silicon was an-
nounced. This technique lends itself very readily to controlling the
position of junctions in silicon. An early rectifier^ made by this tech--
nique was one half cm^ in area and conducted 8 amperes at one volt in i
the forward direction and about 2 milliamperes at 80 volts in the re--
verse direction. The series resistance of this device was approximately'
0.07 ohms.
1.2 In order to understand quantitatively the problems associated!
with power rectifier development, consider Fig. 1(a) which shows what I
an engineer would like in the way of an ideal rectifier. It will pass a
large amount of current in the forward direction without any voltage.
3 Pearson, G. L., and Fuller, C. S., Proc. I.Il.E., 42, No. 4., 1954. I
DIFFUSED p-> JUNCTION SILICON RECTIFIERS 663
drop aiul will pass no current for any applied voltage in the reverse
direction. At present no device with this characteristic exists. A typical
semiconductor rectifier has a characteristic of the type shown in Fig.
1(b). In these devices there is a forward voltage, Vo , that must be de-
veloped before appreciable current will flow and a series resistance,
Rs, thru which the current will flow. In the reverse biased direction
there is a current that will flow due to body and surface leakage and
that usually increases with reverse voltage. At some given reverse volt-
age, Vb, the device will break down and conduct appreciable currents.
To have an efficient rectifier, Vo and Rs should be as small as possible
and Vb should be as large as can be made; also, the reverse leakage cur-
rents should be kept to a minimum. According to semiconductor theory.
To depends mainly upon the energy gap of the semiconductor, in-
creasing with increasing energy gap. Rs consists of two parts; body re-
sistance of the semiconductor and resistance due to the contacts to the
semiconductor. The higher the resistivity of the semiconductor, the
higher is the body resistance part of Rs ■ The leakage currents in the
reverse direction depend to some extent on the energy gap of the semi-
conductor, being smaller with larger energy gap; and Vb depends most
strongly on the resistivity of the semiconductor, being larger for higher
resistivity material. Another factor that is important in the choice of
the semiconductor is the ability of devices fabricated from the semi-
conductor to operate at high temperatures; high temperature operation
of devices improves with larger energy gap semiconductors. Thus there
are two compromises to be made in choosing the material (energy gap)
and resistivity of the semiconductor.
1.3 This paper reports on a special class of rectifiers in which im-
proved performance has been obtained. These devices are made by
using the diffusion technique with silicon. The diffusion process permits
both accurate geometric control and low resistance ohmic contacts,
which in turn makes it possible to reduce Rs to very small values inde-
pendent of the resistivity of the initial silicon. Therefore, high resis-
tivity material can be used to obtain high Vb ■ An explanation of this
result is given in Section 3. Silicon permits small reverse currents and
high temperature operation. Its only drawback is that Fo ^^ 0.6 volts.
Rectifiers made of silicon with the diffusion technique are able to pass
j hundreds of amperes per square centimeter continuously in the forward
( direction in areas up to 0.4 square centimeter. One type of device whose
i area is 0.06 cm- readily conducts ten amperes with less than one volt
forward drop. The forward current voltage characteristic of this family
of rectifiers follows an almost exponential characteristic indicating that
664 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 |
Rs is extremely small (<0.05 ohms). Although the measured reverse
currents are greater than those predicted by theory for temperatures
up to 100°C, the reverse losses are low and do not affect the efficiency
appreciably. ,1
1.4 The diodes made by the diffusion of sihcon are very attractive'
from an engineering standpoint for several reasons. First of all, their ;
behavior is predictable from the theory of semiconductor devices, as
are junction transistors. This makes it possible to design rectifiers of
given electrical, thermal, and mechanical characteristics. Secondly, :
rectifier elements of many sizes are available from the same diffused <
wafers making it possible to use the same diffusion process, material,
and equipment for a range of devices. Thirdly, large enough elements
can be processed so that the power dissipation in the unit is limited
only by the thermal impedance of mount and package.
2.0 DIFFUSION PROCESS
t
2.1 It will be shown in 3.2 that the forward characteristic of these
devices is practically independent of the type (n or p) and resistivity
of the starting material. The reverse breakdown voltage of a silicon p-n
junction depends primarily on the resistivity of the lightly doped region.
With these two considerations in mind; that is, to fabricate rectifiers
having the desirable excellent forward characteristic and at the same
time high reverse breakdown voltage, high resistivity siUcon is used as ;
the starting material for the diffused barrier silicon rectifiers. Single
crystal material has been found to give a better reverse characteristic
than multicrystalline material. Also, it has been found that p-type ma-
terial has yielded units with a better reverse characteristic than n-type
material. Therefore, in the remainder of this paper, we will limit dis-';'
cussion to rectifiers made from high resistivity, single crystalline, p-type /"i
silicon. We will designate this material as ir type silicon.
2.2 In addition to the fine control one has in the diffusion process
(see 2.4), the process lends itself admirably to the semiconductor recti-'
fier field in as much as the distribution of impurities in this process re- ;
suits in a gradual transition from a degenerate semiconductor at the'
surface of the material to a non-degenerate semiconductor a short dis-
tance below the surface. This condition permits low resistance ohmic
metallic; contacts to be made to the surfaces of the diffused silicon.
In order to create a p-n junction in the x silicon, it is necessary to
diffuse donor imjiurities into one side of the slice. Although several donor
type imi)urities have been diffused into siUcon, all the devices discussed
I
DIFFUSED p-n JUNCTION SILICON RECTIFIERS
665
in this paper were fabricated by using phosphorus as the donor impurity.
In order to make the extremely low resistance contact to the tt side of
the junction that is desirable in rectifiers, acceptor nnpurities are dif-
fused into the opposite side of the x silicon slice. Boron was selected
from the several possible acceptor type impurities to use for the fabri-
cation of these devices. A configuration of the diffused slice is shown in
Figure 2.
2.3 It will be shown in Section 3 that there are limits to the thick-
nesses of the three regions, N-{-, x, P+, due to the nature of the opera-
tion of these rectifiers With present techniques, it is necessary to keep
^LOW-RESISTANCE CONTACTSn
/ . . _ -\
ACTIVE p-n
JUNCTION
Fig. 2 — Diffused silicon rectifier configuration.
the thickness of the t region to the order of two or three mils (thou-
sandths of^an inch).
2,4 In the diffusion process of introducing impurities in silicon for
the purpose of creating junctions or ohmic contacts, the diffusant is
deposited on the silicon and serves as an infinite source. The resulting
concentration of the diffusant is given by
9 rx/\/iDt ,
c = Cc 1 - 4- / ^ dy
V TT ''0
(1)
= Co erf c y
where C = concentration at distance x below surface
Co = concentration at surface
D = diffusion constant for impurity at temperature of dif-
fusion
66G THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
t = total time of diffusion
X
y = /jyr- = variable of integration
A plot of C/Co = erfc y versus y is given in Fig. 3. Co is the surface solu-
bility density and depends upon the tempers are of the diffusion proc-
ess/ At some depth, Xj , the concentration C equals the original im-
purity concentration where the silicon will change conductivity type
resulting in a junction. In order to obtain desirable depths of the dif-
fused layers, A^+ and P+, it is necessary to diffuse at temperatures in
the range of 1000°G to 1300°C for periods of hours. With such periods
it is obvious that the diffusion process lends itself to easy control and
reproducibiUty.
.3.0 CONDUCTIVITY MODULATION
3.1 It is well known that the series resistance of a power rectifier is
the most important electrical parameter to control and should be made
as small as possible for several reasons. The series resistance consists
essentially of two parts; the body resistance of the semiconductor and
the contact resistance to the semiconductor. In the early stages of recti-
fier development both parts of the series resistance contributed about
equally to the total series resistance. However, methods were soon found
to reduce the contact resistance. It then became apparent that in order
to reduce the body resistance, the geometry would have to be changed
and the resistivity chosen carefullJ^ By going to larger, thinner wafers
it was possible to reduce this body resistance. However, the cost of
pure silicon made it important that conductivity modulation (described
below) be incorporated in these devices as a method for reducing the
body resistance. Our initial attempts were successful due to the fact
that higher lifetime of minority carriers could be maintained in the ex-
tremely thin wafers that were used as compared to the lifetime remain- ^
ing after the diffusion process in thicker wafers.
3.2 A complete mathematical description of the I-V characteristic
for the conductivity modulated rectifier is practically impossible due
to the fact that the equations are transcendental. However, it is easy
to understand the operation of the device physically.
When the device is biased in the forward direction, electrons from
the heavily doped N-\- region are injected into the high resistivity ir
region. If the lifetime for these electrons in the tt region is long enough,
the electrons will diffuse across the w region and reach the P-f region
* Fuller, C. S., and Ditzenberger, J. A., J. Appl. Phys., 25, p. 143!), li)54.
DIFFUSED jy-n JUNCTION SILICON RECTIFIERS
667
II
10
10
10"
10
10"
10
2
3
4
5
6
7
0.4
O.f
1.6
2.0
y
2.4
3.2 3.6 4.0
Fig. 3. — Error function complement.
with little recombination. To maintain electrical neutrality, holes are
jinjected into the x region from the P+ region. These extra mobile car-
riers (both eleictrons and holes) reduce the effective resistance of the tt
jlayer and thus decrease the voltage drop across this layer. The higher
(he current density, the higher is the injected mobile carrier densities
Mid therefore, the lower is the effective resistance. It is for this reason
iliat the process is termed conductivity modulation. This effect tends
'to make the voltage drop across the tv region almost independent of the
current, resistivity, and semiconductor type.
When the junction is biased in the reverse direction, a normal re-
verse characteristic with an avalanche breakdown is expected and ob-
served.
3.3 The forward characteristic of a typical \uiit is plotted semi-
logarithmically in Fig. 4. The best fit to the low current data can be
G68
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
expressed as
/ = 7oe«^'^'=^
where I = current thru unit
7o = constant
q = charge of electron
V = voltage across unit
k = Boltzmann's constant
T = absolute temperature
and 1< .V < 2.
(2)
10
10"
to
a
UJ
Q.
<
UJ
<£.
o
10
-2
10"
10
10
10
y
/
/
/^
/
/
/
/
/
/
f
/
r
y
/
/
/
qv/i.29kT
I = Ioe
/
/
/
/
v
-6
0.2
0.3
0.4
0.5 0.6
VOLTS
0.7
0.8
0.9
Fig. 4 — Forward characteristic of silicon power rectifier.
DIFFUSED p-n JUNCTION SILICON EECTIFIERS
CG9
I
O
<
UJ
u
z
<
HI
tr
100
50
20
10
1.0
0.5
0.2
O.t 0
0.05
0.02
0.01
1
k
\
N
\,
T
k
S."
\
s.
N
\
V
°\
\,
S
k
N
\
\
0.001
0.01 0.1 1.0
CURRENT, Idci'N amperes
10
Fig. 5 — Small signal resistance versus dc forward current.
The departure of the high current data from the exponential charac-
teristic is due to the contact resistance. Another interesting measure-
ment of the forward characteristic is given in Fig. 5 where the small
signal ac resistance is plotted as a function of the forward dc current
for a typical rectifier element. The departure from the simple rectifier
theory^ where iV = 1 is not surprising inasmuch as p-n junctions made
by various methods and of different materials almost always have A^ > 1.
Several calculations have been carried out using different assumptions
and all indicate that the forward characteristic is independent of the
type and resistivity of the middle region as long as the diffusion length
for minority carriers is the order of or larger than the thickness of the
region.
3.4 In order to go to higher reverse breakdown voltages (>500 volts)
it is necessary to use still higher resistivity starting material. It might
be expected that intrinsic silicon will be used for the highest reverse
breakdown voltages when it becomes available. How^ever, in this case
" Shockley, W., B.S.T.J., 28, p. 435, 1949.
II
070 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1950
thick wafers are necessary since the reverse biased junction space charge
region extends rapidly with voltage for almost intrinsic material, and
high lifetime is necessary in order to get the conductivity modulation
effect in these thick w^afers. Therefore at present it is necessary to com-
promise the highest reverse breakdown voltages with the lowest for-
ward voltage drops, in a similar manner to that discussed in Section 1.
However this is now done at a different order of magnitude of voltage
and current density. |
4.0 FABRICATION OF MODELS
4.1 It has been pointed out in Section 1.2 that a low series resistance,
Rs , is desirable and that it is composed of two parts; the body resistance
and the contact resistance. In Section 3 a method for reducing the body
resistance was described. The contact resistance can also be made very !
low. It has been found to be very difficult to solder low temperature
solders (M.P. up to 325°C) to silicon with any of the standard commer-
cial fluxes. However, it is quite easy to plate various metals to a surface
of silicon from an electroplating bath or by an electro-less process^ to !
which leads can readily be soldered. Some metals used for plating con-
tacts are rhodium, gold, copper, and nickel. This type of contact yields
a low contact resistance. Another techniciue that has shown some prom-
ise for making the necessary extremely low resistance contact is the
hydride fluxing method.'^ 1
4.2 A wafer which may be about one inch in diameter is ready to be i
diced after it is prepared for a soldering operation. Up to this point all ;
the material may undergo the same processing. Now it is necessary to '
decide how the prepared material is to be used; whether low current i
('^l amp) devices or medium or high current ('^10-50 amps) devices;.
are desired. The common treatment of all material for the entire class i
of rectifiers is one reason these devices are highly attractive from a .
manufacturing point of view. |
The dicing process may be one of several techniques; mechanical!
cutting with a saw, breaking along preferred directions, etching alonii
given paths with chemical or electrical means after suitable maskiiiti
methods, etc. In the case of mechanical damage to the exposed junc-
tions, the dice should be etched to remove the damaged material. The
dice are cleaned by rinses in suitable solvents and are then ready for
« Brenner, A., and Riddell, Grace E. J., Proc. American Electroplaters' Society,
33, p. 16, 1946,34,1). 156, 1947.
' Sullivan, M. V., Hydrides as Alloying Agents on Silicon, Semiconductor
Symposium of the Electrochemical Society, May 2-5, 1955.
I
DIFFUSED p-n JUNCTION SILICON RECTIFIERS
671
assemlily into the mechanical package designed for a given current
rating.
4.3 The dice may be tested electrically before assembly by using
pressure contacts to either side. Pressure contacts have been considered
for packaging the units; however, this type of contact was dropped from
development due to mechanical chemical, and electrical instabilities.
4.4 The drawbacks of the pressure contact make it important to find
a solder contact that does not have the same objections. The solder used
should have a melting point above 300°C, be soft to allow for different
coefficients of expansion of the silicon and the copper connections, wet
the plated metal, and finally, be chemically inactive even at the high
temperature operation of the device. These recjuirements are met with
many solders in a package that is hermetically sealed. This combina-
tion of a solder and a hermetically sealed package has been adopted for
the intermediate development of the diffused silicon power rectifiers.
5.0 ELECTRICAL PERFORMANCE CHARACTERISTICS
5.1 Before describing the electrical properties of these diodes, let us
consider some of the physical properties of a few members of the class.
r~=^^T:)
SMALL
0-1 AMPERES
MEDIUM
1-10 AMPERES
LARGE
10-100 AMPERES
Fig. 6 — Development silicon rectifiers.
672
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
10 - 10 -^ 10 ' 10
CURRENT IN AMPERES
1
10'
Fig. 7 — I-V characteristic of medium size rectifier.
Fig. 6 shows a picture of three sizes of units that will be discussed in
this section together with the range of currents that these units can con-
duct. The actual current rating will depend upon the ability of the de-
vice to dispose of the heat dissipated in the unit. A description of how
the rating is reached is given in Section 6.
The smallest device has a silicon die that is 0.030'' by 0.030" in area
10-
10'
10
to
I-
o
>
10
10
SMALL
REVERSE
^-
_^^
. LARGE
_«'
^•"f-^
y"^"^
/
•
/
/
f
//
/
/
/
/
/
/
/
/
f 1
FORV
VARD
*^
'-^^S^
~
'^^
lO"" 10' 10 ° to " 10 ^ 10 10 '^
CURRENT IN AMPERES
10
10
Fig. 8 — I-V characteristics of devehjpment rectifiers.
DIFFUSED y-n JUNCTION SILICON RECTIFIERS 673
i I and all the units have dice about 0.005" thick. The medium size device
has a wafer 0.100" by 0.100" in area. The largest device has a element
0.250" by 0.250" in area. It is obvious that a range of die size could have
been chosen for any of these rectifiers. However, electrical and thermal
considerations have dictated minimum sizes and economic considera-
tions have suggested maximum sizes. The actual sizes are intermediate
in value and appear to be satisfactory for the given ratings.
5.2 Of fundamental importance to users of these rectifiers are the for-
ward and reverse current — voltage characteristics. These characteris-
tics of the medium size iniit are shown in Fig. 7 for two temperatures,
25°C and 125°C, using logarithmic scales. It can be seen that in the
forward direction at room temperature, 25°C, more than 20 amperes
are conducted with a one volt drop in the rectifier. At the higher tem-
perature more current will be conducted for a given voltage drop. In
the reverse direction, this particular unit can withstand inverse voltages
as high as 300 volts before conducting appreciable currents (>1 ma)
even at 125°C. A comparison of the current-voltage characteristics for
the three different size units is shown in Fig. 8 where again the informa-
tion is plotted on logarithmic scales. This information was obtained at
25°C. One can observe that the reverse leakage current varies directly
as the area of the device and the forward voltage drop varies inversely
as the area. These relations are to be expected; however, the reverse
characteristics indicate that surface effects are probably effecting the
exact shape of the curves. The changes in the forward characteristics
can be attributed to the contacts and the internal leads of the packages.
The breakdown voltage can be adjusted in any size device by the proper
choice of starting material and therefore no significance should be placed
on the different breakdown voltages in Fig. 8.
SILICON GERMANIUM SELENIUM
Fig. 9 — Semiconductor rectifiers of different materials.
674
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
CURRENT IN AMPERES
Fig. 10 — Rectifier characteristics at 25°C.
It is quite interesting to compare these units with germanium and
selenium rectifiers that are commercially available. To make the com-
parison as realistic as one can, we have chosen to compare the smallest
silicon vuiit with a commercially available germanium unit and a six
element selenium rectifier stack rated at 100 milliamperes. The com-
parative size of these units can be seen in Fig. 9. Curves of the forward
and reverse characteristics at 25°C are given in Fig. 10. Similar curves
taken at 80°C are given in Fig. 11 and at 125°C in Fig. 12. It can be
seen that the forward characteristic is best for the germanium device
at all temperatures and that the reverse currents are least for the silicon
rectifier. The selenium rectifier is a poor third in the forward direction.
However, if one has to operate the device at 125°C, only the silicon de-
vice will be satisfactory in both the forward and reverse directions.
5.3 Capacitance measurements of all the silicon units have been made
at different reverse voltages and temperatures. The temperature depend-
ence is negligible. However, as expected in semiconductor rectifiers,
the capacitance varies inversely with the voltage according to the rela-
tion VC^ = constant where 2 < N < 3. Measurements are given in
Fig. 13 for a group of medium size units. The other units made from
the same resistivity mat(n'ial have capacitances that vary dii'cctly as
their areas.
DIFFUSED p-n JUNCTION SILICON RECTIFIERS
675
5.4 The reverse breakdown voltage, Vb , of these devices is controlled
by the choice of resistivity of the starting material and the depth of
diffusion of the junction. By keeping the resistivity of the initial p-type
silicon above 20 ohm-cm., it is possible to keep Vb above 200 volts.
Units have been made with Vb greater than 1,000 volts. The deeper
diffusion causes the junction to be more "graded"^ and therefore re-
quire a greater voltage for the breakdown characteristic. This is in line
with the capacitance measurements where the exponent indicates that
the junction is neither a purely abrupt junction which would result in
an exponent of two nor a constant gradient junction which would result
in an exponent of three.
5.5 Another interesting measurement, which is related to the life-
time of minority carriers in the high-resistivity region and the frequency
response, is the recovery time of these devices. During a forward bias on
a p-n junction, excess minoritj^ carriers are injected into either region.
When the applied voltage polarity is reversed, these excess minority
carriers flow out of these regions, giving rise initially to a large reverse
current until the excess carriers are removed. The magnitude and time
variation of this current will depend to some extent upon the level of
the forward current but mostly upon the circuit resistance. If one ad-
justs the circuit resistance such that the maximum initial current in
CURRENT IN AMPERES
Fig. 11 — Rectifier characteristics at 80°C.
676
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
CURRENT IN AMPERES
Fig. 12 — Rectifier characteristics at 125°C.
the reverse direction is equal to the forward current before reversing i
the polarity of the junction, then the reverse current will have a con- i
stant magnitude, limited ])y the circuit resistance, for a time known as •'
the recovery time before it decays to a small steady-state value. Fig. 14 .
shows graphically this effect. The recovery time in diffused junctions |i
is found to be in the range of less than 0.1 microsecond to more than 4
Q 200
<
<
O
tr 100
U
i 80
O
a 60
o
2
40
UJ
U
z
<
20
<
a.
< 10
u
1
6 8 10
20 40 60
VOLTS
100 200 400 600 1000.
Fig. 13 — Capacitance versus reverse voltage in medium size rectifer.
DIFFUSED p-n JUNCTION SILICON RECTIFIERS
677
z
LU
CE
q:
D
O
FORWARD
REVERSE y^
RECOVERY
•*■-- TIME *■
-If
TIME, t — *-
Fig. 14 — Recovery effect in silicon rectifiers.
microseconds. It can be shown that the longer recovery times are associ-
ated with higher Hfetimes of minority carriers. More interesting, how-
ever, is the fact that these devices will have their excellent rectification
characteristics to frequencies near the reciprocal of the recovery time.
Measurements have been made of the rectification ability of typical
small and medium size units by using the circuit shown in Fig. 15. The
results of normalized rectified current versus frequency are given in
[Fig. 16 and it is seen that these units could be used to rectify power up
to 1 kc/sec without any appreciable loss of efficiency.
\ 5.6 It is interesting to note that many of the electrical measurements
,inade with the diffused barrier silicon rectifiers are self-consistent and
jean be related to simple concepts of semiconductor theory. As an exam-
!ple, experimental measurements indicating variations of recovery time
I of units are related to variations in minority carrier lifetime which in
turn are related to experimental variations in the forward characteristic
OSCILLATOR
AAA-
1000 n
Fig. 15 — Rectification measuring circuit.
G78
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
>■
u
2
Z
o
I-
<
u
UJ
>
<
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
<
» — &
^ a I
i «
i
>
▲
• MEDIUM
▲ SMALL
<
i
1
Ua ^
^
•
A
▲
1
•
▲
1
▲
10
I
10'
to''
10'
10-
10°
10'
FREQUENCY IN CYCLES PER SECOND
Fig. 16 — Relative rectification efficiency versus frequency.
of these same devices. Such relationships among the measurable param-
eters of these devices make it possible to design and control the elec-
trical characteristics of the units and therefore make them extremely
attractive from an engineering point of view.
6.0 MECHANICAL AND THERMAL DESIGN
6.1 In order to have a device that is usable for more than experimen-
tal purposes, it is necessary that it be packaged in a mechanically stable;
structure and that the heat generated in the combined unit should not'
lead to a condition ^vhere the device no longer has its desirable charac-
teristics. In earlier sections of this paper several mechanical require-
ments of a satisfactory package have been suggested. These may be
repeated at this point. First, pressure contacts are not satisfactory; sec-
ond, oxidizing ambients are to be avoided; third, approximately one
watt per ampere of forward current is generated and must be disposed ;
and fourth, the package must be electrically satisfactory. The first rc-
(juirement is met by using soldered contacts. Since these rectifiers are,
usable at temperatures over 200°C, a solder was chosen that has a melt-
ing point over 300°C. The second recjuirement necessitated the use of
a hermetic seal structure. If the seal is truly hermetic, no gases can
DIFFUSED p-7l JUNCTION SILICON RECTIFIERS 679
enter or leave the package and thus no changes of the device due to the
enclosed gas should occur as long as the gas does not react with the sili-
con, solder or package. However, no seal is absolutely vacuum tight
and thus care should be used in choosing a package design so that mini-
mum effects should occur to the electrical properties during the use of
the device. The third requirement of the disposal of the internally de-
veloped heat suggested the use of copper due to its high thermal conduc-
tivity. However, a small package alone is capable of dissipating only a
small amount of heat without reaching a temperature that is too high
for the device. This necessitates the use of cooling fins in conjunction
with the device to make use of its electrical properties. This thermal
requirement demands a package to which thermal fins can be attached.
This is met by having the package contain a bolt terminal to which
thermal fins can be attached or by which the unit can be mounted to a
chassis for cooling. The fourth requirement consists of two parts; the
package must have two leads that are electrically separated from one
another and the leads must be sufficiently heavy to conduct the maxi-
mum currents. The first of these requirements is met by using glass-to-
metal seals in the package and the second is met by using copper leads
of sufficiently heavy cross-section. The resulting packages for the units
discussed in this paper are shown in Fig. 6. It should be remembered
that the packages are only intermediate development packages and that
further work will probably alter these both in size and in shape. How-
ever, all the requirements mentioned will be applicable to any package.
6.2 The units pictured in Fig. 6 have a range of dc current ratings
associated with them. The lower rating of each device corresponds to
the maximum rating of the next smaller device. Of course, the larger
units could be used for smaller current applications; however, such use
M'ould be like using a freight car to haul a pound of coal. The maximiuu
rating of each de^'ice has been arbitrarily chosen for it to operate with
a reasonable sized cooling fin at an ambient of 125°C and no forced air
or water cooling. It is known that the ratings could be increased by
either method of forced cooling. It has been found that a copper con-
vection cooling fin is able to dissipate 8 milliwatts per square inch per
degree centigrade. This cooling rate is obtained from the difference be-
tween the average temperature of the fin and the ambient temperature
over the effective exposed area of the fin. For example, a copper fin
S}4, inches scjuare when mounted so that both surfaces are effective for
cooling will })e able to dissipate ten watts and at the same time prevent
the temiK'rature of the fin from exceeding 50°C above the ambient tem-
perature. Another thermal drop is found between the junction and the
680 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
base of the package. This temperature difference depends mostly on
the material of the base and its geometry. In the devices presented
this drop is not more than 15°C at the maximum rated current. Thus
the largest drop in temperature occurs between the cooling fin and the
ambient which means that the design of the cooling fin is the controlling
factor in the operating junction temperature of the rectifier.
6.3 It is possible to use the devices without an attached cooling fin.
In this case, the maximum current is limited essentially by the size of
the package. The small rectifier package is designed for 3^ watt dissipa-
tion and therefore the maximum current that should be rectified is about
500 milliamperes. The medium size unit will comfortably rectify 1 am-
pere without any additional cooling and the large rectifier unit will
conduct 3 amperes under the same conditions.
7.0 RELIABILITY AND LIFE MEASUREMENTS
7.1 One of the desired properties of any device is that it should op-
erate satisfactorily at its rating for a long period of time. The above
general statement contains many implications which should be made
specific for the devices under consideration in this paper. By stating
that these devices should operate satisfactorily we mean that they
should not age during operation; that is, the forward and reverse char-
acteristics at any temperature should not change with time. The state-
ment implies that a rating has been established for the units. Further-
more, a "long period of time" has to be defined. There are applications
where a few hours is considered a long time as in some military appli-
cations. However, in most Bell System applications, a long period of
time may be 20 years or approximately 200,000 hours. Clearly, in the
short time since these rectifiers have been developed, it is impossible
to make a fair statement as to their reliability and their life expectancy. ,
However, it is possible to present some results of some early experi- |
ments and describe where and how the units have lived and died. It is ]
this information that we will present in this section. It is a common ex- I
perience that during the early development of any new component, i
there are many units that do not satisfy all the requirements of the de- |
sired end product. These units will generally deteriorate very rapidly |
on life testing due to some electrical or mechanical instability. The
units used for life testing have been screened to remove the above men-
tioned unstable devices.
7.2 The life tests consist of four types; shelf tests at room tempera-
ture and at 150°C, forward characteristic tests, reverse characteristic
I
DIFFUSED p-n JUNCTION SILICON RECTIFIERS 681
tests, and load tests. The last tests are really the important tests; how-
ever, these require the dissipation of large quantities of power in the
load to test only a few devices. Therefore only a few units were tested
in this condition and the majority tested under other conditions. The
several units under load test have been operating for six months with
no noticeable change in their characteristics. These devices are the small
and medium size development units. The large rectifiers would require
about 10 kilowatts of dissipation each in a load to give them a fair load
test.
The shelf tests at room temperature and at a temperature of i50°C
have been running for six months and have indicated that most of the
units remain practically constant. There have been some units that
improve on standing but there is no method of predicting which ones
will improve. Some units get worse on standing; however, most of these
can be predicted from the initial tests since these units usually have a
noisy reverse characteristic near the reverse breakdown voltage. The
units that change differ only in their reverse characteristic; the forward
characteristic changes are not detectable indicating that the contacts
are stable. The changes in the reverse characteristic are probably due
to the trapping of ions and vapors on the surface of the devices during
the packaging operation. Another source of these variations is due to
the non-hermeticity of the glass-to-metal seals allowing gases to diffuse
into the package where they may cause changes in the reverse charac-
teristic. These leaks have been found in many early units and new as-
semblies are being tried at present.
f The forward characteristic life test was considered a good test since
the device is subject to practically all the internal power dissipation
without reciuiring the relatively high load dissipation. It is tests of this
nature that allow one to rate the various size devices. The medium size
rectifiers that ran at 15 amperes in this test failed after three months
of testing; whereas no units running at 5 and 10 amperes have failed
during the six months since the tests have started although their re-
verse characteristics have changed slightly. It should be noted that
most of the change of reverse characteristic occurred during the first
test period of two weeks. These changes are probably due to the causes
mentioned in the above paragraph.
Reverse characteristic tests have been running for several months on
a group of 10 small rectifiers which we feel have a better gas tight seal
than the other development units. The voltage has been adjusted on
these units such that they are pulsed into the breakdown region with a
682 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
maximum current of one millianipere. None of these units show any ap-
preciable change.
7.3 All of those tests in the past sub-section had to do with continu-
ous dc or ac power being supplied to the units under test. However, in
actual operation the units may be subject to voltage pulses due to
power line pulses, accidental shorts, etc. In order for the rectifier to be
useful, it should be able to take an overload for a period of time suffi-
ciently long to allow a protective device to operate. Pulse tests have been
performed on the medium size rectifier. These devices are able to with-
stand over 300 amperes for times of the order of 50 microseconds. How-
ever, the fastest circuit breakers operate in about 20 milliseconds and
for this period, these units can stand onl}^ approximately 50 amperes
before failing. Since these units have such a low forward resistance at
the operating currents (Fig. 7), any small increase in voltage across the
diode will change the current through the device to a very large cjuan-
tity. Therefore series protective resistances may be necessary where
the possibility of short-circuiting the device is high. Such operation
would reduce the efficiency of the unit and is to be avoided if possible.
Another type of protection may be afforded through the use of a high
impedance, high current inductor. This type of protection is quite bulky
and heavy and suitable only for stationary apparatus. Another common
possibility of burnout of the devices occvu's when using a capacitance
input in conjunction with the rectifier. When the circuit is turned on,
large currents will flow to charge up the capacitors and consequently
burn out the rectifiers. One possible protection from such operation is
the use of a series resistance in conjunction with a time delay relay. The|
series resistance will limit the initial capacitor charging current and the
time delay relay will short out the resistance after the capacitors have
reached near their maximum charge.
7.4 Dissection of burned out units have indicated that the failure
takes place through small spots on the device. This can be explained by
the fact that some small areas of the device have slightly better forward
characteristics. These areas will tend to conduct most of the forward
current. Therefore most of the power will be dissipated there and these
areas will become even more conducting leading to a channeling of the
forward current through these spots with the consequent burnout. The
best way to avoid such mishaps would be to make a more uniform de-
vice. Experiments are in process along this line. Another less satisfactory -
method would be the control of contact resistance such that the current
would be limited in any particular area by the contact resistance. Simi-
lar ideas must be considered when paralleling these diffused junctioiii
DIFFUSED p-n JUNCTION SILICON RECTIFIERS 683
silicon rectifiers. It is possible to use these devices in parallel if oni' ad-
justs the lead resistances such that no one unit will be allowed to con-
duct much more than its share of the current.
7.5 As a conclusion to this section, it should be noted that these rec-
tifiers are expected to have a long life when operated within their rat-
ings. They are able to operate for short periods of time (seconds) at five
times their rated currents. Since the rectifiers have an extremely small
series resistance, they should be protected against accidental surges
and turning on to a capacitance input filter.
8.0 SUMMARY
8.1 The development rectifiers described in the article are silicon
diffused p-n junction rectifiers. These devices together with associated
cooling fins can be used to rectify a complete range of currents from 0
to 50 amperes in a single phase, half wave rectifier circuit. They can be
used in more complex rectification circuits to yield even more dc cur-
rent. Also, they are able to withstand at least 200 volts peak in the in-
verse direction and operate satisfactorily at temperatures as high as
200°C. Furthermore, one process of diffusion and plating is sufficient
for all the devices of the class. This makes it possible for one diffusion
and plating line to feed material for all the rectifiers in a manufacturing
operation.
8.2 The rectifiers discussed behave according to the theory of semi-
conductor devices which makes it possible to design them for given
electrical, thermal, and mechanical characteristics. One failure to meet
ideal theory of a p-n junction is with the forward characteristic.
8.3 The diffused silicon type of rectifier has been compared with
germanium and selenium units and has better reverse characteristics
at all temperatures. In the forward direction, the germanium units have
a smaller voltage drop for any given current than the silicon rectifiers
but the silicon devices are capable of operating at much higher tem-
peratures, thereby permitting higher overall current densities than the
germanium devices.
8.4 The diffused silicon rectifiers are capable of use in any rectifier
application where dc currents up to the order of 100 amperes are re-
fjuired and where inverse peak voltages up to 200 volts are encountered.
Another imoortant use for these devices will be in the magnetic ampli-
fier application where the low reverse currents of silicon will enable
large amplification factors to be realized. Since the forward character-
istics of these devices are so uniform, they can be used in voltage ref-
erence circuits that require voltages near 0.6 volts and in circuits uti-
684 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
lizing the exponential character of the forward characteristic. However,
as is to be expected from devices with the characteristics described in
this paper, the most immediate apphcation will be found in power sup-
plies.
ACKNOWLEDGMENTS
It is obvious that the work reported in this paper is not the result
of one man's labor. Much of the stimulus and many of the ideas are
those of K. D. Smith. Other members of the Semiconductor Device
Department who have contributed considerably to the development of
these devices are R. L. Johnston, R. Ruhson, and R. C. Swenson. D. A.
Kleinman, J. L. Moll and I. M. Ross have been most helpful in dis-
cussing the theoretical aspects of these devices. The author wishes to
thank H. R. Moore for his suggestions on protecting the silicon rectifiers
against large overloads.
The Forward Characteristic of the PIN
Diode
By D. A. KLEINMAN
(Manuscript received January 18, 1956)
A theory is given for the forward current-voltage characteristic of the PIN
diffused junction silicon diode. The theory predicts that the device should
obey a simple PN diode characteristic until the current density approaches
200 amp /cm?. At higher currents an additional potential drop occurs across
the middle region proportional to the square root of the current. A moderate
' amount of recomhiriation in the middle region has little effect on the charac-
teristic. It is shown that the middle region cannot lead to anomalous char-
acteristics at low currents.
t
INTRODUCTION
In some diode applications it is desirable to have a very low ohmic re-
sistance as well as a high reverse breakdown voltage. A device meeting
these requirements, in which the resistance is low because of heavily
doped P"^ and A^"^ contacts and the breakdown \'oltage is high because
of a lightly doped layer between the contacts, has been described by
M. B. Prince. The device is shown schematically in Figure la and con-
sists of three regions, the P^ contact, the middle P layer, and the A'"''
contact. The device is called a PIN diode because the density P of un-
compensated acceptors in the middle region is much less than P"*" or iV"*"
and in normal forward operation much less than the injected carrier
density.^
We shall let the edge of the P^P junction in the middle region be
oj = 0, and the edge of the PN^ junction in the middle region be x = w.
Thus the region 0 ^ .r ^ w is space charge neutral and bounded at each
end by space charge regions whose width is of the order of the Debye
length
1 Prince, M. R., Diffused p-?i .Junction Silicon Rectifiers, B.S.T.,J., page 661
of this issue.
^ A device witli similar geometry has been discussed by R. N. Hall, Proc.
I.R.r:., 40, p. 1512, 1952.
685
G8G
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
(K/^eP)
1/2
l.o X 10" cm.
(1)
where A' is tlie dielectric constant, c is the electronic charge, and )3 is the
constant
^ = e/kT = n„/D,, = fxp/Di
(2)
which at room temperature is 38.7 \'olt~\ We shall denote points in the
P and A'' contacts on the edges of the space charge regions by oo and
WW respectively. Thus Uoo is the electron density in the P^ contact at the
junction, and Ho is the electron density at the same junction in the
middle region. Similarly p„.,„ is the hole density at the junction in the
A^ contact and pu, is the hole density at the junction in the middle region.
We shall denote equilibrium carrier densities in the three regions by
np+ , 7ip , Pp , Pn+ . Typical values for the parameters characterizing
N"
(a)
w
X-
>
-V,
oo/ 1
WW
V=
1=0
(b)
WW
Vj
f
X
f
Vw+Vp
/
>
— — ~-____________^^
/
V-Vi
00/ 1
" ^
v„
!
(Cj
w
V\^. 1 — SchcuKitic represent al ion ol' (lie IMX (li(Ki(! with tli(> 1'+ and N+ con-
tacts regarded as extending to infinity. (1)) .shows the; tdect rostatic potential in
equilibrium and (c) show.s the potential when a forward current Hows.
THE FORWARD CHARACTERISTIC OF THE FIX DIODE 687
the device are
W'^2 X 10"^ cm
P -- 10'' cm"'
(3)
Ar+ p+ ^ 10^' cm"'
L„ , Lj, ^ 10"^ cm
where L„ , Lp are minority carrier diffusion lengths in the contacts.
The present treatment makes three distinct approximations. The first
is to neglect the voltage drop in the contacts. The highest currents ordi-
I narily used are of the order of 500 amp/cm" which should produce an
ohmic drop in the contacts of about 1 volt/cm. Since the entire diode has
a length of about 0.01 cm we are neglecting only about 0.01 ^'olts in this
I approximation.
The second approximation is to regard the Debye length as small
compared to w and the diffusion lengths L„ , Lp . li L„ , Lp are as small
as the typical values given in (3) the error made in this approximation
is not completely negligible. Nevertheless, we use the approximation be-
cause it enables us to regard the device as three relatively large neutral
regions and two relatively narrow space charge regions. The behavior of
the device can then be determined by solving for the diffusion and drift
of carriers in the neutral regions subject to boundary conditions con-
necting the carrier densities across the space charge layers.
The third approximation is to neglect any increase in majority carrier
density in the contacts due to injection of minority carriers. This approxi-
mation is valid until the current density approaches 5 X 10 amp/cm",
which is well above anticipated operating currents. It is conceivable
that in some junctions all the current may flow through small active
spots at which the current density is ^'ery high, perhaps exceeding the
above figure. In such cases the current flow is two or three dimensional
and the present analysis would not apply.
It is also necessary to assume some law for carrier recombination. We
shall assume that recombination in the contacts is linear in the injected
minority carrier density
din ■ n — np+
rKJ
ax T
Modification of the theory to suit other recombination laws is simple in
principle, although considerable analytical complications might be en-
countered. It seems most likely that in silicon FN junctions the re-
combination actuallv is nonlinear. It can be shown that if the rccombi-
688 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
nation follows some power v of the injected density
the forward characteristic of a simple PN junction is of the form
exp W^^iv + 1)F] (6)
Thus nonlinear recombination can account for the observation that in
silicon diodes the slope of V versus log / is usually much less than /3.
Our purpose here is not to study this interesting effect, but to study those
effects which are due to the presence of the middle region. Therefore, we
assume linear recombination for the sake of simplicity. In the last sec-
tion we give a brief consideration of what to expect in the case of non-
linear recombination in the contacts. Recombination in the middle
region will also be assumed to be linear in the injected carrier density,
but this assumption is not critical, since it turns out that a moderate
amount of recombination in the middle region does not change the quali-
tative behavior of the device.
BASIC EQUATIONS
Fig. 1(b) shows the electrostatic potential V{x) for the equilibrium
case 7 = 0. The potential is constant except in the space charge layers.
If w^e call the potential of the middle region zero, the P^ and N^ contacts
are at the potentials — Vi and Vi respectively, where
/3Fi - In (P^/pp)
(7)
^F2 = {n (N^/np)
Figure Ic shows the potential when a forward current I flows and a
forward bias F is produced across the device. We shall define the poten-
tial so that the A^"^ contact remains at V2 , which puts the P"^ contact at
potential F — Fi . The potential at a point x is then given by
V{x) = V2- r E{x) dx (8)
"WW
where E{x) is the electric field assumed zero in the contact regions x >
WW and x < 00. The applied bias F consists of three terms
F = Vo + Vp + F,„ (9)
' This potential distribution has been discussed b^y A. Herlet and E. Sp(MiI<o,
Zeits. f. Ang. Phys., B7, H3, p. 149, 1955.
THE FORWARD CHARACTERISTIC OF THE PIN DIODE 689
where Vo is the forward bias across the junction at x = 0, Vp is the po-
tential drop in the middle i-egion, and V^ is the forward bias across the
junction at x = w. In this notation F(0) = F,„ + Vp and V(w) = Vy, .
The total current density is constant
In{x) + Ij,{x) = I (10)
! We shall denote electric current densities by e/„ , dp , so that In , Ip , I
have the dimensions of (particles/cm -sec) . At x = 0 and x = w the
minority carrier currents must flow into the contacts by diffusion, which
gives the boundary conditions
[Pn+ j
/n(0) = Ins [^ - l]
[np+ J
(11)
where Ips , Ins are saturation current densities
J. _ Pn Dp J _ np Dn / V
^ ps f ) -fns — f {i^^J
jLip Lin
The order of magnitude of the saturation current density is given by
e{Ins + Ips) '^3 X 10~^ amp/cm^ in Si
based on the typical values of (3). Equations (11) contain the assump-
tions of linear recombination and small injection into the contacts as
discussed in the introduction.
In the middle region the current densities satisfy
, j J.et us assume these equations remain valid in the space charge regions.*
' Since these space charge regions are narrow /„ and Ip can be considered
constant and the solution of (13) in the space charge regions is
^ Up JlOW J
nix) = /^^^> L^e-'^'-'^' -{- ^ I
U„ Jo
X
(14)
Dn JOO I
Shockley, W., B.S.T.J., 28, p. 435, 1949.
690 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
Since \/Lp « 1 we can write for the junction at x = id
piw) = e-''- U^y-^ - (P- - y^^"") j e'^'dx
w
/?u>to6
p "WW
(15)1
I
floo
=
Tioiup /np)e
Vo
=
V. e^'»
Wu,
^
np e'""-
where 0(X/Lp) means a term of order X/Lp . Thus we see that if we may:
neglect X/Lp and X/L„ we have the following simple boundary conditions
at the junctions
(16).
It is clear that in order to divide the device into three neutral regions we
must also be able to neglect \/w.
Finally, we have the condition of space charge neutrality
p - n = P (17)
It can be shown that the term K~ dE/dx is of order (A/L)" or (X/w) |
and therefore negligible in our approximation. Therefore (17) is the
Poisson equation for the middle region in our approximation. When we >
use (17) we are not saying that E{x) is constant but only that K~ dE/dx
is negligible compared to p(x) and 7i(x). The basic eciuations then are
(10), (11), (13), (16), (17).
Large Injection, No Recomhinalion
In this section we consider current densities of the order of magnitude
of those that flow in normal operation of the diode as a power rectifier.
These currents inject large densities of electrons and holes into the
middle region greatly increasing its conductivity. The result is that the
\'oltage drop Vp is small even though the normal resistivity of the middle
region is high. For this reason the device has been called a conductivit}'
modulated rectifier. Also in this section we shall neglect recombination
in the middle region, which makes In{x) and Ip{x) constant and greatly
simplifies the analysis. The effect of recombination is to remove carrieis
and increase the drop across the middle region. Therefore, it is desirable
to keep recombination in the middle region as low as possible.
THE FORWARD CHARACTERISTIC OF THE PIN DIODE 691
0Vo
n.y = ppe
Equations (13) can be written
/. -f- 6/,
dn In — bl-o
dx 2Dn
where b = Dn/Dp . Combining (19) and (21) gives the equations
Ho = niHn/Insf""
Tin, = 7li(Ip/IpsY''
where nf = rippp is a constant, and also
/3Fo = Vz (n -^ ^
Pp ^ns
Up Ips
(18)
Under conditions of large injection we can say
n» P, p» P
rioo » np Pww » Pn
so that (11) becomes
In = Insirioo/np'^)
^p — J^ psKPww/pN )
and (17) becomes
n{x) = p{x) 0 ^ X ^ w (20)
Equation (16) becomes
7ioo = Uo^np /np)e
(19)
(21)
(22)
(23)
(24)
I'^rom the first equation (22) we have
SY, = k+J^ f A^ (25)
2Dn .'o nix)
692 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
Upon invoking the second equation of (22) we get
fiVp = i" "^ f ^^ /n — (26)
In — Olp Ho
and
n^=^no+ ^" ~ ^^^ w;. (27)
We see that Vp is always positive in sign whatever the sign of /„ — hip .
We now define a parameter
(28)
7 = rio/ny,
and a device constant
li = J-ns/J-ps
Then from (23) and (10)
h/Ip = i^T'
" 1 + i^T^
1 _/
1 + Ry^
(29)
(30)
Combining (23), (27) and (30) gives the equation for 7 as a function of
total current
7=1-
In — bip W
2Dn Un
_ n (7/7 j^ - 1 ^^^^
y /o VI + &(7/7»)^
where
7co' = &/i2 (32)
and /o is a unit of (particle) current density characteristic of the device
Z. = i^^ = 4 m ^ (33)
A typical value for e /o in a silicon diode is
e /o '-^ 200 amp/cm" (3-1'^
based on (3).
i
THE FORWARD CHARACTERISTIC OF THE PIN DIODE 693
From (26) the potential drop in the middle region can be written
(35)
0Vp
=
y 2-^n7
'00
From
(24) and (30)
KVo + 7.)
= tn
-\-(n-
T
+ ^n
h
+ Hy/yJ'
J-ps
(36)
Thus the total applied bias y as a function of total current density / is
given by
/5F = (iij - V^ ^^ ^ + ^^ 1 , J / v> + ^^^ T- (^^)
/o 7^ - Too 1 + 0(7/7 J- Ips
where y{I) is the (positive) solution of (31).
Thus far we have referred the problem of the V — I characteristic to
the problem of calculating 7(7) from (31). We see that in the limits of
high and low current 7 approaches the limits
7 -> 1 / « /o
(38)
7 — ^ 7oo i » io
and in general lies between these limits. A good approximate solution is
readily obtained by replacing (31) with the cjuadratic equation
7=1- 4(7/700)' - 1]
z = {i/ur (1 + hr"
which has the solution
V7co' + 4(1 + z)zyJ - 7.
7 =
2z
(40)
A plot of this solution is shoAvn in Fig. 2 as a function of z for 7oo = x^"^,
7oo = 2. Since 7(7) is bounded by unity and 700 , which usually will be of
order unity, we can reject some of the dependence of V upon 7 and re-
tain only its essential dependence upon 7. This appears in the first and
second terms of (37). By means of (31) this second term can be written
/n7 (7/7.)^ + 1
^^' [7 - 1 \/l + 6(7/7jd T h
7
(41)
Retaining only the essential dependence on 7 we write this equation
i87p = C(7/7„)^^' (42)
694 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
2.0
0.5
lo Vi+ b
Fig. 2 — The function 7(2) given by equation (40) for two choices of 7^, .
45
40
35
/3V
30
25
20
Sl ^^
0.01 0.02 0.04 0.06 0.1 0.2 0.4 0.6 0.8 1
I/Io
4 6 8 10 20 40 60 100
Fig. 3 — The voltage-current cliaracteristic of the PIN diode accortling to
equation (44). The dashed line represents an ideal PN diode and c/q '^ 200 amp/
THE FORWARD CHARACTERISTIC OF THE PIN DIODE 095
where C is a constant representing the slowly varying coefficient of
' 7„) " in (41). We choose C snch that (42) becomes exact at high cur-
I _nt density when ^Vp is large
C = -^^ S- (43)
7^ - 1 V& + 1
When we regard the third and fom-th tei-nis of (37) together as a constant
jSFc Ave obtain the simplified voltage-current characteristic
/3F = fn ^ + C j/^ + 0Vo (44)
0
In this approximation it is unnecessary to evaluate 7(7) from (31).
Fig. 3 shows plots of jSV versus I/Io calculated from (44). For plotting
the curves the \'alue (' =1.1 was used. To choose a value for 13V c we put
7=1, which gives
1 + fc(7/7oo)- 1 + i^
so that
^Vc -^ HIo/(Ins + Ips)] (4G)
which has the value 27 in silicon according to the values in (3). The dot-
ted line is the asymptote approached by the curve at low current densities
0V -^ (n ■[ I « h (47)
This is the characteristic of a simple PA'' junction Avhen
;Ve retain now to the cjuestion of when the large injection conditions
(18) are satisfied. Let us suppose 7 is much less than 7o so that 7 '^ 1,
7„/7;, ^ R. It follows from (30) and (23) that
rio ^ n,, ^ ni[I/(Ins + Ips)f'~ (48)
Now let us set /?„ » P Avhich gives a condition on the current density
I » (P/mY (L,s ^ Ips). (49)
Setting /;„„ » Hp'^, Pu-w » Vn'^ gives
7 » 7,„ + Ip, . (50)
Usually P » 7ii so that (49) includes (50). When numbers are put in
696 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
from (3) we get the condition for large injection
el » 0.07 amp/cm^ in Si (51)
Since tliis current in (51) is much less than do , we may quite properly
speak of large injection n^ P and small currents / « !„ at the same
time.
Let us denote by
ICM = iP/Uif (Ins + Ips) (52)
the current density at which conductivity modulation starts to be im-
portant. Then we may distinguish three ranges of current: (a) very small
current / < I cm for which large injection analysis does not apply; (b)
low current I cm < I < h for which large injection analysis applies, but
the voltage drop Vp in the middle region is negligible; (c) large current
I > lo for which Vp is sizable. The treatment of this section has covered
ranges (b) and (c) . Range (c) (as treated here) does not extend to infinity
but only up to current densities of the order
L
8 X 10* amp/cm'^
p
so that the diffusion currents in the contacts may be treated as a small
injection.
Small Injection, No Recomhinaiion
In this section, we shall cover ranges (a) and (b) in current density.
We must go back to the basic equations, but we shall make use of two
facts that have come out of the large injection analysis: (a) jSFp is negli-
gible when / « /o ; (b) 7 = no/n^ ^ 1 which means n(x) and p(x) are
essentially constant in the middle region 0 ^ x ^ w when I <^ lo .
When we set
no = n^o, Po = Pw (53)
equations (16) give us
noo = npV^^"^""^ (54)
Pww — Pn ^
Then (11) gives
I = I„^ I^= (/„, + /,,) [/^'^o+^-Li] (55)
Now Vo + Vw is the total applied bias when Vp can be neglected ; there-
THE FOKWAKD CHARACTERISTIC OF THE PIN DIODE 697
fore we obtain the characteristic
PV = ^n ( \_ + l) (56)
which is vaHd until 7 approaches lo . Of course we would not have ob-
tained this ideal characteristic of a simple PN junction had w^e taken
recombination into account; our result depends upon the constancy of
n(x) and pix) in the middle region. For the case of no recombination in
the middle region (56) and (44) cover ranges (a), (b) and (c). Instead of
(44) the more exact expression (37) could be used requiring the evalu-
ation of y{I) from (31). It seems that the extra refinement is of no help
in understanding the device and unnecessary in treating experimental
data. Therefore, we shall adopt (44) and the approximations leading to
it as a model for treating the more complicated recombination case.
That is, we shall seek a generalization of (44) which takes recombination
into account in a sufficiently good approximation.
Large Injection with Recombination
We are interested in determining the effect of recombination in the
middle region upon the operating characteristics of the device. Therefore
we go immediately to the large injection case n = p. Equation (16) be-
come
ny, = npe^^"" p^w = n„,(pivVpp)e^^"'
(57)
no = ppe^^'^ noo = no(np'^/np)e^^°
t which gives
/3(Fo + F„) = (nin^nolnl) (58)
We shall assume that recombination is linear in the injected carrier
density to simplify the calculation. It will be possible, later to approxi-
mate bimolecular recombination by using an appropriate value for the
lifetime r corresponding to the injected carrier density. Therefore we
write
O'i-n ui p n (rj(S\
dx dx T
Eliminating In{x) by use of (13) gives the equation for n(x)
(60)
dn n
dx^ L
%
698
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
where L is the effective diffusion length in the middle region
L = [2Dn r/ib + 1)]^'=^ (61)
The solution of (60) may be written
no sinh (w — z) + w„, sinh z
n{z)
sinh
CO
(62)
where z = x/L is the position variable and w = w/L is the length of the
middle region in units of L. Fig. 4 shows several of these solutions for the
In equation (60) and the solution (62) we have neglected the equi-
librium carrier densities Up , pp . The criterion for the validity of this
approximation is
sinh Hco « (rio/P), inJP) (63)
X/w
Fig. 4 — Tlie carrier (l(Misi(y accordiiii;- (o ('(|ua1i(>n (iS'l) for the case 7?u
and several values of co.
= n.u
THE FORWARD CHARACTERISTIC OF THE PIN DIODE 699
arrived at by considering the minima in the sokitions for co » 1. This is
really a criterion for conductivity modulation, so we shall assume hence-
forth that it is satisfied.
We now modifv (13) by setting n = p and eliminating E{x) by use of
(22)
, . . 67 + 2Dnn{x)
^-^'^ = — mh —
J , . I — 2Dnn (aO
where n'(x) = dn/dx. Inserting these currents into (22) gives E{x) and
integrating gives the potential drop Vp in the middle region
(6 + 1)D„ Jo n 6+1 no
This is the generalization of (26) for linear recombination.
The direct evaluation of (58) and (65) in terms of the total current /
leads to a very complicated expression for the applied voltage. It will be
jshown in the next section that this result reduces in its simplest approxi-
mate form retaining only the essential dependence on w to the formula
I Jn.9 + ips V io(<^)
iwhich is identical with (44) except that the characteristic current density
lis a function of oj
7(co) = /o^(w)
(67)
g{o:>) =
cosh - tan ^ f sinh —
1 _^' + - -
6 ^ 48
(Fig. 5 shows a plot of ^(co). These results show that if co < 1 as we might
lexpect in a good diode recombination has no significant effect on the
jforward voltage-current characteristic in the conductivity modulation
range of operation.
700
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 195G
3
l.U
^^
^
0.8
\
N.
>
\
s
0.6
\
s.
N
\
0.4
\
N^
N
\
0.2
0
0.5
1.0
1.5
2.0
2.5
3.0
Fig. 5 — The function (j(co) of equation (67).
Analysis
We denote
r =
no
rii
From (11) and (67)
/p(co) = Ips^ , ln(0) = Ins^
(68)
(69)
By means of (62) and (64) Ave eliminate /„ and Ip and obtain the equa-
tions
(b + l)Ipsf = / - Ir{^ cosh ic - t)
(b + l)RIpsf = hi + Iri^ - r cosh co)
where Ir is a (particle) current density
2Dnni
Ir =
L sinh CO
(70)
(71)
In principle we could solve (70) for ^ and f as functions of I with R and
oj as parameters; this would determine ^V through (58) and (65) and
complete the problem. First we shall rewrite these equations in terms
of 7 as in the analysis of the second section.
THE FORWARD CHARACTERISTIC OF THE PIN DIODE
701
If we eliminate / from equations (24) we get
J . Ir h cosh O) + 1 nr 2
olps + J r+l " ''^
+ 7
which can be solved for ^
Ir cosh CO + 6
1 b + 1
(72)
y _ Ir cosh CO + ^ To — 7
^ ~ 7;:. 6 + 1 /?7- - ^
where
pi'
70 =
6 cosh cj + 1
cosh CO + 5
Substituting (73) into (70) gives the equation satisfied by y
Ry' cosh CO + 1\ , ^ / [(7/700)' - 1]'
7 r> o , — T ) (7 - 70) = 7
Ry"^ + cosh CO / " ' "' /oo ^7^ + cosh co
■where loo is a characteristic (particle) current density
(73)
(74)
(75)
J^ 00 — -' o
CO
sinh
CO
cosh u -\- h
h + 1
(76)
Now the solution of (75) has two branches which as / -^ 0 approach
N'alues given by
a)
b)
7 -^ 70
Ry" cosh CO + 1
Ry- + cosh CO
(77)
As I increases the first branch remains positive and approaches 700 as
/ — > 00 . The second branch becomes negative and approaches —700 .
Therefore, we choose that branch which satisfies
7(0) = 70 =
b cosh CO + 1
6+ 1
y(cc) =y^= {h/Rf"
7 > 0
(78)
( )n this Ijranch 7 always lies between 70 and y^ , and 7 never approaches
the quantity in (77b). Therefore we replace Ry by b (as if 7 = 700) in
II
702
THE HELL SV8TEM TECHNICAL JOUKXAL, MAY 195G
the first factor on th(> h ft of (7")), and obtain the siniplei- form
7 - 7(1
/oo y/Ry- + cosh
CO
(79)
which is the generalization of (31).
The drop ^Vp in the middle region given by (()o) can be written
^^^ = r^ ^^ ^ + J-^Tx yj;^ V/^y + cosh 0, FM (80)
AN'here Fc^ii) comes from / dx/ n and is defined
p ( \ _ f Mill
Jo 7 siiih fw(l — u)] + sinh [ww]
In
7 snm [(jo(]
1 + Q
1 + Q
(n
1 + e"Q
1 - e^Q
(81)
or
2
\/l — 27 cosh CO + 7-
tan~' e"Q — tan~^ Q
\/27 cosh CO — 1 — 7-
The first form applies when 7 > r", or 7 < c~", and the second applies
when e"" < 7 < <»", and Q is the (luantity
Q =
1 — ye'
■\/\ 1 — 27 cosh CO + 7^
It can readily b(> shown that when co -^ 0
In 7
/'^o(7) =
Thus when co = 0 (80) reduces to
7 - 1
(82)
(83)
/3T>
Ch 7 /> — 1
r, (7 - 1) +
7-16 + 2
(n 7 (7/700)' - 1
6+ 1
-^ \//?7- + 1
l/i
(84)
.7-1 Ry- -{- I
which is identical with (il). It is also clear that (7!J) reduces to (31) as
the recombination goes to zc ro. f'inally we write from (58)
^(Fo + V„.) = tn yt = (n /- + (n ^ ., / . (85)
1 p, Ry- + cosh CO
THE FORWARD CHARACTERISTIC OF THE PIN DIODE
703
2.6
2.0
K 1.5
3
LL
1.0
0.5
s.
^
\ v\
\\
s\^^
\
V^
'^
V
X
^
N
X
h
^
"^
'v
>^
^<^
^
^*-^
^
^
^
^^
1
1
1
1
0.1
0.2 0.3 0.4 0.5 0.6 0.8 1.0
4 5 6 8 10
Fig. 6 — The function F„{y) of equation (81) for several values of co.
which reduces to (3G) when co = 0. Thus the whole theory reduces cor-
rectly in the case w = 0.
The function F„(t) is plotted in Fig. 6 for several values of w including
05 = 0. The expansion of F^{y) to order co" is
FM = -^ - ifM
7—1 4
(t + 1) - 27
/(t) =
(n 7
(86)
(7 - 1)-^
1
= 1 - 27 fn - + • • •
7
i
Our next step is to eliminate from (80) and (85) unimportant depen-
i dencies on I which would be difficult or impossible to detect experi-
I mentally. If in (85) we let 7 = 1, cosh co = 1 we get
^(Fo + F,„) = tn
(87)
In (80) we drop the first term (as if 7 = 1) and in the second term we
704 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
put By^ = 6 (as if 7 = 7„) and FM = PM,
2
1 ^i ^^
/3Fp = ^-pp 4/ J- V6 + cosh CO FM (88)
In this way we retain the correct form of dependence on w, but throw
out the dependence on / that comes from 7(/). It can be shown from|
(81) that
tan ^ f sinh -
sinh ~ (89)
2 4
CO CO
= 1 - — + — - +
12 ^ 180 ^
Thus we define the characteristic (particle) current density of the device
/o(co) =
{b + l)7oo
(b + cosh co)F„(l)2
(90)
and (88) can be written
n2
CO
_F^(1) sinh co_
= /o</(w)
2
i4/£ ^^^H
This formula corresponds to (42) with C = 2/\/b + 1. In the spirit I
of the present theory the exact value of this constant is not important, j
so we may replace 2/-\/b + 1 in (91) by C. Then the sum of (87) and
(91) gives the total applied bias (66).
Non Linear Recombination
In this section we shall consider the forward characteristic of a PIN
diode in which the current densities at the contacts obey the law
/ \"
J J- I 'ion \
,n
+
p
(92)
T = T ( ^"" 1
where /„,, and /,,., are characteristic of the device and a is a number be-
THE FORWAKD CHARACTERISTIC OF THE PIN DIODE 705
tween 0 and 1. We see that (30) must be replaced by
Inllp = Ry"
I Ry'^I (93)
^ / + Ry"^ " 1 + Ry"'
and (23) must be replaced by
no = niiln/Intf^" , ^
(94)
Hu, = ni{Ip/Ips)
The equation for y is now
- 1 _ // Y""'"' (y/y.T - i ,05)
'^ ~ \lj [1 + biy/yjy^Y-'^''-'^^ ^
where yj = (h/RY'" and
/i = hihs/ht-'""-'' (96)
is a characteristic (particle) current density of the device. We now ob-
tain ^Vp from (26)
^Vp ^ C'{I/h)'-'""'' (97)
where C is a slowly varying function
C' = (t/Toc')'" + 1 ^ny ,ggx
[1 + biy/yjy^Y-'""^' 7-1
similar to the coefficient in brackets in (41). From (21) and (94) Ave get
^(Fo + V.) =^ln-^ (99)
If now 7 '^ 1 we get
This shows how we must choose a to agree with the low current charac-
teristic. On the basis of experience with silicon diodes we would choose
a ^' 0.6, which would give
/SFp - C'(I/hf'' (101)
riic characteristic current density would be
I eh ~ 200 X (7p,//o)"'amp/cm' in Si (102)
706 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
The value to use for 7^^ is very uucertain, but it certainly is much less
than /o , so I\ » h • Thus we would not expect to observe ^Vp , and the
characteristic should have the form
I'^he"^ (103)
up to the highest attainable currents.
We have shown in this section how the law of recombination in the
contacts affects the dependence of Vp upon /. In particular if a = i^
there is no dependence of Vp upon /, which means that the conductivitj'
due to injection increases just as rapidly as the current. We may con-
clude from (97) that the smaller the A^alue of a the more effective is con-
ducti\'ity modulation in keeping down the drop Vp in the middle region.
Discussion
We have considered the PIN structure of Fig. 1 having typical param-
eters given in (3). We find that the presence of the middle region causes)
no significant deviation in the voltage-current characteristic from that
of a simple PN diode until very high current densities are reached, of
the order of 200 amp/cm' in silicon. In particular the middle region is
not responsible for an anomalous slope in the plot of V versus log /. We
find that recombination in the middle region can be accounted for by re-
placing the characteristic current density elo of the device with eIog(w/L)
where g(w/L) < 1 is shown in Fig. 5. Thus qualitatively there is no
change in the form of the voltage-current characteristic due to recombi-
nation in the middle region, although the effect of g(iv/L) is to make the
voltage drop somewhat higher than if recombination were absent.
We have suggested that the anomalous slope of V versus log / usually I
observed in silicon diodes might be due to non-linear recombination. If;
the recombination obeys a power law chosen to give a typical (anoma-
lous) V— I characteristic for a PN diode, we have shown that the PIN
diode should manifest the same characteristic up to extremely lai-ge
current densities many times elo . Thus the drop across the middle region l
should be even more negligible with non-lineai- than with linear rccom- ■
bination .
I am pleased to acknowledge my great benefit from discussions with
M. B. Prince and I. M. Ross.
A Laboratory Model Magnetic
Drum Translator for Toll
Switching Offices
By F. G. BUHRENDORF, H. A. HENNING and O. J. MURPHY
(Manuscript received January 24, 1956)
A lahoratory model magnetic drum translator, capable of serving as a one-
to-one alternative to the card translator, has been built to study the problems
arising from the prospective use of microsecond pulse apparatus in a tele-
phone office environment. Electron tube amplifiers and, germanium diode
logic circuits supplement the drum information storage unit to provide the
functional operations required. Results of preliminary laboratory tests indi-
cate the feasibility of equipment of this kind for telephone switching control.
INTRODUCTION
The magnetic drum is one of the most widely used of the modern large-
capacity digital-data storage devices. It is used as a memory unit in many
of the present-day large-scale digital computers and in other applica-
tions such as inventory control of airline ticket reservations and traffic
control of airplanes in flight. Two of the properties of drums as storage
media have been considered particularly advantageous. One is the capac-
ity to store up to several hundred thousand bits of information in a com-
pact space at a low cost per bit; the other is the ability to keep the in-
formation in an easily alterable but nonvolatile form unaffected by power
failure or other interruptions of operation. In terms of the speed with
which information may be stored or i-(V'Overed, drum memories fall near
the middle of the present-day spectrum; they are very much faster than
punched paper tape or groups of telephone relays but are considerably
slower than cathode-ray tube or ferromagnetic-core storage devices. All
of the information stored on a drum may be read out during the course
of one complete revolution and, similarly, new information may be en-
tered anywhere in the storage space within the time of one revolution;
tlius the access time is ordinarily of the order of a few tens of milliseconds.
It has already been pointed out^ that automatic telephone switching
707
708 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
offices bear a generic resemblance to digital computers and it is therefoi-e
not surprising that the magnetic drum has engaged the attention of tele-
phone engineers, since the speed and flexibility of such a device offei-s
much promise in connection with forward-looking telephone office de-
sign. One system has already been described^' ^ involving the use of mag-
netic drums for telephone switching control applications in an entirely
new form of telephone office; it is the purpose of this article to describe
another application of less complexity which could function in coopera-
tion with equipment in existing telephone offices.
The standards of reliability and ruggedness which must be met by any
equipment proposed for Bell System use are in some respects a good deal
higher than those imposed on other commercial sytems such as digital
computers. Thus when a new type of apparatus such as a magnetic drum
and its associated electronic components is considered for a telephone
job, it is necessary to determine whether the apparatus is capable of being
designed to meet these stringent requirements. This was judged to be the
most important objective of the undertaking about to be described, and
it strongly influenced the choice of experimental application for the drum.
The program which the designers set for themselves to determine the
possible suitability of the magnetic drum type of equipment might be
summarized as follows:
(1) Choose an existing telephone application in which a magnetic drum
system can receive a satisfactory work-out without disordering the sys-
tem.
(2) Design a magnetic drum system to work cooperatively with exist-
ing office equipment, using existing power facilities. Assume that the de-
sign is aimed at practical application so that due regard is given to operat-
ing economies, and protection against power failures.
(3) Construct a full-scale model following the design, and test the
model in the chosen environment long enough to determine the failure:
rate and the reasons for each failure.
(4) Evaluate the results in order to determine the sphere of useful-
ness, and the proper design philosophy for applying magnetic drum sys-
tems of any kind in existing telephone offices.
One telephone switching application which meets the qualifications of
(1) above exists in the new No. 4 A toll switching offices. Here, due to the
demands of nationwide dialing, a large-scale translation function is re-
(]uired to convert destination codes into information which will properly
loute each call. The volume of information which nuist be stored foi'
1 laiislation purposes, and the relatively rapid access desired, fall close to
the optinnim parameter values of magnetic drum systems. The action
MAGNETIC DRUM TRANSLATOR FOR TOLL SAVITCHING OFFICES 709
takes place in cooperation with crossbar and other relay-type switching
equipment typical of the present-day telephone office, thus providing an
environment suitable for obser\'ing the behavior of fast pulse circuits in
the presence of electrical disturbances. Finally, there exists a relatively
new piece of apparatus which now performs the translation function,
nair.ely the card translator. Thus, if an exact one-to-one alternative for
the card translator were constructed employing a magnetic drum, full
advantage could be taken of the testing procedures already de\'eloped
and a comparison could be made against a norm of performance; further-
more, a field trial would be possible, if desired, with a minimum of inter-
ference with normal operation of the telephone plant.
It was decided, therefore, to build a full-scale magnetic drum trans-
lator which could substitute for a card translator in order to obtain lab-
oratory e.Kperience with apparatus of this type and to determine its adapt-
ability to telephone standards and practices. The completed equipment
is shown in Fig. 1. The equipment on the one frame illustrated is the
equivalent in function and capacity of one card translator with its asso-
ciated table. This magnetic drum apparatus is not aimed at replacing the
card translator, which is a well-engineered device known to give satis-
factory service in day-to-day operation. For evaluation purposes in this
article, however, it is assumed to be competing with the card translator.
The following sections describe the design features and operating de-
tails of the translator which was constructed. A brief description of the
card translator and that portion of the 4A office in which the drum trans-
lator must function has been included to provide the necessary back-
, ground for the description. It will become evident that the requirement
of interchangeability which necessitates a one-to-one equivalence with
I the card translator has imposed on the drum translator a number of re-
strictions which are not inherent in it. These tend to prevent full exploita-
j tion of the speed and code advantages which might be realized with the
drum. Furthermore, the rapidity with which all of the information on the
' drum is presented on a continuous read-out basis would permit a type of
i centralized operation which will be touched on briefly and which would
i seem to offer apparatus economies not attained in the test model. None
of these factors, however, impairs the usefulness of conclusions which
! may be drawn from test results concerning reliability.
SURVEY OF MAGNETIC RECORDING PRINCIPLES EMPLOYED IN THE TRANS-
LATOR
All magnetic drums have certain features in common : they consist of
a means of moving a thin shell of magnetically-hard material rapidly
710 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
Fig. 1 — Magnetic drum translator, laboratory installation.
MAGNETIC DRUM TRANSLATOR FOR TOLL SWITCHING OFFICES 711
past one or more heads used for writing or reading digital data. Usually,
as in the translator, the same head is used for both functions. In most
drum-system designs the pole-tips of the heads are close to the recording
surface but do not touch it, and the heads themselves bear a resemblance
to those used in conventional magnetic sound recording, giving therefore,
a "longitudinal" polarization to the medium as sketched diagrammati-
cally in Fig. 2. There is very little further resemblance to sound record-
ing, since digital information is stored in a binary or two-valued code
which, on the translator drum, is represented by the two possible polari-
ties of saturation of the magnetic medium. To one of these polarities is
assigned the code value "O," and this condition prevails except where
the opposite polarity is inserted to represent the code value " 1."
It should be mentioned that several other systems have been devised
which employ the two directions of saturation, sometimes accompanied
by a general background of magnetic neutrality, to effect a greater con-
centration of digital information than that used in the translator. Systems
other than the one chosen for this application were, for the most part,
considered to be less reliable.
THIN MAGNETIC
COATING
SIMPLIFIED
WRITING AMPLIFIER
READING AMPLIFIER
r"
THRESHOLD
LINEAR OUTPUT
AMPLIFIER STAGE
•^ V
MONITOR
D
OUTPUT
L.
MAGNETIC READING
AND WRITING HEAD
Fig. 2 — Simplified diagram of magnetic drum digital data storagje system.
712 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
111 order to facilitate an understanding of the action of the translator
as a whole, a simplified account of the magnetic recording and repro-
ducing process will now be given.
Magnetic Drum Geography
The circumferential strip of the drum surface which moves under the
pole-tips of any magnetic head is commonly known as a track. On each
track will be written magnetic perturbations or spots symbolizing " I's."
It is essential that these spots be precisely located so that they may be
readily removed or "altered." For this purpose a synchronizing track or
some equivalent distribution of equally spaced identifying marks asso-
ciated w4th the drum is provided. With the aid of the electronic circuits,
the magnetic spots are restricted to a modular spacing defined by the
synchronizing marks, and this module is spoken of as a "slot." On the
drum surface, each intersection of track and slot is known as a "cell" and
a cell may contain only one magnetic mark and therefore only one bit of
information. As a matter of economics, the cell density should be as great
as possible. The density which may be attained is determined by the de-
gree of interference which can be tolerated among neighboring cells.
Writing Operations
The first step in preparing the drum to receive a recording is to uni-
formly magnetize the tracks to saturation in the polarity arbitrarily
chosen to represent the code-value "O." This is a preconditioning opera-
tion required only when a drum is newly placed in service. Referring to
Fig. 2, this may be done, for the typical head and track shown, by closing
the switch marked "0" for the duration of at least one complete revolu-
tion of the drum. Enough current must flow through the windings of the
head to establish the magnitude of fringing flux, from the pole-tips, re-
rjuired to saturate the thin magnetic coating. In the case of the trans-
lator drum, the coating is about ^-i milli-inch thick; the clearance
between pole-tips and recording surface is about 2 milli-inches; the inter-
pole gap is also about 2 milli-inches at the tips, and about 20 ampere-
turns of energization are recjuired.
With the track thus preconditioned, there is virtually no output \ olt-
age from the head since the magnetization is essentially uniform and
there is no changing flux threading the head to induce a Aoltage in the
windings.
Whenever a " /" is to be written, a pulse of cuireiit from an oIcM'trouic
writing amplifier (indicated, for convenience, on Fig. 2 as a switch) is
MAGNETIC DRUM TRANSLATOR FOR TOLL SWITCHING OFFICES 713
tiiused to flow through the windings of the head in a direction opposite
to that taken by the preconditioning current. This pulse lasts for only
t wo or three microseconds, and movement of the drum surface is negli-
gibly small while the current persists. The peak value of the current pulse
is sufficient to magnetize to saturation in the opposite direction that por-
tion of the track which lies directly under the pole-tips at that instant.
Areas of the track far-removed in each direction from the pole-tips of
the head are, of course, unaffected by this operation, and remain at sat-
uration in the original polarity. A region of transition in magnetization
1 herefore e.xtends in each direction along the track from the area directly
under the pole-tips.
Fig. 3 illustrates some of the wave forms resulting from writing into
and reading from four adjacent cells on one track of the dnun. Line A
' shows the pulses of writing current which were applied to the windings
on the head. These were caused to appear at precisely spaced distances
;ilong the track by the combined operation of the synchronizing system
and an "administration" circuit. In cells 1 and 3 the writing current po-
I larity is chosen so as to write "I's." Cell 2 remains in its original precon-
ditioned state. In cell 4 a 1" was previously written but is now altered
lo a "O" by a writing current pulse of the same polarity as that chosen
1 for the preconditioning operation.
Line B in Fig. 3 illustrates the resultant magnetic state of the drum
.surface as \'iewed by the reading head. The polarization portrayed as re-
sulting from writing a "7" is a bell-shaped curve. When a " 1" is selec-
\We\y altered to a "0" the area of track directly under the pole-tips will
be carried to saturation in the original preconditioned polarity. The whole
I ell area, however, cannot be affected so strongly, owing to the hysteresis
properties of the coating material, and there will remain traces of the
' 1" type of magnetization near the cell edges, as indicated by the solid
: line in cell 4.
i There is no difficulty in rewriting a "7" in a cell which has been sub-
I jected to the above described treatment. The procedure is that outlined
tor the original writing of a "i" and the results are practically indistin-
I guishable from those obtained by writing in a virgin cell.
Heading Operations
On subsequent revolutions of the drum, the passage, under the pole-
tips, of the magnetic irregularities created by writing "i's" will induce
a change of flux through the windings of the head. The change
is, of course, a function of distance along the drum surface but since tl.ri
drum is rotating continuously at a substantially uniform speed the change
714
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
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MAGNETIC DRUM TRANSLATOR FOR TOLL SWITCHING OFFICES 715
may also be represented as a function of time. This time-rate-of-change
of flux within the coils of the head generates a voltage which is of the
order of 50 millivolts peak-to-peak in the case of the translator. This volt-
age, after amplification, appears as shown in line C of Fig. 3. The trace
shown is that which appears at the "linear output" monitor jack of a
translator reading amplifier, and includes a phase inversion, character-
istic of a three stage amplifier. Such a curve is readily recognized as being
quite similar in shape to the first derivative of the normal error-function
and hence we may infer that the magnetic condition of the drum surface,
at least as interpreted by the head, may be portrayed by a bell-shaped
curve, previously mentioned, similar to the error-function itself.
The residual magnetic irregularity pictured in cell 4 resulting from
writing a "0" over a "i" will induce a voltage in the winding of the head
having a different amplitude and wave shape from that occasioned by
reading a "i." It is sketched out approximately to scale in Fig. 3 and is
seen to be a smaller twinned- version of the "i" signal. Its amplitude or-
dinarily lies in the range of }4o to 3^ of that of the " T' signal, and for
about the middle third of the cell its instantaneous polarity is opposite
to that which a "i" signal would have. These facts suggest at least two
means of discriminating between the voltage signals obtained for the
two code values: (a) on the basis of amplitude difference, and (b) on the
basis of instantaneous polarity difference determined or sampled within
a particular epoch in each cell.
The method adopted for the translator is that of simple amplitude
threshold. The threshold value indicated by the dotted line in Fig. 3, is
set so that the strongest of the residual signal outputs never exceeds it
\\ hile, at the same time, the greatest possible proportion of the positive-
going lobe of a " 1" signal is allowed tp produce an output. The threshold
output stage of the amplifier is also arranged for limiting and this has
the effect of blunting the peaks of the applied signals. The over-all result
of these actions is shown by the shape of the signals in line D of Fig. 3.
Cell packing may be of major economic importance in a large installa-
tion. The general effect of making recordhigs closer and closer together
is that the presence or absence of one of the recordings in a series has an
increasing influence on the size and shape of the signals reproduced from
its neighbors on either side. In the translator, the cells are spaced "JO
niilli-inches center-to-center along the track and the influence of action
in one cell on the amplitude of reproduction from neighboring cells is
never more than about 10 per cent. The trace of line C, Fig. 3, is drawn
for this cell spacing and shows a slight inflection at the transition between
the output voltage occasioned by reading cell 3, and the voltage obtained
716 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
from the "^" which was originally written in cell 4. In many applica
tions a much larger "influence factor" may be tolerable, but this usually]
requires greater elaboration of the signal detecting devices. The cell size
is also influenced by physical constants such as design of the head, prop-
erties of the medium, and dimensional clearances. A discussion of suchj
factors is outside the scope of this paper but it is not unreasonable to i
hope for an improvement of two-to-one in packing factor in future de-»
signs.
Reading Synchronization
The magnetic drum used for the translator provides 80 tracks. About
sixteen microseconds is required for each cell in a track to pass under its
head. Information occupying the same slot on the drum (so-called be- J
cause of its obvious relationship to the term "time-slot" commonly used
in the digital computer field) is presented at the various heads essenti-
ally, but not exactly, simultaneously. Departure from exact simultaneity
is occasioned by small variations in the shapes and amplitudes of the
output waves shown typically as line C in Fig. 3, and by small time-vari-
ations occurring in the writing process, as applied to the ^^arious tracks.
To achieve exact simultaneity, as required for certain subsequent op-
erations of the translator circuitry, narrow "Read Synchronizing" pulses
are produced by the synchronizing circuit previously mentioned. These
pulses are located, within the time boundaries of the cells, so that they
fall approximately at the center of the broad output pulses from the
reading amplifiers and thus permit the latter to be sampled. This rela-
tionship is indicated in lines D'and E of Fig. 3. Similar pulses, slightly
displaced in time, are used to control the writing operations, and are des-
ignated "Write Synchronizing" pulses. The necessity for the time-shift
is apparent from an examination of lines A and E of Fig. 3.
This condensed explanation of the technology of magnetic drum digi-
tal data storage devices, particularly as applied to the translator drum,
should serve as sufficient background for the description of the translator
wherein the drum is but one part of a large ensemble of apparatus.
THE JOH WHICH THE CAKD TRANSLATOR NOW DOES
It will be advantageous to examine very briefly the card translator and
its functions in the No. 4A toll switching system so that the analogous
operation of the magnetic di'um equivalent may be more readil,y ex-
plained. A more detailed description is given in Reference 4.
'l'li(> (I'Munnds of nation wid(> toll dialing rcniuire a \'ery extonsi\-c vvp-
MAGNETIC DRUM TRANSLATOR FOR TOLL SAVITCHING OFFICES 717
ertoire of translations between destination codes and routing instruc-
tions, and it must be possible to change the routing instructions with
ease. The card translator fulfills these requirements. Each individual
translation item is contained on a metallic card; the output code of rout-
ing instructions is in the form of selectively enlarged perforations in the
perforated field of the card, arranged so as to be read by photoelectric
means, and the input code, which identifies the card for purposes of selec-
tion, appears in the form of tabs projecting downward from the bottom
edge. Each card is capable of holding a total of 154 bits of information,
input and output, and somewhat over 1,000 cards are stacked in a bin in
each card translator mechanism.
It is possible to classify the elements of any translator into three broad
categories: the memory unit, the translation selecting unit, and the trans-
lation delivery unit. In the card translator the memory unit is, of course,
I the group of cards; the translation selecting unit consists of code bars,
' electro-mechanically actuated, for displacing a selected card sufficiently
' so that it may be "read." It also contains a network of relays which per-
form the function of checking the authenticity of the input codes applied
I to the code bars. The translation delivery unit consists, in the main, of a
number of output channels, each originating with a light beam for prob-
I iiig one of the code elements (a bit of output information) on the card.
[ Each output channel contains a photo-transistor, a transistor amplifier,
a cold cathode gas tube circuit which has been designated a "channel
output detector" and a register relay. The register relays perform work
' functions and therefore are located separately from the translator; some
are in the decoders, others in the markers.
! In the 4A office, the card translator is one of several items of common
I control ecjuipment which cooperate to establish the talking connections.
( )ther items are the sender, the decoder, and the marker. The sender re-
I ceives and registers and subsequently transmits the decimal digits of the
! called designation; the decoder receives the code digits (from 3 to 0 in
' number) from the sender and submits them to the translator for con-
; \ersion into information needed for the proper routing of the call; and
1 the marker selects an outgoing trunk and establishes a transmission path
by operating the crossbar switches. Since this common control equipment
is associated with any one call for only the short interval necessary to
j establish the talking-circuit connection, its speed of operation is a matter
of considerable importance.
It is ob\^ious that the decoder is the intermediary between the trans-
I lator and the remainder of the office. Each decoder, of which there are a
maximum of 18 in a large office, has exclusively associated with itself a
718 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
card translator mechanism ; each of these mechanisms contains an identi-
cal repertory of translations. Each decoder also has available, through
connectors, a common pool of translators containing a large quantity of
less-often used information. In order to better understand the duties
that a magnetic drum translator must be expected to perform it will now
be convenient to follow, in a highly abbreviated manner, a typical opera-
tion of the decoder and its associated card translator.
The first translation on an incoming call is performed using the first
three decimal digits accumulated by a sender. As soon as three digits are
available the sender connects to a decoder which immediately signals its
individual translator to perform certain mechanical chores in preparation
for selecting a card. There are several sequencing signals between the de-
coder and translator during the complete cycle of a translation (several
of these signals must be synthesized by the drum translator); acting
on one of these signals from the translator, the decoder passes the input
code from the sender, adding certain supplemental information of its own.
The three decimal digits of the input code are in checkable combina-
tions of two leads energized in each of three groups of five leads connected
to the translator. The supplementary information supplied by the de-
coder is in a similar checkable combination on six leads. None of the re-
maining leads in the total of 38 is energized, since the translation being
described involves only three code digits.
In the translator, the input code actuates the card selecting mechanism
and also operates relays whose contacts are wired with a checking net-
work which confirms that the input code, and the responsive operation
of the code bars, is an authentic combination. This is done by establish-
ing a path to operate a "code bar check" relay, cbk. (This relay retains
the same identity in the magnetic drum translator.)
Acting upon the authenticity check, the card translator proceeds to
select a card, and signals the decoder to begin timing for a possible non-
appearance. When the card is in a position to be read, the decoder is sig-
naled on two "index" channels, ind. The decoder now "reads" the card
by applying 130 volt battery to the coils of its register relays; the re-
quired relays operate through the ionized cold-cathode gas tubes in the
translator, and lock up, extinguishing the gas tubes.
'{'he first card dropped may provide information sufficient for complet-
ing the connection; in this circumstance the decoder will then call in a
marker. The first card, however, may specify that more digits are re-
quired and the decoder will so instruct the sender. The sender, unless it
already has the necessary digits, is then dismissed by the decoder which
also instructs the translator to restore itself to normal.
MAGNETIC DRUM TRANSLATOR FOR TOLL SWITCHING OFFICES 719
Six-digit translations are obtained in a manner similar to that des-
cribed above except that the checking network on the relays is switched
to check for six rather than three digits. In some instances the decoder
must refer to one of the translators in the common pool of "foreign area
translators" in order to obtain the reciuired information. Frequently, sev-
eral different cards must be dropped successively before a route is finally
established for the outgoing call.
With the above description as a background, we may proceed to discuss
the magnetic drum translator.
THE ANALOGOUS FUNCTIONS OF THE MAGNETIC DRUM TRANSLATOR
The magnetic drum translator is essentially a device which performs
a translation by making a selection from a recurrent pattern of electrical
pulses generated by a magnetic drum unit. A schematic diagram of the
magnetic drum translator, as arranged for direct substitution for a card
translator, is shown in Fig. 4. In this diagram, the system is divided into
three principal functional components: (a) the drum memory assembly
which produces (from the outputs of 80 reading amplifiers and a timing
unit) a repetitive pattern of electrical pulses representing all the transla-
tions on the drum, both input codes and corresponding output codes; (b)
the translation selecting unit which reads that portion of the pulse pat-
tern representing input codes and acts to identify the unique code group
which matches the incoming information from the decoder ; (c) the trans-
lation delivery unit which, under control of the translation selecting unit,
gates-out the particular pulses of the corresponding output code from the
continuous stream of microsecond pulses, and converts them into signals
capable of operating the register relays in the decoder.
To maintain direct interchangeability, two items of apparatus were
adopted virtually without change from the card translator. These are the
(ODE CHECK RELAYS which accept and check input information, and the
CHANNEL OUTPUT DETECTORS comprising cold-cathodc gas tubes and as-
sociated transformers. This allows input and output terminal facilities
to the decoder to be the same for both translators.
It should be noted that the magnetic drum memory assembly differs
significantly in one functional respect from the binful of cards in the card
translator. When a selected card is being read by the photo-electric cells
in the output channels, no other cards are available. In the drum trans-
lator, all translations are continuously available and if a number of trans-
lation selecting and translation delivery circuits are employed, all may
obtain translations from a common drum memory assembly at the same
time without interference. This feature could not be demonstrated in the
720
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1950
test set-iip as planned, but il would have been incorporated in any test
which includcnl more than one decoder in an office. In such an arrange-
ment, the various units illustrated in Fig. 2, except the drum memory
assembly-, would be furnished to each decoder. One drum memory assem-
l)ly (;iii(l lui (Miici-gency standby) would supply Ihc pattei'n of electrical
MAGNETIC DRUM TRANSLATOR FOR TOLL SWITCHING OFFICES 721
pulses to all translation selecting and translation delivery circuits in mul-
tiple. The object of such an arrangement, naturally, is to employ the mag-
netic drum system in the most economical manner. A further extension
along the same lines would involve relay switching of the pulse circuits
TRANSLATION SELECTING UNIT
"n
MATCH
UNIT
NO.t
MATCH
UNIT —
NO. 8
I — T — 1
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-MATCH PULSE
CBKM
DISABLE ^~j»j
BIAS
SLOT-
SPANNING
MEMORY
3_J
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PULSE
GENERATOR
CODE CHECK RELAYS
H
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X
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I
I
INPUT CODE
CHECKING
NETWORK
I I
H
X
T
X
CBK
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IND B
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X
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oS
tr block diagram.
722 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
to give access to the emergency drum memory, or to a "foreign area"
memory where such extra memory capacity is necessary.
Let us now return to the discussion of Fig. 4 and consider the assign-
ment of the translation information to the drum surface where it is stored.
Recall that the drum surface is effectively divided into a grid by the co-
ordinates of tracks, each passing under an individual write-read magnetic
head, and "slots," each defined by the appearance of a timing pulse in a
rhythmic train synchronized from the drum itself, and that the "cells,"
at the coordinate intersections, each accommodate one bit of code infor-
mation.
Since each card in the card translator accommodates 38 bits of input |
code and 116 bits of output, about 160 cells, divided in the ratio of one
cell for input to every three cells for output, must be assigned to each i
translation item. One simple and direct assignment would be to place
the entire translation item in a single slot composed of 160 cells. With i
this layout the slot containing the desired translation would be identi-
fied by reading, or "matching" the input code, and during this same in- 1
terval the output information in the same slot would be gated-out to the I
translation delivery circuits. A 1 ,000-translation drum would then be'
long and narrow, and far too many reading amplifiers would be required. '
Another evident arrangement would be to assign the entire input code:
to the first of each group of four slots proceeding under the heads, with
the output code following in the next three slots. Such an allocation
would require only 40 reading amplifiers but the drum necessary for the
desired capacity, with the cell-spacing chosen, would have been larger'
in diameter than the mechanical designers cared to undertake in their
first trial. A logical choice, therefore, was to place each translation item
in a pair of adjacent slots, and this was done, although it was later recog-
nized that other, more sophisticated, arrangements might offer eertainj
advantages.
In Fig. 4, the apparent location of one translation item is sketched inj
relation to the drum surface. This sketch is not drawn to scale, since thef
slot width is actually only 0.020 inch, and the track width is comparable.
It is also geographically inaccurate; actually the cells of any one slot arei
positioned in four quadrants on the drum, the associated heads being!
positioned in four stacks for mechanical reasons. However, all of the
cells in a time slot pass under all of the heads at the same instant and the|
presentation of Fig. 4 was adopted for the sake of clarity.
Note, then, that the input code and one-third of the output code arel
recorded in the first or a slot of a slot-pair passing undcn- the reading^
heads, and that the remaining two-thirds of the output code occupies
MAGNETIC DRUM TRANSLATOR FOR TOLL SWITCHING OFFICES 723
the B slot which immediately follows. The parallel (simultaneous) pres-
entation of the entire input code to the translation selecting unit permits
that unit to indicate, by a pulse, that the translation item is the one de-
sired and to gate-out the output code in the same slot while it is still
passing under the heads. Having thus identified the first slot of a trans-
lation item, it is a simple matter to pro\'ide the facilit}^ for gating-out
the remaining information recorded in the next succeeding slot.
It will be seen, from the circuit arrangement shown, that the transla-
tion selecting unit also receives a portion of the output code recorded in
the second slot of each pair. It is therefore necessary to distinguish be-
tween the A and b slots of a pair. This is most conveniently done by the
Timing Unit, which is provided with two outputs, the pulses defining
the slots appearing alternately at these outputs. One output lead is cho-
sen to define all the a slots and it is routed to the translation selecting
unit to provide a portion of the pulse-pattern required for complete and
proper identification of an input code.
The action of the magnetic drum translator in making a translation
may now be traced by following the block diagram of Fig. 4. The decoder,
of course, gives the same preliminary signals as for the card translator,
but these are ignored by the drum translator, because it is continuously
presenting all 1024 translations at the rate of 30,000 per second and need
not take any preparatory steps, provided its relays have returned to
normal after the last translation. The normal state of the relays
is checked by means of a circuit through their contacts; if this circuit is
complete, the decoder receives the signal to apply the input code as soon
as it seizes the translator. A more elaborate checking arrangement could
} have made this signal conditional upon other tests, such as a "standard
1 translation," to determine that the electronic circuitry (in bulk) was
functioning properly, but it was not considered worthwhile to do so in
I the system described here.
1 The decoder, then, furnishes the input code of the desired translation
1 item, causing certain of the relays labeled code check relays in Fig. 4
! to operate. Contacts on these relays are interwired to provide the same
checking network as in the card translator, and a check on the authen-
ticity of the input code will be evidenced by operation of the relay labeled
CBK. This event is signaled to the decoder so that it may start its "no-
I card" timer action. When cbk closes, it also operates a chatter-free mer-
cury-contact relay, cbkm, in the translation selecting unit, permitting
that unit to produce an output at the appropriate time. Each code-check
relay which operates applies a positive voltage to one of the input ter-
minals of a "match" unit in the translation selecting unit. For each of
724 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
these input terminal there is a complementary terminal to which are
applied negative-going pulses from one of the drum memory reading am-
plifiers. As will be explained later, advantage is taken of this comple-
mentary arrangement to obtain a signal indicating a match between
either, (1) an operated code relay and a pulse from the reading amplifier,
or (2) a nonoperated relay and no pulse from the reading amplifier. All
of these signals, from 40 sections of the match units, are combined in a
cascade of "and" gates; when all indicate a match, the translation se-
lecting unit delivers an output "match" pulse.
Since this match pulse is not strong enough to enable 40 gates in the
output channels, it is passed to a "pulse generator" (a regenerative pulse
repeater) which produces, virtually coincident in time, a powerful "a"
gate-opening pulse. Note that both the "a" and the similar "b" pulse
generators are enabled to operate only when the input code is authentic,
as evidenced by the operated code check relay cbkm.
In an unrestricted magnetic drum translator design this identifying
pulse would cause immediate registry of part of the desired information.
Here, however, is evidenced one of the penalties for having a direct one-
for-one substitution for a card translator. The decoder and card transla-
tor function in a definite sequence; one of the steps in this sequence is
initiated by the ind signal from the translator which informs the decoder
that the selected card is properly "indexed" so that it may be "read."
Therefore, in the case of the drum translator, to preserve this sequence,
the selected translation is permitted to pass unheeded, except that the
IND signal is synthesized from the identifying b gate-opening pulse. This
operation closes one relay, indb, through a special output channel (top-
most one in Fig. 4) provided for the purpose. The decoder, thus notified
that the desired translation is available, applies battery to its register
relays, and the output channels are completely enabled for a subsequent
registry of the desired information.
The output information is usually registered during its next passage,
one drum-revolution after initial identification of the item. The action of
identifying the translation is again as described above, and there remains
only to follow the operation in the output channels. E\'en before the
translation selecting unit has initiated the identifying gate-opening
pulse, reading amplifiers which are required to deliver an output code
have each commenced delivery of a pulse to their corresponding gate
terminals in the and gate and pulse stretcher units. (See Fig. 4). When
these pulse signals have reached a stable maximum, the gate-opening
pulse (a or b depending on the slot which is being read at the moment) is
free to pass through the gates and to trigger the pulse stretchers. The ,
MAGNETIC DRUM TRANSLATOR FOR TOLL SWITCHING OFFICES 725
latter devices, each containing a single transistor in a monostable circuit
arrangement, deliver 12-volt pulses lasting about a millisecond. The
pulse stretchers from which an output code is not required are not trig-
gered, owing to the absence of pulses from the corresponding reading
amplifiers.
The remainder of the output channel, as previously stated, is borrowed
directly from the card translator, and the action is similar. In the output
detector, a transformer steps-up the 12-volt pulse signal to a voltage more
than sufficient to establish a discharge in the control gap of a cold-cathode
gas tube. Since the decoder has applied voltage through a relay coil to
the main gap, the discharge transfers, and the resultant current flow
operates the relay. The operated relay, which may be in the decoder,
registers the code and locks to ground through an auxiliary contact. This
' action also extinguishes the gas tube, thereby extending its life.
: Except for relay operation, all of the activity described here for two
drum revolutions repeats itself for every subsequent drum revolution
I for as long as the code check relay cbkm remains operated. However,
! once the code is registered, no further use is made of the pulses in the
output channels.
When the decoder has made use of the translation, it transmits a sig-
I lull which is used in the code-check relay system to indicate when all re-
;lays are properly restored. In the card translator this signal is also used
to restore the selected card, but in the drum translator this operation,
of course, is not required.
. idministration Equipment
I
To utilize the magnetic drum translator as described above, it is obvi-
ous that some means for writing-in the translations is as necessary to
t he drum as a card punch is to the card translator. Although a selective
S writing, or "Administration Unit" was required, a highly efficient design
\\ as not essential to the experiment. Consequently there was constructed
a separate, portable aggregation of essential basic electronic circuits,
; arranged for manual control, but designed with a view to possible ex-
'leusion to fully automatic operation. This equipment will be described
ill a later section.
I QIJIPMENT AND CIRCUIT DESIGN DETAILS OF THE TRANSLATOR
(nticrdl Description
'i'lie entire translator is mounted on an 11-foot by 32-inch bay and has
licen made to conform to telephone central office practices as far as pos-
726
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
Fici. 5 — FvowtM- easing containing ])artial complement of reading amplifiers,
liming unit, tilani(Mit transformers and hlowers. Koceptacle at right end of (>acli
amidificr mounting strip allows Administration unit to connect directl}' to mag-
netic heads associated with those amplifiers.
sible; except for the presence of the drum unit at the base of the i-ack,
its appearance is not unhke that of other racks found in central offices.
Mounted directly above the drum unit is a casing of conventional de-
sign (shown open in Fig. 5) which houses the reading amplifiers, timing
unit, filament transformers, and a self-contained forced-air ventilating
MAGNETIC DRUM TRANSLATOR FOR TOLL SWITCHING OFFICES 727
Fig. 6 — Upper casing containing translation selecting unit, and partial com-
plement of pulse stretchers and channel detectors.
system. A second casing, (Fig. 6), located directly above the first, houses
the translation selecting unit, pulse stretchers, and channel output detec-
tors. The various plug-in components used in these sections are shown
in Fig. 7. At the top of the rack are located the code-check input relays,
fuses and terminal blocks.
728
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 195G
r^ 1
-=5.
■^^.J
/^
Fig. 7 — Plug-in units. Left to right, reading amplifier, match unit varistor
cluster, individual varistor, match and-gate, transistor, and pulse stretcher.
In wiring the rack, use of individually-shielded conductors was held
to a minimum. The cable between the drum unit and the reading ampli-
fiers was composed of standard switchboard wire, shielded as a unit by
removable sheet-metal enclosures, thus greatly reducing the bulk as com-
pared to the usual bundle of coaxial cables.
The remainder of the wiring, which carries relatively high-level signals
from unit to unit within the frame was also in the form of cables of switch-
board wire; this type of wiring was tried as an experiment for micro-
second pulse work, and was found to be successful in this instance.
Under normal conditions the entire translator, with the exception of
the tube filaments and drum drive motor, operates from the standard
plant batteries of +130 and —48 volts. Commercial 60-cycle power is
normally used for filaments and motor; the motor is duplex and is de-
signed to transfer automatically to the 48-volt plant battery in case of'
power failure, and the same provision would have to be made for the
filaments in the event of a telephone plant installation. i
Magnetic Drum Unit \
The magnetic drum unit is located at the bottom of the rack, as shown i
in Fig. 1; a close-up view with one of the covers removed is shown in
Fig. 8. A mounting casting supports the machine directly on the floor,
straddling the lower member of the rack so that no load is imposed on
the rack structure. The drum rotates about a vertical axis and is housed
in two cast-iron end-bells spaced by a cast-iron shell. The end-bells carryi^
the bearings for the drum, and serve to mount the motor, while the shell- 1
casting rigidly locates the magnetic heads, each very close to the drum
surface. This design requires a minimum of floor space, insures accurate
bearing alignment, provides a convenient location for the magnetic
heads, and permits the use of tightly-fitting gasketed covers to exclude
i
MAGNETIC DRUM TRANSLATOR FOR TOLL SWITCHING OFFICES 729
Fig. 8 — Magnetic diiun unit pnrllN- uncovered to show magnetic iieads and
wiring terminals.
dirt iiiid foreign material from the magnetic drum surface and the bear-
ings. The Ke-hp motor dri\'es the drum through a spring-diaphragm
coupling.
The drum is comprised of a stress-reheved iron casting of high dimen-
-^ional stabiHty, a press-fitted steel shaft, and a ^^ie" thick brass outer
, sliell which carries the magnetic recording medium. Since both drum and
730 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
housing are of similar materials, and have almost identical temperature-
expansion coefficients, it is expected that pole-tip-to-drum clearance will
remain unchanged under normal conditions of service. The drum, which
is 12.8" in diameter, 10" long, and weighs 150 pounds, is dynamically
balanced and runs without sensible vibration.
Commercial super-precision angular-contact ball bearings, two at
each end, are used to mount the drum in its housing. The lower bearings
are arranged to share the thrust load imposed by the weight of the drum,
and the upper bearings are mounted opposing each other, and are pre-
loaded one against the other. The upper bearings serve only as radial
constraints, the outer races being free to move axially. This type of con-
struction results in a finished unit having a total runout of only a few
ten-thousandths of an inch without the necessity of machining the drum
on its own bearings. For the experimental installation, the bearings were
grease-packed at assembly and can be expected to function satisfactorily
during any reasonable test period. If, however, such a drum unit were
made a permanent part of the telephone plant, other provisions have
been considered which wovdd insure adequate lubrication over a much
more extended period.
The magnetic coating used on the drum is an electro-deposited alloy
of cobalt and nickel (90 per cent Co-10 per cent Ni) approximately
0.0003" thick. This coating was selected because of its hardness, strength,
uniformity, and desirable magnetic characteristics. The thickness of the
coating is such as to result in a satisfactory cell-size without undue sacri-
fice in output. The purpose of the brass sleeve mentioned previously is
to form a nonmagnetic surface between the magnetic coating and the
cast-iron core since, if the coating were applied directly to a ferro-mag-
netic material, its effectiveness would be greatly reduced by the shunting
effect of the base material. The brass sleeve also serves to facilitate plat-
ing the drum, since brass, unlike cast-iron, is amenable to the electro-
plating process.
Read-Write Heads
One of the read-write heads is shown in Fig. 9. The magnetic structured
consists of three rectangular bars of laminated material, arranged in theij
form of a triangle (as schematically represented in Fig. 2). Two legs of j
this triangle carry single-layer coils which are series-connected. These;
two legs also serve as pole-tips, being pointed at the end and separated (
by an air gap. The third leg sorx-es to complete the magnetic circuit and, f
in assembly, is butted tightly against the other members by means of a-,
Icafspring.
MAGNETIC DRUM TRANSLATOR FOR TOLL SWITCHING OFFICES 731
Fig. 9 — Magnetic head and mounting bracket showing means of adjustment.
I
The magnetic structure is assembled on a nickel-silver plate to which
have been soldered two copper shoes which serve to locate the pole pieces
and shield the pole-tips, thereby focusing the recording flux to some de-
gree. After adjustment of the pole-tips, the assembly is clamped in a
I sandwich by means of a second, smaller nickel-silver plate. As is evident
i from the illustration, this magnetic assembly is in turn assembled to a
mounting bracket which contains facilities for precisely adjusting the
clearance between pole-tips and drum surface.
The pole- tips of the head are 0.050" wide and the tracks are on 0.10''
centers, leaving a nominal value of 0.050" between tracks to allow for
misalignment of heads and for flux-spreading. Heads which are physi-
i cally adjacent in each of the four corner stacks are mounted on 0.40"
centers, but the stacks are offset with respect to one another, thereby
interlacing the tracks on the drum.
The read-write heads have been designed expressly for use in liigh-
speed digital recording. Very thin laminations are used and this, coupled
with carefully prescribed manufacturing techniques, results in a head
having a satisfactory frequency response for the very short pulses em-
ployed. When used as a transducer to convert electrical pulses to mag-
732 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 |
i
netic flux, it is capable of responding faithfully to frequencies approach-
ing ten megacycles per second. j
The Timing Wheels and Associated Heads |
The synchronizing pulses derived from the drum originate from aj
ol2-tooth soft-steel gear mounted at the top end of the drum. In com-^'i
bination with a polarized reproducing head, the gear generates a timing i
signal which proA'ides means for permanently locating the various cells '
used to store information on the drum surface. The polarized head differs
from those used on the drum proper, being of a form which is conven-
tional in tone-generators where, as in this instance, a sinusoidal output
is desired. |
A second gear is mounted at the bottom of the drum, carrying a single \
tooth of the same proportions as the teeth on the upper gear. In combina- !
tion with a polarized reproducing head, otherwise quite similar to those
used on the drum proper, this single tooth provides a signal once per rev-
olution of the drum which (as will be shown later) is necessary for the
operation of the administration unit.
The Reading Am-plifier
One of the 80 plug-in reading amplifiers is pictured at the far left in
Fig. 7. It employs two twin-triode vacuum tubes, and consists of a three- :^
stage ac-coupled linear broad-band feedback amplifier, followed by aj
threshold output stage.
As shown in the circuit schematic of Fig. 10, the two halves of vi and]
the left-hand half of V2 constitute the linear broad-band amplifier. A
suitable choice of coupling elements insures that the amplification ^^ill|
diminish, with decreasing frequency, at a controlled rate for frequenciesj
below a few hundred cycles per second. It is unnecessary to provide am-
plification at low frequencies, since the signals to be handled have noJ
low-frequency components, and it is undesirable to do so from the stand-
point of hum pickup. There is about 20db of feedback in the important
part of the frequency range and the amplifier is thus substantially sta-
bilized against variations of gain due to change in operating voltages and
aging of tubes. The over-all operating voltage gain of the linear stages,
with feedback, is about 56 db; the 3 db points are approximately 300
c/sec and 700 kc/sec.
The grid of the fourth stage of the reading amplifier is coupled to the
output of the linear amplifier and is biased to about twice the plate-cur-
rent cut-off value. The output signal from the plate of this stage, occa-
MAGNETIC DRUM TRANSLATOR FOR TOLL SWITCHING OFFICES 733
sioned by reading a "1", will be a negative-going pulse of approximately
40-volt amplitude from a standing potential equal to the plate supply,
+ 130 volts. As a precaution against false signals, an externally-mounted
plate-feed resistor is provided to establish at the output a condition cor-
responding to that of no signal present when the amplifier is removed
from its receptacle.
Timing Unit
The timing unit accepts an approximately sinusoidal timing-wave sig-
nal from the upper timing head, and converts this signal into two pulse-
trains, each having 1,024 narrow pulses per drum revolution, designated
as A sync and b sync, alternating in time and available on separate out-
puts for controlling all the rest of the circuit action of the translator. A
block-schematic indicating how the pulse trains are produced is shown
in Fig. 1 1 .
The general procedure for converting from a sine-wave to a synchro-
nous train of short pulses, two per cycle of input, may be traced through
the upper channel of the drawing. The signal, as represented by voltage
trace 1, is amplified and clipped until a steep-sided square wave is ob-
tained; this wave, trace 2, is applied to a push-pull phase inverter from
which a pair of oppositely-phased outputs is obtained. Each of the two
outputs is then differentiated by means of an r-c network, and the nega-
+ 130V
^pvw
INPUT
FROM HEAD
OUTPUT
A A A -' ^S"^
Fig. 10 — Reading am])lirior circuit.
734
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
s
o3 1
a
MAGNETIC DRUM TRANSLATOR FOR TOLL SWITCHING OFFICES 735
tive-goiug spikes, traces 3 and 4, are combined in a negative-going or
gate of crystal diodes.
These spikes, trace 5, are used to trigger a cathode-coupled single-shot
multivibrator, designed to give a rectangular pulse of about one micro-
second duration. The multivibrator drives a pair of identical out-
put stages: one furnishes the recjuired a sync pulses to other equipment
in the translator bay, and the other delivers its output to a coaxial con-
nector so that, when required, the pulses may be furnished to the admin-
istration unit.
I The B sync pulse-train is produced in the lower channel shown in Fig.
11. After some linear amplification, a part of the original input sine-wave is
applied to a vacuum tube integrator circuit. The constants of the inte-
grator are such that it provides very nearly a quarter-period of phase
shift even if the drum varies from its nominal speed. The output of the
integrator is then treated in the same manner as that described for the
direct input, with the result that the required b sync pulses are produced.
The timing unit also contains a third channel which accepts the once-
per-revolution signal from the special head adjacent to the single-tooth
wheel. The output of this channel provides the fiducial signal, on a low-
impedance basis, for administrative operations.
The Translation Selecting Unit
This unit, which appears as the bottom panel in the photograph. Fig. 6,
performs a number of successive steps in making its selection. These are:
(1) recognition of a match between input information from a decoder
.seeking a translation, and the unique corresponding information from
.the drum, selected from the flow of continuously-presented information;
'(2) production of a gate-opening pulse whose leading edge is substanti-
ally coincident in time with the leading edge of the particular a sync
1 pulse corresponding to the entry for which the match occurred; (3) acti-
\ation of a slot-spanning pulse circuit to bridge the time interval until
jthe next-following b slot; (4) production, at a separate output, of another
igate-opening pulse whose leading edge is substantially coincident in time
with the leading edge of the identified b sync pulse. These actions will
now be considered individually.
(1) Recognition of Match
Responsibility for this function is divided among a group of eight
match-units operating with their associated differential amplifiers. Each
match-unit is capable of comparing the inputs from five code-relays with
the potentially-matching outputs of five reading amplifiers.
A circuit schematic of one of the units, with its associated differential
736
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
amplifier and some of the connected apparatus, is shown in Fig. 12. The j
uppermost channel on this diagram is typical of all five channels. Re-
sistors Ri to R5 are proportioned so that the potential at point c assumes
a value of +115 volts for either of the two acceptable conditions
of match: (1) code-relay unoperated and reading amplifier not drawing
plate current, or (2) code relay operated and reading amplifier drawing a
pulse of plate current. Whenever either of the two possible conditions of
mismatch exists, the potential at point c assumes a value about 15 volts
higher or lower, depending on the nature of the mismatch. Resistor r6
is introduced for protective purposes only. Varistor vri limits the nega-
+130V!
CODE-CHECK
RELAYS
Fig. 12 — Match unit and differential amplifier circuit.
MAGNETIC DRUM TRANSLATOR FOR TOLL SWITCHING OFFICES 737
tive voltage excursion at point b, during a pulse, so that it never goes
below +105 volts. This establishes the uniform pulse amplitude among
Ithe forty match channels which is necessary for proper functioning of
the unit.
To detect and recognize the voltage conditions at the five junction
points, two varistor gates and a differential amplifier are employed. One
gate, comprising six varistors including vr6 and VRii, will transmit the
type of mismatch signal which is more positive than +115 volts. This
signal is dc-coupled to the left-hand grid of the differential amplifier as
illustrated in Fig. 12. The type of mismatch signal which is less positive
than +115 volts is blocked by this gate but is transmitted through the
other gate to the right-hand grid. The threshold for this discriminating
action is established by application of a fixed nominal potential of +115
volts to varistors VRii and vri2.
At match, the output of each of the two gates presents a potential of
+ 115 volts to the differential amplifier. The differential amplifier is bi-
ased (by inequality of r7 and rs) so that for this condition the right-
hand triode is conducting, and the output potential is lower than the
plate supply voltage. Positive-going mismatch signals on the left-hand
[grid, or negative-going signals on the right-hand grid are then equally
jeffective in cutting oft' the right-hand triode, causing the output voltage
to rise to plate supply potential signifying a mismatch.
The outputs from the differential amplifiers of the eight match units
are combined with the a sync pulses in a system of and gates, as illus-
trated in Fig. 4. A match-pulse output from this system thus signifies
that conditions for match have been uniquely determined for 40 pairs
[of items. Thus the match unit, in total, is capable of distinguishing be-
jtween all binary combinations of 40 bits or approximately 10'^ items al-
I though when a self-checking code is employed, as in the translator appli-
cation, many of these combinations are inadmissible.
(2) The A Gate-Opening Pulse
Occurrence of the match-pulse, as just described, indicates that the
40 items constituting one-half the contents of one of the a slots match
the incoming input code; it is then desired to spill out from the other
half of this same a slot the information which is also appearing at ampli-
Ifier outputs at that instant. This is done by means of gates opened by
the action of a gate-opening pulse, triggered by the match pulse.
The a gate-opening pulse is only a few microseconds in duration and
normally is produced only once per revolution of the drum; a quiescent
[blocking-oscillator was chosen as the type of circuit best suited for this
[purpose. Whenever the code-check relays are operated in an authentic
738 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
code combination, relay cbkm is operated, ^emo^•ing a disabling bias
from the driver stage of the blocking oscillator. When in this condition,
each occurrence of the match pulse will trigger the blocking oscillator,
thereby producing the a gate-opening pulse once per drum revolution.
(3) Slot-Spanning Pidser
Whene^'er an a gate-opening pulse has acted to permit read-out of i
information from half of the proper a slot, it is also desired to read out ;
all the information from the next-following b slot. The first step toward :
doing this is to cause the a gate-opening pulse to trigger a single-shot ,
multixibrator whose characteristic period is long enough to just bridge i
the time until the next slot appears. The output of this pulser is combined I
with the B sync pulses in an and gate so that the selected b pulse, cor- i
responding to the wanted b slot, can be used to trigger another gate- .
opening blocking-oscillator just as the match pulse was used to trigger t
the A gate-opening blocking-oscillator. j
(4) The B Gate-Opening Pulse |
The outputs of all the reading amplifiers must be gated for the b slot. |
Hence the b gate-opening pulse must operate twice as many gates as the .
A gate-opening pulse and must be correspondingly more powerful. This ■
requirement is met by using the same circuit design with parallel output
tubes.
Pulse Stretchers and Channel Detectors
Fig. 13 presents a simplified schematic of one of the translator output
channels, together with certain of the relays in the decoder. Package-wise,
the pulse stretchers combine two functions: that of an and gate with two
inputs and a threshold feature, and that of a single-shot multivibrator for
amplifying and lengthening the short input pulse from the gate. A single
point-contact transistor provides the necessary gain for the monostable
action. The inputs to the and gate come from sources which supply nega-
tive-going pulses from a standing potential of +130 volts. When one or
the other, but not both, of these sources supphes a pulse, a larger portion i
of the current being supplied to resistor ri must be drawn from the non-
active source; this extra demand causes a small \oltage drop which be-
comes evident at the gate output. The resultant weak false signal is pre-
vented from affecting the transistor pulser by the action of threshold
diode VRi which is normally back-biased a few volts by the potential di-
\-ider r2, r3. Small negative-going signals from the gate will not over-
come the bias and will therefore be greatly attenuated; normal gate-out-
put pulses, occasioned by coincidence of pulses at both inputs will,
MAGNETIC DRUM TRANSLATOR FOR TOLL SWITCHING OFFICES 739
however, overcome the bias and will be transmitted to the transistor
monostable circuit.
When triggered at the base, the transistor delivers a pulse of about one
millisecond duration to the load represented by the input transformer
and the channel detector gas tube and thus provides the drive required
to initiate ionization in the control gap of the gas tube. When brought
into action, the transistor serves as a switch to connect capacitor c to
collector supply resistor r6. The voltage change, occasioned by the re-
sultant flow of current in r6, is communicated to the transformer primary
through a blocking capacitor and a current limiting resistor. As capacitor
c charges, the voltage at the transistor emitter will approach the collector
supply potential at an approximately exponential rate. When the di-
minishing flow of emitter current can no longer maintain the transistor
in its low-impedance mode, it reverts to its pre-triggered condition, and
the timing capacitor c is then discharged, primarily through forward-
conducting varistor vr2 and resistors r5 and r4.
Owing to the necessity of using early-production samples of the type
of point-contact transistor chosen for this application, the associated
circuitry for biasing the emitter into the normal non-conducting state
is somewhat more elaborate than that which might have sufficed with
later samples whose characteristics were more closely controlled.
The principal components of the channel detector are a step-up trans-
PULSE STRETCHER
CHANNEL DETECTOR ASSOCIATED
EQUIPMENT
IN DECODER
OR MARKER
INPUT
Fig. 13 — Pulse stretcher and channel detector circuit,
i
Fig. 14 — Administration unit. Three eo-ax leads entering under shelf bringi]
A, B and F pidses from translator. Cable leading to plug with bail-handle resting;
on shelf serves to connect writing amplifier output to magnetic heads in translatori|
Bottom cable connects to 60-cycle source which supplies all power,
740
MAGNETIC DRUM TRANSLATOR FOR TOLL SWITCHING OFFICES 741
former designed for the audio frequency range, and a cold-cathode gas
tube. The starter-anode of the gas tube has a dc bias of about +24 volts
with respect to its cathode to reduce the value of pulse voltage required
to ionize it. When +130 volt battery is applied via the winding of the
channel rela.y to the main anode of the gas tube, ionization established
in the starter gap by the pulse stretcher signal will transfer to the main
gap and cause the relay to operate. Closure of one of the relay make-
contacts serves to divert the winding current from the gas tube directly
to ground, thereby extinguishing the tube and prolonging its life. Other
contacts, not shown, make the registered information available.
Co7npo7ients
A full complement of the electronic apparatus described in the last
few sections utilizes plug-in components in the following quantities:
Twin-triode electron tubes 186
Cold-cathode gas tubes 121
Germanium varistors 552
Point-contact transistors 120
Only one type of each of these components is used in the translator;
this uniformity greatly simplifies the maintenance problem and imposed
little if any handicap on the circuit designs.
ADMINISTRATION EQUIPMENT
Whenever it is desired to add, or to change, a translation item on the
drum, the auxiliary administration unit pictured in Fig. 14 is connected
to the translator by three shielded cables, shown leaving the rack just
under the shelf, and a ten-conductor cable, shown with its plug resting
' on the shelf. The shielded cables convey the a and b sync pulses and the
1 once-per-drum-revolution fiducial f pulse to the administrator. The ten-
conductor cable, with plug, is used to establish paths extending directly
i to magnetic heads on the drum. During the recording of any one com-
! plete translation item on the drum, this plug is successively shifted to
each of nine multi-connector jacks located in the amplifier compartment
I )f the translator.
'■ The manual controls are located just above the shelf. At the right are
the two keys for ordering a writing operation, one for the a slot and an-
other for the B slot of the chosen pair. If either key is lifted, it will order
Ihe entry of a magnetic mark (write " 1"). If depressed, the key will order
! the removal of a mark (write "0"). It is obvious that the translation is
742
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
I- -o
^ ounce tr
i-q: _iOO
LU>.l/)Z
5 o
>
, UJ
UJ_j5
Q.UJ u
Q <
UJ
s
a
o
to
a
<5
10
bb
HOivnsNvai do iind onii^ii ox
MAGNETIC DRUM TRANSLATOR FOR TOLL SWITCHING OFFICES 743
inserted piecemeal by working in each track successively. The manual
switching operation of connecting a single pair of writing amplifiers to
each of eighty magnetic heads, in turn, is accomplished partly by setting
the nine-position switch shown at the center of the panel, and partly by
sliifting the plug of the ten-conductor cable. At the left are two signal
lights which serve as alarms to warn the operator of possible incorrect
functioning of the equipment.
The operation of the administration unit can best be traced with the
aid of the schematic block-diagram of Fig. 15. A ten-stage binary counter
is supplied with b sync pulses from the translator; the 1,024 possible
states of the counter are traversed in the course of exactly one revolu-
tion of the translator drum. The f pulse from the translator will, mid-
way between two b pulses, set all counter stages to zero, once per revolu-
tion. After the first such reset, however, if the counter is working
properly, it will always have returned to the zero condition just before
the occurrence of the f pulse, by having counted 1,024 b pulses; under
these conditions the f pulse, though still initiating reset action, does not
change the state of the counter. The basis for the alarm signals mentioned
above is a circuit arranged to detect if a change of state is occasioned by
the F pulse.
Associated with the counter is a coincidence circuit with a keyboard
on which may be set up any "address" between 0 and 1,023. When the
count of B pulses ecjuals the address set up on the keyboard, the coinci-
dence circuit delivers a pulse which persists until the next b pulse alters
the count; this coincidence pulse spans the time of occurrence of an a
pulse, and is used in the read sync selector to gate-out a "selected" a
pulse uniquely assigned to the address set up on the keyboard. A slot-
spanning pulser, triggered bj^ the selcted a pulse, gates-out the associ-
ated "selected" b pulse.
These selected pulses, which occur once per revolution of the drum, are
passed through gates under control of bistable electron-tube pairs which
can be set by the manual writing keys and are re-set by the writing action
itself. This insures that the desired action takes place only once per key
operation, instead of repeating, once per drum-revolution, as long as the
keys are held operated. The manually-gated unique selected a or selected
B sync pulse is then slightly delayed in time to become a selected write-
sync pulse. It is passed on through further gates under direct control of
the writing keys, and is emplo3''ed as an input to a writing amplifier.
A pair of writing amplifiers is provided, one to write " 1" and the other
to write "0"; the circuits are identical quiescent blocking-oscillators shar-
ing a common output transformer, and one or the other is triggered into
744 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 195G
action by the write-sync pulses. The output transformer supplies the
writing current pulses, under control of the selector switch, to the chosen
magnetic head. Arrangements are provided for synchronizing an oscil-
loscope to display the writing current pulses or the voltage outputs from
the head at the selected address, as required.
When a new translation item is to be entered, or an existing one al-
tered, the address corresponding to the desired slot-pair is determined
from a card-index, or ledger, listing all items on the drum. The address
keyboard is then set to the assigned number, thereby singling-out the
desired slot pair so that the writing operation can proceed as described
above. During this procedure, the monitoring oscilloscope may be used
for verifying the new entry, two cells at a time. Over-all verification is
accomplished by exercising the translator through facilities already avail-
able in the toll switching office. There is nothing about this procedure
which precludes the use of automatic facilities for performing the admin-
istration. There is also no fundamental need to take the translator out
of routine service during the administration operation, since each writing
operation disables the equipment for only a few microseconds and would
rarely delay a translation by as much as one drum revolution.
CONCLUSION
After short preliminary tests, the equipment described and pictured
was installed in the switching systems laboratory at Bell Laboratories.
A rapid-transfer arrangement permitted direct interchangeability with a
card translator in a skeletonized model of a toll switching office.
A testing program was then begun entailing continuous 24-hours-per-
day operation of the magnetic drum translator for approximately one
year. After an initial shakedown period during which wiring faults and
other minor troubles were recognized and cleared, many millions of trans-
lations were handled with only a small proportion of failures. The accu-
mulated data on failure rate and cause was significant, being one of the
primary objectives of the experiment. An analysis of the data indicated
the desirability of certain simple design changes in the existing circuitiy
and established a basis for the selection of future designs.
If, ill the future, consideration is given to the design of ciniipineiil of
this type for some specific application, new electronic developments must
also be taken into account. Many more types of transistors are now
available than when the present design was undertaken, and some of the
newer types have capabilities which make them obvious candidates for
many of the jobs now done in the translator with electron tubes. Such a
substitution would not only increase reliability and decrease power con-
MAGNETIC DRUM TRANSLATOR FOR TOLL SWITCHING OFFICES 745
sumption, but since transistors are essentially current-operated devices
t hey would seem to be particularly suitable for working with microsecond
[)ulses in the environment of existing relay-equipped offices where the
majority of interference transients are capacitively-propagated voltage-
tlisturbances.
Evaluation of the magnetic drum reveals it to be a safe and vevy roli-
;il)le means of storing several hundred thousand bits of information. Dur-
ing the course of these tests, the drum functioned perfectly, and the trans-
lations that were recorded at the beginning of the test were retained until
near the end, when they were deliberately altered. During this interval
of nearly continuous operation there was no detectable deterioration, or
iliange in the signals obtained from the drum.
The results obtained from the tests of this particular drum translator
indicate that the associated circuitry, working with microsecond pulses,
ran be designed to measure up to the exacting standards demanded for
i telephone office apparatus, whether the application be that of a magnetic
(hum translator or some other type of equipment.
i;eferences
1. W. D. Lewis, Electronic Computers and Telephone Switching, Proc. I.R.E.,
41, pp. 1242-1244; Oct., 1953.
'2. W. A. Malthaner and H. E. Vaughan, An Automatic Telephone System Em-
ploying Magnetic Drum Memory, Proc. I.R.E., 41, pp. 1341-1347; Oct., 1953.
'■\. .J. H. McGuigan, Combined Reading and Writing on a Magnetic Drum, Proc.
I.R.E., 41, pp. 1438-1444; Oct., 1953.
4. L. N. Hampton and J. B. Newsom, The Card Translator for Nationwide Dial-
ing, B. S. T. J., 32, pp. 1037-1098; Sept., 1953.
I
Tables of Phase of a Semi-Infinite Unit
Attenuation Slope
By D. E. THOMAS
(Manuscript received February 24, 1956)
Five and seven place tables of the integral
B(x,) = ' log
1 +a:
1 — X
dx
X
which gives the 'phase associated with a semi-infinite unit slope of attenua-
tion, are now available in monograph form. The usefulness of this integral
and its tabulation are discussed.
H. W. Bode' has shown that on the imaginary axis, the vahies of the
imaginary part of certain functions of a complex variable may be ob-
tained from the corresponding values of the real part, and vice versa.
This theorem was immediately recognized as a powerful tool in the com-
munications and network fields. The most generally useful function which
was given by Bode for use in applying this theorem to the solution of
communications problems, is the phase associated with a semi-infinite
unit slope of attenuation. This is given by the integral
1 r':=Xc
5(.T.) = - log
1 -\-x
(J/Jy / 1 \
X
1 - X
where: 5(:i-c) is the phase in radians at frequency /c ,
x = ^ ,x, = ^^ < 1.0
Jo Jo
and fo = the frequency at which the semi-infinite unit slope
begins
The usefulness of Integral (1) is illustrated by some of the communica-
tion problems which stimulated its accurate tabulation.
iT
1 Bode, H. W., Network Aiuily.sis and Feedback Amplifier Design, D. Van Nos-
trand Co., Inc., New York, 1945, Chap. XIV.
2 Ibid: Chap. XV, pp. 342-343.
747
748 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
When the development program on deep sea repeatered .submarine
telephone cable systems was reactivated at the close of World War II,
one of the first problems to present itself was the detei-mination of the
delay distortion of a transatlantic repeatered cable system. The only |
means then known of obtaining an answer to this problem was by com-
puting the minimum phase of the system from its predictable attenua-
tion characteristic, using Bode's straight line approximation method,*
and then determining the delay distortion from the non-linear portion of
this minimum phase. However, the non-linear phase is such a small part
of the total phase, that a five figure accuracy tabulation of Integral (1)
was needed for a satisfactory determination of the non-linearity. The
necessary table was therefore compiled. A mmierical computation was
used to evaluate the integral because of the simplicity of its integrand.
The minimum phase of the projected transatlantic repeatered telephone
cables was then computed using this table and the anticipated delay dis-
tortion was determined from the non-linear portion of this minimum
phase.
About this time the delay ecjualization of coaxial cable systems for
television transmission became a pressing problem. Bode's techniciue
proved to be the simplest means for determining the delay to be equal- i
ized and so the existing phase table was immediately put to use in the ji
coaxial cable delay ecjualization program.
The increasing use of the tables led to a decision to publish them in in
The Bell System Technical Journal.^ In order to make the tables
more generally useful, the published paper included a tabulation of the
phase in radians as well as in degrees. The radian tables can, for example, I
be used to determine the reactance characteristic associated with a given
resistance characteristic of a minimum reactance impedance function.
Because of the demand for higher accuracy which occasionally arose
after the publication of the five place tables, it was decided to undertake
the computation of seven-place tables. These tables were also computed
lunnerically using intervals selected to give at least ±1 accuracy in the
final figure. The complete tables require forty-nine pages for tabulation.
Since it is probable that only a fraction of the Journal readers would
need these tables, it did not seem desirable to publish the actual tables iti
the Journal. They are therefore being put)lished in original monograph
form as Bell System Monograph 2550 entitled "Tal)les of Phase of a
Semi-Infinite Unit Attenuation Slope." The phase is tabulated in the
■' Ibid : Chap. XV.
■* Tliomas, D. K., Tables of I'liase Associated willi a Semi Inliiiile I'nil Slope
of Attenuation, B. S.T.J. , 26, pp. 870-899, Oct., 1947.
^ This Monograph will be available about June 15, 1956.
TABLES OF PHASE 749
monograph both in degrees and radians for values of/ greater than /o
as well as for/ less than/o . The tabular intervals are 0(0.001) 0.600
(0.0005) 0.9000 (0.0001) 0.9940 (0.00005) 0.99800 (0.00001) 1.00000.
These intcr\'als were selected to permit linear interpolation for intermedi-
ate values of the phase to an accuracy of the same order as the accuracy
of the tabulated values, i.e., ±1 in the last place. The original Journal
article discussed the construction of the tables and the errors involved
in the numerical evaluation of Integral (1), described and illustrated
the use of the tables, and gave five-place tabulations of the integral.
I'his entire article is therefore included in Monograph 2550 for complete-
ness along with the newer seven-place tables.
B. A. Kingsbury^ has pointed out that the Integral (1) which is tabu-
lated in the phase tables in question is useful in other than the communi-
cations and network fields. A bibliography covering other possible fields
of interest is given in an article by Murakami and Corrnigton.
ACKNOWLEDGMENT
The author is indebted to R. W. Hamming of the Mathematical Ke-
search Department w'ho supervised the computation of the seven place
tables, to Miss R. A. Weiss who planned, programmed, ran, and checked
the IBM computations of the tables and to Miss J. D. Goeltz who com-
puted the ten-figure accuracy check points required for the construction
of the tables. He also wishes to acknowledge the support and encourage-
ment given to the project by R. L. Dietzold and P. H. Richardson, and
the continued interest and helpful comments of B. A. Kingsbury.
^ Kingsbury, B. A., private communication.
'Murakami, T., and Corrington, M. S., Relation Between Amplitude and
Phase in Electrical Networks, R.C.A. Review, 9, pp. 602-631, Dec, 1948.
Bell System Technical Papers Not
Published in This Journal
Anderson, P. W./ and Suhl, H/
Instability in the Motion of Ferromagnets at High Microwave Power
Levels, Phys. Rev., Letter to the Editor, 100, pp. 1788-1789, Dec. 15,
1955.
Andrus, J., see Bond, W. L.
I
I Beaciiell, H. C, see Veloric, H. S.
i
I Beck, A. C.,^ and Mandeville, G. D.^
I Microwave Traveling Wave Tube Millimicrosecond Pulse Generators,
I I.R.E. Trans., MTT-3, pp. 48-51, Dec, 1955.
I
I
j Benedict, T. S.^
Single-Crystal Automatic Diffractometer — Part II, Acta Cryst., 8,
pp. 747-752, Dec. 10, 1955.
Bennett, W. R.^
Application of the Fourier Integral in Circuit Theory and Circuit
Problems, I.R.E. Trans., CT-2, 3, pp. 237-243, Sept., 1955.
Biondi, F. J.'
Corrosion-Proofing Electronic Parts Against Ozone, Ceramic Age, 66,
p. 39, Oct., 1955.
Bond, W. L.^
!
Single-Crystal Automatic Diffractometer — ^Part I, Acta Cryst., 8,
pp. 741-746, Dec. 10, 1955.
' Bell Telephone Laboratories, Inc.
751
752 the bell system technical journal, may 1956
Bond, W. L.,' and Andrus, J/
Photographs of the Stress Field Around Edge Dislocations, Phys.
Rev., Letter to the Editor, 101, p. 1211, Feb. 1, 1950.
Boyle, W. S., See Gernier, L. H.
Boyle, W. S.,^ and Haworth, F. E/
Glow-to-Arc Transitions, Phys. Rev., 101, pp. 935-938, Feb. 1, 1950.
Bozorth, R. M.^
The Physics of Magnetic Materials, Elec. Engg., 75, pp. 134-140,
Feb. 1956.
Bridgers, H. E.^
A Modern Semiconductor — Single Crystal-Germanium, Chem. and
Engg. News, 34, p. 220, Jan., 1956.
BuRRUS, C. A.,^ and Gordy, W.^
Millimeter and Submillimeter Wave Spectroscopy, Phys. Rev., 101,
pp. 599-603, Jan. 15, 1956.
Chynoweth, a. G. I
Dynamic Method for Measuring the Pyroelectric Effect with Special
Reference to Barium Titanate, J. Appl. Phys., 27, ])i). 78 84, Jan.,
1956.
Cutler, C. C.^
Spurious Modulation of Electron Beams, Proc. I.R.E., 44, pp. 61-64,
Jan., 1956.
Davis, H. M., see Wernick, J. H.
Duncan, R. A.,^ and Stone, J. A., Jr.'
a Survey of the Application of Ferrites to Inductor Design, Proc.
I.R.E., 44, pp. 4-13, Jan., 1956.
' Bell Telephone Laboratories, Inc.
^ Duke University.
01
TECHNICAL PAPERS 753
Fehek, G./ Fletcher, R. C./ and Gere, E. A/
Exchange Effects in Spin Resonance of Impurity Atoms in Silicon,
Phys. Rev., Letter to the Editor, 100, pp. 1784-1785, Dec. 15, 1955.
Feldmann, W. L., see Pearson, G. L.
Fkaver, D. R.'
Design Principles for Junction Transistor Audio Power Amplifiers,
l.R.E. Tran.s., AU-3, pp. 183-201, Nov.-Dec, 1955.
Flaschen, S. S.,^ and Van Uitert, L. G.'
New Low Contact Resistance Electrode, J. Appl. Phys., Letter to the
Editor, 27, p. 190, Feb., 195(5.
Fletcher, R. C., see Feher, G.
Fry, T. C.^
Mathematics as a Profession Today in Industry, Am. ]\Iath. Monthly,
63, pp. 71-80, Feb., 1956.
Fuller, C. S., see Reiss, H.
Geballe, T. H., see Hrotowski, H. J.
Gere, E. A., see Feher, G.
Germer, L. H.,^ and Boyle, W. S.^
Short Arcs, Nature, Letter to the Editor, 176, p. 1019, Nov. 26, 1955.
Germer, L. H.,^ and Boyle, W. S.^
Two Distinct Types of Short Arcs, J. Appl. Phys., 27, pp. 32-39, Jan.,
1956.
GlANOLA, U. F.
Photovoltaic Noise in Silicon Broad Area p-n Junctions, .1. Appl.
Phys., 27, pp. 51 53, Jan., 1950.
GoRDY, W., see Burrus, C. A.
1 Bell Telephone Laboratories, Inc.
754 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
Hagelbarger, D. W., see Pfann, W. G.; Shannon, C. E.; and Wil-
liams, H. J.
Hagstrum, H. D/
Electron Ejection from Metals by Positive Ions, Appl. Sci. Res. B5,
Nos. 1-4, pp. 16-17, 1955.
Haworth, F. E., see Boyle, W. S.
Herring, C.,^ and Vogt, E.^
Transport and Deformation Potential Theory for Many-Valley Semi-
conductors with Anisotropic Scattering, Phys. Rev., 101, pp. 944-
961, Feb. 1, 1956.
Herrmann, D. B., see Williams, J. C.
Holden, a. N.,^ Merz, W. J.,^ Remeika, J. P.,' and Matthias, B. T.^
Properties of Guanidine Aluminum Sulfate Hexahydrate and Some of
its Isomorphs, Phys. Rev., 101, pp. 962-967, Feb. 1, 1956.
Horotowski, H. J.,^ Morin, F. J.,^ Geballe, T. H.,^ and Wheatley,
G. H.'
Hall Effect and Conductivity of InSb, Phys. Rev., 100, pp. 1672-1677,
Dec. 15, 1955.
Ingram, S. B.
The Graduate Engineer His Training and Utilization in Industry
Elec. Engg., 75, pp. 167 170, Feb., 1956.
Kaplan, E. L.^
Transformation of Stationary Random Sequences, Mathematicai
Scandinavica, 3, FASCl, pp. 127-149, June, 1955.
Lewis, H. W.^ ;
Superconductivity and Electronic Specific Heat, Phys. Rev., 101, pp.^
939-940, Feb. 1, 1956.
Mandeville, G. D., see Beck, A. C.
1 Bell Telephone Laboratories, Inc.
TECHNICAL PAPERS 755
Matthias, B. T., see Holden, A. N.
Merz, W. J., see Holden, A. N.
Miller, L. E.
Negative Resistance Regions in the Collector Characteristics of the
Point-Contact Transistor, Proc. I.R.E., 44, pp. 65-72, Jan., 195G.
Moll, J. L./ and Ross, I. M.'
The Dependence of Transistor Parameters on the Distribution of
Base Layer Resistivity, rioc. I.R.E., 44, pp. 72-78, Jan., 1950.
Montgomery, H. C, See Pearson, G. L.
iMoRiN, F. J., see Hrotowski, H. J.
MuMFORD, W. W.,^ and Schaferman, R. L/
Data on the Temperature Dependence of X-Band Fluorescent Lamp
Noise Sources, I.R.E. Trans., MTT-3, pp. 12-16, Dec, 1955.
Xesbitt, E. a., see Williams, H. J.
( )lmstead, p. S.^
QC Concepts Useful in OR, lud. Qual. Cent., 12, pp. 11, 14-17, Oct.,
1955.
< )WENS, C. D.'
Stability Characteristics of Molybdenum Permalloy Powder Cores,
Elec. Engg., 74, pp. 252-256, Feb., 1956.
Pearson, G. L.,^ Montgomery, H. C.,^ and Feldmann, W. L.^
Noise in Silicon p-n Junction Photocells, J. Appl. Phys., 27, pp. 91-92,
Jan., 1956.
Pfann, W. G.,^ and Hagelbarger, D. W.^
Electromagnetic Suspension of a Molten Zone, J. Appl. Phys., 27,
pp. 12-17, Jan., 1956.
' Bell Telephone Laboratories, Inc.
756 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 ^
QUINLAN, A. L.^ *
Roll- Welding Precious Metals for Telephone Contacts, Elec. Engg.,
75, pp. 154-157, Feb., 1956.
Reiss, 11.,^ and Fuller, C. S.^
The Influence of Holes and Electrons on the Solubility of Lithium in
Boron-Doped Silicon, .J. of Metals, 12, p. 276, Feb., 1956.
Remeika, J. P., see Holden, A. N.
Ross, I. M., see Moll, J. L.
ScHAFERMAN, R. L., See Mumford, W. W.
SCHAWLOW, A. L.^ I
Structure of the Intermediate State in Superconductors, Phys. Rev.,
101, pp. 573-580, Jan. 15, 1956.
ScHAWLow, A. L.,^ and Townes, C. H.*
Effect on X-Ray Fine Structure of Deviations from a Coulomb Field
near the Nucleus, Phys. Rev., 100, pp. 1273-1280, Dec. 1, 1955.
Shannon, C. E.,^ and Hagelbarger, D. W.^
Concavity of Resistance Functions, J. Appl. Phys., 27, pp. 42-43, j
Jan, 1956.
SiMKiNS, Q. W.,^ and Wogelsong, J. H.^
Transistor Amplifiers for Use in a Digital Computer, Proc. I.R.E., 44,
pp. 43-54, Jan., 195().
Snoke, L. R.^
Specific Studies on the Soil-Block Procedure for Bioassay of Wood
Preservatives, Appl. Mierubiology, 4, pp. 21-31, Jan., 1956.
i
SOUTHWORTH, G. C.^
Early History of Radio Astronomy, Sei. Mo., 82, pp. 55-66, Feb., 1956. |j
^ Bell Telephone Laboratories, Inc.
■'' Western Electric Company.
•* Columbia University.
h
TECHNICAL PAPERS 757
Stone, H. A., see Duncan, R. A.
SuHL, H., see Anderson, P. W.
Thomas, E. E/
Tin Whisker Studies Observation of some Hollow Whiskers and
Some Sharply Irregular External Forms, Letter to the Editor, Acta
Met., 4, p. 94, Jan., 1956.
TowNES, C. H., see Schawlow, A. L.
TOWNSEND, M. A.^
A Hollow Cathode Glow Discharge with Negative Resistance, Appl.
Sci. Research, Sec. B, 5, pp. 75-78, 1955.
\'aldes, L. B.^
Frequency Response of Bipolar Transistors with Drift Fields, Proc.
I.R.E., 44, pp. 178-184, Feb., 1956.
\'an Uitert, L. G., see Flaschen, S. S.
\'eloric, H. S.,^ and Beachell, H. C.
Absorption Isotherms, Isobars and Isoteres of Diborane on Palladium
on Charcoal and Boron Nitride, J. Phys. Chem., 60, p. 102, Jan., 1956.
\'oGELSONG, J. H., see Simkins, Q. W.
\ ogt, E., see Herring, C.
W'eibel, E. S.'
Strains and the Energy in Thin Elastic Shells of Arbitrary Shape for
Arbitrary Deformation, Zeitchrift f. Mathematik and Physik, 6, pp.
153-189, May 25, 1955.
W'krnick, J. H.,^ and Davis, H. M.''
Preparation and Inspection of High-Purity Copper Single Crystals,
J. Appl. Pliys., 27, pp. 144-153, Feb., 1956.
' Bell Telephone Laboratories, Inc.
^ University of Delaware.
^ Penn State University.
758
THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
Wheatley, G. H., see Hrotowski, H. J.
Williams, H. J.,' Heidenreich, R. D.,^ and Nesbitt, E. A.^
Mechanism by which Cobalt Ferrite Heat Treats in a Magnetic Field,!:
J. Appl. Phys., 27, pp. 85-89, Jan., 1956.
Williams, J. C.,^ and Herrmann, D. B.
Surface Resistivity of Non-Porous Ceramic and Organic Insulating'
Materials at High Humidity with Observations of Associated Silver
Migration, I.R.E. Trans., PGRQC-6, pp. 11-20, Feb., 1956.
Wood, Mrs. E. A.'
A Heated Sample-Holder for X-Ray Diffractometer Work, Rev. Sci.j
Instr., 27, p. 60, Jan., 1956.
^ Bell Telephone Laboratories, Inc.
decent Monographs of Bell System Technical
Papers Not Published in This Journal*
Anderson, P. W., and Hasegawa, H.
Considerations on Double Exchange, Monograph 2532.
Baker, W. O., see Winslow, F. H.
Barstow, J. M.
The ABC's of Color Television, Monograph 2529.
Bemski, G.
Lifetime of Electrons in p-type Silicon, Monograph 2534.
Bennett, W. R.
Application of the Fourier Integral in Circuit Theory, Monograph 2533.
Brattain, W. H., see Pearson, G. L.
Brown, W. L.
Surface Potential and Surface Charge Distribution from Semicon-
ductor Field Effect Measurements, Monograph 2501.
Bullington, K.
Characteristics of Beyond-the-Horizon Radio Transmission, Mono-
graph 2494.
Bullington, K., Inkster, W. J., and Durkee, A. L.
Propagation Tests at 505 mc and 4,090 mc on Beyond-Horizon Paths,
Monograph 2503.
* Copies of these monographs may be obtained on request to the Publication
Department, Bell Telephone Laboratories, Inc., 463 West Street, New York 14.
N. Y. The numbers of the monographs should be given in all requests.
759
760 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
DuRKEE, A. L., see Biillington, K.
Freynik, H. S., see Gohn, G. R.
(Jkllkh, S., and Thurmond, (■. D. j
On the Question of the Existence of a Crystalline SiO, Monograph
2530.
Gohn, G. R., Guerard, J. P., and Freynik, H. S.
The Mechnical Properties of Wrought Phosphor Bronze Alloys,
Monograph 2531.
I
Guerard, J. P., see Gohn, G. R. ^'
Hasegawa, H., see Anderson, P. W.
Haynes, J. R., see Hornbeck, J. A.
Hornbeck, J. A., and Haynes, J. R. -
Trapping of Minority Carriers in Silicon, Monograph 2368.
Inkster, W. j., see Bullington, K.
Lewis, H. W.
Search for the Hall Effect in a Superconductor. II. Theory, Mono-
graph 2523.
LiNviLL, J. G., and Mattson, R. H.
Junction Transistor Blocking Oscillators, Monograph 2487.
Logan, R. A.
Precipitation of Copper in Germanium, Monograph 2524.
Logan, R. A., and Schwartz, M.
Restoration of Resistivity and Lifetime in Heat-Treated Germanium
Monograph 2525.
Mattson, R. H., see Linvill, J. G.
MONOGRAPHS 761
Mays, J. M., see Shulman, R. G.
McCall, D. W., see Shulman, R. (i.
Moll, J. L.
Junction Transistor Electronics, Monograph 2537.
Pearson, G. L., and Brattain, W. H.
History of Semiconductor Research, Monograph 2538.
Sandsmark, p. I.
ElHpticity on Dominant-Mode Axial Ratio in Nominally Circiilar
Waveguides, Monograph 2539.
Schwartz, M., see Logan, R. A.
Shulman, R. G., Mays, J. M., and McCall, D. W.
Nuclear Magnetic Resonance in Semiconductors. I, Monograph 2528.
Thurmond, C. D., see Geller, S.
Van Uitert, L. G.
Low Magnetic Saturation Ferrites for Microwave Applications, Mono-
graph 2504.
\ax Uitert, L. G.
Dc Resistivity in the Nickel and Nickel Zinc Ferrite System, Mono-
graph 2540.
:Weible, E. S.
Vowel Synthesis by Means of Resonant Circuits, Monograph 2541.
WiNSLow, F. IL, Baker, W. 0., and Yager, W. A.
Odd Electrons in Polymer Molecules, Monograph 2486,
Vager, W. a., see Winslow, F. H,
Contributors to This Issue
Donald C. Bennett, B.S. 1949 and M.S. 1951, Rensselaer Poly-
technic Institute; Battelle Memorial Institute, 1951-1952; Bell Tele-
phone Laboratories, 1952-. Mr. Bennett has been engaged in the de-
velopment of processes for producing single crystals suitable for use
in transistors. He is a member of the American Institute of Mining and
Metallurgical Engineers.
F. G. BuHRENDORF, B.S.M.E. and M.E., Cooper Union Inst. Tech.
1925. Bell Telephone Laboratories 1925-. Mr. Buhrendorf's early Labo-
ratories work included the design of switchboard apparatus and sound
recording and reproducing equipment ; among the latter were the Mirro-
phone and the stereophonic equipment demonstrated at the New York
World's Fair. During World War II he was concerned with the design
of mechanical components of a number of radar systems, particularly
antenna drives and range units. After the war he resumed his work on
high-quality sound reproduction and more recently has devoted his
efforts to the design of magnetic drum units for digital data storage and
special machinery for the purification and production of single-crystal
semiconductors. He is a New York State Professional Engineer.
Calvin S. Fuller, B.S. 1926 and Ph.D. 1929, University of Chicago.
Bell Telephone Laboratories, 1930-. His early work was on organic in-
sulating material, after which he made studies of plastics and synthetic
rubber including investigations of the molecular structure of polymers
and the development of plastics and rubbers. Since 1948 Dr. Fuller has
concentrated on semiconductor research and the development of semi-
conductor devices. His work led to a techniciue of diffusing impurities -.
into the surface of a silicon wafer, a preparation basic to the Bell Solar (j
Battery and other silicon devices. He is a member of the A.C.S., an
associate member of the A.P.S. and a member of the A.A.A.S.
H. A. Henning, B.S. in ElcctrocluMuical Engineering, Pennsylvania
State College 1926; Columbia University 1930-33. Bell Telephone
762
CONTRIBUTORS TO THIS ISSUE 763
Laboratories, 1926-. Mr. Henning's early Laboratories work was con-
nected with the development of high-quality sound recording and re-
producing equipment and techniques. During this interval he developed
the 9A disc phonograph reproducer. Other pre-war experience included
development of telephone voice recorders, noise reduction studies of the
dynamics of teletype equipment, and design of coin collector slug rejec-
tors and coin disposal relays. During World War II he was concerned
with improvements to the sound power telephone, and later with develop-
ment of specialized magnetic sound recording- reproducing systems.
After the war he resumed his work on high quality sound recording
equipment and supervised the design of the 2A lateral disc feedback
recorder. More recently he has been concerned with the principles and
design of magnetic drum digital data storage and apparatus. He is cur-
rently engaged in investigating the application of square hysteresis
loop magnetic cores to digital computer systems.
David, A. Kleinman, S.B. in Chemical Engineering, 1946, S.M. in
Mathematics, 1947, Massachusetts Institute of Technology; Ph.D. in
physics, Brown LTniversity, 1952. Dr. Kleinman joined Bell Telephone
Laboratories at Murray Hill in Jul}^ 1953. Since then he has studied
theory of transistor devices and has been engaged in research in the band
■theory of solids in the Solid State Electronics Research Department.
I He is a member of the American Physical Society.
F. J. MoRiN, B.S. and M.S., University of New Hampshire, 1939 and
1940; University of Wisconsin, 1940-1941; Bell Telephone Laboratories,
1041-. During World War II, Mr. Morin was involved in research on
j elemental and oxide semiconductors and the development of thermistor
materials. Since that time he has worked on fundamental investigations
into the mechanism of conduction in silicon, germanium and oxide semi-
-conductors. Mr. Morin is a member of the American Chemical Society
and the American Physical Society.
i
0. J. Murphy, B.S. in Electrical Engineering, University of Texas,
1927; Columbia University, 1928-31. Bell Telephone Laboratories,
1927-. Mr. Murphy's early Laboratories projects included studies of
\'oice-operated switching devices, effects of transmission delay on two-
Way telephone conversation, and voice-frequency signaling systems.
1 )uring World War II he was concerned with design and development of
ihe M-9 electrical gun director and related projects. After the war he
resumed his research work on signaling systems and more recently has
764 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956
concentrated on the design of magnetic drum digital data storage ap-
paratus and circuits. He is a member of the A.I.E.E., a senior member
of the T.R.E., and is a licensed professional engineer.
M. B. Prince, A.B., Temple University, 1947; Ph.D., Massachusetts
Institute of Technology, 1951; Bell Telephone Laboratories, 1951-1956;
National Semiconductor Products, 1956-. Between 1949-51 he was a
research assistant at the Research Laboratory of Electronics at M.LT,
where he was concerned with cryogenic research. At Bell Telephone
Laboratories, Dr. Prince was concerned with the physical properties of
semiconductors and semiconductor devices and was associated with the
development of silicon devices, including the Bell Solar Battery and the
silicon power rectifier. Dr. Prince is a member of the LR.E., the Ameri-
can Physical Society, and Sigma Xi.
Howard Reiss, B.A., New York University, 1943; Ph.D., Columbia
University, 1949; Instructor and Assistant Professor in Chemistry,
Boston University, 1949-51; Head of the Fundamental Research Sec-
tion, Celanese Corporation, 1951-52; Bell Telephone Laboratories,
1952-. Dr. Reiss is engaged in the theoretical chemistry of defects in
semiconductors. He is a member of the American Chemical Society,
the American Physical Society, Sigma Xi and Phi Lamda Upsilon.
Baldwin Sawyer, B.E., Yale University, 1943; D.Sc, Carnegie Insti-
tute of Technology, 1952; Manhattan Project, University of Chicago,
1943-1946; Instructor and Research Associate in Physics, Carnegie In-
stitute of Technology, 1948-1951; Bell Telephone Laboratories, 1951-
Dr. Sawyer's first work at the Laboratories was on the development of
semiconductor devices, especially the silicon alloy junction diode. Since
1953 he has been in charge of a group at Allentown concerned with the
growth, measurement and characterization of germanium and silicon
crystals for use in semiconductor devices. He is a member of the Ameri-
can Physical Society, the American Institute of Mining and Metallurgi-
cal Engineers, Tau Beta Pi, Sigma Xi, and an associate of the LR.E.
Donald E. Thomas, B.S. in E.E., Pennsylvania State University,
1929; M.A., Columbia LTniversity, 1932; Bell Telephone Laboratories,
1929-. Mr. Thomas specialized in the development of repeatei'ed sub-
marine cable systems until 1940 when he became engaged in the de\'elop-
ment of sea and airborne radar. In 1942 he entered military service where
he was active in electronic countermeasures research and development.
CONTRIBUTORS TO THIS ISSUE 765
Following the war he took part in the development and installation of
' the first deep-sea repeatered submarine telephone cable system between
i Key West and Havana. During this period he also served as a civilian
! member of the Department of Defense's Research and Development
Board Panel on Electronic Countermeasures. At present Mr. Thomas is
engaged in characterization and feasibility evaluation of research models
of semiconductor devices. He is a senior member of the I.R.E. and a
member of Tau Beta Pi and Phi Kappa Phi.
rHE BELL SYSTEM
Jechnical journa^
mOTEH TO THE SC I E N T I FlC^^r^ AND ENGINEERING
JPECTS OF ELECTRICAL C OM M U N IC AT Io4<C/>j,
EJ
^(JQ .J
C-UME XXXV JULY 1956 NVMi*R4
The Effect of Surface Treatments on Point-Contact Transistors
J. H. FORSTER AND L. E. MILLER 767
The Design of Tetrode Transistor Amplifiers
J. G. LINVILL AND L. G. SCHIMPF 813
The Nature of Power Saturation in Traveling Wave Tubes
C. C. CUTLER 841
The Field Displacement Isolator s. weisbaum and h. seidel 877
Transmission Loss Due to Resonance of Loosely-Coupled Modes in a
Multi-Mode System a. p. king and e. a. marcatili 899
Measurement of Atmospheric Attentuation at Millimeter Wave-
lengths A. B. CRAWFORD AND D. C, HOGG 907
A New Interpretation of Information Rate j. l, kelly, jr. 917
Automatic Testing of Transmission and Operational Functions
of Intertoll Trunks
H. H. FELDER, a. j. PASCARELLA AND H. F. SHOFFSTALL 927
Intertoll Trunk Net Loss Maintenance Under Operator Distance
and Direct Distance Dialing
H. H. FELDER AND E, N. LITTLE 955
Bell System Technical Papers Not Published in This Journal
973
Recent Bell System Monographs
979
Contributors to This Issue
V
985
COPYRIGHT 1954 AMERICAN TELEPHONE AND TELEGRAPH COMPANY
THE BELL SYSTEM TECHNICAL JOURNAL
ADVISORY BOARD
F. R. KAPPEL, President, Western Electric Company
M. J. KELLY, President, Bell Telephone Laboratories
E. J. McNEELY, Executive Vice President, American
Telephone and Telegraph Company
EDITORIAL COMMITTEE
B. McMillan, Chairman
A. J. BUSCH
A. C. DICKIESON
R. L. DIETZOLD
K. B. GOULD
E. I. GREEN
R. K. HONAMAN
H. R. HUNTLEY
F. R. LACK
J. R. PIERCE
H. V. SCHMIDT
G. N. THAYER
EDITORIAL STAFF
J. D. TEBO, Editor
M.E. STRiEBY, Managing Editor
R. L. SHEPHERD, Production Editor
t
THE BELL SYSTEM TECHNICAL JOURNAL is published six times a year
by the American Telephone and Telegraph Company, 195 Broadway, New York
7, N. Y. Cleo F. Craig, President; S. Whitney Landon, Secretary; John J Scan-
Ion, Treasurer. Subscriptions are accepted at $3.00 per year. Single copies are
75 cents each. The foreign postage is 65 cents per year or 11 cents per copy. Printed ,
in U. S. A. §
THE BELL SYSTEM
TECHNICAL JOURNAL
VOLUME XXXV JULY 1956 number 4
Copyright 1956, American Telephone and Telegraph Company
The Effect of Surface Treatments on
Point-Contact Transistor
Characteristics
By J. H. FORSTER and L. E. MILLER
(Manuscript received January 23, 1956)
A description is given of the electrical properties of formed point con-
facts on germanium. A useful technique for observation of the equipotentials
surrounding such contacts is described. The contrasting properties of donor-
free and donor-doped, contacts, used as diodes or transistor collectors are
emphasized.
It is shown that unformed point contacts {which have electrical properties
largely determined by a surface barrier layer) , may exhibit analogous dif-
ferences. Such changes are produced by chemical treatments calcidated to
influence properties of a soluble germanium oxide film on the surface.
The above information is applied to a study of transistor forming as it
is done in present point-contact transistor processing. It is shown that high
yields from the forming process can be expected on oxidized surfaces, and
(hat chemical ivashes which remove soluble germanium oxide drastically
lower forming yields. These and, other effects are evaluated as sources of
variability in forming yield.
Table of Contents
I
[l . Introduction 768
2. Pro]ierties of Formed Point Contacts 770
I 2.1 Effects of Electrical Forming on Point Contacts 770
1 2.2 Donor-Free and Donor-Doped Contacts 774
767
768 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 195G
2.2.1 Potential Probes 774
2.2.2 Use of the Copper Plating Technique 776
2.3 Under-Formed and Over-Formed Contacts 781
3. Properties of Unformed Point Contacts 783
3.1 Physical Properties of Metal -Semiconductor Contacts 783
3.2 Experimental Procedures 785
3.3 Experimental Results 786
3.3.1 Unformed Transistors on Superoxol-Etched Surfaces 786 '
3.3.2 Unformed Transistors on CP4-Etched Surfaces 789
3.3.3 Diode Characteristics on Electro-Etched Surfaces 789
3.3.4 Output Characteristic Anomalies 789
3.3.5 Floating Potential Measurements 790 '■
3.3.6 Contamination of Collector Points and Surfaces 792
3.4 Discussion of Experimental Results 794
3.4.1 Effects of the Chemical Ti-eatment on the Superoxol-Etched
Surfaces 794
3.4.2 CP4-Etched Surfaces 795 :
4. Relation of Germanium Surface Properties to Transistor Forming 796
4.1 Pilot Production Problems 796
4.2 Experimental Results 797
4.2.1 Pilot Process Forming Yields 797
4.2.2 Relation of Unformed Diode Characteristics to Transistor
"Formability " 801
4.2.3 Controlled Ambient Experiments 804
4.2.4 A Statistical Survey Experiment on Transistor Forming 805
4.2.5 Effect of Contamination Before Etching 806 '
4.3 Conclusions 807 <
5. General Concluding Remarks 808
5.1 Point-Contact Transistors with High Current Gain 809
5.2 Current Multiplication in Unformed Transistors 809 '
5.3 Surface Properties and Transistor Forming 810 ,
1. INTRODUCTION j
The point-contact transistor, on the basis of several years use in the I
field in Bell System applications, has proved itself to be rugged and de- ■
pendable. For certain military applications, a lasting demand exists for
high-speed point-contact transistors. The adaptation of cartridge type
units to a hermetically sealed structure has been completed, with further
benefits to reliability. To date, the point-contact transistor is one of
the few transistors to successfully pass all military specifications for
shock, vibration, and high acceleration. Thus, although there are at
present limitations to the electrical characteristics that can be built
into a point-contact transistor which make it unsuitable for use in some
switching circuits, there are many applications in which this type of
transistor can give consistent and reliable performance. In fact, applica-
tions exist w^herein the specific requirements are uniquely satisfied by
the point-contact transistor.
However, the basic operational principles of this kind of device arc
not as well understood as would be desirable for facilitating develop-
mental studies for manufacture. Although considerable effort has been
I
POINT-CONTACT TRANSISTOR SURFACE EFFECTS 769
expended towards the analysis and understanding of the physical mecha-
nisms of the point-contact transistor since its announcement in 1948, a
complete design theory for these transistors is not available. This lack
probably I'esults partially from a more general interest in the readily
designable junction transistor types, and partially from the relative
complexity of the device itself. Actual!}^ the physical mechanisms which
account for the operation of this device have their counterparts in at
least three basically unique devices: the point diode, the junction tran-
sistor, and the filamentary transistor.
Thus, although the empirical knowledge of point-contact transistor
design and operation is large enough to allow a reasonable degree of
designability, and manufacture of these transistors in large quantities is
possible, there are, from time to time, manufacturing problems which
are often difficult to solve without sound theoretical understanding of
the physical mechanisms which make the device work.
This article is concerned with describing the results of a general study
of the physical properties of a few specific kinds of point contacts. The
kinds of contact studied have been those of specific interest to those
concerned with manufacture and processing of point-contact transis-
tors. This investigation was conducted in parallel with the final develop-
ment for manufacture of the hermetically sealed point-contact transis-
tor. The study of these properties has led to practical solutions of several
problems encountered during manufacture of point-contact transistors,
and has provided experimental data which is of interest in consideration
of the basic physical mechanisms involved in the operation of the point-
contact transistor.
The work to be described, primarily experimental in nature, follows
in Sections 2, 3 and 4. In section 2, the properties of formed, or electri-
cally pulsed point contacts, and their relation to the source of output
characteristic anomalies often responsible for lowering forming yields
in point-contact transistor production is discussed. The properties of
point contacts which have received no electrical forming in the conven-
tional sense are considered in section 3. The electrical properties of these
contacts, used as diodes or transistor collectors, are shown to be de-
I pendent on chemical history of the etched germanium surface. Thus
I "chemical forming" of point contacts is possible. Section 4 deals with
application of these results to forming problems which arise during
manufacture of point-contact transistors. The important relation be-
tween the chemical history of the surface and the forming on that sur-
face is considered.
i
770 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
2. PROPERTIES OF FORMED POINT CONTACTS
2.1 Effects of Electrical Forming on Point Contacts
The simplest form of point-contact transistor collector is a metal to
semiconductor contact which has not been subjected to excessive power
dissipation either in short high energy pulses, or in the form of more
prolonged aging at lower power levels. Such contacts will be referred to
as vuiformed contacts, and their properties will be discussed in detail in
Section 3. Unformed point-contact transistors sometimes exhibit power
gain, but in general they are not suitable for use as active devices be-
cause the gain, although it may be highly variable from unit to unit, is
usually low. The electrical characteristics of such contacts depend on a
metal-semiconductor contact at the semiconductor surface, and control
of these properties requires exacting control of surface preparation, sur-
rounding ambient, and mechanical stability of the point.
In early experiments, Brattain used electrical forming to improve
both the power gain and stability of the transistor. For present purposes,
the process of electrical forming will be defined as the passage of a short
pulse of reverse current through a point contact which produces perma-
nent changes in the electrical properties of the contact. This is usually
accomplished by charging a condenser to several hundred volts, and]
subsequently discharging it through a resistor in series with the transis-
tor collector. Bardeen and Pfann," investigating electrical forming of
phosphor bronze points on etched germanium surfaces, indicate, as a
possible explanation of their data, that the forming pulse changes the
height of the potential barrier at the germanium surface. This would, in
absence of large surface conductivity, increase the reverse current
through the point and increase the efficiency of hole collection by the
point.^ Thus, the formed point may, according to theory, act as a col-
lector with a current multiplication (a) greater than unity. Thermal
and potential probing of an ?i-germanium surface under a formed phos-
phor bronze point indicates, according to Valdes, that an appreciable
volume of germanium is converted to p-type conduction. Thus, the
reverse current through a formed point probably depends on the char-
acteristics of a p-n junction a small distance from the point, rather than
on a potential barrier at the germanium surface.
A characteristic of the point-contact transistor is that the current
gain can be substantially greater than unity. The current gain, a, i^^
usually defined as the current multiplication at constant voltage, that
is:
dl
a =
die
i
(1)1
POINT-CONTACT TRANSISTOR SURFACE EFFECTS 771
where /c and le are the collector and emitter currents. The a can be con-
sidered as the product of three terms, that is:
a = aSy (2)
where 7 and /i represent the injection efficiency and transport factor
respectively for minority carriers. The term a^- is the "intrinsic" current
multiplication of the collector itself. As mentioned above, there are
theoretical reasons to account for an ai as large as (1 -f h), where h is
the ratio tin/y^p of the mobilities of electrons and holes, and thus the
term ai may be roughly as large as 3.1. The average current gain, a,
taken over a large interval of emitter current, is seldom found to be
greater than this value, and is usually about 2.5. However, the small
signal a at low emitter current usually is found to be considerably larger
than 3.1.
Several mechanisms have been proposed to account for this excess
current gain at low emitter bias in formed transistors. The most generally
known of these are the p-n hook hypothesis and the trapping model. '
The experiments to be described in this section will be concerned pri-
marily with the characteristics of formed points as transistor collectors,
and thus with the transport factor /S. The subject of the origin of the
intrinsic «»■ will be discussed further in a later section.
The experiment of Valdes indicates that the properties of a formed
point contact depend on the physical properties of a small region of ger-
manium near the point, produced by impurity diffusion from the point
or imperfections introduced during the formmg pulse. A highly idealized
representation of the physical situation is shown in Fig. 1 . This is a radial
model of a formed point contact on a semi-infinite block of n-germanium
(respectively p) , with a hemispherical p-layer (radius c:^ ro) . The electron
and hole concentrations in the formed layer near the junction are desig-
nated as Up and p. If a reverse bias Vc is applied to the point, a potential
difference F(ri) — F(r2) = Vj results from the resistance of the junction
at ro . For r ^ ro , at distances well outside ?'o , the potential V{r) and
the magnitude of the field E(r) are given by
where / is the total current through the point. For
I Fo - V(n) I « 1 F^ I, V{r2) ^V,-Vj,
772
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
and the junction resistance limits the magnitude of the drift field that
can be set up near the point. For example, if the lifetime t„ of electrons
in the p-layer^ is substantially lower than Tp , that of holes in the ger-
manium bulk, the reverse current density across the junction can be
increased by an increase in Up , and junction resistance lowered.
Pfann reports a substantial mcrease in the reverse current of formed
point contacts with donor concentration of the point wire. The increase
in rip will depend on the distribution of donors in the p-layer after the
forming pulse. A high donor concentration near the collector point may
-V,
(r)
\/
Vc
V^
^(H) f
^^
X)
-V2)
r
1
\
\
\
\
s
r,
1
r^ ~~
1
(b)
Fig. 1 — Formed point contact under reverse bias — schematic representation.
POINT-CONTACT TRANSISTOR SURFACE EFFECTS 773
form an 7i-type inversion layer under the point (p-n hook) which, when
the point is under reverse bias, acts as an electron emitter. Such a situa-
tion might arise as a result of diffusion of impurities from the collector
point at the high temperature reached during the forming pulse. An
acceptor element, such as copper, with a high diffusion coefficient
might penetrate substantially farther into the germanium than donor
elements such as phosphorous or antimony^^ with lower diffusion con-
stants. Thus, the donor concentration near the point might be substan-
tially higher than the acceptor concentration if the solubility of the
acceptor element is low.
On the other hand, an appreciable number of donor atoms may pene-
trate the germanium as far as do the acceptors. Thus, the equilibrium
value of Wp may be increased simply by decreasing the effective concentra-
tion of acceptors in the p-layer. Such a case might arise when a collector
point such as copper is doped with a suitable amount of a donor element
with a large diffusion coefficient and limited solubility.
The observation of regions of melted germanium^ under heavily
formed points gives evidence for a somewhat different interpretation of
the forming process. It has been suggested that forming is essentially
a remelt process. For example, forming of a phosphor-bronze point may
produce a copper-germanium eutectic, allowing the introduction of a
sizeable phosphorus concentration in the remelt region which is main-
tained after freezing. Thus the depth of penetration of the donor ele-
ment depends upon the size of the remelt region, and the penetration of
the acceptor element depends upon its solid state diffusion coefficient.
This mechanism can lead either to the formation of a p-n hook, or at
least to a Iyer of p-germanium with a high equilibrium electron concen-
tration.
Whatever the reason for the decrease in resistance of the collector
barrier, if it is sufficient, the magnitude of E(r) for r > r^ can be increased
by forming to sufficient value to ensure efficient collection of holes and
a transport factor /3 close to unity.
It would then be expected that for a formed donor-free point, such
as the beryllium-copper alloy points often used as unformed emitters,
the formed p-region would have a high acceptor concentration, n^ would
be small, and under reverse bias, the magnitude of V j would be large,
with I /co I , I V{r^ I , and average a small, [solid curve. Fig. 1(b). On
the other hand, a formed phosphor bronze point of the kind conven-
tionally used to make transistor collectors, should exhibit under reverse
bias, a lesser magnitude of V j , with | /eo | , | Vir^) \ , and a as much as
an order of magnitude larger, (dashed line in Fig. 1(b)].
774 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
2.2 Donor-Free and Donor-Doped Contacts
The qualitative picture of the conventional formed contact given
above has been substantially supported by the work of Valdes, who ob-
served a large increase in floating potential near the reverse biased col-
lector after the forming pulse and a substantial p-region in the bulk of
the germanium after forming.
Experiments have been directed to a comparison of the properties as
diodes and collectors, between two kinds of points. Phosphor bronze
points of the type used as transistor collectors, and beryllium copper
points, normally used as emitters, were investigated. Thus a direct com-
parison can be made between donor-doped and donor-free points which
have been given similar forming pulses. The forming pulses were of the
capacitor discharge type, with voltage and RC values similar to those
used in conventional transistor forming. The points used were of the
cantilever variety, and the n-germanium was zone-leveled material in
the 3 to 4 ohm-cm range. Two points were supported in a double-ended
micro-manipulator which allowed freedom of movement in 3 dimensions
for each point.
2.2.1 Potential Probes
Conventionally, point-contact transistors are made on a superoxol-
etched wafer. This etch leaves a rough surface which is unsuitable for
accurate potential probing. Some measurements were made of the float-
ing potentials on this kind of surface, but accurate results were difficult |
to obtain. In a later section it is shown that the kind of etch used in
surface preparation can have profound effects on the degree of forming
obtained. However, it is shown that forming characteristics of an "aged"
CP4-etched surface are quite similar to the superoxol surface. Thus this
kind of surface was used, since its topographical uniformity allows very
reproducible results in the measurement of floating potentials.
Fig. 2 is a comparison of the floating potentials for the two kinds of
transistor points examined. The log-log plot shows the magnitude of the
floating potential, Vp , near the reverse biased collector as a function of
r, the distance of the probe from the collector measured between centers
of the two points. The bars represent the uncertainty in measurement of
the linear distance. Three curves are shown. The lowest Curve I repre-
sents the potential near a Be-Cu point formed with a conventional form-
ing pulse. Curve II is a plot of the potential near a similarly formed phos-
phor bronze point, while Curve III represents data obtained using such
a point more heavily formed. In all cases the magnitude of the floating
potential decreases inversely as the distance from the point, and is given
POINT-CONTACT TRANSISTOR SURFACE EFFECTS
775
2.0
1.0
0.8
0.6
0.5
0.4
0.3
0.2
0.1
0.08
1-
0.06
n
0.05
>
z
0.04
>
1
0.03
0.02
0.01
0.008
0.006
0.005
0.004
0.003
0.002
0.001
-
\
-
III,Ic(0. -'0) =-1.5M
\
\
1
\
i
V
-
\
K^^
V
-
k:
1
\
HJc^Oi "10^ =-1.0 MA ^
>1
S,
\
^^
s.
H
H
^J
■1
^^
S
H
\
-
^
-
I,lc(0, -10) = -0.08MaN
1 — I
-^,
H^
\
\
■%
\
\
1
1
^
1
■0^
O.l
0.2 0.3 0.4 0.6 0.8 1.0 2 3 4 5 6 8 10
r IN MILS
20
Fig. 2 — Comparison of floating potentials near formed points.
by pI/2Trr where p is Avell A\ithiii the range of the measured resistivity
(3-4 ohm-cm).
Thus the effect of adding the donor to the point wire is to increase
the reverse current and increase the floating potential near the point by
an order of magnitude. One would therefore expect an accompanying
776 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
5.0
4.5
4.0
3.5
3.0
<
J 2-5
2.0
1.5
1.0
0.5
0
[
Vc =-10 VOLTS
\
\
\
V
N
II,HF -UNFORMED
'
- J
k
I.HjOs-UNFORMED
Y \ ? \ ^'—
— — « 1
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
CURRENT, le, IN MILLIAMPERES
5.0
Fig. 3 — Comparison of alpha-emitter-current characteristics of formed points. ,' I
increase in the drift field near the point and a corresponding increase in
a. Fig. 3 indicates that such is the case. The small signal a is plotted as
a function of emitter current in Curves I and II. The point spacing in
this case is 2.5 mils. It is interesting to note that the peak at low emitter
currents is present in both cases, in spite of the fact that presence of a
p-n hook is not likely when the Be-Cu point is formed.
It is thus apparent that the forming the Be-Cu point produces a struc-
ture which more closely resembles a p-n junction. The effect of adding
the donor is to reduce the resistance of the junction. Further contrast
between these two kinds of contacts is demonstrated by comparing for-
ward currents through the contacts and their capacities. In Table I, a
summary of all the contrasting properties is given. All values quoted
are representative values.
2.2.2 Use of the Copper Plating Technique
During the investigation of these contact properties, an interesting way
of illustrating their physical properties was developed. This technique,
borrowed from junction transistor technology, can be used to identify
visually the boundary between the formed region and the bulk genua- f^
nium in a metallographic section of a point-contact transistor. It further
appears that modifications of the technique will enable determination of k:
POINT-CONTACT TRANSISTOR SURFACE EFFECTS
777
Table 1
Contact
Formed Be Cu
Formed Phosphor Bronze
/CO —10) ma
-0.01 ma
-1.0 ma
2.8 ma
0.25
0.1
3.0 MMf
- 1.0 ma
T„(6 —5) ma
-14.0 ma
7e(0, +0.5) ma
Peak value of a
0.8
4.5
a (5.0, -10)
Capacity (Fc = -5F)
1.7
< 0.1 jUMf
the equipotentials surrounding a collector or emitter point under bias,
and visualization of current flow patterns in point contact transistors
under bias operating conditions.
Use of this technique in identification of formed transistor properties
is quite simple. A transistor container (including only the completed
header, wafer, and point-contact structure) is filled with araldite plastic,
which is allowed to harden. The collector point is then electrically formed.
The plastic is necessary to ensure that the collector point does not subse-
quently move from the formed area. The can itself is then embedded in a
plastic block, which is lapped down to expose a cross section of the unit.
Fig. 4(a) and (b). Both the collector point and the base electrode are well
masked. Fig. 5. A droplet of CuS04 solution of fairly low concentration
is placed on the germanium, so that it is in physical contact only with
with the germanium and the masking plastic. In order to identify the
formed region, a reverse bias of 20 volts or so is applied between the
collector point and the base contact for a time usually of 0.1 second or
less. Actually, best results have been obtained by applying the reverse
PLASTIC -=r-
PLASTIC BLOCK
(a)
Fig. 4 — Preparation of a transistor for copper plating.
n
8
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
bias in the form of a condenser discharge pulse. Care must be taken
to avoid changes in contact characteristics resulting from the plating
pulse. The deposit of copper does not appear instantly after pulse ap-
phcation, but may require several seconds before becoming visible. At
the instant the deposit becomes visible, the plating solution is washed
ofi-.
Fig. G(a) and 6(b) show the results of the plating operation on a formed
collector point and a formed emitter point. Both pulses were similar to,
though somewhat "heavier" than those usually used to form transistors.
These units were plated under the conditions illustrated in Fig. 5(a).
The floating potential in the vicinity of the reversed bias point can be
measured as a function of the distance, r, from its center, using an aux-
iliary tungsten point. Qualitatively this potential is shown as a function
of the distance, r, in Fig. 5(b). In this case most of the drop in magnitude
of the potential appears within a radius, r, less than 0.002 inches, pro-
vided surface conductivity is small. The conductivity of the plating solu-
tion is kept small to ensure that the potential distribution in the ger-
manium is not altered by presence of the solution. Under these
conditions, it is assumed that, although copper ions in solution are at-
tracted towards the highly negative regions of the germanium, the main
current flow is through the germanium, except for regions of high poten-
tial gradients. In these regions some of the current will be carried by
ions in the solution, by -passing the region. If the formed region bound-
ary is a sharp p-n junction, one would expect a plating pattern as ob-
served in Fig. 6(b) and 6(d), as is observed with the donor-free emitter
point. For the more complicated structure produced by forming the
COLLECTOR POINT
MASKING
FORMED REGION
BOUNDARY
CU SO4 SOLUTION
MASKING
n-Ge
17"
■'-BASE CONTACT
-V(r)
(b)
Fig. 5 — Experimental conditions for copixT ])lating.
POINT-CONTACT TRANSISTOR SURFACE EFFECTS
779
Vr = -20 VOLTS
Vp = -20 VOLTS
0.25% CUSO4 (PULSE TIME =: 10//S) 025"y<, CUSO4 (PULSE TIME = lO/ZS)
Mi LS
Vq = -20 VOLTS
(PULSE TIME = 10/uS 1
Vg = -20 VOLTS
[PULSE TIME = 10/US)
Fig. 6 — CopiJer plated formed layers in point-contact transistors.
collector, the pattern obtained is more difficult to interpret, Fig. 6(a)
and (c). However, in both cases the disturbed areas are roughlj^ compa-
rable in shape and size.
Differences in the forward characteristics of the collector and emitter
points may also be graphically observed by means of the plating tech-
nique. In Figs. 7(a) and 7(b) are sketches of patterns obtained by applj'-
ing forward bias to contacts for plating. In this case a more concentrated
solution is used, and the plating time is longer. In Fig. 7(a) is shown
the pattern obtained when an unformed collector point is biased for-
780
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
ward during the plating pulse. The copper deposits to within the order
of a diffusion length from the emitter point. Fig. 7(b) shows the pattern
obtained by plating the region near a forward biased formed collector.
Here again the copper has deposited over practicallj^ all of the base
wafer surface, except for a much smaller hemispherical region near the
collector point.
By adjustment of the plating time and solution concentration, the
almost radial field in the bulk germanium under a reverse-biased col-
lector point can be detected. Under similar conditions, an emitter point
biased to the same voltage shows a plating pattern similar to that of Fig.
6(b), with little evidence of the radial field. This would be expected
from the potential plots shown in Fig. 2.
These techniques serve merely to illustrate graphically the differences
in the two types of contact. Although both points when formed give
rise to a formed region in the bulk germanium of similar size and shape,
the diode characteristics of the junction under the donor-doped point
are degraded.
The plating technique may also be adjusted to allow sensitivity to the
current flow pattern in a transistor with both points biased to operating
values. The example shown in Fig. 8 demonstrates visually the bulk
nature of the current flow in the point contact transistor. Here the cop-
per plates out on the negative regions of the crystal and is noticeably
absent from the regions of high hole density under the emitter point. In
the region to the left of the collector indicated by the arrow, the plating
is partially obscured by masking. The size of the copper-free region under
the emitter point may be i-educed to substantially zero for the same /,
by increasing the bias applied to the collector.
(a) t^^^,
COLLECTOR POINT (BEFORE FORMING) "^"-S COLLECTOR POINT {AFTER FORMING)
Fig. 7 — The effect of forming and current flow in point-contact collectors.
POINT-CONTACT TRANSISTOR SURFACE EFFECTS
781
2.3 Under-Formed and Over-Formed Contacts
One of the problems encountered in the large-scale manufacture of
point-contact transistors is the variation in the forming yield. Thus,
forming to a specified criterion of transistor performance does not always
result in a uniform product. Although considerable care may be taken to
ensure uniformity of all bulk properties and forming technique, a large
variation may be encountered in the output characteristics of the tran-
sistors. In Section 4, a prime factor in determining the efficiency of form-
ing is shown to be the chemical history of the germanium surface. Un-
controllable variations in surface conditions may therefore often account
for much of the variations in results of a specific forming technique.
Such variations often manifest themselves merely as differences in
degree, but may show up as differences in kind, takmg the form of anoma-
lous output characteristics. These have been classified by L. E. Miller^^
into three qualitatively different phenomena. The first of these, referred
COLLECTOR
PLATING
INHIBITED
IN THIS AREA
BY MASKING
COPPER
PLATED
AREA
VERY HEAVY PLATE
UNDER COLLECTOR
EMITTER
- UNPLATED
AREA UNDER
EMITTER
GERMANIUM
TO BASE
OHMIC
CONTACT
0 5
SCALE IN MILS
UNIT OPERATED AT LOW le; PLATED 0.25'Vo CUSO4, 20 SECONDS
le = 0.5 MA, Vc = -20V, Oi - 0.1
Fig. 8 — Flow geometry for a low alpha point-contact transistor.
782
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
to as the type (1) anomaly, is of interest here since it represents a col-
lector contact whose physical properties are between the extremes listed
in Section 2.2. Miller has shown that the source of this kind of outpvit
characteristic can be identified as the formed area under the collector
point.
Essentially this anomaly consists of an abrupt rise in the current gain
as the collector voltage Vc is increased at constant emitter current. Be-
yond the critical value of Vc , the characteristic of the unit resembles
that of a well formed transistor. One is led to consider that such a con-
tact is under-formed, in the sense that at low Vc , collection of holes is
inadequate. Further support is lent to such a definition by the data of
Miller, which shows a definite increase in the occurrence of anomalous
units with a decrease in the Ico of the contact. Such an increase occurs
regardless of whether the Ico decrease is obtained by decreasing the donor
concentration of the point wire, or by increasing the time constant of
the forming pulse. In Table II are compared collector capacity and Ico
measurements made in units with and without output characteristic
anomalies. The capacity of these anomalous collectors also appears to
range between the two extremes listed in Table I. Thus there is evidence
that these collectors are intermediate between the extremes cited in
Table I in the sense that at low reverse biases the drift field is low, and
the properties of the formed barrier resemble those of a formed donor-
free point.
The results of detailed investigation of the properties of such anoma-
lous characteristics now being conducted will be published at a later
date. The present experimental results indicate that the instability oc-
curs when the extra current to the collector. Ale , reaches a critical value.
In this respect, increasing the transport factor (3, by increasing Vc , or
increasing the emitter current are equivalent. At a roughly critical Ale ,
the transition between a low a and a higher value of a occurs. After the
transition, the unit behaves like a conventional point contact transistor,
with a current multiplication on the order of (1 + &) at higher values of
le . Thus the origin of this kind of anomaly may lie in the lowering of
the formed barrier by the space charge of the holes, a mechanism sug-
gested by Bardeen.
Table II
Idle = 0, Fc = -10 volts)
Typical Transistor
Typical Anomalous Transistor .
] .0 Ilia
0.2 ma
Cede = 0, ^0 = -10 volts)
(I. 1 nix(
0.5 fi/jif
POINT-CONTACT TRANSISTOR SURFACE EFFECTS 783
The other anomalous collector characteristics considered by Miller
have their origin in the relation between the transport factor and the
properties of the emitter at various operating conditions. In view of the
relations existing between the occurrence of these anomalies and the
Ico of the collector contact, there is some justification for classification
of these contacts as "over-formed."
3. PROPERTIES OF UNFORMED POINT CONTACTS
3.1 Physical Properties oj Metal- Semiconductor Contacts
The classical ideas on the nature of the rectifying metal-semiconductor
contact have undergone substantial revision since the consideration by
Bardeen of the importance of surface states and the work on the point
contact transistory by Bardeen and Brattain. According to Bardeen's
model, the nature of the space charge layer at such a contact is to be
considered largely independent of the metal used for contact, and is pri-
maril}^ dependent on the charge residing in localized states at the ger-
manium surface. Thus the rectifying properties of the metal semiconduc-
tor contact in air are expected to be largely independent of the work
function of the contact metal.
The question of the exact nature of the surface charges is not yet read-
ily answerable. Charges may arise which consist of electrons and holes
residing in surface states of the type proposed by Tamm.^' On the other
hand, other surface charges may arise as a result of adsorbed impurity
ions, or from adsorbed atoms or molecules having electrical dipole mo-
ments. Brattain and Bardeen^ have shown that the space charge layer
is dependent on the surrounding ambient and have indicated that charge
may reside on the outer surface of a film (presumably an oxide laj^er)
at the germanium surface as well as in surface states of the type men-
tioned above, which are presumably those responsible for surface re-
combination processes.
Thus, it is the surface charge on the semiconductor, rather than the
nature of the metal, which primarily determines the nature of the po-
tential barrier which exists at a metal semiconductor junction.
A schematic electron energy diagram for the contact between a metal
and an 7i-type semiconductor is shown in Fig. 9. The potential barrier
^0 , and the nature of the space charge layer in the semiconductor are
determined by the surface charge system and the bulk properties of
the semiconductor. In turn, the surface charge system is dependent upon
such factors as the ambient at the germanium surface and the chemical
history of the surface.
784
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
-METAL
n-TYPE SEMICONDUCTOR-
Fig. 9 — Electron energy diagram for a metal -semiconductor contact.
The experiments of Brown^ indicate that the presence of charge on
the surface of p-germanium can alter the space charge in the crystal
near its surface and, in some cases, produces an inversion layer of n-
germanium at the surface. Garrett and Brattain^° have shown that a
change of ambient from sparked oxygen to dry oxygen to wet oxygen
can increase Ico and floating potential on n-p-n junction transistors, and
the process is reversible. Their interpretation is that sparked oxygen
builds up a film, presumably germanium oxide. Oxygen atoms on the
surface, negatively charged, can give rise to a p-type inversion layei on
n-germanium. Moisture apparently counteracts this negative charge,
and humid oxygen can cause an n-type inversion layer on p-germanium,
which can be removed with a dry oxygen ambient.
Thus, the electrical resistance of an unformed metal-germanium con-
tact on an etched germanium surface can be expected to be extremely
sensitive to any chemical treatment which tends to affect the constitu-
tion of the oxide layer present on the surface, regardless of the metal
used for contact in air. Bardeen and Brattain,^ in early transistor ex-
periments, have shown that such is the case. They have used transistor
collector points on germanium surfaces which, after etching, were sub-
jected to an oxidation treatment (heating in air).
In this section are described experiments which seem to indicate that
the reverse resistance of unformed diodes on etched n-germanium sur-
faces can be decreased by chemical surface treatment, and the magnitude
of the floating potential near such contacts is increased to sufficient ex-
tent that the point can serve as a multiplying collector. Average a for
POINT-CONTACT TRANSISTOR SURFACE EFFECTS 785
these points approaches values found in electrically formed collectors.
Subsequent parts of this section will be concerned with description of the
experiments involved and comparison of the electrical characteristics of
these points with those of conventionally formed points.
The effections of electrical forming on donor-doped and donor-free
point contacts have been described in earlier sections. It has been stressed
that the addition of the donor element to the point results in a contact
with degraded diode characteristics, but which serves as an excellent
collector.
The possibility of an analogous situation in an unformed point collec-
tor exists, with the electrical forming of the donor-doped point being
replaced by a suitable chemical treatment of the surface. The experi-
ments described below indicate that such is the case.
3.2 Experimental Procedures
The germanium used in these experiments was zone-leveled material.
The n-germanium was in the 3 to 4 12-cm range. Originally, experiments
were run using slices, about 0.025 in thickness, soldered on flat brass
blocks, with the brass well masked with polystyrene. Germanium dice,
already mounted on standard base-header assemblies used in a hermetic-
seal transistor process pilot line, were also used.
The ground surface of a slice was given a three-minute chemical etch
(CP4 or superoxol), washed in pure water (conductivity <0.1 micromho),
and blown dry in a nitrogen stream. This surface could then be exposed
for several minutes to 24 per cent HF, hot zinc chloride-ammonium chlo-
ride solder flux, or other chemical treatments as the experiment might
require. These solutions were applied to the slice or die in the form of
large droplets, so the solution did not come in contact even with the
masking. Later, in order to make doubly sure that contamination from
the base or base contact was not involved, all experiments were repeated
using a two-inch length of a zone leveled bar with a base contact soldered
on one end, and the other end, freshly ground between treatments, used
as the surface under examination. The etching was done by lowering
one end of the bar about one-half inch into the etch, leaving the contact
end a good distance from the etch. The etched surface could subsequently
be exposed to any desired chemical treatment. After the chemical treat-
ment, the sample surface was again washed in low conductivity water
for several minutes and blown dry with nitrogen.
The sample, after chemical treatment, was placed on a double ended
manipulator base, used to control the position and pressure of two canti-
786 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956 «
'J
lever points on the treated surface. The electrical characteristics of a
beryllium copper point, operating as transistor collector on the treated
surface, could then be investigated. An auxiliary etched tungsten point
doubled as a potential probe and as an emitter. A switching arrangement
allowed oscilloscope presentation of the h-Vc collector family and the
alpha-emitter current sweep, measurement of the emitter floating poten-
tial on a high impedance VTVM, and determination of other transistor
parameters for any desired position of the emitter point.
Phosphor bronze collector points were not used since it was found that,
on certain chemically etched surfaces the mere application of a negative
bias of 15-40 volts for a few seconds sometimes is sufficient to cause elec-
trical forming of the point in the sense that Ico and average a are in-
creased by an appreciable amount.
The beryllium copper points were carefully cleaned to prevent con-
tamination by donor elements. Their cleanHness was then tested by
other methods described in Section 3.3.6.
With this arrangement, most of the electrical properties of a given
manipulator unit could be inspected during the time the unit ''survived."
These electrical measurements were made in room air (R. H. between
20 and 30 per cent), although provision was made for directing a con-
tinuous stream of dry nitrogen at the points and surrounding surface.
3.3 Experimental Results
3.3.1 Unformed Transistors on Superoxol Etched* Surfaces
A striking difference was observed in the electrical characteristics of
unformed collector points on the \'arious n-germanium surfaces ex-
amined. In particular, surprisingly large values of 7c.(0, —10) and
/c(6, —5), (the latter taken as a measure of average a), were encountered
on the superoxol etched surface subsequently "soaked" for about 10
minutes with 24 per cent HF. At these locations the unformed transis-
tor action was quite similar to that observed with a conventional phos-
phor bronze point formed on a freshly etched surface.
These large values were found only in specific locations on the treated
surface, there being a random fluctuation of 7,(0 —10) and /c(6, —5)
with location of the points on the surface. However, no such large values
of these parameters were found (together) on surfaces freshly etched in
superoxol. The a as a function of emitter current for the unformed points
(2.5 mil spacing) on a superoxol etched surface, before (Curve I) and
after (Curve II) HF treatment is shown in Fig. 10. Comparison with
One part 30 por cent H2O2 , one part 48 per cent HF and four parts water.
POINT-CONTACT TRANSISTOR SURFACE EFFECTS
787
4.5
4.0
3.5
3.0
< 2.5
I
Q.
< 2.0
1.5
1.0
0.5
K
Vr =-10 VOLTS
\
\
k
\
>
II,Ph Br -FORMED
M
' —
[
~
<^^
'
I, Be CU- FORMED
> 1 g 1 <
9
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
CURRENT, Ig, IN MILLIAMPERES
4.5
5.0
Fig. 10
collectors.
Comparison of alpha-emitter-current characteristics for unformed
Curve II, Fig. 3, indicates that the «(/£), obtained after the HF treat-
ment, is comparable to that of a phosphor bronze collector formed con-
ventionally on the same etched surface before treatment. (It turns out
that conventional electrical forming on the etched surface after the HF
treatment is more difficult, and in cases as referred to above, where the
a is not initially high, requires an excessive number of pulses to bring
the a to a normal value.)
In Table III are listed the maximum and minimum values of some
transistor parameters found on the same superoxol-etched surface be-
fore and after the HF treatment (point spacing about 2 mils).
It is seen that the effect of the subsequent HF treatment after the
superoxol etch is at least in some locations on the treated surface to in-
crease the /c(0, —10) and the average a, in some cases to values ap-
proaching those encountered in conventionally formed point-contact
transistors. There is also a lowering of the forward current of the un-
formed collector point after the HF treatment. It is not to be implied
from this table that the Ico is always found to be low on fresh superoxol-
etched surfaces. Actually high values of 7c(0, —10) have been occa-
sionally found on surfaces freshly etched in superoxol. However, these
collectors seldom have high values of average a, and it is suspected that
here the higher reverse current is associated with excessive surface
conductivity. Treatment of such a surface with HF always serves to
increase the average a, and decrease the forward emitter current, with
788
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
Table III
Parameter
/c(0, -10) ma. .
/c(6, —5) ma. . ,
7c (0, +0.5) ma.
Peak value of a
a (5.0, -10)....
After 3 Min.
Supero.xol Etch
Max. Value
Observed
-0.16
-7.0
2.8
3.0
0.50
Min. Value
Observed
-0.06
-0.95
2.0
0.15
0.09
After Subsequent 10 Min.
"Soak" in 24% HF
Max. Value
Observed
- 0.98
-13.5
2.3
6.0
2.0
Min. Value
Observed
-0.20
-7.0
1.3
2.0
0.5
no significant changes in the extreme values of IdO, —10) encountered
initially. Some of the unformed units have collector families quite simi-
lar to those of an electrically formed point-contact transistor. However,
the resemblance ends when stability of operation is considered. Wlien
the unformed units are operated in room ambient, hysteresis loops are
occasionally observed, either in the Ic-Vc output characteristic sweep,
or the a-emitter current sweep. This hysteresis can be eliminated by di-
recting a stream of dry nitrogen across the germanium surface in the ,
vicinity of the points. It is not known whether the hj^steresis is thermal
or electrolytic in nature. The operation of these unformed units, even ;
in the absence of hysteresis, is extremely erratic and unstable. Operating ^>
a unit at a high power level will cause loss of a and Ico , and mechanical
shock delivered to the collector point while the unit operates under bias
may cause loss or gain of a and Ico • In cases where Ico (and a) are low
when the collector point is initially set down on the treated surface, an
increase in Ico and a may be brought about by mechanical motion of the
point, (such as "tapping" the manipulator base, or dragging the point
across the surface). In other cases the high a and Ico are found immedi-
ately after the point is set doAvn on the freshly treated surface, without
any such procedure. None of these effects is observed to an appreciable
degree on a freshly etched surface without further treatment.
The effect of zinc chloride-ammonium chloride solder flux on fresh
superoxol-etched surfaces was also investigated. In this case, after
the etch, the surface was immersed in almost boiling solder flux for about
ten minutes. The effect of this surface treatment on the performance of
the unformed transistors was entirely similar to the results quoted in
connection with the HF treatment. The treatment increased the reverse
collector current and average a, and decreased the forward collector
current, on the average. Magnitudes of /c(0, —5) as high as 14 ma were
observed on surfaces treated in this way.
POINT-CONTACT TRANSISTOR SURFACE EFFECTS
789
3.3.2 Unformed Transistors on CPi-Etched Surfaces
With reference to unformed point contact properties, the CP4-etched
surface is not at all similar to the superoxol etched surface. If two beryl-
lium-copper points are put down on a ground surface freshly etched; in
CP4 , and operated as a transistor, high values of 7c(0, — 10) and
/<.(6, —5) are often encountered. However, after an hour or so in room
air, both these parameters decrease and after an overnight exposure to
room air, the properties of the surface with regard to the transistor ac-
tion resemble those of a surface freshly etched in superoxol. At this point,
a treatment in 24 per cent HF will return /c(0, —10) and 7c(6, —5) to
their originally high values. These effects are summarized in Table IV.
3.3.3 Diode Characteristics on Electro-Etched Surfaces
It has been found that the rectification properties of unformed point
diodes may also be changed conveniently by changing the conditions
during an electrolytic etch in KOH solution. These results are summa-
rized in Table V which represents typical variation in reverse current,
Ir , with surface variation attainable by adjusting the current density
and etching time. In each case the measurements represent data taken
on germanium cut from adjacent sections of the same ingot and given
the surface treatment noted in the table. In general the electro-etched
and chemically etched results agree; that is, any treatment which ap-
pears most likely to leave an oxide film (such as the use of a high current
density during electro-etching) will yield a diode with improved rectifica-
tion characteristics.
I 3.3.4 Output Characteristic Anomalies
In the process of examining these chemically treated surfaces, some
i of the superoxol-etched n-germanium surfaces were given additional
Table IV
Value after 3 Min.
CP4 Etch
Value after 16 Hrs.
in Room Air
Value after 10 Min.
in 24% HF
Max. Value
Observed
Min. Value
Observed
Max. Value
Observed
Min. Value
Observed
Max.
Min.
/e (0,-10) ma..
/c(6, —5) ma. .
Peak value of
a (5.0, -10)''^'
-1.7
-13.3
4.5
1.8
-0.30
-11.0
2.5
1.0
-0.10
-7.0
2.0
1.0
-0.04
-2.0
0.75
0.25
-1.0
-17.5
9.0
2.0
-0.06
-8.0
3.0
0.75
790
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 195G
Table V
Etch Treatment in 0.1% KOH
/, (-10 volts)
10 ma for 30 sec
5 ma for 30 sec
2.5 ma for 30 sec
5 ma for 1 min
-0.16 ma
-0.37
-0.55
-0.04
2.5 ma for 1 min
1 . 75 ma for 1 min
-0.18
-0.74
treatments in H2O2 (superoxol strength). In general, no great differences
were observed in the unformed alpha and /c(0, — 10) after the treatment.
However, in isolated cases, unformed units made on etched p-gerraanium
treated in this way exhibit output characteristic anomalies of the type
characterized by Miller as type (1). It was later found that the same
surface treatment can produce a similar result on etched 11-germanium
surfaces, again only in isolated locations on the surface. An output char-
acteristic of this form is shown in Fig. 11. This unformed unit was made
on a superoxol-etched n-germanium surface with a subsequent three-
minute soak in H2O2 . This characteristic was extremely sensitive to
variation in point pressure.
Miller has also referred to output anomalies of types (2) and (3), which
are usually associated with close point spacing in conventional point-
contact transistors. Such types of anomaly have been observed in un-
formed units (with high average alpha) made on HF treated surfaces.
3.3.5 Floating Potential Measurements
In all cases where the /c(0, —10) and average alpha on etched sur-
faces are increased by the HF or solder flux treatment, these increases
are accompanied by an increase in the magnitude of the floating poten-
tial near the reverse-biased collector. In Fig. 12 the magnitude of the
floating potential Vp of a sharp tungsten probe near the reverse-biased
collector is shown as a function of r, the distance of the probe from the
collector (r is approximately the distance between the center of the two
point contacts). The surface used in this experiment was prepared by
chemical polish for three minutes in CP4 and subsequent storing in room
air for sixteen hours. This provided a smooth surface which resembled,
at least with regard to electrical characteristics, a freshly etched super-
oxol surface.
Curve I represents the potential-distance plot for an unformed BeCu
point on the aged superoxol-etched surface. Curve II represents a similar
plot for an unformed BeCu point taken after the surface was given a
ten-minute soak in 24 per cent HF.
POINT-CONTACT TRANSISTOR SURFACE EFFECTS
791
The measured resistivity of the germanium used in this experiment
was 3.3 to 3.6 fl-cm. It can be seen from Curves I and II that increase
in the magnitude of the floating potential near the unformed point on
the etched surface after the HF treatment is, to a rough extent, propor-
tional to the increase in /c(0, — 10) produced by the treatment. Values
of 2irVpr/I taken from lines of slope ( — 1) drawn for best fit through
points on the individual curves give reasonable agreement with the
measured resistivity. For curve I, 27r F^r// = 3.3 ohm-cm, and for
Curve II, 2TrVpr/I = 3.5 ohm-cm.
By comparing Curves I and II of Fig. 2 with Curves I and II of Fig.
12, it can be seen that the effect of treating the surface under the un-
formed point with HF is analogous to adding donor to the formed point
-10
CURRENT, Ic.lN MILLIAMPERES
-7 -6 -5 -4 -3 -2
Fig. 11 ■ — Type (1) collector anomaly observed in unformed unit (n-t,\])e
germanium) .
I
792
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
0.20
0.10
0.08
0.06
0.05
0.04
0.03
O 0.02
>
t
0.010
0.008
0.006
0.005
0.004
0.003
0.002
0.001
^N
-
1 — c
\,
-
\
S^
H, Ic(0,-10) = -0.9M
A
^
1
\
-OH
\
^
fO'
N
'^^
-
\
-
i-K>^
k
I, Ic(0,-10) = -0.07MA^
i-C
k
N
K
V
>■
1
1
1
1
I
0.1
0.2
0.3 0.4
0.6 0.8
1.0
r
2
IN MILS
4 5 6
8 10
20
Fig. 12 — Comparison of floating potentials for unformed point-contact col-
lectors.
on the etched surface. It seems reasonable to ascribe the increased nega-
tive floating potential after the HF treatment to an increase in current
density through the surface under the point, rather than to any increase
in surface conductivity. It is worth noting that on superoxol-etched sur-
faces, the negative floating potential near an unformed collector point
can often be increased by an order of magnitude by blowing a stream
of dry nitrogen near the point. This effect may possibly be a result of
excess surface conductivity, but in these cases is not accompanied by any
appreciable changes in IdO, — 10) or average alpha.
3.3.6 Contamination of Collector Points and Surfaces
Past experience Avith use of point-contacts as transistor collectors indi-
cates that experiments may often be confused or confounded by unsus-
POINT-CONTACT TRANSISTOR SURFACE EFFECTS 793
pected contamination of the points used. For this reason, particular
attention was given to chemical processing of the beryllium copper points
used in the preceding experiments. These points were chemically cleaned
to remove oxides and unwanted contaminants, and carefully washed
before use. Several lots were processed at different times, and all experi-
ments repeated on the different lots, with no contradictory results.
It is particularly important that the point be free from donor elements,
since it has been observed that that phosphor bronze points or "poi-
soned" beryllium copper points washed with a lithium chloride solution
often exhibit on superoxol etched surfaces a kind of "forming" after the
application of reverse bias. The symptoms of this are a sudden increase
in I CO which take place as the reverse bias is increased above 15-20 volts.
The alpha emitter current sweep shows evidence of excessive noise in
such a case, and it is not until the collector is given a conventional form-
ing pulse that this excessive noise is ehminated, and the unit becomes
stable in operation.
A donorless point can be reasonably identified by the fact that elec-
trical pulsing, heavy or light, will not increase the initially low average
alpha on a superoxol-etched surface to values much above 1 .0, although
J CO may be increased or decreased depending on the type of condenser
discharge used. The beryllium copper points used were tested on super-
oxol-etched surface to make sure they showed no tendency to form
electrically.
If high values of alpha can be found when these points are used as un-
formed collectors on the surfaces treated in HF or solder flux, the ques-
tion arises whether such values may be attributable to presence of a
donor element left on the surface in some mysterious way by the chemi-
cal treatment. If such is the case, the donor might, at high enough re-
\ erse bias, be responsible for an increased alpha in a manner similar to
that observed in connection with the forming in under bias of phosphor
bronze collectors on etched surfaces. Two precautions were taken in this
connection. No reverse bias greater than 10 volts was ever applied in-
tentionally to these collectors during experiments (with exception of the
iunit in Figure 11), and secondly, forming characteristics of both phos-
jphor bronze points and the beryllium copper points on this type of sur-
face were investigated.
It was found that on a superoxol surface treated with HF or the solder
iflux, a phosphor bronze point would form to a high average a, but this
invariably required more forming pulses than on a superoxol etched
[surface. "One-shot" forming is common for a superoxol etched surface,
'whereas after the HF or solder-flux treatment, forming to high average
794
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
Table VI
/c(0, -10).
a(5.0, -10)
Noisv
Point
Beryllium Copper Collector
Phosphor Bronze Collector
Occasion
Before Forming
-0.75
1.5
Yes
After Four
Forming Pulses
-0.50
0
Yes
Before Forming
-0.80
1.5
Yes
After Four
Forming Pulses
-2.5
2.0
No
alpha invariably requires at least three and sometimes many more-,
''shots", although it can be done. This type of formed unit does not
exhibit excessive noise in the a-I^ sweeping gear. However, pulsing of
the beryllium copper points on the latter kind of surface, in similar fash-
ion, invariably results in loss of alpha and never eliminates the exces-
sive noise. Initially, the pulsing decreases the Ico magnitude, but con-
tinued pulsing will eventually cause large increases in this case. These
results provide circumstantial evidence, at least, that the treated sur-
face and the point are operationally free of any donor element and that
the transistor collector barrier involved is at the germanium surface.
For example, in Table VI are given some typical data obtained during
pulsing of points on a superoxol-etched surface after treatment with
near boiling zinc chloride-ammonium chloride solder-flux. A tungsten
emitter was used.*
3.4 Discussion of Experimental Results
.3.4.1 Effects of the Chemical Treatment on the Superoxol-Etched Surfaces
It might be presumed that an inversion layer and a relatively high
surface conductivity is responsible for the increase in negative floating
potential and reverse current observed on the superoxol-etched n-ger-
manium surface after the HF treatment. On the other hand, if it be
assumed that at the etched surface, in room air, an inversion layer ex-
ists which does not introduce excessive surface conductivity, one can
say that the effect of the HF treatment is merely to raise the surface
potential, (i.e., to reduce the barrier height for electrons). This might
* Alpha values are usually lower in any given situation when the conventional
chisel-type beryllium copper emitter point is replaced by an etched tungsten
point.
POINT-CONTACT TRANSISTOR SURFACE EFFECTS 795
account for the increase in reverse current density* and a proportional
increase in the magnitude of the floating potential near the point. In
this case the geometry of current flow across the contact should remain
relatively unchanged as indicated by the floating potential measure-
ments. In this way the effect of the HF treatment is somewhat analogous
to the addition of a small donor concentration near the surface to coun-
teract the inversion layer. Since soluble oxide layers' have been identified
on etched germanium surfaces, it is not unlikely that HF (known to
dissolve germanium oxide)" might act to reduce the effective thickness
of an oxide layer. Such a hypothesis is in agreement with the results of
other experimenters/^ who have attributed a surface inversioji layer
under the point of an n-germanium rectifier to the presence of germa-
nium oxide. They have presumed the oxide is essential to the formation of
a good point contact rectifier. The fact that, for a given ambient, the
surface potential is determined by the oxide layer thickness has been
postulated b}- Ivingston.''*
3.4.2 CPi-Etched Surfaces
Sullivan,"" in connection with an experimental investigation of hu-
midity stability of electrolytically-etched and chemically-etched p-n
grown junction diodes, shows that CP4 chemically-etched surfaces be-
come more stable \\ith respect to humidity variation after humidity
exposure and cycling at room temperature. Referring to the fact that
electron diffraction studies fail to reveal a crystalline oxide film on CP4
chemically-polished surfaces and to the results of Law,"*" which indicate
that oxide films may be formed slowly at room temperature on exposure
1 0 water vapors, he attributes the changes of stability on the CP4 polished
surface to the building up of an oxide film. If such a change can take
place on the CP4 chemically-polished surface on exposure to humid room
air, then the results of Section 3.3 can be understood under the assump-
tion that the action of the HF treatment is to remove the oxide film.
After the chemical polish, values of /c(0, —10) and average alpha for
the unformed units are high, as might be expected if the polishing opera-
tion leaves the germanium surface with no appreciable oxide film. As
the oxide film builds up on continued exposure to room air, both of these
parameters are reduced. The subsecjuent application of HF tends to
lestore these parameters to their original ^'alues by removal of some of
this oxide film. Thus, the results of this section are in accord with the
* Evidence for an increase in surface recombination velocity on HF treated
surfaces is given in Section 4.2.3.
796
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
hypothesis discussed in the previous section to account for the effect of
HF on the unformed transistors.
Such evidence, however, is at best only indirect evidence for the build-
up of an oxide layer on prolonged exposure to room air. In experiments
Avith grown p-n junction diodes, the authors have found great variations
in the length of time required for the electrical properties of the diodes
to recover after short wash periods in low conductivity water. Thus the
slow changes mentioned above may at this point result from simply a
longer time required for the surface to "dry out" after the washing treat-
ment. However, a substantial difference in the physical properties of the
oxide layer left by the two etches concerned is still implied. In this con-
nection it is also worth noting that hysteresis effects appear primarily in
unformed units made on HF treated surfaces.
The results of these experiments have important implications in the
technology of point contact transistors. The results of an application of
these results to transistor forming procedures are given in the following
section.
4. RELATION OF GERMANIUM SURFACE PROPERTIES TO TRANSISTOR
FORMING
4.1 Pilot Production Problems
The pilot production and early manufacturing stages of cartridge-
type point-contact transistors has generally been characterized by peri-
ods during which the forming yields have been very high and similar
periods of very low yield. Often these alternate periods occurred during
the use of germanium taken from the same rod-grown or zone-leveled
crystal. Considerable effort has been expended in attempting to corre-
late these variations in yield to variations, from crystal to crystal, or
in different portions of the same crystal, or such bulk properties as re-
sistivity or minority carrier lifetime. Although these properties of ger-
manium do have some effect on device parameters such as average alpha,
reverse emitter current, and Ico , there has not been any positive indica-
tion that variations in yield are attributable to the amount of variation
of bulk properties normally found in the germanium which meets the
specifications of the particular device concerned.
This problem was compounded during the early stages of the develop-
ment of the process for hermetically sealing the point-contact transistor.
It was found that although reasonable yields were obtained in the car-
tridge process, equivalent transistors in the hermetically sealed structure
were made only with greatly reduced yield. Further, although micro-
POINT-CONTACT TRANSISTOR SURFACE EFFECTS 797
manipvilator units could be made with no difficulty, the same material
fabricated into a completed structure showed completely different char-
acteristics. In the course of investigation of this problem, it was ofund
that the nature of the germanium surface treatment and specifically
treatments calculated to produce or react with germanium oxide can
profoundly affect the "formability" of the germanium surface as well
as a number of other transistor parameters in the fabricated units.
It is the purpose of this section to emphasize the importance of con-
sidering the surface properties of germanium in attempting to solve such
specific problems of development encountered in devices of this type.
In particular, the striking variability of transistor forming on etched
germanium surfaces subjected to varying chemical treatments and am-
bients will be described, as well as the effects of such pre-forming treat-
ments on the parameters of the finished units. The experiments discussed
in the previous section indicate how changes in the double layer at the
germanium surface can influence the characteristics of an unformed
point diode. In turn, the experiments below indicate how the character-
istics of the unformed diode are related to the device properties of the
transistor collector produced by forming the diode.
4.2 Experimental Results
4.2.1 Pilot Process Forming Yields
The forming yield of a point-contact transistor is determined by the
\'alues of the acceptance criteria and the allowable limits for each of these.
Often, different criteria as well as different forming techniques are used
j for different transistors, so that direct comparison of results is quite
I
complex. There are, however, certain common requirements placed on
all point-contact transistors:
(a) The unit is formed so that the average alpha is roughly two or
more. The collector current at a relatively high emitter current and low
! collector voltage is usually an approximate measure of this value,
/c(6, —5) for example.
(b) The collector current with no emitter current flowing should be
as low as is commensurate with the first objective.
The other transistor parameters are either directly or indirectly re-
lated to these. The number of pulses required to achieve the minimum
forming objective, therefore, is one direct measure of the formability of
a particular transistor; the average alpha obtained after pulsing is an-
other. However, one must consider both average alpha and Ico , since
\\ hile forming to a given average alpha, the Ico may increase prohibi-
798 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
19
^ 18
O
z
tr 1 7
o
u.
\^ 16
< 1 5
5
z
m
I
"t. 1 3
T
12
tr
U
1 1-
10
A,
micromanipulator/ \
n
^
/\
N
/^
i )
-\
\
l\
r
N
r
\/
\
1
Y
A
U
V header/
k
^
k
A
U
^^
Ly
^^
-\
/;
U1
M
1
V
V'
V
/
KJ
' yX UNITS ?
/
N
J
W
4 6 8 10 12 14 16
GROUP FROM SAME ZONE LEVELED BAR
18
20
Fig. 13 — A pilot production process control chart.
tively. In later sections the authors have adopted the ratio Ic(Q, —5)
/c(0, —20) as a measure of the success of the forming.
The 2N21 transistor is a hermetic seal version of a point -contact
medium-speed switching transistor. During the early stages of the de-
velopment of this device, it became evident that although similar ger-
manium and point wire are used for l^oth structures, the electrical
parameters by which the devices are characterized belong to different
universes. However, if the geometery of the 2N21 unit is duplicated in
a manipulator transistor, the resulting device parameters do resemble
those of the earlier unsealed unit. It is therefore likely that an unknown
variable in the 2N21 process is responsible for the different universes
mentioned above. The effect of such a variable is shown in Fig. 13, which
shows a chart of a continuous process control. Each point represents
the average of foin- different units sampled at the particular point in the
process denoted in the legend. The micromanipulator data represents
measurements taken on wafers which have been processed up to but not
including point wire attachment. The curve denoted ''header" repre-
sents data taken immediately after the point-wire attachment. This is
one additional process step beyond th(^ point at which the manipulator
data was found. It is evident from this curve that a severe degradation
POINT-CONTACT TRANSISTOR SURFACE EFFECTS
799
Table VII
Treatment
None
ZnCl2-NH4Cl Flux
Flux and heat ....
Ave. No. of
Pulses to Form
2
3
7
Average
/c(6, -5)
-13.8 ma
-13.5
-10.4
Average
/c(0, -20)
-1.7 ma
-1.8
-6.0
Fig. of Merit
/c(6, -5)/
IciO, -20)
8.1
7.5
1.7
in the attainable average alpha has oeciirred even though the forming
objective was the same. Finally, the curve denoted "unit" represents
data on the first four completed units out of the same group from which
the manipulator and header samples were taken, A slight decrease in
average alpha is ol^serA^d at this point. However, previous experience
has indicated that this is an expected effect caused by the addition of the
impregnant. This chart suggests that the point soldering operation in
the process is causing a significant degradation in the formability of
transistors passing through this step.*
This process step consists of placing the germanium wafer, which has
already been etched and mounted on the header, in a point alignment
tool. The point spacing and force is adjusted and the points are then
soldered to the header point-wire support. In the early stages of this
process a corrosive zinc chloride-ammonium chloride solder flux was
necessary to obtain efficient soldering. The effect of this solder flux on
the formability of micromanipulator transistors made on such surfaces
is shown in Table VII. These units were formed to the acceptance cri-
terion of Vc(S, —5.5) ^ 2.0 volts. Each figure represents the average
of ten imits treated in the same way.
The value of the use of a figure of merit such as suggested earlier is
illustrated in this table. Since the average alpha (denoted here by
/c(6, —5) is related to the forming objective, one might presumably
keep forming until the average alpha was the same as for an easily formed
transistor. In this case Ico tends to increase. Under these conditions, if
one examined only average alpha, the data might easily be misleading.
From an examination of the figures of merit in Table VII one concludes
that the corrosive flux plus a heating cycle tends to degrade the ger-
manium surface to such an extent that transistors are formed only with
great difficulty.
The finiction of a flux during the soldering process is to remove any
* Curves of this nature have also been obtained by N. P. Burcham in in-
vestigation of soldering flux effects in hermetically sealed point contact transis-
tor processes.
800
TEH BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
Table VIII
Treatment
No. of Pulses
to Form
Average
/c(6, -5)
Average
/c(0, -20)
Figure of Merit
/c(6. -5)/
IciO. -20)
3 min. in normal superoxol
etch
1 min. in 48% HF
2
4
1
— 15.5 ma
-10.2
-17.7
-0.69 ma
-3.2
-1.9
22.4
3.2
1 min. in 30% H2O2
9.3
oxides which are present so that a good solder joint may be made. Since
the oxide on chemically-etched germanium is likely of the soluble form,
one might assume that the results of Table VII imply that the action
of the flux and heat tends to dissolve or remove this layer. Also implied
by the data is that the presence of such an oxide layer is essential to
efficient forming.
The experiments summarized in Table VIII further substantiate this
hypothesis. These data represent manipulator transistors made on the
same germanium wafers which had been treated in succession to a normal
superoxol etch, a treatment in 48 per cent hydrofluoric acid, and a treat-
ment in hydrogen peroxide, superoxol strength. Since the soluble form
of germanium dioxide is known to react with hydrofluoric acid, it is
presumed that the action of the HF is to partially or wholly remove any
oxide left by the etch. The H2O2 tends to restore the original surface
conditions left by the etch. Each figure represents the average of five
transistors formed to the 2N21 acceptance criterion, (Vc(S, —5.5) ^
2.0 volts).
In this case the hydrogen peroxide treated units have an extremely
high average alpha, but the Ico is also higher than for normally etched
units. In terms of the device properties, a unit with a more or less typical
average alpha with a low Ico is more desirable than the one Avith an
extremely high average alpha but accompanying high Ico • It has not
been determined whether the Ico would be lower for the superoxol treated
units if it had been possible to form to the same average alpha as the
normally etched units. This is an important piece of device design in-
formation which is currently under investigation.
It is clear from these experiments that the nature of the germanium
surface, and most probably the nature of the germanium oxide layer on
it, to a large extent, determines the properties of the transistor formed
on this surface. Direct application of this knowledge to the fabrication
process of the hermetically sealed point contact transistor has been
carried out by N. P. Burcham.
POINT-CONTACT TRANSISTOR SURFACE EFFECTS
801
4.2.2 Relation of Unformed Diode Characteristics to Transistor "Forma-
bility"
From the results of the previous sections, it appears that superoxol-
etched germanium surfaces treated with reagents in which germanium
dioxide is soluble provide point contact diode characteristics unsuited
to electrical pulse forming. Part of this difficulty, manifested in the in-
ability to reach a specified value of average a without a prohibitive in-
crease in I CO , probably results from a lower injection efficiency, 7, for
the emitter on such a surface. This seems reasonable in view of the lower
forward and higher reverse currents indicated in Table III produced by
an HF soak. In Section 4.2.3 evidence will be shown that surface recom-
bination is greater on n-type germanium surfaces treated with HF. This
effect can also lead to difficulty in forming to high a without increase
in Ico , since, for the same drift field, one would expect more minority
carriers to die at the surface during their transit to the collector.
On the other hand, there is evidence for believing that the nature of
the forming process itself may be quite different on an HF treated sur-
face. Fig. 14(a) shows the time dependence of the collector voltage dur-
ing a typical condenser discharge forming pulse.
The envelope of the voltage pulse follows roughly an exponential de-
cay of a condenser-resistor series combination. However, inspection
shows that during the discharge time, the resistance of the combination
400
300
_l
o
> 200
z
>
100
V
(a)
v
Ih
r\
y'«^
t, V
y
r
^
r-
—
I— ( tri
..LU
Z liJ
uj Q-
q: <
D
o z
(b)
n /
—
s
A^
^U
l>
~^
S-
50 100 150 200 250 300 350
TIME IN MICROSECONDS
400
450
500
Fig. 14 — Collector current and voltage versus time for a condenser discharge
forming pulse.
802 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
if)
o
>
2
>
300
200
100
V
\
\
\
V
^-
0
.
0 50 100 150 200 250 300 350 400 450 500
TIME IN MICROSECONDS
Fig. 15 — Forming voltage pulse for HF treated surface.
undergoes a succession of breakdown and recovery intervals. In Fig.
l-l(b) is the accompanying plot of current against time. Comparison of
these two plots shows that following the application of the voltage, the
resistance of the contact decreases until a rather sudden more rapid de-
crease in resistance occurs, taking place at time h . In view^ of this time
scale, the first decrease can be attributed to a heating of the contact,
a form of thermal breakdoAvn at the metal-semiconductor surface.^^
Any reason invoked to account for the second more rapid decrease in
resistance must account for the short time (a few /xs) in which this change
occurs. In any event, shortly after the second "breakdown," a quenching
results, with the collector resistance returning to a \'alue nearer to its
original value. This sequence of events is roughly repeated until the
condenser is discharged.
The properties of the contact at nominal reverse voltage and currents
are usually changed as soon as one such condenser discharge pulse has
occurred, and often one such pulse is sufficient to reach the forming ob-
jective. A typical forming pulse obtained under similar conditions to
those for Fig. 14 is shown in Fig. 15, with the exception that the surface
has been treated in HF for a few minutes. On this case it is apparent that
the second, rapid breakdown is entirely absent. The well-defined form-
ing pulse of Fig. 14 is usually obtained on surfaces with good pre-forming
diode characteristics, and results in production of a usable transistor.
From results of the previous sections it is well established that etched
surfaces treated with reagents in which germanium dioxide is soluble
provide point contact diode characteristics unsuited to electrical pulse
forming.
It is often assumed, on the basis of the results of Valdes,^ that forming
effects result from the diffusion of impuiities from the point into the
semiconductor during the forming pulse. Since the high temperature
required for such diffusion results from the power dissipated at the metal
POINT-CONTACT TRANSISTOR SURFACE EFFECTS
803
to semiconductor contact, more efficient forming probably results on
surfaces which display very low initial saturation currents. On surfaces
which produce a poor initial rectifying diode, the local energy of the
forming pulse may be dissipated too far out into the bulk of the semi-
conductor. This situation would result in inefficient forming.
Since the low-voltage diode characteristics and the forming are proba-
l)ly related, one should be able to predict the "foi-mability" of any par-
ticular surface. Fig. 16 shows that this can be done qualitatively. In the
(!,raph each point represents the average of at least five units formed
on electro-etched surfaces to the forming objective, Fc(3, —5.5) ^ 2.0
^'olts. Fig. 16(a) represents the reverse emitter current before forming
plotted on a log scale versus the percentage of units taking more than five
pulses to form. The reverse emitter current rather than the reverse col-
lector current is a desirable preforming parameter to use since this pre-
100
80
Z 60
UJ
o
cr
LU 40
D.
20
(a) PERCENTAGE OF UNITS TAKING MORE
THAN 5 PULSES TO FORM TO Vc(3,-5.5)<2
y
y
/.
^•"
X
•
_
.^
—
•
t
1
dV,
(b)
= IGURE OF MERIT FOR THE SAME
ZA
•
FORMED TRANSISTORS
I
20
"o 16
V •
\
k^
6_
8
•
^
s
N
^
•
«
*
""^•■>
*
4
■■■
•
0
1
1
1
1
0.02 0.04 0.06 0.1 0.2 0.3 0.4 0.6 0.8 1.0
CURRENT, Igl'^OjO) IN MILLIAMPERES (BEFORE FORMING)
Fig. IG — Relation of forming to pre-forming characteristics: electro-etched
surfaces.
804 THE BELL SYSTEM TECHNICAL JOUKNAL, JULY 1956 }
eludes any premature forming which could occur. This curve shows that
a low reverse emitter current (high back impedance) is associated with
easy forming and that a high reverse emitter current is associated with
hard forming. Fig. 16(b) represents data on the same group of units
with /c(6, — 5)//c(0, —20) plotted versus the reverse emitter current on
a log abscissa. It is significant to note that the figure of merit is consist-
ently high for units with low reverse emitter current and low for units
with high reverse emitter currents. It was possible to achieve this wide
range in reverse currents on the same material by adjusting the current
density in the manner summarized by Table V. In each case a high cur-
rent density results in the low reverse currents.
Some other oxidizing agents may be used interchangeably with the
materials just discussed. A dilute nitric acid solution produces a surface
on which excellent diode properties are observed and good forming re-
sults on these surfaces. It has also been found that a treatment in potas-
sium cyanide results in a surface which appears to be well oxidized.
There are, however, some indications that certain chemical treatments
tend, more than others, to passivate the germanium surface to any sub-
sequent treatment.
Although it has been shown that variations in the surface oxide layer
markedly affect the transistor made on that particular surface, varia-
tions in forming yield such as illustrated by the manipulator line in Fig.
13 are still unaccounted for. The etching procedure in the fabrication of
the point contact transistor has always been one of the most carefully
controlled steps. It therefore becomes necessary to examine the process
for some subtle interaction between the germanium surface and the
ambient to which the surface is subjected during processing.
4.2.3 Controlled Ambient Experiments
The experiment summarized by Fig. 17 represents a "dry box" ex-
periment designed to investigate the effect of ambient on the forming
yield. Ten germanium wafers were mounted on hermetic seal headers,
they were electro-etched, and then five treated for one minute in HF.
The wafers were rinsed in deionized water, dried for three minutes in a
stream of nitrogen, and placed in a nitrogen dry box where the relative
humidity was maintained at less than 1 per cent. One micromanipulator
transistor was formed on each wafer immediately and then at subsequent
intervals of one day, always in widely different locations on the wafer.
These manipulations Mere carried out inside the dry box using rubber
gloves so that at no time was the RH greater than 1 per cent. After two
days the box was opened to room air and the experiment continued.
POINT-CONTACT TRANSISTOR SURFACE EFFECTS
805
ETCHED FOR 1 MINUTE IN
IN 0.1% KOH AT 5 MA.
SAME ETCH FOLLOWED
BY 1 MINUTE IN 48% HF
<
5
z
oi
cr
^
DRY Ns"
ROOM
AIR
''V
■~9—
(a)
Ie(+0.5, 0)
BEFORE FORMING
16
if)
_l
D
12
O 8
d:
LJJ
CD
5 4
D
z
D 2
5
z
UJ
5
^
r'
-9"
""V
(b)
NUMBER OF FORMING
PULSES REQUIRED TO
FORM TO Vc(3,-5.5)<2
V
(c)
^
FORMING
^
"^
y^
■— -
■"^
\
C
'~~«.
~^o
•o-
>-— --
>
0.5
1.0
1.5
2.0 2.5 3.0 3.5 4.0 4.5
DAYS AFTER ETCHING
5.0
5.5
6.0
Fig. 17 — Effect of storage ambient on transistor characteristics — electro-
etched surfaces.
Each point on Fig. 17 represents the average of five units on five differ-
ent wafers.
The difference in the electrical properties of the two surfaces in air
already noted in previous sections is observed. In addition an increase
in surface recombination is indicated on the HF treated surface by a
decrease in the turn-off-time measurement (TOT).* Finally, any influence
of ambient on the electrical properties of the two surfaces used is ap-
parently small.
4.2.4 A Statistical Survey Experiment on Transistor Forming
The experiment described here was designed to check some of the
effects noted in earlier sections as well as to investigate possible interac-
tions between the germanium surface and various ambients experienced
during the processing of point contact units. The experimental design
* TOT is a nonparametric measurement indicative of the switching speed when
used in a specific circuit.
806
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1950
Table IX — Experimental Design of Randomized Block
Experiment
Surface Treatments
A
B
C
D
E
F
Ambient Shelf Conditions
Electro
1 min. H2O2
after
Normal
Etch
1 min. H2O2
1 min.
HF after
Normal
Etch
1 min. HF
Normal
Etch 5 ma.
after
after
Superoxol
Etch
for 1 min.
in 0.1%
KOH
Normal Etch
and Shelf in
Ambient
Normal
Shelf in
Ambient
Formed immediately
X
X
X
X
X
X
after treatment
Formed after shelf in
X
X
X
X
X
X
room ambient
Formed after shelf
X
X
X
X
X
X
over drierite
Formed after shelf in
X
X
X
X
X
X
dry No
Formed after shelf at
X
X
X
X
X
X
76.5% RH
Note: Shelf represents storage for 24 hours.
used is a 5 X 6 randomized block experiment with multiple subgroups.^*
Table IX shows the general plan of the experiment. The six columns
represent different etch treatments, and the five rows represent some pos-
sible variations in storage conditions. Each subgroup represents five
transistors, and the experiment represents a total of 150 transistors made
on germanium from the same zone-leveled slice, given 30 different treat-
ments. Although nine measurements were made for each transistor, the
figure of merit appeared to be most significantly dependent on the
treatments.
As expected from the results already quoted, the major variability
was found in units formed on surfaces freshly treated with HF, with
considerable improvement in formability during storage. However,
the looked for influence of storage ambients does not appear when the
column F has been removed from consideration. One concludes that the
variation between treatments is small, and the effect of ambient is even
less than the effect of the treatments. Thus when surface treatment does
not vary to extremes, the effect of storage ambient is relatively minor.
Thus variations found in such experiments as exemplified on the manipu-
lator line in Fig. 13 must be attributed to a still unknown factor.
4.2.5 Effect of Contamination Before Etching
Since etching removes the damaged surface and is usually done with
highly corrosive materials, it seems unlikely that any contamination
POINT-CONTACT TRANSISTOR SURFACE EFFECTS 807
before etching could affect the efficiency of etch. There have, however,
])een some indications that this does occur. Certain chemical treatments
appear to passivate the surface to any subsequent treatment, for ex-
ample, the results in Sections 4.2.3 and 4.2.4. The electro-etched sur-
face followed by an HF treatment does not change rapidly with time in
room air, while the superoxol-etched .'^urface followed by an HF treat-
ment changes quite rapidly. Surfaces which have been etched in CP4
and subseciuently treated in HF appear to be as stable as electro-etched
surfaces. Subsec^uent treatments in superoxol do not appear to result in
significant changes in the surface characteristics. Experiments on un-
ctched germanium wafers indicate that none of the components of CP4
alone will prevent normal etching, but if an unetched Avafer is treated
with a combination of 50 per cent nitric acid plus 48 per cent HF for a
few moments, the surface will be stabilized as to retard the formation of
the normal pyramidal etch pattern when the eurface is etched in super-
oxol etch. Taken together these ol)servations may imply that certain
types of oxide surfaces are more stable than others and perhaps may even
])e passivated to subsequent environmental conditions.
With this background of information it becomes more believable that
chemical treatments before etching could affect the surface of the ger-
manium resulting from the subseciuent etching. It is not unreasonable
to believe that any variation in surface potential resulting from pre-etch
treatment might influence the reaction between the etchant and the
germanium. An experiment was performed using gold-bonded bases to
isolate the contribution of the solder flux normally used in the base-
wafer attachment. Twenty wafers from the same slice were divided into
four subgroups of five. The groups were treated in such a way that any
effects of HF or solder flux soaking before superoxol etching could ])e
detected.
The results of this experiment do indicate that presence of flux before
etching significantly affects the collector currents and turn-off time of
transistors made on such surfaces. Although there was no apparent dif-
ference in forming yield between sub-groups, it is felt that this variation
would show up as a difference in forming yield in a process where the
forming efficiency is decreased somewhat by the impregnant.
4. .3 Conclusions
Treatment of an etched surface with germanium dioxide solvents such
as HF or KOH degrades the surface to such an extent that transistor
forming efficiency is decreased. A similar effect is produced by corrosive
flux and heat. Thus, pre-forming measurements may be used to predict
808 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
the formability of a particular germanium surface. It is shown that poor
diode characteristics are usually associated with poor forming yields.
One convenient way of controlling the diode characteristics to ensure
successful forming is to etch electrolytically. High current density results
in the most desirable surface characteristics. Electro-etched germanium
which has been subsequently treated in hydrofluoric acid shows little
tendency to oxidize either in room air or dry nitrogen ambient, while
superoxol-etched germanium, given the same HF treatment, changes
quite rapidly in room air presumably due to oxidation of surface. Sulli-
van^^ has also observed differences in the stability of electro-etched and
chemically-treated surfaces.
Different surfaces can be prepared chemically which show more than
the amount of variation normally found in pilot and manufacturing
process lines. However, extreme variations in storage ambients have
relatively little significant effects on any of these surfaces. It is therefore
concluded that although certain chemical treatments may affect forming,
the variations in process yields are not attributable to interaction
between the germanium surface and storage ambients.
The results of Sections 4.2.2 and 4.2.3 suggest the possibility of passi-
vation of the germanium surface. An electro-etched surface followed
by an HF treatment exhibits a higher degree of stability to ambient
than does a superoxol-etched surface treated in the same way. Treat-
ment of a lapped germanium surface with two components of CP4
(HF -f HNO3) will inhibit subsequent etching in superoxol.
The possibility that contamination before etching may affect the char-
acteristics of the germanium surface after etching is considered. Experi-
ments show that contamination of the germanium with corrosive zinc
chloride-ammonium chloride flux before etching significantly affects the
rectification properties of the germanium surface obtained after etching.
The surface recombination velocity (in so far as it is determinative of the
turn-off time of the transistor) is also significantly affected. However,
on the basis of the results quoted here, it is not possible to conclude
that such contamination can account for an appreciable amount of the
unassignable variability in forming yields experienced in pilot and manu-
facturing process lines involving soldered base-wafer connections.
5. GENERAL CONCLUDING REMARKS
The experiments which have been described have implications which
are important in both design and processing of point-contact transistors.
These are summarized below:
POINT-CONTACT TEANSISTOR SURFACE EFFECTS 809
5.1 Point-Contact Transistors with High Current Gain
In most switching applications the combination of high current gain
and low reverse current is desirable. The measurements of current gain,
taken together with the potential probe measurements in Section 2.2.1,
indicate that, for the structures used here, the reverse collector current
at operating voltage must be large enough to set up a substantial drift
field before efficient collection of holes can occur. If this condition is not
met, either the unit has low gain at all values of emitter current (un-
formed), or develops a bistability of the kind described in Section 2.3
(partially formed). For a given structure, the drift field can be increased
by increasing resistivity of the germanium at the expense of increased
base resistance. Here thermal stability of the contact also provides a
limit. A more likely expedient, in the case of germanium, is to decrease
the area of the formed collector junction by using sharper points and
modified forming technique. The limits here are produced by reliability
requirements for mechanical stability of the point structure.
5.2 Current Multiplication in Unformed Transistors
Many experiments have reported on junction transistors with high
current gains which are attributable to the p-n hook mechanism. The
high values of current gain observed with conventionally formed point
contact transistors have been attributed to various mechanisms, among
, which is the hypothesis of a p-n hook structure, primarily in the bulk of
the germanium, introduced by the pulsing of the donor-doped point. In
particular, at small emitter currents small signal a-values in conven-
tionally formed collectors may reach values as high as ten, and values of
a as large as 100 are encountered in formed collectors exhibiting anoma-
lous output characteristics. However, the average a over a 6-ma emitter
current range is usually near the value of 3.1 which would be expected
from the mobility ratio of holes and electrons with the Type-A transis-
tor geometry. The increase in reverse current of a formed collector by
t addition of donor to the point wire may result from the production of a
hook structure. However, information is needed concerning the impor-
tance of the hook structure in accounting for the high values of a en-
countered at low emitter currents, or in connection with collector char-
acteristic anomalies in conventionally formed point-contact transistors.
The unformed transistors discussed in this article differ from electri-
cally formed units in that the collector barrier is the one at the metal-
semiconductor surface. It has been found that certain chemical treat-
ments can produce a collector barrier which allows an increased reverse
810 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
current flow and a substantial drift field near the emitter. Some of these
units show an a vahie at all emitter currents quite comparable in magni-
tude to that of conventionally formed collectors, and surface treatment
alone can also introduce in these unformed collector characteristics
anomalies similar to those found in some formed units. It is difficult to
visualize a p-n hook structure arising at the germanium surface as a re-
sult of the chemical treatments discussed. If such a possibility is pre-
cluded, the p-n hook mechanism does not seem necessary to the attain-
ing of high a values at low emitter currents, or an a emitter current
dependence of the kind normally observed in anomaly-free units. To
account for values of a obtained with unformed collectors at low emitter
currents, other mechanisms, such as the suggestion of Shockley, involv-
ing hole trapping in the germanium under the collector point *"' ^ or the
suggestion of Van Roosbroeck, involving conductivity modulation,
might in this case be more suitable.
Further, unformed transistors made by appropriate chemical treat-
ments can duplicate qualitatively the electrical characteristics of con-
ventionally formed units, including alpha-emitter cvuTent dependence
and output characteristic anomalies of types (1), (2) and (3). These
phenomena can thus occur under circumstances where a well-defined
hook structure is improbable.
5.3 Surface Properties and Transistor Fornmig
It has been found that a major factor in determining the forming yield
of point-contact transistors is the chemical history of the surface. Thus
in processing of point-contact transistors, major attention should be
paid to ensuring chemical control of the base wafer surface if the forming
yield is to be kept high. On the other hand, considerable variation may
apparently be tolerated in storage ambients. Of course it has not been
shown that such variations in storage conditions do not have an efl'ect
on subsequent reliability of the product. Processes which permit expos-
ure of surfaces to solder fumes either before or after etching are to be
regarded with suspicion. Monitoring of the reverse emitter diode char-
acteristics should prove useful as a means of securing proper control of
the pre-forming surface.
ACKNOWLEDGEMENT
The authors wish to acknowledge the help of M. S. Jones, who carried
out many of the experiments mentioned here, and N. Carthage who did
the electroetching work. The continued support and encouragement of
N. J. Herbert has been greatly appreciated.
1-
POINT-CONTACT TRANSISTOR SURFACE EFFECTS 811
KEFERENCES
1. J. Bardeen and W. H. Brattain, Physical Principles Involved in Transistor
action, Phvs. Rev. 75, p. 1213, April 15, 1949.
2. J. Bardeen and W. G. Pfann, Effects of Electrical Forming on the Rectifying
Barriers of n- and p-Germanium Transistors, Phys. Rev. 77, p. 401-402,
Feb. 1, 1950.
3. W. Shockley, Electrons and Holes in Semiconductors, D. VanNostrand Com-
pany, New York, N. Y., p. 110.
4. Reference 3, p. 111.
5. L. B. Valdes, Transistor Forming Effects in n-Type Germanium, Proc. I.R.E.
40, p. 446, April, 1952.
6. W. Shocklev, Iheoiies of High Values of Alpha for Collector Contacts on
Geimanium, Phys. Rev. 78, p. 294-295, May 1, 1950.
7. W. R. Sittner, Current Midti] licalion in the Type A Transistor, Proc. I.R.E. ,
40, pp. 448-454, April, 1952.
8. Valdes (Reference 5j reports large concentrations of copper present in the
p-germanium under heavily formed phosphor-bronze points.
9. W. G. Pfann, Significance of Composition of Contact Point in Rectifjing
Junctions on Germanium, Phys. Rev. 81, p. 882, March 1, 1951.
10. C. S. Fuller and J. D. Struthers, Copper as an Acceptor Element in Germa-
nium, Phys. Rev. 87, p. 526, Aug. 1, 1952.
11. C. S. Fuller, Diffusion of Acceptor and Donor Elements into Germanium,
Phys. Rev. 86, p. 136, April 1, 1952.
12. Reference 5, p. 448.
13. Personal communication, H. E. Corey, Jr.
14. L. E. Miller, Negative Re.sistance Regions in the Collector Characteristics of
Point Contact Transistors, Proc. I.R.E., 40, p. 65-72, Jan. 1, 1956.
15. Reference 1, p. 1225.
16. John Bardeen, Surface States and Rectification at a Metal Semiconductor
Contact, Phys. Rev., 71, p. 717-727, May, 15, 1947.
17. I. Tamm, iiber eine Mogliche Art der Elektronenbindung an Kristallober-
flitchen, Physik, Zeits, Sowjetunion, 1, 1932, p. 733.
18. W. H. Brattain and J. Bardeen, Surface Properties of Germanium, B. S. T. J.
32, pp. 1-41, Jan., 1953.
19. W. L. Brown, n-T}'pe Surface Conductivity on p-Tvpe Germanium. Phvs.
Rev. 91, pp. 518-527, Aug. 1, 1953.
20. W. H. Brattain and C. G. B. Garrett, private communication.
21. R. D. Heidenreich, private communication.
22. O. H. Johnson, Germanium and its Inorganic Compounds, Chem. Rev. 51,
pp. 431-469, 1952.
23. M. Kikurchi and T. Onishi, A Thermo-Electrical Study of the Electrical
Forming of Germanium Rectifiers, J. App. Phys., 24, pp. 162-166, Feb., 1953.
24. R. H. Kingston, Water-Vapor Induced n-Type Surface Conductivity on p-
Type Germanium, Phys. Rev., 98, 1766-1775, June 15, 1955.
25. M. V. Sullivan, personal communication.
26. J. T. Law, A Mechanism for Water Induced Excess Reverse Current on Grown
Germanium n-p Junctions, Proc. I. R. E., 42, pp. 1367-1370, Sept., 1954.
27. E. Billig, Effect of Minority Carriers on the Breakdown of Point Contact
^ Rectifiers, Phys. Rev. 87, p. 1060, Sept. 15, 1952.
28. G. W. Snedcor, Statistical Methods, The Iowa State College Press, Ames,
Iowa, 1946.
29. W. VanRoosbroeck, Design of Transistors with Large Current Amplification,
J. App. Phys., 23, p. 1411, Dec, 1952.
The Design of Tetrode Transistor
Amplifiers
By J. G. LINVILL and L. G. SCHIMPF
(Manuscript received March 7, 1956)
The design of tetrode transistor amplifiers encounters problems of the type
that occurs with other transistor uses. Desired frequency characteristics,
limitations of parasitic elements, and other practical considerations impose
constraints on the range of terminations that can he employed. With many
transistors, one can terminate a transistor so that it will oscillate without
external feedback; this oscillation or other exceedingly sensitive terminations
must be avoided.
The two-port parameters of the transistor in any orientation in which it
is to be used constitute the fixed or given information which is the starting
point of the amplifier design. Using this starting point, methods are de-
veloped by which one can select, on simple bases, the kinds of terminations
that will be suitable. To facilitate the design of amplifiers, a set of charts has
been developed from which one can read power gain and input impedance
as functions of the load termination.
Illustrative tetrode amplifiers are described. These include a common base
20-mc video amplifier, a common-emitter 10-mc video amplifier, an IF
amplifier centered at SO mc, and an IF amplifier centered at 70 mc. Pre-
dicted and measured gains are compared.
INTRODUCTION
Junction tetrode transistors^ of the type currently produced for re-
search purposes at Bell Telephone Laboratories are suitable for high-
frequency applications. They are being studied for use in video ampli-
fiers, as IF amplifiers where the center frequency is below 100 mc, for
oscillators up to 1,000 mc and for very fast pulse circuits.
Their application in amplifiers brings up design considerations similar
to those encountered for other transistors but with differences resulting
1 R. L. Wallace, L. G. Schimpf and E. Dickten, A Junction Transistor Tetrode
for High-Frequency Use, Proc. I.R.E., 40, pp. 1,395-1,400, Nov. 1952.
813
814 THE BELL SYSTEM TECHNICAL JOUENAL, JULY 1956
from different parameter values and variation. The analysis presented
in this paper regarding amplifier design was motivated by the study of
t(>trodes, but the results are ecjuall}^ applicable for other types.
The design of an amplifier begins with a characterization of the
transistor which is suital)le for the study of its performance as an am-
plifier. From this characterization, or functional representation, one
CORRESPONDING QUANTITIES
I
n
n
E
h„
z„
yii
911
h,2
Z12
yi2
912
ha,
Z2,
y2,
92,
h22
Z22
y22
922
I,
I,
E,
E,
E,
E,
I,
I,
E2
I2
E2
I2
I2
E2
I2
E2
Es
Es
Is
Is
Zs
Zs
Ys
Ys
Yl
Zl
Yl
Zl
Zl
Zl
yl
Yl
Yo
Zo
Yo
Zo
RELATIONSHIPS BELOW ARE BETWEEN QUANtrjl
IN COLUMN I. CORRESPONDING RELATIONSHIPS]
WRITTEN DIRECTLY FOR CORRESPONDING QUA^^
IN ANY OTHER COLUMN.
(1) E,= I,h„ + E2h,2
(2) l2= I,h2,+E2h22
h,2h2,
(3) Zl= h„ -
(4) Yo
(5) 1,=
Yl + 1^22
h,2h2i
^zz
Zs + h„
h2,EsYL
(h„ + Zs)(h22 + YL)-h,2h2,
Fig. 1 — Two-port parameters with summary of relationships.
THE DESIGN OF TETRODE TRANSISTOR AMPLIFIERS 815
determines the potentialities of amplifiers employing the transistor and
designs a suitable amplifier circuit. This step in^'olves answering two
(luestions: What performance, maximum power gain for instance, is it
possible to obtain? What source and loatl impedances should the tran-
sistor be associated with?
Two-Port Parameters of Transistors
For circuit applications, the two-port parameters are the most con-
venient for characterization of the transistor. These parameters implicitly
but completely characterize the device from the performance standpoint.
Four sets of two-port parameters are illustrated in Fig. 1. Any set can
be calculated from any other set, and the choice of the set to employ is
determined only by convenience in the use of available measuring eciuip-
ment and the preference of the designer. The relationships between
parameters, input and output impedances, voltage and current ratios
are summarized on Fig. 1. The same expressions given there for /i's can
be used for any parameter set so long as one uses the corresponding
quantities applicable to the desired parameter set.
Though the transistor can be operated as an amplifier with the base,
emitter or collector common between the input and output terminal
pairs, the two-port parameters for any of the connections can be used
to calculate the parameters for any other connection.
For determination of the two-port parameters of tetrode transistors,
R. L. Wallace suggested the use of two-terminal impedance measure-
ments with subsec^uent calculation of the two-port parameters of in-
terest from these. The impedances indicated in Fig. 2 have proved
simple to measure at typical operating points with conventional high-
: frecjuency bridges. These impedances have been measured at a set of
frequencies extending to 30 mc. Because of the number of transistors
measured it has been economical to program a digital computer to cal-
culate two-port parameters and other ciuantities of interest from the
measured two-terminal impedances.
THE RELATIONSHIPS OF TRANSISTOR PARAMETERS TO AMPLIFIER PER-
FORMANCE
Any of the sets of two-port parameters implicitly characterize all of
I the linear properties of the transistor for the range of frequencies for
which the parameters ha\'e been measured. As mentioned before, it is
necessary to translate the parameters into answers to the following
questions. How much amplification can the transistor give at a particular
816
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
frequency? What impedance should it be supplied from? What impedance
should it feed? What gain will be obtained using a pair of impedances
different from the optimimi ones? The answering of these and related
(juestions amounts to establishing a convenient means of translating
the parameter values into the ciuantities of interest applying to the
amplifier. Such a convenient translating means for solving these problems
is described in this section.
Earlier explicit solutions to special cases of the problem are well known.
Wallace and PietenpoP have given simple expressions in terms of the
transistor parameters for matching input and output impedances and
the maximum available gain when the transistor has purely real parame-
ters. An implicit solution for optimum source and load impedances for
maximum gain in the complex case has been known for a long time. It
is simply that the transistor be terminated at the input and output by
conjugate matching impedances. The implicit nature of this solution
arises from the fact that the input impedance is a function of the load
impedance, and the output impedance is a function of the source impe-
dance for transistors wdth internal feedback. The solution for optimum
source and load impedance from this approach amounts to the solution
of simultaneous quadratic equations with complex unknoA\nis and be-
comes involved.
c
■)
/
le
■ >
r
-X
"h
J)
h-
v^
V(
Fig. 2 — Two terminal impedance measurements for determination of two-port
parameters.
^ R. L. Wallace and W. J. Pietenpol, Some Circuit Properties of n-p-n Transis-
tors, Proc. I.R.E., 39, pp. 753-67, July, 1951.
THE DESIGN OF TETRODE TRANSISTOR AMPLIFIERS 817
From the approach to the problem taken in this paper, one solves first
for the maximum power gain and subsequently determines the optimum
terminations. It turns out that the solutions leads to explicit relation-
ships for optimum performance and terminations and also leads to
charts from which power gains and input impedance can be read for any
terminations.
In all expressions to be developed, the h parameters are used. Pre-
cisely the same expressions can be obtained for z's, y's, or ^'s provided
that one uses the corresponding quantities in the table of Fig. 1.
The maximum power gain is a quantity of primary interest in tran-
sistors since the transistor ordinarily has a resistive component in its
driving-point impedance. Thus voltage or current amplification is con-
strained by the limited power gain attainable. In some cases, however,
because of the inherent feedback internal to the device, instability can
result simply from proper passive terminations without application of
any additional feedback. Such cases are distinct because of this property.
Transistors exhibiting this possibility are said to be potentially unstable
at the frequency in question.
A quantity of interest presented here and derived later is a particular
power gain defined for /i-parameters as
power out _ Poo _ | h
21
power in Pm 4:hnrh22r — 2ReQinh2i)
(1)
where hnr and h^ir mean the real part of hn and of /122 • ReQinhi^ means
the real part of the product of /ii2 and hn . Unless the amplifier is po-
tentially unstable, the quantity Poo/Pio is M'ithin 3 db of the maximum
available gain for the transistor.
The matter of potential instability of the transistor is of great interest.
Certainly the transistor is potentially unstable if Poo/-Pio is negative.
Otherwise potential instability is indicated by greater than unity values
of the criticalness factor
C = 2^
PiO
h2i
(2)
If the transistor is not potentially unstable the maximum available
gain is Ko(Poo/Pio) where
K, = ^(1 - ^[^'^ (3)
For O^C^ 1,1 ^ Ko ^ 2. A plot of Kg as a function of C is shown
in Fig. 3. The function is seen to be exceedingly flat near Kg = 1 for
818
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
C between zero and 0.6. Thus the value Pm/Pio in the majority of cases
^^•here the transistor is not potentially unstable is a close approximation
to the maximum available gain.
The optimum source and load impedances can be expressed in terms
of the transistor parameters and other quantities given in terms of them
by the following relationships where the transistor is not potentially
unstable.
G
1
irg i — hnhn) = e
je
Zs opt = Zin = hn
hnh
21
CKgG^
Zh'>'>r
Yl opt = —ho-z +
2h
22r
1
CKgG
2
(4)^
(5)
(6)
Though explicit relationships for ideal terminations and for the maxi-
mum power gain which one can achieve with a transistor are of interest,
such terminations limit the band width of the amplifiers. Therefore, it
is important to have convenient means for evaluating power gain and
input impedance for other than ideal terminations in order to realize a
desired bandwidth. A chart which facilitates computation of these quan-
tities is now developed from an analysis which leads to the other results
quoted above.
Kf
2.0
1.5
/
/
1.0
0.5
0
0.2
0.4
0.6
c
0.6
1.0
1.2
Fig. 3 — K^ plotiod ms a f unci ion of C.
^ If —hxih^i \s c + jd, then d = tau~'(r//c) ; G = c' and —hvihn is the conjugate
of —hiohii .
THE DESIGN OF TETRODE TRANSISTOR AMPLIFIERS
819
Power Flow in a Two-Port Device
A convenient point of departure in the analysis of power amplification
iu a transistor or other linear two-port device is the arrangement shown
ill Fig. 4. The two-port is supplied by a unit current at the frequency of
interest and at reference phase at the input terminal pair. The output of
the two-port is connected to a voltage source of the same frequency. The
input-current and output-voltage time functions are
ti
= Re\/2€'"' = ReV2li£'"'
(7)
iiid
= ReV2(a + jb)e^"' = ReV2(L -f jM) (-AA
\2h22r/
jolt
(8)
= Re\^E2e
jat
In (8), L and M are introduced for simplicity in some later relation-
ships.
The whole analysis is essentially a study of power flow in the circuit
shown in Fig. 4 as L and M of (8) are varied. All possible terminations
and excitations can be simulated simply by varying L and M. Under
some conditions the voltage source will absorb power; under others it
w ill supply power to the two-port. Ordinarily the current source supplies
power to the two-port, but for appropriate ranges of L and M if the two-
l)ort is potentially unstable, the transistor may supply power both to the
current source and the voltage source. The problem of evaluating maxi-
mum power gain is simply finding the values of L and M corresponding
lo the greatest ratio of power out to power in. The load impedance to
which this situation corresponds is E-il — l-i . The input impedance for
t his condition is simply £"1//! , and the optimum source impedance is
the complex conjugate of the latter quantity.
Ii=i+jo
I
£2= a+jb =
Fig. 4 — A two-port device .supplied bj^ a current source and feeding into a
voltage source.
820
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
Fig. 5 — Sketch of power output as a function of L and M.
PROJECTION IN L-M PLANE OF GRADIENT
LINE IS G OR Arg-h,2h2,
^21^12
SLOPE OF PLANE ALONG G IS
2h
22r
Fig. 6 — Sketch of power input as a function of L and M.
THE DESIGN OF TETRODE TRANSISTOR AMPLIFIERS 821
The output power can be readily evaluated in terms of L and M.
h = /l/i21 + ^2/i22 (9)
/2 = (1 + mn + (L + jM)h,, tM (10)
I Powerout = Po = fl«(-^2/!) (11)
^ ^^ [-(L -jM)h, ^^ _ , ^ ^j,^ ^^^ (12)
L 2/i22r 4/i22r J
'21 r /t2 , tit2\ ^21
|2
On the basis of (13) the power output plotted as a function of L and
M is a paraboloid as shown in Fig. 5, having the pertinent dimensions
indicated there. Only within the circle centered at L = 1, ikf = 0 and
passing through the origin does one obtain positive power output. The
apex of the paraboloid corresponds to
P, = P,„ = IM (14)
4/i22r
The input power can similarly be evaluated in terms of L and M.
El = hhn + E^hn (15)
= (1 + jO)hn +{L+ jM) t^ hn (16)
Power in = Pi = Re[E,h] (17)
{ — h2^)hn
Pi = Re
hn + (L + jM)
2h
22r
(18)
7 T Ti (^12^2l) , Tirr \h\2h2V f-,rs\
= hur - LRe — T — + MIm -— — (19)
where /m[(/ii2/i2i)/2/i22r] means the imaginary part of the expression in
parenthesis.
On the basis of Eq. 19 the input power plotted as a function of L and
M is simply an inclined plane having the properties indicated on Figure 6.
Since Figures 5 and 6 turn out to be such simple geometrical figures
the problem of finding the point of maximum ratio of Po to P, is very
simple and other interpretations are easy to make. First, a negative value
of Pio{Pi at 1, 0) certainly indicates potential instability for both input
and output terminations receive power from the two-port. Even if the
plane of P.- intersects the L-M plane within the unit circle centered at
822
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 195G
1, 0, then the two-port is potentially unstable since on one side of the
intersection both input and output terminations receive power from the
two-port. The change in Pi from the minimum value found on the unit
circle centered at 1, 0 to Pio divided by Pjo is the criticalness factor, C.
A^alues of C greater than unity indicate potential instability.
The power input at 1, 0 is
-PiO
2hnrh22r — Re{hnh2i)
2h
11r
Using (14) and (20), one obtains
00
/i21
Pio 4/iiir/i22r — 2Re{hi2h2i)
hnfh
12«21
C
2/l2
'2hiirfl22r — Ke{hi2'l21J
= 2
00
PiO
hu
h2i
(20)
(21)
(22)
2h
22r
Now if the plane of power input, Fig. G, is parallel to the L-M plane
and above it, certainly the point of maximum power gain is the apex of
the paraboloid, 1, 0 in Fig. 5. If the plane is incliued but alwaj's above
the unit circle centered at 1, 0 certainly the point of maximum power
gain is downward along the gradient line which lies above the point 1, 0.
This must be so since for any contour of equal power out (a circle of
fixed elevation around the paraboloid) the minimum power input (or
greatest gain) lies along the line of steepest descent from 1, 0 in Fig. 6.
Thus the problem of evaluation of the maximum available gain reduces
to the simple problem of finding the abscissa of Fig. 7 where the ratio of
ordinates of the parabola and straight line is a maximum. The parabola
Pl or Po
PROJECTION IN L-M
PLANE OF GRADIENT
LINE OF PLANE
THROUGH 1,0
Fig. 7 — Section of paraboloid and inclined plane of Figs. 5 and 6.
THE DESIGN OF TETRODE TRANSISTOR AMPLIFIERS
823
and straight line are sections of the paral)oloid and plane through the
gradient line of the plane over 1, 0.
A straightforward analysis indicates that the point in the L-M plane
\\ here the maximum of Po/Pi occurs is at
L + jAI = 1 -
CKgG
(23)
^\liere these quantities are defined as in (2), (3), and (4). The power gain
cit this optimum point is Kg times that obtained at 1, 0. One finds that
1 he maximum gain is only two times Pm/Pio even if C approaches unity
A\ hich corresponds to the marginal case of potential instability.
The analysis just described leads to the maximum values of power
I gain and to the best terminating impedances. For many design problems
1 liese answers are a guide but one may prefer to use other than optimum
' \alues for other compelling reasons. For such a case charts from which
I one can get the pertinent quantities are very helpful.
P^^IGUE lN^DEGRee3
G2+jB2= YL+h22
^22 — i'22n +jh22l
Fig. 8 ■ — Gain and impedance chart.
824
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
-1.0
Pl=Plo(i + cx)
C = 2
Pqo
LO
h„
hs,
■0.8
-0.6
'21
P'lo 4h„rh22r-2Reh,2h2i
-0.4
x=o
■0.2
LO
0.2
0.4
0.6
0.8
ANGLE OF"G"iN L-M PLANE IS: ARG -^^z^z^
Fig. 9(a) — Input power as a function of X.
Development of Transmission and Impedance Charts
The same point of departure employed in the evakiation of optimum
cases leads to a convenient set of charts. Equation 12 shoAvs that a setj
of concentric circles centered at 1, 0 are loci in the L-M plane of constant
power output for a unit current source at the input. It is convenient to
plot these as is done on Figure 8, showing Pq as a fraction of Poo •
h
21
Po
Poo
l-(L-lf- M'
(24)
4/i
22r
Since Yl , the load admittance, is —I2/E2 , using (10) one obtains
-h
= Yl = -A22 +
2h
22r
E2 - ' L+ jM
Now it is clear that if one defines G2 and B2 by
2/l?2r
^2=^2+ JB2 = Yl + h22 =
L + jM
(25)
(26)
THE DESIGN OF TETRODE TRANSISTOR AMPLIFIERS
825
loci of constant real and imaginary parts of Y2 become the mutually
orthogonal circles shown in Fig. 8. Thus the value of L + jM is deter-
mined by the load admittance and two-port parameters.
Contours representing constant input power, with equal increments
of power between successive contours, are always parallel equally-spaced
lines in the L-M plane. However, as may be seen from (19) and Fig. 6
different cases have different directions for the line normal to the con-
tours, (the gradient line) and also different power increments for a given
spacing of equal-power-input contours. It is convenient to define a new
\ariable A^ which is the component along the gradient line of the vector
starting at L = 1, M = 0 and going to L, M. Thus
Pi = P.o(l + CX)
(27)
Equation 27 suggests Fig. 9(a) which shows loci of constant power input
plotted as a function of X. If Fig. 9(a) is shown on a transparent ma-
90
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
80
^
70
^
K
^
' z„-h„=
\^ 4(
\ 30
^
.
V,20
\
V-10
- n
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
h,ah
2"21
2h
22r
^(L.jM)
^n22r
R,+jx,
1.8
Fig. 9(b) — Input impedance as a function of L and M.
826
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
terial, its center (at X = 0 along the gradient line) can be superposed
with the point L = 1, ilf = 0 of Fig. 8. With the gradient line of Fig.
9(a) oriented at the argument of —hnh^i , or S in the L-M plane, one can
easily determine graphically the power gain at any point in the L-M
plane compared to the power gain at 1, 0. With Fig. 9(a) superposed on
Fig. 8 as just described the viewer gets a bird's-eye-impression of tlic
paraboloid of power output and the inclined plane of power input simul-
taneously. With such a bird's-eye view, it is easy to assess possibilities
for power gain with all possible angles of load termination.
The evaluation in input impedance is done through use of (16) from
which is obtained
^ = Z,. = hn + (L + jM) t^^
or
Zin = hn + (L +jM)(e-n
hnh
21
Zhf22r
(28)
(29)
For evaluating the second component of (29), it is convenient to have
a second transparent overlay, Fig. 9(b), consisting of a rectangular grid
to the same scale as the L-M plane. Fig. 8, with coordinates marked as
(Zin — hn) Ri
and
hiihii
2/l22r
hiohn
2/l22r
This overlay is placed over the L-M plane with the
^1
hioh
12fl'21
2ihj22r
axis making the angle d with respect to the L axis. Thus on the rec-
tangular overlay for any point in the L-M plane, one reads
Zin — /ill
hiih
■21
2/?.,.
r.\i;TI('UL.\U DESIGNS OF TETKODE TRANSISTOR AMPLIFIERS
IMie charts and optimum rc^lationships developed in the preceding
section are convenient starting points in the design of amplifiers. They
THE DESIGN OF TETRODE TRANSISTOR AMPLIFIERS 827
do not ordinarily constitute a finished solution, however, since practical
constraints frequently modify the design used. Moreover, all of the
relationships are expressed on a single frequency basis, and many times
the amplifier must operate over a range of frequencies broad enough that
parameters change significantly over the range.
Four amplifier designs are described in this section: a single stage,
common-base, 20-mc ^ddeo amplifier; a common-emitter, 10-mc video
amplifier; an IF amplifier at 30 mc and a 60 to 80-mc IF amplifier.
Parameter measurements made with bridges support the first three
designs.
Parameter values and associated constants of a typical tetrode
transistor are given in Table I. The quantities shown there reveal some
interesting facts about the typical tetrode transistor represented. First,
in the common-base connection the tetrode is potentially unstable at
30 mc but not at the lower fre(|uencies. The common-emitter amplifier
is potentially unstable at 1 and 3 mc. Second, the power gains of common-
emitter and common-base stages are about the same at 30 mc, the com-
mon-emitter connection giving more gain at low frequencies.
The matter of potential instability requires further consideration from
a practical point of view. Potential instability at a frequency neither
implies that a stable amplifier cannot be built at that particular fre-
quency, nor does it imply that one can obtain an unlimited amount of
stable amplification at that frequency. It does mean that by simul-
taneously tuning output and input one can adjust for oscillation. The
region of potential instability corresponds to a region in which the input
resistance may be negative for appropriate loads. Instability is avoided
in the physical amplifier if one supplies the amplifier from a sufficiently
high impedance that the input loop impedance always has a positive
real part. To operate the amplifier Avith such a load that it presents a
negative resistance to the source is attended by the difficulty that the
amplification is more sensitive to changes in the source impedance than
it is when the input resistance is positive. Hence the possible higher gain
with internal positive feedback goes along with a greater sensitivity to
changing termination impedance.
! A Common-Base 20-Mc Video Amplifier-
The data presented in Table 1 gives a ciuite comprehensive picture
of possibilities for amplifier designs. To it must be added a practical
fact. It is difficult to connect the load impedance without adding about
2 jujuf of capacitance. This means that any termination considered must
include about this amount of capacitance. By a theorem regarding
1
828
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
CQ «0
' CO
fe^fe
h 7
y-i O
• rH
^-vO-'-v
.^t^ .
^i-H ^O
0(N •,— ^
o
Oi-H , ■*
Tt< .<Nt^
d
'-l(M"'-5>-H
rO
^•'^l , •<>>
I 00 +
Ti-H •
I 1 ' +
00 -* t^o
• OiO coo O
OOOOO -lOCO
•-IIM 1 COO -Tt^ IC
CO I-H •■"*!•* • O lO
•0-— 1 ^-'Tt<.-i<r> i-H
,-1 -^O ^-"* O "-H CO
o
CO
CO
1
CO
•
o
I-H CO
1
O f
I-H
^
• ^o
o
•'-^ " T-H
^~N y—t
to o .
_o
H
o
• ^^•-"x
O .l-H^-v
O
^l-H -00
,_i
(M-'^Tf.-H
o
C^ ' -r-i
■'^J , ■^•<-s
«
u
iC »Oo
• OOO CIO
o ■ 00 Tfi T-H r^ 00 i-f
H
Oi-H 1 (M t^ • »0 f^
(M,-H -COIN -iM '-I
UJN^ 1 ^— COO CO l>
(M>^C^-~^,-iO>-i <-<
o
eo
CO
1 <s
1 >A
5^
o"3 1
O 1
Eh
•-'So
th (b
!z;
• O I— 1
T-H
<
cop^-v
_C5 _^-^
H
-^ • "^"5
O •cOt>.
S
^
O
Or-< , (N
O
o
i-<N -00 OS
1 + + + !L
0,05 t^
•O .0000 O
O -(N •t^CO'-i O
Q
CI 1—1 1 CD CO • lO <N
Tfi 00 • --I CD • 1 lO
w
■*-^ 1 — 'C^ O'* --I
^ ^Ci-t>.v_-io .-( 1 (N
Eh
<1
CO
o
o
1 •=
CO «0
2co<|r>
t t
CC
• 22'-"
rH rH
CO
^^o .
• •
<
^.dcs"
^co 00
o
• <^ .
o .
Q
VH
OO , 00
^-jT^cooi
C^ c~> • ■«-»
;g
■'^s . ■* .
<;
•-^+co +
1 +'"^+
cc
"Ti-i -t^ C5
1 1 >o
o 1 coo ^
• O .Ot^o o
O • . CO T-H I— 1 I— 1
tf
OS T-i 1 CO '-I • O IQ
CO CO C^ 00 CO -I 00
w
Tt<^— • 1 ^^COO(N 1-H
CO ^ 'I— I^I-Hl— 1 1 CO
PS
g
1 «»
CO "»
<
Sioi,
i=. ^
K
■ ?^'-*
1-H 1—1
,-^o .
• •
^ CD CO
00 ^
\q
• '-I .
d
OO , lO
CO (m' CO CD
1— I-C--V • -c^
^ . CO ,
1— 1
•-^+co +
1 +'^+ %.
W
i_ C5
i-i-H • CO 00
1 1 CI
o 1 -^ OOCO
•O -Ot-o o
o • -r^ooi-H 05
hJ
CI r-( 1 CO ■— 1 • >— < CO
<N (M coco lO -1 "0
P9
Tt<--' 1 ■^eOO'-H r-i
!>. ^^.-H ^— -l-H O 1 CO
<1
t-i
0)
+=
o
(D
HJ
;§
CO
c9
*§
pq
w
o
0 •» s
S ~^ „. -
^<
C3 o ,^ '-'
-e
(M
3 rf C< -1 « S «> r«; (M
S r ^ " cS'CLt:-, 1
o -< •< •*? -< *^ "O '
g "s; -sj -s; rjg Wh <o 1
O
O
1
THE DESIGN OF TETRODE TRANSISTOE AMPLIFIEES
829
passive impedances this puts an upper limit on the level of impedance
presented by the load over a band of frequencies. The greatest possible
constant level of load impedance over 20 mc is
^1 ~C~o.-
2.10-12. 2.10^- 27r
= 7,96012
(30)
Thus number, though not strictly applicable to this case, nonetheless
gives a measure of the sort of value which one can expect. Hence one
observes that for a broad-band video amplifier the load impedance is
certainly going to be considerably less than 1/| /i22 1 which up to 10 mc
is not less than 15,000 ohms. Moreover, the gain, if it is to be uniform,
will certainly be limited by the gain obtainable at 20 mc.
Recognition that the load admittance will be a number of times h^ir ,
\.SfJ.IJ.P
\^z\ ~0. 84-0. 93
Fig. 10 ^ — A rough approximant for the common base video amplifier. The
variation of | /i. 21 | is a function of frequency and not variation between units.
five to ten, means that in Fig. 8 one will be operating near the origin
where (L + jM) is much less than one. Thus Z,-„ in (28) will be approxi-
mately hn • Moreover, by superposing Fig. 9(a) on Fig. 8 at the correct
angle for a frequency of 30 mc {d = —64°) one observes that negative
power input occurs only in the small section of circle cut-off by a chord
running from the 80° to the 155° points on the periphery. This region is
quite a way from the likely point of operation. Thus, this points out that
the low impedance termination precludes instability due to internal
feedback.
If the amplifier is supplied by a 75-ohm source, its output admittance
at 30 mc (Equation 4, Figure 1) is (7.0 + ^20) -10"^ mho. At 10 mc the
output admittance is (4.2 -f- j8.8)-10~ mhos.
These computations reveal that the amplifier in the common-base
connection appears quite like the model shown in Fig. 10. Clearly, the
^ H. W. Bode, Network Analysis and Feedback Amplifier Design, D. Van
Nostrand Co., New York, 1945.
830
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
o COMPUTED GAIN USING
25
APPROXIMANT OF FIG. 10
MEASURFD GAIN WORKING INTO
20
15
2000 OHM RESISTIVE LOAD
MEASURED GAIN INTO THE LOAD
SHOWN ON FIG. 12
— i-W-
•^--
1
10
^
i
5
0
0.01 0.02
0.05 0.1 0.2
FREQUENCY
0.5 1.0 2
IN MEGACYCLES
5 10 20
PER SECOND
50 100
Fig. 11 — Measured and computed gain of a common base video amplifier.
amplification is obtained through the ratio of impedances of load to
source.
Since it is impossible to match the output impedance for maximum
gain due to reasons outlined above, Equation 5 of Fig. 1 can be used to
compute the gain once the load impedance is determined. If we use a
load impedance of 2,000 ohms and a source impedance of 75 ohms, the
difference between the computed gain using the approximate of Fig. 10
and the exact expression (Equation 5 of Fig. 1) amounts to less than 1
db at frequencies up to 10 mc. At 30 mc, the exact expression results in
a computed gain 1.5 db lower than that obtained from the approxima-
tion. A comparison of measured and computed gain for a common base
video amplifier is shown on Fig. 11. Using a resistive load of 2,000 ohms
a gain of 14.5 db is obtained at low freciuencies and the response is down
3 db at 17 mc. To equalize the decreasing | h-n \ with frequency and the
increasing effect of the capacitance, a load consisting of an inductor and
a resistor is used. The circuit is shown on Fig. 12 and it ^^•ill be noted
from the response on Fig. 11, that the low frequency gain is 14.5 dl) with
the 3 db point occurring at about 26 mc.
Common base stages can, of course, be cascaded to advantage only if
impedance transformation is provided in the interstage coupling. Prac-
tical transformers or coupling networks may introduce undesirable band
limitation. In the next section we will consider common-emitter stages
which can be cascaded without impedance transformation.
Common Emitter 10-Mc Video Amplifier
To get a first idea of feasible impedance levels for a common-emitter
video amplifier, one recognized from Table I that the input impedance
!1
THE DESIGN OF TETRODE TRANSISTOR AMPLIFIERS
831
will be within an order of magnitude of /?ii , perhaps in the vicinity of 500
ohms. One sees that in this case if the termination impedances are equal,
Yl ^ h22 . Again, with reference to Fig. 8, the point of operation will be
close to the origin of the L-M plane. Again the input impedance approxi-
mates All . The output admittance is given by
^22 —
hnh
12't21
An + Zs
^-4
(31)
land if Zs = 500 12, Yo is (3.3 + il.0)10~ mhos. A rough approximant to
the common-emitter transistor is shown in Fig. 13. On an order of mag-
initude basis, one expects an iterative power gain of | hn f per stage.
Final choice of elements amounts to computation using the approxi-
mant of Fig. 13 and experimental adjustment.
A video amplifier circuit employing the common emitter connection
is show-n in Fig. 14. If it is assumed that Ri is zero and no compensating
metwork is used in the output circuit, the gain characterictic can be com-
iputed from the approximant of Fig. 13, or if desired, using the exact
expression (Equation (5) of Fig. 1). The two methods agree to within
-4 5 V
Fig. 12 — Circuit of a common base video amplifier. The series coil compen-
sates for the decrease of | hn \ with increasing frequency.
:C
4.5
c
3-9/J.fJ.P
Fig, 13 — An approximant for a common-emitter stage video amplifier when
terminated in a few hundred ohms. The variation of | hii \ and C are a function
of frequency.
832
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
about 1 db at frequencies up to 10 mc. Comparison of the measured and
computed values is shown on Fig. 15 for a load of 500 ohms with no
high-frequency compensation. The low-frequency gain is higher than
for the common base connection but the response is down 3 db at 7 mc.
By using the combination of Ri in parallel with 800 nnf in the emitter
circuit, negative feedback is introduced at low frequencies which results
in the reduction of low frequency gain tending to make the response
more uniform. In addition the L-C network has been added in the output
to compensate for the drop of | /i2i | with increasing frequency and the
increasing effect of the output capacitance.
This results in the response shown as the dotted curve on Fig. 15. The
low-frequency gain has been reduced to 17.5 db, but the response is now
flat to within dzO.3 db up to 13 mc and is 3 db down at 18 mc.
Although the data given on video amplifiers shows the results ob-
tained using one transistor, similar response curves were obtained from
some 6 or 8 units.
An I-F Amplifier Centered at 30 Mc.
The design of an IF amplifier at 30 mc is distinct from the preceding
two cases in that one can use matching techniques over the narrow band.
Reference to Table 1 reveals that the common-base connection pro-,
vides more potential gain at 30 mc than the common emitter connection;
in fact, the common-base connection can be made to oscillate with
certain terminations. The common-base connection is chosen for the
30-mc amplifier.
Vc = 1 0 V
11-13yUH
5-25/U/J-F
^^
■5oon
OUT-
PUT
i
+ 10.5V
i-7.5 V
Fig. 14 — Circuit of a common emitter video amplifier. 7?i in parallel with
800 pLui and the LC network in the output circuit peak the response at 10 to 12
mc.
THE DESIGN OF TETRODE TRANSISTOR AMPLIFIERS
833
35
«o 30
_i
UJ
ffl
O 25
UJ
o
20
<
O
a:
UJ
o
Q
to
Z
<
a:
15
10
o
COMPUTED GAIN, 500 OHM LOAD
NO COMPENSATION
MEASURED GAIN. 500 OHM LOAD
NO COMPENSATION
MEASURED GAIN, 500 OHM LOAD
HIGH FREQUENCY COMPENSATION
SHOWN ON FIG. 14
^,
"n
-^O
\
\
\°
0.01 0.02 0.05 0.1 0.2 0.5 1 2 5 10 20
FREQUENCY IN MEGACYCLES PER SECOND
50 100
Fig. 15 — Computed and measured response of a common emitter amplifier.
In the design of the IF amphfier one is mterested in a moderate range
of frequencies. It will generally be true that the most frequency de-
, pendent parameters are the output and load admittances, since the load
is to be tuned. One can take as a suitable load a parallel combination of
a fixed conductance with a frequency dependent susceptance, the sort
I of termination typical of tuned circuits. Thus on Fig. 8, the locus of
!(r2 + JB2 is one of the G2 = Const, circles.
Superposition of Fig. 9(b) on Fig. 8 with the
huh
urm
2h
22r
axis making an angle of —64° with the L axis reveals that Z,„ — hn
has a negative real part on the upper left edges of all of the contours of
constant G2 . On the G2 = 2/i22r contour, Re{Zin) reaches a minimum of
22.5 ohms. We select a load with Gl = 2/i22r((?2 = 3/i22r) to avoid low
values of input resistance resulting from the internal feedback.
Superposition of Fig. 9(a) on Fig. 8 with the gradient line making an
angle of —64° through the point L, Tlf = 1, 0 reveals that the maximum
value of Pa/ Pi on the G2 = 3/i22r circle is 1.87 Poo/Pio and it occurs for
B2 = — 2/i22r . The input impedance at this point is 36 + jS7 ohms.
For an amplifier one is primarily interested in
Po
Power Available from Source
(which is called transducer gain) rather than Po/Pi , the quantities just
83-4
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
Rs+JXs
to
^Es
Rln +jXLn
■Pi.
Fig. 16 — Typical input circuit.
read from the charts. From the source-load arrangement shown in Fig.
16, one readily computes
I ^-' s I •'^tin
Pi '^ ^
{R. + RinY + (X. + XinY
Power Available from Source
Es
4:Rs
'iihsJttin
(32)
(Rs + RinY + (Xs + XinY
The source impedance selected for the amplifier is 75 — j87 ohms at 30
mc. The 75 ohms is selected to reduce the effect of variations in input [
impedance when it is reduced further by the internal feedback. The 87
ohms of capacitive reactance is selected to tune the input reactance at f
the peak of response. Using Fig. 8 with the overlay of Fig. 9(a) along
with (32) under the assumption that Xs varies insignificantly over the
frequencies involved one obtains Table II. This table shows the varia-
tion of transducer gain as the value of B2 is changed as well as indicating
the value of B2 required for the maximum gain. Thus, if the total output
capacitance is known, the load admittance required to give the maxi-
mum gain at the desired frequency can be computed. As Avill be shown
Table II — Evaluation of Transducer Gain of I-F
Amplifier
Po/Pi
^in
P,/Power avail-
able from
source
Transducer gain
Gain, db
—ShiiT
50
22 + ;48
0.61
30
14.8
-4/»2
64
23 -j- yss
0.66
42
16.2
-ihi
73
28 + i73
0.78
57
17.5
-2/j!2r
75
36 -F i87
0.87
66
18.2
—hi^T
59
67 + ;99
0.98
58
17.6
Ohiir
50
96 + jU
0.98
49
16.9
hiiT
00
120 + j67
0.94
36
15.5
THE DESIGN OF TETRODE TRANSISTOE AMPLIFIERS
835
^ below, the bandwidth at which the response is down a given number of
db can also be computed.
From Table II one observes that this design provides a gain of about
18 db with half power frequencies where the susceptance B2 has changed
by ±3/i22r mhos from its value of — 2/i22r at the center of the pass band.
The value of h22i corresponds to approximately 1 fifxi of capacitance and
if the stray capacitance amounts to 3.5 nni, then the bandwidth is
AB2/2C since the slope of the susceptance of a tuned circuit is
I .
2C-
m
hos
rad/sec
I Thus the bandwidth is approximately
I
6 -3.5 -10"'
I 2 -2.5 -10-12.6.28
(ir 3.7 mc. This is the actual value of load capacitance measured on an
experimental amplifier with a vacuum tube voltmeter connected to the
output. The measured response of this amplifier with a load of Yl =
(08 - j215) • lO"*^ at 30 mc (Gl = 2/?22r) shows a peak gain of 18.3 db and
I half power points separated by 3.8 mc. For a given value of Gl , the
bandwidth of the amplifier will varj^ inversely with the total capacitance
in the output circuit. The same gain as obtained in the sample given
above, can be obtained over a narrower band by increasing the load
capacitance. Since the minimum capacitance is fixed, if one wishes to
increase the width of the pass band, a higher value of G2 must be used.
;In the same manner as is used to arrive at the data shown on Table II,
Table III is computed for a value of G2 = 6/?22r (Gl = 5/?22r).
In this case, the maximum value of Po/Pi occurs when B2 = — 3/i22r •
Ihe source impedance is selected to be 75 — j45 ohms at 30 mc and the
jcmainder of the table is computed. The maximum computed gain is
approximately 16 db with half power frequencies where the susceptance
Table III
B2
Evaluation of Transducer Gain of I.F.
Amplifier
P./Pi
/„.
/',,,/Power avail-
able from source
Transducer gain. .
< iain db
-8/r22r
— 5//22r
-3/j22r
-2/2 22r
— /J22r
-l-/«22r
25
35 + y22
33
35 + jS5
43
50 + ;45
40
56 + i46
39
65 + ;48
31
77 + i39
0.S3
21
13.2
0.86
28
14.5
0.96
41
16.1
0.97
39
15.9
0.99
39
15.9
0.99
31
14.9
21
83 + j20
0.97
20
13.0
836
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
Bo has changed by ±6/i22r mhos from its value at the center of the band.
Using the same value of circuit capacitance as above, the indicated band-
width is about 7.4 mc. The measured response on an amplifier with this
value of load impedance indicates a gain of 16.1 db at 30 mc, with the
frequencies at the half power point separated by 7.6 mc.
Often it is desirable to build tuned amplifiers to work between like
impedances in which case at least the output network must perform both
the function of selectivity and impedance transformation. An example
of a simple network to perform these functions is shown on Fig. 17. The
impedance transforming properties of such a circuit are w^ell know^n.
With a given value of load resistance, the load admittance presented to
the transistor can be made to have a given value at a certain frequency.
However, since the circuit performs both the function of impedance
transformation and selectivity the bandwidth is determined by the out-
put impedance selected. This circuit does not present a fixed value of
conductance as a function of frequency but for frequencies near the
maximum gain it is a fair approximation to assume it constant. The out-
put circuit of Fig. 17 w^as designed to present a load admittance such that
G2 + JB2 = 3/i22r — i2/i22r at 30 mc. This is tJhe same condition as com-
puted in Table II so one would expect the same value of maximum gain.
However, in order to present the proper value of load impedance, a total
load capacitance of about 4 /^/xf must be used. This indicates a bandwidth
of 3.3 mc between the half power points. The measured response of this
amplifier is shown on Fig. 18 as the solid line. The points indicate the
computed maximum gain and the frequencies at which the gain is down
3db.
-4.5V
+ 15V
Fig. 17 — Simple tuned amplifier. The output circuit performs both the func-
tions of impedance transformation and selectivity.
THE DESIGN OF TETRODE TRANSISTOR AMPLIFIERS
837
20
18
16
U
gl4
< 12
o
Q 10
z
<
8
(
MEASURED RESPONSE
O COMPUTED POINTS
)
/
\
/
\
i
/
\
/
\
\
24 26 28 30 32 34 36
FREQUENCY IN MEGACYCLES PER SECOND
38
Fig. 18 — Measured and computed response of the stage shown on Fig. 17.
An IF Amplifier Centered at 70 Mc.
Although we do not have complete data on the parameter values of
tetrode transistors in this frequency range, amplifiers with a center fre-
quency of 70 mc have been built and their performance measured. The
amplifier was designed to provide a flat gain characteristic over the fre-
quency range from 60 to 80 mc. The stage was designed with the equiv-
alent of a double tuned transformer, interstage circuit with the trans-
former being replaced by the equivalent tee section. The selective circuit
is terminated at its output into the load resistance in the case of the last
stage or by the input impedance of the following transistor when it is
used as an interstage network. The impedance transformation of the
network is approximately 75 ohms to 1,500 ohms so it is essentially un-
terminated at the collector. By using a sweeping oscillator, such a stage
can be adjusted to result in a fairly flat frequency response. A typical
stage is shown on Fig. 19. The output terminals are connected to either
the load or the next emitter. The response obtained from a 3-stage am-
plifier is shown on Fig. 20. In order to determine the variation of gain
838 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
33 K
OUT
soon
I+15V
Fig. 19 — Circuit of a 60 to 80-mc band pass amplifier stage.
32
in
0^ (1)
lU CO
28
< -
cr
Q 24
Z
< 20
O
16
/\
r^
k
/
>)
54 58 62 66 70 74 78 82
FREQUENCY IN MEGACYCLES PER SECOND
86
Fig. 20 — Gain of a 3-stage band pass amplifier working between 75-ohm im-
pedances. Each stage uses the circuit shown on Fig. 19.
(0
cc
o
\-
Z 3
<
cr
I-
u.
^2
a.
UJ
CD
Z 1
4 —
5 6 7 8 9 10 n
GAIN IN DECIBELS
12
Fig. 21 — Variation of gain for a grouj) of transistors used in the circuit of
Fig. 19.
THE DESIGN OF TETRODE TRANSISTOR AMPLIFIERS
839
6 -
tr ^
o
(-
to
o
q:3
ID
^2
p5!^ p: : J jwp
8 9 10 11 12 13 14 13 16
NOISE FIGURE IN DECIBELS
Fig. 22 — Noise figure for a group of transistors used in the circuit of Fig. 19.
If) A
1^3
or
o
1-
<ri
■■":::■■>"
10
;:;-:::o;
z ^
—
p*r<*-|
v:::-:;:;
<
:":■:::::■:
CL
(-
U-
C>
CC^
~
i!i
:-:-x:;-:
Hi
■■■y-yA
::::■:;:"::
m
2
D
Z 1
"
0
1
1
5 6 7 8
NOISE FIGURE IN DECIBELS
10
Fig. 23 — Noise figure for a group of transistors used in a 10-mc bandpass
amplifier.
840 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
between various transistors, 18 tetrodes were measured in the first stage
of the amplifier. If the measured gain of each transistor is rounded off
to the nearest db and the number of transistors having this gain plotted
as the abscissa, the results shown on Fig. 21 are obtained. Of the 18
transistors measured, 11 have a gain of 8 db or greater. Similar data has
been obtained on the noise figure of the same 18 transistors, the results
being shown on Fig. 22. In general, the transistors having the highest
gain also have the lowest noise figure. The noise figure depends to some
extent on the source impedance but a 75-ohm source results in a noise
figure which is within a few tenths of a db of the minimum. The value
of the noise figure does not vary a great deal as the collector voltage and
emitter current are changed except that if the collector voltage is lowered
below 6 or 8 volts the gain decreases and in general the noise figure in-
creases.
Noise Figure at 10 Mc.
Although not described here, bandpass amplifiers centered at 10 mc
with a 200-kc pass band have been constructed using tetrode transistors.
A gain of slightly over 20 db per stage can be realized at this frequency.
The noise figure of transistors tried in this circuit is shown on Fig. 23,
the data being shown in the same manner as described above. At 10 mc
the noise figures are lower than at 70 mc. The remarks made above con-
cerning variation of noise figure with operating conditions also apply to
this case.
ACKNOWLEDGMENTS
We are happy to acknowledge the advice and encouragement given
us by R. L. Wallace, Jr., and others in the Laboratories. We also wish
to express our thanks to E. Dickten who fabricated the transistors used
to obtain the experimental data presented. W. F. Wolfertz made the
transistor parameter measurements used in the computations. R. H.
Bosworth and C. E. Scheideler were responsible for construction of the
circuits and some of the gain measurements. We also wish to thank W. R.
Bennett for his aid in preparing the manuscript.
The Nature of Power Saturation in
Traveling Wave Tubes
By C. C. CUTLER
(Manuscript received February 2, 1956)
The non-linear operating characteristics of a traveling wave tube have
been studied using a tube scaled to low frequency and large size. Measure-
ments of electron beam velocity and current as a function of RF phase and
amplitude show the mechanism of power saturation.
The most important conclusions are:
I. There is an optimum set of parameters (QC = 0.2 and yro = 0.6)
giving the greatest efficiency.
II. There is a best value of the gain parameter "C" which leads to a best
efficiency of about 38 per cent.
III. A picture of the actual spent beam modidation is now available
which shows the factors contributing to traveling wave tube power saturation.
INTRODUCTION
The highest possible efficiency of the travehng wave tube has been
estimated from many different points of view. In his first paper on the
subject^ J. R. Pierce showed that according to small signal theory, when
the dc beam current reaches 100 per cent modulation an efficiencj^ of
, = § (1)
is indicated,* and thus the actual efficiency might be limited to some-
thing like this value. Upon later consideration" he concluded that the ac
convection current could be twice the dc current and that one might
expect an efficiency of
r) = 2C (2)
He also considered the effects of space charge, and concluded on the
* Symbols are consistent with Reference 2 and are listed at the end of this
paper.
841
842 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
same basis that under high space charge and elevated voltage conditions,
efficiencies might be as high as
77 = 8C (3)
J. C. Slater^ on the other hand considered the motion of electrons in a
traveling wave and concluded that the maximum possible reduction in
beam velocity would also indicate a limiting efficiency of 2C. Taking a
more realistic account of the electron velocity, Pierce showed that these
considerations lead to a value of
V = -^yiC (4)
which, since t/i ranges between —}'2 and —2, leads to the same range of
values as the other predictions.
None of these papers purport to give a physical picture of the over-
loading phenomenon, but only specify clear limitations to the linear
theory. L. Brillouin on the other hand found a stable solution for the
flow of electrons bunched in the troughs of a traveling wave. This he
supposed to represent the limiting high level condition of traveling wave
tube operation. His results give an efficiency of
V = 2hC (5)
In the first numerical computations of the actual electron motion in a
traveling wave tube in the nonlinear region of operation, Nordsieck pre-
dicted efficiencies ranging between 2.5 and 7 times C and showed that
there would be a considerable reduction in efficiency for large diameter
beams, due to the non-uniformity of circuit field across the beam diame-
ter. He also gave some indication of the electron dynamics involved.
Improving on this line of attack, Poulter calculated some cases includ-
ing the effect of space charge and large values of C.
Tien, Walker and Wolontis carried computations still further for small
values of C by including the effect of small beam radii upon the space
charge terms, and showed that space charge and finite (small) beam radii
result in much smaller efficiencies than were previously predicted. J. E.
Rowe^ got similar results and gave more information on the effects of
finite values of C. Computations for large values of C by Tien showed
that a serious departure from the small C conditions takes place above
values of C = 0.1 if space charge is small (i.e., below QC = 0.1) and
above C = 0.05 for larger values of space charge. They indicated that a
maximum value of efficiency as high as 40 per cent should be possible
using C = 0.15, QC = 0.1 and elevated beam voltages.
These five papers give some insight into the electron dynamics of power
NATURE OF POWER SATURATION IN TRAVELING WAVE TUBES 843
saturation, but still involve questionable approximations which make it
desirable to compare predictions with the actual situation.
Theoretical considerations of the effects of attenuation upon efhciency
have not led to conclusions coming even close to the observed results.
Measured characteristics^^' ^^ show that the effect of attenuation is very
large, but that attenuation may be appropriately distributed to attain
stability and isolation between input and output of the tube without de-
grading the output power.
There are also several papers in the French and German periodicals
which deal with the question of traveling wave tube efficienc3^ Some
of these are listed in References 12 through 20.
This paper describes measurements of efficiency and of beam modula-
tion made on a traveling wave tube scaled to large size,* and low fre-
quencies. The construction of the tube, shown in Fig. 1, and the measure-
ment of its parameters were much more accurate than is usual in the
design of such tubes. The results are believed to be generally applicable
to tubes having similar values of the normalized parameters.
OUTPUT
TERMINATION
INPUT
TERMINATION
INTERMEDIATE
TAP
VACUUM HEADER
/
^ VELOCITY
ANALYZER
SAMPLE
OF HELIX
SUPPORTS
SECTION OF
FOCUSING SOLENOID
Fig. 1 — The scale model traveling wave tube. The tube is 10 feet long with a
c-opper helix supported by notched glass tubing from an aluminum cylinder over-
wound with a focusing solenoid. It is continuously pumped and readilj^ demount-
able.
See Appendix.
844 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
Two kinds of measurements are described. First, the efficiency and
power output are determined for various conditions of operation, and
second the spent beam ac velocity and current are measured. The prin-
cipal results are shown in Figs. 2 to 4 which give the obtainable effi-
ciencies, and in Figs. 7 to 10 which show some of the factors which con-
tribute to power saturation. These figures are discussed in detail later.
The most significant phenomenon is the early formation of an out-of-
phase bunch of electrons which have been violentl}^ thrown back from
the initial bunch, absorbing energy from the circuit wave, and inhibiting
its growth. The final velocity of most of the electrons is near to that of
the circuit wave which would lead to a value of
limiting efficiency t] = —2yiC (6)
if the wave velocity maintained its small signal value. Actually the wave
slows down, under the most favorable conditions giving rise to a some-
what higher efficiency. For other conditions, space charge, excess elec-
tron velocity, or nonuniformity of the circuit field enter in various ways
to prevent the desired grouping of electrons and result in lower effi-
ciencies.
The observed efficiencies are a rather complicated function of QC,
yvo and C. To compare with efficiencies obtained from practical tubes one
must account for circuit attenuation and be sure that some uncontrolled
factor such as helix non-uniformity and secondary emission is not seri-
ously affecting the tubes' performance. Measured efficiencies of several
carefully designed tubes have been assembled and are compared with
the results of this paper in Table I.
The results of these measurements compare fa^'orably with the com-
putations of Tien, Walker and Wolontis , and of Tien . There are, how-
ever some important differences which are discussed in a later section.
TRAVELING WAVE TUBE EFFICIENCY MEASUREMENTS
Reasoning from low level theory, efficiency should be a function of the
gain parameter, "C," the space charge parameter "QC," the circuit,
attenuation, and (for large beam sizes), the relative beam radius "yro ."
It was soon found that efficiency is a much more complicated function of
y)\i than expected. The iiiilial ()l)jecti\-e was to detoiniine the effect of
QC, C, and yr^ separately on efficiency, but it A\'as necessary to gi^'e a
much more general coverage of these parameters, not assuming an>' of
them to be small.
Most of the measurements ha\^e been made with small \alues of loss
NATURE OF POWER SATURATION IN TRAVELING WAVE TUBES 845
Table I
Laboratory
Freq.
mc.
QC
yrr,
c
V
meas-
ured
V
(from
Fig. 3)
7) (From
Fig. 3 with
allowance
for circuit
attenuationio
McDowell*
4,000
0.27
0.62
0.078
19.5
26
21.6
6,000
0.29
0.8
0.058
13.2
16.2
12.5
Brangaccio and Cutlerf
Danielson and Watson*
4,000
11,000
0.61
0.35
0.87
1.2
0.041
0.05
11
6.6
6
7
6
4.8
R. R. Warnecke^e, n, is
870
0.32
0.3
.125
27
33
33
W. Kleen and W. Frizes
4,000
0.5
0.43
0.05
7.8
11.5
5.7
W. KleenJ
L. Bruck§
4,000
3,500
0.2
0.19
0.94
0.6
0.1
0.065
20
15
26
23
22
18.5
Hughes Aircraft Co.
3,240
0.19
0.94
0.12
39
31
29
9,000
0.15
1.3
0.11
25
15.5
12.7
* At Bell Telephone Laboratories.
t Reference 10 (a slight beam misalignment could account for most of this
difference).
t Siemens & Halske, Munich, Germany.
§ Telefunken, Ulm, Germany.
and of the gain parameter, where efficiency is proportional to C, as ex-
pected from small-signal small-C predictions. This reduces the problem
to a determination of -q/C versus QC and 7ro .
Many measurements of this kind have been made, and the data are
summarized in Figs. 2 and 3, with efficiency shown as a function of QC
and yro . In Fig. 2 we have the efficiency when the beam voltage is that
which gives maximum low-level gain. Fig. 3 shows the efficiency ob-
tained when the beam potential is raised to optimize the power output,
and contours of constant efficiency have been sketched in. There is
significantly higher efficiency than before in the region of maximum effi-
ciency, but not much more elsewhere.
Fig. 4 shows how efficiency varies with C for a small value of QC, a
representative value of 7ro , and with beam voltage increased to maxi-
mize the output. This indicates a maximum of about 38 per cent at
C = 0.14.
Some of the computed results of Tien, Walker and Wolontis, and of
Tien are also indicated in the figures. Their results generally indicate
somewhat greater efficiencies than were observed, but in the most sig-
i nificant region the comparison is not too bad as will be seen in a later
section.
The measurements are for conditions having negligible circuit loss
near the tube output. There are no new data on the effect of loss, but
earlier results'** have been verified by measurements at Stanford Uni-
versity and are still believed to be a satisfactory guide in tube design.
846
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
3.0
0.5
Fig. 2 — Values of efficiency/C as a function of QC andyro at the voltage giving
maximum gain per unit length. The shaded contours and triangular points are
from the computations^ of Tien, Walker and Wolontis. The circled points are from
the measurements and the line contours are estimated lines of constant efficiency.
The most significant difference is for large beam radii, where the RF field varies
over the beam radius in a way not accounted for in the computations.
SPENT BEAM CHARACTERISTICS
The scale model traveling wave tube was followed by a velocity an-
alyzer as sketched in Fig. 5 and described in the Appendix. A sample of
the beam at the output end of the helix is passed through a sweep cir-
cuit to separate electrons according to phase, and crossed electric and
NATURE OF POWER SATURATION IN TRAVELING WAVE TUBES 847
magnetic fields to sort them according to velocity. The resulting beam
draws a pattern on a fluorescent screen as shown in Fig. 6 from which
charge density and velocity can be measured as a function of signal
phase. The velocity coordinate is determined by photographing the
ellipse with several different beam potentials, as in Fig. 6(a), and the
phase coordinate is measured along the ellipse. From pictures like this
a complete determination of electron behavior is obtained from the
linear region up to and above the saturation level.
The results of such a run are plotted in Fig. 7. The upper lefthand
2.0
Fig. 3 — Values of efficiency/C as u function of QC and yro at elevated beam
voltage. Raising the beam voltage has little effect at large QC and small yro ,
and less than expected anywhere. Again the triangular points are from Tien, Walker
and Wolontis,^ and the line contours are estimated from the measured data.
848
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0
A
\
\. 40% EFFICIENCY
\
\
s.
n
a
S-&
1
s.
^ o
U
u
a.ZM—a
on"
^
---..'^
^
D
D
c
^^).^
*^..
---
o
o
"^■.
□ TAKEN WITH 7ro = 0.78 QC=0,1
o TAKEN WITH 7ro=0.41 QC=0.06
A FROM TIEN REFERENCE 9
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
i.a
Fig. 4 — Efficiency/C for large values of C and with elevated beam voltage.
Efficiency seriously departs from proportionality to C at C = 0.14, where a maxi-
mum efficiency of about 38 per cent is measured.
MAGNETIC
SHIELD
COIL
ELECTROSTATIC
ELECTRON LENS (3)
FLOURESCENT
SCREEN,
NOTCHED
GLASS
RODS (3)
DEFLECTING
PLATES
DEFLECTING
COILS
DEFLECTING
PLATES
Fig. 5 — The velocity analyzer. A sample of the spent electron beam is ac-
celerated to a high potential, swept transversely with a synchronous voltage,
sorted with crossed electric and magnetic fields, and focused onto a fluorescent
screen.
pattern, Fig. 7(a), is representative of the low level (linear) conditions
(22 db below the drive for saturation output) . The dashed curve repre-
sents the voltage on the circuit, inverted so that electrons can be vis-
ualized as rolling down hill on the curve. The phase of this voltage rela-
tive to the electron ac velocity is computed from small signal theory, but
NATURE OF POWER SATURATION IN TRAVELING WAVE TUBES 849
everything else in Fig. 7, including subsequent variations of phase, are
measured. The solid line patterns represent the ac velocity, and the
shaded area, the charge density corresponding to that velocity. Thus in
each pattern we have a complete story of (fundamental) circuit voltage,
electron velocity and current density as a function of phase, for a par-
ticular signal input level. The velocity and current modulations at small
signal levels check calculated values well, and it is not difficult to visu-
alize the dynamics giving this pattern.
Consider first the situation in the tube at small signal amplitudes.
At the input an unmodulated electron beam enters the field of an elec-
tromagnetic wave moving with approximately the same velocity as the
electrons. The electrons are accelerated or decelerated depending upon
their phase relative to the wave, and soon are modulated in velocity.
The velocity modulation causes a bunching of the electrons near the
potential maxima (i.e., the valleys in the inverted potential wave shown)
and these bunches in turn induce a new electromagnetic wave com-
ponent onto the circuit roughly in ciuadrature following the initial wave.
I'he addition of this component gives a net field somewhat retarded from
the initial wave and larger in amplitude. Continuation of this process
Fig. 6 — Velocity analyzer patterns. The beam sample is made to traverse an
ellipse at }i the signal frequency. Current density modulation appears as intensity
variation, and velocity variation as vertical deflection from the ellipse.
2
1
0
- I
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-22 DB
(a)
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240
180
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RELATIVE PHASE
IN
60 120
DEGREES
180
240
Fig. 7 — Curves of current and velocity as a function of phase for various input
levels. The velocity becomes multivalued at a very low level, a tail forming a
nucleus for a second electron bunch which eventually caused saturation in the
output. For this run C = 0.1 Q,C = 0.06, t^o = 0.4 and h = 0.26.
850
- 1
-2
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X'
J ^
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9 DB
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160
120 60 0 60 120
RELATIVE PHASE IN DEGREES
180
240
851
852 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
may be seen to give a resultant increasing wave traveling somewhat
slower than the initial wave, and thus slower than the electron velocity.
Returning to Fig. 7 we see that electrons in the decelerating field [from
+30 to +210° in Fig. 7(a)] have been slowed down, and because of their
initial velocity being faster than the wave velocity, have moved forward
in the wave giving a region of minimum velocity somewhat in advance
of the point of maximum retarding field (greatest negative slope in the
wave potential). Also, bunching due to acceleration and deceleration of
electrons has produced a maximum of electron current density which,
because of the initial excess electron velocity, is somewhat to the right
of the potential maximum (downward).
As the level is increased the modulation increases and at 17 db below
saturation drive, Fig. 7(b), some nonlinearity is evident. The velocity
and current are no longer sinusoidal, but show the beginnings of a cusp
in the velocity curve and a definite non-sinusoidal bunching of the
electrons in the retarding field region (between +30 and 210°).
In the next pattern, Fig. 7(c), at 14 db below saturation a definite cusp
has formed with a very sharp concentration of electrons extending sig-
nificantly below the velocities of the other electrons. We already have a
wide range of velocities in the vicinity of the cusp, and at this level the
single valued velocity picture of the traveling wave tube breaks down.
Although it cannot be distinctly resolved, the study of many such pic-
tures leaves little doubt that the cusp and its later development is really
a folding of the velocity line.
The next pattern at 12 db below saturation drive. Fig. 7(d), shows a
greater development of the spur and a somewhat greater consolidation
of current in the main bunch between +60° and +180°. It is interesting
that the velocity in this region has not changed significantly. In order
for this to be true the space charge field must just compensate for the
circuit field. In the vicinity of the 60° point the space charge field ob-
viously must reverse, accounting for the very sharp deceleration evident
in the very rapid development of the low velocity spur. The decelerating
field must be far from that of the wave, inasmuch as the electrons just
behind the cusp are much more sharply decelerated than those preced-
ing the cusp. We conclude that there are very sharply defined space
charge fields much stronger than the helix field. At this relatively low
drive, the velocity spread has already achieved its maximum peak value.
The succeeding three patterns show a continuing growth of the spur,
a continued bleeding of electrons from the higher velocity regions, and
a consolidation of the main bunch just in advance of the spur. Presum-
ably the increased concentration of space charge in the bimch has kept
NATURE OF POWER SATURATION IN TRAVELING WAVE TUBES 853
pace with the increasing hehx field, so that the net decelerating field
still balances to nearly zero. At 4 db below the saturation drive, Fig.
7(h), the spur has moved well into the accelerating region, and has been
speeded up. The main bunch of electrons is still to the right of the spur,
and has been consolidated into a 60° interval. The few electrons in ad-
vance of this region evidently no longer find the space charge field suffi-
cient to balance the circuit field, and are being decelerated into a second
low velocity loop.
The next three patterns show a continued growth of this second low
velocity loop, further consolidation of the 'main bunch', and^the rapid
formation of a second bunch in the accelerating field at the end of the
spur. It is interesting that at saturation drive, Fig. 7(k) the two bunches
are very nearly equal, and in equal and opposite circuit fields, nearly
180° apart. The reason for the saturation is that while the main bunch
is still giving up energy to the wave, the new one is absorbing energy at
an equal rate. The fundamental component of electron current is evi-
dently small, and is in quadrature with the circuit field. The current
density in the dashed regions is less than 1 per cent of that in the bunches,
and probably more than 95 per cent of the electrons are in the two
bunches. Two new effects are observable at this level. The second elec-
tron bunch has begun to come apart, presumably because of strong lo-
calized space charge forces. These forces are also evident in the kink in
the velocity pattern drawn by the fast electrons at the same phase as
the second bunch.
Since the majority of the current is in the two bunches at a reduced
velocity of
^^ = -1.1
2FoC
one would expect an output efficiency of
^ = 2.2C
The actual measured efficiency
RF power output
DC power input
was 2.0 C. Under the conditions described, (6) would give 1.4 C.
At still higher drive levels the pattern continues to develop, electrons
from the first bunch falling back into the second, which in turn continues
to divide, one part accelerating ahead into a new spur, and the other
I
854 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956 1
i
slowing down and falling further back in phase. At 9 db above satura- >
tion, Fig. 7(o), the pattern is quite complex, and at still higher levels it
is utterly indescribable. ■
It is interesting that the ^'elocity gives a line pattern, even though a '
multi^'alued one. It is reasonable to suppose that the development of
the spur is really a folding of the \'elocity line so that the spur is really a
double line. Thus, at the 9 db level, and at 0° phase, for instance, there
must be electrons originating from five different parts of the initial dis- ;
tribution. In an attempt to verify this the resolution of the velocity an-il
alyzer was adjusted so that a difference in velocity of 2 per cent of the-
overall spread could be observed, but there was no positive indication of r-
more than one velocity associated with any line shown. :
There has been a long-standing debate as to whether or not electrons j
are trapped in the circuit field, or continue to override the w^ave at large
amplitudes. The observations indicate that with low values of space
charge and near synchronous voltage the electrons are effectively trapped:
in the wave until well above saturation amplitude. In other circum-
stances this is not the case, as we shall see.
SPACE CHARGE EFFECTS
The data of Fig. 7 were taken with a very small value of the space
charge parameter QC, so small in fact as to be almost negligible as far
as low level operation is concerned. Yet the space charge forces evidently
played a very strong role in the development of the velocity and currenti'
patterns. It is doubtful that space charge would ever be negligible in thisii
respect, because if the space charge parameter were smaller, the bunch-i
ing would be more complete, the electron density in the bunch would be
greater limited only by the balance of space charge field and circuit field
in the bunch. The effect of decreaising QC further therefore is a greater
localization of the space charge forces, rather than a reduction of their
magnitude, at least until the bunch becomes short compared to the
beam radius.
Increasing the value of the space charge parameter has quite the op-'
posite effect. In Fig. 8 are shown three velocity-cm-rent distributions ati
the saturation level, for different A-alues of QC. It can be seen that a re-'
suit of increased space charge is a greater spread of velocities, and a wider
phase distribution of current.
With the introduction of space charge, the velocity difference between
the electrons and the circuit wave at low levels is increased. Consequently
electrons spend a longer time in the decelerating field before beingj
thrown back in the low velocity spur, and thus lose more energy. Thel
i
NATURE OF POWER SATURATION IN TRAVELING WAVE TUBES 855
-^
r- ' ""'
' ^
NO
(a)QC
= 0.064
/
>
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Vo
^-'
\^
Hi y
L -^ w_ 1
/-^
1
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cr
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(b)
QC=0.22
y
\
Vo
^x^
-
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1 c
^
,--;;
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°
o
3
^
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-2
-3
-4
240
o
o
o
(c)
o
QC = 0.48
o
o
o °
o
o
" \°
o o
o
o
/^
o
o
\°
^0
° oc'
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t^^^
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<
o
%
^
o
o o
^^
^^
°
180
120 60 0 60 120
RELATIVE PHASE IN DEGREES
180
240
Fig. 8 — A comparison sliowing the effect of the space charge parameter QG
1 on the velocity and current at overload. The points represent the disc electrons of
{ the computations^ of Tien, Walker and Wolontis. For this run 7ro = 0.4 and h is
I chosen for maximum X\ .
I greater reduction of velocity results in a faster and farther retarding of
I the current in the spur before the retarded electrons recover velocity in
i the accelerating region. Also the larger space charge forces prevent as
I tight bunching of the electrons anywhere, so that at overload they are
•spread over a much wider phase interval (about 360° for QC = 0.5).
! Space charge also prevents electrons from the forward part of the bunch
j from being trapped so that more electrons escape ahead of the decelerat-
' ing field and more current is found in the upper half of the velocity
j curve. This very likely is the reason that efficiency decreases when QC
\ is increased above about 0.3.
856
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
EFFECT OF BEAM SIZE
In small signal operation, decreasing the beam radius below that which
assures a constant circuit field throughout the beam has no effect except
that accounted for by its effect on QC. Fig. 9 shows that for large signals,
however, it has a pronounced effect. When the beam is made smaller
(with QC maintained by changing frequency and beam current), the
slowed up tail is formed at a much lower signal level (not shown), by a
very few electrons which begin to collect in the accelerating region before
the beam is strongly modulated. As the level is increased, the current is
redistributed, more going into the tail without much alteration in the
shape of the velocity pattern, and with no strong bunching at any part
of the curve. This result is exaggerated in Fig. 9(c) by measuring with a
o
o
>
(J)
z
<
I
o
>-
H;
O
O
_I
LU
>
z
o
tr
o
UJ
_l
UJ
>
UJ
(a) 7ro = o.64
^
— ■ -
^,
^^
^
\
%
\
>
1^ V'
I
^
/<^M^
j|'"vw~
' ^^
^^
^ttin
^%
^^
240 180 120 60 0 60 120
RELATIVE PHASE IN DEGREES
1
1
(b) •5fro=0.22
/
*"*\,
y
\
Vo
^
--"
^
3 V,
^
^*^^
^
^
"-'-^ Ui
w
^**^
'^Jjy^
^ \
\
I
^^^
,riin4+ft:
(C) 7 '0 = 0.06
^
^icnxct;
■0!^
^3^
Vo
[???*?s^rt
^
'>'■
V
^IL
rtjff#
■ip>
p>
4^
^\.
,
— L
L.
W^-^i'
^
^•^^m-rf
180
240
Fig. 9 — Curves of current and velocity as influenced by yr^ . Space charge
becomes a very potent factor near overload, especially when the beam is small.
For this run QC = 0.34 and 6 = 1.0.
NATURE OF POWER SATURATION IN TRAVELING WAVE TUBES 857
ridiculously small beam. By comparison with curves taken for larger
beams, the tail is diminutive, electrons are much more uniformly dis-
tributed over all velocities and phases, and a peculiar splitting of veloci-
ties in the main bunch is found. The latter indicates that electrons
entering from the higher velocity region move forward in the bunch, and
the rest gradually retard. The smaller reduction in velocities, and the
spread of electrons into the higher velocity regions is consistent with the
lower efficiency measured (Fig. 2).
To explain the observed difference in high level performance of tubes
with different size beams we must consider the character of the ac longi-
tudinal space charge field. The coulomb field from an elemental length
of an electron beam is inversely proportional to the square of the dis-
tance from the element
E = Const 7-^, (7)
provided (z — Zi) » ro and {z — Zi) « a.
For (z — zi) not small compared to a, (i.e., circuit radius not awfully
large) the field would drop even faster with (z — zi) due to the shielding
effect of the circuit. On the other hand, very near to the beam element
{z — zi <K To), the field is approximately that of a disc, which is nearly
independent of z, i.e.,
E = Const -^^ (8)
Trro
independent of z for z <^ro .
Thus to a fair approximation the space charge field may be considered
to be uniform for an axial distance of the order of a half a beam radius,
and to drop rapidly at greater distances. For a given current element, a
small diameter beam has an intense field extending only a short dis-
tance, while an equal charge element in a larger beam has a weaker longi-
tudinal field extending to a greater distance.
At low amplitudes the extent of the forces makes no difference in
operation, for a sinusoidal current gives a sinusoidal space charge field in
either case. However, at large amplitudes, a sharp change in current
density has a very high short range space charge field if the beam is
small, or a much smaller smoothed out long range field if the beam is
large. For 7/-o = 0.5 which appears to be an optimum compromise be-
tween the effects of space charge and field non-uniformity, the space
charge field could scarcely be confined closer than about ±30° in phase.
< )n the other hand, a sharp bunching of electrons in a beam having
858 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
7/'o = .05 would have 100 times the space charge field, extending how-
ever only one tenth as far from the current discontinuity.
Returning to Fig. 9 we can see how these considerations enter into the |
development of the beam modulation. In the case of the small beam,
Fig. 9(c), at the very beginning of the formation of a cusp, the strong
highly concentrated space charge force causes a rapid deceleration of
nearby electrons, resulting in the relatively early formation of a diminu-i
tive tail. The very high localized space charge force also prevents as tight
bunching of electrons, forcing some to move forward and continuously ;
repopulate the accelerating part of the wave. The relatively early falling;
apart of the initial bunch and the greater acceleration of the overriding;
electrons evidently give the latter enough velocity to penetrate the main i
bunch of electrons and form the second class of electrons in the main
bunch, 90°-150° in Fig. 9(c). Thus the net result of reducing the beami
size is a severe aggravation of space charge debunching effects, with ai
consequent reduction in efficiency. To get high efficiency, we conclude,
the beam should not be small. It should not be larger than 77-0 = 0.7 '
however, for then the circuit field is not uniform enough over the beam i
cross-section to excite it properly, resulting in a loss in efficiency as is ,
evident in Figs. 2 and 3.
EFFECT OF INCREASED BEAM VOLTAGE
It is common practice in the operation of traveling wave tubes to ele-
vate the beam voltage, taking a sacrifice in gain in order to obtain in-
creased power output. The effects on the beam modulation are shown in
Fig. 10. In Fig. 10(a), the voltage is somewhat below that giving maxi-
mum gain. The curve is characteristic of what we have already seen but
the bunching is less pronounced and the velocities are less reduced. In
Fig. 10(b) the voltage is somewhat above that giving maximum gain and \
the curve is much like that of Fig. 8 except that the decelerated elec-
trons are slowed by a greater amount, consistent with the increased
separation of electron and wave velocity, and also with the measured
increase in power output.
Increasing the beam voltage still further gives only a slight increase
in efficiency. Fig. 10(c) shows that even though electrons are slowed to
still lower velocities, and the velocity spread is increased, many more
electrons override the circuit Avave and are accelerated, thereby off-
setting the greater contribution of the slower electrons. This is much
like what was seen with increasing space charge (QC) and indeed the
effects are almost ecjuivalent. As one would expect therefore, little is
gained by elevating the beam voltage if the space charge is large, the
NATURE OF POWER SATURATION IN TRAVELING WAVE TUBES 859
O
o
>
! o
z
<
I
o
>
u
o
_l
z
§
I-
u
LU
_l
UJ
UJ
>
<
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\
\
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(a)
b = o
x"
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Vq.v,
^r-K
-^w
/r^:':?-
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-iii
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-1
-2
-3
2
1
0
-1
-2
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-4
r"''
,-''''
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(b)
b = 0.77
^
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Vo
/^^
y
m/
M^
N" V,
vw
^
A
"\
/t''
y:a
^ V
^
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(c)
b = ).56
^^^
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Vo
1
.___ .
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Vw
(171
N
V,
i
k.
/
240 180 120 60 0 60 120
RELATIVE PHASE IN DEGREES
180
240
Fig. 10 — The influence of beam velocity on ac velocity and current. When the
velocity is raised too high, the electrons are not effectively trapped by the wave,
and override into the accelerating field. With large QC and/or small 7ro the elec-
trons override in any case, and little is gained by increasing h. For this case QG
= 0.13 andTfo = 0.21.
^main effect being to push more electrons forward into the accelerating
j region.
KLECTRIC FIELD IN THE BEAM
' Besides telling a clear story of the non-linear dynamics of the traveling
, wave tube, the foregoing curves contain a lot of information about aver-
jage current and velocity distributions. From the current or velocity
curves we can in turn deduce the distribution of longitudinal electric
field in the beam. Figs. 11(a) and (b) show the instantaneous current as
a function of phase, taken from the curves of Figs. 8(a) and (b). The
infinite differential in the velocity curve necessarily gives a pole in the
charge density (at about 88°). The total charge in the vicinity of the
860
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
z
UJ
(T
a.
O
UJ
>
u
EC
(a)
A
h
^lo+L
/
n
V
>
^ ^
^ — '■
/
\
o
>
y o
i-\
o u
u
-J I
> LJ
< I-
erg
UJ
-2
-6
(b)
p\
^
,/^
\
\ ^
CIRCUIT
' FIELD
//
r
\
y
)^'--
V
TOTAL
FIELD
\\
« 1
V
-180
120
-60 0 60
RELATIVE PHASE IN DEGREES
120
180
Fig. 11 — AC current and electric field in the beam. The upper curve comes
directly from Fig. 8(a). The lower curve is deduced by an approximate method
from the velocity curve of Fig. 8(a). The double value below 90° is partly due to
inconcistency between the two parts of the velocity curve, and partly due to the
nature of the approximation.
pole, and the range of the space charge force (dependent upon QC and
7ro) determines its effect upon the electron dynamics.
Most of the current is incorporated in the two bunches nearly 180°
apart, as we have seen, each bunch having a current density many times
the average.
We might obtain the space charge fields from the current density, but
this would require a rather definite knowledge of the characteristic
space charge field versus distance as influenced by beam diameter. It
would also be pushing the accuracy of charge density measurement,
which is crude at best. A better way is to compute the electron accelera-
tion from the velocity curves. This may be done by taking two velocity
patterns at slightly different signal levels, and tracing electrons from one
to the next, using the measured velocity to determine the relative phase
shift of any electron.
In the appendix it is shown that a close approximation to this is
E^ = 2/3CYo
[
(Fo - FJ + A7'
2FoC
(10)
NATURE OF POWER SATURATION IN TRAVELING WAVE TUBES 861
where the parameters are all obtained from a single velocity curve, and
is field strength in volts meter at phase $
is the value of the ordinate of the velocity characteristic of
of interest (Figures 7 to 10) and
is the ^'alue of the ordinate corresponding to the wave
velocity. (To be precise, the wave velocity at the associ-
ated output level, but to a reasonable approximation, that
of the wave velocity at low levels. (This value is indicated
by Vw in the velocity curves.)
i The total electric field has been computed for the case of Figs. 8(a) and
(b) and is given in Figs. 11(b) and 12(b) together with the circuit field
.calculated for the associated power level and plotted with an arbitrarily
chosen phase. In each case it is seen that the space charge field is com-
parable in magnitude to the circuit field, is far from sinusoidal, and
z
UJ
cr
q:
D
O
UJ
>
111
cc
1
(a)
1 .
T 4- i
io + i*
^_^
A
Ao
J
^"^
-^■v;^--
^
■ — v
jL
_^^
u u
UJ
-J I
UJ H
o
> UJ
I- tc
< H
CE 9
CIRCUIT
FIELD
r\
(b)
y^
;-
\l\
/
^
K
V
/
/
/]
\
\
/ y
'^y
\V
V,.
^^
TOTAL
FIELD
u
V 1
\\
-J
■180
-120
-60 0 60
RELATIVE PHASE IN DEGREES
120
180
Fig. 12 — AC current and electric field in the beam deduced from Fig. 8(b).
The greater space charge results in a less defined bunch, and smoother space
charge field than in Fig. 11.
862 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
10
>°
o
en
<
CO
o
-10
OUTPUT
POWER
-.^
'
X
/
Si
RELATIVE HARMONIC CURRENT
,2 ND
rK \ ,ST
CALCULATED
1ST
x-^
srd'^-^
V6
\
X
-30 -20 - 10 0 10
RELATIVE INPUT LEVEL IN DB FROM SATURATION DRIVE
Fig. 13 —^Curves of output level, fourier component amplitudes of beam cur-ij
rent, and peak velocity as a function of input level for low space charge. These-:
curves were deduced from Fig. 8 (a). j
0.6
Fig. 14 — Maximum velocity reduction as a function of space charge (from Fig. J
8). The velocity reduction is about 3.5 iji . i
NATURE OF POWER SATURATION IN TRAVELING WAVE TUBES 863
agrees qualitatively with what would be expected from the associated
curve of beam current.
To determine the curves of Figs. 11 and 12 is rather stretching the
accuracy of the measurements as can be seen by the large discrepancy in
the field calculated from the two parts of the velocity curve which of
course should be identical. The figures do give an interesting qualitative
picture of traveling wave tube behavior however, and are included here
for that reason.
OVERALL VELOCITY SPREAD
Of more practical importance is the overall velocity spread in the
spent beam. It is often desirable to reduce the power dissipation in a
traveling wave tube by operating the collector at a potential below that
of the electron beam, and it is interesting to see how far one might go.
Fig. 13 shows how the velocity reduction of the slowest electron, together
with the output level and fourier current components of beam current
vary with input level. For small amplitudes, the low level theory ac-
curately predicts the velocity, but near overload, as we have seen, the
minimum \'elocity drops sharply to a value several times lower than that
projected from small signal theory.
The maximum velocity spread dependence upon the space charge
parameter QC is shown in Fig. 14. Similar data for values of the other
parameters may be obtained from the velocity diagrams.
From the foregoing data, one can deduce the amount of reduction of
collector potential that should be theoretically possible wdthout turning
back any electrons. An idealized unipotential anode could collect all the
current at a potential AF (in the foregoing figures) above the cathode,
decreasing the dissipated power by a factor of AF/Fo below the dc beam
power.
STOPPING POTENTIAL MEASUREMENTS
Information on spent beam velocity has also been obtained by a stop-
ping-potential measurement at the collector of a more conventional
4,000-mc traveling wave tube.* Two fine mesh grids were closely spaced
to a flat collecting plate, and collector current was measured as a func-
tion of the potential of second grid. The first grid was very dense, to
prevent reflected electrons from returning into the helix. One curve taken
with this arrangement is shown in Fig. 15 and for comparison we have
* Similar measurements have been reported by Atsumi Kondo, Improvement
of the Efficiency of the Traveling Wave Tube, at the I.R.E. Annual Conference on
Electron Tube Research, Stanford University, June 18, 1953.
864
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
plotted the distribution predicted from Fig. 9(b). The RF losses in the
4,000-mc tube were not neghgible, and probably account for slightly
smaller power output and greater proportion of higher velocity electrons.
COMPARISON WITH COMPUTED CURVES
Non-linear calculations of traveling wave tube behavior have been
made by Tien, Walker and Wolontis' and by Tien^ covering the same
region of parameter values as is reported here. In Figs. 2, 3, 4 and 9 are
shown some of their data on our coordinates. The similarity of the
results over much of the range is rather reassuring. It is interesting that
in order to make the computations it was necessary to assume two space
charge factors, just as was found experimentally. There are, however,
some significant differences:
1. In general, the computed values give a higher ^alue of efliciency
than is measured, by about 25 per cent. Thus, the computations indicate
rwm(m^
^
Hill
zero signal
characteristic:
IDEAL ^>4
MEASURED ^j
I
I
l(
-400
0 400 800
STOPPING GRID VOLTAGE
I
1200
■ F^^' A ZZ. '^^^\^^ current versus stopping potential. The oscilloscope curve
IS tor a 4,0n0-mc tube, and the other that predicted from the scale model meas-
urements. By integrating current as a function of velocit v for Figs. 7-10 stopping
potential distributions can be deduced for other conditions
NATUEE OF POWER SATURATION IN TRAVELING WAVE TUBES 865
3.5
3.0
2.5
2.0
c
1.5
(.0
0.5
• ^
• \
\
,j
.. ^,
\
\
S
V
0.2
0.4
0.6
0.8
1.0 1.2
7ro
1.4
1.6
1.8
2.0
2.2
Fig. 16 — Efficiency versus 7ro for small QC. The dashed curve is proportional
to the amount of beam current in the circuit field strength having at least 85 per
cent of the intensity at the edge of the beam. This illustrates the fact that for
large beams only the edge of the beam is effective.
that with the reasonable vahies of QC = .25 and 7ro = 0.8 {kr = 2.5),
the efficiency would be about 3.8C, whereas the measured value is 3.1C.
2. The largest discrepancy in the measured and computed value of
r]/C is for large values of yro (small kr), where the computations show a
steady increase in efficiency instead of a sharp decrease. This arises be-
cause the computational model assumed the electric field to be uniform
across the beam, whereas in the actual tube it varies as loiyr), and for
large values of 77-0 the field is weak near the beam axis. This effect is
shown in Fig. 16 where rj/C is plotted versus yro for small values of QC,
on the same scale with a curve proportional to the square of the fraction
of the beam within a cylindrical shell such that
1 -
Io(yn)
hiyro)
= 0.85
(11)
where ri is the inside radius, and ro the outside beam radius (i.e., the
fraction of the beam in a field greater than 85 per cent of that at the
beam edge).
No serious studies of velocity were made for large beams, but on cur-
sory examination it was evident that the beam modulation varied con-
siderably over the cross section when the beam was very large, and
scarcely at all when it was smaller than around yro < 0.8.
866 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
3. The observed effect of small beam radius upon efficiency is not as
pronounced as was found in the computations. The reason is not kno^^^l
but may be due to modulation of the beam diameter at large signal levels.
This effect would be neghgible with the larger Tro's, due to the focusing
fields being relatively much larger.
4. The computations, and also those of Nordsieck, Poulter and Rowe^
indicate a much higher efficiency than has been observed at elevated
beam voltages and small C and QC. The reason for this may be that
the limited number of "electrons" used in the computational models
fail to adequately account for the very sharp space charge cusp that
forms under low QC conditions, or that interpolation between their
points should not be linear, as assumed in making the comparison.
On the other hand it would be difficult to be sure that nonuniformities
in electron emission were not influencing the measurements in the case
of the large beams by giving a larger QC than calculated.
5. The increase in efficiency to be had by elevation of beam voltage is
much smaller than is indicated by the computations. This may be a real
difference, or it may be that at elevated voltages, the measurements are
beginning to feel the influence of overloading in the attenuator. The
margin of safety on attenuator overloading is not as great as one would
like at the higher frequencies.
6. The velocity curves, Fig. 8, compare the computed and measured
data on three runs. For small QC, Fig. 8(a), the agreement is remarkably
good considering the fact that in the computation only 24 "electrons"
were used to describe a rather complicated function. The effect of the
lumping of space charge in the artificial 'disc' electrons causes a scatter-
of points which is different from that in an actual tube as is especially
apparent in Figure 8c. In spite of this the computational results indicate
a velocity spread and current distribution not greatly different from that
observed.
CONCLUSIONS
The large scale model traveling wave tube is a means for the deter-
mination of non-hnear behavior, and has been valuable in determining
relationships and limitations important to efficient operation of such
tubes. It has shown that there is a broad optimum in tube parameters
around C = 0.14 QC = 0.2 and 7ro = 0.5 for which values it is possible
to obtain efficiencies well above 30 per cent. The measured ac beam
velocity and current near overload show that it is unlikely that signifi-
cant increase in efficiency can be obtained by any simple expedients such
NATURE OF POWER SATURATION IN TRAVELING WAVE TUBES 867
as operations on the helix pitch alone, or the use of an auxiliary output
circuit.
The results being in normalized form, are believed to be generally
applicable to conventional traveling wave tube design. With determina-
tion of an equivalence yi beams, they should even be a useful guide in
the design of tubes using hollow beams or other configurations.
The work described could not have been done without the able assist-
ance of G. J. Stiles and L. J. Heilos and the helpful council of many of
my colleagues at Bell Telephone Laboratories.
Appendix
scale model tube design
There were a larger number of factors to be accounted for in the de-
sign of this tube. Its proportions should be such as to make it repre-
sentative of the usual design of traveling wave tube. Its size should be
such as to make it easy to define the electron beam boundary, and to
dissect the beam. The size should also be such that the electron beam
velocity analysis could be done before the beam character would be
changed either by space charge, or its velocity spread. The voltage should
he low so that further acceleration in the velocity analyzer would not
lead to an inconveniently high voltage. Finally, the availability of suit-
able measuring gear over a 3-1 frequency range, and the size of the
laboratory must be considered. All of these factors led to low frequency
operation, limited principally by the laboratory size and the mechanics
of construction.
A moderate perveance of around 0.2 X 10~ was taken, with a 7a of
1.2 and 7ro of 0.8 in a representative helix with small impedance reduc-
tion due to dielectric and space harmonic loading. This is representative
of practical tube design in the microwave range and is centered on the
parameter values of most general interest. At a frequency of 100 mc and
a beam potential of 400 volts this resulted in a helix 10 feet long and l}^
inches in diameter, with an electron beam 1 inch in diameter. The
choice of frequency was finally determined by the availability of meas-
uring equipment, and the voltage was selected to give a convenient size
for dissection of the electron beam.
By changing frequency, beam current, and beam diameter it was
! possible to cover a reasonable range of yro , and QC, and to make some
observations into the region of large C operation.
In all of the measurements described, a very strong uniform magnetic
field was used to confine the beam, and therefore scaling of the magnetic
868 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
focusing field need not be considered. The electron beam was produced
in a gridded gun and is thus near to the ideal confined flow, which is the
only focusing arrangement which is known to determine a reasonably-
uniform boundary to the beam. The beam size and straightness was
checked using a fluorescent screen at the collector end. \
NORMALIZING FACTORS
The measurements described are expressed relative to the linear
theory, in Pierce's' notation, which are generally used in the design of
traveling wave tubes. Thus, instead of being presented in the terms of
measurement or simply normalized to efficiency, perveance, impedance,
etc., they are expressed in terms of C, QC, yro , etc., with normalized
fields, currents and velocities. In this way the results become adjuncts
to the linear theory and are more easily applied to tube design. Electron
velocity is plotted on the same scale as the relative velocity parameters
b and yi used in low level theory, (i.e., normalized to AV/2VoC). Effi-
ciency is normalized as r]/C, which for C less than 0.1 is relatively inde-
pendent of C. Field strength in the linear region is proportional to
v't
{ri being efficiency measured at the appropriate signal level). Solving
the equation for C ,
>3 E lo
^ ~WP2Vo ^^^^
gives us
V
^ (13)
C /3C2F,
which we use as the normalizing parameter for electric field. Circuit po-
tential is the integral of circuit field over a quarter period, giving a
normalized parameter V/VoC . For convenience in the use of common
coordinates, circuit potential was plotted as —V/2VoC^ in Figure 7.
The other curves are plotted as values relative to dc quantities or to
saturation level.
Strictly speaking, the results hold only for tubes having the same pro-
portions as the model. Practically, however, as long as the helix imped-
ance and radius {ka or ya) are not different by orders of magnitude from
the values used, and as long as the perveance is low (below 2 X 10~^ for
NATURE OF POWER SATURATION IN TRAVELING WAVE TUBES 869
instance), the results are believed to be significant for tubes having the
indicated values of 7ro and QC.
Il HELIX IMPEDANCE
It is important to the measurements to have an accurate evaluation
[of the helix impedance. Several methods of measurement have been
discussed in the literature.^^ ' ^^ That described by R. Kompfner was
I selected, wherein the circuit impedance is correlated with the beam
current and voltage which gives a null in the output signal. When the
beam voltage and current are adjusted to give zero transmission for a
lossless section of helix (neglecting space charge) CN = 0.314 and
5F/Fo = 1/A^. Using the measured length of the helix, and measuring
the voltage and current giving the null in signal transmission, we can
compute C, and thus the impedance and velocity (synchronous voltage)
of the hehx.
The impedance was calculated by P. K. Tien,^' and the results are
compared in Fig. 17. The measured impedance at the high frequency
end was much too low until space charge in the beam was accounted for
in interpreting the measurements. Fortunately, in the absence of attenu-
1000
800
600
400
^ 200
UJ
u7 100
o
z
<
Q
Hi
Q.
5
80
60
40
20
10
-
^
-
N
-
\(
-
CALCULATED -
\
\
\
\
-
\
-
\
-
MEASURED POINTS-
-^
V
-
N
I
40 80
FREQUENCY
120 160 200
MEGACYCLES PER SECOND
240
Fig. 17 — Helix impedance as a function of frequency. The impedance was
calculated taking into account dielectric loading and wire size. It was measured
using the Kompfner dip method, taking account of space charge.
870 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
ation, the conditions for start of oscillation in a backward wave oscillator
are the same as for the output null in a traveling wave tube. Space charge
was first accounted for using the results of H. Heffner'^' " giving an
excellent check between predicted and computed helix impedance. Later
C. F. Quate showed that the same measurement could be used to de-
termine the space charge parameter QC as well as the helix impedance.
Since thermal velocity effects and the uncertainty of some of the assump-
tions used in evaluating the small signal effects of space charge cast
some doubt on the proper evaluation of this term, further measurements
were made on this factor, and a satisfactory correlation between the ob-
served value of QC and that computed from the Fletcher^'^ curves was
obtained.
TOTAL ACCELERATING FIELDS
From the velocity characteristics shown in Figs. 7 through 10, we can
deduce the electron accelerations, and thus the electric fields at any
point. While the curves are actually diagrams of velocity as a function
of phase, they closely correspond to the velocity- time or distance distri-
bution of the electrons in the traveling wave tube. Knowing these charac-
teristics we can deduce the motion of any element of charge, and thus the
force under which it moves. It is observed that over most of the curve
the shape of the velocity pattern does not change nearly so rapidly as
the redistribution of electrons within the pattern. Thus, we can approxi-
mate the situation at any amplitude by assuming the velocity pattern
to be constant, and that electrons move within the pattern according to
simple particle dynamics. This is a good approximation except where
the acceleration is high (i.e., vertical crossings of the wave velocity line).
Consider then an element of the velocity pattern at phase $i and
velocity (wo + Aw). In an interval dt this element will move a distance
(wo + Aw) dt (14)
and will change velocity by
du = E -dt (15)
m
At the same time the wave will have moved a distance v dt, resulting in
a relative change in phase between wave and current element of
d^ = ^(uo - V -\- Aw) dt (16)
In terms of equivalent differences the term in brackets can be written
(«. - . + A„) = a/7T7. c (^° - ;: + "0 <i^>
NATURE OF POWER SATURATION IN TRAVELING WAVE TUBES 871
from (16) and (17) we can write:
du
du d^
It
d^ dt
d ( AV
d<p \2VoC y
giving (from 15)
E
y m
^FoC2
= 2
Yo - F,
. 2Fo(7
)*(.
AF^
2FoC,
- F. + AF^
2FoC
AF ^
2FoC,
. (18)
(19)
;8, Fo and C are constants of the tube, the first inner parenthesis may
be calculated from the tube constants and is shown in the curves.
AF/FoC and its differential are the value and the slope of the velocity-
curve in question.
The important approximations here are that the velocity-phase curves
are representative of velocity-distance characteristics, which is true for
small values of C, and that the electrons move roughly tangent to the
given velocity pattern. By comparing several patterns at different signal
levels it is observed that this is true to a fair accuracy over most of the
curve. Also it is assumed that the wave velocity at large amplitudes is
the same as that for small signals, which is not quite true. The resulting
curves give at least a qualitative picture of the field distribution within
a traveling wave tube, and serve to emphasize the importance of space
charge fields in determining the non-linear characteristics.
ELECTRIC FIELD OF THE HELIX WAVE
In order to see what part of the field is due to space charge we must
evaluate the corresponding helix fields. A value for this can be derived
from the basic traveling wave tube equations assuming the helix fields to
be sinusoidal and not seriously affected in impedance by the beam (small
C again) . By definition
E"- h
2jS2P 4Fo
= C'
(18)
and
1
C
/oFoC
(19)
where 77' is normalized power level, i.e., efficiency corresponding to the
signal level E of interest. From this we deduce for the normalized circuit
872 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
field
which integrates to give a normalized ac circuit voltage
V
2V2V0C''
i/i
(20)
(21)
RELATIVE PHASE BETWEEN WAVE, VELOCITY AND CURRENT
The velocity analyzer provides no convenient measure of relative
phase between the helix w^ave and the beam modulation. Therefore we
compute the relation of helix field and beam modulation for a small ]|
signal, and for large amplitudes measure the phase of each relative to
that at small amplitudes.
-VTV
Pierce gives the relationship'
V =
Uo(j^ - r)
which using (9) and the fact that j3eC8 — jjSe — T
gives for the small signal beam modulation
(22)
(23)
AV
V2
4/l=^v1IHi:)-i (-)
2VoC ' b
Similarly we have for the small signal current modulation
h
\/-'l
■8-
2 tan-
Vi
(25)
The value of 8(= xi + jiji) is given in Fig. 18, drawn from data sup-
plied by P. K. Tien, from Pierce' and from Birdsall and Brewer. ^^ This
figure was also used as a basis for determining the values of yi and h used
in several of the curves.
MEASUREMENT OF POWER
The output power, and relative output phase was measured using a
tnicro-oscilloscope." The subharmonic of the signal was used for a sweep
voltage, and phase was measured from the shape of the observed lissajou
figures. The oscilloscope deflection was compared with the dc deflection
from a battery standard, and checked on occasion with a bolometer
power meter at the operating frequency.
THE VELOCITY ANALYZER
There are many ways in which one may separate velocities in an elec-
tron stream. Crossed electric and magnetic fields were used in this ex-
NATURE OF POWER SATURATION IN TRAVELING WAVE TUBES 873
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
.^^^
^
,-'
-;;
(-y,)
\'<
>' ^
^
y
■::;
A,
/
^
/
/
/
/
/
/
/
/
/
^
f
/
^,
/
/
0.1
0.2
0.3
0.4
0.5 0.6
QC
0.7
0.8
0.9
1.0
1.1
Fig. 18 — Increasing wave propagation factors used in interpreting the meas-
urements. These are the maximum value of x\ and the corresponding value of 6
and y\ for given values of QC.
^ periment because a simple control of sensitivity was important in order
I to study velocity differences ranging from 1 per cent up to as much as
1 100 per cent of the dc beam velocity.
The velocity analyzer is sketched in Fig. 5. It consists of an aperture
which transmits only a few microamperes of the electron stream; a mag-
netic pole piece (not shown) terminating the focusing field; a pair of
horizontal deflection plates; an electrostatic lens system; pole pieces and
j deflection plate to provide a region with crossed electric and magnetic
'fields; and finally a drift tube, a post deflection acceleration electrode
,aiid fluorescent screen. The whole assembly is raised 1,000 volts above
the helix potential and the 0.001 " aperture is very close to the end of the
helix, so that the electrons are very quickly accelerated to a high voltage.
V>Y this means, the region of debunching outside of the helix field is kept
t)clow 1.4 radians transit angle and the velocity spread within the ana-
lyzer is reduced by a factor of four. Space charge within the analyzer is
<'iitirely negligible because of the small current transmitted.
In order to discriminate in phase before the electrons are scrambled
87*1 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
due to their spread in velocity, the horizontal sweeping plates are
mounted just as close to the aperture as is deemed practical. The ob-
served velocity spreads in the beam were such as to give less than 0.2
radians error in phase under the worst conditions.
The horizontal deflecting plates were driven synchronously with a
sub-harmonic of the RF input to the helix, and the resulting deflection
served to separate electrons according to phase in the final display.
Placing the focusing lens after the deflection plates results in a con-
siderable reduction in deflection sensitivity. However, undesirable mag-
nification of the pinhole aperture dictated that the lens could not be
close to it, and it was important to initiate the deflection as early as
possible. The lens consists of three discs, the center one being biased to
about 800 volts above the mean voltage of the rest of the system.
Immediately after the lens there are two iron pole pieces and two insu-
lated electric deflection plates which extend parallel to the beam for IJ^
inches. The pole pieces provide a dc magnetic field up to about 20 gausses
induced by small coils outside of the envelope, and the electric deflection
plates are biased with up to a corresponding 50 volts dc polarized to
oppose the magnetic deflection of the beam. The electric and magnetic
fields are adjusted so that the normal unmodulated electron beam tra-
verses the region with no deflection and strikes the center of the fluores-
cent screen. In the crossed field region
1= W^2^Fo. (26)
Electrons having greater or lesser velocity are deflected parallel to the
electric field, and give a corresponding deflection from the center of the
fluorescent screen.
To get a display in which the various elements are not hopelessly en-
tangled, it was necessary to sweep the trace in an initial ellipse at a
subharmonic rate. The sweep voltage was applied to the horizontal de- :
flection plates, with just a little applied to the vertical plates through a ,
phase shifter. The relative phase of any part of the trace was measured k
from the ellipse, and the velocity sensitivity was calibrated by observing |
the ellipse deflection as a function of the dc beam potential, as shown f
in Fig. 6(a). There is a small error due to the sensitivity of deflection to (
velocity, and due to distortion of the ellipse by fringing fields. (
In order to measure velocity and current density in the displayed pat- ;;
tern, the fluorescent screen was photographed, and the negati^'e pro- h
jected in a microcomparator. It was assumed that with the small ciu'rents P
used, the light intensity was proportional to current, and the film i
linearity was calibrated by making exposures of several different dura- j
tions. The trace density was measured with a densitometer, sweeping
NATURE OF POWER SATURATION IN TRAVELING WAVE TUBES 875
over the trace width to account for variations in focus for different parts
of the pattern. Admittedly, the process is not very accurate, but it does
give a rough measure of current density and helps considerably in in-
terpreting the observed velocity patterns.
NOMENCLATURE
a Circuit radius
6 Parameter relating electron velocity to that of the cold circuit
wave Uq — Vi/uqC = AF/2FoC
B Magnetic field
(8 the axial phase constant co/^i
C The gain parameter = (E^/2l3^P) (/o/4Fo)
7 Radial phase constant = ^ = co/^i
8i Complex propagation constant for the increasing wave
I E Electric field
A'* Electric field at phase $
c/m Charge to mass ratio of the electron
i h Beam current in amperes
/„( ) Modified Bessel function
' /,> Tien's constant k, = 2/7^0
l.ri Circuit circumference measured in (air) wavelengths
X Number of wavelengths
7] Maximum efficiency
f]' Efficiency at an intermediate power level
^ P RF power obtainable from the circuit
j, QC Space charge parameter
I q Charge per unit length in the electron beam
/■ Radial distance from the axis
j Vq Beam radius
t Time variable
Electron velocity
DC beam velocity
V AC velocity of the electron beam
t\ Wave velocity
Fo DC beam voltage
7',„ Voltage corresponding to the wave velocity
AF ^^oltage difference corresponding to the difference in velocity of
an electron and the dc beam velocity
bV Difference between synchronous voltage and that giving the
Kompfner dip
$ Relative phase
z Distance measured along the beam
"0
876 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
REFERENCES
1. Pierce, J. R., Theory of the Beam Type Traveling Wave Tube, Proc. I.R.E.,
35, pp. 111-123, Feb., 1947.
2. Pierce, J. R., Traveling Wave Tubes, D. VanNostrand Co., Chapter XII.
3. Slater, J. C, Microwave Electronics, D. VanNostrand Co., 1950, pp. 298.
4. Brillouin, L., The Traveling Wave Tube (Discussion of Waves of Large Ampli-
tudes), J. Appl. Phys., 20, p. 1197, Dec, 1949.
5. Nordsieck, A., Theory of the Large Signal Behavior of Traveling Wave Ampli-
fier, Proc. I.R.E., 41, pp. 630-647, May, 1953.
6. Poulter, H. C, Large Signal Theory of the Traveling Wave Tube, Tech.
Report No. 73 Electronics Research Laboratory, Stanford University,
Stanford, California, Jan., 1954.
7. Tien, P. K., Walker, L. R., and Wolontis, V. M., A Large Signal Theory of
Traveling Wave Amplifiers, Proc. I.R.E., 43, pp. 260-277, Mar. 1955.
8. Rowe, J. E., A Large Signal Analysis of the Traveling Wave Amplifier, Tech-
nical Report No. 19, Electron Tube Laboratory, Universit.y of Michigan.
9. Tien, P. K., A Large Signal Theory of Traveling Wave Amplifiers Including!
the Effects of Space Charge and'Finite C, B.S.T.J., 34, Mar., 1956.
10. Brangaccio, D. J., and Cutler, C. C, Factors Affecting Traveling Wave Tube
Power Capacity, Trans. I.R.E. Professional Group of Electron Devices,
PGED 3, June, 1953.
11. Crumly, C. B., Quarterly Status Progress Report No. 26, Electronics Re-
search Laboratory, Stanford Universitj', Stanford, California, pp. 10-12.
12. Doehler, O., et Kleen, W., Phenomenes non Lin^aires dans les Tubes a Propa-
gation D'onde" Annales de Radioelectricit^ (Paris), 3, pp. 124-143, 1948.
13. Doehler, O., et Kleen, W., Surle Rendement du Tube a Propagation D'onde,"
Annales de Radio^lectricite, Tome IV No. 17 Juillet, 1949 pp. 216-221.
14. Berterotidre, R., et Convert, G., Sur Certains Effets de la Charge D'espace
dans les Tubes a Propagation D'onde, Annales de Radio^lectricit^, Tome
V, No. 21, Juillet, 1950.
15. Klein, W., und Friz, W., Beitrag zum Verhalten von Wanderfeldrahren bei
Hohen Engangspegeln, F.T.Z., pp. 349-357, July, 1954.
16. Warnecke, R. R., L'^volution des Principes des Tubes Electroniques Modernes
pourMicro-ondes, Convegno di Elellronica e Televisione, Milano, p. 12-17,
Aprile, 1954.
17. Warnecke, R. R., Sur Quelques R^sultats R^cemment Obtenus dans le Do-
maine des Tubes Electroniques pour Hyperfrequences, Annales de Radio-
^lectricite. Tome IX, No. 36, Avril, 1954.
18. Warnecke, R., Guenard, P., and Doehler, O., Phenomenes fondamentaux dans
les Tubes k onde Progressive, Onde Electrique, France, 34, No. 325, p
323-338, 1954.
19. Briick, L., und Lauer, R., Die Telefunken Wanderfeldrohre TL6, Die Tele
funken-Rohre Heft 32, pp. 1-21, Februar, 1955.
20. Briick, L., Vergleich der Verschiedenen Formeln fiir den Wirkungsgrad einer
Wanderfeldrohre, Die Telefunken-Rohre Heft 32, pp. 23-37, Februar, 1955
21. Cutler, C. C, Experimental Determination of Helical Wave Properties, Proc
I.R.E. , 36, pp. 230-233, Feb., 1948.
22. Kompfner, R., On the Operation of the Traveling Wave Tube at Low Level
Journal British I.R.E., 10, p. 283, Aug.-Sept., 1950.
23. Tien, P. K., Traveling-Wave Tube Helix Impedance, Proc. I.R.E., 41, pp
1617-1623, Nov., 1953.
24. Heffner, H., Analysis of the Backward-Wave Traveling-Wave Tube, Proc
I.R.E., 42, pp. 930-937, June, 1954.
25. Johnson, H. R., Kompfner Dip Conditions, Proc. I.R.E., 43, p. 874, July, 1955
26. Quate, C. F., Power Series Solution and Measurement of Effective QC in
Traveling-Wave Tubes, Oral presentation at Conference on Electron Tube
Research, University of Maine, June, 1954.
27. Fletcher, R. C, Helix Parameters in Traveling Wave Tube Theory, Proc.
I.R.E., 38, pp. 413-417, Apr., 1950.
28. Birdsall, C. K., and Brewer, G. R., Traveling Wave Tube Characteristics for
Finite Values of C, Trans. I.R.E., PGED-1, pp. 1-11, Aug., 1954.
29. Pierce, J. R., Traveling Wave Oscilloscope, Electronics, 22, Nov., 1949.
I
The Field Displacement Isolator
By S. WEISBAUM and H. SEIDEL
(Manuscript received February 7, 1956)
A nonreciprocal ferrite device (field displacement isolator) has been con-
structed with reverse to forward loss ratios of about 150 in the region from
5,925 to 6,425 mc/sec. The forward loss is of the order of 0.2 dh while the
reverse loss is 30 dh. These results are obtained by using a single ferrite
element, spaced from the sidewall of the guide. The low forward loss suggests
the existence of an electric field nidi at the location of a resistance strip on
one face of the ferrite. We discuss the various conditions, derived theoretically,
under which the electric field null may be obtained and utilized. Further-
more, a method of scaling is demonstrated which permits ready design to
other frequencies.
I. INTRODUCTION
The need for passive nonreciprocal structures has long been recog-
nized.^ In the microwave field, Hogan's gyrator' paved the way for an
increasingly important class of such devices. The isolator, in particular,
has emerged as one of the more useful ferrite components. It performs
the function, as its name implies, of isolating the generator from spurious
mismatch effects of the load. Unlike lossy pads, which consume generator
power, the isolater provides a unidirectionally low loss transmission
path.
A. G. Fox, S. E. IMiller and M. T. Weiss'' have pointed out that non-
reciprocal ferrite devices may exploit any of the following waveguide
effects :
1. Faraday rotation
2. Gyromagnetic resonance
3. Field displacement
4. Nonreciprocal phase shift
In the present paper we shall discuss an isolator, based upon the field
displacement effect, which was developed to meet the following require-
ments for a proposed microwave relay system (5,925-6,425 mc/sec):
1 . Forward loss 0.2 db
877
878
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
2. Reverse loss 20 db
3. Return loss 30 db
The field displacement isolator employs an ordinary rectangular |
waveguide and requires no specialized adaptation to the rest of the
guide system. It is relatively compact and does not require excessive
magnetic fields. In contrast to the field displacement structure of Ref-
erence 3, in which a symmetrically disposed pair of ferrite slabs is used,
the present unit (see Fig. 1) contains only a single slab. Other differences
of a more substantial nature may be noted — in the present case the
slab is displaced from the guide wall, it occupies a partial height of the
waveguide, and it employs a novel disposition of the absorption material
on one face. These features result in a broadband device.
In the analysis presented in this paper the isolator field characteristics
for a full height slab are determined by exact solution of Maxwell's
equations, as opposed to the "point-field" perturbation approximation
used in Reference 3. An exact solution of the partial height geometry of
the experimental device would be exceedingly difficult to obtain. How-
ever, such a solution did not appear to be essential for this investigation
since good correspondence has been obtained between the experimental
results and the idealized full height slab calculations.
The following performance of the isolator was obtained from 5,925-
6,425 mc/sec:
1. Forward loss --^ 0.2 db
PERMANENT
MAGNET
V/y/////y/^y>///////y///y///////////y'////y^A
._FERRITE
^ RESISTANCE
I ""COATING
L-
'////////////////////////////////////////y'yy//A
h = 0.550 IN.
^■ = 0. 180 IN.
b = 0.074 IN.
L= 1.590 IN.
3 = 0.795 IN.
T
I
I
I
I
I
S
I
Fig. 1 — Field displacement isolator.
THE FIELD DISPLACEMENT ISOLATOR 879
2. Reverse loss ^ 30 db
3. Return loss ^^ 30 db
The extremely low forward loss strongly suggested the existence of an
electric field null in the plane of the resistance material. Consequently,
a theoretical investigation of the null condition was made and a set of
criteria estal)lished for the existence and utilization of the null. (E. H.
Turner^ independently developed the same null conditions.) An exten-
sion of the analysis leads directly to a set of scaling laws which permits
the ready design of isolators of comparable performance at other fre-
quency bands.
i II. DESCRIPTION OF OPERATION
I
In Section IIA we will show how the "point-field" approach^ is used
to predict the ciualitative behavior of the structure and in Section IIB
we will apply a more rigorous analysis to the determination of the op-
timum design parameters.
.1. Qualitative
Prior to introducing the actual isolator configuration, we shall re-
^'iew some elementary properties both of the ferrite medium and of an
unloaded rectangular waveguide. It is in terms of these properties that
we can understand, in a qualitative sense, the interaction of an rf wave
with a ferrite in such a waveguide. Since the behavior of a ferrite medium
in the presence of a static magnetic field and a small rf field has been
discussed in the literature^ the following resume is not intended to be
detailed. It is presented, however, to maintain continuity.
If a static magnetic field is applied to a ferrite medium the unpaired
electron spins, on the average, will line up with the field. If now an rf
magnetic field, transverse to the dc field, excites the spin system these
1 electrons will precess, in a preferential sense, about the static field. The
precession gives rise to components of transverse permeability at right
{ angles to the rf magnetic field, leading to a tensor characterization of
the medium. This tensor has been given by Polder^ and may be diag-
onalized in terms of circularly polarized wave components. Correspond-
, ing to the appropriate sense of polarization we use the designation -|-
' and — . When the polarization is in the same sense as the natural pre-
cessional motion of the spin system, gyromagnetic resonance occurs for
an appropriate value of the static magnetic field. The scalar permea-
bilities /i_ and M+ are shown in Fig. 2 as functions of the internal static
magnetic field as would be observed at an arbitrary frequency.
880
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
o
u~ 1
r 1
t i
^^X^+ /
Hres
Hi
Fig. 2 — Permeability versus magnetic field.
Clearly, in employing a ferrite medium, we intend to use the basic dif-
ference between the scalar permeabilities ix^ and /i_ . To this end we may
exploit the fact that the magnetic field configuration at any given point
in a rectangular waveguide is, in general, elliptically polarized. Travel-
ing loops of magnetic intensity appear in Fig. 3 for the fundamental
(TEio) mode. At point P an observer sees a counterclockwise elliptically
polarized magnetic intensity if the wave is traveling in the (+y) direc-
tion.* The propagating wave may be decomposed into two oppositely
rotating circularly polarized waves of different amplitudes:
+ O
For propagation in the ( — y) direction the rj polarization is reversed:
+ O
Let us now consider the actual experimental configuration shown in
Fig. 4 (the partial height geometry was chosen on an experimental basis,
in that it gave VSWR considerably less than that for a full height ferrite
slab). The precession of the spin magnetic moments is counterclockwise
* It is evident that a point converse to P exists symmetrically to the right of
center. This is utilized in a double slab isolator which has been investigated by fi
S. Weisbaum and H. Boyet, I.R.E., 44, p. 554, April, 1956. '
THE FIELD DISPLACEMENT ISOLATOR
881
looking along the direction of the dc magnetic field shown in Fig. 4.
Since the major component of circular polarization for (+?/) propagation
is also counterclockwise the permeability will be less than unity for this
direction of propagation. This occurs provided we are using small static
fields, as is readily verified from Fig. 2. The permeability will be greater
than unity for ( — y) propagation. Physically, this is equivalent to energy
being crowded out of the ferrite for ( + ^) propagation and to energy
being crowded in, in the reverse direction. The electric field will thus be
distorted as shown in a qualitative way in Fig. 5. The vertical dimen-
sion in this figure serves both to identify the guide configuration and to
provide an ordinate for the electric field intensity.
The fields as shown in Fig. 5 merely represent a (iualitative picture of
the distributions in the guide and are not intended to be exact. There is
no question, however, that the electric fields at the ferrite face are dif-
Fig. 3 — Magnetic field configuration — Dominant TEjo mode.
Hoc
FERRITE
ELEMENT
^,w/^////j/y/////Ay/yyy^//^^^////^^^^^^^^^^^y/-'/w////y'^.
RESISTANCE STRIP
;^/////,v.vy/yy/-^^^/'y/yy^/V////'-^y^yy^vAvyyyy^^/yy/////-^////^^
-4<-d-A
, 1_
Fig. 4 — Experimental configuration.
882
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 195G
FERRITE-K-
Fig. 5 — Electric field distortion.
ferent in magnitude corresponding to the two directions of propagation.
Hence, if resistance material is placed at the interior face of the ferrite
(see Fig. 1) we may expect to absorb more energy in one direction of
propagation.
B. Analysis of Electric Field Null:-Full Height Ferrite
The description we have given in Section IIA is based on a perturba-
tion approach and does not take into account the higher order interac-
tion effects of the ferrite and the propagating wave. In this section we
consider an analysis of the idealized case, namely that of a full height
ferrite slab, and impose the condition of an electric field null at the face
of the ferrite for the forward direction of propagation. While this too
does not represent the true experimental situation, we believe it to be a
better approximation than the "point-field" perturbation viewpoint.
The fields of the various regions shown in Fig. 6 are described as
follows :
E^
(1)
sm a]X
E,^'^ = Ae-'"'''' -^ 5e'"^"' where x = x
^,"^ = V sin aix" where x" = x - L
a
(II -1)
where
aj = transverse wave number in the j*'^ region
a = transverse dimension from narrow wall to ferrite face
L = broad waveguide dimension
X = variable dimension along broad face
z = height variable
A, B, V = constants
Setting up the wave equation, there results
THE FIELD DISPLACEMENT ISOLATOR
883
2 7^2
a2 = K
tr / 2
— iMr
kr')
+ ai"
(II -2)
where nr and /iv are the relative diagonal and off-diagonal terms of the
Polder tensor, respectively, K is the free space wave number and £r is
the relative dielectric constant.
Mr = 1 +
4:7rMsyo}o
kr = ±
4:irMsyo}
7 = 2.8 X 10^ cycles/sec/oersted
4iTrMs = saturation magnetization in gauss
Ho = static magnetization in oersteds
COo = yHo
27r
X
K =
The following transcendental equation results from satisfying the
boundary conditions on E and H:^
(II -3)
tan aia\jjLT(X2 + kr^ tan a28] + (/Mr — kr) ai tan a2B tan ai6
+
= 0
Oil
(|3^ — K'HrSr) tan aia tan q:25 + ai(ju,Q;2 — Av/3 tan aaS)
where /3 is the propagation constant.
The minimum nontrivial value of an causing a null to appear at the
ferrite face is ai = t/g. Placing this value in (II • — • 3) produces the fol-
lowing transcendental equation for the null:
TT / 2
a
(jur — kr) tan a28
UrOCi — kr^ tan a28
-j- tan aih =0
(II -4)
y///////////////^//////////////////////" "//
••• •; '
>v2v;
^////y/////yy/////y//////////w/vy//'/////,v/>'>///>/^////y/'^
=. a
.4..4.-b-J
Fig. 6 — Full height geometry.
884 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
where h = L-a-8. Equation (II — 4) demonstrates that the null condi-
tion is nonreciprocal since, in general, the solutions differ for Av positive
and kr negative. The quantity Av has the same sign as the direction of
the dc magnetic field; reversing the sign of Av is equivalent to reversing \
the direction of propagation.
A numerical analysis of etiuation (II • — 4) has led to the conclusion
that the null condition is most broadband when | /x^ | < | Av |.* We use
the criterion \ Hr\ = [ A\ | to determine a critical magnetic field:
Hc = --^tM8 (11 — 5)
7
Clearly we require co/7 > AttIMs for physically realizable solutions. The
saturation magnetization (47rM's) is subject to the following:
1 . A choice of too large a 4^ttMs might create a mode problem and in
addition will not satisfy the limit on AtvMs implied in (II — 5).
2. 4xil/s must be sufficiently large so that the field needed to make
I jUr I < I Av I not be excessive.
3. y\/H(H + 4:tM) (this being the slab resonance frequency for
small slab thickness^) must be sufficiently far from the operating fre-
quency to avoid loss due to resonance absorption. In addition, this con-
dition improves the frequency insensitivity of the null.
Further analytic considerations are presented in Section IV.
III. EXPERIMENTAL DESIGN CONSIDERATIONS
Aside from the partial height nature of the slab, there are two other
basic factors in the experimental situation which are not present in the
analysis of Section IIB (see also Section IV). First, the ferrite has both
finite dielectric and magnetic loss. Second, higher order modes may be
present. These deviations from the simplified analysis are by no means
trivial and it would not be surprising if one found a considerable modifi-
cation of the analytic results. As it turns out, there are broad areas of
general agreement between the theoretical and experimental results
and in no case examined here does one find a basic inconsistency. In
considering the various parameters which must be adjusted to optimize
the broadband performance of the isolator we will point out, where
possible, how the theoretical results are modified by the factors men-
tioned above. The parameters of interest are:
* This is partially evident from eciuation II — 4. The quantity fj.r \ must be
less than | A;, | if the angle (aib) is to be small and in the first quadrant. Second
quadrant solutions cause the guide cross section to be excessively large, with
attendant higher mode complication.
I
THE FIELD DISPLACEMENT ISOLATOR 885
A. The saturation magnetization {4:TrMs) and the applied magnetic
field (Hnc).
B. The ferrite height.
C. The thickness (5) of the ferrite and its distance (b) from the nearest
side wall.
D. The placement of the resistance material and its resistivity (p).
E. The length of the ferrite (^).
A. 4:TrMs and Hoc
Theoretically, minimum forward loss occurs with a true null at the
face of the loss film and has been given in the condition \ fXr\ < \ kr\.
Although this inequality is required in the full height slab analysis,
lexperiment (Fig. 7) indicates the low loss region to be so broad as to
extend well into the low field, or | /Ur | > \K\ region.
There is inherent loss in the ferrite so that a more accurate statement
of the bandwidth of operation is that in which the losses in the film are
of equal order to the ferrite losses at the band edges. Even discounting
ferrite losses, it will be shown in Section IV that we have a good analytic
basis for the observed broadness of the low loss region. In general, there-
fore, we need not be as restrictive as the null analysis of Section JIB
would imply. It is not surprising then that optimum operation actually
occurs in the region | /x^ | > \ kr\. There are several reasons why this may
be so:
1. Shift of operation occurs due to the partial height nature of the
ferrite slab.
2. Reverse loss has a peak in the low field region, requiring a compro-
mise of low forward loss and high reverse loss for best isolation ratios
(see Fig. 8).
3. Optimum compromise between low ferrite loss and low film loss
must be made.
The internal magnetic field, determining | ju^ | and | Av |, differs from
the applied field by the demagnetization of the ferrite slab. Although not
ellipsoidal, it may nonetheless be considered to have an average demag-
netization which has been computed, for this case, to be 460 oersteds.
A further complication in knowledge of the internal field is the proximity
effect of the pole pieces. This latter correction was obtained experi-
mentally and, all in all, it was determined that the internal field for
optimum operation was of the order of 300 oersteds. For the given
ferrite and the I'ange of frequency of operation, this internal field corres-
ponds to the condition that \ ij.,- \ > | Av |, as stated above.
Taking all effects into account, it was found that optimum permanent
magnet design occurred for an air gap field of 660 oersteds.
886
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
_i
LLI
CO
o
UJ
Q
tf)
O
_l
Q
a.
<
cr
O
u.
ferrite: R)
4;rMs=t700 GAUSS
6r=0.160 IN.
h = 0.550 IN.
1 = 5.000 IN.
1
1
1
AT 5925 MC PER SECy
f
/
/
AT 6425 MC PER SEC
A
/
/
^ ^*w 660 OERSTEDS _^ ,
y^
0.4 0.8 1.2 1.6 2.0 2.4 2.8
MAGNETIZING CURRENT IN AMPERES
3.2
3.6
Fig. 7 — Forward loss versus magnetizing current.
Using the experimental values 4:tMs — 1,700 gauss and internal mag-
netic field = 300 oersteds, the frequency at which ferromagnetic reso-
nance occurs was estimated to be about 2200 mc/sec. This value is suf-ii
ficiently far from our operating range (5,925-6,425 mc/sec) that we|
would expect a negligible loss contribution due to resonance absorption.},
This is confirmed by the low forward loss actually observed.
B. Ferrite Height
We have already pointed out that when the ferrite height is reduced
from full height a more reasonable VSWR is obtained. This is due to the
fact that we have relieved the stringent boundary requirements at the
60
^ 50
LU
O
UJ 40
if! 30
(/)
o
_J
UJ 20
CO
CC
UJ
>
yj 10
(^
k.
660
OERSTEDS
^— -<
AT 6425 MC PER SEC
7
Fl
N
\,
/
l\
1 >
^_ __
N
k
AT 5925 MC PER SEcS;
^..
V
0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6
MAGNETIZING CURRENT IN AMPERES
Fig. 8 — Reverse loss versus magnetizing current.
THE FIELD DISPLACEMENT ISOLATOR
887
top and bottom faces of the ferrite and approach, in a sense, a less critical
rod type geometry. A ferrite height of 0.550" gave a VSWR -^ 1.05
(iver the band. With full height slabs (0.795"), A^SWR values as high
as 10:1 have been observed for typical geometries.
I j C. 8 and h
Experimentally, we have examined various ferrite thicknesses at dif-
ferent distances from the sidewall until optimum broadband performance
. jwas obtained. Table I shows the ferrite distance from the wall which
• I gave the best experimental results (highest broadband ratios, low for-
,ward loss, high reverse loss) for each thickness 8 of one of the BTL
I materials. It is interesting to note that the empirical ctuantity 8 -\- 6/2 —
I
Table I
5 (mils)
b (mils)
s + 1 (mils)
t (mils)
S + ~2t (mils)
201
11
206.5
3
200.5
189
35
206.5
3
200.5
186
42
207.0
3
201.0
176
65
208.5
3
202.5
189
42
210.0
6
198.0
2t, where t is the thickness of the resistive coating, is very nearly con-
stant (within a few mils) for the stated range of 8 and for this type of
[design.*
i In Section IV a theoretical calculation using the null condition at
i 6175 mc/sec for a full height ferrite gives
5 = 180 mils
b = 38.7 mils
so that 8 -f b/2 = 199.3 mils. In the theoretical case t is assumed to be
very small. It will be noted that the theoretical result for 8 + b/2 (with
small t) agrees quite well with the experimental 5 -f 6/2 — 2t. The ques-
tion of the possible phj^sical significance of this quantity is being
investigated.
D. Placement of Resistance Material and Choice of Resistivity
The propagating mode with a full height ferrite slab is of a TEo
variety, the zero subscript indicating that no variation occurs with re-
* In one design of the isolator we used a General Ceramics magnesium manga-
nese ferrite with 5 = 0.180", b = 0.074" and t = 0.009" so that 8 + b/2 - 2t = 199
mils, in good agreement with Table I.
888
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
Fig. 9 — Distribution of jsmall tangential electric fields at interior ferrite faceJ
Fig. 10 — Resistance configuration.
spect to height. A field null in this construction therefore extends across
the entire face of the full height ferrite and all of this face is then "active"
in the construction of an isolator. This field situation no longer accurately;
applies to the partial height slab. The departure of the ferrite from the
top wall creates large fringing fields extending from the ferrite edges, and
large electric fields may exist tangential to the ferrite face close to these
edges. We would therefore expect the null condition to persist only in a
small region about the vertical center of the ferrite face. We may, how-
ever, also expect longitudinally fringing modes (TM-like) to be scattered!
at the input edge of the ferrite slab so that a longitudinal field maximum
will exist at the central region of the ferrite. However, this is a higher:
mode, so that this maximum decays rapidly past the leading edge.
Considering all the effects, the distribution of small tangential electric
fields at the ferrite face may be expected to appear as shown in Fig. 9.
Experimentally, we have utilized this low loss region and have avoided
the decay region of the higher TM-like modes by using the resistance
configuration shown in Fig. 10. The resistivity is uniform and about 75
POLYSTYRENE-
COPPER PLATE
RESISTANCE STRIP
FERRITE
V/M///////^^^^J/^^^.';^/^J^^//^/////^^^^?^??j//?^/^9r»'/
m
Fig. 11 — Elimination of longitudinal components.
THE FIELD DISPLACEMENT ISOLATOR
889
30
25
20
15
10
FREQ
H
= 6425 MC
= 1150 OERSTEDS
477Ms= 1700 GAUSS
d= 0.180 IN.
h= 0.550 IN.
1=5.000 IN. /
A
k
/
s
\,
/
V
•
^^
■-— <
>
y
/
C
/
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
LENGTH OF LOSS FILM IN INCHES
4.5
5.0
5.5
Fig. 12 — Attenuation versus length of resistance strip.
'ohms/square. Variations of about d=30 ohms/square about this value
result in little deterioration in performance.
Some further discussion of the perturbed dominant mode is of interest.
jWe may think of the height reduction as primarily a dielectric discon-
itinuity where we have effectively added a negative electric dipole den-
Isity to a full height slab. Since this addition is smaller for the forward
case (where there was initially a small electric field) than for the reverse
case, we may expect the longitudinal components to be smaller for the
forward propagating mode. The other type of longitudinal electric field,
50
-I 40
O
UJ
O
, 30
If)
if)
O
-■ 20
LU
If)
a.
LU
I '0
a.^__
REVERSE LOSS
FORWARD LOSS
.J^
0.5
0.4
0.3
If)
If)
o
0.2
0.1
Q
a:
<
cc
o
5900 6000 6100 6200 6300 6400
FREQUENCY IN MEGACYCLES PER SECOND
Fig. 13 — Loss versus frequency.
6500
890
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
Fig. 14 — Isolator model.
which occurs due to the scattering of the TM-Uke lono;itudinal modes,
decays rapidly and is not of consequence in an experiment now to be
described. This experiment was designed to demonstrate the nonre-
ciprocal nature of the longitudinal electric fields associated with the dis-
torted dominant mode. It also shows that the existence of these com-
ponents is significant as a loss mechanism for the reverse direction of
propagation in the isolator. The geometry employed is shown in Fig. 11.
The copper plate was inserted to minimize longitudinal electric field
components, and we may therefore expect to obtain less reverse loss than
in the condition of its absence. The result of this experiment was that
the reverse loss decreased from about 25 db* without the plate to 18 db |
with the plate. The forward loss was unaffected.
E. Determination of Length
Given a dominant mode distribution in a waveguide, attenuation will
be a linear function of length, once this mode has been established. Con-
sequently, one would expect that doubling the loss film length would
double the isolator reverse loss. The isolator does not exhibit this be-
havior, however, as is illustrated in Fig. 12.
This occurrence might be explained by the appearance of still another
longitudinal mode, peculiar in form to gyromagnetic media alone, which
propagates simultaneously with the transverse electric mode, and is
essentially uncoupled to the loss material. The maximum reverse loss
* This experiment was conducted with a different ferrite than that employed ini'
the eventual design.
THE FIELD DISPLACEMENT ISOLATOR 891
thus obtainable is limited by the scattering into this mode. The charac-
ter of these singular modes will be discussed in a subsequent paper.
Results
The performance of the isolator as a function of frequency is shown
in Fig. 13. Fig. 14 shows a completed model of the isolator.
IV. FURTHER ANALYSIS
While an exact characteristic equation is obtainable for the overall
geometry of the full height isolator, including the lossy film, the ex-
pressions which result are sufficiently complex to be all but impossible to
handle. However, if the resistance film is chosen to have small conduc-
tivity we may utilize a simple perturbation approach in which the field
at the ferrite face is assumed to be unaffected by the presence of the
loss film. A quantity rj may then be defuied* so that
. = LM (IV- 1)
For small conductance values ri is proportional to attenuation to first
order in either direction of propagation, Er , in equation (IV ^ — ■ 1), is
the electric field adjacent to the film and P is the power flowing across
the guide cross section. The loss in the ferrite material is not taken into
account in this approximation, but it would naturally have a deteriorat-
ing effect on the isolator characteristics.
The ratio of the values of 77 corresponding to backward and forward
direction of propagation defines the isolation ratio, given in db/db, for
the limit of very small conductivity.
Fig. 15 shows a calculated curve of the forward value of 17 and Fig.
16 shows the backward case. The isolation ratio shown in Fig. 17 dem-
onstrates surprisingly large bandwidth for values of the order of 200
db/db. Fig. 18 portrays propagation characteritics for both forward
and backward power flows and provides the interesting observation, in
conjunction with Fig. 16, that peak reverse loss occurs in the neighbor-
hood of X = \g .
Fig. 19 is a plot of ai , the transverse wave number, over the fre-
quency range. The flatness of the forward wave number means that the
position of null moves very little with frequency across the band. Hence
the lossless transmission in the forward direction is broadband. Since
the forward and backward wave numbers have such radically different
See Appendix
892 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
0.6
0.5
0.4
^f
0.3
0.2
0.1
I
5800 5900 6000 6100 6200 6300 6400
FREQUENCY IN MEGACYCLES PER SECOND
6500
Fig. 15 — Relative attenuation — forward direction
rates of variation, a simple adjustment of parameters may be made to
cause the forward null and maximum reverse attentuation to appear
at the same frequency, resulting in an optimum performance.
The occurrence of the reverse maximum loss in the region of X = Xj
may roughly be explained as follows. As the transverse air wave number
decreases, the admittance of the guide, defined on a power flow basis,
increases. The electric field magnitude distribution must therefore gener-
ally decrease in such a fashion as to cause the overall power flow to re-
600
500
400
300
200
100
0
/^
^
s.
/
N
)
f
/
/
/
/
f
^
X
5600 5900 6000 6100 6200 6300 6400
FREQUENCY IN MEGACYCLES PER SECOND
6500
Fig. 16 — Relative attenuation — backward direction
THE FIELD DISPLACEMENT ISOLATOR
893
lU
5
^
V
2
^
^
<
o ^
<
cr 2
g 10^
1-
o
J
t-
\.
X.
/
^v
1
^
/
/
<0
2
5
/
/
/
2
10
v
/
1
5900 6000 6t00 6200 6300 6400
FREQUENCY IN MEGACYCLES PER SECOND
6500
Fig. 17 — Ideal isolation characteristics.
main constant.. On the other hand as the transverse air wave number
decreases through real vahies, the electric field adjacent to the ferrite
becomes relatively large. At X = X^ the distribution is linear with rela-
]\ tively large dissipation at the ferrite face. As the transverse air wave
number increases through imaginary values the distribution becomes
exponential such that the field adjacent to the ferrite is always the maxi-
mum for the air region and the growth of the field at the face of the
ferrite would not seem to be so great as formerly. One would therefore
expect a maximum reverse loss somewhere in the region X = Xy .
The abo^^e considerations plus the transcendental equation for the
null show consistency with the experimental design values which were:
8 = 0.180"
L = 1.59
47rilf s = 1 ,700 gauss
Using Hue = 000 oersteds in the calculation we obtain the spacing from
the guide wall h = 0.0387". The fact that we used 600 oersteds for the
full height slab calculation as opposed to the internal field of 300 oersteds
found experimentally for the partial height slab should not be a source of
confusion. It has been indicated earlier that the peak reverse loss shifts
894 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
1.4
t.2
1.0
0.8
0.6
0.4
0.2
^^
^
BACKWARD
PROPAGATION,^-^
^
^
-
m
'forward PROPAGATION
~""~"
...
5900
6000 6100 6200 6300 6400
FREQUENCY IN MEGACYCLES PER SECOND
6500
Fig. 18 — Ferrite isolator characteristics.
5800
5900 6000 6100 6200 6300
FREQUENCY IN MEGACYCLES PER SECOND
64001
Fig. 19 — Transverse characteristics of a ferrite isolator
THE FIELD DISPLACEMENT ISOLATOR 895
with ferrite height reduction. It is not inconsistent therefore to choose
600 oersteds for the full height analysis in contrast to the value deter-
mined from the experiment.
V. SCALING
Once the optimum set of parameters has been decided upon for a
given frequency range (e.g., 5,925-6,425 mc/sec, 5 = 0.180", b = 0.074",
( = 5", h = 0.550", 4wMs = 1,700 gauss, Hoc = 660 oersteds) it is a
simple matter to scale these parameters to other frecpency ranges. From
Maxwell's equations:
Curl H = icceE + gE
Curl^ = -iwT-H
where T is the permeability tensor, and g is the conductivity in mhos/
meter. The first of Maxwell's equations suggest that frequency scaling
may be accomplished by permitting both the curl and the conductance
to grow linearly with respect to frequency. The curl, which is a spatial
derivati^'e operator, may be made to increase appropriately by shrinking
all dimensions by a 1/co factor, which will keep the field configuration
the same in the new scale.
Having imposed this condition on the first equation we must satisfy
the second of Maxwell's equations by causing 7" to remain unchanged
with frequency. T is a tensor given as follows for a cartesian coordinate
system:
(Hr ikr 0\
-ikr Mr 0 (V— 1)
0 0 1/
for a magnetizing field in the z direction. The components may be ex-
panded in the following fashion:
Mr =
4
X
^ ^ (V— 2)
h =
CO
m - ^
896 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
where AtMs is the saturation magnetization in gauss and y is the mag-
netomechanical ratio. The Polder tensor evidently remains unchanged
if Ms and H are both scaled directly with frequency.
Since the field distributions are assumed unchanged relative to the
scale shift, normal and tangential E and H field components continue
to satisfy the appropriate boundary equalities at interfaces. Then, in-
voking the uniqueness theorem, the guide characteristics are only as
presumed and the model has been properly scaled as a function of fre-
quency.
The scaling equations are:
di
=2
C02
d2
gi
=
032
92
Ms,
=
CO2
Ms,
Ho)i
=
COl
C02
{Ho)2
(V-3)
where d is any linear dimension.
CONCLUSION
An isolator with low forward loss and high reverse loss can be con-
structed by a proper choice of parameters. Once a suitable design has
been reached the scaling technique can be used to reach a suitable design
for other frequencies.
As yet, a theoretical analysis of this problem has been carried out only
for a full height ferrite.
ACKNOWLEDGMENT
We would like to thank F. J. Sansalone for his assistance in developing
the field displacement isolator. We would also like to thank Miss M. J.
Brannen for her competent handling of the numerical computations.
APPENDIX
It is desirable to establish an isolator figure of merit. A simple quan-
tity characterizing the isolator action is the normalized rate of power
THE FIELD DISPLACEMENT ISOLATOR
897
loss in the resistive strip, for an idealized ferrite, in the low conductive
limit of such a strip. Let
12
Er
V =
where 77 is the appropriate quantity, Er is the field at the resistance, and
P is the total power flow across the guide cross-section. This figure of
merit is related to the rate of change of the attenuation constant (A)
with respect to strip conductance in the following manner:
p = 0.0434377/1 (db)(ohms)/cm
where h is the fractional height of the loss strip, and g is the reciprocal
of the surface resistivity in ohms/square.
The total power flow may be divided into integrations of the Poynting
vector over the three regions of the guide cross-section. The following
results are obtained normalized to Er = sin aia:
Region 1: 0 ^ a; ^ a
p (1) _
Region 2: a ^ x ^ a -\- 8
(2) /3 / /Xr3
^
2co/xo
/ sin 2aia\
V 2^7
/ , 2 , , 2n , sin 2a28
fXridi^ — di) — -^ a2{2did^
+
1 — cos 2a25
y.r{2dd2) + ^ id,' - d,')
Region Z: a -\- b ■^ x S L
p (3) _
^y —
/3
2cJ)Uo
h -
sin 2 a]b\ {d\ cos aih -\- di sin a-^
where
and
2q;i
d\ = sin aia
sin aj)
do =
yird-l
[{nr — kr)oci cos aitt -f- /cr/3 siu aia]
898
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
BIBLIOGRAPHY
1. Tellegen, B. D. H., Philips Res. Rep., 3, 1948.
2. Hogan, C. L., B.S.T.J. 31, 1952.
3. Fox, A. G., Miller, S. E., and Weiss, M. T., B.S.T.J. 34, p. 5., Jan. 1955.
4. Turner, E. H,, URSI Michigan Symposium on Electromagnetic Theory, June,
1955.
5. Polder, D., Phil. Mag., 40, 1949.
6. Lax, B., Button, K. J., Roth, L. M., Tech Memo No. 49, M.I.T. Lincoln Lab-'
oratory, Nov. 2, 1953.
7. Kittel, C, Phys. Rev., 73, 1948.
Transmission Loss Due to Resonance
of Loosely-Coupled Modes in a
Multi-Mode System
By A. P. KING and E. A. MARCATILI
(Manuscript received Januarj' 17, 1956)
In a multi-mode transmission system the presence of spurious modes
which reso7iafe in a closed environment can produce an appreciable loss to
the principal mode. The theory for the evaluation and control of this effect
under certain conditions has been derived and checked experimentally in
the particularly interesting case of a TEoi transmission system, where mode
conversion to TE02 , TE03 • • • is produced by tapered junctions between
two sizes of waveguide.
INTRODUCTION
In a transmission system, the presence of a region which supports
one or more spurious modes can introduce a large change in the trans-
mission loss of the principal mode when the region becomes resonant for
one of the spurious modes. This phenomenon can occur even when the
mode conversion is low and the waveguide increases in cross section
smoothly to a region which supports more than one mode. In general,
the conditions required to resonate the various spurious modes are not
fulfilled simultaneously and, in consequence, interaction takes place
between the principal mode and only one of the spurious modes for each
resonating frequency. Under these conditions the resonating environ-
ment can be visualized as made of only two coupled transmission lines,
one carrying the desirable mode and the other the spurious one. This
simplification makes it possible to calculate the transmission loss as a
function of (1) the coefficient of conversion between the two modes and
(2) the attenuation of the modes in the resonating en\-ironment. The
theory has shown good agreement with the measurement of transmission
loss of the TEoi mode in a pipe wherein a portion was tapered to a larger
diameter which can support the TE02 mode.
899
900
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
TRANSMISSION LOSS OF A WAVEGUIDE WITH A SPURIOUS MODE RESONATING
REGION
Let US consider a single-mode waveguide connected to another of
different cross-section that admits two modes. Since these two modes
are orthogonal, the junctions may be considered as made of three single-
mode lines connected together, provided we define the elements of the
scattering matrix properly. The three modes, or lines in which they
travel, are indicated by the subscripts 0, 1, and 2, as shown in Fig. 1.
If ao , tti , Qi and 6o , &i , ?>2 are the complex amplitudes of the electric
field of the incident and reflected waves respectively, then
"6o'
ao
6i
= [S]
ai
h.
_«2_
where
Too Foi ro2
[S] = Toi Tu ri2 (1)
_ro2 Flo r22_
is the scattering matrix.^
This specific type of change of cross section may be treated as a
three-port junction.
Now, if a length / of a two mode waveguide is terminated sym-
metrically at both ends mth a single mode waveguide (Fig. 2), each
joint is described by the same matrix (1), and the connecting two mode
wave guide has the following scattering matrix:
(10
0
e-'"'
0
0
^-m
0
0
0
0
0
0
e
0
0
^-ie.
0
in which
je, = y,(. = («i +JiSl)f
je2 = 72^ = (a2 + jS-^t,
7i and 72 are the propagation constants of modes 1 and 2.
• N. Marcuvitz, Waveguide Handbook, 10, M.I.T., Rad. Lab. Series, McGraw-
Hill, New York, 1951, pp. 107-8.
TRANSMISSION LOSS DUE TO RESONANCE OF CONVERTED MODES 901
Matrices 1 and 1' describe the system completely and from them, the
transmission coefficient results,
ao
— 1 oie
rlze
-jlBiA*
1 +
ri2
1 22
1 Too
r*
1 02
r22
o ri2
(2)
[1 - (r?2 - TnT,,)e-'''^^'''Y - (rue"^'' + r226-^''^)^
where
A = 1 +
£02^
.roi/
-y(92-«i)
A * is the complex conjugate of A
Toi* is the complex conjugate of Toi
ro2* is the complex conjugate of ro2
Furthermore, let us make the following simplifying assumptions
I
|ro2
/3=2
|3=0 I^U,
-,/l.
00 = 0
(3)
«1
(4)
if w = n = 0, 1, 2
(5)
if m ^ n
Equation (3) indicates that if in Fig. 1, lines 1 and 2 were matched,
line 0 would also be matched looking toward the junction. Equation (4)
states that almost all the transmission is made from 0 to 1 , or that there
is small mode conversion to the spurious mode 2. Equation (5) assumes
that the transition is nondissipative. The first two conditions are ful-
filled when the transition is made smoothly. The last is probably the
most stringent one, especially if the transition is a long tapered wave-
guide section, but it is always possible to imagine the transition as
lossless and attribute its dissipation to the waveguides.
0- —
- — bo ^ — aa
—2
Fig. 1 — Schematic of a three-port junction.
902
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 195G
From (2), (3), (4) and (5)
V =
I r,o |2
2|ri.2|2(l - cos ^)
1 +
T22
J«l12
1 - [rooe"' - + Tne"''']
(6)
Avliere
i 22 1 22 6
(f = 61 — 02 — <pn ~{~ <P
22
111 order to understand this expression physically, let us suppose first
that there is no attenuation. The transmission coefl&cient r becomes 0
when the following equations are fulfilled simultaneously
and
182^ — <P22 = PT
(f = (2q -\- l)x
p = 0, 1,2, 3--- (7)
5 =^ 0, 1,2, 3 ••• (8)
The first of these equations states that the line carrying the feebly
coupled mode must be at resonance, since this condition is satisfied when
the electric length of this line is modified by a multiple of tt radians. The
second condition, (8), implies that both paths, in lines 1 and 2, must
differ in such a way that electromagnetic waves coming through them
must arrive in opposite phase at the end of the two-mode waveguide.
This is quite clear if we think that, in order to get complete reflection,
signals coming through lines 1 and 2 must recombine again Avith the
same intensity and opposite phase. In order to get both modes with the
same intensity, the converted mode must be built up through resonance;
the opposite phase is obtained by an appropriate electric length adjust-
ment. When attenuation is present, F will not be 0, and conditions (7)
and (8) for minimum transmission are modified only slightly if the
0--
ap — » D,^-^ bp — »
•* t)o ^ 32
* — l--- *
Fig. 2 — Schematic of a two-mode waveguide terminated symmetrical!}' on
each side with a single-mode waveguide.
TRANSMISSION LOSS DUE TO EESONANCE OF CONVERTED MODES 903
ATTENUATION OF SPURIOUS MODE IN DECIBELS
Fig. 3 — • Relative insertion loss as a function of the spurious mode attenuation
and mode conversion level.
attenuation is low, but the general interpretation of the phenomenon is
still the one given above.
From (6) we can calculate the extreme values of | r | differentiating
with respect to I, and we define the relative insertion loss I in db, as the
ratio between the minimum and maximum transmitted power expressed
in db.
7 = 20 log
10
i min
r
■•■ max
= 20 logio ^
1
2 1 ri2 Kl + cosh at)
1 - c' I r
22
2 —2a'>t
1 -
2|ri2|2(l - cosha^)
(9)
l + B'\ r22 Ye
2 — 2a2^
where
E = 1 +
ri2
•l 22
-at
C
1 -
ri2
i 22
-a(
a = ai — a2
For the most important practical case, that is, when the maximum value
attainable by cosh aC is of the order of 1, and knowing from (3), (4) and
(5) that
12
ro2 r (1 - I ro2 p)
r22 1' ^ 1 - 2 I ro2
904
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
7^201ogio(l + 2lro2re""0
(10)
1 -
2 I ro2 Kl + cosh ap \
1 _ e-2"2^ + 2 I ro2 I'd + e-"')e-'"''l
From this expression we deduce
(a), / is strongly reduced when a^C » ro2.
^ (b), Attenuation in line 1 is not an important factor until ail and
I ck:i — a2 1 ^ ^re of the order of 1 . In other words, for low attenuation in
both lines, aot assumes a major importance in the determination of I
because it influences the conditions of resonance. That the effect of ail
is small is shown in Fig. 3 (dotted line for the particular case ai = 0:2/4).
In order to handle the general problem, (10) has been plotted in Fig.
3. We can enter with any two and obtain the third following quantities:
Zi , relative insertion loss in db; 10 logio e~^"^ , attenuation in db of the
spurious mode in the resonating environment; and 20 logio ro2 conversion
level at the junction, in db, of power in the spurious mode relative to
that in the first line.
APPLICATION OF THESE RESULTS TO A TEqi TRANSMITTING SYSTEM
The results of the preceding section have been checked experimentally
by measuring the relative insertion loss of different lengths of %" di-
ameter round waveguide tapered at both ends to round waveguides of
J4.6" diameter. This waveguide is shown in Fig. 4 with a schematic
diagram of the measuring set. In the round transmission line A-B,
section A will propagate only TEoi . Section B, which has been expanded
by means of the conical taper Ti , can support TE02 and TE03 in addition
to the principal TEoi mode. This section is a closed region to the spurious
modes ( TE02 , TE03) whose length can be adjusted to resonate each one
of these modes. A sliding piston provides a means for varying the
length, /, of section B.
&^
T
T
X
fl e-
./^
1
2
r~y
TE
01
B
TEo,
TE02
TE03
1
RECEIVER
Fig. 4 — Circuit used to measure TEoi insertion loss due to resonance of the
TE02 and TE03 modes.
TRANSMISSION LOSS DUE TO RESONANCE OF CONVERTED MODES 905
•lOr
U°
-12
-14
-16
-16
-20
-22
-24
-26
-28
O -30
O
^ -32
-34
-36
-38
-40
-42
-44
■46
-48
-50
\\
1
;
PtEo2 /
PtEo3 (
\
\
hTEo,-|.
t
d
\
\^
s.
*- L
\
\
k
\
\
i
\
\
\
\
\
\
^
s
\
\
k
\
\
\
\ \
\ \
\ \
\
\
\
\
\
\
\
\
\
\
s
\ \^°'
\
TEo\ \
<d-^
tl
\
\
\
\
\
\
rPni
x
\ '^
\
\
\TEo3
\
\
JL"\
8 >
\^
D = 2"
TEo)
\
\
V "7"
7"
\T6
\
\
V
\
7
k
\
\
1
\
\
\
\
k
\TEo3
ie
\
\
V"
\
\
\
V
\
\
\
7"\
8
\
\
\
\
k
d=*-^
V
\
\ \
\ \
\ V
\
\
\
\^ 8
\ \
\ \
\
\
\
\
\
\
1
1
\
\
\
1
1
0.1
0.2 0.3 0.4 0.6 0.8 1.0 2 3
TAPER LENGTH, L, IN METERS
5 6 8 10
Fig. 5 — Mode conversion of TE02 and TE03 relative to TEoi generated by a
conical taper.
The relative levels of TE02 and TE03 conversions, which have been
calculated from unpublished work of S. P. Morgan are shown plotted in
Fig. 5 for the waveguide sizes employed in the millimeter wavelength
band. The conversions, 20 logio ro2 , are plotted in terms of the TE02
and TE03 powers relative to the TEoi mode power and are expressed in
db as a function of the taper length L, in meters.
Fig. 6 shows the theoretical and experimental values obtained for
TEoi relative insertion loss. Since the minimum length of pipe tested is
906
THE BELL SYSTEM TECHNICAL JOUENAL, JULY 1956
-102
8
UJ
u
UJ
O
to
to
o
-10
z
o
z
>
<
_l
cr
-t
TEo2
ATTENUATION
RELATIVE
INSERTION
-
/
l(M) (DB)
0.37 -0.024
1.135 -0.074
2.39 -0.157
3.73 -0.245
LOSS (DB)
-6.0
-3.2
- 1.7
- 1.3
-
EXPERIMENTAL .
DATA ^
\
2
3
-
-
'N,
^
^
V
ro2=-27DB
-
N
-
X
-
1 N
N
-
^
N
\
2
\
\,
EORETICAL VALUES
lASURED VALUES
\
4
o ME
-
\
-
s
-
,
1
1
_L
1
1
1
_L
1
1
1
1
\
I
1
-10"
6 8-,
-10 2
-10
■1
ATTENUATION OF SPURIOUS MODE IN DECIBELS
Fig. 6 Theoretical and measured relative insertion loss in the TEoi trans-
mission system of Fig. 4.
several times the length of the tapers, the losses in the transitions are
fairly small compared to the losses in the multimode guide and this
justifies assumption (5). The resonance due to the other modes is too
small to be appreciable. This is understandable since, according to (10),
the value of the mode conversion for the TE03 (Fig. 5) and the attenua-
tion for the shortest length of pipe tested, the calculated relative inser-
tion loss is less than —0.1 db.
CONCLUSIONS
The resonance of spurious modes in a closed environment can produce
a large insertion loss of the transmitting mode. In a fairly narrow band
device it is possible to avoid this problem by selecting a proper wave-
guide size for the closed environment. In a broad-band system the losses
can be minimized by providing a high attenuation and a low mode con-
version for the spurious mode. For example, it may be noted, by refer-
ring to Fig. 3, that mode conversion as high as —20 db with a spurious
mode loss of — 8 db results in only an —0.1 db insertion loss for the
transmitting mode.
Measurement of Atmospheric Attenuation
at Millimeter Wavelengths
By A. B. CRAWFORD and D. C. HOGG
(Manuscript received September 20, 1955)
A frequency -modulation radar technique especially suited to measure-
ment of atmospheric attenuation at millimeter wavelengths is described.
This two-way transmission method employs a single klystron, a single an-
tenna and a set of spaced corner reflectors whose relative reflecting properties
are known. Since the method does not depend on measurements of absolute
antenna gains a7id power levels, absorption data can he obtained more
readily and with greater accuracy than by the usual one-way transmission
methods.
Application of the method is demonstrated by measurements in the 6 -mm
to 6-mm wave band. The residts have made it possible to assign an accurate
value for the line-breadth constant of oxygen at atmospheric pressure; the
constant appropriate to the measurements lies between 600 and 800 MCS
per atmosphere.
INTRODUCTION
It is well known that certain bands in the microwave region are at-
tenuated considerably due to absorption by water vapour and oxygen
in the atmosphere. A theory of absorption for both gases was given by
Van Vleck.^ Numerous measurements have been made on the gases when
confined to waveguides or cavities- and several when unconfined in the
free atmosphere.^ Nevertheless, there is some uncertainty regarding the
line-breadth constants which should be used in calculating water vapour
and oxygen absorption. In particular, at atmospheric pressure there is
doubt as to the amount of absorption on the skirts of the bands where
the absorption is small. The present work was undertaken to test a new
method of measurement and to improve the accuracy of experimental
data measured in the free atmosphere.
The method of measurement is one of comparison of reflections from
907
908 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
spaced corner reflectors whose relative reflecting properties are known.
The free-space attenuation is readily calculated and any measured at-
tenuation in excess of this represents absorption by the atmospheric
gases.
A description of the method and the apparatus is followed by a dis-
cussion of data taken in the wavelength range 5.1 to 6.1 mm (which in-
cludes the long wavelength skirt of the oxygen absorption band centered
at 5 mm). These data, when compared with the theory,^ indicate that
the line-broadening constant of oxygen at atmospheric pressure is of
the order of 600 mc. Some rain and fog attenuation measurements at a
wavelength of 6.0 mm are included.
METHOD
The experimental setup is shown in Fig. 1. It consists of a high-gain
antenna for both transmitting and receiving and a pair of spaced corner
reflectors. Corner reflectors can be built to have good mechanical and
electrical stability, and their reflecting properties are relatively insensi-
tive to slight misalignments. The reflectors are mounted well above the
ground to ensure free-space propagation conditions.
At the outset, the relative reflecting properties of the corner reflectors
are measured by placing them side by side at a convenient distance (cfi
for example) from the antenna. By alternately covering one and the other
with absorbent non-reflecting material and measuring the reflected sig-
nals, the relative effective areas are determined. The reflectors are then
separated as shown and consecutive measurements are made of the sig-
nals returned from each reflector. From these measurements, knowing the
distances di and d^ and the calibration of the reflectors, one determines
the attenuation over the path d2-di in excess of the free-space attenua-
tion.* This excess, in the absence of condensed water in the air, repre-
sents absorption by the atmosphere.
The power received from the reflector at distance di is,
A' A,''
Pi = Pt -tt^- Q(K dd
X di
where A and Ai are the effective areas of the antenna and corner-reflector respec-
tively, and Pr is the transmitted power; Q(\, d\) is a loss factor which accounts
for atmospheric absorption. A similar relation holds for the power received from
the reflector at distance ^2 . The ratio of the received powers is then,
'2 [aJ \dj
f^= (t^) It) QlKid^"- d.)\
ATMOSPHERIC ATTENUATION AT MILLIMETER WAVELENGTHS
909
The accuracy of the measurements Avill be affected, of course, by spuri-
ous refiections in the neighborhood of the corner-refiectors. The sites for
the experiment were chosen to minimize such refiections and checks were
made by observing the decrease in the return signals when the corner-
refiectors were covered by absorbent material. In all cases, the back-
ground reflections were at least 30 db below the signal from the corner-
reflector.
The method of measuring the reflected signals is illustrated in Fig. 2.
The transmitted signal is frequency modulated in a saw tooth manner
with a small total frequency excursion, F. The signal reflected from the
near corner-reflector is delayed \ni\\ respect to the transmitted signal
by a time, n , equal to twice the distance to the reflector divided by the
velocity of light. During a portion, Ti — rx , of the sa^^i:ooth cycle, there
is a constant frequency difference, /, between the transmitted and re-
ceived signals, {f/F = ti/Ti). Power at this frequency is produced by
mixing the initial source signal with the delayed received signal and am-
plifying the difference frequency in a narrow-band amplifier centered at
frequency /. The output of this amplifier is, therefore, a pulse at fre-
quency /, of length Ti — n and repetition rate 1/Ti .
To measure the signal returned from the far corner-reflector it is neces-
sary merely to increase the period of the sawtooth modulation propor-
tionate to the increase in distance. The frequency excursion, F, re-
mains the same; hence the average power output of the transmitter is
unchanged. As may be seen in Fig. 2, the freciuency difi"erence, /, between
the transmitted and received signals is unchanged; thus the same am-
plifier and output meter can be used for the two cases. Another advan-
tage in changing only the sawtooth repetition rate is that the delay is
the same fraction of a period in both cases; therefore the duty cycle is
unchanged and the intermediate frequency pulses can be detected by
either an average or a peak measuring device.
Since the beat frequency, /, is not affected by slow changes in the fre-
ANTENNA
EFFECTIVE AREA
CORNER REFLECTOR
R1
EFFECTIVE AREA At
SOURCE
\>-
-d,-
HI
_i_
CORNER REFLECTOR
R2
EFFECTIVE AREA Ag
Fig. 1 — Siting arrangement for the atmospheric absorption measurements.
910
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
qiiency of the transmitter, the bandwidth of the intermediate frequenc}^
amplifier need be only wide enough to take care of non-linearity in the
sawtooth modulation. A signal-to-noiso advantage is obtained by the
use of the narrow-band amplifier.
Table I gives the distances, heights and effective areas of the reflectors
as well as the sa^^iiooth repetition rates that were used in the experiment.
The frequency excursion of the sawtooth modulation was 5.8 mc.
It will be noted that three reflectors were used; this was done to pro-
vide a long path (comparison of reflections from Rl and 7?3) for wave-
lengths at which the absorption was relatively low, and a short path
(comparison of Rl and R2) for wavelengths at which the absorption was
high. The small reflector, Rl, was one foot on a side; the large reflectors,
7?2 and i?3, were about 5.6 feet on a side. Fig. 3 is a set of side-by-side
measurements sho^^ing the reflecting properties of the large reflectors
relative to the small one for the wavelengths at which they were used.
J
APPARATUS
A schematic diagram of the wa^•eguide and electronic apparatus is
shown in Fig. 4; Fig. 5 is a photograph of the waveguide eciuipment so
mounted that it moves as a unit with the horn antenna. The antenna is
adjusted in azimuth and elevation by means of the milling ^-ise at the
bottom of the photograph. The box at the left contains the transmitting
tube, a low voltage reflex klystron* which has an average power output
of about 12 milliwatts over its 5.1- to 6.1-mm tuning range. About 2 mil-
liwatts of the klystron output is fed through a 6-db directional coupler
to a balanced converter that contains two wafer-type millimeter rectifier
units, t The remainder of the power proceeds into a 3-db coupler which
TRANSMITTED DELAYED
SIGNAL RETURN SIGNAL
1 1
' 1 ^/
-1 /
/ X
>\ /
A ^
y^
-.^ 1
\ //
1 1 / /
1 »x /
1 y ^
1 //
1 F
^X-
y
y/
\ A/
//
/' '
y^
^-'f
^
y'
/ u
/v
f 1/
/v ;
^^"^
0^ 1^'
^--T,— -
T\W
TIME *■
<
-T2 — -
— >
<72>
%
NEAR REFLECTOR
FAR REFLECTOR
Fig. 2 — Transmitted and reflected frequency-modulated signals.
* This klystron was developed by E. D. Reed, Electron Tube Development
Department, Murray Hill Laboratory.
t These millimeter-wave rectifiers were developed by W. M. Sharpless, Radio
Research Department, at the Holmdel Laboratory.
ATMOSPHERIC ATTENUATION AT MILLIMETER WAVELENGTHS
Table I
911
Reflector
Distance
Height
Effective Area
(Average)
Sawtooth
Rep. Rate
Intermediate
Frequency-f
Rl
R2
R3
km
di = 0.59
do = 1.36
ds = 2.87
m
6.7
21.5
75
«»2
0.05
0.67
0.79
kc
33
14.4
6.8
kc
750
750
750
has the antenna on one arm and an impedance composed of an adjustable
attenuator and shorting phniger on another arm. This impedance is ad-
justed to balance out reflections from the antenna so that a negligible
amount of the power flowing toward the antenna enters the converter
which is on the remaining arm of the coupler. The delayed energy that
re-enters the antenna after reflection from a corner reflector passes
through the 3-db coupler to the converter.
The intermediate frequency amplifier shown in Fig. 4 operates with a
bandwidth of 300 kc centered at/=750 kc. The output of the amplifier
is fed to a sciuare law detector and meter for accurate measurement and
to an oscilloscope for checking operation of the equipment. Oscillograms
of the pulses obtained from the three corner reflectors are shown in Fig. 6;
these are all on the same time scale. The gap between the pulses is the
delay, r, shown schematically in Fig. 2.
12.6
12.4
IXJ
o
LU
Q
z
<
LU
<
12.2
12.0
11.8
u
LU
<
CC
1.5
11.4
1.2
11.0
\
A? A,
"-— ^, — ^ THEORETICAL
A, A,
<
<^
y
\
1
1
Y
A3 \
-r^ MEASURED^
A,
\,
s
J.
b
K
/-
/^- MEASURED
r A,
\
V
5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1
WAVELENGTH, \, IN MILLIMETERS
Fig. 3 — Calibration of corner-reflectors R2 and R3 using Rl as a standard.
912 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
SAWTOOTH
GENERATOR
SYNC
OSCILLOSCOPE
^
r
DETECTOR
AMPLIFIER
f = 750 KC
PRECISION
ATTENUATOR
BALANCED TO
UNBALANCED
TRANSFORMER
HYBRID .
JUNCTION
[>
\
-0
BALANCED
CONVERTER
X
REED
KLYSTRON
6DB
COUPLER
RECORDER
METER
ADJUSTABLE
SHORT
X
3 DB
COUPLER
ANTENNA
Fig. 4 — Schematic diagram of frequency-modulation radar.
Fig. 5 — Waveguide apparatus and antenna.
'
ATMOSPHERIC ATTENUATION AT MILLIMETER WAVELENGTHS
913
^^- W^ -^W S
: li Wi W^- WmWai 'i^
Rl
R3
Fig. 6 — 750-kc pulses corresponding to the data in Table I.
Fig. 7 shows the conical horn-lens antenna supported by two bearings
to allow adjustment of azimuth and elevation angles. The aperture of
the antenna is fitted with a polyethylene lens 30 inches in diameter. The
antenna has a gain of about 51 db and a beam width of about 0.5 degrees
in the middle of the 5- to 6-mm wave band. This narrow beam, together
wath well-elevated reflectors, essentially eliminated ground reflections
from the measurements.
%iM -^ ..«S.JS
Fig. 7 — Conical horn-lens antenna and mount.
914
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
ID
r
14
r
1
13
p
f
A
»^~x
12
3
Y /
/
y
' /
/
/
1 i
f
1 1
It
6
J
1
5
/
r
1 1
11
1
f a
4
^
'/
^^m^"
0
^ r
48 49 50 51 52 53 54 55 56 57 58 59
FREQUENCY IN KILOMEGACYCLES PER SECOND
60 61
Fig. 8 — Calculated and measured absorption by air at sea level. The dots
represent the experimental data; the vertical lines indicate the spread in the meas-
ured values. Curves A and B are calculated curves of oxygen absorption using
line-breadth constants of 600 and 1200 mc, respectively^, and a temperature of
293° K. (Courtesy of T. F. Rogers, Air Force Cambridge Research Center.)
RESULTS
The data to be discussed are shown in Fig. 8; they were taken at Hohn-
del, N. J., during the months of December, 1954, and January, 1955, on
days when the temperature was between 25 and 40 degrees Fahrenheit ;
the absolute humidity was less than 5 grams/meter^ during the measure-
ments. It is believed, therefore, that the resonance of the oxygen mole-
cule is the main contributor to the absorption.
The spread in llie measurements is indicated by vertical lines through
the average values. Each point represents an average of six or more meas-
m'oments taken on different days. In the range 49 to 54.5 kmc, (5.5 to
ATMOSPHERIC ATTENUATION AT MILLIMETER WAVELENGTHS 915
'6 1 1 1 1 1 1 1 1 1 1 rr — I 1 i
1 1 r
"I r
._ SEA LEVEL
_---8 KILOMETERS
,--11 KILOMETERS
.--32 KILOMETERS
50
52
54 56 58 60 62 64 66
FREQUENCY IN KILOMEGACYCLES PER SECOND
68
70
Fig. 9 — Calculated curves of oxygen absorption at various altitudes for a
line-breadth constant of 600 megacycles and a temperature of 293° K. (Courtesy
of T. F. Rogers, Air Force Cambridge Research Center.)
6.1 mm) the measurements were highly consistent, due mainly to the
longer path that was used. Errors in the absolute values of the absorption
are estimated not to exceed ±0.05 db/km in the 49 to 54.5 kmc region,
±0.25 db/km in the 55.5 to 59 kmc region. The errors in absolute absorp-
tion are governed mainly by the structural and thermo-mechanical sta-
bility of the corner reflectors.
-I
o
Q
0
-2
-4
-6
10
16
/^
\
\
A~^
A
/
\
y
I
/^
J n
/
iry
\
/
\
a/
V
\i\
V
\
a/
\j>A
y "
v/v
V/~v^
r
3:20
3:30
3:40
3:50 4:00
TIME OF DAY. P.M.
4:10
4:20
4:30
Fig. 10 — Attenuation of 6.0-mm radiation caused by a light rain.
Round-trip path length = 2.72 kilometers
Average rainfall rate = 5 millimeters per hour
916 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 195G
Table II
Approximate Optical Visibility
(miles)
Attenuation due to Land Fog DB/KM
0.06
0.13
0.22
In Fig. 8, measured values are compared with the theory of Van Vleck
as calculated by T. F. Rogers using line-breadth constants of 600 mc
and 1200 mc per atmosphere. The fit with the 600-mc curve is good from
49 to 55.5 kmc, but discrepancies are evident between 56.5 and 59 kmc.
For completeness, Rogers' calculations for the absorption at higher alti-
tudes are reproduced in Fig. 9.
A few continuous recordings of rain attenuation have been made at a
wavelength of 6.0 mm; a record taken during a light rain is shown in
Fig. 10. The median value of the signal is —6.7 db which corresponds to
an attenuation of 2.5 db/km for this 5 mm per hour rainfall. During more
intensive rainfalls, short-term attenuations in excess of 25 db/km have
been observed.
On one occasion, it was possible to measure attenuation by land fog.
The measurements given in Table II were made at a wavelength of 6.0
mm. No information regarding water content or drop size was available
for this fog.
CONCLUSION
A frequency-modulation, two-way transmission technique has proven
reliable for measurement of atmospheric attenuation at millimeter wave-
lengths. Prerequisite to the success of the method are corner reflectors
with good mechanical, thermal and electrical stability.
The frequency-modulation method has been demonstrated by absorp-
tion measurements in the free atmosphere in the 5.1- to 6.1-mm band.
The data thus obtained are in good agreement with Van Vleck 's theory
of oxygen absorption; the line-breadth constant appropriate to the meas-
urements lies between 600 and 800 mc per atmosphere.
REFERENCES
1. J. H. Van Vleck, Phys. Rev., 71, pp. 413 ff, 1947.
2. R. Beringer, Phys. Rev., 70, p. 53, 1946. R. S. Anderson, W. V. Smith and W.
Gordy, Phys. Rev. 87, p. 561, 1952. J. O. Artman and J. P. Gordon, Phj^s.
Rev., 96, p. 1237, 1954.
3. R. H. Dicke, R. Beringer, R. L. Kyhl, A. B. Vane, Phys. Rev., 70, p. 340, 1946.
G. E. Mueller, Proc. I.R.E., 34, p. 181, 1946. H. R. Lament, Phys. Rev., 74,
p. 353, 1948.
A New Interpretation of Information Rate
By J. L. KELLY, JR.
(Manuscript received March 21, 1956)
7/ the input symbols to a communication channel represent the outcomes
of a chance event on which hets are available at odds consistent with their
probabilities (i.e., "fair'' odds), a gambler can use the knowledge given
him by the received symbols to cause his money to grow exponentially. The
maximum exponential rate of growth of the gambler's capital is equal to
the rate of transmission of information over the channel. This result is
generalized to include the case of arbitrary odds.
Thus we find a situation in which the transmission rate is significant
even though no coding is contemplated. Previously this quantity was given
significance only by a theorem of Shannon's which asserted that, with suit-
able encoding, binary digits coidd be transmitted over the channel at this
rate with an arbitrarily small probability of error.
INTRODUCTION
Shannon defines the rate of transmission over a noisy communication
channel in terms of various probabilities. This definition is given sig-
nificance by a theorem which asserts that binary digits may be encoded
and transmitted over the channel at this rate with arbitrarily small
probability of error. Many workers in the field of communication theory
have felt a desire to attach significance to the rate of transmission in
cases where no coding was contemplated. Some have even proceeded
on the assumption that such a significance did, in fact, exist. For ex-
ample, in systems where no coding was desirable or even possible (such
as radar), detectors have been designed by the criterion of maximum
transmission rate or, what is the same thing, minimum equivocation.
Without further analysis such a procedure is unjustified.
The problem then remains of attaching a value measure to a communi-
^ C. E. Shannon, A Mathematical Theory of Communication, B.S.T.J., 27,
pp. 379-423, 623-656, Oct., 1948.
917
918 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 195G
cation system in which errors are being made at a non-negligible rate,
i.e., Avhere optimum coding is not being used. In its most general formu-
lation this problem seems to have but one solution. A cost function must
be defined on pairs of symbols which tell how bad it is to receive a cer-
tain symbol when a specified signal is transmitted. Furthermore, this
cost function must be such that its expected value has significance, i.e.,
a system must be preferable to another if its average cost is less. The
utility theoiy of Von Neumann shows us one way to obtain such a cost
function. Generally this cost function would depend on things external
to the system and not on the probabilities which describe the system, so
that its average value could not be identified with the rate as defined
by Shannon.
The cost function approach is, of course, not limited to studies of com-
munication systems, but can actually be used to analyze nearly any
branch of human endeavor. The author believes that it is too general to
shed any light on the specific problems of communication theory. The
distinguishing feature of a communication system is that the ultimate
receiver (thought of here as a person) is in a position to profit from any
knowledge of the input symbols or even from a better estimate of their
probabilities. A cost function, if it is supposed to apply to a communica-
tion system, must somehow reflect this feature. The point here is that
an arbitrary combination of a statistical transducer (i.e., a channel) and
a cost function does not necessarily constitute a communication system.
In fact (not knowing the exact definition of a communication system
on which the above statements are tacitly based) the author would not
know how to test such an arbitrary combination to see if it were a com-
munication system.
What can be done, however, is to take some real-life situation which
seems to possess the essential features of a communication problem, and
to analyze it without the introduction of an arbitrary cost function.
The situation which will be chosen here is one in which a gambler uses
knowledge of the received symbols of a communication channel in order
to make profitable bets on the transmitted symbols.
THE GAMBLER WITH A PRIVATE WIRE
Let us consider a communication channel which is used to transmit the
results of a chance situation before those results become common
knowledge, so that a gambler may still place bets at the original odds.
Consider first the case of a noiseless binary channel, which might be
^ Von Neumann and Morgenstein, Theory of Games and Economic Behavior,
Princeton Univ. Press, 2nd Edition, 1947.
A NEW INTERPRETATION OF INFORMATION RATE 919
used, for example, to transmit the results of a series of baseball games
between two equally matched teams. The gambler could obtain even
money bets even though he already knew the result of each game. The
amount of money he could make \\'ould depend only on how much he
chose to bet. How much would he bet? Probably all he had since he
would win with certainty. In this case his capital would grow expo-
nentially and after N bets he would have 2^ times his original bankroll.
This exponential growth of capital is not uncommon in economics. In
fact, if the binary digits in the above channel were arriving at the rate
of one per week, the sequence of bets would have the value of an invest-
ment paying 100 per cent interest per week compounded weekly. We
will make use of a quantity G called the exponential rate of growth of
the gambler's capital, where
G = Urn -^ log ^
iVH.00 iV V 0
where Vn is the gambler's capital after A'' bets, Vo is his starting capital,
and the logarithm is to the base two. In the above example (j = 1.
Consider the case now of a noisy binary channel, where each trans-
mitted symbol has probability, p, or error and q of correct transmission.
Now the gambler could still bet his entire capital each time, and, in
fact, this would maximize the expected value of his capital, (Fjv),
which in this case would be given by
(F;v) = (2qfVo
This would 1)6 little comfort, however, since when A^ was large he would
probably be broke and, in fact, would be broke with probability one if
he continued indefinitely. Let us, instead, assume that he bets a frac-
tion, (, of his capital each time. Then
v^ = (1 + (y\i -^fvo
where W aiid L are the number of wins and losses in the N bets. Then
G = Lim
^logd -f o+^iog(i -i)
= g log (1 -f /') -1- p log (1 — i) with probability one
Let us maximize G with respect to /. The maximum value with respect
to the Yi of a quantity of the form Z = ^ Xi log Yi , subject to the
constraint ^ Yi = Y, is obtained by putting
Y
Yi = j^ Xi ,
920 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
where X = ^ Xi . This may be shown directly from the convexity of
the logarithm.
and
Thus we put
(1 + ^) = 2q
(1 - -f) = 2p
G^max = 1 + P log p + g log g
= R
which is the rate of transmission as defined by Shannon.
One might still argue that the gambler should bet all his money
(make ^ = 1) in order to maximize his expected win after N times. It
is surely true that if the game were to be stopped after N bets the answer
to this question would depend on the relative values (to the gambler)
of being broke or possessing a fortune. If we compare the fates of two
gamblers, however, playing a nonterminating game, the one which uses
the value € found above will, with probability one, eventually get ahead
and stay ahead of one using any other i. At any rate, we will assume
that the gambler will always bet so as to maximize G.
THE GENERAL CASE
Let us now consider the case in which the channel has several input
symbols, not necessarily equally likely, which represent the outcome of
chance events. We will use the following notation:
p{s) the probability that the transmitted symbol is the s'th one.
p(r/s) the conditional probability^ that the received symbol is the
r'th on the hypothesis that the transmitted symbol is the s'th
one.
p(s, r) the joint probability of the s'th transmitted and r'th received
symbol.
q{r) received symbol probability.
q(s/r) conditional probability of transmitted symbol on hypothesis
of received symbol,
a, the odds paid on the occurrence of the s'th transmitted symbol,
i.e., as is the number of dollars returned for a one-dollar bet
(including that one dollar),
a(s/r) the fraction of the gambler's capital that he decides to bet on
the occurrence of the s'th transmitted symbol after observing
the r'th received symbol
^
A NEW INTERPRETATION OF INFORMATION RATE 921
Only the case of independent transmitted symbols and noise will be
considered. We will consider first the case of "fair" odds, i.e.,
1
Ois =
p{s)
In any sort of parimutual betting there is a tendency for the odds to be
fair (ignoring the "track take"). To see this first note that if there is no
"track take"
Ei = i
since all the money collected is paid out to the winner. Next note that if
p(s)
for some s a bettor could insure a profit by making repeated bets on the
s* outcome. The extra betting which would result would lower a., .
The same feedback mechanism probably takes place in more compli-
cated betting situations, such as stock market speculation.
There is no loss in generality in assuming that
Z a(s/r) = 1
s
i.e., the gambler bets his total capital regardless of the received symbol.
Since
he can effectively hold back money by placing canceling bets. Now
r,s
where Wsr is the number of times that the transmitted symbol is s and
the received, symbol is r.
Log ^ = X) ^V^r log oisa{s/r)
vl " "^
G = Urn ^ log -f/ = X) P(^> ^) log oLsa{s/r)
N^x I\ Vq ts
with probability one. Since
1
oil =
' Pis)
922
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 195G
here
G = H P(s, r) log
a(s/r)
- J2v(s, r) log a(s/r) + H{X)
rs
where H{X) is the source rate as defined by Shannon. The first term is
maximized by putting
^kP{k, r) q{r)
Then (7max = H(X) — H{X/Y), which is the rate of transmission de-
fined by Shannon.
WHEN THE ODDS ARE NOT FAIR
Consider the case where there is no track take, i.e.,
but where as is not necessarily
1
V{s)
It is still permissible to set ^s a{s/r) = 1 since the gambler can effec-
tively hold back any amount of money by betting it in proportion to
the I /as . Equation (1) now can be written
G = ^ P(s, r) log a(s/r) -f- J2 Pi^) log a. .
rs s
G is still maximized by placing a(s/r) = q{s/r) and
G^max = -H{X/Y) + Y. Pis) log as
s
= H(a) - HiX/Y)
where
H{a) = X pis) log as
Several interesting facts emerge here
(a) In this case G is maximized as before by putting a{s/r) ^ qis/r).
That is, the gambler ignores the posted odds in placing his bets!
A NEW INTERPRETATION OF INFORMATION RATE 923
(b) Since the minimum value of H{a) subject to
s as
obtains when
a. =
p(s)
and H(X) = H(a), any deviation from fair odds helps the gambler.
(c) Since the gambler's exponential gain would be H{a) — H(X) if
he had no inside information, we can interpret R = H{X) — H{X/Y)
as the increase of Gmax due to the communication channel. When there
is no channel, i.e., H{X/Y) = H{X), Gmax is minimized (at zero) by set-
ting
1
as = —
Ps
This gives further meaning to the concept "fair odds."
WHEN THERE IS A "TRACK TAKE"
In the case there is a "track take" the situation is more complicated.
It can no longer be assumed that ^s a{s/r) = 1. The gambler cannot
make canceling bets since he loses a percentage to the track. Let br =
1 — X)s ais/r), i.e., the fraction not bet when the received symbol is
the r one. Then the quantity to be maximized is
G = 11 p(s, r) log [br + aMs/r)], (2)
rs
subject to the constraints
br+ E«(sA) = 1.
In maximizing (2) it is sufficient to maximize the terms involving a
particular value of r and to do this separately for each value of r smce
both in (2) and in the associated constraints, terms involving different
r's are independent. That is, we must maximize terms of the type
Gr = q(r)^ q(s/r) log [6, + asa(s/r)]
s
subject to the constraint
924
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
Actually, each of these terms is the same form as that of the gambler's
exponential gain where there is no channel
(? = X; p(s) log [b + a.a(s)]. (3)
a
We will maximize (3) and interpret the results either as a typical
term in the general problem or as the total exponential gain in the case
of no communication channel. Let us designate by X the set of indices,
s, for which a(s) > 0, and by X' the set for which a(s) = 0. Now at the
desired maximum
p(s)as
dG
da{s) b + a(s)ai
log e = k for seX
dG y-^ p{s) , ,
-1- = Z^ -, — . \\ — log e = k
dG p(s)as , ^ J r .f
— T-r = ^ / log e :^ /c for SfX
da{s) b ^ ~
where /c is a constant. The equations yield
k = log e, b =
b
ais) = pis) -
1 -P
1 - a-
for seX
as
where p = Xxp(s), a- = ^x (1/as), and the inequalities yield
p(s)as ^ b =
1 -p
for SfX
We will see that the conditions
(X < 1
p(s)as >
p(s)as ^
1
P
1 - a
1 -P
1 - <r
se\
for seX
completely determine X.
If we permute indices so that
p(s)ae ^ p(s + l)as+i
A NEW INTERPRETATION OF INFORMATION RATE 925
then X must consist of all s ^ i where t is a, positive integer or zero.
Consider how the fraction
I — (Xt
varies with t, where
t t ^
Pt = ^ p(s), <Tt = ^ — ; Fo = 1
I 1 as
Now if p(l)ar < 1, Ft increases with i until at ^ 1. In this case t = 0
satisfies the desired conditions and X is empty. If p{l)ai > 1 Ft de-
creases with t until p(t + l)at+i < Ft or at ^ 1. If the former occurs,
i.e., p(t + l)oit+i < Ft , then i^^+i > Ft and the fraction increases until
cr< ^ 1. In any case the desired value of t is the one which gives Ft its
minimum positive value, or if there is more than one such value of /,
the smallest. The maximizing process may be summed up as follows:
(a) Permute indices so that p(s)as ^ p(s + l)Qrg+i
(b) Set h equal to the minimum positive value of
-I t < -
— where Pt = ILp (s), at = ^ —
i- — (Tt 1 1 ffj
(c) Set a(s) = p(s) — b/as or zero, whichever is larger. (The a(s)
will sum to 1 — h.)
The desired maximum G will then be
(rmax = Z) P(s) log p(s)as + (1 - Pt) log
1 -Pt
I - CTt
where t is the smallest index which gives
1 -Pt
1 - <rt
its minimum positive value.
It should be noted that if p{s)as < 1 for all s no bets are placed, but
if the largest p(s)as > 1 some bets might be made for which p(s)as < 1,
i.e., the expected gain is negative. This violates the criterion of the
classical gambler who never bets on such an event.
CONCLUSION
The gambler introduced here follows an essentially different criterion
from the classical gambler. At every bet he maximizes the expected
value of the logarithm of his capital. The reason has nothing to do with
92(i THE BELL SYSTEM TECHNICAL .lOlKXAL, JCLY 195G
the value function Avhich he attached to his money, but merely with the
fact that it is the logarithm A\hic'h is additive in repeated bets and to
which the law of large numbers applies. Suppose the situation were
different; for example, suppose the gambler's wife allowed him to bet
one dollar each week but not to reinvest his winnings. He should then
maximize his expectation (expected value of capital) on each bet. He
would bet all his available capital (one dollar) on the event j-ielding the
highest expectation. With probability one he would get ahead of any-
one dividing his money differently.
It should be noted that we have only shown that our gambler's capital
will surpass, with probability one, that of any gambler apportioning his
money different!}^ from ours but still m a fixed way for each received
sjanbol, independent of time or past events. Theorems remain to be
proved showing in what sense, if any, our strategy is superior to others
involving a{s/r) which are not constant.
Although the model adopted here is draAvn from the real-life situation
of gambling it is possible that it could apph' to certain other economic
situations. The essential requirements for the validity of the theory are
the possibilit}' of reinvestment of profits and the abilit}^ to control or
vary the amount of money invested or bet in different categories. The
"channel" of the theory might correspond to a real communication
channel or simply to the totality of inside information available to
the investor.
Let us summarize briefly the results of this paper. Tf a gambler places
bets on the input symbol to a comnumication channel and l)ets his money
in the same proportion each time a particular symbol is receiA'cd his,
capital will grow (or shrink) exponentially. If the odds are consistent
with the probabilities of occvu'rence of the transmitted symbols (i.e.,
equal to their reciprocals), the maximum value of this exponential rate
of growth will be equal to the rate of transmission of information. If the
odds are not fair, i.e., not consistent with the transmitted symbol proba-
bilities but consistent with some other set of probabilities, the maximum
exponential rate of growth will be larger than it would have been with no
channel by an amount equal to the rate of transmission of information.
In case there is a "track take" similar results are obtained, but the
formulae involved are more complex and have less direct information
theoretic interpretations.
ACNOWLEDGMENTS
I am indebted to R. E. Graham and C. E. Shannon for their assist-
ance in the preparation of this paper.
Automatic Testing of Transmission
and Operational Functions of
Intertoll Trunks
By H. H. FELDER, A. J. PASCARELLA and
H. F. SHOFFSTALL
(Manuscript received October 19, 1955)
Conditions brought about by nationwide dialing increase intertoll trunk
maintenance problems substantiaUy. Under this switching plan with full
automatic alternate routing there is a considerable increase in the amount
of multiswitched business, and as many as eight intertoll trunks in tandem
are permissible. In addition, operator checks of transmission on the connec-
tions are lost on most calls. These factors iynpose more severe limitations on
transmission loss variations in the individual trunks and throw on the
maintenance forces additional burdens of detecting defects in the distance
dialing network.
New methods of analyzing transmission performance to locate the points
where maintenance effort will be most effective continue to be studied. The
automatic testing arrangements described in this paper enable the main-
tenance forces to collect over-all transmission loss data quickly and with a
minimum of effort. They also facilitate the collection of such data on groups
of trunks in a form to make statistical analyses easier. The use of these
testing arrangements will permit the maintenance forces to keep a closer
watch on intertoll trunk performance and will assist in disclosing trouble
patterns.
INTRODUCTION
The advent of nationwide dialing, especiall}' with full automatic
alternate routing, has presented additional problems in the maintenance
of intertoll trunks. Transmission reciuirements are more rigorous, the
intertoll trunk connections are more complex, and certain irregularities
in the performance of the distance dialing network are difficult to detect.
Automatic test equipment has been provided to aid and increase the
efficiency of over-all testing. This equipment is capable of automatically
927
928 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
testing the operational (signaling and supervisory) functions of dial-type
intertoU trunks, and of making two-way transmission loss measurements
and a noise check at each end. The test results may be recorded at the
originating end by means of a Teletypewriter.
Automatic trunk testing has been used for many years in the local
plant for checking the signaling and supervisory features of interoffice
trunks. The automatic intertoll trunk testing equipment serves a similar
function with respect to these operational features of the intertoll trunks.
Because published material is available on automatic operational test-
ing,* these features will not be discussed in detail in this paper; more
emphasis is given to the transmission testing features which are new.
MAINTENANCE ARRANGEMENTS FOR INTERTOLL TRUNKS
Except in the very small offices, intertoll trunks usually have a test
jack appearance in the toll testboard for maintenance purposes. Cord
ended testing equipment in the toll testboard positions enables the
attendants to perform various operational tests and to make transmis-
sion loss, balance, noise or crosstalk measurements. Facilities are pro-
vided for communication with distant offices and with intermediate
points where carrier or repeater equipment may be located. Testing of
carrier or repeater equipment as individual components or systems is
an important aspect of the trunk maintenance problem but is beyond
the scope of the present paper.
The maintenance of intertoll trunk net losses close to their specified
values is currently a most important transmission problem. Various
aspects of the problem are discussed in a companion paper, f
Although the manual testing equipment mentioned above is vital to
trunk net loss maintenance, the need for reduction in time and effort
required to make measurements has led to the provision of semi-auto-
matic testing arrangements. These arrangements permit a testboard
attendant to check transmission in the incoming direction by dialing
code 102 over a trunk. The trunk is connected to a source of one milli-
watt test power at the far end and a measurement of the received power
indicates the net loss. The equivalent of a semi-automatic two-way test
may be obtained by making a code 102 test in each direction. If com-
plete information on the test results is desired by one testboard at-
tendant, the attendant at the other end of the trunk must report back
his results.
* R. C. Nance, Automatic Intertoll Trunk Testing, Bell Labs. Record, Dec,
1954.
t H. H. Felder and E. N. Little, Intertoll Trunk Net Loss Maintenance Under
Operator Distance and Direct Distance Dialing, page 955 of this issue.
AUTOMATIC TESTING OF INTEETOLL TRUNKS 929
In both the manual and semi-automatic methods of measurement, the
results must be recorded manually. For statistical analysis of trunk
transmission performance in terms of "bias" and "distribution grade",
as discussed in the companion paper,* deviations of the measured losses
from the respective specified losses must be computed and summarized
manually.
The automatic testing equipment described in this paper has been
developed as an additional maintenance tool. It will not supplant exist-
ing arrangements discussed above but rather is intended to increase the
capabilities of plant personnel to do an effective maintenance job. The
following features of the equipment contribute particularly to this end:
1. Large numbers of trunks can be tested and the results recorded
without the continuous attention of a testboard attendant.
2. The attendant is informed by an alarm whenever the loss of a
trunk deviates excessively from the specified value.
3. Computation and summarizing of net loss deviations into class
intervals are done automatically, thus facilitating statistical analysis of
trunk performance.
4. Data can be collected quickly in large volume for indicating the
performance of groups of trunks. Confusion occurring with manual
measurements because of changing conditions with time is reduced.
5. Stability of an individual trunk may be checked by a series of
repetitive tests.
6. Semi-automatic two-way trunk tests can be made by one attendant
when required.
To do an equivalent job entirely by manual methods would require
an appreciable increase in the amount of manual test equipment and in
the number of test personnel. A comparison of the times required for
operational and transmission tests by manual, semi-automatic and auto-
matic methods is shown in Fig. 1. The time shown for the code 102 test
does not include coordination time required if information on test re-
sults in both directions is required at one end.
GENERAL DESCRIPTION OF AUTOMATIC TESTING EQUIPMENT
Automatic intertoll trunk testing requires automatic equipment at
both ends of the trunk.At the originating or control end, an automatic
test circuit sets up the test call and controls the various test features. In
the distant offices, test lines reached through the switching train provide
appropriate automatic test terminations. The automatic equipment for
* H. H. Felder and E. N. Little, Intertoll Trunk Net Loss Maintenance Under
Operator Distance and Direct Distance Dialing, page 955 of this issue.
930
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
use at the control end, adapted for transmission testing, is presently
available only for No. 4 type toll switching offices.
Fig. 2 is a block schematic of the arrangement for automatic intertoll
trunk testing, including transmission tests. In the originating No. 4 toll
crossbar oflicc an automatic outgoing intertoll trunk test circuit is used
which consists of an automatic outgoing intertoll trunk test frame and
one or more associated test connector frames. These frames have been
provided in all No. 4 type offices and perform the functions of setting up
MANUAL (2 MEN)
NEAR END
OFFICE
FAR END
" OFFICE
If) 4
lij
i3
CIRCUIT
OPERATION
TESTS
TEST
BOARD
TEST
BOARD
5
H 0
1 -
2 -WAY
TRANSMISSION
MEASUREMENTS
■■
3.5
8.0
MAN MINUTES PER TEST
SEMI-AUTOMATIC {l MAN)
TEST
BOARD
103
OR
102
OR
104
TEST
LINE
(CODE 104 TEST
INCLUDES
NOISE CHECK)
CODE TEST
/ ' s
102 104
a? 0.9 1.8
MAN MINUTES PER TEST
FULLY AUTOMATIC
<n 4
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(-
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Fig. 1 — Time required for manual tests versus semi-automatic and fully auto-
matic tests. (1) Average time per test for 52,000 field test measurements in 20
offices under normal operating test conditions (includes test preparation, time
waiting to be served, testing time, and recording of results). (2) Average time j)er
test for test measurements made in rapid sequence during light load period. The
semi-automatic code 104 test includes a noise check at the far end only.
AUTOMATIC TESTING OF INTERTOLL TRUNKS 931
the test call and making operational tests on the intertoll trunks. For
automatic transmission tests an automatic transmission test and control
circuit, provided in a separate frame as an adjunct to the test frame, is
brought into play. A Teletypewriter, mounted in the transmission test
frame, is adapted for use with the equipment in the originating office for
recording test results. The Teletypewriter is used to make a record of
trunks having some defect in their operational features, busy trunks
passed over without test and, during transmission tests, to record the
results of the transmission measurements. The test frame and associated
transmission test and control circuit and Teletypewriter are used prin-
cipally by the toll test board forces and, therefore, are usually located
near the toll test board. Figure 3 shows such an installation.
The intertoll trunk test connector frames in the originating office, not
shown in Fig. 3, are frames of crossbar switches and there may be several
such frames in a large office. Each crosspoint on the switches of the test
connector frames represents an individual intertoll trunk. When a trunk
is to be tested, the test frame closes the crosspoint of the test connector
switches which serves that particular trunk. This extends the selecting
leads (trunk sleeve and select magnet leads) of the trunk to the test
frame for use in setting up the call. A class contact on the test connector
crosspoint also operates one of several class relays in the test frame when
the crosspoint is closed. The function of the class relay is discussed later.
The test frame has an appearance on the incoming link frame of the
office switching train. The intertoll trunks to be tested appear on the
outgoing link frames of the office switching train. When a trunk is to be
tested, the test frame engages the office common control equipment (de-
coder and marker) , through a connector, and requests a path between the
test frame appearance on the incoming link frame and the particular in-
tertoll trunk which is to be tested. The common control ecjuipment is
able to set up this path since the test frame has closed a test connector
cross-point to bring the selecting leads of the trunk to be tested into the
test frame. The common control equipment uses the select magnet lead
to identify the trunk to l)e tested and thus is able to set up the path to
that particular trunk. The test frame uses the trunk sleeve lead for busy
test purposes and for controlling the test call.
In the distant offices separate groups of test lines provide automatic
test terminations for operational and transmission tests, respectively.
These are reached through the switching train as indicated in Fig. 2. The
three digit service code 103 is reserved in toll switching offices for i-each-
ing the operational test lines and code 104 is reserved for reaching the
transmission test lines. A transmission measuring and noise checking
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932
AUTOMATIC TESTING OF INTERTOLL TRUNKS
933
Fig. 3 — Automatic intertoll trunk testing equipment.
circuit, sometimes referred to as "far end equipment," is associated
with the group of code 104 test lines for performing the transmission
measurements. When simultaneous transmission test calls arrive in the
distant office from different originating offices, the calls wait on the
code 104 test lines and are served by the transmission measuring and
noise checking circuit, one at a time, in their proper turn.
After the trunk test frame has obtained a path through the switching
train in the originating office to the trunk to be tested as explained
above, it pulses forward over the trunk the desired test line code, either
code 103 or code 104. In response to the code, the switching equipment
in the distant office sets up a path through the switching train to one of
934 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1950
the code 103 or oode 104 test lines. A steady off-hook signal is returned
over the established connection to the test frame at the originating office
to indicate that the test may proceed.
The process of setting up a test call, as described above, simulates
very closely the procedures followed in setting up a normal call from an
incoming trunk in the originating office to a desired number in the
distant office. Therefore, any irregularities in the operational features
while setting up the test call will be detected by the test frame and will
result in appropriate trouble indication at the test frame at the originat-
ing end.
The automatic testing arrangements aaIU operate with offices where
terminating calls are switched either on a terminal net loss (TNL) or
on a via net loss (VNL) basis. This is done by including appropriate
pads for use at VNL offices.
FEATURES OF INTERTOLL TRUNK TEST FRAME
Control of Test Connector
When the trunk test frame is put into operation, it closes the first
crosspoint of the first test connector crossbar switch on the test con-
nector frames to prepare for testing the first trunk in the test sequence.
When the trunk test is completed, the test frame advances to the next
crosspoint for testing the next trunk. This progression continues through
all the test connector frames until all intertoll trunks in the office have
been tested. The test frame stops when the test cycle is completed. Par-
ticular circuit selection keys are provided on the test frame so that the
test connector can be directed manually to any point for testing an
individual trunk or for starting a test cycle at some intermediate point
in the test sequence, rather than with the first trunk. As the test frame
progresses through a test cycle, it also displays on lamps a 4-digit "trunk
identification number" corresponding to the test connector crosspoint
which is closed. When a trouble is encountered, the attendant uses this
4-digit luimber to identify the trunk being tested as a particular trunk
to a particular destination. The Teletypewriter prints the trunk identifi-
cation number as a part of each trunk test record.
Busy Test
Before starting a test, the test frame tests the trunk sleeve lead for
busy. If the trunk is busy, the test frame waits for the trunk to become
idle. A "pass busy" key is provided which, when operated, cancels the
waiting period and causes the test frame to immediately pass over busy
AUTOMATIC TESTING OF INTERTOLL TRUNKS 935
trunks to save time. The circuits are arranged so that, if desired, the Tele-
typewriter may print a record of busy trunks passed over without test.
By means of a timing key this record can be delayed two minutes or four
minutes to wait for the trunk to become idle. This is used when it is
preferable to wait a reasonable time for trunks to become idle to secure
tests on a larger proportion of the trunks.
Trunk Classes
A class relay, operated by a contact on the test connector crosspoint
as previously mentioned, indicates to the test frame the type of trunk
being tested so that it can properly handle the test call. There are 33 of
these relays. A flexible cross-connection in the path of the class contact
on each test connector crosspoint permits each crosspoint to be assigned
to the particular one of the 33 class relays which represent the charac-
teristics of the intertoll trunk associated with that crosspoint. Twenty-
eight of the class relays are used in connection with trunks on which auto-
matic transmission tests are made and indicate, among other things, the
specified loss of the trunk being tested. These relays are provided in such
a manner that, for any trunk, a class can be chosen w^hich agrees with the
specified loss of the trunk to within ±0.1 db over the range 3.8 db to 12.1
db. The specified loss is used by the automatic transmission test and
control circuit when computing the deviation of the measured loss from
the specified value, as covered later.
Test Cycles
The test frame may be set up by means of control keys to perform
^'arious kinds of test cycles. Some of these test cycles, are described
briefly below.
Code 103 Tests. A complete check is made of all the circuit operating
features including the ringing and the supervisory features while the
connection is established. If this test is passed successfully, one may
assume that the intertoll trunk circuit and the associated signaling chan-
nel will properly handle normal calls although this does not prove that
the transmission performance is satisfactory.
Signaling Channel Tests. This is an abbreviated code 103 test to verify
the integrity of the trunk and its signaling channel. It can be made quite
rapidly and is useful for checking the correctness of patching after daj''
and night circuit layout changes.
Pass Idle Test. This is a test cycle which may be I'un occasionally
during a very light load period to detect trunks which may l)e falsely
busy.
936 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
Repeat-2 Tests. This consists essentially of two code 103 tests on the
same trunk in rapid succession. It is used to insure that a connection
through the switching train in the distant office will be properly broken
down when a call is completed.
Repeat Test. A "repeat test" key on the test frame cancels the advance
of the intertoll trunk test connector. Since the test frame cannot then
advance to the next test connector crosspoint, it tests the same trunk
repeatedly. This is useful for verifying a trouble condition and for de-
tecting an intermittent trouble, or for obtaining data on stability versus
time.
Manual Tests. When the test frame is set up for making manual tests,
it engages the office common control equipment to set up a path through
the switching train to the trunk to be tested but does not pulse forward
code 103 or 104. Instead the attendant can pulse forward the proper
code to reach the toll test board at the distant end. This permits dial
type trunks to distant offices, not equipped with test lines, to be tested
manualh^
Code 104 Tests. A 3-position key controls transmission testing. When
the key is normal, the test frame makes operational tests. When the key
is operated to the transmission and noise position, a two-way transmis-
sion loss measurement is made and is followed by a noise check at each
end of the trunk. When the key is operated to the transmission only
position the noise checks are omitted. The latter position is used when
it is permissible to omit the noise checks to save time. When making code
104 tests, the test frame sets up and breaks down the test connection in
the same way as when making code 103 tests and, while the connection
is established, it receives supervisory signals from the far end. Thus
most of the trunk operating features, except for ringing, are also checked
as an incidental part of the transmission test. Irregularities in the circuit
operating features can result in a trouble indication in the same way as
when making operational tests.
Trouble Indications
During a test, progress lamps display the progress of the test call and,
when trouble is detected, one of a number of trouble indicating lamps
may also be lighted. The progress and trouble indicating lamps indicate
the general nature of the trouble.
When the Teletypewriter is not in operation, a trouble indication
causes the test frame to stop, to hold the trunk busy and to sound an
alarm while awaiting the attention of the attendant. It is the usual
practice for the attendant to make a repeat test on the same trunk to
AUTOMATIC TESTING OF INTERTOLL TRUNKS 937
verify the trouble condition. He notes the nature of the trouble from
the progress and trouble indicating lamps and then causes the test
frame to resume testing by advancing it to the next trunk with a manual
advance key.
When the associated Teletypewriter is provided and operating, it is not
always necessary to sound an alarm and thus interrupt the regular work
of the attendant. Instead the Teletypewriter may print a trouble record.
For this purpose troubles are grouped into 18 categories. When a trouble
is detected, the Teletypewriter prints a record of the trunk identification
number together with a letter in a separate column indicating one of
these categories. The test frame then usually makes a repeat test on the
same trunk to verify the trouble except when the connection must be
held, as discussed later. If the second test is satisfactory, the trouble was
of a transient nature and the test frame resumes testing, leaving a single
line trouble record on the Teletype tape. If the trouble is still present on
the second trial, a second record is printed on the next line for the same
trunk.
If the nature of the trouble, as indicated by its category, is such as to
render the trunk unfit for service, the test frame will stop after the second
trial, hold the trunk busy, and sound an alarm to attract the immediate
attention of the attendant. If, however, the trouble is of a minor nature
that can be tolerated temporarily, the test frame advances automatically
to the next trunk after the second record is printed, and resumes testing
without sounding an alarm. By periodic inspection of the Teletype record
the attendant can note those trunks needing maintenance attention by
means of the double line trouble records. A test cycle can thus be com-
pleted with the minimum of supervision on the part of the attendant.
When the nature of a trouble is such that its identity is likely to be
lost if the original connection is broken down, e.g., failure of a holding
ground, the test frame will not attempt a second trial but stop, hold the
trunk busy, and sound an alarm. Failure to complete a transmission test
satisfactorily is included in this class because such failures can be due
to the testing equipment itself.
AUTOMATIC TRANSMISSION TESTS
Basic Scheme of Measurement
An automatic transmission loss measurement consists essentially of
adjusting the loss of a pad at the receiving end of the trunk to bring the
test power level at the pad output to a fixed value. A functional diagram
of the arrangement is shown in Fig. 4.
938 THE B?:LL system TECHXICAL journal, JULY 1956
The standard one milliwatt source of test power is used at the sending
end. The receiving end includes an amplifier, a set of adjustable resistance
pads which are relay controlled and an amplifier-rectifier with a measur-
ing relay (m) in its output circuit. Relay (m) is a polarized relay of a
type widely used in the telephone plant.
The amplifier has a fixed gain of 19.9 db and it includes considerable
negative feedback so that its gain is constant. The pad components are
precision resistors to insure accuracy.
The amplifier-rectifier consists of a two-stage amplifier followed by a
rectifier tube and a detector tube for controlling relay (m). This circuit is
designed so that the margin between the input power which will hold
relay (m) operated and the input power which will insure that relay (m)
will release is less than 0.1 db. The gain is adjusted, by means of a poten-
tiometer, so that relay (m) will operate when the test power level at the
output from the receiving pads in Fig. 4 is one milliwatt or higher and
so that it will release when the power level at this point is 0.1 db or more
below one milliwatt. This close margin between operate and release
permits relay (m) to be used as an accurate measuring device with a pre-
cision comparable with that of manual transmission measuring equip-
ment using direct reading meters. Negati^^e feedback, built into the
amplifier portion of the amplifier-rectifier, insures gain stability and the
amplifier-rectifier will maintain its gain adjustment over a long period.
When making a transmission loss measurement, the power from the
sending end operates relay (m) in the amplifier-rectifier. The loss in the
receiving pads is then increased, by means of control circuitry, until the
power level at their output is reduced to one, milliwatt. In making this
adjustment, relay (m) is used as the power level indicating device. When
this adjustment is finished the trunk loss will be
Intertoll Trunk Loss = 19.9 db — Receiving Pad Loss.
Adjustment of Receiving Pads
The receiving pads, shown in Fig. 4 consist of 9 individual pads
having losses of 10, 5, 4, 2, 1, 0.5, 0.4, 0.2 and 0.1 db. Each pad is in-
serted into the input circuit to the amplifier-rectifier by the operation
of a corresponding pad control relay. Adjustment of the pad loss takes
place in steps.
When relay (m) operates on arrival of the test power, the control
circuit operates relay 10 to insert the 10 db pad. If this reduces the test
power level at the output from receiving pads to a \'alue below one milli-
AUTOMATIC TESTING OF INTERTOLL TRUNKS 939
watt, relay (m) in the amplifier-rectifiei- will release. The control circuit
then releases relay 10 also to remove the 10 db pad before it proceeds
to the next step. If the test power level remains one milliwatt or higher
after the 10 db pad is inserted, relay (m) remains operated. The control
circuit then locks relay 10 in its operated position to retain the 10 db
pad before it proceeds to the next step. In the next step, pad control
relay 5 is operated to insert the 5 db receiving pad. The 5 db receiving pad
will then be rejected or retained, as described above, depending upon
which position relay (m) takes after the 5 db pad is inserted. This
process continues until all 9 individual receiving pads have been tried in
descending order ending with the 0.1 db pad. When this process is com-
pleted, the combination of the 9 pad control relays which remain locked
in the operated position determines, additively, the receiving pad loss
and consequently, this combination is related directly to the trunk loss.
At the originating or control end this combination of operated relays will
be translated to the measured loss of the intertoll trunk being tested,
when the results of the measurement are recorded. The method of trans-
mitting the measured loss from the far end to the originating end is
discussed later.
The transmitting and check pads shown in Fig. 4 are a separate set
of pads also controlled by the pad control relays. At the start of the test
the total loss in these pads is 19.9 db. Whenever a pad control relay
operates to insert a receiving pad, it removes an equal loss from the
transmitting pads. Therefore, when the receiving pad adjustment is
finished, the loss remaining in the transmitting pads will be equal to the
loss of the trunk. Also, the sum of the losses in the two sets of pads is
always 19.9 db regardless of the trunk loss being measured, provided all
pad components and all pad control relay contacts are in perfect order.
This condition permits a precise accuracy check to be made, as discussed
later.
Whenever the control circuit leaves pad control relay 4 or 0.4 in its
operated position to retain the 4 db or 0.4 db pad, the subsequent 2 db
and 1 db or 0.2 db and 0.1 db pad control relays are disabled. There will
will then be no action as the control circuit passes through the 2 db and
1 db or the 0.2 db and 0.1 db steps. This limits the maximum receiving
pad loss to 19.9 db, which is the maximum range of the automatic meas-
urement. This range amply covers the range of losses of intertoll trunks
in a usable condition. Loss measurements attempted outside the range
of 0 to 19.9 db will cause failure of the built-in checks, mentioned later,
and will result in an alarm at the control end of the trvuik.
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AUTOMATIC TESTING OF INTERTOLL TRUNKS 941
Accuracy Checks
If the receiving pad adjustment has been successful, the power level
at the pad output will be very close to one milliwatt and the measuring
relay (m) will be just on the verge of moving from its front to its back
contact, or vice versa. Errors may creep in, however, to prevent these
things from being true. Some such sources of error are:
(1) One or more of the pad control relays might fail to lock in the
operated position when they should, or fail to release when they should.
It would then be impossible to adjust the total receiving pad loss to the
correct value.
(2) The trunk loss might change suddenly while the pad adjustment
is in progress and make it impossible, with the pads remaining to be
tried, to bring the power level at the pad output to one milliwatt.
(3) The amplifier or amplifier-rectifier gains might increase or de-
crease due to a defective component.
(4) The milliwatt test power supply might deviate from the standard
value.
(5) Defective components or faulty control relay contacts might cause
the individual pad losses to be incorrect.
To detect errors of the type in items (1) and (2) a "trunk check" is
made immediately after the pad adjustment is finished. Referring to
Fig. 4, two 0.5 db pads, a and b, are provided in the input circuit to the
amplifier-rectifier, pad a being normally out. Before the sending end re-
moves the test power, pad a is inserted, momentarily. The resulting
decrease in input power to the amplifier-rectifier should cause relay (m)
to release. Both pads a and b are then cut out. The resulting increase in
input power should cause relay (m) to operate. If relay (m) fails to pass
either of these checks the receiving pad loss is in error by 0.5 db or more
and another trial is needed to secure a more accurate adjustment. Pre-
mature removal of the test power at the sending end would, of course,
cause relay (m) to fail on the second check and result in another trial.
Immediately after the trunk check and while pad b is still cut out, the
receiving end rearranges its circuit locally as shown in Fig. 5 for a "loop
check" to guard against errors of the types mentioned in items (3), (4)
and (5) above. This rearrangement inserts a 0.3 db pad in place of the
0.5 db pad b, which is cut out. The local milliwatt supply then applies
power to the amplifier-rectifier at a level about 0.2 db higher than
necessary to operate relay (m) . Relay (m) will fail to operate and pass
this check if the combined effect of any decrease in the value of the milli-
watt test power supply, any decrease in the amplifier and the amplifier-
rectifier gains and cumulative errors in the receiving pads and check
pads adds more than 0.2 db loss. After the above check, a 0.5 db loss is
942
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 195G
added in the looped circuit. This reduces the input power to the ampli-
fier-rectifier about 0.2 db below that which causes relay (m) to release.
Relay (m) will remain operated and fail to pass this check if the com-
bined effect of increases in the milliwatt test power supply or amplifier
and amplifier-rectifier gains and cumulative errors in the pads exceeds
0.2 db gain. By means of the loop check the maintenance forces will be
notified whenever the measuring equipment drifts more than ±0.2 db
from the initially calibrated setting.
After the loop check the receixing end restores its circuit to the
original connections shown in Fig. 4 and by means of relays not shown,
cuts out all of the receiving pad loss. Relay (m) then reoperates. The
circuit I'ests in this condition to await the removal of the test power at
the sending end.
When the sending end removes the test power, relay (m) releases. If
all accuracy checks have been passed successfully, the receiving end then
prepares for the next phase of the test. If, however, the accuracy checks
failed in any respect, the receiving end restores its circuit to the original
condition at the start of the measurement and returns a signal to the
sending end to request reconnection of the test power for another trial.
Intertoll Trunk Loss Measurement and Noise Check
An intertoll trunk loss measurement consists of two successive one-way
measurements, as described above, one for each direction of transmis-
sion. The transmission test call is set up to one of the code 104 test lines
in the distant office. If the transmission measuring and noise checking
circuit at the far end is already engaged because another call arrived
CONNECTION
DURING
MEASUREMENT
AND
TRUNK CHECK
CONNECTION
DURING
LOOP CHECK
19.9 DB
GAIN
RECEIVING
PADS
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19.9 DB MINUS
TRUNK LOSS
TRANSMITTING
PADS
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EQUALS
TRUNK LOSS
TRUNK
CHECK PADS
LOOP
CHECK PADS
ONE MILLIWATT
TEST
POWER SUPPLY
Fig. 5 — Arrangement for loop check.
AUTOMATIC TESTING OF INTERTOLL TRUNKS 943
just previously from some other originating office, this call waits on the
test line. When the transmission measuring and noise checking circuit
is ready to serve this call, it connects to the test line on which this call
is waiting and then returns a steady off -hook signal to the originating end.
This notifies the originating end that the transmission test may begin.
The philosophy of a two-way transmission measurement is as follows.
The near end sends test power over the trunk and the far end measures
the loss as previously described. In this process the loss of the trans-
mitting pad at the far end is adjusted to a value equal to the trunk loss
in the near to far direction. The far end then returns test power, first
directly over the trunk and next, through the transmitting pad. The
power levels received at the near end are a measure of first, the trunk
loss in the far to near direction and next, the sum of the losses in the two
directions. Measurement of these levels provides data for recording the
loss in each direction at the near end.
The two-way transmission measurement takes place in four steps as
shown in Fig. 6. These steps are described below.
Slevl
The near end sends one milliwatt and the far end adjusts its pads and
checks the measurement. After about 3 seconds the near end removes
the test power and then pauses for a short interval to wait for a signal
denoting whether or not the accuracy tests were successful.
If they were unsuccessful, the far end will restore itself to the condi-
tion prevailing at the start of Step 1 and will also return a short (about
3^2 second) on-hook signal to the near end. The near end then reconnects
the test power for three seconds for another trial. The test frame at the
near end stops and sounds an alarm after a third unsuccessful trial.
If the far end is successful in any one of the first three trials, an on-hook
signal will not be returned to the near end when the test power is re-
moved. The near end, after the short pause, then sends a short spurt of
test power which reoperates the measuring relay at the far end. This
signal at the far end, after a successful Step 1, indicates to the far end
that this is a full automatic test.
Step 2
For Step 2 the near end connects a far-near amplifier, a set of far-near
receiving pads and an amplifier-rectifier. The far end disconnects its
receiving eciuipment and returns one milliwatt over the trunk. The far-
near receiving pads at the near end are now inserted in the proper com-
944 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
bination to reduce the power level at their output to one milliwatt. The
combination of the nine far-near pad control relays remaining operated
after the adjustment is finished will be translated later to measured loss
of the intertoll trunk in the far to near direction. After about 3 seconds
the far end removes the test power and pauses for a short interval. This
completes Step 2. Each end then prepares for Step 3.
Steps
For Step 3 the near end retains the far-near amplifier and the setting
of the far-near receiving pads and adds a near-far amplifier and a set of
near-far receiving pads in tandem in the input circuit to the amplifier-
rectifier. The far end, after the short pause, again sends one milliwatt
but this time it sends through the transmitting pad which was adjusted
in Step 1 to represent the near-to-far trunk loss. The near-far receiving
pads at the near end are now automatically arranged to reduce the power
level at their output to one milliwatt.
In the adjustment of Step 2 the over-all loss, including the trunk in
the far-to-near direction, the far-near amplifier and the far-near receiv-
ing pads, was made 0 db. Consequently, the net loss being measured in
Step 3 is simply that of the transmitting pad at the far end, which is the
same as the trunk loss in the near-to-far direction. Therefore the com-
bination of the 9 near-far pad control relays remaining operated after
Step 3 is finished can be translated to measured loss of the intertoll trunk
in the near-to-far direction. After about 3 seconds the far end will re-
move the test power to complete Step 3 and it will then pause for a short
interval before proceeding with Step 4.
At the near end there are also two sets of check pads, not shown, which
are associated with the far-near and near-far receiving pads, respectively,
as indicated in Fig. 4. During Step 2 and Step 3 the near end makes the
trunk check previously described to verify the accuracy of the pad loss
settings and, in addition, in Step 3, rearranges its circuit in the manner
shown in Fig. 5 for the loop check. Thus at the near end the two sets of
check pads, the far-near and near-far amplifiers, and the two sets of
receiving pads are all connected in tandem for the loop check.
During the short pause following Step 2 and Step 3 the far end re-
connects its amplifier and amplifier-rectifier as shown for Step 1 in
Fig. 6. If the near end is unsuccessful in the trunk check in Step 2 or
in either the trunk check or loop check in Step 3, it will restore the
circuit to the original condition at the beginning of Step 2 and will also
send a short spurt of test power to the far end as shown for Step 1 in
Fig. 6. This reoperates the measuring relay (m) at the far end momentar-
AUTOMATIC TESTING OF INTERTOLL TRUNKS 945
ily. The far-end then repeats Steps 2 and 3 for another trial. The test
frame at the near end will stop and sound an alarm after a third unsuc-
cessful attempt.
If the trunk loss in the near-to-far direction exceeds 10 db, the loss in
the transmitting pad at the far end will exceed 10 db. Under this condi-
tion the far end will, prior to Step 3, remove 10 db loss from the trans-
mitting pad to increase the test power level on the trunk. This is done to
improve the test power level-to-noise ratio and to reduce the error when
measuring losses of intertoll trunks having apparatus whose loss is de-
pendent on signal amplitude. The far end will also return to the near
end a short on-hook signal. This on-hook signal at the near end, just
prior to Step 3, is an "add 10" signal and causes the near end to add 10
db to its loss measurement in Step 3, to compensate for the loss which
Avas removed at the far end.
Immediately after Step 3, if the transmission test control key on the
test frame is in the transmission only position, the test frame will cause
the teletypewriter to record the results of the measurements and will
then break down the connection and advance to the next trunk. If the
transmission test control key is in the transmission and noise position, the
test frame will wait after Step 3 for each end to complete a noise check
in Step 4.
816^4
For Step 4 the near-end removes its near-far amplifier and the near-far
and far-near receiving pads and increases the gain of the amplifier-recti-
fier for a noise check at the near-end. Likewise, the far-end removes the
receiving pads and increases the gain of the amplifier-rectifier for a noise
check at the far end. Each end rests in this condition while the amplifier-
rectifier at each end integrates the noise voltage over a 5-second interval.
If the integrated value of noise voltage at either end exceeds a pre-
determined value, the amplifier-rectifier at that end will operate measur-
ing relay (m) in its output which causes a high noise condition to be
registered at that end. If neither end registers a high noise condition,
the test call proceeds to completion without a noise indication being
recorded at the near end.
When the transmission measuring and noise checking circuit at the
far end completes the noise check, it releases itself from the test line and
is then free to serve a new call while the test line returns an on-hook
signal to notify the originating end that the test is completed. This will
be either a steady on-hook signal if the far end has not registered a high
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AUTOMATIC TESTING OF INTERTOLL TRUNKS 947
noise condition, or a 120 TPM flashing signal if the far-end has registered
a high noise condition. The near end is thus advised of the results of the
noise check at the far end. The test frame, on receipt of this signal,
causes the Teletypewriter to complete the record and then breaks down
the connection and advances to the next trunk.
The amplifier, which precedes the amplifier-rectifier includes a net-
work which provides FlA noise weighting during the noise check. The
amplifier-rectifier is adjusted in the noise checking condition (that is,
when its gain is increased) so that a noise indication will be given when
the noise exceeds about 35 or 40 or 45 dba. Since this test is intended
only as a rough check to detect any abnormal noise condition, the noise
rejection limit used in any given office will be governed by the types of
intertoll trunk facilities terminating in that office. Xo correction is made
for the measured loss of the trunk at the time of the noise check, hence
the noise is checked at the receiving switchboard level. For the usual
types of noise the results of the noise check agree roughly with those
which would be obtained by an average observer using a 2-B Noise
Measuring Set for a similar "go-no go" type of check.
As is evident from the previous description, each end is expected to
complete the various steps of its functions within allotted time intervals.
Timing intervals at the far end ai'e controlled by a multivibrator circuit.
Timing at the near end is controlled by a similar multivibrator in
the intertoll trunk test frame. To insure that the test circuits always
perform as they should and that the timing circuits are functioning
properl}^, checks are built into the circuits so that anything which pre-
vents the successful completion of a 2-way measurement on schedule
causes the automatic outgoing intertoll trunk test frame at the near end
to stop, hold the trunk busy and sound an alarm while awaiting attention
of the attendant. The transmission measuring and noise checking circuit
at the far end will, however, release itself from the test line so that it will
be free to handle other calls.
Semi- Automatic Test
One-milliwatt test power supply outlets ha\'e been provided in toll
offices for some time for making a one-way transmission measurement
freciuently referred to as a code 102 test. A test board attendant can reach
the one milliwatt test power supply l)y pulsing forward code 102 or bj^
requesting an operator at the distant end of a manual trunk for a con-
nection. The test power is applied at the distant end for about 10 seconds
diu-ing which time the attendant measures the loss in the receiving
(far-to-near) direction. This is a fairly fast semi-automatic test luit. of
948 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
course, has the disadvantage that it is a one-way test and cannot be
used for all purposes.
In order to provide a semi-automatic two-way test, the far-end equip-
ment is arranged so that a test board attendant can make a code 104
measurement unassisted. This measurement is carried out in 3 steps as
shown in the lower portion of Fig. 6.
Step 1
The attendant connects a test cord to the test jack of the intertoll
trunk and pulses forward code 104 using his test position dial or key set.
When the far end is ready, it returns an off-hook signal which retires
the test cord supervisory lamp. He then connects the other end of the
cord to the one milliwatt test power supply. The far end then adjusts
the receiving and transmitting pads in the same way as for a full auto-
matic test. After about 3 seconds the attendant disconnects the test
power and at that time observes the cord supervisory lamp ; a single flash
indicates that the far end was unsuccessful and is requesting a second
trial. If the supervisory lamp remains steadily dark he connects the
cord to the receive jack of his transmission measuring circuit to prepare
for Step 2.
Step 2
The far end will pause about 2 seconds after the attendant removes the
test power to give him time to prepare for Step 2. During this pause the
far end will not receive a short spurt of test power as in the case of a full
automatic test. Consequently, after the 2 second interval the far end
will return one milliwatt for 10 seconds on a semiautomatic test to give
the attendant time to complete a measurement. The received power is
read directly on the meter of the transmission measuring circuit and is
the loss in the far-to-near direction. When the far end removes the test
power, the meter reading drops back to the position of no current (in-
finite loss) and at that time the attendant observes the cord lamp. A
single flash at this time is an "add 10" signal and indicates that 10 db
should be added to the next measurement. A steady dark lamp indicates
that the next measurement should be recorded without correction.
Step 3
After about 2 seconds delay to give the attendant time to record the
first measurement, the far end again returns 1 milliwatt, this time
through the transmitting pad set up in Step 1 . The meter now reads the
AUTOMATIC TESTING OF INTERTOLL TRUNKS 949
loss of the trunk plus the loss of the transmitting pad at the far end.
Since the transmitting pad loss equals the trunk loss in the near-to-far
direction, the difference between the measurements in Step 3 and Step 2
is the trunk loss in the near-to-far direction. After about 10 seconds the
far end removes the test power and starts the noise check in the same
way as if this were a full automatic test.
When the far end removes the test power after Step 3, the attendant
leaves the connection intact until the cord supervisory lamp lights to
indicate completion of the noise check at the far end. A flashing lamp
indicates that the noise at the far end exceeds the prescribed limit and a
steadily lighted lamp indicates the noise at the far end is below this
value. A noise test at the near end may be made by the attendant if he
judges, after a listening test, that a noise test is desirable. For this test
he uses the standard noise measuring equipment.
PRESENTATION OF TEST RESULTS
When making operational tests and a Teletypewriter is not being used,
troubles are registered by means of an audible alarm and accompanying
display lamps. When making transmission loss measurements, however,
a complete record of the measurements on all trunks tested, both good
and bad is frequently needed. A Teletypewriter then becomes a practical
necessity; otherwise the attendant would be required to supervise the
automatic equipment continuously and to record, from a lamp display
or similar indication, the results of each measurement as it was made.
Having provided the Teletypewriter for transmission testing, its ability
to print letters to represent trouble indications is utilized to avoid halt-
ing the progress of the tests when operational troubles are experienced,
except when completely inoperative conditions are encountered.
Computer Circuit
As mentioned earlier intertoll trunk transmission performance is
rated in terms of bias and distribution grade which are calculated from
the deviations of the measured losses of the intertoll trunks from their
specified values. For such calculations the maintenance forces are, there-
fore, more interested in the deviations than they are in actual measured
losses. Accordingly, the automatic transmission test and control circuit
at the near-end has a computer built into it which will compute the
deviation for each measurement so that the deviation can be recorded
by the Teletypewriter.
The computer is a bi-quinary relay type adder similar to those used
950 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 195G
for other purposes in the telephone plant, for example, in the computer
of the automatic message accounting system. It obtains the specified net
loss of the trunk being tested from the class relay which remains operated
throughout the test. When a computation is to be made of the deviation
in the far-to-near direction, for example, the control circuit extends to
the adder a number of leads from the contacts of the far-near pad control
relays. Some combination of the 9 far-near pad control relays remains
operated after the far-near pad adjustment is finished and therefore some
combination of the leads extended to the adder will be closed. These
leads furnish to the adder the measured loss of the intertoll trunk in the
far-to-near direction. The adder then subtracts the specified loss from
the measured loss and presents the answer together with the proper
sign, -|- or — , to the teletypewriter for a printed record. The deviation
in the near-to-far direction is computed in the same manner by extending
corresponding leads from the near-far pad control relays to the adder
at the proper time.
Deviation Registers
In determining bias and distribution grade by the method discussed
in the companion article,* the deviations from specified net loss are cal-
culated for each measurement. These deviations are grouped together in
0.5 db increments from +8 db to —8 db, all deviations exceeding +7.8
db or —7.8 db being considered as -(-8.0 db and —8.0 db respectively.
For example, all deviations of -|-0.3 db to -f-0.7 db, inclusive are con-
sidered to be -f 0.5 db and are so tallied on the data, or stroke, sheet.
To assist in this work the automatic test equipment includes thirty-
three manually resettable counters corresponding to the 0.5 db incre-
ments from -f-8.0 db to —8.0 db inclusive. Just prior to a transmission
test cycle all these counters are reset to zero. At the time a deviation
computation is made, the computer also causes the proper counter to
register one count. After the test run on a group of trunks, the counter
readings can be transcribed directly as the final tally on the stroke sheet
and may be used to determine the bias and distribution grade. A "total
tests" coimter keeps a tally of all the computations. At the end of the
test run the total count serves as a check of the total count of the other
33 counters.
Check for Excessive Deviations
In addition to obtaining data for the calculation of bias and distribu-
tion grade, the maintenance forces would also like to know promptly
* H. H. Felder and E. N. Little, Intertoll Net Loss Maintenance Under Opera-
tor Distance and Direct Distance Dialing, page 955 of this issue.
AUTOMATIC TESTING OF INTERTOLL TRUNKS 951
when the loss of an intertoll trunk deviates an abnormal amount from
its specified value. The maintenance practices currently require that,
Avhenever an intertoll trimk is found to have a deviation of ±5 db or
more in either direction, the trunk should be removed from service im-
mediately and the cause of the abnormal deviation corrected. Accord-
ingly, the computer circuit includes an alarm feature which sounds
an alarm to attract the immediate attention of the attendant whenever
the computed deviation is ±5.0 db or greater.
The maintenance forces may also like to know promptly about trunks
with wide deviations but which are not so bad as to recjuire immediate
remo\-al from service. For this purpose the computer also includes a
limit checking feature. This can be set, by means of optional wiring, to
detect deviations in excess of dz3.0 db, dz4.0 db or ±5.0 db. Whenever
a deviation exceeds the limit for which the computer is wired, this
feature performs as follows:
(1) When the Teletypewriter is not in operation the test frame stops
and sounds an alarm.
(2) When the Teletypewriter is recording all measurements, the
letter U is added in a separate column at the end of the test record. The
letter stands out on the record to j^ermit fiuick spotting of trunks wdth
abnormal deviations.
(3) By means of a control key, a transmission test record can be
printed only for those trunks whose deviation exceeds the computer
checking limit or which are "noisy" at either end.
Teletypewriter Record
The Teletypewriter is put into operation by means of a key on the
test frame. When this key is normal, no records are printed. Under this
condition a trouble causes the test frame to stop and sound an alarm.
When the Teletypewriter is operating it prints various records and a mi-
nor operational trouble may result only in a record, without an alarm.
Each record occupies a separate line on the tape. Each line starts wdth the
four-digit trunk identification number in the first column. Fig. 7 shows a
short specimen of the the Teletypewriter record.
When the pass busy key on the test frame is in its nonoperated posi-
tion, the Teletypewriter will print the trunk identification number, fol-
lowed by the letter B, for each trunk passed over without test because it
was busy. This is done on both operational and transmission test cycles.
When the pass busy key is operated no record is made of busy trunks
passed without test.
During operational tests no record is printed for trunks which are
952
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
satisfactory. Troubles during either operational or transmission test
cycles result in a record of the trunk identification number followed by a
cue letter in a separate column denoting the nature of the trouble. This
may be a single line record or a double line record for a repeat test on the
same trunk as previously discussed. For example, in Fig. 7, the letter Y
in the second line indicates that on trunk 1267 the far end was unable
to complete its transmission measurement successfully. The letter A in
lines 3 and 4 indicates that the test frame was unable to establish a con-
nection over trunk 1293 on either its first or second attempt. The record
of transmission tests is printed in several columns. Reading from left
to right (see Fig. 7) these are (1) trunk identification number, (2) speci-
fied net loss, (3) deviation in the far-to-near direction together with the
sign, and (4) deviation in the near-to-far direction together with the
sign. In columns 2, 3, and 4 the decimal points are omitted and the
ten's digits are omitted when they are zero (0). Column 5 will contain
an N if the far end is "noisy" or the letter U if the deviation in the far-to-
near direction exceeds the computer check limits, preference being given
to N if both conditions occur on the same trunk. Likewise column 6
contains an N if the near end is "noisy" or a U if the deviation in the
near-to-far direction exceeds the computer check limits. Transmission
test cycles will, of course, include a trouble record whenever an opera-
tional trouble is encountered or whenever the transmission test cannot
be completed successfully.
z
o
3
z
h-
O
o
g
<
Ul
p
1-
1-
(J
;?! <^
1-
z
a.
<
LL
5 in
a:o
< 7
>
1-
z
UJ
^ LU
8 3
cr
1- Q
cr y
o t
>- u
<cr
"4
y cr
5s
LLI LJJ
03
3^
lO LU
><
> cr
Z^
^i
1
3 a
CD i/l
LU LU
Q Z
LU <
Qu:
cncr
<o
1234
1267
Y 1
1293
A i
1293
72
1376
+
08^
"^
bv
'
1377
75
—
11
+
07
N
1378
75
-
52 +
07
U
1379
75
+
07
-
51
U
Fig. 7 — Teletypewriter test record.
AUTOMATIC TESTING OF INTERTOLL TRUNKS
953
APPLICATION
Maximum benefits can be derived from the automatic testing equip-
ment by locating it at points having a considerable number of intertoll
trunks. This suggests that the near-end installations be placed in offices
in larger cities and far-end installations be placed at points with enough
trunks available to near-end equipment to justify the far-end equipment.
As has been indicated the far-end equipment can operate with either an
automatic transmission test and control circuit or with a test board
attendant at the opposite end. Therefore, once an office has been supplied
with far-end test equipment, all incoming and two-way dial type intertoll
trunks from offices provided with near end equipment can be tested on
a fully automatic basis and all incoming and two-way dial type intertoll
NO. 4
OFFICE
NO. 4
OFFICE
RC OR SC
RC OR SC
NEAR-END
TEST CIRCUIT
FAR-END
TEST CIRCUIT
FULLY-AUTOMATIC
' CODE 104
FAR-END
TEST CIRCUIT
PC
NEAR-END
TEST CIRCUIT
FAR-END
TEST CIRCUIT
I
NEAR-END
TEST CIRCUIT
FAR-END
TEST CIRCUIT
SC OR PC
k
tpL
^
SEMI-
AUTOMATIC
"CODE 104 '
OR CODE 102
FAR-END
TEST CIRCUIT
>
FULLY-AUTOMATIC
CODE 104
I
NO. 4
OFFICE
FULLY-AUTOMATIC
CODE 104
FAR-END
TEST CIRCUIT
SxS
CROSSBAR
TANDEM
NO. 5
CROSSBAR
\
\
\ ^^
SEMI-AUTOMATIC
CODE 104 _-
OR CODE 102
I
I
PC ORJTC
I
-SEMI-AUTOMATIC CODE 102'
SxS
CROSSBAR
TANDEM
NO. 5
CROSSBAR
note:
it is assumed that code 102 mw
supply circuits will be available at
all offices and can be used, or that
test board to test board measurements
can be made when desired
LEGEND
RC = REGIONAL CENTER
SC = SECTIONAL CENTER
PC = PRIMARY CENTER
TC = TOLL CENTER
TP = TOLL POINT
Fig. 8 — Typical layout for automatic testing.
954 THE BELL SYSTEM TEC?IXICAL JOURNAL, JULY 1956
trunks from other toll offices can be tested on a semi-automatic basis
from the toll test board in the distant office.
Fig. 8 shows a possible application of automatic test circuits. In such
an application, all No. 4 type toll crossbar offices would have both near-
end and far-end equipments. Other offices would have far-end equipment
only when they have a sufficient number of direct trunks to No. 4 type
offices to justify its use. The several types of tests which would be pos-
sible are indicated in the illustration.
It can be seen that a well distributed number of near-end and far-end
test circuits will make it possible to test automatically a large percentage
of the intertoll trunks throughout the country. This is particularly true
in the more populous sections, where the concentration of trunks results
in the probability of toll centers having trunks to more than one office
furnished with near-end equipment.
ACKNOWLEDGMENTS
Automatic intertoll trunk testing arrangements, including transmis-
sion tests, are the result of the ideas, efforts and experiences of many
people concerned with intertoll switching and maintenance problems
throughout the Bell System. Mr. L. L. Glezen and Mr. L. F. Howard
deserve particular mention in this regard. Specific credit should also be
given to Mr. B. McKim and Mr. T. H. Neely for the basic scheme of
two-way transmission measurements and accuracy checks and to Mr.
C. C. Fleming for the design of the amplifier and amplifier-rectifier.
Appreciation is given to various departments of the American Tele-
phone and Telegraph Company for their assistance during the develop-
ment and trial of this equipment. Mention should also be made of the
hearty cooperation and aid given by the A.T. & T. and Associated
Company plant forces during the field trial of automatic transmission
testing.
«
Intertoll Trunk Net Loss Maintenance
under Operator Distance and Direct
Distance Dialing
By H. H. FEEDER and E. N. LITTLE
(Manuscript received March 15, 1956)
Nearly all of the components of an intertoll trunk contribute in some degree
to its variations in transmission loss. Automatic transmission regulating de-
vices in carrier systems and in many voice-frequency systems control in-
herent variations in the intertoll trunk plant. These variations in transmis-
sion come mainly from unavoidable causes such as temperature changes. The
success of these devices depends on how precisely the trunk is lined up and
the manner in which the maintenance adjustments are made. When the na-
tionwide dialing plan with automatic alternate routing is in full swing, main-
tenance requirements will be more severe because of the material increase in
switched business and the number of possible links in tandem, and because
operator checks will not be obtained on most calls. Therefore, the maintenance
forces will have to keep closer watch on intertoll trunk transmission perform-
ance and insure that the necessary adjustments are made in the right places.
This article discusses some of the maintenance techniques now used and sug-
gests fields for further study.
TABLE OF CONTENTS
Page
Introduction 956
The Prolilem of Net Loss Maintenance 956
Effect of Switching Plans 957
Manual Operation 957
Dial Operation 958
Effect of Carrier Operation 960
Table 1 960
Quantitative Aspects of the Problem 962
Table II 963
Use of Transmission Loss Data 964
Procedure for Analyzing Measurements 965
Effectiveness of Over-all Trunk Test and Analysis 969
Simple Layouts 969
Complex Lajouts 970
Need for Education 971
Summary and Conclusions 972
955
956 THE BELL SYSTEM TECHNICAL JOURNAL, JLUY 1956
INTRODUCTION
Currently there are over 230,000,000 long distance calls made in the
Bell System per month. They range from relatively simple connections
involving a single intercity trunk to complex connections involving sev-
eral intercity trunks in tandem, perhaps totaling 4,000 miles in length.
In each case there is a toll connecting trunk at each end. Almost half of
this traffic involves distances over 30 miles. The transmission engineer's
problem is how to provide uniformly good and dependable transmission
so that every one of these calls will be satisfactory to the customers in-
volved. To accomplish this requires among other things that:
1. The design loss of every trunk must be the lowest permissible from
the standpoint of echo, singing, crosstalk and noise.
2. The actual loss of every trunk must be kept close to the design loss
at all times.
Meeting the first requirement is a matter of system design and circuit
layout engineering. The factors involved have been covered in a previous
article.^ Meeting the second requirement is an important function of the
maintenance forces and is discussed in this article.
THE PROBLEM OF NET LOSS MAINTENANCE
The transition from manual operation under the ''general toll switch-
ing plan" to dial operation under the "nationwide dialing plan"^- ^ is re-
quiring material changes in intertoll trunk design and also in techniques
for maintaining these trunks. While precise maintenance is becoming in- j
creasingly necessary, it is also becoming more difficult to achieve. There
are three important reasons for this.
First, the nationwide dialing plan increases both the possible number
of trunks used in tandem for a given call and the variety of the connec-
tions in which any particular trunk may be used. This increases'
the chances of impairment due to deviations from assigned loss in indi-
vidual trunks since these deviations may combine unfavorably in multi-
switched connections. To minimize this, the transmission stability of the
individual trunk links must be better than under the old plan.
Second, more and more of the trunks are being put on carrier because
* H. R. Huntley, Transmission Design of Intertoll Telephone Trunks, B. S.T.J. ,
Sept. 1953.
2 H. S. Osborne, A General Switching Plan for Telephone Toll Service, B. S.T.J. ,
July, 1930.
' A. B. Clark and H. S. Osborne, Automatic Switching for Nationwide Tele-
phone Service, B.S.T.J., Sept., 1952.
* J. J. Pilliod, Fundamental Plans for Toll Telephone Plant, B.S.T.J., Sept.
1952.
INTERTOLL TRUNK NET LOSS MAINTENANCE
957
it is the best solution to the transmission and economic problems. How-
('\er, carrier involves many more variable elements and requires higher
precision of adjustment than voice-frequency systems need. These in-
crease the difficulty of maintaining trunk losses close to design values on
a day-by-day basis.
Third, as operator distance and direct distance dialing grow, there is
constantly diminishing opportunity for operators to detect and change
unsatisfactory connections or to report unsatisfactory transmission con-
ditions to the appropriate testboards for action.
Thus the maintenance problem is in two parts:
1. How can we reduce departures from design standards even in the
[face of increasing complexity of plant?
2. What substitute can we find for operator detection of troubles, and
can we find even better means of detection?
The ways in which switching plans and the use of carrier reflect upon
Ithe problem of trunk net loss maintenance is discussed in more detail in
the follo\\dng sections.
EFFECT OF SWITCHING PLANS
Manual Operation
For many years long distance traffic has been handled on a manual ba-
sis under the "general toll switching plan" illustrated in Fig. 1. Between
two points indicated by toll centers, TC and TC", it was theoretically
possible to get as many as five trunks in tandem. This rarely occurred be-
RC'
Po'(>:
I"-
TC
■&
.'I
.1.
I
! /
^^.
RC"
"O PO"
\
"-A
■B TC"
TC = Toll Center PO = Primary Outlet RC = Regional Center
Fig. 1 — General toll switching plan — manual operation.
958
THE BP:LL system technical journal, JULY 195G
cause handliug .switched connections manuully was so complicated and
expensive that direct trunks were provided wherever they were econom-
ical and alternate routes were assigned and used sparingly. The result
was that the manual switching plan was characterized by a minimum of
switching.
Under manual operation, operators passed information over every
trunk in the connection, as w^ell as over the completed connection, before
it was turned over to the customers. If anything was radically wrong with
a trunk, the operators recognized it and substituted another trunk. When
this was necessary, they could report the defective trunk to the appropri-
ate testboard for action. Under these conditions, if trunk losses wandered
appreciably from their specified values, the consequences were seldom
serious.
Dial Operation
With dial operation, not only is the plan more complex (as shown on
Fig. 2), with an abundance of alternate routes, but intertoll trunk switch-
ing is so fast and reliable that the number of switching points has little
effect on speed of service. Thus the dial operating plan can take full ad-
vantage of alternate routing and the use of trunks in tandem \\\\\ occur
much more freciuently than with manual operation.
TC = Toll Center PC = Primary Center SC = Sectional Center
RC = Regional Center
Fig. 2 — Nationwide dialing plan — dial operation.
INTERTOLL TRUNK NET LOSS MAINTENANCE 959
Here again the alternate routing follows a definite plan.^ As shown in
iMg. 2, a call from toll center, TC, to toll center, TC", will follow the
direct route, if it is available and not busy. A second choice will be via a
higher ranking office in the chain from TC" to the regional center, RC".
A third choice may be available to a still higher ranking office. Thus, if
the originating office cannot use its direct route, the call will be advanced
over the alternate routes according to a predetermined pattern. If all
other alternatives fail, the call will follow the heavy solid line 7-link route
shown on Fig. 2, or, in special cases, the 8-link route via RC".
These attempts involve many operations but the automatic equipment
completes them cjuickly. This makes it feasible to provide small, high
usage, direct trunk groups between two points, with the realization that
in busy periods alternate routes can handle the overflow^ traffic with neg-
ligible time delay. Thus over a good part of the day, the direct trunks
or first choice trunks will handle the traffic. In the busy periods, use of
alternate routes with a mnnber of links in tandem vdW be a frequent
occurrence. Therefore, it is important to have losses on alternate routes
not greatly different from those on direct routes so customers will not
experience noticeable contrasts.
Operators will seldom talk to each other over the complete connection,
and even less over the individual trunks. Only on person-to-person or col-
lect calls will they talk even to the called party. On station-to-station
calls they merely dial or key up the desired number and rely on super-
visory signals to disclose the progress of the call.
On operator dialed calls, the operator may sometimes pick up the in-
tertoU trunk in her switchboard multiple, but in many cases she will
reach it over a tandem trunk. In the former case she can identify the in-
tertoll trunk forming the first link in the connection but assistance would
be needed at intermediate testboards to identify succeeding trunks. In
the latter case, testman assistance would be required at the originating
office in order to identify even the first trunk of the connection. In either
case the need for holding the customer's line during identification, to
avoid breaking down the connections makes such means of identifica-
tion impracticable Avith presently available techniques.
On direct distance dialed calls there are no operators involved and pres-
ent means of identification of trunks in trouble after the connection has
])een established are even more impracticable. This is because the calling
party must release the connection before he can report a trouble, thus
destroying any possibility of trunk identification.
6 R. I. Wilkinson, Theory for Toll Traffic Engineering in the U. S. A., B.S.T.J.,
March, 1956.
960
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
Thus under dial operation there is a need for better trunk stability.
Therefore, a greater burden is placed on the plant forces to locate unsatis-
factory trunks so that proper maintenance action can be taken before
customers experience difficulty.
EFFECT OF CARRIER OPERATION
Carrier is the principal transmission instrumentality which makes it
possible to go ahead A\dth natiomvide dialing with assurance that people
can talk satisfactorily over the complex connections set up by the switch-
ing sj^stems. But it brings with it formidable problems of maintenance.
The high attenuation per mile of the hue conductors at carrier frequencies
increases the number of variable elements as well as the precision with
which they must be adjusted. The interrelation between the elements
adds to the complication.
Table I illustrates this by giving some figures comparing 100 miles of a
voice-frequency cable trunk with 100 miles of a typical trunk on K car-
rier, which is \\idely used on cable facilities. The figures apply in both
cases to one direction of transmission.
The ten-to-one ratio in the number of electron tubes represents a
greater chance of trouble developing in the carrier trunk due to aging or
failure of electron tubes. In the carrier trunks there are more automatic
adjustable features. For instance, in a typical K2 carrier system there are
five flat gain regulators and one twist regulator in one twist section of
approximately 100 miles, against a single regulator in a voice-frequency
trunk 100 miles long. These regulators are depended upon to keep the
loss variations to tolerable amounts. Any malfunction can have a serious
effect on trvmk loss. Furthermore, they must be adjusted to the desired
regulating range and therefore they are points at which maladjustments
may be made.
The channels of any one carrier system or of a 12-channel group are
commonly routed by the circuit layout engineers to a number of terminal
Table I
Total Conductor Loss -db
Gain Required to Reduce to Via Net Loss -db
Percentage of Line Loss Represented by a 2 db Variation
Number of Electron Tubes
Number of Amplifiers
Number of Automatic Regulators
V-f
K2 Carrier
Trunk
Trunk
35
378
31
377.4
5.7
0.53
3
28
3
7
1
6
INTERTOLL TRUNK NET LOSS MAINTENANCE
961
ALPHA
BETA
GAMMA
'
'
--\
r —
— ._ ^
— 1 j —
— -
-
T,
A j
1 c 1
T,
1^
-*
^-
^ 1
^_ V
f 1
■X-
T2
T3
\
/
•
\
/
<
T3
B
/
\
1 D
T2
\
-*
■x--
/
,, , \
^
J
>
T4
T4
* TO THIS OR OTHER DESTINATIONS
Fig. 3 — Typical carrier channel assignments.
points even though circuit requirements to a given point are sufficient to
utilize 12 or more channels. This is done to minimize the chances that all
of the trunks between two points will be interrupted by a system failure.
A simple case is illustrated by Fig. 3 which shows trunks between Alpha
and Gamma connected at an intermediate point, Beta, in such a manner
that a failure in any one of the systems A, B, C, or D will affect only
half the trunks.
This routing problem, however, complicates the maintenance problem.
For example, if trunk Tl were found to have excess loss in the Alpha-
Gamma direction it could be corrected by raising the channel gain at
Gamma. On the other hand, a correct diagnosis might have disclosed that
the trouble was due to a repeater in system A. If this were the case,
merely compensating for the excess loss in Tl by changing the channel
gain would still leave all other trunks associated with system A in
trouble. Later on, if the repeater difficulty were corrected, and no further
action were taken, the net loss of Tl would then be too low.
Thus, the flexibility which is so desirable to minimize interruptions of
whole circuit groups leads to a difficult problem in the administration of
trunk loss adjustment and maintenance. Furthermore, because of the
larger numbers and greater dispersion of trunks and terminal points, the
situation in the actual telephone plant is much more complex than in the
above example. Also, the diagnosis of trouble conditions is made more
difficult by the normal variations of channel losses in the carrier systems
and consequently of the trunk losses about their design values. This can
962 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
be better appreciated when some quantitative aspects of the problem
are considered.
QUANTITATIVE ASPECTS OF THE PROBLEM
When the nationwide dial switching plan began to take shape some 8
or 10 3'ears ago, intensiA-e study of the transmission maintenance prob-
lem was undertaken. The existing situation was examined to determine
whether or not the plant ^^'ould continue to be satisfactory under the
changed conditions. This was done by analyzing the results of many
thousands of transmission measurements which had been made on a rou-
tine basis in toll test rooms all over the Bell System. Both the measured
and the assigned losses were available so the differences between them
could be derived and analyzed statistically.
Although the distribution of differences expressed in db for an office
did not necessarily follow precisely a normal probability law, the distri-
butions were close enough to normal law so that they could be treated as
normal. The results were similar throughout the System. The differences
within an office were random as also were the means of the differeJnces
from office to office. However, the means tended to be biased in the direc-
tion of excess loss. The performance of trunks in multi-link connections
which would be set up by the switching machines could therefore be esti-
mated with reasonable accuracy. In the statistical analysis of measure-
ments on the group of trunks, the performance was expressed in terms
of "distribution grade" and "bias." In telephone transmission mainte-
nance terminology, bias is the algebraic average of the measured trans-
mission departures in db from individual specified net losses for the group
of trunks. The distribution grade is the standard deviation of the differ-
ences between measured and specified trunk losses about this bias value.
The distribution grades found in these studies were about as follows:
For trunks under 500 miles — about 1.8 db.
For longer trunks — about 2.5 db.
Table II illustrates the effects of the distribution grades on connections
involving various combinations of these trunk links, assuming that bias
can be neglected.
The design loss objective for a 4-link connection, say 1,000 miles long,
is abovit 7 or 8 db (including 2 db of connecting trunk or pad loss at each
end), ^rable II shows that, in an appreciable percentage of the 4-link con-
nections in\'olving the above type of plant, the \'ariations can he ex-
pected to exceed the design loss. Variations of this magnitude can result
in transmission impairment d\w to (H'ho, hollownoss, singing, crosstalk,
INTERTOLL TRUNK NET LOSS MAINTENANCE
963
Table II
Number of IntertoU Trunks in the Connection .
Distribution Grade in db
Per cent of Connections Departing
from Average
±2 db or more
±4 db or more
±8 db or more
2.5
42
11
0.
4.4
65
36
7
5.0
69
42
11
8*
5.6
73
47
15
Includes two trunks over 500 miles long.
noise or low volume. Furthermore, undesirable contrast may be encoun-
tered on successive calls between the same two telephones.
The results of the study as well as experience with the beginning of
automatic alternate routing show that the performance of the existing
trunk plant must be improved. Three immediate objectives have been
set:
1. Reduction of distribution grades to about }^ of the values men-
tioned above, i.e., about 1.0 db.
2. Maintenance of office bias within ±0.25 db.
3. Removal from ser\'ice of individual trunks differing widely from
their design losses (in the order of 4 or 5 db).
To achieve these objecti^'es requires effort along four lines. First,
systems should be designed to have sufficient stability once they are
adjusted. This involves the inclusion of stable circuit elements and the
provision of automatic regulating devices to compensate for unavoidable
transmission variations arising from natural causes. These features have
been applied to existing systems within limits imposed by economic con-
siderations and the state of the art. Further extension of these features
will be required in the future in order to meet the above objectives.
Second, before a trunk is placed in service, each of its component parts
and the over-all trunk should be adjusted to give the correct loss. From
the transmission maintenance point of view, it is extremely important for
each trunk to start out with all of its adjustments correctly made.
Third, existing and incipient troubles, and deterioration or maladjust-
ment of components, must be detected and corrected by routine mainte-
nance of indi\'idual systems used in making up trunks. Such activity
must make up for the inability to design systems to have the desired
stal)ility.
Fourth, significant departures from trunk design losses must be de-
tected by over-all transmission measurements, and must be corrected be-
964 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
fore service reactions occur. Such measurements will also be of aid in de-
termining the effectiveness of efforts along the first and third lines.
As discussed earlier, the presence of the operator on every call was of
material assistance in the detection of unsatisfactory trunks. On operator
or direct distance dailed calls, there will be little or no operator conversa-
tion over the intertoll trunk connection. As a substitute, the maintenance
forces may need to make more frequent checks of the transmission per-
formance of the trunks unless the stability of individual systems and
components of systems can be improved. Manual methods have been
used by the maintenance forces in the past to measure trunk losses. Semi-
automatic measuring methods have been developed to reduce the time
and effort required. In many cases the necessary number of measurements
will be economical only when made by automatic devices. One form of
such gear is described in a companion paper. ^
The ability to measure over-all trunk losses simply and frequently is
of direct aid in detecting when loss deviations exceed maximum toler-
ances. Such measurements in themselves, however, are insufficient to
detect incipient troubles or to indicate the component part responsible
for unsatisfactory transmission. An attempt has been made to achieve
these objectives by using statistical analysis of the measured data as
an aid to diagnosis. The following sections discuss the application of such
analysis.
Use of Transmission Loss Data
It has been shown that considerable variation can be expected in trunk
losses even in the absence of trouble conditions. For any given group of
trunks selected for analysis, the performance is described by the distri-
bution grade and the bias. If a group of trunks is found to have bias, it
is usually an indication of some assignable cause. One such cause might
be a change in gain of an amplifier common to the group. Another cause
might be improper gain adjustment for channel units of a carrier termi-
nal associated with the group.
If a group of trunks is found to have a greater distribution grade than
the distribution grade for all the trunks in the office, this may indicate
excessive instability in a component part common to the trunks in the
group. If analysis of all the trunks terminating in an office shows a higher
distribution grade than is usually fomid in similar offices, the fault may
be due to maintenance routines being inadequately or improperly ap-
plied.
* H. H. Felder, A. J. Pascarella and H. F. Shoffstall, Automatic Testing of
Transmission and Operational Functions of Intertoll Trunks, page 927 of this
issue.
INTERTOLL TRUNK NET LOSS MAINTENANCE 965
Statistical analyses must thus be made of data for small groups as
well as for large groups of trunks. Furthermore, the groups which arc
studied must have elements or factors in common in order for the statis-
tics to have significance. Analyses of periodic measurements of losses for
the same trunk or groups of similar trunks can likewise indicate signifi-
cant changes in performance.
As yet, the problems of properly selecting the trunks to be analyzed
and of correlating the results of the analyses with particular system ele-
ments needing maintenance attention have been solved only partially.
In addition to the need for proper procedures, there is the need for thor-
ough training of maintenance personnel. The complexity of the telephone
plant today is increasing the importance of all maintenance personnel
ha\dng a thorough knowledge of how individual systems function and
how the performance of the various system elements reacts upon over-
all trunk performance.
Procedure for Analyzing Measurements
In an effort to facilitate the application of statistical analysis of trunk
performance by plant personnel, a special data sheet and associated
templates have been devised. These are shown in Figs. 4, 5, and 6. The
method of analysis gives only approximate results but has been found
to be sufficiently accurate for reasonably large amounts of data. It is
simple, rapid and easily comprehended by the plant personnel. The
procedure to be followed consists first of subtracting the specified loss
from the measured loss for each of the trunks under study. A stroke is
placed on the chart for each of the resulting deviations at the intersection
of the appropriate classification and tally lines. For example, the first
deviation between —3.25 db and —3.75 db would be stroked on the
horizontal line for that band, just to the left of the vertical line for tally 1
(See Fig. 4). The second deviation in that band would be stroked just to
the left of the tally 2 line. This is continued until all the deviations have
been recorded.
The last stroke in each j^^ db band indicates the number of deviations
found having values within that band. As shown on Fig. 4, for the
analysis by the template method this value is written in the first column,
marked "Line Tots. (A)." These values are added and should equal the
total number of measurements in the study (533 in the example).
Next, the column "Cum. to 3^^" is filled out. Beginning at the top
line, totals are accumulated to the point where adding the next line total
will result in a value exceeding 3-^ the grand total of measurements (266
in the example). Similarly a value is obtained accumulating the totals
from the bottom. In Fig. 4 these values are 246 and 166, respectively.
966
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
P 1 1 -F 1 1 1 1 1 1 1 1 1 1 \ 1 1 1 1 1 \ 1 1 T t I 1 1 f 1 I i
o
rrnpmqmp<»)or?ocnomom_rooc»>Ofop':PP;^P'^P'3SSS
Xi
! 1
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'ui6ih6in6tfi<b»ii6'^ii/>i>>^ ,h d3 ^ <ti li^ <i> m i3 <tt C </t, O it) o ity a
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1 1 1^ ' '
Is
r
o
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7
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Therefore, the BIAS-
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enter line on the
located at the -l/4 _
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he chart*
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«A t/1 tn ^ ^
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t/i u^ M^ Lr> (it u^
fsj r^ cs> 1-^ c>j r^
tiS u~> (O ix> r^ f^
+ ♦♦■♦•■•■ +
INTEKTOLL TRUNK NET LOSS MAINTENANCE 967
Fig. 5 — Combined template on stroke chart.
By use of this information the approximate bias is determined. The
scale of the bias values on the stroke sheet is shown in ^^ db steps along
the left-hand edge of the "Line Tots. (A)" column, and bias is deter-
mined to the nearest }^-i db. If the two cumulative totals differ from each
other by less than 25 per cent of the larger value, an arrow indicating
the bias is placed midway between the two class lines representing these
cumulative totals. Its value is read on the bias scale. If the two cumula-
tive totals differ from each other by 25 per cent or more of the larger
value, an arrow indicating the bias is placed ^?^ of the distance between
the two class lines representing these cumulative totals and nearer the
larger value. In Fig. 4, since 246 minus 166 (80) is greater than 25 per
cent of 246 (61.5), the arrow is placed ^4 of the way from the line repre-
senting 166 toward the line representing 246; i.e., at the — 3>^ db point
on the bias scale. A second arrow is placed at the corresponding point on
the tally 1 line.
As shown in Fig. 5, a combined template is then placed over the chart
so that the center line of the template coincides with the two arrows.
Along the center line of the template there is a scale indicating numbers
of measurements from 50 throvigh 700. The template is moved horizon-
tally so that the point on the scale corresponding to the grand total of
measurements (533 in the example) is placed on the 1 tally line. En\^elope
9G8
THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
— r-
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■H 'T * "^ ^
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0 1^
iti ' tr> p iS p tA p"
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J — . -^ t t t t r
~o K 5 S S iK S S~3
»»^if)ir)ibibr>^r<o6
trrttrtt
'iiw
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I I
''I
INTERTOLL TRUNK NET LOSS MAINTENANCE 969
curves for distribution grades from 0.38 db to 3 db are shown on the
template. The smallest envelope having not over 8 per cent of the grand
total of measurements outside of the envelope represents the approxi-
mate distribution grade. In the example, this is the 1 db curve, for which
22 points or 4.1 per cent of the total fall outside of the curve. Using a
cut-out template corresponding to the distribution grade, a trace is
placed on the stroke sheet, as shown on Fig. 6.
In cases where the small number of measurements or the character
of the dispersion makes it difficult to fit the data with any of the en-
velope curves of the template, RMS methods of determining the distri-
bution grade and bias afford a better estimate. In the example on Fig.
6, the bias is thus found to be —0.18 db and the distribution grade is
found to be 1.14 db.
When the automatic transmission test and control circuit described
in the companion paper is used for measuring net losses, the bias and dis-
tribution grade can be determined more quickly and easily. This circuit
measures the transmission in terms of deviations from the specified loss
and records these by a teletypewriter. In addition, registers indicate the
total number of measurements and the number of deviations falling in
the ^'2 db bands shown on the stroke chart. The final strokes for each
band can thus be placed on the chart directly without the need for
stroking each measurement. From this point on, the analysis and the
final tracing of the envelope curve which is selected are the same as in
the case illustrated by Fig. 6.
EFFECTIVENESS OF OVER-ALL TRUNK TESTS AND ANALYSES
Simple Layouts
With simple trunk layouts particularly those involving one voice-
frequency or carrier link, plant forces have been able to use over-all
trunk measurements and analyses as a direct aid in maintenance. Early
field trials of the stroke chart method were made at two operating tele-
phone company offices. The testers made up stroke sheets from their
routine measurements and interpreted the results to find clues as to
what to investigate. Stroke sheets made at successive routine testing
periods also showed them what improvements they were obtaining in
the operation of the trunks.
Both offices started with distribution grades of about 1.8 db and with
biases of about ^^ db. The trunk plant was then given a thorough cleanup
and realignment more rigorous than that called for in the maintenance
practices at the time. Similar rigorous circuit order tests were followed
970 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 195G
as circuit order changes were made. Many small troubles were found and
cleared. As the result of such rigorous circuit order work and the use of
statistical analyses, the distribution grades at the end of the trial were
reduced to about 1 db and the biases were brought close to zero.
The maintenance activities were conducted by the regular test forces
during normall}' available maintenance time. Although the initial work
in\'oh'ed in cleaning up the trunks necessitated some slippage in the
periodic maintenance tests, troubles requiring realignment were eventu-
ally reduced to the point where it became possible to carry on the periodic
testing work concurrently with the more rigorous circuit order work.
Complex Layouts
During the field trial of the automatic transmission test and control
circuit discussed in a companion paper, there was an opportunity for
studying transmission data taken on intertoll trunks of greater length
and complexity of layout. These trunks were composed of two or more
carrier links and connected Washington, D.C. to several outlying points;
namely, Atlanta, Georgia; Boston, Massachusetts; Hempstead, New
York; New York, New York; Oakland, California; and Richmond, Vir-
ginia. A total of 231 trunks were in the groups. When the trial began,
without preliminary rigorous circuit order work on the trunks involved,
the distribution grade was 2.26 db and the bias was -|-0.35 db. Mainte-
nance investigation was initiated only when trunks were foimd to have
departed more than a prescribed amount from their specified net losses.
Initially this value was 4 db and later it was reduced to 3.5 db.
As many of these wide de\'iations were investigated and corrected as
available manpower permitted. The layouts were so complex, however,
that it was found impracticable to give prompt attention to all of them;
and in many cases it was impossible to check carrier systems that were
suspected of being the source of some of the deviations. At the end of
the trial the distribution grade had been reduced from the original 2.26
db to a range of about 1.8 to 2 db. The bias had not been changed sig-
nificantly from the original -1-0.35 db.
These results indicated very little improA'ement from the limited re-
adjustments found practicable diu'ing the tests. Analysis of the test re-
sults has shown that transmission maintenance methods must be im-
proved in some respects. An example of this was a case where the data
indicated several trunks to be affected by excessive variation from some
common cauKC. This was traced to a group pilot being out of limits. If
routine maintenance methods had indicated this difficulty earlier, the
amount of time in which service could have been affected by thesc^ trunks
would have been reduced. This is important because of the difficulty of
finding evidence of common trouble sources, with complex layouts.
INTERTOLL TRUNK NET LOSS MAINTENANCE 971
The scope of the trial was then limited to a smaller group of intertoll
trunks which could be given close attention. The 42 trunk group between
Washington, D.C., and Atlanta, Ga., was selected and these trunks were
put through rigorous circuit order tests and adjustments approaching
the completeness of initial line-up tests. A test cycle composed of trans-
mission loss measurements made on the 42 trunks in both directions
was performed four times daily for a period of about five months. During
the period covered by this phase of the trial, adjustments were made
only as indicated by carrier pilot ^'ariations, by deviations from specified
net loss large enough to operate the limit feature of the automatic trans-
mission test and control circuit, or with other trouble clearance.
The tests for each day were analyzed as a group. On the first day the
distribution grade of the deviations from specified net loss for the group
was 0.8 db and the bias was +0.5 db. On the last day the distribution
grade was 1.2 db and the bias was —0.25 db. For the entire group of
measurements (584 test cycles), the distribution grade of the deviations
was 1.26 db and the bias was —0.08 db. This represented a substantial
improvement over the results obtained in the first phase of the trial. It
showed that a great deal can be accomplished by improving the circuit
order procedures and increasing the thoroughness with which they are
carried out.
It was found that combination carrier trunks composed of perma-
nently connected links, thus not having the benefit of control by ter-
minal-to-terminal pilots, have more variability than individual trunks
having over-all pilots. Adjustment of such combination trunks requires
coordinated action at the various pilot terminals through which the
trunk passes, in order that readjustment of the over-all trunk loss can
be made at the point in the system responsible for the deviation. In the
case of many route junctions, the complexity of the layout makes it
difficult to coordinate the necessary measurements at several points so
that the proper point for adjustment can be determined.
NEED FOR EDUCATION
The complexity of carrier system layout as indicated above, has im-
posed a difficult task on the plant transmission maintenance forces. Al-
though our present transmission maintenance practices seem to be ade-
cjuate for systems in simple layouts, some expansion appears needed for
the more complex layouts. This will recjuire further study.
It is important to keep in mind, however, that the pro\'ision of good
practices and training of personnel in following the detailed steps therein
are not in themselves sufficient to assure good transmission maintenance.
There is an additional need for education of plant personnel in fundamen-
tal considerations affecting operation of carrier systems. This must in-
972 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
elude over-all objectives, inherent capabilities and limitations, and the
interrelation of functions of the many basic blocks comprising carrier
systems. Personnel so educated can approach the problems of transmis-
sion maintenance with understanding and avoid the maladjiistments
and troubles due to "man-failure" which are potential hazards in any
complex systems.
SUMMARY AND CONCLUSIONS
In summary, the problem of maintaining satisfactory transmission
over trunks under distance dialing involves, primarily :
1 . Impro\dng the over-all trunk net loss stability so that the distribu-
tion grade does not exceed 1 db, as an initial objective.
2. Reducing trunk loss bias for individual offices to less than ±0.25 db.
3. Removing from operation those trunks having excessive loss devia-
tions before unfavorable service reactions occur.
To do these things in the face of the increasing complexity of our plant
and the absence of operator surveillance will require that:
1 . Individual systems have adequate short term stability to keep day-
to-day variations small.
2. Routine tests and adjustments be made on individual systems and
components to correct for long-term deterioration.
3. Frequent over-all trunk tests be made to locate trunks whose per-
formance is beyond acceptable limits and, as a quality control measure,
to monitor the performance of the trunk plant.
4. Trunk trouble-shooting be performed on a well coordinated basis
to locate and correct the source of trouble. (Compensating maladjust-
ments must be avoided.)
Although facilities are available and methods are known for doing
some of these things, considerable effort is required as follows:
1. Study of performance of individual systems to determine capabili-
ties of present design and major sources contributing to over-all trunk
instability.
2. Study of transmission maintenance procedures, both routine and
trouble-shooting, to determine the proper test intervals and how best
the procedures can be carried out on a coordinated basis.
3. Development of improvements in systems and test facilities as
indicated by the above studies. Convenience is an important factor in
test arrangements.
4. Thorough education of personnel in the over-all make-up, function
and interrelation of systems within the trunk plant, and in the significance
of transmission maintenance in pro\'iding uniformly good and depend-
able transmission.
Bell System Technical Papers Not
Published in This Journal
Abbott, L. E./ and Pomeroy, A. F.^
How To Get More Range From An Air Gage, Am. Machinist, 100, pp.
113-115, Feb. 27, 1956.
Ahearn, a. J.,1 and Law, J. T.^
Russell Effect in Silicon and Germanium, J. Chem. Phys., Letter to
the Editor, 24, pp. 633-634, Mar., 1956.
Anderson, P. W., see Clogston, A. M.
Arlt, H. G.i
Standardization of Materials, Standards Engineering, 8, pp. 6-7,
Mar., 1956.
Bashkow, T. R}
DC Graphical Analysis of Junction Transistor Flip-Flops, A.I.E.E.
Commiin. and Electronics., 23, pp. 1-6, Mar., 1956.
Becker, J. A.,^ and Brandes, R. G.^
A Favorable Condition for Seeing Simple Molecules in a Field Emis-
sion Microscope, J. Appl. Phys., 27, pp. 221-223, Mar., 1956.
Bennett, W. R}
Characteristics and Origins of Noise — Part I., Electronics, 29, pp.
154-160, Mar., 1956.
Bennett, W. R.^
Electrical Noise — Part II: Noise Generating Equipment, Electronics,
29, pp. 134-137, Apr., 1956.
Bennett, W. R.^
Synthesis of Active Networks, Proc. Symp. Modern Network Syn-
thesis, MRI Symposia Series, 5, pp. 45-61, 1956.
^ Bell Telephone Laboratories, Inc.
973
974 the bell system technical journal, july
Blecher, F. H.^
A Junction Transistor Integrator, Pioc. National Electronics Con-
ference, 11, pp. 415-430, Mar. 1, 1956.
BoMMEL, H. E.,1 Mason, W. 1\,' and Wainer, A. W.^
Dislocations, Relaxations and Anelasticity of Crystal Quartz, Phys.
Rev., 102, pp. 64-71, Apr. 1, 1956.
BOZORTH, R. M.i
Quelques Proprietes Magnetiques, Electrioques Et Optiques Des
Films Obtenus Par Electrolyse Et Par Evaporation Thermique, Le J.
De Physique Et Le Radium, 17, pp. 256-262, Mar., 1956.
BoYET, H., see Weisbaum, S.
Brady, G. W.^
X-Ray Study of Tillurium Oxide Gas, J. Chem. Phys., Letter to the
Editor, 24, p. 477, Feb., 1956.
Brandes, R. G., see Becker, J. A.
Brattain, W. H., see Garrett, C. G. B.
Braun, F. A}
Moimting Scheme for Large Cathodes, Rev. Sci. Instr., Lab. and
Shop Notes Section, 27, p. 113, Feb., 1956.
Clogston, a. M.,1 Suhl, H.,^ Walker, L. R.,^ and Anderson, P. W.^
Possible Source of Line Width in Ferromagnetic Resonance, Phys.
Rev., Letter to the Editor, 101, pp. 903-905, Jan. 15, 1956.
DE Leeuw, K.,^ Moore, E. F.,i Shannon, C. E.,^ and Shapiro, N.^
Computability by Probabilistic Machines, Automata Studies, (Prince-
ton Univ. Press), pp. 183-212, Apr., 1956.
EiGLER, J. H., see Sullivan, M. V.
Fox, A. G.i
Wave Coupling by Warped Normal Modes, LR.E. Trans., PGMTT,
3, pp. 2-6, Dec, 1955.
^ Bell Telephone Laboratories, Inc.
•3,
TECHNICAL PAPERS 975
Francois, E. E., see Law, J. T.
Gardner, I\I. B.^
Speech We May See, Volta Review, 58, pp. 149-155, Apr., 1956.
Garrett, C. G. B.,^ and Brattain, W. H.^
Some Experiments on, and a Theory of. Surface Breakdown, J. Appl.
Phys., 27, pp. 299-306, Mar., 1956.
Haynes, J. R.,^ and Westphal, W. C.^
Radiation Resulting fron Recombination of Holes and Electrons in
Silicon, Phy«. Kev., 101, pp. 1676-1678, Alar, lo, 1956.
Herrmann, D. B., see Williams, J. C.
Kelly, M. J}
Contributions of Research to Telephony — A Look at Past and
Glance into Future, Franklin Inst. J., 261, pp. 189-200, Feb., 1956.
Kleimack, J. J., see Wahl, A. J.
Law, J. T.,1 and Francois, E. E.^
Adsorption of Gases on Silicon Surface, J. Chem. Phys., 60, pp. 353-
358, I\Iar., 1956.
Law, J. T., see Ahearn, A. J.
Lloyd, S. P.,i and McMillan, B.i
Linear Least Squares Filtering and Prediction of Sampled Signals,
Proc. Symp., PIE, V, pp. 221-247, Apr., 1955.
Logan, R. A.^
Thermally Induced Acceptors in Germanium, Phys. Rev., 101, pp.
1455-1459, Mar. 1, 1956.
Mason, W. P.^
Comments on Weertman's Dislocation Relaxation Mechanism, Phys.
Rev., Letter to the Editor, 101, p. 1430, Feb., 15 1956.
Mason, W. P., see Bomniel, H. E.
McMillan, B., see Lloyd, S. P.
1 Bell Telephone Laboratories, Inc.
976 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
Mendel, J. T.^
Microwave Detector, Proc. I.R.E., 44, pp. 503-508, Apr., 1956.
Merz, W. J., see Remeika, J. P.
Moore, E. F}
Gedanken-Experiments on Sequential Machines, Automata Studies
(Princeton Univ. Press), pp. 129-153, Apr., 1956.
Moore, E. F., see de Leeuw, K.
PoMEROY, A. F., see Abbott, L. E.
Remeika, J. P.,^ and Merz, W. J.^
Guanidine Vanadium Sulfate Hexahydrate: A New Ferroelectric
Material, Phys. Rev., Letter to the Editor, 102, p. 295, Apr. 1, 1956.
Robertson, S. D.^
Ultra-Bandwidth Fmlme Coupler, I.R.E. Trans., PGMTT, 3, pp. 45-
48, Dec, 1955.
Rose, D. J.^
On the Magnification and Resolution of the Field Emission Electron
Microscope, J. Appl. Phys., 27, pp. 215-220, Mar.., 1956.
Shannon, C. E., see de Leeuw, K.
Shapiro, N., see de Leeuw, K.
SUHL, H.^
Subsidiary Absorption Peaks in Ferromagnetic Resonance at High
Signal Levels, Phys. Rev., Letter to the Editor, 101, pp. 1437-8,
Feb. 15, 1956.
SuHL, H., see Clogston, A. M.
Sullivan, M. V.,^ and Eigler, J. H.^
Five Metal Hydrides as Alloying Agents on SiHcon, J. Electrochem.
Soc, 103, pp. 218-220, Apr., 1956.
Sullivan, M. V.,^ and Eigler, J. H.^
Electrolytic Stream Etching of Germanium, J. Electrochem. Soc,
103, pp. 132-134, Feb., 1956.
^ Bell Telephone Laboratories, Inc.
technical papers 977
Trent, R. L.^
Design Principles of Junction Transistor Audio Amplifiers, I.R.E.
Trans., PQA, 3, pp. 143-161, Sept.-Oct., 1955.
Turner, D. R.^
The Anode Behavior of Germanium in Aqueous Solutions, J. Electro-
chem. Soc, 103, pp. 252-256, Apr., 1956.
Uhlir, A., Jr.^
High-Frequency Shot Noise in PN Junctions, Proc. I.R.E. , Corre-
spondence, 44, pp. 557-558, Apr., 1956.
Van Haste, W.^
Statistical Techniques for a Transmission System, A.I.E.E. Commim.
and Electronics, 23, pp. 50-54, Mar., 1956.
Van Haste, W.^
Component Reliability in a Transmission System, Elec. Engg., 75, p.
413, May, 1956.
Van Roosbroeck, W.^
Theory of the Photomagnetoelectric Effect in Semiconductors, Phys.
Rev., 101, pp. 1713-1724, Mar. 15, 1956.
Van Uitert, L. G.^
High Resistivity Nickel Ferrites — The Effects of Minor Additions
of Manganese or Cobalt, J. Chem. Phys., 24, p. 306, Feb., 1956.
Wahl, a. J.,^ and Kleimack, J. J.^
Factors Affecting Reliability of Alloy Junction Transistors, Proc.
I.R.E., 44, pp. 494-502, Apr., 1956.
Wainer, a. W., see Bommel, H. E.
Walker, L. R., see Clogston, A. M.
Weisbaum, S.,^ and Boyet, H.^
A Double-Slab Ferrite Field Displacement Isolator at 11 KMC, Proc.
I.R.E., 44, pp. 554-555, Apr., 1956.
Westpiial, W. C, see Haynes, J. R.
^ Bell Telephone Laboratories, Inc.
978 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
Williams, J. C.,^ and Herrmann, D. B.^
Surface Resistivity of Nonporous Ceramic and Organic Insulating
Materials at High Humidity with Observations of Associated Silver
Migration, I.K.E. Trans., PGRQC, 6, pp. 11-20, Feb., 1956.
WOLONTIS, V. M.l
A Complete Floating-Decimal Interpretive System for the IBM 650
Magnetic Drum Calculator, IBM Technical Newsletter, 11, Mar.,
1956.
Bell Telephone Laboratories, Inc.
Recent Monographs of Bell System Technical
Papers Not Published in This Journal*
Arnold, W. O., and Hoefle, R. R.
A System Plan for Air Traffic Control, Monograph 2483.
Babcock, W. C, Rentrop, E., and Thaeler, C. S.
Crosstalk on Open-Wire Lines, Monograph 2520.
Beck, A. C, and Mandeville, G. D.
Microwave Traveling- Wave Tube Millimicrosecond Pulse Gener-
ators, Monograph 2551.
BozoRTH, R. M., Williams, H. J., and Walsh, Dorothy E.
Magnetic Properties of Some Orthoferrites and Cyanides at Low
Temperatures, ]\Ionograph 2591.
Bridgers, H. E.
A Modern Semiconductor — Single -Crystal Germanium, Monograph
2552.
Cetlin, B. B., see Gait, J. K.
Chynoweth, A. G.
Measuring the Pyroelectric Effect with Special Reference to Barium
Titanate, Monograph 2545.
CoRENZwiT, E., see Matthias, B. T.
Cutler, C. C.
Spurious Modulation of Electron Beams, ^Monograph 2543.
Dail, H. W., Jr., see Gait, J. K.
* Copies of these monographs ma}' be obtained on request to the Publication
Department, Bell Telephone Laboratories, Inc., 46.3 West Street, New York 14.
N. Y. The numbers of the monographs should be given in all requests.
979
980 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956 j
1
Davis, H. M,, see Wemick, J. H.
Dbsoer, C. a.
Iterative Solution of Networks of Resistors and Ideal Diodes, Mono-
graph 2583.
Duncan, R. S., and Stone, H. A., Jr.
A Survey of the Application of Ferrites to Inductor Design, Mono-
graph 2579.
Feldman, W. L., see Pearson, G. L.
Fewer, D. R., see Kircher, R. J.
Fry, Thornton C.
Mathematics as a Profession Today in Industry, Monograph 2585.
Galt, J. K., Yager, W. A., Merritt, F, R., Cetlin, B. B., and Dail,
H. W., Jr.
Cyclotron Resonance in Metals: Bismuth, Monograph 2535.
Geballe, T. H., see Hrostowski, H. J.
GlANOLA, U. F.
Photovoltaic Noise in SiUcon Broad Area p-n Jimctions, Monograph
2546.
Goss, A. J., see Hassion, F. X.
Gyorgy, E. M., see Heinz, O.
Hagelbarger, D. W., see Pfann, W. G.; also Shannon, C. E.
Harker, K. J.
Periodic Focusing of Beams from Partially Shielded Cathodes, Mono-
graph 2553.
Hassion, F. X., Thurmond, D. C., Trumbore, F. A., and Goss, A. J.
Germanium: on the Melting Point; on the Silicon Phase Diagram,
Monograph 2489. a
Heidenreich, R. D., see Williams, H. J.
MONOGRAPHS 981
Heinz, 0., Gyorgy, E. M., and Ohl, R. S.
Solid-State Detector for Low-Energy Ions, Monograph 2568.
Herrmann, D. B., see Williams, J. C.
HoEFLE, R, R., see Arnold, W. 0.
Hrostowski, H. J., MoRiN, F. J., Geballe, T, H., and Wheatley,
G. H.
Hall Effect and Conductivity of InSb, Monograph 2586.
Ingram, S. B.
The Graduate Engineer — His Training and Utilization in Industry,
Monograph 2554.
Kelly, M. J.
Contributions of Research to Telephony, Monograph 2590.
Ketchledge, R. W.
Distortion in Feedback Amplifiers, Monograph 2488.
KiRCHER, R. J., Trent, R. L., and Fewer, D. R.
Audio Amplifier AppUcations of Junction Transistors, Monograph
2484.
KuH, E. S.
Special Synthesis Techniques for Driving Point Impedance Func-
tions, Monograph 2581.
Lee, C. Y.
Similarity Principle with Boundary Conditions for Pseudo -Analytic
Functions, Monograph 2587,
Mandeville, G. D., see Beck, A. C.
Matthias, B. T., and Corenzwit, E.
Superconductivity of Zirconium Alloys, Monograph 2526.
Merritt, F. R., see Gait, J. K.
Miller, L. E.
Negative Resistance Regions in Collector Characteristics of Point-
Contact Transistor, Monograph 2574.
982 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 195G
Moll, J. L., and Ross, I. M.
Dependence of Transistor Parameters on Distribution of Base Layer
Resistivity, Monograph 2575.
Montgomery, H. C, see Pearson, G. L.
MoRiN, F. J., see Hrostowski, H. J.
Nesbitt, E. a., see Williams, H. J.
Ohl, R. S., see Heinz, 0.
Owens, CD.
Stability Characteristics of Molybdenum Permalloy Powder Cores,
Monograph 2576.
Pearson, G. L., Montgomery, H. C., and Feldmann, W. L.
Noise in Silicon p-n Junction Photocells, Monograph 2555.
Pedersen, L.
Aluminum Die Castings for Carrier Telephone Systems, Monograph
2593.
Pederson, D. 0.
Regeneration Analysis of Junction Transistor Multivibrators, Mono-
graph 2452.
Pfann, W. G., and Hagelbarger, D. W.
Electromagnetic Suspension of a Molten Zone, Monograph 2556.
Prince, M. B.
High -Frequency Silicon-Aluminum Alloy Junction Diodes, Mono-
graph 2557.
Rentrop, E., see Babcock, W. C.
Ross, I. M., see Moll, J. L.
Schawlow, A. L.
Structure of the Intermediate State in Superconductors, Monograph
25()9.
MONOGRAPHS 983
Shannon, C. E., and Hagelbarger, D. W.
Concavity of Resistance Functions, Monograph 2547.
SiMKiNS, Q. W., and Vogelsoxg, J. H.
Transistor Amplifiers for Use in a Digital Computer, Monograph 2548.
Snoke, L. E.
Specific Studies on Soil-Block Procedure for Bioassay of Wood Pre-
servatives, Monograph 2577.
SOUTHWORTH, G. C.
Early History of Radio Astronomy, Monograph 2544.
Stone, H. A., Jr., see Duncan, R. S.
Tanner, T. L.
Current and Voltage-Metering Magnetic Amplifiers, Monograph
2582.
Thaeler, C. S., see Babcock, W. C.
Thurmond, D. C, see Hassion, F. X.
Trent, R. L., see Kircher, R. J.
Trumbore, F. A., see Hassion, F. X.
Ulrich, W., see Yokelson, B. J.
YoGELSONG, J. H., see Simkins, Q. W.
Walsh, Dorothy E., see Bozorth, R. M.
Wernick, J. H., and Davis, H. M.
Preparation and Inspection of High-Purity Copper Single Crystals,
Monograph 2571.
Wheatley, G. H., see Hrostowski, H. J.
Williams, H. J., see Bozorth, R. M.
Williams, H. J., Heidenreich, R. D., and Nesbitt, E. A.
How Cobalt Ferrite Heat Treats in a Magnetic Field, Monograph
2558.
984 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
Williams, J. C, and Herrmann, D. B.
Surface Resistivity of Non-Porous Ceramic and Organic Insulating
Materials, Monograph 2560.
Yager, W. A., see Gait, J. K.
YoKELSON, B. J., and Ulrich, W.
Engineering Multistage Diode Logic Circuits, Monograph 2592.
Contributors to This Issue
Arthur B. Crawford, B.S.E.E. 1928, Ohio State University; Bell
Telephone Laboratories 1928-. Mr. Crawford has been engaged in radio
research since he joined the Laboratories. He has worked on ultra short
wave apparatus, measuring techniques and propagation; microwave
apparatus, measuring techniques and radar, and microwave propagation
studies and microwave antenna research. He is author or co-author of
articles which appeared in The Bell System Technical Journal, Pro-
ceedings of the I.R.E., Nature, and the Bulletin of the American Me-
teorological Society. He is a Fellow of the I.R.E. and a member of Sigma
Xi, Tau Beta Pi, Eta Kappa Nu, and Pi Mu Epsilon.
C. Chapin Cutler, B.S. 1937, Worcester Polytechnic Institute. Bell
Telephone Laboratories 1937-. Mr. Cutler's early work was in research
related to the problems of the short wave multiplex radio transmitter.
During World War H he was engaged in research on the proximity fuse
and microwave antennas for radar use. Since the war he has been con-
cerned with research on the microwave amplifier and the traveling wave
tube. Mr. Cutler is a member of the LR.E. and Sigma Xi.
Harry H. Felder, B.S. in Electrical and Mechanical Engineering,
ClemsonA. and M., 1918. After some months in the U. S. Signal Corps
he joined the Engineering Department of the American Telephone and
Telegraph Company in 1919. He joined the Laboratories in 1934. He
has been engaged in general transmission problems in connection with
telephone repeater development and toll circuit layout and switching.
During World War H, Mr. Felder assisted in the development of a
method of lapng telephone wires from airplanes. Since that time he has
continued to work on the transmission aspects of intertoll trunk design,
switching, maintenance and loading. He was also associated with adapt-
ing of cable carrier circuits for radio broadcast networks. Mr. Felder is a
member of Tau Beta Pi.
J. H. FoRSTER, B.A. 1944, M.A. 1946, University of British Colum-
bia; Ph.D. 1953, Purdue University; Bell Laboratories 1953-. Since join-
ing the Laboratories, Dr. Forster has been engaged in research on semi-
985
986 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
conductor devices including point-contact transistor development,
transistor reliability studies and the development of low-noise alloy-
transistors. He also served as instructor of semiconductor electronics in
the Laboratories Communications Development Training program. At
present he is engaged in surface studies and semiconductor device re-
liability. Member of Sigma Pi Sigma and Sigma Xi.
David C. Hogg, B.SC, University of Western Ontario, 1949; M.Sc.
and Ph.D., McGill University, 1950 and 1953. Dr. Hogg joined Bell
Telephone Laboratories in July 1953 and has worked at the Holmdel
Laboratory. He has been engaged in studies of artificial dielectrics for
microwaves, antenna problems, and over-the-horizon and millimeter
wave propagation as a member of the Radio Research Department.
During World War II Dr. Hogg was in the Canadian Army and spent
five years in Europe. From 1950 to 1951 he was engaged in research for
the Defense Research Board of Canada. He is a member of Sigma Xi.
John L. Kelly, Jr., B.A. in 1950, M.A. in 1952, and Ph.D. in 1953,
all in Physics at the L^niversity of Texas. Dr. Kelly joined Bell Tele-
phone Laboratories in 1953 as a member of the Television Research De-
partment at the Murray Hill Laboratory. He has been engaged in ex-
perimental work on the nature of television pictures as w^ll as theoretical
investigations pertaining to applications of the Information Theory to
television. In 1944 he was commissioned a Navy pilot and served three
years.
Archie P. King, B.S. California Institute of Technology, 1927. After
three years with the Seismological Laboratory of the Carnegie Institu-
tion of Washington, Mr. King joined Bell Telephone Laboratories in
1930. Since then he has been engaged in ultra-high-frequency radio re-
search at the Holmdel Laboratory, particularly with waveguides. For the
last ten years Mr. King has concentrated his efforts on waveguide trans-
mission and waveguide transducers and components for low-loss circular
electric wave transmission. He holds at least a score of patents in the
waveguide field. Mr. King was cited by the Navy for his World War II
radar contributions. He is a Senior Member of the I.R.E. and is a Mem-
])er of the American Physical Society.
J. G. LiNviLL, A.B., William Jewell College, 1941 ; S.B. in 1943, S.M.
in 1945 and Sc.D. in 1949, all in electrical engineering at Massachusetts
Institute of Technology. Dr. Linvill served at M. I. T. as assistant pro-
'
CONTRIBUTORS TO THIS ISSUE 987
fessor in electrical engineering from 1949 to 1951 and was a consultant
to Sylvania Electrical Products. He joined Bell Telephone Laboratories
in 1951 and worked on active network problems involving applications
of transistors as the active element. In March, 1955, he became Asso-
ciate Professor of Electrical Engineering at Stanford University. He is a
member of the American Institute of Electrical Engineers, Institute
of Radio Engineers, Sigma Xi, and Eta Kappa Nu.
Edward N. Little, A.B., Yale, 1916; S.B., Massachusetts Institute of
Technology, 1919; Signal Corps and Air Service Radio Officer training.
World War I. Joined Long Lines Department of A. T. & T. in 1919 to
work on transmission studies. Transferred to Transmission Section of
0. & E. Department in 1922 in work dealing with telephone repeaters.
Nine years later joined the group working on transmission maintenance,
and since then has worked principally on various phases of voice-
frequency toll transmission maintenance. For the last eight years he has
been working on the problems of intertoll trunk transmission mainte-
nance posed by the advent of nationwide intertoll dialing with full auto-
matic alternate routing. One angle of this work has been the develop-
ment and application of statistical analyses as tools for helping to attain
the required reduction in net loss variations.
Enrique A. J. Marcatili, University of Cordoba, Argentina. Mr.
Marcatili was awarded the Argentine title of Aeronautical Engineer in
1947 and the title of Electrical Engineer in 1948. He received a Gold
Medal from the University of Cordoba for the highest scholastic record.
He joined Bell Telephone Laboratories in 1954 after studies of Cherenkov
radiation in Cordoba, and has been engaged in waveguide research at
Holmdel. Specifically, Mr. Marcatili has been concerned with the theory
and design of filters in the ixdllimeter region to separate channels in w^ave-
guides. He has published technical articles in Argentina and belongs to
the A. F. A. (Physical Association of Argentina).
Lewis E. Miller, B.S. in Engineering Physics, Lafayette College,
1949; General Aniline and Film Corp., 1949-1952; Bell Telephone
Laboratories, 1952-. Since joining the Laboratories Mr. Miller has
specialized in the development of transistors. His early work was on the
development for manufacture of the point-contact transistor. From 1954
to May 1956 he was concerned with surface problems and the develop-
ment of germanium alloy transistors. At present he is concentrating on
diffused silicon transistors. Mr. Miller is a member of the American
Physical Society.
988 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956
A. J. Pascarella, E.E., Columbia University, 1916. After his gradu-
ation he entered the student course of the General Electric Company at
Schenectad3^ Shortly after our entrance into World War I, Mr. Pasca-
rella joined the U. S. Navy and was put in charge of the electrical labora-
tory of the Gas Engine School at Columbia. In 1921 he joined the
Western Electric Company and in 1925 the Technical Staff of the Labo-
ratories. Here with the Systems Department he was concerned with the
development of toll testboards, toll signaling, telegraph, carrier and
miscellaneous testing equipment. Later his work consisted of formu-
lating maintenance requirements for the over-all testing of toll lines
and the detecting and location of faults on toll cables. During World
War II he was concerned with developing high level auditory systems
for use in psychological warfare. He also acted as editor of repair manuals
used by the Armed Services. At the present time he is working on mili-
tary projects. Licensed Professional Engineer, New York State.
L. G. ScHiMPF, B.E.E., Ohio State University, 1937; Bell Telephone
Laboratories, 1937-. From 1937 to 1940 Mr. Schimpf was engaged in re-
search on the application of electronic devices to switching functions,
with particular emphasis on cold cathode tubes. With the outbreak of
World War II, he turned his attention to research and development work
on military projects. For six years after the war he specialized in trans-
mission research studies of local subscriber station circuits and acoustics.
Since 1952 he has been engaged in transistor circuit research. In this field
he has concentrated particularly on the high frequency operation of
transistors in transmission circuits. Senior Member of I.R.E., member
of Acoustical Society of America, Eta Kappa Nu, and Tau Beta Pi.
H. F. Shoffstall, B.E.E., Ohio State University, 1916; American
Telephone and Telegraph Company, 1916-35; Bell Telephone Labora-
tories, 1935-. Mr. Shoffstall worked on the development of telephone re-
peaters and on toll equipment for central offices until he came to the
Laboratories in 1935. Since then he has been associated with the switch-
ing development group engaged in the design of toll-switching circuits.
Member of the American Institute of Electrical Engineers.
Harold Seidel, B.E.E., College of the City of New York, 1943;
M.E.E., D.E.E., Polytechnic Institute of Brooklyn, 1947 and 1954. Dr.
Seidel joined Bell Telephone Laboratories in 1953 after employment with
the Microwave Research Institute of the Polytechnic Institute of Brook-
lyn, the Arma Corporation and the Federal Telecommunications Labora-
I
CONTRIBUTORS TO THIS ISSUE 989
tories. His work at the Laboratories has been concerned with general
electromagnetic problems, especially regarding waveguide applications,
and with analysis of microwave ferrite devices. Dr. Seidel is a member
of Sigma Xi and the I.R.E.
S. Weisbaum, B.A., M.S. and Ph.D., New York University, 1947,
1948 and 1953; instructor in physics, New York University, 1950-53;
Bell Telephone Laboratories, 1953-. Since joining the Laboratories, Dr.
Weisbaum has specialized in the development of microwave ferrite de-
vices, such as isolators and circulators. He is a member of the American
Physical Society and Sigma Xi.
HE BELL SYSTEM
meal lournal
OTED TO THE SCIENTIFIC ^^^ AND ENGINEERING
»ECTS OF ELECTRICAL COMMUNICATION
UME XXXV SEPTEMBER 1956 NUMBER 5
Electronics in Telephone Switching Systems a. e. joel 991
Combined Measurements of Field Effect, Surface Photo-Voltage
and Photo-Conductivity w. h. brattain and c. g. b. garrett 1019
Distribution and Cross-Sections of Fast States on Germaniimi
Surfaces c. g. b. garrett and w. h. brattain 1041
Transistorized Binary Pulse Regenerator l. r, wrathall 1059
Transistor Pulse Regenerative Amplifiers f. h. tendick, jr. 1085
Observed 5-6 mm Attenuation for the Circular Electric Wave in
Small and Medium-Sized Pipes a. p. king 1115
Automatic Testing in Telephone Manufacture d. t. robb 1129
Automatic Manufacturing Testing of Relay Switching Circuits
L. D. HANSEN 1155
Automatic Machine for Testing Capacitors and Resistance-Capaci-
tance Networks c. c. cole and h. r. shillington 1179
A 60-Foot Diameter Parabolic Antenna for Propagation Studies
A, B. CRAWFORD, H. T. FRIIS AND W. C. JAKES, JR. 1199
The Use of an Interference Microscope for Measurement of Ex-
tremely Thin Surface Layers w. l. bond and f. m. smits 1209
Bell System Technical Papers Not Published in This Journal 1223
Recent Bell System Monographs 1230
Contributors to This Issue 1233
COPYRIGHT 1956 AMERICAN TELEPHONE AND TELEGRAPH COMPANY
THE BELL SYSTEM TECHNICAL JOURNAL
ADVISORY BOARD
F. R. KAPPEL, President, Western Electric Company
M. J. KEiiLY, President, Bell Telephone Laboratories
E. J. McNEELY, Executive Vice President, American
Telephone and Telegraph Company
EDITORIAL COMMITTEE
B. MCMILLAN, Chairman
A. J. BUSCH
A. C. DICKIESON
R. L. DIETZOLD
K. E. GOULD
E. I. GREEN
R. K. HONAMAN
H. R. HUNTLEY
F. R. LACK
J. R. PIERCE
H. V. SCHMIDT
G. N. THAYER
EDITORIAL STAFF
J. D, TEBo, Editor
R. L. SHEPHERD, Production Editor
THE BELL SYSTEM TECHNICAL JOURNAL is published six times a year
by the American Telephone and Telegraph Company, 195 Broadway, New York
7, N. Y. Cleo F. Craig, President; S. Whitney Landon, Secretary; John J. Scan-
Ion, Treasurer. Subscriptions are accepted at $3.00 per year. Single copies are
75 cents each. The foreign postage is 65 cents per year or 11 cents per copy. Printed
in U. S. A.
THE BELL SYSTEM
TECHNICAL JOURNAL
VOLUME XXXV SEPTEMBER 1956 number 5
Copyright 1956, American Telephone and Telegraph Company
Electronics in Telephone Switching
Systems
By A. E. JOEL
(Manuscript received March 18, 1956)
In recent years a number of fundamentals has been discovered through
research which place new tools at the disposal of the circuit and system de-
signers. Examples of this ^'new art" are concepts such as information
theory, dealing with the quantization and transmission of information, and
solid state principles from which have developed the transitor and other de-
vices. This paper surveys certain new art principles, techniques and devices
as they apply to the design of new telephone switching systems.
Over the past forty years a great background and fund of knowledge
has developed in the field of telephone switching. Constant improvement
in available devices has resulted in increasing the scope of their appli-
cation. The field has almost reached a point of perfection as an art and
is now rapidly entering a more scientific era.
The tools of the present day telephone system design engineer are
well known and some are illustrated in Figure 1. These are the relay
and the various forms of electromechanical switching apparatus. But
over the years, while the art employing these tools was developing,
the field of electronics has also been developing. Its applications were
most needed when dealing with its characteristics of sensitivity rather
991
992 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
^i''^ *t^s^<iS ^ '</g^pi^f.%
Fig. 1 — Typical telephone relays and switches.
ELECTRONICS IN TELEPHONE SWITCHING SYSTEMS
993
than speed. Even in the telephone switching field, this property of
electronics has made its inroads to provide us with better signaling and
more accurate timing.
It was not, however, until World War II that the speed advantages
of electronics were exploited. This exploitation came primarily in the
quantizing of information, both in transmission and information proc-
essing equipment. In the latter field new digital computers made their
appearance. These machines brought forth the development of new
forms of electronic devices, most important of which are those classified
as "bulk memory" devices.^ Later in this paper the characteristics of
many of these devices will be discussed in more detail.
In the post-war period the exploitation of another phase of electronics
developed from research in semiconductor devices. The transistor is
perhaps the best known invention to emerge from these investigations.
The impact of the application of semiconductor devices is yet to be
felt in the electronics industry and it will most likely find greatest
application in the information processing field and in communications
generally.
Before one may understand and appreciate the impact electronics
will have on the design of new telephone switching systems it is nec-
essary to consider the question: "What is a Telephone Switching Sys-
tem?" By evolution it is now^ generally recognized that the central
office portion of a telephone switching system consists of two prin-
cipal parts and certain physical and operational characteristics of these
parts. These parts, as illustrated in Figure 2, are the interconnecting
network, or conversation channel, and its control.
In some switching systems, particularly those of the progressive
LINES-
SWITCHING NETWORK
CONC
N I
T I
GATHERING
DIST
EXP
CONTROL
INFORMATION
PROCESSINGS
INTERPRETING
-TRUNKS
EFFECTING
Fig. 2 — Principal parts of common control telephone switching system.
i
994 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
direct control type, such as the step-by-step system, these parts are
inexorably integrated. But in the modern systems they have largely
been separated. For purposes of the following discussion this type of
sj^stem, viz., common control, will be assumed. The bulk nature of thei
electronic memory devices makes them more readily adaptable to sys-
tems of the common control type, where the control functions con-
sisting of the receipt, interpretation, and processing of input signals and
the effecting of output signals may be concentrated.
INTERCONNECTING NETWORK
In electromechanical switching systems the interconnecting network
is composed of crossbar switches or other electromechanical devices.
Each connection through the network is physically separated in space
from the others and hence the type of network can be called generically
a "Space Division" type of network. Such networks are subdivided
functionally. First there is the concentration stage where active lines
are separated from those not being called or served at a particular time.
Next there is distribution stage where interconnection of active lines
and trunks is accomplished. Finally there may be an expansion stage
where active call paths are connected to selected destinations.
In electronic switching systems three classes of switching networks
have been described. 2 These are:
a. "Space Division" similar to the space division for electromechani-
cal apparatus except that electronic devices such as gas tubes are
employed in place of mechanical contacts as the crosspoint element.'^
b. "Time Division" where calls are sampled in time, each one being
given a "time slot" on a single channel.^ -^
c. "Frequency Division" such as employed in carrier systems where
each call is modulated to a different frequency level on a single trans-
mission medium. ^'^
Thus in electronic switching the interconnecting networks derive
their basic characteristics from the known methods of telephone trans-
mission. Since transmission techniques are used it is generally not
feasible to pass direct current signals through such networks. Also
certain ac signals such as 20-cycle current now used for ringing are of
such a high power level that they would overload the electronic switch-
ing devices employed. For this reason it appears that to accomplish
switching with an electronic interconnecting network a change is re-
quired in the customer's apparatus to make it capable of responding to
a lower level ac for the call signal. Telephone sets with transistor ampli-
fiers and an acoustical horn are being developed. (See Fig. 3.) Interrupted
ELECTRONICS IN TELEPHONE SWITCHING SYSTEMS
995
tones in the voice frequency range can be used effectively to call the
user to the telephone.^
As in most electromechanical switching networks, the concepts of
connecting successive stages of switching devices (stages to perform
the functions of concentration, distribution and expansion) to form
the network also apply. Since there is more than one method of inter-
connection, the successive stages of a network may employ different
switching techniques — electronic, electromechanical, or both. In
electromechanical switching, different devices may also be used in
different stages.
In electromechanical space division networks certain types of cross-
points are more adapted to common control operation than others.
Systems with electromechanical selector switches most generally are
set progressively. In systems with relays or relay-like crosspoints all
crosspoints involved in a connection may be actuated simultaneously.
In either case the switching device, or the circuit in which it is used,
has a form of memory. This memory, shown as a square labeled M in
Fig. 4, may be the ability of a selector to remain mechanically held in a
particular path connecting position or in a locking or holding circuit
associated with a crosspoint relay or crossbar switch magnet.
To minimize the time consumed by the common control elements,
simultaneous operation of relay or relay-like crosspoints is most de-
sirable. However, this type of network requires a grid of link testing
and control leads such as shown in Fig. 5 for a typical stage of a cross-
bar switching network. In a network of this type the calling rate ca-
pacity is limited by the slow actuating speed of the electromechanical
relay or switch. Efficient network configurations can be devised for
Fig. 3 — Tone ringer telephone set.
996 THE BELL SYSTEM TECHXICAL JOURNAL, SEPTEMBER 1956
large capacity. To set up connections at a high rate in such a network
requires a pluraHty of controls each capable of operating on all or part
of the network. In any case, the controls function in parallel on the
network because of the speed considerations.
With electronics applied to space division switching networks, two
improvements over the operation of relay type space division networks
may be achieved. First, the speed of operation of the crosspoint elements
may be made high enough so that only one control is needed to operate
on networks of the size now requiring a plurality of controls. Second,
the properties of proposed electronic crosspoint elements are such that
the principle of "end-marking" may be employed.
In contrast to the grid of testing and actuating wires required in
electromechanical versions of space division networks, the electronic
space division switching network requires only the selectors at each end
of a desired network connection to apply the marking potentials. (This
is what is meant by "end-marking"; see Fig. 6). The electronic cross-
I o
•C-
-^
2 O-
m
z
a
->
-O A
m
A
-O 8
m
b
m
B
Fig. 4 — Space division switching.
CROSSBAR
SWITCHING NETWORK
Dn
^B.
^
[}
X )(
COMMON CONTROL
(MARKER)
): )?
NETWORK
CONNECTOR
Fig. 5 — Typical common control of a crossbar switching network.
ELECTRONICS IN TELEPHONE SWITCHING SYSTEMS
997
point element will be actuated if the link to which it connects is idle.
h]ventually all available paths between input and output will be
marked. Means must be provided for sustaining only one of the possible
idle paths. Here the memory property of the crosspoint device takes over
to hold the path until it is released by release marks or removal of the
sustaining voltages. So it may be seen that in space division networks
the memory requirements must be satisfied the same as in electrome-
chanical networks.
Multiplexing and carrier transmission systems^ employ time and fre-
quency division but the physical terminals at both ends of a channel
for which the facilities are derived have a one-to-one correspondence
Avhich can only be changed manually. In a switching system means
must be provided to change automatically the input-output relations
as required for each call. Here the need arises for a changeable memory
for associating a given time or fref[uency slot to a particular call at any
given time. At some other time these points in time or frequency must
be capable of being assigned automatically to different inputs and out-
puts. For the period that they are assigned, some form of memory must
record this assignment and this memory is consulted continuously or
periodically for the duration of the call.
With time division switching this new concept in the use of memory
in a switching network appears most clearly, see Fig. 7(a). To associate
an input with an output during a time slot the memory must be con-
sulted which associates the particular input with the particular output.
To effect the connection during a time slot the input and output must
be selected A memory is consulted to operate simultaneously high speed
GAS TUBE
SWITCHING NETWORK
Fig. 6 — Typical "End Marking" control of a gas tube switching network.
998 THE RET.L SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
selectors for both the input and output. Each selector receives informa-
tion from a memory which actuates crosspoints to associate the input
or output with the common transmission medium. The information
from the memory which controls the selection process is known as an
"address". The crosspoint is non-locking since it must open when the
selector receives its next address. The individual memory of crosspoints
for space division networks has thus been changed by time division to
changeable memory, usually in the form of a coded address associated
with each time slot. Furthermore since the successive addresses actuate
the same selectors and hence may be held in a common high speed
device, electronic bulk memory is ideally suited for this task. The
memory must be changeable to allow for different associations of input
to output at different times.
In frequency division the control characteristics of the interconnect-
ing network require a modulation frequency to be assigned each simul-
taneous conversation to be applied within the bandwidth of the com-
mon medium. As shown in Fig. 7(b) the application of the modulation
frequencies requires a separate selector for each input and output. These
I o-
20-
1
-O A
-OB
COMMON
MEDIUM
Fig. 7(a) — Time division switching.
selectors are nothing more than space division switching networks and
therefore require memory in the switching devices whether they are
electromechanical or electronic.
In addition to memory for associations within the switching network,
selecting means are also needed to activate a terminal to be chosen in
space division (e.g.. Fig. 6), to place address information in the proper
time slot in time division switching or to set the frequency applying
switching network in frequency division.
CONTEOL
The control of the switching system provides the facilities for receiv-
ing, interpreting and acting on the information placed into it. In par-
ELECTRONICS IN TELEPHONE SWITCHING SYSTEMS
999
20
Fig. 7(b) — Frequency division switching.
ticular this is the address of the output desired. A service request de-
tector (SR-D) is provided for each hne or trunk.
In electromechanical systems these logic and information gathering
functions are performed by relays or electromechanical switches. In
order to keep up with the flow of information from a large number of
customers, a number of register circuits must be provided to perform
the same function simultaneously on different calls. Here information
is being gathered on a "space division" basis and therefore a control
switching network may be visualized as depicted in Fig. 8. The regis-
ters designated R-M constitute the memory used to store the input in-
formation as it is being received in a sequential manner from lines and
trunks. As in the case of the conversation switching network, a space
division control switching network has been used in electromechanical
systems because the speed of these devices is not adequate to accom-
modate the rate at which information flows into the system. It is inter-
esting to note in passing that in the step-by-step system the control
and conversation switching networks are coincident. In the No. 5
crossbar system^" the same network is used for both control and con-
\ersation on call originations but when so used the functions are not
coincident, that is, the network is used for either control or conversa-
tion. In other common control systems, separate control networks
known as "register or sender links" are employed.
When using relays to receive the information pulsed into the office
l)y customers or operators a plurality of register circuits are needed.
The number of the registers required is determined by the time required
to actuate the calling device and for it to pulse in the information. The
1000 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
registering function has two parts, one to detect or receive the informa-
tion and the second to store it until a sufficient amount has been re-
ceived for processing. The processing function is usually allotted to
other circuits such as the markers in Crossbar systems.
SR-D
CONVERSATION
SWITCHING
NETWORK
CONTROL
SWITCHING
NETWORK
R-M
R-M
R-M
Fig. 8 — Control access.
Since the input of information to a switching system is usually limited
to two conductors, a serial form of signaling is used. It would seem only
natural that if a detector were fast enough it could function to receive
the serial information in several simultaneously active inputs. Relays
are not fast enough to do this, but high speed time sharing electronic
devices have been designed to perform this information gathering func-
tion. Since it is a time sharing arrangement it is analogous to the time
division switching. A time division control access as shown in Fig. 8 and
9 requires memory to control the time division switching function. Time
sharing when applied to the gathering of information in telephone
switching systems has been called "scanning". The individual register
memories are still in parallel form because of the relatively long time
required for sufficient information to be received before processing may
start. Higher speed means for placing information into switching sys-
tems such as preset keysets is one way of reducing, if not eliminating,
this need for parallel register storage in the switching system prior to
processing. However, with this type of device one merely transfers the
location of the storage from the central office to the customer's telephone
set. The fundamental limitation is the rate at which a human being is
able to transfer information from his brain into some physical repre-
sentation.
Lower cost memory is a practical means for improving this portion
ELECTRONICS IN TELEPHONE SWITCHING SYSTEMS
1001
1
M
M
M
-^
iR-m
fR-ivn
1
Fig. 9 — Time division control access with separate functional memory.
of the switching system. Many small low cost relay registers have been
designed and placed into service.^" Electronics, however, offers memory
at one tenth, or less, of the cost per bit if used in large quantities with
a common memory access control. New low cost bulk electronic mem-
ories are now available to be used in this manner. As shown in Fig. 10
the memor^y for the control of the time division control access network
and the register memory may be combined in the bulk memory.
o-
\o
[> — "^
BULK
MEMORY
.
t
Fig. 10 — Time division control access with bulk memory.
Memory appears in the control portion of a switching system in
many ways. Some are obvious and others are more subtle. Fig. 11 shows
a typical electromechanical switching system, much like No. 5 crossbar
and attempts to indicate various memory functions. First there is
active memory designated A such as the call information storage A2
whether in a register, sender or marker during processing. There is
also certain pertinent call information storage associated with trunk
circuits such as a "no charge class" on outgoing calls or the ringing
code used on incoming calls. Another type of active memory Ai has
been mentioned in connection with switching networks to remember the
input-output associations. In most electromechanical systems active
memory has been emplemented with relaj^s or switches.
Another form of memory is also employed in all telephone switching
systems and much effort has been devoted to devising improved means
for effecting this memory. This memory is of the type that is not
changed with each call but is of a more permanent nature. Examples
of this type of memory, which may be called passive memorj^, designated
P, (Fig. 11), are the translations required in common control sytems to
obtain certain flexibility between the assignment of lines to the switch-
ing network and their directory listing. These translations between
1002 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
equipment numbers (network location) and directory numbers are
required to direct incoming calls to the proper terminals (such as the
number group frame in No. 5 crossbar, Fig. 12) and to provide on
originating calls information for charging purposes (such as the AMA
"Dimond" ring translator,!^ pig 13) Each of these translators for a
10,000 line office represent about 10^ bits of information. Another use
for passive memory is to translate central office codes into routing in-
formation. In local central offices this is also done by cross-connections
as shown in Fig. 14.
Another form of passive memory is the punched card or tape. These
have been used widely in telephone accounting systems. A step toward
electronic memory is the card translator which provides routing in-
formation in the crossbar toll switching system^^ (see Fig. 15). Here the
cards represent passive memory and are selected and read by a com-
bination of electromechanical action and light beam sensing with
phototransistor detectors. One such device equipped with 1,000 cards
represents the storage of approximately 10^ bits of information.
In all of the above types of passive memory limitations in the speed
are involved in the choice of devices used within the memory or the
access to it. This is one of the reaons these translators are subdivided so
that the various portions may be used in parallel in order to satisfy the
total information processing needs of the office.
A discussion of passive memory would not be complete without one
further illustration, Fig. 16. This is a wiring side view of a typical relay
circuit in the information processing portion of a switching system. It
o-
EN
SWITCHING
NETWORK
A|
MARKER
A2-P1
DN-^EN
P2
REGISTER
A = ACTIVE MEMORY
P = PASSIVE MEMORY
ON
Fig. 11 — Memory in typical electromechanical switching system.
ELECTRONICS IN TELEPHONE SWITCHING SYSTEMS
1003
Fig. 12 — No. 5 number group.
could be any other unit, for example, a trunk circuit. The principal
point is that each wire on such a unit is remembering some passive
f| relationship between the active portions of the circuit, such as relays.
This is the memory of the contact and coil interrelationships as con-
ceived by the designer and based on the requirements of what the cir-
cuit is required to accomplish. It is the program of what the central
office must do at each step of every type of call. Modern digital com-
puters have been built with the ability to store programs in bulk
memories for the solutions of the various types of problems put to them.
It is conceivable that the program of a telephone contral office may also
I >e stored in bulk memories to eliminate the need for much of the fixed
wiring such as appears in relay call processing circuits.
1004 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
Fig. 13 — AMA translator.
ELECTRONICS IN TELEPHONE SWITCHING SYSTEMS
1005
Fig. 14 — No. 5 route relay frame.
The form of memory available in electronics is considerably different
from that which has been previously available. Electronic memory has
been characterized as "common medium" or "bulk" memory. A single
device is used capable of storing more than a single bit of information
which is the limit of most relays or other devices capable of operating in
a bistable manner. A number of different types of electronic bulk
memories have been devised for digital processing. They differ appre-
1006 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
Fig. 15 — No. 4A card translator.
cig.bly in physical form, each taking advantage of the phenomenon of
some different area of the physical sciences — electrostatic, electromag-
netic, optic. Magnetic tapes" and drums^^ (Fig. 17), cores^^ (Fig. 18),
electrostatic storage in tubes^^' ^"^ (Fig. 19) and ferroelectrics^^' 2"
(Fig. 20) and photographic storage^' (Fig. 21) are available.
Several properites of these memory devices are of interest. Being
electronic, the speed with which stored information may be read is of
primary interest. This is known as "access speed". Another property
of these common medium memory systems or devices is the ability to
change what has been written. If the changes can be made rapidly
enough they may be used in electronic systems in much the same man-
ner as relays are used in electromechanical systems to process informa-
tion. If the change must be made relatively infrequently, such as
changing photographic plates, they may be used as substitutes for the
type of memory in these systems which are provided by cross connec-
tions and wiring. The required fixed or semipermanent electronic mem-
ory may be characterized primarily b}^ a high reading speed, large
capacity, and the ability to hold stored information even during pro-
ELECTRONICS IN TELEPHONE SAVITCHING SYSTEMS
1007
iiFi<i:mM^^'&'^-'m.
Fig. 16 — Wiring side of relay unit.
longed intervals of loss of power. The amount of memory is measured
in terms of binary digits or "bits". The number of bits equivalent to
single cross connection can be rather large. Therefore, electronic mem-
ory replacing fixed memory such as in the card translator in modern
electromechanical systems should be high in bit capacity, from 10^ to
10^ bits for 10,000 lines.
Fig. 17 — Magnetic drum.
1008 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
Fig. 18 — Magnetic core array (Courtesy of IBM).
One way in which electronic memory for various system applications
may be evaluated is given by the chart of Fig. 22. This chart attempts to
show, for the various forms of storage, the relation between the ca-
pacity in bits and cycle time, which includes access, reading and, if
necessary, the regeneration time of the stored information. For sake of
simplicity, ferroelectric and magnetic core memories have been com-
bined as coordinate access arrays. Single bit electronic memory will be
described in more detail later.
ELECTRONICS IN TELEPHONE SWITCHING SYSTEMS
1009
In the control portion of a switching system it is not only necessary
to gather and store information but it must be interpreted and appro-
priate action taken. This function is called "processing". Processing
circuits control the information gathering and storage functions and
perform logical functions to produce the necessary flow of information.
In the logic circuits of electronic systems, to keep pace with the time
sharing nature of the information gathering function, the devices used
must be several orders of magnitude faster than their counterparts, the
relays, of the electromechanical system. The scanning and bulk memory
Fig. 19 — Electrostatic storage tube.
1010 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
Fig. 20 — Ferroelectric array.
access speeds must be comparable in speed if they are not to become the
speed bottleneck. All portions of the system must be in balance time-
wise.
Devices and techniques for use in the design of high speed logic cir-
cuits are available. ^^ With such devices information processing pre-
viously carried out by complex relay circuitry may be carried out in
microseconds instead of milliseconds. Devices such as semiconductor
diodes and transistors seem to be pointing the way to the future in per-
forming these functions.2^ Previously, hot cathode tubes with high
power consumption were needed to achieve the same functions at simi-
lar high speeds and for a long time this has been one of the greatest
deterrents to electronic switching.
Semiconductor diode gate circuits are now quite familiar^* and take
ELECTRONICS IN TELEPHONE SWITCHING SYSTEMS 1011
the place of the conventional make and break contacts in the electro-
mechanical switching art (see Fig. 23 for the "AND" function).
Magnetic core circuitry is also being exploited to perform high speed
switching functions-^ (Fig. 24).
There are a number of differences between the circuit configuration
used for relay contacts and diode or magnetic core gates for switching
logic. When interconnecting such gates to realize complex logic func-
tions other gates are required when circuit elements are placed in series
or parallel, whereas in the wiring of relay contacts in series or in parallel
no additional circuit elements are required (Fig. 25). Pulse signals
passing through diode gate circuits are usually attenuated since the
electronic device is not a perfect switcher (infinite impedance open cir-
cuit to zero impedance closed circuit). Some minute currents flow
when open and some resistance is encountered when closed. Therefore,
some amplification is needed at various places in logic circuits and this
can be provided by transistor amplifiers. The use of transistors as the
gating element eliminates this shortcoming by providing amplification
in each gate (see Fig. 24). Transistors have also been successfully used
in a new form of logic to provide relay contact like logic thus eliminating
the need for gate elements to represent the series of paralleling func-
tions^^ (see Fig. 26).
The processing of information usually requires a sequence of logic
actions. To provide such sequences, momentary elements similar to
locking relays but with microsecond action times are required. When
this condition obtains a bistable or "flip-flop" circuit using transistors
may be emplo3^ed. Several forms of transistor circuits have been de-
vised using either the Eccles-Jordan principle,^^ negative resistance
properties,'^ such as achieved with a gas tube, or a regenerative ap-
proach.2^ Some suggestions have been made on the use of semiconductor
diodes in special energy storing circuits to amplify pulses instead of the
more conventional transistor amplifiers.^"
CYLINDRICAL
LENS
^ EMULSION
TUBE "^ COLLECTOR
CATHODE RAY _„,. „^^ ^ f"
SLIT
.^OUTPUT
VOLTAGE
-- 1 ■)
CATHODE pHOTOMULTIPLIER
FIELD LENS TUBE
ROTATING PLATE
FLYING SPOT SCANNING A ROTATING DISC
Fig. 21 — Photographic storage (from Proc. I.R.E., Oct. 1953).
1012 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
EQUIPMENT CONCEPTS
111 what has been said, consideration was given only to the concepts
and circuitry of electronic telephone switching systems, but the things
which the manufacturer and user come in contact with are the physical
or equipment realizations of these concepts. One thing that is outstand-
ing about the physical aspects of an electronic system is the large num-
ber of small components which are required. Fortunately, most of these
components such as resistors, diodes, transistors, condensers, etc., are
all of the same physical or similar mechanical design. From the manu-
facturer's point of view the problem then is to find the most economical
way in which these many devices may be manufactured, assembled and
tested, because of the large numbers required in a system. The basic
solution appears to be: automatic production. This has led to the con-
cept of small packages of components. These packages are the building
blocks of a system and contain basic circuits which may be used repeti-
tively. The trend in making such packages appears to be the use of
printed wiring with automatic means of placing the components on the
printed wiring boards. ^^
Despite the fact that there are large numbers of these small com-
10'
10^
lO'
m
V 10'
h-
<
°- 3
< 10
o
lO'
10
PHOTOGRAPHIC STORE
1
ELECTRO-
STATIC
- TUBE
STORE
10'
IR
1 COORDINATE
ACCESS
ARRAY
MAGNETIC
DRUM
MAGNETIC
/ TAPE
/ SINGLE BIT
/ MEMORY
J (_L
_L
I 10 10' lO' 10* 10* 10*
CYCLE TIME -MICROSECONDS
10'
10' 10'
Fig. 22 — Memory system capabilities.
ELECTRONICS IN TELEPHONE SWITCHING SYSTEMS
1013
ponents required in electronic telephone switching they are small and
when eciuipment using a multiplicity of printed wiring boards is assem-
bled it takes on the aspect of a three-dimensional arrangement of
components, with components mounted in depth as well as on the sur-
face. This is in contrast to electromechanical systems where all com-
ponents are generally mounted on a vertical surface. By using only one
or two common control circuits of a given type (due to high speed) and
r^
4
A'
B-
■♦C
WITH RELAYS
AB=C
FUNCTION AND SYMBOL
A
_n_
B N *
-TL
TRANSMISSION TYPE
DIODE GATE
DC COUPLED
DIODE GATE
Fig. 23 — The "And" function.
_rL
-TL
_n_
MAGNETIC CORE
"AND" GATE
DC COUPLED
TRANSISTOR "AND" GATE
Fig. 24 — Other "And" circuits.
1014 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
(•omnioii medium bulk memory, fewer system elements are required
which ill the overall result in material space saving.
Another phase of the equipment aspects of electronic switching is that
the devices reciuire closer environmental control. Air conditioning
appears necessary in early systems because of temperature limitations
and other characteristics of some of the devices presently available.
Also, vacuum tubes and other high power devices may develop objec-
tionable hot spots in the equipment which make it advisable to exhaust
hot air.
MAINTENANCE CONCEPTS
There is insufficient experience at this time to say what the main-
tenance problems of electronic telephone systems will be. Much has
been written about the problems encountered in maintaining electronic
A-
B-
AB+CD=E
A LOGIC FUNCTION
f^T
WITH RELAYS
Fig. 25 — A logic function with relays.
ELECTRONICS IX TELEPHONE SWITCHING SYSTEMS
lOlo
computers; however, in designing a telephone system an entirely dif-
ferent philosophy must be pursued since it should not be necessary to
have engineering caliber maintenance forces. At no time should the
system be incapable of accepting and completing calls. This does not
mean that portions of the system may not be worked on for routine or
trouble maintenance.
A promising approach appears to be the use of marginal condition
routine tests for detecting in advance components which are about to
fail.^^ Automatic trouble locating arrangements may be devised for
giving information as to the specific location of a package in trouble
when it occurs.^^ This automatic trouble locator combined with the
equipment concept of plug-in units means that service may be main-
tained without long interruptions. By designing devices which are
reliable, employing them in a manner to give maximum service life and
A
a) —
^
\^^
\ ,^-''
r-
B^
""
D
<
1^ J
>
J
+
>
A - ,-,
n 1-
<
>
•>
J
>
>
->
1
1*
D —
-^ J
-H J
i — i
WITH DIODES
WITH TRANSISTORS
Fig. 26 — A logic function with diodes or transistors.
1016 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 195G
by judiciously introducing redundancy into the equipment, the chance
of simultaneous failures of any two identical parts should be extremely
improbable.^- With automatic trouble locating, the maintenance forces
will not be reciuired to have a thorough understanding of the device
characteristics and the circuitry used. Centralized repair of defective
units as in modern telephone transmission systems^^ and perhaps even
expendability of defective units are a distinct possibility.
As a result of some of these maintenance considerations it is quite
likely that equipment in the future, besides being smaller and more com-
pact, will appear more generally in enclosed low cabinets rather than
exposed frames. The administrative control may be from consoles
rather than vertical panels. More attention will be paid to appearance.
The appurtenances, such as ladders required for high frames in electro-
mechanical systems, may be eliminated.
Another change in concept which may come with electronics in tele-
phone switching is the form of the power supply. Present day telephone
systems use a centralized single voltage dc distribution system with
reserve battery. The wide variety of devices and associated voltages,
and the need for close regulation in some portions of electronic systems
make a reliable ac distribution system with individual power rectifiers at
the point of use appear quite attractive. To insure reliability of service
the ac distribution must be continuous and not dependent directly upon
the commercial sources.
There is no question that reliability is imperati\'e if electronic switch-
ing systems are to survive among electromechanical systems which
have achieved a high degree of reliability over a long period of years.
The device reliability of the first electronic system may not be com-
parable since some of the components of the electronic switching sys-
tems will not in their initial applications be as reliable as the least reli-
able component in our present day systems. Reliability will be earned
and this will probably require considerable effort. Even if initially some
devices employed in electronic systems do not measure up to the present
high standard which has been set, continuity of high (luality service is
a must. It is, therefore, necessary to design a system which will mask
the shortcomings of any individual electronic component. ^^ As their
reliability is proven an optimum balance will be sought between system
redundancy and component quality. Telephone engineers familiar only
with the high degree of reliability of present day apparatus will have to
accommodate themselves to the characteristics of new electronic de-
vices.
ELECTRONICS IN TELEPHENE SWITCHING SYSTEMS 1017
REFERENCES
1. J. R. Eckert, A. Survey of Digital Computer Memory Systems, I.R.E. Pro-
ceedings, 41, pp. 1393-1406, Oct., 1953.
2. T. H. Flowers, Electronic Telephone Exchanges, Proceedings I.E.E., 99, Part
I, pp. 181-201, 1952.
3. U. S. Patent 2,387,018.
4. U. S. Patent 2,490,833.
5. U. S. Patent 2,408,462.
6. U. S. Patent 2,379,221.
7. W. A. Depp, M. A. Townsend, Cold Cathode Tubes for Audio Frequency
Signaling, B.S.T.J., 32, pp. 1371-1391, Nov., 1953.
8. Tone Ringer May Replace Telephone Bell, Bell Laboratories Record, pp.
116-117, March, 1956.
9. W. R. Bennett, Time Division Multiplex Systems. B. S.T.J. , 20, p. 199, 1941.
10. F. A. Korn, J. G. Ferguson, No. 5 Crossbar Dial Telephone Switching System,
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11. J. W. Dehn, R. E. Hersev, Recent New Features of the No. 5 Crossbar Switch-
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12. T. L. Dimond, No. 5 Crossbar AMA Translator, Bell Laboratories Record,
p. 62, Feb., 1951.
13. L. N. Hampton, J. B. Newsom, The Card Translator for Nationwide Dialing,
B.S.T.J., 32, pp. 1037-1098, Sept., 1953.
14. Review of Input and Output Equipment LTsed in Computing Systems. A.LE.E.
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15. Cohen, A. A., Magnetic Drum for Digital Information Processing Systems,
Mathematical Aids to Computation. 4, pp. 31-39, Jan., 1950.
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Storage Tubes, B.S.T.J., 43, p. 1241, Nov., 1955.
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IS. M. K. Haj-nes, Multidimensional Magnetic Memory Selection System. Trans-
actions of the I.R.E. , Professional Group on Electronic Computers, pp.
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19. D. A. Buck, Ferroelectrics for Digital Information Storage and Switching,
Report R212, M.I.T. Digital Computer Laboratories, June, 1952.
20. J. R. Anderson, Ferroelectric Materials as Storage Elements for Digital Com-
puters and Switching Svstems, Communications and Electronics, pp. 395-
401, Jan., 1953.
21. G. W. King, G. W. Bi-own, L. N. Ridenour, Photographic Techniques for In-
formation Storage, Proc. I.R.E., pp. 1421-1428, Oct., 1953.
22. Staff of Harvard Computation Laboratorj-, Synthesis of Electronic Computing
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23. B. J. Yokelson, W. Ulrich, Engineering ^Multistage Diode Logic Circuits,
Communications and Electronics , pp. 466-474, Sept., 1955.
24. M. Karnaugh, Pulse Switching Circuits Using Magnetic Cores, Proc. I.R.E.,
43, pp. 576-584, May, 1955.
25. R. H. Beter, W. E. Bradley, R. B. Brown, M. Rubinoff, Surface Barrier Tran-
sistor Switching Circuits, I.R.E. Convention Record, Part 4, pp. 139-145,
1955.
26. R. L. Trent, Two Transistor Binary Counter, Electronics, 25, pp. 100-101,
July, 1952.
27. A. E. Anderson, Transistors in Switching Circuits, Proc. I.R.E., 40, pp. 1541-
1558, Nov., 1952.
28. J. H. Felker, Regenerative Amplifier for Digital Computer Applications, Proc.
I.R.E., 40, pp. 1584-1956, Nov., 1592.
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Communications and Electronics, pp. 175-182, July, 1952.
1018 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMEER 1956
30. Promising Electronic Components — Diode Amplifiers, Radio Electronics
p. 45, Nov., 1954. '
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32. C. J. Crevelens, Increasing Reliability by the Use of Redundant Circuits
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35. MAID Service for Computer Circuits, Automatic Control, p. 23, Aug 1955
%
Combined Measurements of Field Effect,
Surface Photo-Voltage and
Photoconductivity
By W. H. BRATTAIN and C. G. B. GARRETT
(Manuscript received May 10, 1956)
Combined measurements have been made of surface recombination veloc-
ity, surface photo-voltage, and the modulation of surface conductance and
surface recombination velocity by an external field, on etched germanium
surfaces. Two samples, cut from an n-type and a p-type crystal of known
body properties, were used, the samples being exposed to the Brattain-
Bardeen cycle of gaseous ambients. The results are interpreted in terms of
the properties of the surface space-charge region and of the fast surface
states. It is found that the surface barrier height, measured with respect to
the Fermi level, varies from —0.13 to -\-0.13 volts, and that the surface
recombination velocity varies over about a factor of ten in this range. From
the measurements, values are found for the dependence of charge trapped
in fast surface states on barrier height and on the steady-state carrier con-
centration within the semiconductor.
I. INTRODUCTION
This and the succeeding paper are concerned with studies of the
properties of fast surface states on etched germanium surfaces. The ex-
periments involve simultaneous measurement of a number of different
physical surface properties. The theory, which will be presented in the
second paper, interprets the results in terms of a distribution of fast
surface states in the energy gap. The distribution function, and the
cross-sections for transitions from the states into the conduction and
valence bands, may then be deduced from the experimental results.
Early experiments^ on contact potential of germanium, and on the
change of contact potential with light, indicated that there are two
kinds of surface charge associated with a germanium surface, over and
above the holes and electrons that are distributed through the surface
space-charge region. One kind of surface charge, usually called "charge
1019
1020 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
in fast traps" can follow a change in the space-charge region very fast
in comparison with the light-chopping time used in that work (Koo
sec); the other kind, imagined to be more closely connected with ad-
sorbed chemical material, can only change rather slowly. In a previous
paper by the authors it was pointed out that the Brattain-Bardeen
experiments, taken by themselves, do not furnish unambiguous infor-
mation concerning the distribution of these "fast" traps, but that such
information might be obtained by performing, simultaneously, other
measurements on the germanium surface. More recently Brown and
Montgomery^' ^ have provided a valuable tool in their studies of large-
signal field effect; they point out that if, under given chemical conditions,
it is possible to apply a field, normal to the surface, large enough to
force the surface potential to the minimum in surface conductivity;
then it becomes possible to determine the initial surface potential ab-
solutely (provided certain considerations as to the mobility of the
carriers near the surface are valid).
This paper concerns studies of a number of physical properties that
depend on the distribution and other characteristics of the surface
traps or "fast" states. Measurements are reported of (i) the change
of conductivity of a sample with field; (ii) the photoconductivity;
(iii) the change of photoconductivity with field; (iv) the filament life-
time; and (v) the surface photo-voltage. Measurements were made in a
series of gaseous ambients, first described by Brattain and Bardeen.
Evidence is presented to the effect that the variation in gas ambient
changes only the "slow" states, leaving the distribution and other
properties of the traps substantially unaffected. From measurements
(i) to (iii) it is possible to construct the whole field-effect curve (con-
ductance versus surface charge), even though the fields used were in
general not large enough to reach the minimum in conductance.
Using the field effect data, values for the surface potential Y in units
of kT/e could be obtained at each point, and also of the quantity
(d'Ls/dY)s=o , where 2s is the charge in surface traps, and the suffix 5 = 0
implies zero illumination. From measurements (ii) and (iv), the sin'face
recoml)ination velocity s could be deduced. (A more detailed study of
photoconductivity in relation to surface recombination \'elocity will
be reported at a later date.) Combined with the field effect data, this
enables one to deduce the relation between s and Y.
Measurements of the surface photo-voltage may be presented in terms
of the quantity dY/d8, where 5 is ec|ual to Ap/ui , Ap being the density
of added carrier-pairs in the body of the material, and Ui the intrinsic
carrier density. The quantity dY/d8 is closely related to the ratio of the
COMBINED MEASUREMENTS ON ETCHED GERMANIUM SURFACES 1021
change in surface potential produced by illumination of the surface to
the change in the quasi-Fermi level for minority carriers. By measuring
dY/db rather than dY/dL, discussed in Reference 2, the surface re-
combination velocity is eliminated from the surface photo-voltage data:
the limiting values of dY/dd, after correction for the Dember effect,
ought to be (po/ni) and — (ni/po) , no matter what the surface recombina-
tion velocity may be.
By combining this information with the field-effect data, one can de-
duce the quantity (5Ss/55)r • This and the previous differential, deduced
directly from the field-effect data, completely define the dependence of
charge in surface traps on the two independent parameters Y and
8 — that is, the dependence on chemical environment and on the bulk
non-equilibrium carrier level.
The further interpretation of the cjuantities (dI,s/dY)s=o , (52s/55)r
and s in terms of the distribution of surface traps is postponed to the
succeeding paper. Here it is sufficient to say that the results are con-
sistent with the assumption that the traps responsible for surface re-
combination are also those pertinent to the field effect and surface
photovoltage experiments. Then the ciuantity (d2s/^F)a=o depends only
on an integral over the distribution in energy of traps; (31,^/88) y depends
also on the ratios of cross-sections for transitions to the valence and
conduction bands; and s depends in addition on the geometric mean
cross-sections.
II. OUTLINE OF THE EXPERIMENT
The experiment is carried out with a slice of germanium, 0.025 cm
thick, which is supported in such a way that there is a gap 0.025 cm wide
between the slice and a metal plate. Substantially ohmic contacts are
attached to the ends of the slice. Three kinds of experiment are now
carried out:
(i) The conductance of the slice is modulated by illuminating it
with a short flash of light; the subsequent decaj^ of photoconductivity
with time is studied, and the time-constant of the exponential tail
measured.
(ii) A sinusoidally varying potential difference of about 500 volts
peak-to-peak is applied between the metal plate and the germanium.
Facilities are available for measuring the changes in conductance pro-
duced by the field. The sample is also illuminated with light chopped
at a frequency different from that of the applied field. One measures:
(a) the magnitude of the peak-to-peak conductance change in the dark;
(b) the same in the presence of the light; and (c) the change in con-
1022 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
ductance, at zero field, produced by the light. The applied field is suffi-
ciently small for the dark field effect and the apparent field effect in the
presence of light to be substantially linear.
(iii) The metal plate, disconnected from the high voltage supply, is
connected to a high-impedance detector; chopped light is shone on the
germanium, and the change in contact potential produced at the sur-
face opposite the metal plate by illumination of the sample measured,
and compared with the photoconductivity.
The interpretation of the field effect data has been given by Brown
and Montgomery^' ^ and by the authors." The surface conductance AG
is equal to enp{Tp + 6r„),2 where Tp and r„ are surface excesses of holes
and electrons, and are, in equilibrium (i.e., in the absence of light)
functions of the surface potential Y and of the body type and resistivity.
The minimum in the surface conductance curve occurs at a particular
value of Y, so that, if a field effect experiment allows passage through
this minimum, values of Y may be obtained.*
In our experiments, measurements were made in a series of different
chemical environments, and the minimum in surface conductance did
not, in general, occur within the range of field employed. However, it
was found to be possible to piece together the complete surface con-
ductance curve (AG versus surface charge) by making use of simulta-
neous measurements of the photoconductance and the change in photo-
conductance with field. (See Section VI.) From the surface conductance
curve, one may deduce the fraction of the surface charge (whether in-
duced electrically, by application of a field, or chemically, by changing
the environment) which goes into the fast surface states or traps. ^' ^
There is, indeed, an assumption here, to the effect that the distribution
of traps is unaffected by a change in the chemical environment. The
justification for this is the observation of Brown and Montgomery*
that it was possible to superpose overlapping large signal field effect
curves obtained in different environments. There is also evidence for
the validity of this assumption from the self-consistency of the procedure
used (see Section V and Fig. 4).
The photoconductivity measurements have been interpreted on the
following basis. Illumination of the sample will do two things: it will
change the surface excesses Tp and r„ ,^ and it \\ill also change the
* The question of the mobility of carriers near the surface should be mentioned
liere. For extreme values of Y, the mobility of the carriers tliat are constrained to
move in the narrow surface well is reduced. Values for this reduction in mobility
have been calculated by Schrieffer.^ However, for values of }' near zero the Schrief-
fer correction is small, and at somewhat larger (positive or negative) values AG
is increasing so fast that the error in Y introduced by ignoring the Schrieffer cor-
rection is small.
COMBINED MEASUREMENTS ON ETCHED GERMANIUM SURFACES 1023
steady-state carrier density deep inside the sample. If the sample is
thin in comparison with the body diffusion length and with (D/s), as
was the case in our experiments, the added carrier density Ap will be.
almost uniform throughout the thickness t of the sample, and one can
easily convince oneself that the photoconductance arising from this
cause is of the order of it/£) times larger than that arising from the
changes in the surface excesses, where £ is a Debye length for the
I material. This being the case, the photoconductivity may be considered
I to be a bulk rather than a surface effect, the surface entering only
i through the surface recombination velocity s. Under the conditions of
the present work the magnitude of the photoconductivity w^as in fact
inversely proportional to s, as was verified in a separate set of experi-
I ments. Surface recombination is of interest in that this also calls for
I "fast" trapping centers on the surface; in fact any trap contributing
\ to the field effect experiment may be a recombination centre, if the
i cross-sections are right. The questions as to whether the recombination
I centres and the "fast states" affecting the field effect are the same, or
I not, is taken up in the succeeding paper.
I The surface photo-voltage, like the field effect, is affected both by
I changes in the surface excesses and by changes in Ss , the charge in sur-
I face traps. In the experiments, the change in contact potential in a cer-
I tain light (usually chosen so that the change i s small in comparison
[ with kT/e) is compared with the change in conductance produced by the
same light. From the latter one may calculate 8 (defined as Ap/ui)
directly. The change in contact potential, measured in units of kT/e, is
I taken to be equal to AY. Thus the surface photo-voltage experiment
I measures the quantity (dY/d8), the differential being taken at constant
surface charge. By a slight generalization of the argument previously
given by the authors," one can show that:
dy ^ _ (d/d8)Y{Tp - rj + id2jd8)Y (..
(18 (d/dVUTp - r„) + (dXs/dVh ^ ^
Now the first terms in the numerator and denominator on the right-
I hand side are determinate functions of Y, and so are known ; the quantity
I {d'2s/dY)B may be deduced from the field-effect measurements, so that
I the only remaining ciuantity, (53,, /(95) r , niay be deduced from the
I measurements of surface photo-voltage.
In concluding this section, a word as to the meaning to be attached to
(dT^s/dS) Y is in order. The sign of this quantity depends, roughly speak-
ing, on whether the traps in question (i.e., those near the Fermi level
under the conditions of the experiment) are in better contact with the
1024 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
conduction or the valence band. This in turn depends both on the surface
potential and on the ratio of cross-sections for transitions to the two
.bands. For F « — 1, one expects (52^/(95) y/(62s/ay)5 to have the value
— X~'; for F » +1, the vakie +X. These limiting values may be deduced
by a somewhat general argument.
At some intermediate value of surface potential, the above ratio
must change sign. If the distribution of surface states in energy is known
from the field effect measurements, then the value of F at which the
above ratio changes sign determines the ratio of cross-sections for those
traps which are close to the Fermi level for that value of F. By repeating
the experiment for samples of differing bulk resistivity, it is then possible
to determine whether the same ratio holds for the states at some dif-
ferent position in the energy gap.
III. EXPERIMENTAL DETAILS
Fig. 1 shows the experimental arrangements. The sample of ger-
manium, of dimensions shown, was prepared by cutting, sandblasting,
etching in CP4 and washing in distilled water. The exposed faces were
approximately (100). The end contacts were made by sandblasting and
soldering. The slots A, A' in the ceramic were incorporated in order to
GERMANIUM
GOLD
GOLD
--GERMANIUM
BINDING POSTS-
Fig. 1 — Experimental arrangement.
COMBINED MEASUREMENTS ON ETCHED GERMANIUM SURFACES
1025
reduce the high field that would otherwise be present near the edges of
the ceramic. The gold electrode was deposited by evaporation through
a mask. Connections from the gold and from the ends of the sample were
made to binding posts passing through the ceramic block.
The ceramic block was set into a metal box, divided into two com-
partments. In the upper compartment, which contained the sample,
there were inlet and outlet tu}:)es, to allow the gas to be changed. The
lower compartment contained electrical components, which were
thereby protected to a large extent from the changes in gas in the upper
compartment. Facilities were available for the type of cycle of gas en-
vironment described by Brattain and Bardeen,^ which cycle was found
by them to produce reversible cyclic changes in surface potential. In
the top of the box was a window, through which light could be shone
onto the germanium either from a chopped or a flash source.
The electrical circuit is shown in Fig. 2. The condenser Ci is that
formed between the germanium and the gold, and has a capacity of
about 2 ijlijlF. Impedances Zi and Zo form a Wagner ground, which has
to be balanced first. Then, by adjusting resistance Ri and condenser
C2 , one may obtain a balance in the case that there is no dc flowing
through the sample. A current (determined by the battery B and the
HORIZONTAL
VERTICAL
ELECTROMETER -
TUBE
PRE-AMPLIFIER
:!^ B
Fig. 2 — Electrical circuit.
1026 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
resistance Rz)is now switched in, and the resulting off-balance (repre-
senting the field modulation of conductivity) presented on the vertical
plates of an oscilloscope. The supply voltage is connected, via the high.j
bleeder resistance Ri , to the horizontal plates. The frequency of the
oscillator was chosen to be 25 cyc/sec, a value sufficiently low to obviate
lifetime difficulties; the peak-to-peak swing was generally 500 volts.
During a field-effect measurement, the sample was also illuminated
with light chopped at 90 cyc/sec. This had the result of causing to be
presented on the oscilloscope screen a pattern such as that shown in
Fig. 3. The lower tilted line represents the (dark) field effect curve; the
vertical separation represents the photoconductivity, as modified by the
applied field. Measurements were made of the mean vertical separation,
and of the slopes of the upper and lower lines (by reading gain settings).
During a surface photo-voltage measurement, the gold electrode was
disconnected from the high-voltage supply, and connected to a high-
impedance detector, similar to that used in the work of Brattain and
Bardeen.^ A value for the chopped light intensity was chosen to give a
contact potential change that was generally not more than 5 mV. A
simultaneous measurement of the photoconductivity was also made.
The gas cycle was similar to that described by Brattain and Bar-
deen.^ Some variations were made in it to try to spread out the rate of
change with time so that the data could be obtained without large gaps.
The cycle used was: (i) sparked oxygen 1 min, (ii) dry O2 , (iii) mixture
of dry and wet O2 , (iv) wet O2 , (v) wet No , (vi) a mixture of dry and
wet N2 , (vii) dry O2 , (viii) dry O2 , triple flow, and (ix) ozone normal
flow. The normal rate of gas flow was about 2 liters per minute; the wet
gas was obtained by bubbling through water (probably about 90 per
Fig. 3 — Picture of field effect-photoconductivity pattern, as observed on
oscilloscope. Dark curve at the bottom. ,
COMBINED MEASUREMENTS ON ETCHED GERMANIUM SURFACES 1027
cent r.h.) and the mixture of dry and wet was obtained by letting ap-
proximately one-half the gas flow bubble through H2O. In carrying out
the experiment, it was found convenient to carry out alternately a com-
plete cycle of field effect and surface photo-voltage measurements. The
values of the photoconductivity at equivalent points in successive cycles
could be compared, in order to check that no systematic error was intro-
duced by this procedure.
In addition to the foregoing, the folloAving measurements Avere made:
1. All dimensions were determined.
2. The resistivity of the sample was found, and also the body life-
time, on another specimen cut from the same crystal.
3. The amplitude of the voltage swing was measured.
4. The amplifiers in the field effect circuit were calibrated.
5. The capacity of the germanium-gold condenser was determined
(by a substitutional method). The value obtained was larger than
that calculated from the parallel-plate formula, because of the edge
effects.
6. A standard square-wave voltage was introduced into the surface
photo-voltage circuit, in order to calibrate the high-impedance detector.
7. At several points in the cycle, the fundamental mode lifetime of the
sample was determined by the photoconductivity decay method. This
calibrated the 90 cyc/sec photoconductivity measurements, without the
necessity for a knowledge of the light intensity.
IV. RESULTS
Measurements were made on two samples: one n-type, 22.6 ohm cm
(X = 0.345), the other p-type, 8.1 ohm cm (X = 17.7). The body life-
time for both samples was greater than 10~ sec, so that for slices of the
thickness used (0.025 cm. or less), and for values of s in the range en-
countered, body recombination may be ignored.
Results of typical field-effect runs for the two samples are indicated
in Tables I and II. The first column in each table gives the time in
minutes from the beginning of the cycle at which the measurements
were made. The second column shows the "effective mobility," dAG/d'2,
obtained from the observed (dark) field effect signal voltage AFi (see
Fig. 3) by use of the formula: jueff = wh^AVi/Ipo^CVapp , where w is the
width of the slice, t the thickness, / the dc flowing through it, po the re-
sistivity, C the capacity of the germanium-gold condenser, and Fapp
the voltage applied across it. The third column shows the mean value of
8{ = Ap/ni), obtained from the mean photoconductivity signal voltage
1028 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 195G
Table I — 22,6 ohm cm n-TYPE Cycle 12.
Relative Light Intensity 0.082
Time min.
cm^
s
^ cm2
cm
'^" volt sec
""^ volt sec
sec
0
Sparked O2
1
Changed to dry C
>o
1.5
334
7.85 X 10-2
520
90
2.5
344
6.9 X 10-2
585
103
5.5
344
6.2 X 10-2
595
114
6.5
344
6.07 X 10-2
595
117
7.0
Changed to mixture of dry & wet O2
7.5
136
4.4 X 10-2
520
161
8.5
84
4.02 X 10-2
440
177
9.0
52
3.60 X 10-2
270
196
10.0
Changed to full wet O2
11.0
-660
2.26 X 10-2
-440
314
11.5
-890
1.74 X 10 2
-780
408
12.0
-960
1.67 X 10-2
-910
425
13.0
Changed to full wet N2
18.0
Changed to mixture of dry & wet No
19.5
-1150
1.67 X 10-2
-1060
425
20.5
-1050
1.74 X 10-2
-960
408
22.5
-990
1.83 X 10-2
-890
390
23.0
Changed to dry C
).,
23.5
-430
2.98 X 10-2
-220
238
23.8
-290
. 3.2 X 10-2
0
222
24.0
-84
3.81 X 10-2
240
186
24.5
31
4.3 X 10-2
310
165
26.5
146
4.7 X 10-2
410
151
27.0
Tripled flow of dry O2
27.5
220
5.1 X 10-2
450
139
29.5
260
5.7 X 10-2
510
124
31.5
280
6.2 X 10-2
510
114
35.0
Changed to ozone
35.5
310
6.8 X 10-2
510
104
37.5
320
8.2 X 10-2
490
87
AF2 by use of the formula: 8 = wtpiAVn/Kmpo', where p, is the intrinsic
resistivity and fm the length of the illuminated part of the slice. The
fourth column shows the apparent effective mobility in the presence of
light,* obtained from the field effect signal voltage AF3 in the presence
of light, using the same formula as that giving iJen . The last column
shows the surface recombination velocity, which is proportional to 8"
for fixed light intensity, the constant of proportionality being deter-
mined by comparison with measurements of the fundamental mode
lifetime.
The results of typical surface photo-voltago nms are sho\\n in Tables
* One must be careful to avoid thinking of Mtif* as a true field clfect mobilit.y,
since it is really a sum of two cjuite different components: the true held effect
mobility Meff , and a term, proportional to thickness of the slice, arising from the
jjhotoconductivity.
?!
COMBINED MEASUREMENTS ON ETCHED GERMANIUM SURFACES 1029
Table II • — 8.1 ohm cm ^-type Cycle 5.
Relative Light Intensity 0.25
Time min.
cm2
s
, cm2
cm
Me f f 1 ^
Meff ■ fi
volt sec
volt sec
sec
0
Started sparked O2
1.0
Changed to dry O2
1.5
307
4.1 X 10-2
490
503
3.5
318
3.2 X 10-2
490
660
6.0
Changed to mixture of
wet & dry O2
7.5
273
1.4 X 10-2
376
1480
9.5
239
1.3 X 10-=
320
1580
11.0
Changed to wet C
)2
11.5
94
1.2 X 10-2
-194
1690
12.5
-200
1.1 X 10-2
-230
1820
15.5
-216
1.2 X 10-2
-285
1690
17.0
Changed to wet N2
IS. 5
-352 1
1.6 X 10-2
-570
1310
22.0
Changed to mixture of
wet & dry O2
25.0
-80
1.1 X 10-2
-137
1820
26.5
0
1.2 X 10-2
31
1690
27.5
3.3
1.3 X 10-2
58
1630
28. 0
Changed to dry C
)■!
29.0
193
1.9 X 10-2
330
1070
29.5
239
2.2 X 10-2
400
1000
30.5
250
2.4 X 10 2
420
873
33.0
Tripled flow of dry O2
33.5
296
3.2 X 10 2
500
645
fc 34.5
296
3.7 X 10-2
525
560
■ -^6.5
296
4.2 X 10-2
570
490
■ 37.5
296
4.6 X 10-2
570
455
■^ 38.0
Changed to ozone
42.5
330
6.4 X 10 2
535
323
III and 1\'. Values of 8 were obtained from the photoconductivity signal,
as before, taking the actual ilhiminated length as the length of the
sample. In making use of the standard square-wave calibration for the
surface photo-voltage measurement (Section III), it is necessary to
allow for the fact that the measured capacity involves the whole length
of the sample, plus end and side fringing effects, whereas the surface
photo-voltage measurements im'ohcs only the illuminated length, plus
the fringe effect at the sides.
The penultimate column in Tables III and 1\ shows the ratio of the
change in contact potential, measured in units of (kT/e), to the added-
carrier parameter 5, which was deduced from the photoconductivity.
This is not j^et, however, the true surface photo- voltage function
{dY/d8), since the observed change in contact potential includes also
the Dember potential AF/^"^ which occurs between the illuminated and
non-illuminated parts of the body of the semiconductor. The last column
in Tables III and lY shows the true values of (dY/d8), obtained by sub-
1080 THE HELL SYSTEM TECHNICAL JOURNAL, SErTEMBER
]mC)
Table III — 22.6 ohm cm ti-type
Cycle 7
Time mins.
Relative Light
Intensity
«
ACP volts
/3ACP
6
dV
ds
Starting condition wet N2
6.5
2.25
0.36
6.5 X 10-3
0.7
-0.10
11.5
2.25
0.34
1.0
0.115
-0.045
12.0
Changed to mixture wet and dry N2
12.5
2.25
0.32
2.2
0.27
0.10 !
13.0
2.25
0.34
3.5
0.40
0.23
13.5
2.25
0.35
4.6
0.51
0.34
14.5
2.25
0.38
6.8
0.70
0.53
15.5
0.56
0.10
3.1
1.2
1.03
17.5
0.56
0.11
3.7
1.33
1.16
18.0
Changed to dry O2
18.5
0.56 0.16
5.7
1.4
1.2 :
19.5
0.14 0.06
3.4
2.2
2.0
22.0
Changed to dry O2 triple flow
24.5
0.14
0.082
6.1
2.9
2.7
Table IV — -8.1 ohm cm p-type Cy'cle 8
Time mins.
Relative Light
Intensity
ACP volts
/3ACP
S
dV
dS~
Starting condition wet N2
0
Changed to
mixture wet
and dry No
0.5
0.14 0.011
-3.5 X 10-3
-12.5
-12.6
1.0
0.14 0.0088
-2.1
-9.6
-9.7
5.0
Changed to mixture wet
and dry O2
5.5
0.56
0.0275
-1.8
-2.6
-2.7
6.0
0.56
0.03
-1.45
-1.9
-2.0
7.5
0.56
0.0325
-1.16
-1.4
-1.5
9.5
0.56
0.035
-1.08
-1.2
-1.3
10.0
Changed to dry O2
10.5
0.56 0.044
-0.71
-0.63
-0.69
11.5
0.56 0.055
-0.49
-0.35
-0.41
14.0
Changed to dry O2 tripl
3 flow
14.5
0.56
0.0625
-0.32
-0.20
-0.26
16.5
2.25
0.28
-0.72
-0.10
-0.16
20.5
2.25
0.33
-0.42
-0.05
-0.11
30.0
Changed to ozone
31.5
2.25
0.47
+0.47
+0.039
-0.023
32.5
2.25
0.53
+ 1.4
+0.103
+0.041
tractiiig from (8A c.p./5) a Dember potential correction, given by
{b — 1)/(X + b\'^). (The boundaries of the illuminated region were
sufficiently distant from the contacts for this formula to apply.)
Tables III and IV include only data from the second half of the
cycle (wet N2 -^ ozone), since the rate of change of A c.p. during that
part of the first half in which dry oxygen was replaced by wet oxygen
was too fast to follow.
COMBINED MEASUREMENTS ON ETCHED GERMANIUM SURFACES 1031
The reproducibility of all the data from cycle to cycle was good. One
surprising result is that the surface recombination velocity assumed
its maximum value close to the "wet nitrogen" extreme for both p-type
and n-type. This behavior is quite different from that reported by
Brattain and Bardeen/ who found s to be constant within 20 per cent
throughout the range and Stephenson and Keyes,* who found a maxi-
mum value sometimes at one end, sometimes at the other, and some-
times in the middle. There is quite good agreement on the other hand,
with the results of Many et al.^^"\ who report a maximum in s near the
wet end of the cycle. The result of Brattain and Bardeen is not under-
stood at the present time, and is probably wrong. The differences between
the present work and that of Stephenson and Keyes may be associated
with differences in surface preparation.
V. ANALYSIS OF THE RESULTS
From now onwards we shall express all experimental and calculated
c[uantities in terms of the following dimensionless ratios:
Xs = :2s/eni£, S = Ss + Tp - r„ (2)
AG — AG/enilJLp£, /leff = J"eff/Mp , /"eff* = MeffV^P
where AG is the surface conductance, £ the Debye length for intrinsic
germanium (1.4 X 10~ cm), and /Xp is the mobility for holes (1800 cm v"
sec~^). Tables V and VI show values of the quantities we shall need, as
functions of the surface potential F, calculated from the theoretical
considerations of Garrett and Brattain." The surface conductance, and
the differentials in the fifth and sixth columns, are evaluated for
8 = 0.
Table V — 22.6 ohm cm
n-TYPE
Y
F- InX
Vp - r„
AG
/a(Tp-f„)\
V dY Js
-4.1
/diTp - r„)\
V ds )y
3
4.1
-10.3
17.5
-1.3
2
3.1
-7.0
10.6
-2.6
-0.8
1
2.1
-4.9
6.2
-1.8
-0.4
0
1.1
-3.4
3.3
-1.3
0.0
-1
0.1
-2.3
1.45
-1.1
0.5
-2
-0.9
-1.2
0.36
-1.1
1.3
-3
-1.9
0.0
0.0
-1.4
2.7
-4
-2.9
1.7
0.65
-2.1
5.2
-5
-3.9
4.4
2.65
-3.5
9.4
-6
-4.9
8.9
6.8
-5.8
16.3
-7
-5.9
16.4
14.4
-9.5
27.7
1032 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
Table VI — 8.1 ohm cm p-type
Y
F - InX
ip - r„
AG
/afrp - r„) \
{d{Tp - Vn)\
8
5.1
-8
9.8
-5.5
-87
7
4.1
-4
3.4
-3.1
-42
6
3.1
-2
0.8
-1.9
-19
5
2.1
0
0.0
-1.45
-8.2
4
1.1
1
0.25
-1.3
-3.4
3
0.1
2
1.3
-1.45
-1.5
2
-0.9
4
2.8
-1.75
-0.62
1
-1.9
6
4.8
-2.4
-0.21
0
-2.9
9
7.4
-3.4
0.0
-1
-3.9
12
10.9
-4.3
0.15
-2
-4.9
18
16.4
-6.4
0.31
-3
-5.9
26
25.0
-10.0
0.53
The first problem is the constructing, from the experimental results,
of the curve relating AG and S. The experiments provide a series of pic
tures like Fig. 3, each one corresponding to a different chemical environ-
ment, and so to a different Y. At each of two succeeding pictures of this
sort one knows (i) the vertical displacement (photoconductivity) be-
tween the dark and light field effect curves; and (ii) the mean difference
in the dark and light slopes, and hence the rate of change of photocon-
ductivity with applied field, and therefore with S. The problem is to de-
duce the horizontal displacement (in 2) between the two pictures.
A corrrection must first be made for the fact that the ambient changes
2 uniformly on both surfaces, whereas the applied field induces charge
only on the lower surface, plus fringing effects.* The correction is applied
by taking the difference in slopes (lUei* — /Jen), and multiplying this by
(2/1.27), where the number 1.27 is deduced for the given geometry from
the standard edge-effect formula. This having been done, it is now pos-
sible to take the revised pictures and piece them together to form tA\()
smooth curves (Fig. 4). The process of assembling such a diagram de-
termines the horizontal and vertical distances, and therefore the change
of 2 and AG, between successive experiments.
This argument may be given analytically as follows. First notice that
the photoconductivity ^•oltage in the absence of field (AT% in Fig. 3) is
proportional to (1/s). The application of a voltage between the gold
and the germanium induces some charge density 2 at each point on the
germanium surface, 2 being (due to fringing effects) a complicated
function of position. At each point (1/s) is changed by an amount
2[(i(l/s)/(/2]. This causes the photocondu(!tivity in the presence of field
We are indebted to W. L. Brown for l^ringing this to our attention.
COMBINED MEASUREMENTS ON ETCHED GERMANIUM SURFACES 1033
24 —
22-
20-
18 -
16 -
14 -
G 12
10
8
6
4
2
\
\
\
/
J L
I I I I
iLUdi
•
•
•
J L
J L
-50
-40
-30
-20
■10
0
St
10
20
30
40
50
Fig. 4 — Construction of the curve relating AG (surface conductivity, in units
of ejupMjcC) and s (surface charge, in units of en,£).
to differ from that in zero field, and gives rise to the voltage difference
(AFs — AFi) shown in Fig. 3. Expressing this difference in terms of the
difference (jUeff* — Meff) between the apparent and true effective mobilities
in the presence of light (see Section IV), one finds:
^.f/(l/s) /CuniA
iMeff* ~ Meff) —
di:
2w
(3)
where K is the constant of proportionality between (1/s) and the photo-
I conductivity signal AVo , and C'unit is the capacity per unit of the ger-
manium-gold condenser in the illuminated region, which is 1.27 times
[ the parallel-plate formula. From a series of measurements of (^eff* — fJeu)
I and AFo it is now possible to obtain S by graphical integration:
S =
2/2
^ unit
dAV-2
eni£>/ \/po'C/ \ 2w / J ijl^.u* — Meff
(4)
This and the giuplucul method are of course e(iuivalent. it is worth-
while emphasizing again that either technitiue depends for its validity
I on the fact that the distribution of fast states is unaffected by the gas
I changes in the Brattain-Bardeen cycle, as shown in the experiments of
jl Brown and Montgomery.^ If, however, the assumption were too far from
the truth, the fitting of both slopes in Fig. 4 would be impossible. The only
1034 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
18
16
14
12
10
p3
1
\
1-2
\
\
-1
y
I
/
V,0
y
/
\-2_'
./
-50
■50 -25
0
St
-25
25
50
75
100
125
28
26
24
22
20
18
16
14
12
10
150
Fig. 5 — Curves showing AG (surface conductivity, in units of eij.pni£) and
S surface charge, in units of en,£) for the 22.6 ohm-cm sample (upper curve) and
for the 8.1 ohm-cm sample (lower curve). Values of Y, deduced from the surface
conductivity, are indicated on the curves.
place at which fitting was at all difficult was at the extreme wet end. For
most of the range, therefore, the method is at least internally consistent.
Fig. 5 shows the result of carrying out this procedure for the n and p-
type samples. The data were averaged over a number of runs. The num-
bers appearing on the curves represent values of Y, obtained by reference
to Tables V and VI.
COMBINED MEASUREMENTS ON ETCHED GERMANIUM SURFACES 1035
From Fig. 5 one may now calculate* the changes occurring in Xs ,
the (reduced) charge in fast states, since Fp — r„ may be read from
Tables V and VI, and Ss - S - (f^ - f,). Fig. 6 shows (d2s/dY)i
as a function of 1" — In X, calculated from the experimental results in
this way. [The reason for plotting against Y — In X instead of Y is that
this quantity represents the difference, in imits of (kT/e), between the
electrostatic potential at the surface and the Fermi level. In this way the
effects of difference from sample to sample in the position of the Fermi
level in the interior are eliminated.] Notice that the measurements of
{dT^s/dY)s for the two samples have the same general shape, and that
the turning points of the two curves occur at about the same value of
dY
-30
Fig. 6 — Differential charge in fast states versus surface potential. The graphs
show {dZs/dY) plotted against F — In X. Dots: p-type; circles: n-type. Atypical
result of Brown and Montgomery, using 28 ohm-cm p-type germanium, is also
shown.
1036 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
(F — 111 X). Fig. 7 shows the variation of surface rerombiiiation velocity
with F — hi X, using the experimental photoconductivity data and values
of y read from Fig. 5. The values of s have been divided by (X + X~'),
as indicated, since s/(X + X" ) is expected to be the same, at a given
value of ()' — In X), for all samples, so long as the distribution of fast
states is the same. The agreement shown in Fig. 7 is probably closer
than would be expected in the light of the experimental accuracy.
Fig. 8 shows the observed dependence of dY/d8 on (F — In X) for both
samples, using the data of Tables III and IV, and using the photocon-
ducti^'ity to determine, from Fig. 7, the value of F at each point. On
the figiu'e the expected limiting values ( — X and X~ ) are shown for both
samples. Of the four asymptotes, the higher limit of (dY/d8) for the
At-type sample is satisfactorily reached for large negative values of Y;
the experimental values for the p-type sample appear to be approaching
the expected limit for large positive values of F, while the information
regarding the approach to the two lower limits is too fragmentary to do
more than show that the order of magnitude is as expected. Now taking
the data shown in Fig. 8, making use of (1) and the calculations given
in Tables III and IV, one calculates (82^/88) Y/(d2,/dY)s . The values
so found are plotted against Y in Fig. 9. Fig. 6, 7 and 9, showing the ob-
served variation of {dXs/dY)s , s and {d2s/d8)Y/id2s/dY)s with F,
furnish a complete description of the properties of the fast states at the
200
CO
100
80
60
k 50
+
-^40
30
20
10
o
o
o
o
._5 1
— o
: • •
o
o
^2 ?
.o •
o •
o
-2
-1 0 1
Y-mx
Fig. 7 — Surface recombination velocity versus surface potential. The curves
show s/(X + X~') plotted against F — In X. Dots: p-type; circles: n-type.
COMBINED MEASUREMENTS ON ETCHED GERMANIUM SURFACES 1037
10
dY
drf" 4
10-'
e
10
y
^
,»— —
-
^/^
r
/^-
-
P^
•
— -2
8
«5.
»
»
/.
r
•
c
\
-
/
\
-
/
\
0
-
-wl
/'
\ ®
-
/
•^
£3" a
3
<»
1»
4
/
O
a,
/
i
-
/
a
'
-
/
1
-
"~~~""
^s
/
» /
5^
-
1
^
\
/
/
\l
-4
-2
-1 0 1
Y-ln\
Fig. 8 — Surface photo-voltage (change in contact potential in relation to
added carrier concentration). dY/d8 is shown plotted against F — In X. Dots: p-
fype; circles: 7i-type. Data from different runs are distinguished by modifications
to these symbols. The left-hand branches denote absolute magnitudes, since the
ratio is negative there. At the extreme left hand of the diagram, the fast states
near to the Fermi level are in good contact with the valence band: at the extreme
right hand, to the conduction band. The theoretical asymptotes (X~i to the left
and X to the right) are also indicated.
temperature studied. This is the basic information which any theoreti-
cal treatment must explain. In the succeeding paper this matter is dis-
cussed from the point of view of the statistics of a distribution of fast
states, and information on the cross sections, as well as on the distribu-
tion itself, is derived from the data just presented.
1038 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
10
w
> 4
10
W
10"
10-2
-
y
^
-
-
/
/
^-
^
u —
8--.
,^^
■o^.
/
/
/
^^
V
/
<
N.
-
/
\
-
/
i
\
-
/
\
\
-
/
-
-
-
-
-6 -5
-3 -2-1 0 1
Y-ln\
Fig. 9 — The function (a2s/S5)y/(9S,/ay)j plotted against F - In X. Dots:
p-type; circles: n-type.
VI. FURTHER COMMENTS
The development given in the previous section has concerned particu-
larly the properties of the fast states. As to the slow states, the experi-
ments are much less informati^'e. The variations of 1^ with gas are
generally consistent with the variations of contact potential previously
reported/ although the total range in Y (±0.13 volt) is smaller by about
a factor of 2 than that in contact potential found in the previous work.
One must say that roughly half the change of contact potential is in
Y B , (i.e., 8Y) and half in Vd , the potential drop across the ion layer.
COMBINED MEASUREMENTS ON ETCHED GERMANIUM SURFACES 1039
It may be seen from the figures that it is the quantity (F — hi X),
lather than Y, which appears to be characteristic of the point in the cycle
reached. This property of a semiconductor surface, and possible reasons
therefore, have often been discussed in the literature." The total range
of surface potential is illustrated in Fig. 10, which is drawn to scale, and
also shows sundry other points of interest found in the present research.
The potential diagrams for n-type and p-type are drawn with the Fermi
levels aligned, to show the relation between the property (F — In X) =
const, and the frequently observed smallness of the contact potential
difference between n and p-type germanium.
As to the reproducibility and accuracy of the work presented here,
the following points may be of interest: (i) The measurements were re-
peated on another n-type sample of nearly the same resistivity as the
one reported here, but cut from a different crystal. The results on this
sample were indistinguishable, within the experimental error, from those
found on the first n-type sample, (ii) If the sample was re-etched in pre-
cisely the same way as before, and the experiments repeated, the re-
sults were in good agreement with those obtained before. However,
variations in the etching procedure sometimes gave quite different re-
X MAXIMUM IN S
o ZERO OF dv/dcT
□ INVERSION POINT
p-TYPE SAMPLE
n-TYPE SAMPLE
Fig. 10 — The shapes of the surface space-charge regions for the p-type and
/i-type samples in the extremes of gaseous environment. The two surfaces are to
the center of the figure. The solid curves show the center of the gap (intrinsic
Fermi level) plotted against distance, in units of an intrinsic Debj-e length. Also
shown are the positions of the zeros of (dY/dS), the maxima of s, and the minima
of surface conductivitj'.
1040 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
suits. Wc hope to discuss this at a future date, (iii) The accuracy of the
measurements is not high. Some of the more directly-derivable quanti-
ties, such as s, should be known to 5 per cent, but a quantity
like (d'2s/d8)/(dZs/dY), which is only obtained after a long and elabo-
rate calculation involving a number of corrections, is perhaps uncertain
to 30 per cent. ^
VII. CONCLUSIONS
This paper has presented results of combined measurements of field
effect, photoconductivity, change of photoconductivity with field, fila-
ment lifetime and surface photo-voltage, on slices of germanium. From
the measurements, the surface potential Y has been found at each point,
and the variations of the quantities (dZs/dV), s and {dI,,/d8)/(dI,s/dY)
with Y determined.
It is a pleasure to record our thanks to W. L. Brown, for comments
on field effect techniques and many stimulating discussions, to H. R.
Moore, mIio constructed the high-voltage power supply, and to A. A.
Studna, who assisted in the experiments. We are also grateful to C\
Herring for comments on the text.
BIBLIOGRAPHY
1. W. H. Brattain and J. Bardeen, Surface Properties of Germanium, B. S.T.J. ,
32, pp. 1-41, Jan. 1953.
2. C. G. B. Garrett and W. H. Brattain, Physical Theory of Semiconductor Sur-
faces, Phys. Rev., 99, pp. 376-387, July 15, 1955.
3. W. L. Brown, Surface Potential and Surface Charge Distribution from Semi-
conductor Field Effect Measurements, Phys. Rev., 98, p. 1565, June 1, 1955.
4. H. C. Montgomery and W. L. Brown, Field-Induced Conductivity Changes in
Germanium, Pliys. Rev., 103, Aug. 15, 1956.
5. J. R. Schrieffer, Effective Carrier Mobility in Surface Charge Layers, Phj's.
Rev., 97, pp. 641-646, Feb. 1, 1955.
6. C. G. B. Garrett and W. H. Brattain, Interfacial Photo-Effects in Germanium
at Room Temperature, Proc. of the Conference on Photo Conductivity,
Nov., 1954, Wiley, in press.
7. W. H. Brattain and C. G. B. Garrett, Surface Properties of Germanium and
Silicon, Ann. N. Y. Acad, of Science, 58, pp. 951-958, Sept., 1954.
8. D. T. Stevenson and R. J. Keyes, ]\Ieasurements of Surface Recombination
Velocity at Germanium Surfaces, Physica, 20, pp. 1041-1046, Nov., 1954.
9. J. Clerk Maxwell, Electricity and Magnetism, 3rd Edition, 1, p. 310, Clarendon
Press, 1904.
K). W. van Roosbroeck, Theory of Photomagnetoelectric Effect in Semiconduc-
tors, Phys. Rev., 101, pp. 1713-1725, March 15, 1956.
11. J. Bardeen and S. R. Morrison, Surface Barriers and Surface Conduction,
Physica, 20, p. 873, 1954.
12. 1']. Harnik, A. Many, Y. Margoninski and E. Alexander, Correlation Between
Surface Recombination Velocity and Surface Conductivity in Germanium,
Phys. Rev., 101, pp. 1434-1435, Feb. 15, 1956.
Distribution and Cross- Sections of Fast
States on Germanium Surfaces
By C. G. B. GARRETT and W. IL BRATTAIN
(Manuscript recieved May 10, 1956)
A theoretical treatment uf the Jield effect, tiurface photo-voltage and surface
recombination phenomena has been carried out, starting with the Hall-
Shockley-Read model and generalizing to the case of a continuous trap dis-
tribution. The theory is applied to the experimental results given in the
previous paper. One concludes that the distribution of fast surface states is
such that the density is loivest near the centre of the gap, increasing sharply
as the accessible limits of surface potential are approached. From the sur-
face photo-voltage measurements one obtains an estimate of 150 for the ra-
tio (a-p/an) of the cross-sections for transitions into a state from the valence
and conduction bands, showing that the fast states are largely acceptor-type.
On the assumption that surface recombination takes place through the fast
states, the cross-sectioris are found to be: dp '-^6 X 10"^ cm and o-„ -^
4 X 10"'' cm~.
I. INTRODUCTION
The existence of traps, or "fast" states, on a semiconductor surface,
becomes apparent from three physical experiments: measurements of
field effect, of surface photovoltage,' and of surface recombination ve-
locity s. Results of combined measurements of these three quantities on
etched surfaces of p- and r?-type germanium have been presented in
the preceding paper. ^ The present paper is concerned with the conclu-
sions which may be drawn from these experiments as to the distribution
in energy of these surface traps, and the distribution of cross-sections
for transitions between the traps and the conduction and valence bands.
The statistics of trapping at a surface level has been developed by
Brattain and Bardeen^ and by Stevenson and Keyes,^ following the work
on body trapping centers of Half and of Shockley and Read.
It is known that surface traps are numerous on a mechanically dam-
aged surface or on a surface that has been bombarded but not annealed;
1041
1042 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
and that on an etched surface their density is comparatively low. It is
also known that the available results cannot be accounted for by a
single level, or even two levels, so that one is evidently dealing either with
a large number of discrete states or a continuous spectrum. A given trap-
ping centre is completely described by specifying: (i) whether it is donor-
like (either neutral or positive) or acceptor-like (neutral or negative);
(ii) its position in energy; and (iii) the values for the constants Cp and
Cn (related to cross-sections) occurring in the Shockley-Read theory.
In this paper we shall deduce what we can about these quantities, using
the experimental results previously presented.
At the outset it must be admitted that it is by no means certain that
the same set of surface states appear in the field-effect experiment and
give rise to surface recombination. However, (i) it is found that such sur-
face treatments as increase s also reduce the effective mobility in the
field-effect experiment; (ii) any surface trap must be able to act as a
recombination centre, unless one of the quantities Cp and C„ is zero;
and (iii) the capture cross-sections obtained by assuming that the field-
effect traps are in fact recombination centres are, as we shall see below,
eminently reasonable.
As to the nature of the surface traps, not too much can be said at the
moment. The lack of sensitivity to the cycle of chemical environment
used argues against their being associated with easily desorbable surface
atoms; the intrinsically short time constants (Section 5) suggest that
they are on or very close to the germanium surface. The possibility that
the surface traps are Tamm levels remains; or they could be corners
or dislocations. However, the reproducibility with w hich a given value of
s may be obtained by a given chemical treatment of a given sample,
followed by exposure to a given ambient, suggests that there is nothing
accidental about their occurrence.
II. STATISTICS OF A DISTRIBUTION OF SURFACE TRAPS
We start by quoting results from the work of Shockley and Read
and Stevenson and Keyes'' on the occupancy factor ft and the flow U
of minority carriers (per unit area) into a set of traps having a single
energy level and statistical weight unity:
ft = (Cnfi. + Cpp,)/[Cn(n. + ni) + Cp(p, + p,)] (1)
U = CnCp(p,ns - ni)/\(\{n. + m) + C,(p.. + pOl , (2)
where the symbols ha\^e the following mc^anings:
ns , Ps — densities of electrons and iioles present at the surface
DISTRIBUTION AND CROSS-SECTIONS OF GERMANIUM SURFACES 1043
>h , pi — values which the equilibrium electron and hole densities
at the surface would have if the Fermi level coincided with
the trapping level
Cn = NtVTnCTn ', Cp = NiVrpCTp , where iV^ stands for density of traps per
unit area, Vm is the thermal speed for electrons and Vtp that
for holes, and a„ and a,, are the cross-sections for transitions
between the traps and the conduction and valence bands
respectively.
If we introduce the surface potential Y and the c^uantity 5, defined as
(Ap/'Hi), where Ap is the added carrier density in the body of the semi-
conductor, we may write:
ris = X~^/iie^(l + X5)
Ps = Xn;e~^(l + \~^8)
where X = po/ni , po being the e(iuilibriiun hole concentration in the body
of the semiconductor. We further introduce the notation:
7ii = iiier" pi = nj-e"
(4)
(Cp/CnY = X
The quantity v thus represents the energy difference, measured in
units of (kT/e), between the trapping level and the centre of the gap;*
and is positive for states below, negative for those above, this le^'el. The
parameter x ^vill be most directly associated m ith whether the state is
donor-like or acceptor-like. If it is donor-like (neutral or positive), a
transition involving an electron in the conduction band will be aided by
Coulomb attraction whereas one involving a hole will not; so one would
expect X « 1- For an acceptor-like trap, (neutral or negative) the con-
trary holds, and one expects x ^ 1-
Using (4), the occupancy factor (1) becomes
. ^ X~'X-Va + X3) + xe'
' X-'\-'e^l + X5) + x-'e-" + xXe-'Xl + ^''8) + xe" (5)
= iX~*e~*''e*'' sech ii {Y + v) - h (n X] for 5 = 0
Note that, in thermodynamic ec[uilibrium, the occupancy factor does
not depend in any way on the cross-sections, whereas for 5 5^ 0 it does,
through the ratio x-
* Strictly speaking, one should say "position of the Fermi level for intrinsic
semiconductor" instead of "centre of the gap." These will fail to coincide if
the effective masses of holes and electrons are unequal, as they certainly are in
germanium.
1044 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
Similarly, the flow of carrier-pairs to the surface (2) becomes:
U =
(6)
x-iX-ie^(l + X5) x-'e-" + xXe"''(l + X'^S) xe"
wliich, for 6-^0, tends to the linear law U = sniS, where s, the surface
recombination velocity, is given by:
s/{:VTnVTpf'' = NtSt
where
St ={\ + X'')ian<7,y''/2\ch(p + fnx) +ch(Y - (n\ - fnx)] (7)
The surface density Sg of trapped charge is given by:
= Nd\ (8)
2.,
where ft is the occupancy factor, given by (5).
Now let us turn to the question of a distribution of surface traps
through the energy v. Suppose that the density of states having v lying
lietween v and v -\- dp is N(v) dv, expressed in units (ni£). Then the total
surface recombination velocity arising from all traps, and the total
trapped surface charge density, are given by :
s/ivrnVrpY" = ni£ J St{p)N{v) dv (9)
2, = \ Jt{v)N{v)dp (10)
where St{v) and /«(i') are explicit functions of v, given by (5) and (7).
The limits of the integrals in (9) and (10) are the values of v correspond-
ing to the conduction and valence band edges; however, as we shall see,
it is often possible to replace these limits by ± «= .
In summing up the contributions in the way represented l\v (9), we
ha\'e implicitly ignored the possibility of inter-trap transitions, suppos-
ing that the popidation of each trap depends only on the rates of ex-
change of charge with the conduction and valence bands, and is inde-
pendent of the population of any other trap of differing energy.
What kind of function do we expect N{v) to be? Brattain and Bardeen'
postulated that N{v) was of the form of two delta-functions, correspond-
ing to discrete trapping levels high and low in the band. This assumption
is not cousislciit with the observed facts in ri'gard to field cITi^-l, surface
DISTRIBUTION AND CROSS-SECTIONS OF GERMANIUM SURFACES 1045
photo-voltage, or surface recombination velocit}'. The general difficult}'
is that the obser\'ed cjuantities usually vary less rapidly with surface
potential than one would expect. It is possible to fit the field-effect obser-
vations of Brown and Montgomer}'" with a larger number of discrete
levels, but this would call for a "sharpening up" of the trapped charge
distribution as the temperature is lowered, and this appears to be con-
trary to what is observed.* It is always possible that the surface is patchy,
in w^hich case almost any variation with mean surface potential could be
explained. The simplest assumption, however, seems to be that N{v)
is a rather smoothly-varying function. All we need assume for the
moment is that it is everywhere finite, continuous and differentiable.
We may then differentiate equation (10) with respect to Y and 5 under
the integral sign, and get {d^s/dY)^ and (5Ss/55)f, the cjuantities for
which experimental measurements were reported in the previous paper :^
i-^ = [-
\dYji J 4
N{p) ch
ch\h{v -f Y) - \tn X]
N{v){h{\-' + \)m{v - Y) -f i ^n X
+ In x] + \{\~' - X)) civ
4.ch\h{v +Y) ~\ (n X]
(11)
(12)
Notice that the expression in brackets in the numerator of (12) gener-
ally has the value X~ or —X, except near the point v = Y — fn\ — 2fnx-
This is indicative of the fact that, whatever the exact form of N(v), the
ratio of — (32s/35)y/(3Ss/(9F)5 tends to these limiting values (X^^ and
—X) for sufficientlj^ large negative and positive Y respectively.
It may be verified from (7), (11) and (12) that {dXs/dY)^ , found from
the field effect experiment, depends only on N(v) ; (d'Zs 88) y , found from
the surface photo- voltage, depends on N{v) and x; while s, the surface
recombination velocity, depends in addition on the geometric mean
cross-section (anapY''. Both x and (a-„(7p) '"^ might themselves, of course,
be functions of p. Thus relations (7), (11) and (12) are integral eciuations,
from which the three unknown functions of v may in principle be de-
duced from the experimental results. (Equation 11 , in fact, may be solved
explicitly. P. A. Wolff'^ has shown, how^ever, that, to determine N{v)
unambiguously, it is necessary to know (52^/(9 F)j for all values of Y
in the range ± ^ .)
The foregoing considerations apply to "small-signal" measurements.
* There are some changes with temperature, but not what one would expect if
there were only discrete surface states.
1046 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
z
>-
w
>-
in
3.0
2.5
2.0
1.5
1.0
0.5
-0.5
-1.0
-1.5
>w,
^
N
\
N
\
•<j
s/\
1
k
^-.
p
<
r^
•^.
c
N.
X.
•
;
-5
-2
-1 0
Y-Ln\
Fig. 1 — The fit between Equations (13) and (14) and the experimental data.
The circles and dots give the experimental data for the n and jo-type samples
respectively and the solid straight lines represent Equations (13) and (14).
But it is also possible, once A^(j'), x and (cr^o-p)^'^ are known, to calculate
the expected behavior of the surface photo-voltage and surface recombi-
nation rate at high light intensities, and compare the answer with the
experimental findings. We hope to discuss this matter in a later paper.
III. ANALYSIS OF THE EXPERIMENTAL DATA BY USE OF THE DELTA-
FUNCTION APPROXIMATION
Let US first consider the interpretation of our field effect measure-
ments by means of (11). We start by finding empirical expressions that
describe the observed dependence of (d'Zs/dY) on Y (Fig. 6 of the pre-
ceding paper^). Except at values of (F —(n X) close to the extremes
reached one may fit quite well by a hyperbolic cosine function. Fig. 1
shows the function whose hyperbolic cosine is {d'2s/dY)/(d'Es/dY)min
plotted against Y — tn X. From this figure we find:
22.6 ohm-cm n-type:
^" ) = 4.5c/i[0.36(y - (n X) - 0.8]
(13)
(for (F - (n X) > -4
DISTRIBUTION AND CROSS-SECTIONS OF GERMANIUM SURFACES 1017
8.1 ohm-cm p-type:
= 9.7c/; [0.31 (F - (n X) - 0.5] (14)
for 2 > (F - (n X) > -4
For values of (F — (n X) less than —4, it appears that Ss is changing
more rapidly with F than is indicated by (13) and (14). We shall comment
on this point later. Excluding this region, we note that in both cases the
variation with F is everywhere slow in comparison with e^, and proceed
on the assumption that N{v) is a function of v that varies everywhere
slowly in comparison with c" . Then (11) indicates that there is one fairly
sharp maximum in the integrand in the range ± « , occurring at that
value of V which coincides with the Fermi level:
V ^ -F + (n X (15)
The integral in (11) could be evaluated in series about this point
(method of steepest descents). The zero-order approximation is got by
replacing
i sech' \h{v + F) - \(n X] by 6(i^ + F - Cn X).
Later we shall proceed to an exact solution, and we shall find that this
delta-function approximation is not too bad. From (11) we now find:
-f F - (ri X) dv = N{-Y + (n. X) (15)
This mathematical procedure will be seen to be eciuivalent to identify-
ing {d'Ls/dY)i with the density of states at the point in the gap which
coincides with the Fermi-level at the surface. Using (13) and (14), one
gets:
22.6 ohm-cm n-type:
N{v) = 4.5 chiOMv + 0.8) (16)
8.1 ohm-cm p-type:
N{v) = 9.7 chiQMv + 0.5) (17)
As we shall see in the next section, the exact solutions differ from (16)
and (17) only in the coefficients preceding the hyperbolic cosines.
Turning to the surface photo-voltage measurements, we take (12)
and again replace
I sech' [^{v + }') - \tn XJ by h{v + Y - In X)
1048 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
Using (15), one gets:
~ (dXs/dY)B
= i(X-' + X) th(-Y + fn\+ (n x) + hO^~' - X)
(18)
This procedure, inaccurate as it is, has the advantage that no particu-
lar assumption need be made concerning the functional dependence of
X on V, it being understood that x in (18) has the value holding for v =
— Y -\- (n X. In particular, if }^o is that ^•alue of Y at which the ratio
-(a2s/a5)y/(a2,/a}')5 changes sign,
/"wxo = To - Cn X + t}r\{\ - X"')/(X + X~')] (19)
From the experimental data, one linds, for the /^-tj-pe sample, In xo '^
2.4 (at V = —3.5); for the p-type sample, (n xn ^' 1.0 (at v = 1.9).
In \-iew of the approximations made, these estimates would not be
expected to be more precise than ± 1 to 2 units. Notice that both \alues
are positive, and that the difference between them is small in compari-
son with the difference in v. This suggests that we start afresh with the
assumption that x is independent of v, and woi'k out the surface photo-
voltage integral exactly. This is done in the next section.
IV. EXACT TREATMENT FOR THE CASE N{v) = A ch {qv + B) , AVITH CON-
STANT CROSS-SECTIONS
The results of the previous section suggest the procedure of assuming
that N{v) is of the functional form given by (16) and (17), and evaluat-
ing the integrals (9), (11) and (12) exactly. The integral for {dliJdY),
(11), depends only on the form of N{v) and ma}^ be eA'aluated at once.
To get idfijdb), (12), one must know how x depends on v. On the
basis of the work of the previous section, we shall suppose that x is in-
dependent of V. (Properly, we need only assume that x varies with v
more slowly than e^ Since the function th[\{v — Y) -f ^Cn X + (n x]
has one of the values ±1 everywhere except close to j' = Y — (n X
— 2Cn X, and since the denominator of (12) has a sharp minimum at
V = — Y -\- (n X, it follows that the region in which (3Ss/d5)y changes
sign will be governed mainly by the value of x at ^ = — (n x) To get s [(9),
using (7)], one must also assume something about the geometric mean cross-
section, {an(T,^ ". In the absence of any information on this score, we
shall assume that (o-„a-p)' " also is independent of v, and see how the com-
puted variation of s with Y compares with the experimental results.
DISTRIBUTION AND CROSS-SECTIONS OF GERMANIUM SURFACES 1049
We assume:
N(v) = A ch (qv + B) (20)
and substitute in (11), (12) and (7). In view of the sharp maximum in
the integrands of these expressions, it is permissible to set the limits
which should correspond to the edges of the gap or of the state distribu-
tion equal to ± <» . The integrals are conveniently evaluated by the con-
tour method (see Appendix 1) and yield the following results:
( -^ j = Attq cosec TQ ch [B — q{Y — /n X)]
/aS,\ ^ _ATrq cosec vq ch [B - q{Y - (n X)] X
where
'y = }' - (n X - (n X
(S, = B - qtnx
(21)
(22)
(23)
{VrnVrp)"-' (24)
= I (X -f X~^)(o-„(Tp)^'^ni£ 2x A sh qy ch (B cosec irq cosech 'y
Comparing (21) with (15), we see that the delta-function approxima-
tion is in error to the extent that it replaces irq cosec irq by 1. With the
value of q found experimentally, this is not too bad; we can now, how-
ever, by fitting the right-hand side of (21) to the experimental facts,
(13) and (14), obtain exact solutions for A''(j'):
22.6 ohm-cm n-type
iY(j;) = 3.6 chiQMu + 0.8) (for u < 4)
8.1 ohm-cm p-type (25)
N(v) = 8.3 chiOMp + 0.5) (for p < 4)
The question arises as to whether this solution for the distribution is
unique. We have already pointed out that the mathematical methods
fail if the distribution is discontinuous. It seems that (25) represents the
only solution that is slowl3^-^'arying, in the sense used in the previous
section; its correctness could presumably be checked by carrying out
experiments at different temperatures. For v > 4:, the abo\-e expressions
1050 THK BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
do not fit the observed facts, because, for F — ^n X < — 4, the charge in
fast states is found to change more rapidly than is given by the empirical
expressions in (13) and (14). The behaviour in this region is perhaps in-
dicative of the existence of a discrete trapping level just beyond the
range of v which can be explored by our techniques. The observations
(see Fig. 6 of preceding paper^) can be described by postulating, in addi-
tion to the continuous distribution of states given above, a level of den-
sity about 10 ^ cm" , situated at j^ = 6, or a higher density still further
from the center of the gap. Statz et al,^' using the "channel" techniques,
which are valuable for exploring the more remote parts of the gap, have
proposed a level of density '^ 10 cm~^, situated at about 0.14 volts be-
low the center of the gap (v = 5.5) : this is not in disagreement with the
foregoing.
In order to compare (22) with the experimental data derived from the
surface photo-voltage, it is necessary to choose a value for x- Fig- 2 shows
the comparison with the results presented in the preceding paper. On the
vertical axis, the values of (dl^s/d8)/(d'2s/dY) plotted have been divided
by (X + X" ), in order to show the n and p-type results on the same scale.
(Note that the limiting values of this quantity should be X/(X -|- X"^)
and — X~V(^ + ^~^)j so that the vertical distance between the limiting
values should be 1, independent of X). The theoretical curves have been
drawn with the value Inx = 2.5, in order to give best fit between theory
and experiment at the points at which the ordinate changes sign. (It
may be seen from the form of (22) that, with the actual value of the other
parameters, the main effect of adopting a different value of in x would
be to shift the theoretical curve horizontally, while a change of X shifts
it vertically without in either case greatly modifying its shape). The fit
between theory and experiment is not quite as good as could be expected,
even taking into account the rather low accuracy of the measurements.
The variation of (6Ss/55)/(6Ss/6F) with Y found experimentally seems
to be rather slower than the theory would lead one to expect. The main
points to make are : (i) the difference in Y between the zeros for the two
samples (5.4 ± 1) is about what it should be (4.8) on the assumption
that in X is the same for both samples and of the order of unity; and (ii)
paying attention mainly to the zeros, the estimate (nx — 2.5 is likely to
be good to ±1.
Now let us consider the surface recombination velocity. Here we are
on somewhat shakier ground, in that, in deriving (24), we have had to
assume not only that x is independent of v, but (o-„crp)^'^ also. First we note
from (24) that the maximum value of s should occur at F — (n X = in x-
Comparing with the experimental results given in the preceding paper,
DISTRIBUTION AND CROSS-SECTIONS OF GERMANIUM SURFACES 1051
10
W
to
10
to
1.0
0.8
0.6
0.4
0.2
-0.2
-0.4
-0.6
-0.8
1.0
/
^^
/
/
•/
1
y
V
,__,s^
>
./
^
—
k
/
/
Vi
/
■
>^
y
J
—
y
-6
-2 0 2
Y-Ln\
Fig. 2
Experiment and theory for
95
)K^-
X + X-
Solid lines theory; circles and dots, with smooth curves through the points, repre-
sent experimental results for n and p-type samples, respectively.
we see maxima at F — ^w X = 2.0 for the p-type sample, and 3.5 for the
n-type sample. Both these values are within the limits to (n x given in
the previous paragraph, thus confirming the estimate made there. Fig.
3 shows a comparison between the experimental results and (24). The
graph has been fitted horizontally, by setting (n x = 2.5, as found above ;
vertically, to agree with the mean value at that point. The agreement
with experiment is reasonable, although again, just as in Fig. 2, the ex-
perimental variation of s with ( Y — in X) is rather slower than one would
expect.
The fact that the experimental values, both of surface photo-voltage
and of surface recombination velocity, vary more slowly than expected,
is susceptible of a number of interpretations: (i) The deduced distribu-
tion of fast states might be wrong. However, the most likely alternative
distributions — isolated levels, or a completely uniform distribution —
1052 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
give (in at least some ranges of F) a more rapid instead of a smoother
variation of these quantities so long as the surface is homogeneous, (ii)
The estimates of the changes in Y might be too large. It is unlikely that
our calibration is sufficiently in error, and other workers have obtained
results comparable to ours. The only possibility would be that the mo-
bility of carriers near the surface is larger (instead of smaller, as found by
Schrieffer) than inside • — which seems cjuite out of the question, (iii)
The ratio of capture cross-sections varies with v. This, however, w^ould
only be in the right direction if one were to assume that the ratio x 'in-
creases with the height of the level in the gap — i.e., that the high states
behave like acceptors, and the low ones like donors. While not quite
impossible, this is an unlikely result, (iv) The surface is patchy. It is
probable that a range of variation of two to four times (kT/e) in surface
potential would be sufficient to account for the observed slow variation
of surface photo-voltage and recombination \'elocity with mean surface
potential. We ha\'e refrained from detailed calculations of patch effects,
on the grounds that, without detailed knowledge of the magnitude and
distribution of the patches, it would be possible to construct a model
that could indeed fit the facts, but one w^ould have little confidence in
the result. The possibility of patches warns us to view with caution the
exact distribution function deduced for the fast states. It would still
be conceivable, for example, that one has but two discrete states, as
originally proposed by Brattain and Bardeen," and that the apparent
existence of a band of states in the middle of the gap arises from the fact
that there are always some parts of the surface at which the Fermi level
is close to one or other of these states. Fortunately the conclusions as to
the cross-sections are not too sensitive to the exact distribution function
assumed.
Using the mean of the two coefficients in (25), substituting //,• =
2.5 X 10'^ cnr^ £ - 1.4 X 10"'' cm, {vrnVrp)"' = 1.0 X 10' cm/sec, in
(24), and using the experimental result (see Fig. 3) that s,nax/(X -f X~\) =
1.2 X 10" cm/sec, one obtains ((Tp(T,y~ = 5 X 10~' cm'. Now setting
(ap/a„) = x" '^ c' ^^ 150, one gets for the separate cross-sections:
o-p = <) X 10"'' cm"
an = l X 10"'' cm'
There values appear lo he emiiicntly reasonable. Burton et al, " who
studied re('()inl)ination through body centres associated with nickel and
copper ill germanium, found cr^ > 4 X 10 '"^ cm", o-,, = 8 X 10"'^ cm*
for nickel, and a„ = 1 X 10 '%„ = 1 X 10"'' for copper. The fact that
DISTRIBUTION AND CROSS-SECTIONS OF GERMANIUM SURFACES 1053
200
m
100
90
80
70
~
60
u
LU
■sn
(/)
5
40
o
u
30
+
,<
20
10
8
7
-6
.V
o
•
o
o
->
X
1
• \
• /
/
>
V
<u
/
\
•
/
\,
) •
i
/
>
^
0
•
/
•
0
•
/
0
•
/
•
•
/
/
f
/
/
-5
-4
-3
-2
-1 0
Y-lnX,
Fig. 3 — Experiment and theory for surface recombination. Solid curve theory
circles and dots for n and p-type samples, respectively.
our estimates for ap and o-„ appear to be of the expected order of magni-
iitudes lends strong support to the view that identifies the traps appear-
ing in the field-effect and surface photo-voltage experiments with those
responsible for surface recombination.
The result that (o-p/cr„) = 150 is good evidence that the fast states are
acceptor-like. This statement must be restricted to the range \ v \ < 4;
the states that are outside this range might be of either type. Also one
might allow a rather small fraction of the states near the middle to be
donor- type, without serious trouble; but the experimental results compel
one to believe that most of the fast states within 0.1 volts or so of the
centre of the gap are acceptor-like.
V. TRAPPING KINETICS
The foregoing considerations have concerned the steady-state solution
to the siu'face trapping problem. If the experimental constraints are
changed sufficiently rapidly, however, there may be effects arising from
the finite time required for the charge in surface states to adapt itself
1054 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
to the new conditions.' This section will concern itself with the trapping
time constants (which are not directly related to the rate of recombina-
tion of minority carriers).
One case of trapping kinetics has been discussed by Haynes and Horn-
beck.^ A general treatment of surface trapping kinetics is necessarily quite
involved, and will be taken up in a future paper. Here we shall restrict
ourselves to giving an elementary argument relating to the high-fre-
quency field effect experiment of Montgomery. To simplify the discus-
sion, we assume that the surface in question is of the "super" type; i.e.,
the surface excess of the bulk majority carrier is large and positive. At
time i = 0, a large field is suddenly applied normal to the surface; the
induced charge appears initially as a change in the surface excess of the
bulk majority carrier; as time elapses, charge transfer between the space-
charge region and the fast states takes place, until equilibrium with the
fast states has been re-established. What time constant characterizes
this process?
Take electrons as the majority carrier. Then the flow of electrons into
the fast states must equal the rate of decrease of the surface excess of
electrons. For a single level one may write:
Un = NtVTn(rn[(l " ft)ns - Ml]
(26)
= -r„
For a continuous distribution of levels, one can say that only those
levels within a few times (kT/e) of the Fermi level at the surface will be
effective, so that one may regard the distribution as being equivalent to
a single state with rii = rii exp (Y — In X), which will be about half full.
We assume further that the density of fast states is sufficient for the
changes in r„ to be large in comparison with those in ft , as is reasonable,
having regard to the relative magnitudes of the measured values of
(dI,s/dY)i found in the present research, and of (dTp/dY)5 and {dT„/dY)s .
Thus/< may be treated as a constant in equation (26). Further, we may
set Hs = 4r„ /nj£ , as may be proved from considerations on the space-
charge region.' Solving (26) with these conditions, one finds, for the
transient change in r„ between the initial and the quasi-equilibrium
state :
Ar„ cc M - th-] (27)
where
r = \e-''&/[NtVTn(rnV2 Vftil - ft)]
DISTRIBUTION AND CROSS-SECTIONS OF GERMANIUM SURFACES
1055
I
I
To clarify the order of magnitude of time constant invoh'ed, let us
substitute £ '^ 10" cm, Nt ~ 10^^ cm~^, tv,. ~ 10^ cm/sec, cr„ ~ 10"^^
cm ,/t '^ 0.5, Ae~ '~ 1. This gives r -^ 10~' sec, which suggests that one
would be unlikely to run into trapping time effects in the field-effect ex-
periment at frequencies less than 10 Mcyc/sec. This conclusion is con-
sonant with the findings of Montgomery.
Appendix 1
evaluation of the integrals in section 4
The integrals occurring in Section 4, giving the experimentally acces-
sible quantities (d2s/dY), (dXs/d8) and s in terms of the surface trap
distribution and cross-sections, are conveniently evaluated by contour
integration. In view of the general applicability of this method in deal-
ing with integrals of the sort that arise from such a distribution of traps,
we include here a short note on the precedure used. The integrals needed
are :
.+00
/T-ou
ch{cx + g) sech" x dx
00
/+00
th{x -\- b) ch(cx -{• g) sech^ x dx
00
-L
+00
h
chicx -\- g)
con-
e/la; -\- chk
To evaluate /i , we evaluate / ch(cz + g) sech^ z dz around the
tour shown in Fig. 4. The contributions from the parts z = ±R vanish
in the limit R -^ oo , so that the integral has the value :
/+00 /.+00
ch(cx -\r g) sech'^ x dx — i sin ctt /
00 •'—00
sh(cx + g) sech'^ x dx
Fig. 4 — Evaluation of 7i .
1056 THE BELL SYSTEM TECHXICAL JOURNAL, SEPTEMBER 1956
The integrand has one pole Avithin the contour, at x = ^iw, at which the
residue is — c(cos ^cr sh g -\- i sin ^cir ch g). Multiplying by 2x1 and
equating the real part to that in the above expression, one obtains:
/i = xc cosec \cir ch y
The same contour is used in evaluating lo ; there are now poles at z =
^/tt and at z = \iir — b, and one obtains:
1-2 = TTC coth b ch g cosec ^ctt
— 27r cosec ^CTT cosech" b sh ^bc ch{}/'2bc — g)
To evaluate h , one integrates / [ch{cz + g)/(chz + chh-)] dz around
the contour shown in Fig. 5. There are poles at iw ± k. Proceeding as
before, one finds:
I3 = 2ir sli ck ch g cosec ire cosech k
Appendix 2
limitation of surface recombination arising from the space-
charge barrier
The ([uestion of the resistance to How of carriers to the surface arising
from the change in potential across the space-charge layer has been
discussed by Brattain and Bardeen. Here we shall recalculate this effect
by a better method, which again shows that, \\ithin the range of surface
potential studied, the effect of this resistance on the surface recombina-
tion velocity is for etched surfaces ciuite negligible.
Let Ip and /„ be the hole and electron (particle) currents towards the
surface, and let x be the distance in a direction perpendicular to the sur-
face, measuring .r positive outwards. Then the gradient of the fiuasi-
Fermi levels (pp and <pn at any point is given by:
n n 7i x"'/
(1)
-R +R
Fig. 5 — Evaluation of I3 .
DISTRIBUTION AND CROSS-SECTIONS OF GERMANIUM SURFACES 1057
Then the total additional change in (pp and <pn across the space-charge
t-egion, arising from the departure in uniformity in the carrier densities
t) and n, is :
A,, = -£. / (i - 1) ,,.
Mn J \n no/
(2)
Suppose now that the true surface recombination rate is infinite, so
that the ciuasi-Fermi levels must coincide at the surface, and:
(Pp -f A<Pp = <pn -+- A(pn (3)
These equations, together with the known space-charge equations,
icomplete the problem. Notice first, from (2), that A<pp will be large only
if there is a region in which p is small (F ^ 1), while A^„ is large onl}^
when, in some region, n is small (F <3C — 1). Introducing the cjuantity 5,
approximating for 8 small, equating Ip and /„ and setting the result eciual
to sriid, one finds:
F « - 1
{Dn/£)(\"' + X"'^')e^''
F » 1 (4)
The coefficients {Dn/S) and (Dp/£) are of the order of 4 X 10' cm/sec.
The most extreme case encountered in our work is that occurring at the
ozone extreme for the n-type sample (X = 0.34, F = —6), for which the
surface recombination velocity, if limited by space-charge resistance
alone, would be about one-quarter of this (10'' cm/sec). The fact that
the observed surface recombination velocity is lower than that by more
than two orders of magnitude shows that space-charge resistance is not
a limiting factor in the present experiments. Equations 4 might Avell
hold on a sand-blasted surface, however, where the trap density is much
higher.
'!-)*
References
1. W. L. Brown, Surface Potential and Surface Charge Distribution from Semi-
conductor Field Effect Measurements, Phys. Rev. 98, p. 1565, June 1, 1955.
2. W. H. Brattain and J. Bardeen, Surface Properties of Germanium, B.S.T.J.,
32, pp. 1-41, Jan., 1953.
3. W. H. Brattain and C. G. B. Garrett, page 1019 of this issue.
1058 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
4. D. T. Stevenson and R. J. Keyes, Measurements of Surface Recombination
Velocity at Germanium Surfaces, Physica, 20, pp. 1041-1046, Nov. 1954.
5. R. N. Hall, Electron-Hole Recombination in Germanium, Phys. Rev., 87, p.
387, July 15, 1952.
6. W. Shockley and W. T. Read, Jr., Statistics of the Recombination of Holes
and Electrons, Phys. Rev., 87, pp. 835-842, Sept. 1, 1952.
7. T. M. Buck and F. S. McKim, Depth of Surface Damage Due to Abrasion on
Germanium, J. Elec. Chem. Soc, in press.
8. H. H. Madden and H. E. Farnsworth, Effects of Ion Bombardment Cleaning
and of O.xygen Adsorption on Life Time in Germanium, Bull. Am. Phys.
Soc, II, 1, p. 53, Jan., 1956.
9. J. A. Hornbeck and J. R. Haynes, Trapping of Minority Carriers in Silicon.
I. P-Type Silicon. II. N-Type Silicon, Phys. Rev., 97, pp. 311-321, Jan. 15,
1955, and 100, pp. 606-615, Oct. 15, 1955.
10. Ig. Tamm, Uber eine mogliche Art der Elektronenbindung an Kristallober
flachen, Phy. Zeits. Sowj., 1, pp. 733-746, June, 1932.
11. H. C. Montgomery and W. L. Brown, Field-Induced Conductivity Changes in
Germanium, Phys. Rev., 103, Aug. 15, 1956.
12. J. A. Burton, G. W. Hull, F. J. Morin and J. C. Severiens, Effects of Nickel and
Copper Impurities on the Recombination of Holes and Electrons in Ger-
manium, J. Phys. Chem., 57, pp. 853-859, Nov. 1953.
13. H. Statz, G. A. deMars, L. Davis, Jr., and H. Adams, Jr., Surface States on
Silicon and Germanium Surfaces, Phys. Rev., 101, pp. 1272-1281, Feb. 15,
1956.
14. C. G. B. Garrett, The Present Status of Fundamental Studies of Semicon-
ductor Surfaces in Relation to Semiconductor Devices, Pi'oc. West Coast
Electronics Components Conf. Los Angeles, pp. 49-51, June, 1955.
15. H. C. Montgomery and B. A. McLeod, Field Effect in Germanium at High
Frequencies, Bull. Am. Phys Soc, II, 1, p. 53, Jan., 1956.
16. C. G. B. Garrett and W. H. Brattain, Physical Theory of Semiconductor Sur-
faces, Phys. Rev., 99, pp. 376-387, July 15, 1955.
17. P. A. Wolff, Private communication.
i
Transistorized Binary Pulse Regenerator
By L. R. WRATHALL
(Manuscript received March 14, 1956)
A stjnple transistorized device has been constructed for amplifying and
regenerating binary code signals as they are transmitted over substantial
lengths of transmission line. By the use of simple circuitry, means are pro-
vided whereby the distortion in the output of one repeater due to low fre-
quency cutoff is compensated in the next repeater. Furthermore, the repeater
is effectively and simply timed from its own regenerated output. A brief
discussion of the theory of the circuit is presented along with measured re-
sults and oscillograms showing its performance. The effects of extraneous
interference on the production of errors in such a repeater are reported.
These results are in substayiiial agreement with theory.
1. INTRODUCTION
Long distance communication using digital transmission is not new
but was used by man in his earliest communication system. In fact, his
first successful electrical system, the telegraph, made use of binary
pulse codes. It was not until the invention of the telephone that the
emphasis was shifted from the digital to carrier and voice systems.
During recent years the development of new electronic devices and
techniques have brought digital transmission into the picture again,
and it now seems possible to use it not only for telephony but for tele-
vision as well. Future systems will probably make use of the binary
code, this choice being dictated by circuit simplicity and performance.
The fundamental requirement for perfect binary transmission is to
be able to detect the presence or absence of a pulse in each of a regular
set of discrete time intervals. From this requirement the principal ad-
vantages of such a system may be tabulated. First, a pulse can be
recognized in the presence of large amounts of interference. Second,
when a pulse is recognized it can be faithfully regenerated, suppressing
the effect of the interfering noise to any desired degree. Third, simple
high-efficiency non-linear devices such as multivibrators or blocking
oscillators can be used to regenerate the pulses. The great disadvantage,
1059
1060 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 195()
common to all pulse systems is the large bandwidth required for trans
mission.
On wire linos this large transmission band will create a number of
problems. The phase-loss ^'ariations, crosstalk and temperature effects
will be greatly increased over the transmission band as compared to that
of the more conventional systems. It can be shown however that if the
repeater spans are made sufficiently short these problems will largely
disappear. Only rough equalization will be needed, crosstalk and tem-
perature effects become negligible. Furthermore the repeater power
requirements will be small and the circuitry comparatively simple,
since only partial regeneration will be required. The problem remains
to build a regenerative repeater so simple that it will be economically
sound to use on short spans of line. The development of the transistor
with its small size and low power requirements has made such a repeater
feasible. |
1.1 Pulse Distortion Caused by Low Frequency Cutoff
Since the frequency spectrum of a binary pulse train will extend down
to and include dc, the ideal repeater should be able to handle the complete
frequency band to avoid signal distortion. This would preclude the use
of coupling transformers and condensers which attenuate the low fre-
quencies and remove the dc. Practical considerations however dictate
the use of these elements which means that the repeater will have a
low frequency cutoff. The distortion of a binary pulse train produced by
low frequency cutoff presents one of the most vexing problems the
designer of a regenerative repeater must cope with. It produces what is
probably the most potent source of intersymbol interference found in an
average binary pulse communication system. This interference consists
of a transient response whose effect may be appreciable far beyond the
end of the pulse itself.
When a train of ideal fiat top pulses with infinitely steep sides is applied
to a load through a condenser or a transformer, the transient response
persisting beyond the end of the pulse is an exponential and may be
expressed as
T = kPoe~'' (1)
The time t, is measured from the end of the pulse and the damping co-
efficient 6 is a function of the low frequency cutoff.* Po is the amplitude
* The value of b may be approximated by
b = 27r/o
\vhere/o is the frequent-y in cycles/sec at which the low fre(iuency loss characteris-
tic of the transformer is 6 db above that of the pass band.
TRANSISTOR BINARY PULSE REGENERATOR
1061
I of the pulse and k is given as
k = 1
-htr.
where fp is the pulse duration. The sum of the transients of a sequence
of pulses will shift the zero potential from the base of the pulse toward
its average value as shown on Fig. 1(b). This phenomenon has been re-
(aj
(b)
(cj
TRIGGER
THRESHOLD
TRIGGER
THRESHOLD
(d)
(e)
(d-b)
(f)
A
zx/\zx./x/\
A
r
L
r
L
L LL
r r r
L
r r r
L
TRIGGER
THRESHOLD i
(9)
(d-b + f)
7
x^
&
r\
\J
^
ta~P""a
M
n
n
a
n
oi
^
^
r\
r>
^^\
TIME
Fig. 1 — (a), a perfectly regenerated pulse train; (b) showing the effect of low-
frequency cutoff; (c), showing (a) after passing over equalized line; (d), showing
(b) after passing over equalized line; (e), effect of (d) minus (b); (f), inverted
pedestal timing wave; (g), composite wave at input to repeater, namely, (d) minus
(b)plus (f).
1062 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
ferred to as "zero wander." In a regenerative repeater the trigger poten-
tial is tied to the zero level by a constant bias. Zero wander then will
produce a changing bias which reduces the signal to noise margins of
the repeater, or in some cases even prevents regeneration. Suppose, for
example, a transmission line is equalized so the ideal pulse train shown
on Fig. 1(a) will appear as Fig. 1(c) after being transmitted over the
line. The individual pulses have widened until the envelope of a sequence
of consecutive pulses shows as a ripple with a much smaller amplitude
than the individual pulse. If the pulse train distorted by low frequency
cutoff shown on Fig. 1(b) is transmitted over this line its output will
appear similar to that shown on Fig. 1(d). The portion of the signal where
the peak amplitude Hes below the trigger threshold will not be regener-
ated.
1.2 Compensatio7i for Low-Frequency Distortion
In the past many circuits have been devised to prevent zero wander,
but none have been completely satisfactory. The repeater described in
this paper effectively eliminates zero wander in a string of consecutive
repeaters by means of a new and simple method. This may be better un-
derstood by referring to Fig. 2. Here are represented two successive re-
peaters of a transmission system. These repeaters have what appears as
a conventional negative feedback loop consisting of a pair of resistors, R.
The function performed by this feedback loop bears little if any resem-
blance to the negative feedback of linear amplifiers and is referred to as
"Quantized feedback" in this paper.*
Suppose an isolated pulse of amplitude P,„ is regenerated in repeater
M and is applied to the line through its output transformer. The low
freciuency cutoff" of this transformer will produce a transient response to
the regenerated pulse as given in (1). A spectrum analysis of the transient
tail shows that most of its energy occurs in the lower portion of the pass
band of the equalized line. Consequently, it will be transmitted over the
line to the next repeater with little if any frequency or phase distortion,
but will be attenuated by a factor a. This transient at the input of the
following repeater may be expressed as
Tm - akMPMe~'' (2)
where t is again measured from the end of the pulse. Suppose the re-
generation of the pulse at the output of repeater N is delayed by time ti
* A paper by Rajko Tomovich entitled "Quantized Feedback" was published
in the I.R.E. Transactions on Circuit Theory. There are some fundamental dilTer-
ences in the meaning of the term, quantized feedback, as used in these papers.
TRANSISTOR BINARY PULSE REGENERATOR
LINE
INPUT
K
Z>^
LINE
EQUALIZER
REGENERATIVE
REPEATER
M
R
AAAr
A^A^■
R
LINE
Da
R
AAA-
R
REGENERATIVE
REPEATER
N
SIGNAL
OUT ,
>c
1063
— I LINE
Fig. 2 — Block diagram of a section of equalized line and its terminating
regenerative repeaters.
compared to the pulse at the input of the repeater. The transient re-
sponse of the regenerated pulse after passing through its output trans-
former f will be
Tiv = fcivPive"'^'-'^^ (3)
7 T^ '''l ~~^^
KN^Ne e
(4)
If the transient (4) is attenuated by factor 3 and added in opposite phase
to Tm through the feedback loop at the input of the repeater, their sum is
T,r
BT.y = ak-MPMc''' - 8kNPNe"'e~'"
-bl.
bt\
= e-'Xak,,PM - Bk^Pj.e"'')
This can be made equal to zero if
akufPyi = Bk^PiijC
(5)
(0)
(7)
which is accomplished by adjusting the value of d which represents the
feedback attenuation introduced by resistances R. If the regenerated
t It is assumed that the electrical characteristics of the output transformers
of all the repeaters are identical. In this case the damping coefficients will be
identical for all the regenerated outputs.
1064 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
output pulses of .1/ and N are identical, then Pm = Fj^ and Icm = Id^
and eq. (6) becomes
Tm - QTs = e-^'huPMioc - 8e"') (8)
This expression can be made equal to zero if
8 = ae"^'' (9)
By this means zero wander produced in one repeater can be eliminated
at the input of the next repeater. The low frecjuency distortion of one
repeater corrects for the corresponding distortion produced in the pre-
vious repeater.
If the electrical characteristics of uU the repeater output transformers
are identical it is possible to completely remove the effects of the tran-
sient tails due to low frequency cutoff.* It is important however that t\
should not be so large that the feedback pulse occupies the next timing
interval. W. R. Bennett has shown that a similar cancellation of tran-
sients can be accomplished for more complicated types of low frequency
cutoff characteristics. In this case the transient tails ^^ ill be the sum of a
number of exponentials having different amplitudes and damping co-
efficients. Here the ciuantized feedback must be provided by multiple
loops, of greater complexity.
It may be disturbing at first to observe the resultant sum of the incom-
ing signal and feedback as shown on Fig. 1(e). It should be noted how-
ever that the signal is not changed in any way until the repeater has
triggered the regenerated pulse, and at the next time slot the tails have
been cancelled, so that when the next pulse arrives it too will begin at
the zero axis. Tails may also be produced by high fre(|uency phase-loss
characteristics. These however, may be removed by proper equalization.
1.3 Timing In a Regenerative Repeater
The binary regenerative repeater must not only regenerate the shape
and amplitude of each individual pulse but it must also keep them in
proper time seciuence with other signal pulses. To accomplish this a suit-
able timing wave must be provided. This timing wave may be trans-
mitted over separate pairs of wires or it may be derived from the signal.
In the past it has been connnon to obtain a sine wave of the repetition
* It can be shown that, with reasonable differences in damping coefficients,
quantized f(!edback will fjreatly reduce interyyml)()l interference even when con-
sidei'ing a single pulse. If the coiil ril)utions from all the transients of an infinite
train of random pulses are summed, the resvUt;int interference is further reduced
and can be considered negligible.
TRANSISTOR BINARY PULSE REGENERATOR 1065
I frequency by exciting a high Q filter circuit from the received pulse train.
[Short timing pips generated from this wave are used to time the regen-
erated output pulses precisely. This procedure is far too involved to be
used in a simple repeater. If less precision in timing is acceptable it may
be accomplished with a minimum of circuitry by use of a sinusoidal wave
derived from the repeater output. This is referred to in this paper as
"self timing."
Self timing prohibits the use of short timing pips derived from the
i-egenerator output. In this case most of the timing control would be
exercised by the filter circuit and little, if any, by the input signal. The
direct use of the sinusoidal output of this filter provides suflficient control
by the input signal with only a small penalty due to less precise timing.*
Self timing also sets certain requirements on the regenerator. If the tim-
ing wave is derived from an independent source it can be added to the
signal in such a way as to act as a pedestal, lifting the signal above the
tiigger level. In such a circuit neither the signal nor the timing wave
alone can trigger the regenerator. If the timing wave is derived from the
output it is obvious that the signal alone must be able to trigger the
regenerator, since the generation of a timing wave depends upon the sig-
nal triggering the regenerator. A timing wave derived by filtering the
output of a random pattern of binary pulses will also have a varying
amplitude which could cause variations in repeater noise margins. It is
apparent then that self timing output cannot be used as a pedestal in a
regenerator. All these objections can be overcome by the use of "inverted
pedestal" timing.
Inverted pedestal timing is produced by tying the peaks of the timing
wave having the same polarity as the signal pulses to a fixed level by
means of a diode. This is illustrated on Fig. 1(f). The timing wave is added
to the signal at the input so the sum of the signal, feedback and timing
looks somewhat like the wave on Fig. 1(g). The effect of the inverted
pedestal timing is to inhibit triggering except in the time interval near
the peaks of the timing wave. This permits the signal to trigger the re-
generator without a timing wave, yet allows timing control to be exer-
cised as the amplitude of the timing wave builds up. With sinusoidal
timing, noise often causes the regenerator to trigger either early or late,
introducing a phase shift in the regenerated ouput which will be reflected
in the timing wave. Since the timing wave is derived from the code pat-
tern by a relatively high Q tuned circuit, the phase distortion of the tim-
ing wave from a shift of a single pulse will be small. With a random dis-
* E. D. Sunde, Self-timing Regenerative Repeaters (paper being prepared for
publication).
106G THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
tribiition of noise the resultant phase shift of the timing wave will be
negligible. If the interference has low frequency components, the phase
shift of the timing wave may be appreciable but these are slow and con-
sequently will not seriously effect the performance of the regenerator.
2.0 DESCRIPTION OF REPEATER CIRCUIT
The circuit diagram shown on Fig. 3 will aid in understanding the op-
eration of the repeater. The incoming signal after being transmitted over
the equalized line is applied through the input transformer Ti to the
emitter of transistor (1). The function of this transistor is to provide gain
to the incoming signal. This amplified signal is applied to the emitter
of transistor (2) through the blocking condenser C2 . The second transis-
tor functions in a single shot blocking oscillator circuit being biased in the
"off" condition through the resistance i?2 . When the positive signal ex-
ceeds the trigger threshold, a pulse is regenerated by the blocking oscil-
lator. During the pulse period a large emitter current flows through Di
in the conducting direction. T^ is the output transformer while trans-
former T3 provides the essential positive feedback for the blocking oscilla-
tor.
L, R,
-'TW VW
N
BOOTSTRAP TIMING
TUNED TO 672 K.C
INPUT
QUANTIZED FEEDBACK
AAA-
Fig. 3 — Circuit diagram of the regenerative repeater.
TRANSISTOR BINARY PULSE REGENERATOR 10G7
2.1 Inhibiting in Blocking Oscillator
The secondary of Ts is connected between the transistor base and
ground with the diode D2 and resistor R^ in series across it. The combina-
tion of diode and resistance across T^ serves a very important function,
the inhibiting of multiple triggering on a single input pulse. During the
interval in which the pulse is regenerated a negative potential is applied
between the base and ground. A current h flows through the base of the
transistor, the diode Do being poled to restrict the flow of current in 7?3 .
At the end of the pulse the current h in T^ drops suddenly to a low value.
This current change in the inductive winding of T3 induces a relatively
large potential across the base of the blocking oscillator. The impedance
of D2 becomes low and current flows in Rz and T3 . The potential across T-s
decays exponentially and with proper circuit values will take the form of
a damped cosine wave.
E = Eoe~"' cos wo^ (10)
I where t is the time measured from the peak of the pulse. The values of
a and coo can be adjusted by varying the inductance the transformer and
the capacity and resistance connected across it. E should become sub-
stantially zero at or near the next timing interval. The damping coeffici-
ent a should be sufficiently large to prevent an appreciable negative ex-
cursion of E since this will reduce the effective bias on the repeater and
consecjuently its noise margins. This will be further discussed in the sec-
tion on the measurements of errors.
2.2 Quantized Feedback
The quantized feedback is provided by coupling the input and output
transformers by means of resistances R. The fed back pulse must be in
the opposite phase compared to the input signal.
2.3 Timing Wave Circuit
The timing wave is derived by means of the parallel resonant tank cir-
cuit L2C5 which is tuned to the signal repetition frecjuency. The regen-
erated pulses are applied to this network through the relatively large
resistance 7^4 . The amoimt of energy added to the network by each pulse
as well as the amount dissipated in it is a function of Q. The higher the Q
the smaller will be the variations of timing wave amplitude as the aver-
age pulse density of the signal train changes. This does not mean that
the highest Q will be the most desirable for increased Q means larger,
1068 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
more expensive coils. Higher Q's also produce greater variations in im-
pedance and phase with small changes of resonant frequency which re-
(luirc much closer control of inductance and capacity with temperature.
In the circuit described here the Q has a value of about 100 and its opera-
tion is quite satisfactory'. The tank circuit is coupled through the small
condenser Cz to the diode Dz . This diode ties the positive peaks of the
timing wave to ground as is reciuired for inverted pedestal timing. The
network N pro^'ides the timing delay needed for optimum repeater per-
formance.
2.4 DC Compensation in Timing Wave
The timing wave amplitude from the tank circuit is insufficient to allow
it to be applied directly to the emitter of the blocking oscillator. Conse-
quently in the interest of circuit simplicity the signal amplifier is used
for the timing wave as well. To avoid the complications introduced by
dc coupled circuits when close bias tolerances must be maintained, the
amplifier was coupled to the blocking oscillator by condenser C2 . This
presents a problem as to how to neutralize the charge the dc component
of the timing wave builds up on C2 . The means by which this is accom-
plished can be more easily understood by referring to Fig. 4.
In this figure the time constant of the feedback loop RoCiRi , is made
large so that substantially equal charges are added to Ci by each regen-
erated pulse. In the timing loop this is also nearly true even though noise
INPUT
T
yf
Cp
REGENERATIVE
REPEATER
R,
:C,
.^ A A _.
V V ^
X
X
c
T
Roy r^i
x''
OUTPUT
Fig. 4
QUANTIZED FEEDBACK
Method for maintaining the dc values of timing wave.
TRANSISTOR BINARY PULSE REGENERATOR 1069
may change the phase of indi^•idllal pulses. The change of amplitude of
the sinusoidal timing wave in one pulse period will be
AAr = Ar[l - e-''"^""] (11)
w here Q = wL/R and tm is the timing interval. In a similar manner the
\ariation of the amplitude of the voltage across Ci will be
AAc = AcW - e-'-'/^i^^] (12)
If now 7?i and Ci are adjusted until
TV 1
Q RiC,
(13)
and Ro varied initil the amplitude Ac is eriual to the a^•erage value of
At , the charge on the interstage coupling condenser should be effectively
neutralized at all times. Since both loops are made up of passive elements
with common inputs and outputs a single adjustment should suffice
even though the pulse amplitude, width, or signal pulse density may vary.
In the repeater circuit shown on Fig. 3 this neutralizing principle is
used but is more difficult to see. When a pulse is regenerated, a large
emitter current flows in Di , which produces a sharp negative voltage
spike. This voltage adds a charge to C2 which tends to neutralize the one
the timing wave adds to it. The time constant of C2 and its associated
circuit may be made to equal the decrement of the tank circuit and the
two amplitudes made equal by adjusting the level of the timing wave.
By this means effective dc transmission of the timing wave is achieved
through capacity coupling.
2.5 Line Equalization
The line equalizer is not essentially a part of the repeater itself. It is
however so intimately connected with the repeater it is logical that they
be considered together. One of the important ecjualizer requirements is
simplicity, another, that the impedance seen from the repeater input
shall be substantially constant over a relatively large frequency range.
This latter requirement comes from the need of transmitting the feed-
back pulse around the feedback loop to the emitter of the first transistor
without too much distortion. The equalizer is not used to equalize the
low frecjuency losses of transformers but only the frequency characteris-
tic of the line. The eciualization must be such that the individual pulses
are allowed to widen but not enough to cause inter-symbol interference.
1070 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
A gaiLssian shaped pulse at the output of the Hue is one of the most eco-
noniical to use and can have a maximum span of on(! timing interval at
its base. Howe^'er, in this case the envelope of a long consecutive se-
(juence of such pulses will show substantially no ripple. It can be readily
seen that in such a seciuence the onl}- timing control exercised by the
input upon the timing wnve comes from the first pulse. In the interest
of better timing and consecjuently better repeater performance one should
be content with narrower pulses at the repeater input. The resulting rip-
ple of the envelope of a consecutive pulse sequence allo^^"S each incoming
pulse some control over the repeater timing.
3.0 REPEATER PERFORMANCE
To check the performance of the regenerative repeaters a binary
code generator was built having a nominal pulse repetition rate of 672 kc
producing an eight digit code. Any code combination from the possible
256 can be selected or the code automatically changed at periodic inter-
vals reproducing all possible codes in orderly sequence. Random codes
may also be generated by making the absence or presence of a pulse
52
<rt 48
44
z
g
z
UJ
40?
< 36
32
0.56 MILES OF
EQUALIZED 32 GAUGE-,
CABLE USED IN TEST \
^— ^-n— n __Q_ I n I '■
10
..-cr
--?'
2.3 MILES OF
EQUALIZED
19 GAUGE CABLE.
20 40 60 80 100 200 400
FREQUENCY IN KILOCYCLES PER SECOND
600
1000
PULSE
CODE
GENERATOR
-EQUALIZERS ^^
(b)
Fig. 5(a) — Equalized characteristics of 19 and 32 gauge line.
Fig. 5(b) — Block diagram of equalizer for 32 gauge line.
TRANSISTOR BINARY PULSE REGENERATOR 1071
ill anj^ time slot dependent on the polarity of random noise. The output
(if the code generator was made substantially the same as the outputs
I »f the repeaters both in shape and amplitude. Two types of transmission
line were used, a line from a 51 pair 19 gauge exchange cable and a pair
from a 32 gauge experimental cable. The nominal lengths of cable be-
tween repeaters was 2.3 miles for the 19 gauge and 0.56 miles for the 32
nauge cable. Fig. 5(a) shows the equalized characteristics for both these
lines. The important differences between the two is a greater flat loss
w ith a better high frequency characteristic for the 32 gauge cable. This
was advantageous in the study of error production and consequently,
the error measurements were all made with this cable. The 19 gauge
characteristic represents about the maximum high frequency loss that
can be tolerated by these regenerative repeaters.
The performance of the regenerative repeater circuit can best be shown
by photographs taken from a cathode ray oscilloscope representation.
Plate I shows the effect of the 19 gauge line equalizer. The output pulse
(1) transmitted over the unequalized line has become very broad, ex-
tending over several timing intervals, which are indicated by small
pips along the trace. The addition of the equalizer reduces the width
of the received pulse (2) until it is somewhat narrower than the normal
pulse interval of the code. Plate II shows a series of photographs taken
of the input and output of a repeater with or without interference added
at the repeater input.* A signal code at the input of the repeater is
shown on (a) and its regenerated output on (b). A sinusoidal inter-
ference having a frequency of about 100-kc pictured on (c) is added to the
signal as represented on (d). The regenerated output of input (d) is
shown on (e) . From these it can be seen that while interference does not
change the pulse shape or size, it does produce a phase modulation.
Plate I — Single pulse at output of 2.3 miles of 19 gauge cable. 1 — Unequa-
lized. 2 — equalized.
* The input signal of this and some of the following photographs was taken
with the repeater in an inoperative condition. This was done in order to avoid the
resulting complexity that results when both the quantized feedback and timing
wave are added to the combinations of incoming signal and interference.
1072 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
(a)
AJ^
(0
(d)
rsa
(e)
Tl^
Plate II — (a), repeater input, no interference; (b), regenerated output with
input (a); (c), sinusoidal interference; (d), repeater input, signal (a) plus sinusoi-
dal interference (c); (e), regenerated output of (d).
3.1 Performance of Repeaters in Tandem
Plate III shows the results when certain phase modulated codes are
transmitted through a series of repeaters in tandem. The regenerated
signal from each successive repeater is transmitted over 2.3 miles of
equalized 19 gauge line. One code which has two out of a possible eight
pulses present has most of the phase jitter removed after passing through
the three additional repeaters. The other fixed code shown contains four
out of a possible eight pulses. The jitter is removed much more rapidlj^
with this code, after passing through two repeaters it is regenerated al-
most perfectly. The reason for the difference in the regeneration of the
two codes is variations in the amplitude of the timing wave. In any period
of time the energy delivered to the tank circuit is proportional to the
number of regenerated pulses in that interval. The amplitude of the
timing wave for a fixed code with two pulses of the eight will be half
the one produced by the code having four pulses out of eight present.
The average number of pulses in a normal PCM signal will be half the
maximum possible pulses. The timing wave should then average the
same as that produced by the fixed code having four out of a possible
eight pulses present. The phase jitter of the random code should be re-
moved as quickly as it was with this fixed code. This is confirmed by
TRANSISTOR BINARY PULSE REGENERATOR
1073
regenerating a noise-dictated random code having the same pulse
density expected of a normal PCM signal. The results are shown on
Plate III(c). After passing through two repeaters the jitter has been
substantially removed as shown by the sharp vertical lines marking the
pulses. The thickening of the horizontal lines are produced by transients
produced by low frequency cut off distortion. In all these photographs
the oscillograph synchronization was obtained from the code generator.
3.2 Possible Effects of Line Temperature Variations
The gain and phase characteristics of a particular wire transmission
line is a function not only of its length but of temperature as well. To
the first order approximation the effect of an increase in temperature
may be considered as caused by an increase in the length of the line.
In order to better understand the effect of temperature change on re-
peater performance the following steps were taken; The repeater was
adjusted for optimum performance with 2.3 miles of line between it and
the preceding repeater and then the length of the connecting transmis-
sion line was decreased by about 25 per cent. It was found that for the
same interference on the input of the repeater no difference in the
performance of the repeater was observed. Plate IV shows a fixed code
signal after it has traversed 2.3 miles of equalized cable. Superimposed
TWO-PULSE CODE
lb)
FOUR-PULSE CODE
(C)
RANDOM CODE
Plate III — (a), set code having 2 pulses out of possible 8; (b), set code having
4 pulses out of possible 8; (c), random code having an average of 4 pulses out of a
possible 8.1 (a and b), input signal plus interference; 2 (a and b), regenerated
output of 1; 3, expanded section of 2; 4, output of 2nd repeater; 5, output of 3rd
repeater; 6, output of 4th repeater. 1(c), input signal alone; 2(c), imput signal
plus interference.
1074 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
on this is the same signal after traversing a 1.75 mile length of line and
the same equalizer. Shortening the line results in the transmitted pulses
having higher peak amplitudes and narrower widths. Faulty high fre-
quency equalization of the shorter lengths produces the short tail
following the pulse. It is interesting to observe that the transient tail
due to the low frequency cut off has not changed appreciably as the
line was shortened. This is to be expected since it can be shown that
the energy of the low frequency cut off transient is concentrated in low
frequency end of the transmission spectrum. In this region changes in
the length of the line, or changes in the primary constants will result
in inconsequential changes in attenuation and phase as is shown on
Fig. 6. If the quantized feedback is adjusted for the worst condition,
i.e., the highest temperature likely to be encountered, it will not need
to be changed with lower temperatures.
4.0 ERROR PRODUCTION BY EXTRANEOUS INTERFERENCE
A knowledge of the performance of a regenerative repeater with
various types and amounts of interference added to the input signal is
important. Consequently a study of such errors produced in one of
these repeaters was undertaken. Two general types of extraneous inter-
ference was used in this study. The first is impulse noise, the type which
is produced by telephone dials, switches, lightning surges and crosstalk
from other pulse systems. The second is sinusoidal noise, the type which
come from power line or carrier crosstalk. This interference may affect
the regenerated output in a number of ways. It may produce a phase
shift or "jitter" in the output; cause a pulse to be omitted; or cause a
spurious pulse to be inserted in the signal code. The phase jitter will be
largely removed by timing regeneration in subsequent repeaters, but
omission and most insertion errors will be carried through the remaining
repeaters, causing distortion in the decoded signal.
Plate IV — Superimposed picture of the outputs of 2.3 and 1 .75 miles of 19 gauge
cable with identical injjuts.
TRANSISTOR BINARY PULSE REGENERATOR
1075
60
55
50
45
40
35
30
25
20
15
10
5
0
,
y
/
EQUALIZED 2.3 MILES
/
1
/
—
_!L.
^_ .»
V
>
1
EQUALIZER
= LUS
"-y
^
1.75 MILES CABLE
A
^^
\
2.3 MILES CNB
19 GAUGE CABLE
.^
^'
1
1
1
1
1
1
1
1
1
1
1
8 10 20 40 60 80 100 200
FREQUENCY IN KILOCYCLES PER SECOND
400 600 1000
Fig. 6 — Effect of changing the length of 19 gauge line with fixed equalization.
4.1 Description of Error Detecting and Counting Circuit
An error detecting and counting circuit was built to count insertion
and omission errors. This circuit (block diagram, Fig. 7) is a coincidence
detector in which each pulse or space of the repeater input signal is
compared to its corresponding regenerated output. As long as the two
sources are the same, i.e., having corresponding pulses or spaces, there
is no output from the detector. If the two differ the detector produces
an output pulse which may be caused to actuate the counting circuit.
The code generator as has already been described produces a number of
different types of signal codes.
The output of the code generator is transmitted over 0.56 miles of
equalized 32 gauge cable to the regenerative repeater under test. Inter-
ference is introduced at the repeater input when desired. A portion of
the code generator output is differentiated and passed over a delay
cable whose delay is substantially that of the section of 32 gauge line
over which the signal is transmitted. This delayed signal is regenerated
without error by the single shot blocking oscillator A, The width of the
blocking oscillator pulses are adjusted to be about half of the total
timing interval. The width of the pulses from the regenerative repeater
1076 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
are likewise widened to a corresponding width by blocking oscillator B.
Unfortunately a variable phase shift is introduced in the repeater output
by interference and by variations in the timing wave amplitude and
phase. This variable phase shift prevents perfect coincidence between
the outputs of blocking oscillators A and B. An example of phase "jitter"
caused by interference is shown on Plate V(a). To overcome this a
sharp sampling pip; as shown on the same plate, is provided to enable
the detection of the narrow region of coincidence between the two signals.
These pips are generated from the repeater timing wave, hence they
follow the timing wave phase variations. The regenerated signal pulses
also follow the timing wave phase. If the sampling pulse is positioned to
fall in the center of the regenerated pulses, it will tend to maintain that
position as the timing wave changes.
The gates require a signal pulse and sampling pip to be present
simultaneously before there can be an output. This output, then, will
have substantially the same shape and position as the sampling pip.
When a signal pulse is simultaneously applied to each gate the two
outputs can be made to cancel when added in opposite phase as is done
in Ti . If however there is a pulse on one gate and a blank on the other,
an output pulse will be produced. The polarity of this pulse will depend
upon which gate contains the signal pulse. Since the decade counter is
PULSE
CODE
GENERATOR
■w-v
DELAY
LINE
BLOCKING
OSCILLATOR
(A)
V\AP
AMPLIFIER
DIFFEREN-
TIATOR
iULJL
"and"
GATE
(A)
VvV MAI
SAMPLING
BLOCKING
OSCILLATOR
BLOCKING
OSCILLATOR
(B)
J] n.
"and"
GATE
(B)
OMISSION ERROR
OUTPUT TO CABLE
"AND NEXT REPEATER
11_L
TI
JLJ_
POLARITY
REVERSING
SWITCH
JL
BLOCKING
OSCILLATOR
(D)
JL
DECADE
COUNTER
Fig. 7 — Block diagram of error detecting circuit.
TRANSISTOR BINARY PULSE REGENERATOR
1077
(a)
(b)
Plate V — (a) with 1, repeater output; 2, jitter on output pulse; 3, sampling
pulse, (b) with 1, signal pulse at repeater input; 2, 672-kc timing pips; 3, interfer-
ence input.
triggered by pulses of one polarity, the reversing switch permits the
independent measuring of different types of errors. The counter used
in this study has 9 decades capable of counting and recording (10^ — 1)
errors at 10^ counts per second.
4.2 Discussion of Impulse Noise Generator
A study of the noise in cable pairs leading from a central office indicate
that impulse noise will cause much of the expected interference on pulse
systems. In order to simulate the effect of this type of interference, a
generator was built which produces uniformly shaped pulses over a wide
range of rates. The polarity of these pulses can be reversed and their
amplitude varied continuously from zero to a value exceeding the
peaks of the signal pulses. These impulses were introduced into the
center of a transmission cable through a high impedance. Plate V(b)
shows photographs comparing the impulse with a signal pulse. The
repetition rate for the impulse interference used in this investigation
was lOVsec, which is low compared to the nominal pulse repetition rate
of the signal (6.72 X lOVsec). With the relatively large separation be-
tween interfering impulses, there is no measurable interaction between
errors produced in the repeater. At the same time the impulse rate is
high enough to get an excellent statistical distribution in the 10 second
interval used in these measurements.
1078 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
4.3 Production of Impulse Errors — Nomenclature and Discussion
To expedite the discussion of impulse errors, the following system of
nomenclature is used. Any impulse having the same polarity as the
signal pulse is designated as "plus." Those having the opposite polarity
are "minus." Two types of errors are produced. First, a spurious pulse
may be added to the regenerated signal; this is called an "insertion"
error. Second, a signal pulse may be removed, which is called an "omis-
sion" error. A "plus insertion" error is a spurious pulse introduced bj^
an impulse having the same polarity as the signal. A "plus omission"
error on the other hand is pulse omitted because of a pulse of same
polarity as the signal. A "minus omission" error is a pulse omitted be-
cause of an impulse having a polarity opposite to that of the signal.
A positive pulse, if large enough, can produce a spurious pulse at
any instant of time not already occupied by a pulse. The only require-
ment for the production of such a pulse is that the sum of the impulse
and timing wave exceed the trigger level.* On the other hand, a nega-
tive impulse cannot produce a spurious pulse but can only cause a
signal pulse to be omitted. If a pulse is to be omitted the sum of its
amplitude, the timing wave and the impulse must not exceed the trigger
level. It would be expected that the number of plus insertion errors will
exceed the minus omission errors. This follows from the fact that a
spurious pulse may be produced at any point not already occupied by a
pulse. On the other hand if a signal pulse is to be omitted the negative
impulse must occur in the time interval occupied by the signal pulse.
A positive impulse is indirectly responsible for the positive omission
error. When a spurious pulse is produced a short interval of time ahead
of a signal pulse, the latter may be removed by the inhibiting reaction
of the spurious pulse. There is no apparent way in which a minus insertion
error can be produced. This is confirmed by the fact that no error of this
type was observed in this investigation. Thus we have three types of
errors produced: plus insertion, minus omission and plus omission.
4.4 Results of Impulse Interference Measurements
Preliminary measurements of errors as functions of impulse amplitude
were made using random code. These measured values, shown on Fig. 8
exhibit many of the expected characteristics. For example the insertion
errors are more numerous than the omission and the threshold of the
plus omission errors is considerably higher than those of the other two.
* The trigger level is normally considered to be the negative dc bias applied to
the emitter of the blocking oscillator. There are however other components of the
bias that will be discussed later.
TRANSISTOR BINARY PULSE REGENERATOR
1079
If)
/
UJ
X
0)
/
_1
J
fi
2 25
^
/
/
5
/ ^
/
PLUS
/o/
o
INSERTION/ /'
z
ERRORS/
/
/
/
fe20
A
/
/ /
a.
LU
m
5
Z)
/ ^
/ /
MINUS
/ /
OMISSION
z
f /
/
ERRORS,
s"
c/
^^ — ^"^
/
/
"
'""'^
o
/
^^^^
1—
/ /
y^
>
o
/ ^
/ /
•
1-
2 10
/ /
/ /
/ f
A'
f /
P
/ / /
/ / /
/ 1 /
A^'
•■^
UJ
Q-
1 1 /
r^
CALCULATED
X o A MEASURED
f)
1 1 /
/
<
tr ^
o
\ /
y 9^'
CE
7 /
PLUS
UJ
A
/ /
/
OMISSION
^.5.
, ^
/J
ERRORS
^x-^'-
'■^'
I ^ ^x^^'^
0
wr /
v „ X — "—^ "T"*'^
40 50 60 70 80 90 100
IMPULSE AMPLITUDE AS PER CENT OF SIGNAL AMPLITUDE
Fig. 8 — Repeater errors as a function of interference amplitude.
On the other hand there are some deviations from the simple theory of a
perfect regenerator such as the low common threshold value of the plus
insertion and minus omission errors. Some of the differences can be
attributed to the extremely sensitive method of measuring errors. Here
the maladjustments of timing tank circuit, quantized feedback ampli-
tude as well as other factors which cannot be readily detected by other
means are reflected as sources of error. However with care these errors
can be made small and the measured values should follow the theoretical
values reasonably well.
Most variations from theoretical values are due to changes in the
effective bias caused by intersymbol crosstalk. This can be demon-
strated by measurements made using set codes. In all these codes the
number of pulses equaled the number of blanks but combinations varied
from one to another. On Fig. 9 the omission errors are plotted for a
fixed impulse amplitude as a function of the nimiber of pulses which
1080 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
1-4
CODE; 1
CODE COMBINATIONS
' juiriji
2 jirL.._.._n_rL.._..
3 iirL.A..A.._..
- _rL..A..jL._n...
1 2 3 4 5 6
NUMBER OF PULSE - BLANI<, COMBINATIONS IN EACH CODE GROUP
Fig. 9 — Repeater errors as a function of pulse distribution in code.
are followed by a space in the particular code. The codes used for various
points on the abscissa are shown on the graph. The omission error curves
plotted in this manner are linear. These data demonstrate that the
presence of a pulse modifies the trigger level in the next timing interval.
This is largely due to the negative excursion of the damped cosine volt-
age from base to ground in the blocking oscillator. On Fig. 10(a) is
shown the circuit of the single shot blocking oscillator used in the
repeater. With no timing an incoming signal must overcome bias V dc
to trigger the repeater. The solid curve on Fig. 10(b) shows the dc bias
with the timing wave added at the blocking oscillator emitter. Fig. 10(c)
shows the base voltage when a pulse is produced in the first timing inter-
val. The pulse begins at U and ends at U . As previously mentioned the
sudden rise of the base and collector impedance coupled with the fall
of the current in the transformer windings, produces an inductive voltage
surge across transformer Tz at h . The decay of this voltage surge can
be controlled by the inductance of the transformer and the damping
resistor Rf, . This positive decay voltage across the base will inhibit the
blocking oscillator from triggering. It is essential that this decay be
adjusted so it will inhibit triggering until the following time slot. If
TRANSISTOR BINARY PULSE REGENERATOR
1081
the decay transient is a damped oscillation and the base voltage passes
through zero at the next normal triggering time, sufficient damping must
be provided so the negative excursion is negUgible. The dashed line
shows how the effective bias at the emitter is modified by this voltage
across the base.
Fig. 1 1 shows the measured values of plus insertion and minus omis-
sion errors for two set codes. These are plotted as functions of impulse
amplitude. The first code has alternate pulses and blanks while the
second consists of pairs of pulses separated by pairs of blanks. With
these two curves the error threshold values may be determined from
REPEATER
BLOCKING
OSCILLATOR
OUTPUT
NO. 2 PLUS
I INSERTION
I THRESHOLD
I
TIME
TIME
Fig. 10 — (a) Circuit diagram of blocking oscillator showing various compo-
nents of the effective bias, (b) The effective bias as a function of time, (c) Inhibit-
ing voltage Vb produced by a regenerated pulse.
1082 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
30
UJ
CODE
rL.Ji..Ji..Ji
nR....jin_._.
CALCULATED MEASURED
o X
45 50 55 60 65 70 75 80
IMPULSE AMPLITUDE AS PER CENT OF SIGNAL AMPLITUDE
Fig. 11 — Calculated and measured repeater errors for two set codes.
1 ST NEGATIVE
OMISSION
THRESHOLD ^
PULSE
HEIGHT
2 ND POSITIVE
INSERTION
THRESHOLD
= C=Vd
1ST POSITIVE
INSERTION
THRESHOLD
= b
Fig. 12 — Bias levels used in calculating repeater errors.
the points of discontinuity. Fig. 12 illustrates these various error thresh-
olds with reference to a signal pulse. Theoretical curves were plotted
using these values and the observed values of timing and signal aniph-
tudes as shown on Fig. 11. It can be seen that very good agreement exists
between the measured and computed values.
The separate lower thresholds for insertion and omission errors may
TRANSISTOR BINARY PULSE REGENERATOR
1083
be explained from Fig. 10(b). These are caused by the phase shift intro-
duced by the inhibiting voltage to the effective bias compared to that
of the timing wave. The omission thresholds are determined chiefly by
the maximum signal amplitude. On the other hand the insertion thresh-
olds are determined by the point of maximum trigger bias. There exists
then two separate threshold values for a timing interval which follows a
regenerated pulse. These values can be measured from points "a" and
"b" on Fig. 10(b).
4.5 Result of Sinusoidal Interference Measurements
On Fig. 13 are shown the errors produced by sinusoidal interference.
Here a 110-kc sine wave is added to the signal and the various types
10
1.0
a:
o
(£
UJ
to
I-
3
m
UJ
2
10"
li.
o
10"
OJ
u
a.
10"
10"
^^
TOTAL
errors yP^
<**
^
V"^
x''
/ /
/'
/
/
l/l
7
l/l
///omission
/// errors
1
1 1
HI
pi
1 '
1 1
'I
' 1
INSERTION ^
ERRORS ''
/
1
1
1
f
50 55 60 65 70 75 80
PEAK-TO-PEAK AMPLITUDE OF INTERFERENCE
X 100%
85
Fig. 13 -
interference
PEAK AMPLITUDE OF SIGNAL
Repeater errors as a function of interferences level for sinusoidal
1084 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
of errors counted. Random code was used in this case and the repeater
bias was adjusted to provide equal omission and insertion thresholds.
The threshold for this particular case occurred when the peak to peak
sinusoidal interference was 63 per cent of the signal amplitude. This is
lower than the theoretical maximum which with a constant bias centered
at the half amplitude point, would be 100 per cent of the peak to peak
signal amplitude. For the bias conditions illustrated on Fig. 12, this
percentage would be 86 per cent for the positive insertion threshold and
88 per cent for the minus omission. This becomes apparent when the
negative and positive excursions of the interfering sine wave are con-
sidered as minus and positive impulses respectively. The remaining loss
in the interference margins can easily be due to maladjustments of tim-
ing, quantized feedback or inhibiting.
When the frequency of the sinusoidal interference is varied, the
number of errors for a constant interference voltage at the blocking os-
cillator emitter does not change appreciably. However, the input trans-
former and condenser coupling introduce a substantial frequency charac-
teristic. This reduces considerably the errors caused by power line
crosstalk. One of the striking things about the sinusoidal interference
errors is the rate at which they increase above the threshold. For ex-
ample, a change of 1 per cent of the interference amplitude can triple
or quadruple the total number of errors.
5.0 SUMMARY
New techniques and devices now" make it possible to build practical
regenerative repeaters for use in digital transmission. Such a repeater
which is suitable for a 12-channel, 7-digit PCM system, is discussed.
Simple, inexpensive devices are used to eliminate the effects of distortion
due to low frequency cutoff and to provide self timing for the circuit.
Experimental evidence is presented which shows the repeater to func-
tion as expected.
ACKNOWLEDGEMENTS
I am deeply indebted to J. V. Scattaglia for his aid in tliis project and
to the pioneering work of A. J. Rack on quantized feedback which was
of great help in the development of this regenerative repeater. I also
wish to thank W. R. Bennett, C. B. Feldman and Gordon Raisbeck for
their aid and many valuable suggestions.
Transistor Pulse Regenerative
Amplifiers
By F. H. TENDICK, JR.
(Manuscript received April 5, 1956)
A pulse regenerative amplifier is a histate circuit which introduces gain
(ind pidse reshaping in a pulse transmission or digital data processing
system.. Frequently it is used also to retime the ptdses which constitute the
flow of information in such systems. The small size, r-eliahility , and low
power consumption of the transistor have led naturally to the use of the
transistor as the active element in the amplifier. It is the purpose of this
paper to describe some of the techniques that are pertinent to the design of
.synchronized regenerative amplifiers operating at a pulse repetition rate
of the order of one megacycle per second. An illustrative design of an amp-
lifier for use in a specific digital computer is presented.
1. INTRODUCTION
A basic building block of many modern digital data processing or
transmission systems is a pulse regenerative amplifier. The particular
high speed transistor regenerative amplifiers to be discussed in this
paper are intended for use in systems where the logic operations on the
digit pulses are performed by passive circuits and the amplifiers are
inserted at appropriate intervals to amplify, reshape, and retime the
pulses. The design of these amplifiers for any specified system involves
a knowledge of the environment of the amplifier in the system, a study
of possible functional circuits which are combined to form an amplifier
circuit, and the selection of a combination of these functional circuits
to achieve the desired amplifier performance. Although a study of the
functional circuits constitutes the major portion of this paper, the
design of an amplifier for a particular digital computfM' is presented to
illustrate the general design procedure.
One important way in which these amplifiers differ from many pulse
amplifiers is that they must function properly under adverse conditions.
That is, instead of merely expecting superior performance most of the
1085
1080 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
time under relatively special operating conditions, consistently good
performance is demanded at all times, even with wide variations of cir-
cuit parameters and operating conditions (as, for example, a twenty-to-
one variation in the required output current). Therefore, various circuit
possibilities will be examined from the standpoint of reliable per-
formance.
When the switching and mathematical operations of a digital data
processing system are accomplished by a network of passive logic cir-
cuits with amplifiers interspersed to overcome circuit losses,^- ^ the
environment of an amplifier is generally as indicated in Fig. 1. The
signal information that passes from one logic network to another is
represented in a code by a group of discrete pulses. Due to the nature
of this digital information, utmost reliability of each amplifier is an
important requirement that greatly influences the amplifier design.
Since the position of a pulse in time or place determines its significance
to the system, it is necessary that each pulse be identically amplified
and that noise or extraneous disturbances do not cause false output
pulses from an amplifier. The effect of an error or a failure in operation
is different for different systems and in a given system depends upon
the time or place of the failure. In some computers a single mistake will
invalidate an entire computation cycle, while a permanent failure of
even a single amplifier will cause complete system failure in almost any
digital machine. Experience with the type of amplifier under discussion
indicates that failure rates of less than a tenth of one percent per thou-
sand hours are attainable.
Jf
LOGIC
LOGIC
t!
LOGIC
DELAY
u
it
LOGIC
U
LOGIC
It
LOGIC
LOGIC
n
DELAY
Fig. 1 — Typical environment of an am])lifier.
TRANSISTOE PULSE REGENERATIVE A.MPLIFIERS
1081
This goal of reliable circuit operation can be realized if the amplifiers
have :
a. Simple circuitry with a minimum number of parts.
b. The ability to operate with wide variations of signal level.
c. Ample margins against crosstalk and noise.
d. Low sensitiveness to changes in component values.
e. Low power dissipation to realize long component life.
f . Sufficient gain margins with system variations.
Although these features are desirable in any circuit, they are often
subordinated in order to obtain special performance, usually at the ex-
pense of reliability. In the amplifiers under discussion these features rep-
resent the primary design goal.
As is so often true, some compromises usually must be made to obtain
a suitable balance of these features in a particular design. It is sometimes
possible to accept an increase in power consumption for other desired
performance. However, because of the large number of amplifiers em-
ployed, low power operation is desirable in order to reduce the physi-
cal size and weight of a system. In this paper considerable emphasis is
placed on efficient low power circuits which do not require critical com-
ponents.
A convenient way to study regenerative amplifiers is to consider an
amplifier as a small system. The following functional breakdown has-
been found useful:
a. Transistor properties.
b. Feedback circuits.
c. Input trigger circuits.
d. Output coupling circuits.
e. Synchronizing circuits.
The block diagram of an amplifier then might take the form shown in
TIMING
SIGNAL
INPUT
SYNCHRONIZING
CIRCUIT
FEEDBACK
CIRCUIT
' '
1
SIGNAL
INPUT
TRIGGER
CIRCUIT
TRANSISTOR
OUTPUT
CIRCUIT
OUTP
~
"*"
Fig. 2 — Regenerative amplifier block diagram.
1088 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
Fig. 2. In the following sections the relation between each of the above
functional features and amplifier performance is discussed, various circuit
configurations to achieve each function are investigated, and the inter-
actions between the functional circuits are examined. The design of any
particular ampUfier then consists of a suitable selection of a transistor
and functional circuits to achieve the desired amplifier performance.
2. TRANSISTOR PROPERTIES
In a regenerative amplifier the transistor operates as a switch with
power gain. The "on" and "off" state usually are characterized, re-
spectively, by high and low collector current levels, and changes of state
are initiated by applied control signals. The performance items of interest
are the power dissipation in the two states, the speed with which the
transistor changes state, the amount of power gain available, and the
attainable margins against false operation. The transistor parameters
related to these items, as discussed below, are listed in Table I with
typical values for several classes of transistors. Desirable and satisfactory
values have been indicated in italics.
The power dissipated in a transistor in the "off" state is proportional
to Ico , the collector current with the emitter open circuited, and to the
collector supply voltage. This is wasted power and, since the minimum
collector supply voltage usually is dictated by other considerations, a
low Ico current is desirable to reduce standby power. Point contact units
are relatively poor in this respect. In junction imits the 7,0 power is
almost negligible compared to other circuit standby power.
The power dissipated in a transistor in the "on" state is proportional
to the saturation voltage between the collector and the common terminal.
Table I — Transistor Switching Properties
Switching Features
Ico at Vc = lOv
Collector to emitter satura-
tion voltage at Ic = 10 ma.
fa cut-off
Base resistance
Collector capacitance at
Vo = lOV
Collector breakdown volt-
age
Punch through voltage
llmitter breakdown voltage
Ratio of alpha at le = 10 /xa
to alpha at lo = 1 ma . . .
Point Contact
Transistors
(Low Resistivity Ge)
1500 Ma
0.8 V
15 VIC
SO oJmis
0.5 UUF
40 V
no punch through
40 V
3
Junction Triode Transistors
Ge Grown
5 fxa
0.5 V
2 mc
500 ohms
10 UUF
100 V
100 V
5 V
0.8
Ge Alloy
5fxa
0.05 V
4 mc
100 ohms
20 UUF
35 V
35 V
35 V
0.8
Si Grown
0.01 iM
4 V
4 mc
500 ohms
10 UUF
100 V
100 V
1 V
0.6
TRANSISTOR PULSE REGENERATIVE AMPLIFIERS 1089
Again, this represents wasted power, but also important is the fact that
it places an upper limit on the output power available from the transistor.
Hence, it is desirable to have as low a saturation voltage as possible.
Alloy junction transistors are especially good in this respect.
The speed with which a transistor changes state is principally a func-
tion of the alpha cut-off frequency (which should be high), base re-
sistance, and collector capacitance (both of which should be low).*'*
Both the rise and fall times of the transistor response are greatly in-
fluenced by the associated circuitry; generally a blocking oscillator
circuit yields the fastest response.
The amount of effective power gain available from a regenerative
amplifier is influenced by two transistor properties. One property is the
breakdown voltage, which may be the collector to base breakdown volt-
age or the collector to emitter punch through voltage (whichever is
lower). This limits the output power by limiting the collector supply
voltage. The other factor is the variation of alpha with emitter current,
especially at low emitter currents. The minimum average emitter current
required to initiate self-sustaining positive feedback determines the
minimum input power. Point contact units are especially good in this
respect in that alpha may approach ten at emitter currents as low as
five microamperes. Junction units are poor since alpha generally de-
creases rapidly at emitter currents below one hundred microamperes.
Even though the attainable margins against false operation are largely
a matter of circuit design, two transistor properties occasionally become
important. In point contact units trouble with lock up in the "on" state
may occur due to internal base resistance. Although this property of base
resistance is exploited in negative resistance feedback circuits, it is un-
desirable in circuits where the feedback is obtained by external coupling.
In grown junction units the emitter to base reverse breakdown voltage
may limit the voltage margin against false triggering caused by noise or
crosstalk. Normally it is desirable to have a one or two volt margin.
From the above discussion it can be seen that no one type of transistor
is outstanding in all features. The choice of which unit to use in a specific
amplifier depends upon the repetition rate, gain, and power requirements
desired of the amplifier. Although the point contact type has the best
overall performance of the types shown in Table I, it is quite possible
that new types (such as PNIP or diffused triodes^^) and improved de-
signs of the present types will change the picture.
3. FEEDBACK CIRCUITS
The use of positive feedback in an amplifier results in high gain and
short rise time. If the input circuit is isolated from the feedback loop by
1090 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
a diode or large resistor, these effects are enhanced and the shape, dura-
tion, and ampHtude of the output signal become independent of the
input signal. These results are possible because once the circuit has been
triggered and the feedback loop gain is greater than unity, the response
proceeds independently of input conditions and is determined solely by
the transistor and circuit parameters.
By definition a regenerative amplifier must have positive feedback
sufficient to cause instability during the transition period between the
"off" and "on" states. When investigating various circuits, it is neces-
sary to eliminate circuits which are never unstable when a pulse is
applied to the input circuit. If the circuit is unstable under either of the
conditions shown in Fig. 3, sufficient instability is possible. However,
if the circuit is stable, linear, and either the small signal open circuit
voltage gain or the short circuit current gain is less than unity or nega-
tive at all frequencies, it is impossible to have instability. These latter
conditions for instability often can be easily checked by inspection with-
out tedious computation or experimentation.
This use of positive feedback requires that attention be given to its
control. To be useful, the amplifier must be stable in one state and at
least quasi-stable in the other state. The change from instability in the
transition period to stability in the end states is accomplished by a non-
linear change in the gain or impedance of some element in the feedback
loop. Usually the "off" state is made stable by causing the voltage and
current conditions in the input circuit to reverse bias the transistor in-
put. The "on" state may be made stable (or quasi-stable when there are
reactive coupling elements in the loop) in several ways. For example,
the transistor may be permitted to saturate when the desired pulse
voltage is reached; a "catching" diode may be used to clip the pulse
voltage at an appropriate level; or a current switch may be used to
FEEDBACK
TRANSISTOR
FEEDBACK
TRANSISTOR
Voc ef'v
iSC
(a) OPEN-CIRCUIT LOOP VOLTAGE (W SHORT-CIRCUIT LOOP CURRENT
Fig. 3 — A check for instability.
TRANSISTOR PULSE REGENERATIVE AMPLIFIERS 1091
introduce an impedance in the feedback loop at a predetermined current
level.
The degree of stability of the amplifier in the "on" state may be
thought of as the amount of power required to initiate the transition to
the "off" state. During the early portion of the output pulse duration
the degree of stability should be large, but near the end of the pulse
duration it should be relatively small to make turn-off easier. Also, the
degree of stability should not change over the range of output loading
expected for the amplifier and should be effected without excessive
wastage of pulse or supply power. These conditions are difficult to fulfill
when the range of output load current may be as large as 20 to 1 .
Three methods of obtaining positive feedback in transistor circuits
will now be considered: (a) negative resistance feedback; (b) capacitor
coupled feedback; and (c) transformer coupled feedback. Of these,
transformer coupled feedback appears to be the best for most applica-
tions. It will be assumed that the type of feedback under discussion is
the dominant or only type present; circuits employing more than one
feedback mechanism generally violate the premise of simple circuitry
and will not be discussed.
3.1 Negative Resistance Feedback
With the advent of point contact transistors a novel form of negative
resistance was offered to circuit designers for use in positive feedback
applications.^ This negative resistance property occurs when the current
gain of a transistor is greater than unity and the emitter and base small
signal currents are in phase.* At first sight this property appears to
lead to attractively simple regenerative amplifiers. However, as systems
become more complex and, consequently, amplifier requirements more
severe, the original simplicity often is lost due to the additional circuitry
required to control the negative resistance. An example, shown in Fig.
4, is similar to a regenerative amplifier described by J. H. Felker.^ The
functional circuits are indicated by dashed outlines.
This amplifier operates at a one megacycle pulse repetition rate with
one-half microsecond, three volt pulses. It is capable of driving from one
to six similar amplifiers. The output pulse rise time is 0.05 microsecond,
the average dc standby power is 33 milliwatts, only a few components
operate at as much as half of maximum ratings, and the supply voltage
marginsf are greater than ±15 per cent. Seven hundred of these ampli-
* Although point contact transistors are noted for this property, certain types
of junction transistors also exhibit it. For example, see Reference 7.
t Supply voltage margins, the amount by which the supply voltage may be
1092 THE BELL SYSTEM TECHNICAL JOUKXAL, SEPTEMBER 1950
fiers operated in a system for over 17,000 hours with a faihire rate of]
slightly less than 0.07 per cent per thousand hours.
These features, however, are obtained at the expense of relative com-]
plex circuitry. This negative resistance type of high speed regenerative
amplifier has the following inherent limitations.
1. The degree of stability in the "on" state depends critically on the
collector current. In the example a dummy load must be strapped in
when the amplifier drives less than four logic circuits.
2. A steering diode (D3) and a timing circuit diode (Dl) have critical
reverse recovery time^ specifications.*
3. The requirements on transistor parameters (primarily the dynamic
alpha versus emitter current and base resistance characteristics) are
relatively critical.
4. A relatively large amount of synchronizing power is required.
5. With transformer output coupling (as discussed in Section 5.1) a
large amount of the total standby power is absorbed by a circuit required
to protect the transistor in case the timing voltage fails (In the example
21 milliwatts, or 64 per cent of the standby power, is absorbed by R3.)
INPUT TRIGGER CIRCUIT
!+6V
FEEDBACK
CIRCUIT
TRANSISTOR
OUTPUTS
20V
PEAK-TO-PEAK
1 MC
SINE WAVE
SYNCHRONIZING
CIRCUIT
OUTPUT
COUPLING
CIRCUIT
DUMMY
LOAD
Fig. 4 — Negative resistance feedback amplifier.
varied without causing an operational failure, are an indication of the sensitivity
of the amplifier to changes in component values.
* At lower pulse repetition rates this property may not be critical.
TRANSISTOR PULSE REGENERATIVE AMPLIFIERS
1093
The use of an inductor, instead of a resistance, in the base lead does
not appear to mitigate the hmitations. *
3.2 Capacitor Coupled Feedback
A second method of obtaining positive feedback is by external coupling
through a capacitor or capacitor-resistor network. This method is sel-
dom used for the principal feedback for reasons to be mentioned. Oc-
casionally, in conjunction with some other type of feedback, it may be
used to provide additional feedback during the rise time of an amplifier.
Since the voltage and current gain of a capacitor can not exceed
unity, the open circuit voltage gain and the short circuit current gain of
the rest of the loop (Fig. 3) must be greater than unity for instability.
This criterion indicates that capacitor feedback is limited to point con-
tact, or other transistors with an alpha greater than unity, or to a junc-
tion transistor in the common emitter configuration.*
A circuit with capacitor feedback around a short-circuit stable point
contact transistor might take the form shown in Fig. 5. Although this
type of circuit has the merit of simplicity, it has the following limitations :
1. The initial feedback current is highly dependent upon the incre-
mental output load impedance. This may result in a failure to trigger
when the load approximates a short circuit, as in the case of diode gates
or a large stray capacitance.
2. The degree of stability in the ''on" state is critically dependent on
the load current and the collector supply voltage. Variations in either
may cause a foreshortened output pulse or require an excessive timing
signal current for turn-off.
FEEDBACK CIRCUIT
R
V, \AAr
TRIGGER CURRENT
FROM
INPUT CIRCUIT ■
INPUT TRIGGER
CIRCUIT
AAA-
c
SINE WAVE
TIMING
VOLTAGE
SYNCHRO-
NIZING
CIRCUIT
n:i
.^^^UTPU T ^
TRANSISTOR I
OUTPUT COUPLING
CIRCUIT
Fig. 5 — RC feedback amplifier.
An inverting transformer is necessary with the junction transistor.
1094; THE BELL SYSTEM TECHNICAL JOvJRNAL, SEPTEMBER 1956
3. The necessity of a feedback circuit time constant equal to or shorter
than the output pulse length results in a relatively low output power
efficiency.
Due to the above considerations, capacitor feedback appears to be the
least attractive type of feedback.
3.3 Transformer Coupled Feedback
A transformer appears to be the most convenient and versatile com-
ponent for feedback coupHng in a regenerative amplifier. The pertienent
features* of a transformer are:
1. Current or voltage gain (impedance matching.) This feature per-
mits full use of the power gain of the transistor, even if such gain be in
the form of voltage or current gain only.
2. Bias isolation between circuit parts and the possibility of supplying
dc voltage bias without the use of additional elements.
3. Phase inversion, if desired.
All of these featvu-es, conveniently combined in a transformer, provide
great design freedom to meet specified circuit objectives. Since positive
feedback is possible with any type of transistor (with power gain, of
course), the choices of transistor and connection are determined by other
circuit requirements.
The use of transformer coupled feedback yields the familiar blocking
oscillator circuit. An important feature of this circuit is the fast rise time
that is obtainable. Linvill and Mattson^ have shown that a junction -
transistor with an alpha cutoff frequency of two megacycles may exhibit
a rise time of 0.1 microsecond in an unloaded blocking oscillator with
collector to emitter coupling. Fig. 6 (a). It can be shown that the same
response may be expected with collector to base or base to emitter
coupling, provided that the transformer turns ratio is modified. Figs.
6 (b) and 6 (c) . When the circuit is providing useful output power into a
load, a slightly different turns ratio would be used for optimum rise ■
time, which may be appreciably slower than in the unloaded case. How-
ever, it should be noted that the foregoing gives no information about the
initial response of the circuit from the time that the input trigger is
applied until the output reaches ten per cent of its final value. In some
instances this initial time, which is a complicated function of the trans-
istor non-linearities, may be comparable to the output rise time.
In a blocking oscillator circuit with a fixed output load, the degree of
stability in the "on" state decreases with time. The reason is that the
* The operation of a transformer over the non-linear portion of its magnetiza-
tion characteristic is outside the scope of this paper.
TRANSISTOR PULSE REGENERATIVE AMPLIFIERS
109
O
voltage across the coupling transformer, which is approximately constant
during the pulse duration, causes an increasing magnetizing current to
be subtracted from the initial feedback. When the feedback current can
no longer support the required output current, the circuit turns off. In
a synchronized amplifier the value of the feedback transformer mutual
inductance may be specified to give the desired degree of stability at the
end of the predetermined pulse length. Thus, the least stable condition
occurs at the end of the pulse duration and is under the circuit designer's
control. At other times during the pulse duration the circuit is more
stable, which reduces the possibility of premature turn-off.
Other considerations, such as stability variations with output current,
power dissipation, and output voltage regulation, depend upon whether
the output load is in series or in shunt with the feedback loop. Therefore,
these considerations are discussed in connection with output coupling in
n+i: 1
(a) COMMON BASE
(b) COMMON EMMITER
n+1
(C) COMMON COLLECTOR
P + CVc
te
(d) ASSUMED TRANSISTOR
EQUIVALENT CIRCUIT
Lg = LEAKAGE INDUCTANCE OF TRANSFORMER
n = TURNS RATIO FOR COMMON EMMITER CONNECTION
CCq = LOW FREQUENCY VALUE OF COMMON BASE
SHORT CIRCUIT CURRENT GAIN
CVq = CUTOFF RADIAN FREQUENCY OF Ot
Fig. 6 — Transformer coupled blocking oscillator circuits.
109G THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
Section 5.2. For constant voltage, variable current loads, transformer
coupled feedback with the output load in series with the feedback loop
results in low power dissipation, relatively small degree of stability
variations versus output current variations, and non-critical com-
ponents. The possible limitations are that transformers generally are
more expensive than other passive components and are not as readily
available in a variety of stock values.
4. INPUT TRIGGER CIRCUITS
The primary function of the input trigger circuit is to initiate the tran-
sition from the "off" to the "on" state when there is an input signal. At
all other times the input circuit must provide a threshold or margin
against false triggering due to noise or spurious disturbances.
Although the input circuit must supply sufficient energy to establish
regeneration, it is unnecessary and undesirable that any additional energy
be supplied. To do so reduces the gain of the amplifier, since gain may be
defined as the ratio of the output power to the input power during one
cycle of operation. Because regeneration makes the input and output
power independent of each other, any reduction in input power results
in greater amplifier gain.
In an amplifier with external feedback coupling it is possible, but not
always practical, to have the input circuit trigger the transistor at the
collector, base, or emitter terminal. The collector terminal seldom is
selected because then the input circuit must supply energy to the output
load as well as to the transistor. Also, the base is usually not used (ex-
cept occasionally with negative resistance feedback) because extra com-
ponents are required to steer the triggering energy into the transistor
and it is diffiult to apply a timing signal.* However, the following dis-
cussion and the dc input characteristic of Fig. 7 (a) are equally valid for
triggering at the base or emitter terminal of junction or point contact
transistors which are short-circuit stable.
One of the simplest types of triggering circuits is shown in Fig. 7 (b).
The voltage and current increments assumed necessary to initiate regen-
eration are designated Vt and /, . Therefore, the required input signal
voltage Vs and current /« are :
Vs ^ V, + IJix (1)
^ Ri\ , Vt , Fi - V2
'■^'■['+m) + w. + '^^ '■■'^
* Also, for junction tninsistors, about twice as much energy is required to trig-
ger at the base as at the emitter.'
TRANSISTOR PULSE REGENERATIVE AMPLIFIERS
1097
The purpose of diode Di is to provide a low impedance current threshold,
the amount of current given by the last term of (2) . This type of thresh-
old is especially effective for preventing false operation from electro-
statically induced crosstalk. Also, it allows a faster rate of discharge of
stray capacity on the input terminal at the end of the input pulse period.
Although the circuit of Fig. 7 (b) is attractively simple, it is undesir-
ably sensitive to variations in signal voltage. An increase in the input
pulse voltage causes excessive triggering current and a decrease may
easily result in failure to trigger. Since the circuit must be designed to
operate reliably with the smallest expected input pulse, it is wasteful of
input power with the average amplitude of input pulse.
'1
h-it
A
f
^1
— V,
(a) TRANSISTOR INPUT CHARACTERISTIC
.Sr\ J,
±
D1
I
V,
R1
TRIGGER
CURRENT
R2
(b)
SIMPLE INPUT CIRCUIT
V^
,1^
V,
D2
R2
I+V3
'R3
It
TRIGGER
CURRENT
V
' r'l
A
1
^
s, T-
/
_j
V,
(C) ONE TERMINAL AND-TYPE INPUT CIRCUIT
Fig, 7 — Input trigger circuits.
1098 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
The single terminal AND-type circuit^ ■ ^° Fig. 7 (c) has the desirable
characteristics of the previous circuit, and is relatively insensitive to
input signal variations. In this circuit the input pulse switches the cur-
rent through R3 into the transistor input and then encounters the rela-
tively high resistance R2, as compared to the parallel resistance of R2
and El in Fig. 7 (b). The blocking action of D2 thus reduces variations in
the input signal current. However, R2, R3, F3 and V2 cannot be increased
without limit to reduce the variations; the dc power dissipated in R2
and R3 would become excessive.
Another advantage of the AND-type circuit is that several inputs may
be paralleled with a common R3 to provide an AND logic function as
well as an input trigger function. This feature, when desired, saves com-
ponents and does not reduce the gain of the amplifier.
When both the input circuit and the feedback circuit terminate at the
same transistor input terminal, as is usually the case, some additional
components are generally required to prevent one circuit from shunting
the other circuit. To steer the trigger current into the transistor, a diode
may be placed in the feedback path so that the diode is reverse biased
except when there is feedback current. Similarly, a diode or a resistor
may be placed in the input circuit so as to prevent the feedback current
from flowing into the input circuit.*
Although the discussion has assumed positive polarity input pulses,
the remarks apply equally well to negative pulses if the polarity of the
diodes and the supply voltages are reversed.
It is recognized that the preceding remarks assume that the minimum
triggering energy is known and that a step function of current or voltage
is the optimum form of the triggering energy. Actually, until a study is
made of the circuit and transistor parameters (including the non-linear
aspects) that affect the initial triggering before the feedback is estab-
lished, the design of an optimum input trigger circuit will remain an
experimental art. Experience with the AND-type input circuit has indi-
cated that appreciably more current is required to trigger junction luiits
than point contact units.
5. OUTPUT COUPLING CIRCUITS
In addition to the obvious function of efficient power transfer from
the amplifier to a load, the output coupling circuit is a convenient point
at which to perform other functions, as for example, dc level restoration
i
* This precaution is not necessary if the transistor input exhibits appreciablr
negative resistance.
TRANSISTOR PULSE REGENERATIVE AMPLIFIERS
1099
[and pulse inversion. In a system of logic circuits interspersed with ampli-
fiers at regular intervals, it is apparent that the dc level at similar points,
such as the outputs of the amplifiers, must be identical if the amplifiers
are to be interchangeable. Without some circuit or element to restore the
dc level, the levels along the transmission path will monotonically de-
crease* due to the dc voltage loss through the logic circuits and across
the transistor in the amplifier. The output circuit is one point where
restoration of the dc level may be readily combined with other functions.!
In the following two sections three methods of output coupling are
discussed and the interaction between the output and feedback circuits
is considered.
5.1 Output Coupling Elements
Three types of coupling circuits are RC, transformer, and diode cou-
pling. Each of these methods permits the dc level of the signal pulses to be
corrected to a predetermined level. However, the restoration,! efl&ciency,
and versatility characteristics of each circuit are quite different.
Although RC coupling is common in linear amplifiers, it is seldom used
in transistor pulse amplifiers that operate at duty cycles near 50 per
cent. The reason is that the time constants encountered do not permit
both proper restoration of the capacitor and high efficiency of the output
circuit. As indicated in Fig. 8 (a), the transistor is a low impedance in
TRANSISTOR
TRANSISTOR
ON
R1 yOFF
(SMALL)
".RS
-—\
I
>(LARGE)
■R3
(a) RC COUPLING
(b)
TRANSFORMER COUPLING
Fig. 8 — Reactive output coupling circuits.
* Decrease for positive pulses; increase for negative pulses.
t An exception, to be discussed, is diode output coupling where it is occasionally
more convenient to correct the dc level in the input of the logic circuits or the
amplifier.
t This refers to restoration of a reactive element (i.e., the return to a quiescent
state) and is not to be confused with restoration of the dc level of a circuit.
llOO THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
the "on" state and a high impedance in the "off" state. Since C must be
relatively large to make the voltage drop across it small during the pulse
duration, R3 must be equal to or smaller than Rl for satisfactory restora-
tion (50% duty cycle assumed). But then the current transmission
efficiency of the coupling network is less than 50 per cent because gener-
ally Rl is smaller than the input resistance of the driven circuits during
the pulse duration. Unless the pulse length is only a small fraction of the
pulse repetition period, it is seldom possible to effect a suitable compro-
mise. Also, it might be noted that variations of Ico current, which flows
through R3, cause variations in the output pulse amplitude. Finally it
is not possible to obtain pulse inversion.
A transformer coupled circuit. Fig. 8 (b), works efficiently with a
transistor. Diode D2 isolates the transformer from the load and inter-
lead stray capacitance during the interdigit period* so that the restora-
tion time of the transformer is controlled by the value of R3. The restora-
tion time is approximately proportional to the mutual inductance divided
by the total shunting resistance. Diode Dl prevents R3 from shunting
down the output during the pulse duration, thus permitting high output
efficiency and proper restoration. f
As noted in Section 2, the maximum output power from the transistor
is determined by the maximum collector voltage (as set by breakdown
or punch-through) and the maximum collector current consistent with
the permissible dissipation in the transistor. Usually this maximum
voltage exceeds the desired amplifier output voltage and, occasionally,
the maximum collector current is insufficient; in such instances a voltage
step down is desirable. When the transistor is not required to operate at
maximum power dissipation, it often is advantageous to balance the
"off" and "on" power dissipation. An increase in the collector supply
voltage increases the "off" power and decreases the "on" power (by
decreasing the required collector current for the same output power).
Thus the collector voltage may be adjusted to give the lowest total power
dissipation consistent with the average duty cycle of the amplifier. The
transformer turns ratio is specified to match the optimum collector
voltage to the desired output voltage. Furthermore, Ico variations have
negligible effect on the output voltage amplitude and pulse inversion (if
desired, for example, for inhibition) is possible. For these reasons trans-
former coupling appears to give optimimi output coupling performance.
* The minimum time interval between the end of one pulse and the beginning
of a succeeding pulse; for a 50 per cent duty cycle the interdigit period is equal to
the pulse duration.
t Occasionally it is possible to specify the collector impedance, the transformer
losses, and the reverse impedance of D2 so that Dl and R3 are not necessary.
TRANSISTOR PULSE REGENERATIVE AMPLIFIERS
1101
A third method of couphng, which is attractive for systems using only
AND- and OR -type logic, utilizes the reverse characteristic of a break-
down diode, Fig. 9 (a). The interesting feature of this diode is the sharp
transition between the high and low incremental resistance regions of the
reverse characteristic. With this diode it is possible to shift dc levels by
an amount ec^ual to the rcA^erse breakdown voltage of the diode, as indi-
cated in Fig. 9 (b). In the ciuiescent state D2 operates in the breakdown
region and Dl serves to clamp the collector voltage at — F3 ; during the
pulse duration D2 operates in the high resistance portion of its reverse
characteristic. If the driven circuit has a ^'oltage threshold, like the
transistor threshold in Fig. 7 (a), less than — F^ + Vb + Vs and Vs
<|Fb|, the circuit operates like a normal AND-type circuit except for
the dc level change. For this reason it is convenient with AND-OR logic
circuits to include only Dl and R2 in the output circuit of the amplifier
and use D2 and Rl as the AXD input elements in the logic circuits.
The principal advantages of diode coupling are simplicity and the
lack of an energy storage element. The limitations are that there is no
opportunity to match transistor and output conditions, variations in
-V
♦--BREAKDOWN REGION -*•
' +v-
RRFAKDOWN ^|
VOLTAGE 3W
Vb I
1 ;
'
(a) BREAKDOWN DIODE
V-I CHARACTERISTIC
-V.
If^
Dl
BREAKDOWN
DIODE N
I
W
l+v,
R1
-V3)
OUTPUT
D2
(-V3 + VB)
R2
-V3 -V2
(b) COUPLING CIRCUIT UTILIZING
A BREAKDOWN DIODE
Fig. 9 — Direct output coupling circuit.
1102 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
diode breakdown voltage reduce amplifier margins, and pulse inversion
is not possible. For these reasons diode coupling has limited utility, but
is attractive for some applications.
5.2 Connection of Output and Feedback Circuits
The performance of the amplifier is greatly affected by the method used
to connect the output circuit and the feedback circuit together at the |
output of the transistor. Should these two circuits be connected in a
shunt or a series fashion? Performance features, such as rise time, suf-
ficient output voltage, degree of stabihty versus load current variations,
and power dissipation directly depend upon this choice. With transformer
output coupling, the choice always exists; with other types of output
coupling the choice may or may not exist, depending upon the type of
feedback coupling. The following discussion is in terms of transformer
coupled output and feedback circuits and the general conclusions may
be extended to other cases.
Y\ . t--
OUTPUT OF
AMPLIFIER
_!_
■
LOGIC CIRCUIT
.
Vs
1
NUMBER 1
,
i '^
LOGIC CIRCUIT
Vs
NUMBER n
(a) CONNECTION OF AMPLIFIER LOAD
■nl.
I
T
(b) V-I CHARACTERISTIC OF AMPLIFIER LOAD
Fig. 10 — Output load characteristic.
TRANSISTOR PULSE REGENERATIVE AMPLIFIERS
1103
The principal factor that influences the choice of the output-feedback
connection is the nature of the output load of the ampHfier. In the
majority of computer and switching systems the ampUfier must drive a
multiplicity of paralleled load circuits, as indicated in Fig. 10 (a). The
input characteristic of each load circuit is assumed to be of the threshold
type, like the AND-type input characteristic of Fig. 7 (c), which results
in the amplifier load characteristic of Fig. 10 (b). During the initial por-
tion of the rise time of the output pulse the incremental impedance
is almost zero and during the remainder of the pulse duration it is rela-
tively large. Due to the voltage threshold nature of the load, the ampli-
fier load variations are current variations at a constant voltage. The
minimum current is encountered in the system position where the ampli-
fier drives the smallest number of logic circuits, often a single logic cir-
cuit; the maximum current is hmited by the maximum output power of
the amplifier. Although a desirable ratio of maximum to minimum cur-
rent may be as high as 20 : 1 , the amplifier is expected to exhibit optimum
performance at any load current within this range.
The shunt connection of the output and feedback circuits is illus-
trated in Fig. 11.12 Windings l:wi constitute the feedback couphng and
1 : Hi the output coupling. The two circuits shunt each other in the sense
that the ratio of the feedback to the output current is determined by the
ratio of the impedance of these circuits as modified by the turns ratio
of the transformer.
INPUT TRIGGER CIRCUIT
-TL
OUTPUT
SINE WAVE
TIMING VOLTAGE
SYNCHRONIZING CIRCUIT
OUTPUT
COUPLING CIRCUIT
Fig. 11 — Shunt connection of output and feedback.
1104 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
There are two limitations associated with this output-feedback con-
nection. In the first place there is the possibility of insufficient output
voltage, slow rise time, or complete faihu'e of regeneration. This is
caused b}' the shunt effect of the output load which places an almost zero
initial incremental impedance across the feedback path. In order to
overcome this limitation a current switch (R5 and DO in Fig. 11) is used
to obtain a low initial feedback impedance and the output diode (D4)
is reverse biased so that the initial load impedance is large. The price
paid is the undesirable power dissipation in the current switch. ]\Iore-
over, stray capacity across the output terminal or a load current that
exceeds the design value may still result in a long rise time, low output
voltage, or regeneration failure.
The series connection of the output and feedback circuits is shown in
Fig. 12. In this connection the output load is in series with the feedback
loop. Thus, the transistor output current, feedback current, and output
load current are all proportional to each other. This situation assures
regeneration regardless of output load current variations.
The regeneration cycle of the series type amplifier is as follows. In
the quiescent state diode D2 is reverse biased by VI to prevent false
triggering. After the arrival of an input signal, the timing signal voltage
goes positive and steers the trigger current into the transistor. Xo
TRIGGER
CURRENT
R1
INPUT TRIGGER
CIRCUIT
FEEDBACK CIRCUIT
D2
1^
Dt
TIMING
SIGNAL
SYNCHRONIZING
CIRCUIT
Lp
TRANSISTOR
D6
I
I
I
I
V4
»l t
_rL
OUTPUT
I I OUTPUT COUPLING
Fig. 12 — Series connection of output and feedback.
TRANSISTOR PULSE REGENERATIVE AMPLIFIERS 1105
appreciable output current flows until the voltage across transformer Tl
is sufficient to forward bias diode D2. Then both the feedback and output
current build up simultaneously and rapidly since the turns ratio l:ni
of Tl is selected to give a feedback loop gain greater than unity. When
the sum of the voltages across the primaries of the feedback and output
transformers almost equals the collector supply voltage, the transistor
saturates and stabilizes the feedback loop. At the end of the pulse dura-
tion the timing signal voltage goes negative and robs current from the
feedback loop, thus forcing the transistor out of saturation and causing
the amphfier to turn off.
Because the feedback current is proportional to the output current
during the rise time, the amplifier can deliver any value of load current
up to the current corresponding to the maximum allowable collector
current. Also, assuming that the leakage inductances of the transformers
are small, a large stray capacitance across the output terminal does not
appreciably degrade the rise time. Since a current switch is not neces-
sary, the standby power dissipation in the feedback loop is negligible.
These are the outstanding features of the series connection.
Two important performance considerations of the series type amplifier
are the change in the degree of stability versus load current variations
and the action of the amplifier when the timing signal fails. Both of these
items may be controlled by the selection of suitable values for the turns
ratio and the primary inductance of the feedback and output transform-
ers.* In order to prevent burnout of the transistor in the event that the
timing signal fails, the amount of excess feedback current must decrease
during the pulse duration. Due to the low impedance of the feedback
loop, this condition may be approximately f stated in terms of the pri-
mary inductances as:
Vi
niLi
>
a
(3)
where Vsat is the collector saturation voltage and Li and L2 are the
primary inductances of Ti and T2 respectively.
The degree of stability in the series amplifier at the end of the pulse
duration is proportional to the output load current. This situation may
be seen more clearly if a "catching" diode (D6 in Fig. 12) is added to the
* If the transistor is not short circuit stable, it is also usually necessary to
use a small resistance in series with the emitter.
t The principal approximation is that alpha is constant versus collector current.
The value of alpha at the end of the pulse duration is a conservative value.
1106 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
circuit to prevent saturation in the transistor,* Because the feedback
loop gain, as determined by the alpha of the transistor and the turns
ratio 111 , must be greater than unity for regeneration reasons, there will
be current flow through D6 during the pulse duration. This current is
proportional to the degree of stability. An increase Aiout in the output
current causes an increase of
Az, = ^^^^'-^ (1)
in the collector current. Therefore, the current in D6 increases by an
amount equal to
AZdb =
^-1
\_ni
riiAiont (5)
This variation in the degree of stability may be reduced by selecting
a/rii close to unity and reducing no . However, since it is desirable to
have a/rii much larger than unity for short rise time and since any reduc-
tion in n2 increases the Ico standby power, f a compromise is necessary.
6. SYNCHRONIZING CIRCUITS
The majority of modern digital data processing systems employ coin-
cidence gate circuits to perform the logical functions. In order to insure
that digit pulses will coincide at the inputs to the logic circuits, it is con-
venient to synchronize the amplifiers. Usually a master oscillator, or
"clock," produces the timing signals that are distributed to the ampli-
fiers. The function of the synchronizing circuit in the amplifier is to turn
on and to turn off the amplifier at predetermined time intervals in re-
sponse to the clock signal.
In a regenerative amplifier there is always a small delay from the time
triggering commences until the full output pulse is developed. Then
there are variations in the transmission time to other amplifiers. For
these reasons the clock signal must lag the input signal to the amplifier
in order to maintain control of turn-on and to obtain a uniform pulse
length from all amplifiers. Generally the time lag is one-fourth of the
* In an actual amplifier D6 is not required if the transistor saturation voltage
is relatively constant versus collector current and the pulse fall time is not ad-
versely affected by minority carrier storage in the transistor. Often the inductive
"kick" of the transformers and the regenerative feedback are sufficient to make
the minority carrier storage effect negligible. If D6 is used, its reverse recovery
time may adversely affect the pulse fall time, thus nullifying its usefulness.
t The Ico standby power is proportional to V2 , which, for a given output volt-
age, is inversely proportional to no .
TRANSISTOR PULSE REGENERATIVE AMPLIFIERS 1107
repetition period and, in such a case, the clock signal is made available
in four phases.
Although the clock signal may have any one of a number of forms, a
sine or a square wave are the most common forms. Usually a sine wave
is preferred because it is simpler to distribute to a large number of
amplifiers. Exceptions occur in cases where exceptionally precise timing
is necessary, or the use of a square wave requires considerably less clock
power. In the following discussion of where to synchronize, a square wave
will do as well or better than the assumed sine wave. With either signal
it is desirable to keep the clock power to a minimum.
If the synchronizing circuit is to be effective, the clock signal must be
capable of accomplishing the following actions:
a. It must be able to hold the transistor in the "off" state in the pres-
ence of trigger current in order to control turn-on.
b. At the turn-on time it must rapidly inject the trigger current into
the transistor.
c. At the turn-off time it must alter the conditions in the feedback
loop in such a manner that the transistor turns off promptly.
In other words the synchronizing circuit must act like an inhibit logic
circuit with the clock signal appearing as the inhibit signal during the
interdigital period.
It is recognized that there are many amplifier configurations and
several ways to synchronize each configuration. Generally it is preferable
to synchronize at only one input terminal of the transistor or at only one
point in the feedback circuit. A relatively complete discussion can be
given with the aid of the following four examples.
A circuit that employs negative resistance feedback, such as in Fig. 4,
requires a relatively large amount of clock power for synchronization.
Because a capacitor (C2) is required on the emitter foi regeneration, ^
the clock signal must be applied to the base of the transistor to control
turn-on accurately. As far as turn-off is concerned, another clock signal
might be applied to the emitter or to the current gate in the feedback
circuit. However, this would result in additional components, a second
clock signal 180° out of phase with the base clock signal, and approxi-
mately the same required clock power as if the base clock signal alone
were used. Turn-off at the emitter is impractical due to the negative re-
sistance characteristic. The power that the clock signal on the base must
furnish is made up of two parts. One part is the average standby power
that is absorbed every time the clock voltage is positive. It is composed
of the Ico power supplied to the transistor plus the power dissipated in
in Rl and R2. R2 and D2 serve to reduce the clock current in Rl and
1108 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
R2, but the maximum value of R2 is limited by stray capacitance from
the transistor base to ground.* The average clock standby power for
this circuit (with a 10 volt peak clock voltage) is approximately 13 milli-
watts. The second part of the clock power occurs at turn-off when the
clock must supply approximately the full "on" state collector current.
In this design the clock supplies about 20 milliamperes of current for 0.1
microsecond at voltages up to about 6 volts peak before the transistor
turns off. Therefore, a negative resistance feedback circuit usually re-
quires a relatively large amount of standby clock power continuously
and a high peak clock power at turn-off. Also it should be noted that
diode Dl must have a short reverse recovery time in order to prevent
false triggering during the negative portion of the clock cycle.
A second example of synchronization is shown in Fig. 11. Here the
clock signal is introduced in the feedback circuit to control turn-off. It
is also applied to R2 in the input circuit so as to control turn-on. In this
circuit most of the clock power is dissipated in R5 and R6 when the clock
voltage is positive during the output pulse time slot (whether or not an
output pulse is produced). Necessarily, this power is relatively large be-
cause the clock must supply the full amount of feedback current. Also,
it is necessary to clip the positive peak of the clock voltage in order to
prevent false triggering via R2 when there is no input pulse. A square
wave clock signal would eliminate the need for R6 and D7, but would
not change the power in R5. The average clock power in a typical circuit
of this type is approximately 20 milliwatts, which is relatively large. The
principal advantage of this method is that diode reverse recovery time
is not a problem.
A third method of synchronization is to apply a square wave clock
signal (a sine wave is not suitable in this case) between the base of the
transistor and ground (for example, assume in Fig. 11 that R2 and
R5 are returned directly to V6 and that the base of the transistor is
the clock terminal instead of ground). Before turn-on the clock voltage
must be more positive than the trigger voltage on the emitter. At turn-
on the clock voltage drops rapidly to ground potential and triggering
takes place. During the pulse duration the base current of the transistor
is supplied by the clock source. At turn-off the clock voltage must rise
rapidly several volts until D6 conducts and robs current from the feed-
back loop. The clock power required by this method is relatively large
(order of 20 milliwatts) for point contact transistors because the base
current of such units is large. In a junction transistor with alpha close
* The capacitance causes the base voltage to lag the clock voltage at turn-on
if R2 is large, which degrades the timing.
TRANSISTOR PULSE REGENERATIVE AMPLIFIERS 1109
to unity the base current is small and the required clock power may be
as low as 3 milliwatts. However, it should be noted that this method of
synchronization applies only to amplifiers with a gated feedback circuit
(such as R5 and D6 in Fig. 11). In other circuits (Fig. 12, for example),
a clock voltage applied to the base terminal of the transistor may never
be able to turn off the transistor (the feedback current may actually
increase instead of decrease). Thus, this method of synchronization is
limited and is a low power method only when used with junction tran-
sistors.
A fourth synchronization method, which avoids the limitations cited
in the previous examples, is illustrated in Fig. 12. The timing circuit
is simply diode Dl. The operation of the circuit, which is like an inhibit
logic circuit, is as follows. When trigger current commences, the clock
voltage is negative and Dl conducts the trigger current away from the
emitter terminal. As the clock voltage rises positiveward, the emitter
voltage follows until it reaches the threshold voltage of the transistor,
usually ground potential. Then the trigger current flows into the tran-
sistor which turns on. As the clock voltage continues positiveward the
emitter conduction clamps the emitter voltage so that Dl opens and the
clock does not shunt the feedback path during the pulse duration. At the
end of the pulse duration the clock voltage goes negativeward through
ground potential and Dl becomes conducting. This action robs current
from the feedback loop, thus causing the transistor to turn off. If no
input pulse is present, Dl is always non-conducting and any small re-
verse leakage current is drained off through El (which is returned to
voltage VI).
Because diode Dl is always non-conducting when no input pulse is
present, the standby clock power is essentially zero. During a pulsing
cycle the clock conducts only a small current before turn-on and only
instantaneously at a low voltage at turn-off. Hence, the required clock
power is usually less than two milliwatts.
It is important to note that the amplitude of the negative peak of the
clock voltage usually should not be more negative than the quiescent
bias voltage on the emitter. If it should be, Dl will conduct and, due to
minority carrier storage, may cause false triggering when the clock volt-
age goes positive. The current through Dl at turn-off might have the
same effect in the succeeding cycle except that the flyback voltage of
the transformers during the interdigit period removes the minority car-
riers from both Dl and D2. Since D2 carries a larger current for a longer
period than Dl, the carriers are cleared from Dl first. It is then reverse-
biased for almost one-half the repetition period before there is any chance
1110 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
of false triggering. Hence, diode reverse recovery time is not a problem.
However, Dl should have a short forward recovery time in order that :
turn-off will occur rapidly.
One possible limitation of this synchronization method is that a low
impedance clock source is necessary. This is usually not difficult to ob-
tain with a resonant circuit in the output of the clock signal source.
Offsetting this point are the advantages of low clock power, esentially
zero standby clock power, only one additional component, and no criti-
cal component tolerances.
7. ILLUSTRATIVE DESIGN
In the preceding sections the features of various configurations for
the functional circuits of an amplifier have been described. The following
discussion illustrates the application of these ideas to an amplifier design
for use in a digital computer system. It is intended that the descrip-
tion of the design philosophy be sufficient to permit its application to
other systems.
In the computer under consideration the amplifier is to be combined
with a single level, diode logic circuit to form a logic network. The logic
networks, together with delay lines, will be connected in appropriate
arrays to perform the logic functions of the sytem, such as addition,
multiplication, etc. Digital information is to be represented by one-half
microsecond pulses and the amplifiers are to be synchronized at a one
megacycle pulse repetition rate by a four phase sine wave master oscil-
lator. Other system requirements are mentioned in connection with the
selection of the corresponding functional circuit.
Since the amplifier is considered as a small system of functional cir-
cuits, it is necessary, as in most system designs, to re-examine, and pos-
sibly change, circuit choices as the design progresses. However, for the
sake of clarity, the following discussion omits the re-examination and
frequently refers to the final schematic shown in Fig. 13.
The first step in the design is to select the feedback configuration most
suitable to the computer requirements. For this computer the dc and
clock power are to be minimized and the amplifier should be able to drive
from 1 to 12 logic networks. Miniaturization of the computer implies
that there may be an appreciable amount of stray capacity across the
amplifier output. These considerations suggest transformer coupled feed-
back connected in series with an output circuit. Since both positive and
negative output pulses are to be required (one polarity for AND and
OM logic and the other polarity for inhil)ition), transformer output cou-
pling is indicated.
TRANSISTOR PULSE REGENERATIVE AMPLIFIERS
nil
The next basic selection is the choice of an appropriate transistor. In
this computer it is expected that pulses will occur in only about one
third or less of the pulse time slots due to the nature of the digital in-
formation. In order to minimize the dc standby power an alloy junction
transistor is a logical choice for this application because of the low Ico
current. However, even with a junction unit possessing an alpha cut-
off frequency of eight megacycles, it is difficult if not impossible to ob-
tain acceptable gain and rise time with the desired output load current
at a one megacycle repetition rate. If the rise time is improved by in-
creasing the trigger current, the gain is decreased. The principal cause
of the poor "gain-bandwidth" appears to be the depletion layer capaci-
tance.^^ The difficulty can be overcome by selecting a point contact
transistor. A particular germanium transistor coded GA-52996* appears
to be suitable and has the following pertinent characteristics:
a. Collector capacitance less than 0.5 uuf,
b. Alpha cut-off frequency in excess of 80 mc,
c. Base resistance less than 100 ohms.
Since the alpha of this unit is greater than 2 at collector currents of
the order of 10 ma, the common base connection will yield the greatest
current gain. The disadvantage of a point contact unit, of course, is the
Ico current. For this reason the amplifier will have to be designed to use
the smallest possible collector supply voltage.
The point contact transistor, due to its high cut-off frequency relative
to the amplifier pulse repetition rate and its high alpha at small emitter
T~L
INPUT
I
-8V
I
I
+6V
3 VOLT PEAK
i I MEGACYCLE
SINE WAVE
VOLTAGE
I-2V
_rL
-w-
OUTPUT
Fig. 13 — Illustrative design
* This is a relatively special unit especially suited for high speed switching
applications.
1112 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 195G
currents,* permits the use of a simple input circuit. The AND type input
circuit is suitable and desirable for another reason. When AND type
logic is added to the amplifier, it may be paralleled with the basic input
circuit and the input sensitivity of the complete network will be the same
as for the amplifier alone. Other logic circuits will be added to an ampli-
fier in a manner similar to that described by Felker- so that the input
sensitivity will be reduced at most by the voltage drop across one series
diode (approximately 0.3 volts).
The input pulse voltage and current requirements depend upon the
voltage threshold necessary to prevent false operation and the minimum
trigger current for reliable regeneration. A test of several sample tran-
sistors indicates that approximately 0.3-ma emitter current is required
to trigger the transistor with an estimated collector supplj^ voltage of
10 volts. The emitter breakpointf voltage is found to vaTy between
— 0.25 and +0.25 volts. To allow for aging variations of the transistor
and of R2, it seems reasonable to use a 6-volt source and R2 ec^ual to
9090 ohms, which results in a trigger current a little more than twice the
required minimum. Previous experience with computers of this type in-
dicates that a 2-voIt threshold will be sufficient to prevent false trigger-
ing. Thus, the secondary winding of the feedback transformer is returned
to —2 volts and Rl is chosen to give a quiescent emitter voltage of —2
volts. With these considerations and an estimated voltage drop across
R3, the input pulse amplitude is calculated to be 2.3 volts and 0.9 ma.
Allowing 0.3 volts for a series logic diode, the minimum output voltage
and current of the amplifier are 2.6 volts and 0.9 ma per driven network.
The selection of the collector supply voltage and the turns ratio of T2
depends upon the dc power dissipation due to Ico current and output
voltage regulation versus collector current. For this transistor a unity
turns ratio appears to represent a reasonable compromise. Then, by
estimating the voltage drops across Tl, T2, and the transistor, it is
found that a collector supply voltage of — 8 volts is suflScient to produce
an output pulse voltage about 0.5 volt greater than the required
miminum.
The next step is the selection of the turns ratio of Tl and the primary
inductances of both Tl and T2. The two considerations involved are
sufficient feedback with the minimum output current (the worst case
with respect to feedback) and the maximum collector dissipation in the
event that the clock fails. By means of the formulas and assumptions
indicated in section 5, primary inductance values of 0.4 mh for Tl and
* Usually a > 4 for ie = 0.5 ma.
t The transition point of the emitter diode from cut-ofT to conduction.
TRANSISTOR PULSE REGENERATIVE AMPLIFIERS 1113
0.2 mh for T2 together with a turns ratio of 1.4 for Tl are selected. Since
the GA-52996 transistor is not quite short circuit staple, a 50-ohm
resistor is added in series with the emitter. The excess emitter current
at the end of the pulse duration is greater than 2 ma, thus assuring suffi-
cient stability, and, if the clock fails, the amplifier will turn off by itself
in approximately 7 jusec, at which time the instantaneous collector dissi-
pation will be approximately 240 mw (considered to be a safe instan-
taneous dissipation for this transistor).
For low clock power and circuit simplicity the single diode synchroniz-
ing circuit is chosen. Although a peak clock voltage of 2 volts would nor-
mally be used (this value corresponds to the quiescent emitter bias volt-
age) it is found that the clock may be varied between 1 volt and 6 volts
peak without a failure occurring. Therefore, the nominal clock voltage
is set at a centered value of 3 volts peak. The dc level of the clock voltage
is 0 volts, which approximately corresponds to the emitter break point
voltage of the transistor. This concludes the basic selections in the de-
sign procedure.
The power dissipated in the amplifier is quite modest. In the quiescent
state the amplifier absorbs only 0.2 mw average clock power and 30 mw
dc power (this would be only 10 mw if the I co power w'ere negligible).
When the amplifier is pulsing every microsecond the dc power is 50 mw
and the averge clock power is 2 mw. Since the amplifier is so conser-
vative of power, it is possible to use 4,000 networks in a computer and
require less than 200 watts dc power.
One indication of the component sensitivity of a pulse amplifier is the
magnitude of the supply voltage margins. In this amplifier the supply
voltages may be varied, one at a time, over ±12 per cent of the nominal
values before a failure occurs. Generally margins of this magnitude under
the worst conditions are considered sufficient to guarantee against fail-
ures caused by aging, or to insure that such failures will be indicated by
routine checks before they occur. It is interesting to note that in a tem-
perature test the amplifier continued to operate properly over a tempera-
ture range from —20 to +80°C. Even at -f75°C the supply voltage
margins were 10 per cent or better.
8. SUMMARY
A method of analysis and design procedure have been presented in
which a transistor regenerative amplifier is considered as an intercon-
nected system of functional circuits. Each functional circuit may be
evaluated or chosen in terms of the requirements of the complete digital
system in which the amplifier is to be used. In general no particular cir-
1
lU-i THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
cuit or collection of circuits can result in an amplifier suitable for use
in every type of digital system. The use of an AND type input circuit,
transformer coupled output and feedback circuits, and an inhibit type
synchronizing circuit appear to be an optimum set of functional circuits
to make up an amplifier for use in a synchronous digital computer system
emplojdng passive logic circuits. An illustrative design is presented for
such an amplifier which operates at a pulse repetition rate of 1 mc,
uses 12 components (none of which are especially critical), requires an
average of 40-mw dc power and 1-mw clock power, is capable of driving
from 1 to 12 similar amplifiers, and has voltage margins in excess of 12
per cent. Although the design philosophy was developed for this type of
amplifier, it is believed that much of the philosophy is applicable to
regenerative amplifiers for use in other digital data processing systems.
9. ACKNOWLEDGEMENT
The final design and the performance data of the illustrative amplifier
are due to L. C. Thomas and H. E. Coonce. The author also wishes to
express his appreciation for the many helpful and stimulating discus-
sions with other colleagues, especially A. J. Grossman, T. R. Finch,
J. H. Felker, and J. R. Harris.
REFERENCES
1. S. Greenwald, et al., SEAC, Proc. I.R.E., Oct., 1953.
2. J. H. Felker, Regenerative Amplifier for Digital Computer Applications, Proc.
I.R.E., Nov., 1952.
3. J. L. Moll, Large-Signal Transient Response of Junction Transistors, Proc.
I.R.E., Dec, 1954.
4. J. G. Linvill and R. H. Mattson, Junction Transistor Blocking Oscillators,
Proc. I.R.E., Nov., 1955.
5. A. E. Anderson, Transistors in Switching Circuits, B. S.T.J. , Nov., 1952.
6. T. E. Firle, et. al., Recovery Time Measurements on Point-Contact Germa-
nium Diodes, Proc. I.R.E., May, 1955.
7. S. L. Miller and J. J. Ebers, Alloyed Junction Avalanche Transistors, B.S.
T.J., Sept., 1955.
8. J. J. Ebers and S. L. Miller, Design of Alloyed Junction Germanium Transis-
tors for High Speed Switching, B.S.T.J., July, 1955.
9. T. C. Chen, Diode Coincidence and Mixing Circuits in Digital Computation,
Proc. I.R.E., May, 1950.
10. L. W. Hussey, Semiconductor Diode Gates, B.S.T.J., Sept., 1953.
11. J. M. Early, Design Theory of Junction Transistors, B.S.T.J., Nov., 1953.
12. Q. W. Simkins and J. H. Vogelsong, Transistor Amplifiers for Use in a Digital
Computer, Proc. I.R.E., Jan., 1956.
13. M. Tanenbaum and D. E. Thomas, Diffused Emitter and Base Silicon Tran-
sistors, B.S.T.J., Jan., 1956.
Observed 5-6 mm Attenuation for the
Circular Electric Wave in Small and
Medium-Sized Pipes
By A. P. KING
(Manuscript received March 20, 1956)
At frequencies in the 50-60 kmc region the use of circular electric wave
transmission can provide lower transmission losses than the dominant
mode, even in relatively small pipes.
The performance of two sizes of waveguide was investigated. In the small
size (Kg" ^•^- X Me" wall) the measured TEoi attenuation was approxi-
mately 5 db/100 ft and is appreciably less than that of the dominant mode.
The measured attenuation for the medium sized (%" I.D. X }^i'^ wall)
waveguide was 0.5 dh/100 ft which is about one-fourth that for the dominant
mode.
This paper also considers briefly some of the spurious mode conversion-
reconversion effects over the transmission band and their reduction when
spurious mode filters are distributed along the line. Allowance has been
made for the added losses due to oxygen absorption when air is present.
INTRODUCTION
Since 5.4-mm dominant-mode rectangular waveguide has attenuations
of the order of 60 db/100 ft, another transmission technique is required
in applications which involve appreciable line lengths. Losses may be
reduced by the use of oversize waveguide ; some earlier work with domi-
nant mode transmission in slightly oversize round waveguide (two or
three propagating modes) has been reported.^ The possibility of still
lower losses exists with circular electric wave transmission in an over-
size round waveguide. Miller and Beck- have computed the theoretical
relative transmission losses of the TEoi and TEn modes as functions of
' A. P. King, Dominant Wave Transnaission Characteristics of a Multimode
Round Waveguide, Proc. I.R.E., 40, pp 966-969, Aug., 1952.
2 S. E. Miller and A. C. Beck, Low Loss Waveguide Transmission, Proc. I.R.E.,
41, pp 348-358, March, 1953.
1115
1116 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
guide size and frequency. At 5.4 mm, a J^e" I-I^- waveguide has an
appreciably lower attenuation with the circular electric mode than with
the dominant mode. A %" I.D. guide has a circular electric attenuation
approximately one-fourth that of the dominant mode in the same pipe.
It is the purpose of this paper to present some experimental results
which have been observed with circular electric wave transmission in
the 5-6 mm wavelength region. The attenuation for three different hnes
and the transmission variations due to moding effects are reported. Al-
lowance for the loss due to oxygen absorption has been included.
DESCRIPTION OF THE TEST LINES
The TEoi mode attenuation measurements were made on approxi-
mately straight runs of line ranging from about 100 to 200 feet in length.
The copper pipe comprising these lines is believed to conform to the
best tolerances and internal smoothness which are current manufacturing
practice for waveguide tubing. The relative tolerances and their effect
upon transmission are considered in a later section. Three kinds of copper
line were measured: a waveguide of oxygen-free copper, one line of low
phosphorous-deoxidized copper and one line of steel with a 20-mil low
phosphorous-deoxidized copper inner lining. The oxygen-free high-con-
ductivity-copper with its higher conductivity and somewhat greater
ductility was chosen to provide comparative performance data with the
low phosphorous-deoxidized copper which is commonly used in wave-
guide manufacture. A waveguide whose outer wall is constructed of
steel to provide the necessary strength and wall thickness to support a
very thin copper inner wall has the advantage that such waveguide re-
quires less copper. This composite wall tubing was obtained to ascertain
whether the tolerances and the nature of the inner surface would yield
transmission data comparable to solid copper waveguide.
The lines Avere supported on brackets which were accurately aligned
and spaced at 6-ft intervals. Although the brackets provided for an
accurately straight line, the manufactured pipe was not perfectly straight
but, in some samples, varied as much as %" in a 12-ft length. Installing
the pipe on the brackets tended to straighten the line and reduce these
variations to about half this amount. A general view of the lines is shown
in the photograph of Fig. 1.
The sections of waveguide were joined together with a more or less
conventional threaded coupling, but with one very important difference.
The threads, which are cut at the ends of each section, are cut relative
to center of the inside diameter and not the outside diameter. This is
achieved by employing a precision pilot to provide a center for the cut-
i
5-6 MM ATTENUATION FOR THE CIRCULAR ELECTRIC WAVE 1117
^''■m
m 9^
m #%
Fig. 1 — General view of the circular waveguide lines and the millimeter wave
measuring equipment.
ting die. Since the internal diameter is made as precise as possible, the
variations of outside diameter become a function of the tolerances of
both the internal diameter and wall thickness and cannot be as precise
as the inside of the pipe. Any thread cut relative to the outside diameter
as in regular plumbing practice, will not, in general, be concentric to the
1118 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
inside wall. To avoid an offset at the joint it is therefore important that
the thread be centered relative to the inside diameter. After a section
was threaded the ends were faced off to make the ends square and thus
avoid any tilt between sections when the ends are butted together.
Of the two sizes tested the smaller diameter (Ke" I-D. X Ke" wall)
was chosen to provide a moderate line loss, while limiting the number
of propagating modes. In the band of interest (5.2-5.7 mm) the theoreti-
cal TEoi wave attenuation is about 4 db/100 ft. The number of modes
which can be supported at X = 5.2 mm is limited to 12 modes and to
only one of the circular electric modes. The higher order TEon modes are
beyond cut-off. These features limit the number of spurious modes and
simplify the mode filtering problem. Furthermore, in this smaller sized
waveguide, the associated components which may set up TEon waves,
for example conical tapers, need not be as long proportionately as in
larger waveguides. The %6" I-I^- guide has the advantage of smaller
size, lower cost and greater ease of transmitting TEoi through specially
constructed bends. The attenuation of this smaller diameter guide is
large enough that system requirements will usually restrict its usage to
lengths of line of a hundred feet or so.
The larger size (J^'' I.D. X 3^" wall) is exactly twice the diameter of
the small size discussed in the preceding paragraph but has only one-
tenth the attenuation, or about 0.4 db/100 ft. The low loss of this larger
size becomes more attractive for runs as long as several hundred feet.
This diameter guide will, of course, support more modes, 50 at X = 5.2
mm; four of which are circular electric modes — • TEoi , TE02 , TE03
and TE04 . Some of the disadvantages which accompany the increased
diameter are: (1) greater care must be taken as to line straightness, (2)
longer conical tapers are required when converting from one guide diam-
eter to another, and (3) longer mode filters are required since the desired
mode-filtering attenuations vary inversely with the filter diameter at a
given frequency. Flexible spaced-disk lines employed as uniform bends
for TEoi transmission require much greater bending radii than bends in
the smaller diameter guide if the bend loss is to be kept proportionately
low. This problem is considered in some detail in another paper.^ With
reasonable care the accumulative effect of these foregoing factors can
be held to a reasonably low value. Expressed in terms of the ratio of
measured to theoretical attenuation the values are, on the average,
about 10 per cent higher in the %" I.D. waveguide than in the J4.6"
I.D. waveguide.
A. P. King, forthcoming paper on bends.
5-6 MM ATTENUATION FOR THE CIRCULAR ELECTRIC WAVE 1119
»» ' • " K>if
.^^. .^W- -^P- .I^P.
Fig. 2 — Waveguide portion of millimeter wave measuring set.
MEASURING PROCEDURE
With straight runs of round, TEoi waveguide lines whose length lies
in the 100-200 ft range, it is convenient to make attenuation measure-
ments on a round trip basis. This method has the advantage of conven-
ience in that the attenuation can be measured directly by using a wave-
guide switch but has the disadvantage of requiring a careful impedance
match of the measuring equipment to the line. Fig. 1 shows an overall
view of the lines; Fig. 2 shows the arrangement of the 5-6 mm measuring
set, and Fig. 3 shows a block diagram of the set-up employed.
This measuring set makes use of two klystrons developed by these
laboratories.* The double detection receiver features a separate beating
oscillator klystron which is frequency modulated and a narrow band
(1.7 mc at 60 mc) IF ampHfier. The resulting IF pulses are detected
wuth a peak detector and then amphfied to provide the usual meter
indication. This method with its circuitry has been developed by W. C.
Jakes and D. H. Ring,^ and provides a greater amplitude stability than
is possible with a cw beating oscillator.
In the waveguide schematic of Fig. 3 about a tenth of the power is
^ E. D. Reed, A Tunable, Low Voltage Reflex Klystron for Operation in the
50-60 Kmc Band, B.S.T.J., 34, p. 563, May 1955.
* W. C. Jakes and D. H. Ring, unpublished work.
1120 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
taken from the signal oscillator to provide monitoring and wavemeter
indication. The remaining power, after suitable padding, is fed into a
3-db directional coupler or hj^brid junction 2. This junction is employed
as a waveguide bridge so that, when arms A and B are properly termi- '
nated, no power flows in receiving arm C. Any reflection in line A will,
WAVE
METER
0
MONITOR
SIGNAL
OSCILLATOR
X
•-10DB
, Q
oDB v_y
I
^4-
2>/
^3DB COUPLER WAVEGUIDE
/-^{HYBRID JUNCTION) SWITCH
/ y^ ROUND
TUNER TAPER ^^ <• WAVEGUIDE
LINE
X TE
TEo, TEo,
Fig. 3 — Schematic of measuring equipment.
ADJUSTING
KNOB
-RG 98/u
Fig. 4 — Structure of impedance matching tuner.
5-6 MM ATTENUATION FOR THE CIRCULAR ELECTRIC WAVE 1121
Fig. 5 — Structure of waveguide switch.
however, produce a power flow in the arm C to the balanced converter
of the receiver and an indication in the output meter. So far this set is
similar to a setup for measuring the round trip loss in a terminated
waveguide system. The impedance of the TE?o ^ TEoi wave trans-
ducer,^ taper section and mode filter connected as shown in the section
A-D of Fig. 3 can be matched to the rectangular waveguide at A by an
appropriate adjustment of the dielectric post tuner^ Ti whose structure
is shown in Fig. 4. Under these conditions a conical taper termination
placed in the round waveguide at D will again produce a balance and
again no power will flow in arm C. A ^vaveguide switch whose structure
is shown in Fig. 5 is connected between the point D and the line under
test. A movable short at the far end of the line completes the set-up.
With the impedances matched as described above, the only reflection
which reaches the receiver wdll be from the far end of the line when the
switch S is open or, when shorted, from the switch itself. The round-
trip attenuation is the difference in attenuation measured for the two
positions of the switch. By means of a movable short at the far end of
the line, the line length can be varied to produce mode conversion and
mode reconversion effects, and the resultant variation in TEoi mode
transmission can be observed. This phenomena is described in some de-
tail elsewhere.^
" Reference 2, page 354, Fig. 14.
■ C. F. Edwards, U.S. Patent 2,563,591, Aug. 7, 1951. The millimeter tuner
employs an adjustable dielectric post in place of a metallic tuning screw described
in the patent.
* Reference 2, pp 356, 357.
1122 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
LOSSES DUE TO OXYGEN ABSORPTION
In addition to the losses which result from imperfect conductivity,
surface effects, and mode conversions, there is a very appreciable loss
due to oxygen absorption when the guide is open to the atmosphere. In
a waveguide the loss due to O2 absorption is:
where
A is the absorption due to oxygen in the atmosphere
= X/Xc
= free space wavelength
= cut-off wavelength
V
X
Xc= ^ =
k 3.83 -.: ._
d = internal diameter of waveguide ^
k = Bessel root for TEoi mode = 3.832
The loss due to absorption of oxygen which is present in the at-
mosphere (at approximately sea level) was obtained from the experi-
mental data of D, C. Hogg.^ The added loss produced by the presence
0.5
o
o
CO
o
O
o
I-
UJ
D
Q
(/)
W
o
_l
in
<
a.
o
z
0.4
0.3
0.2
0.1
\
\
V
V
■h-
\
v\
\
2,.c-
>\
\
\
\
\
\
\
\
X
^^
=--
5.0 5.2 5.4 5.6
WAVELENGTH IN MM
5.8
Fig. 6 — TEoi transmission loss in waveguides due to oxygen absorption.
' A. B, Crawford and D. C. Hogg, Measurement of Atmospheric Attenuation
at Millimeter Wavelengths, B.S.T.J., 35, pp. 907-917, July, 1956.
5-6 MM ATTENUATION FOR THE CIRCULAR ELECTRIC WAVE 1123
of oxygen in the waveguide in terms of (1) is plotted in Fig. 6. It will
be noted that this loss becomes very appreciable at the short wave-
length end of the band. At X = 5.2 mm this loss is in the 0.3-0.4 db/100
ft range. For the larger size waveguide hue (J^" I.D.) the loss due to
O2 is approximately equal to the theoretical wall losses; for the smaller
size lines this amounts to about a tenth the wall loss. At the other end
of the millimeter band the O2 losses are very small, being in the 0.02
- 0.03 db/100 ft range at X = 5.7 mm.
The relative effects of theoretical wall and expected oxygen ab-
sorption losses are shown plotted in Fig. 7. For the two sizes of wave-
guide the upper dashed curve represents the combined effect of these
two factors and the lower solid line curve is the theoretical attenuation
of the TEoi mode in empty pipe. The shaded area indicates the increase
which is the result of oxygen absorption.
In order to minimize the transmission losses in any practical system
it becomes desirable to exclude the presence of oxygen from the hne, for
example, by introducing an atmosphere of dry nitrogen. Since the ex-
5.0
4.5
I-
UJ
ID
O
o
a.
Ill
Q.
HI
m
o
UJ
o
4.0
3.5
3.0
WAVEGUIDE
+O2 LOSS
rO
J LOS
S
-3--'
^
\
V/^
>2
7^
■^.^^
/
^
y^
^
THEORETICAL
WAVEGUIDE LOSS
5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8
WAVELENGTH IN MILLIMETERS
(a) TEq, loss IN 7/16" I.D COPPER
0.8
Z
O
w
z
<
a.
0.7
0.6
0.5
0.4
0.3
0.2
THEORETICAL WAVEGUIDE LOSS
5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8
WAVELENGTH IN MILLIMETERS
(.b) TEq, loss in ys" I.D. COPPER
Fig. 7 — TEoi transmission losses.
1124 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
tn a.
D OJ
<. o
O Q-
cc^-'ai
- Q.
LINE
RLTE
JOINT
T LIN
1 to q
Z LUl"-
- <^ M
< gO'O
I N
-i 9<S
Q. O
a. ^oi^
Q X
1
-■ O
1
1 HI
1
r~|<DQ
1
I
h-
z
LL)
OJ
z
cr
U-
z cc II
o <->
z
LU
OJ
z
«
I
k
\
^ y
_/>
\ -J
\l
7
' <
Q \
\
1-
UJ \
\
Ol
cr
N.\
QC
CO
\'
S. iJJ
<
>
/^I
UJ
/^
^<r-
«
A
1
Q
ai
z
O- _)
UJ LU
CL UJ
O to
U
tr I-
Lu y z
-I Li. -1
Z UJ I
< 9'-'
_j 9<
Q- 2 UJ
r-|oo
z
UJ
_l
UJ
z
\
vi
\
?it
\.
\y N
V.
\ \
v^
.^ \
\\-
/ K \
UJ
1 / \
A^
/
lUJ
/\
'l
f\ \
|i-
Sv
\
«
^vS
- \
^\ \
A
. 1
vi
\
^
iy
in
^ 5
in
z
in H-
rt z
^. UJ
in -I
LU
m 5
(\j
in
for^ (Din ^ nco^^ to
dddddddod
Id 001 H3d aa Nl NOIlvnN3iiV
in
o
LU
CL
CL
o
u
fO
LU
cc
.U.
d
LU
O
>
X
o
t-|<o
d
Q
UJ
Q
Q
<
I
u.
Q
UJ
I-
L)
D
Q<
UJ H-
Q <
Q
UJ UJ
Z Q
li o
if
(O 5
UJ o
lO CC
(O U.
o
O
OJ
o
ID
03
O
o
t3
a
O
CO
W)
Id 001 ySd 90 Nl N0liVnN3iiV
5-6 MM ATTENUATION FOR THE CIRCULAR ELECTRIC WAVE 1125
elusion of oxygen was not very feasible in the experimental TEoi lines,
the effects due to oxygen absorption were included in the measurements.
However, in order to simpHfy the presentation of the attenuation data
these absorption losses, as indicated in Figs. 6 and 7, have been sub-
tracted from the measured data.
The measured attenuation of the four lines are shown in Fig. 8 as a
function of wavelength (5.1-5.8 mm). In each case the dash-dot-dash
lines represent the theoretical attenuation for copper. Each plot shows
two solid lines which indicate the range of values measured over the mm
band. The same range was observed either by varying the length of the
line by means of a sliding piston at the far end of the line or by imposing
a sweep voltage on the repeller of the signal klystron to produce a small
frequency modulation. These variations in attenuation correspond to
piston movements which are greater than a half wavelength and are due
to the mode interference effects produced by spurious modes generated
in the line. The resultant signal fluctuations which are due to mode con-
version and reconversion effects have been described in considerable
detail by Miller.^o
Referring again to Fig. 8, the measured data shown by the solid lines,
which are for a plain line without mode filters, indicates that the oxygen-
free high conductivity copper line gave the lowest measured average
attenuation as well as the least variation. The low phosphorous deox-
Table 1
■'At' LD.
%" I.D.
W I.D.
W I.D.
OFHC Copper
OFHC Copper
Low Phos.
Deoxidized Copper
Copper Lined
Steel
Wall Thickness
Me"
W
W
W
ameas. (db/100 f t) . .
a meas
4.33 ± 0.24
1.17
1/1100
0.0004"
1/730
0.0006"
1/310
0.0014"
0.47 ± 0.02
1.29
1/1100
0.0008"
1/875
0.001"
1/730
0.0012"
0.49 ± 0.05
1.34
1/1200
0.00075"
1/875
0.001"
1/430
0.002"
0.52 ± 0.04
1.42
a calc
Average ovality
A
B
Maximum ovality
A
B
Maximum tolerance
A
B
1/585
0.0015"
1/290
0.003"
1/290
0.003"
'" S. E. Miller, Waveguide as a Communication Medium, B. S.T.J. , 33, pp.
1229-1247, Nov. 1954.
1120 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
idized copper was next best while the steel line with a 20-mil inner copper
lining was the poorest.
In the "J/ig" I-I^- oxygen-free high conductivity copper line the meas-
ured attenuation was 17 per cent higher than the calculated value (see
a meas/a: calc in Table I). This higher loss is attributed to spurious mode
conversion and to surface conductivity effects. In the %" line of the
same material the a meas/a calc = 1.29 which is an increase of 12 per
cent relative to the smaller waveguide. Since the %'' diameter line sup-
ports about four times the number of modes of the Jite" diameter line,
this increase in loss is attributed to mode conversion. In the other two
%'' diameter guides the added losses are believed to be increased mode
conversion which results from the poorer dimensional tolerances. These
data are listed in Table I together with dimensional tolerances. In this
table Q!meas is the measured attenuation averaged over the 5.2-5.7 mm
band together with the variations shown in Fig. 8; acaic is the average
theoretical attenuation for standard (I ACS) copper. The I.D. tolerances
are listed in two sets of rows A and B ; row A gives the fractional variation
CARBON-LOADED
NEOPRENE
END'
COUPLING
SECTION
TYPE
MEDIUM
SMALL
O. P.
2"
I.D.
7/ a"
7/16"
o.oao"
0.081"
i
Fig. 9 — Structure of spaced-disk mode filter.
5-6 MM ATTENUATION FOR THE CIRCULAR ELECTRIC WAVE 1127
-e
Fig. 10 — Mode filters.
I
ji relative to the average diameter and the rows marked B indicate the
corresponding variations in inches. The average ovahty gives the aver-
, age difference between maximum and minimum diameters, maximum
i ovahty the maximum difference in diameter and the maximum toler-
ance gives the maximum difference between diameter and ovality.
' These measurements have been limited to measuring at the two ends
of each section of pipe. In spite of this small sampHng the TEoi loss
measurement appears to follow the I.D. tolerances quite well; the
OFHC line shows both the lowest attenuation and the best tolerances.
Mode interference effects can be reduced considerably by increasing
the loss to the undesired modes. This effect can be accomplished by modi-
fying the structure so that the spurious modes are highly attenuated
while the TEoi losses are increased only slightly. One way is to construct
Table II — Average Performance of TEoi Waveguides with
Mode Filters
a measured (average db/100 ft.).
a measured
a calculated
Vie" I.D. OFHC
copper
4.24 ± 0.1
1.16
W l.p. low phos.
deoxidized copper
0.51 ± 0.025
1.39
%" I.D. copper
lined steel
0.56 ± 0.012
1.52
1128 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
the waveguide wall with a series of disks which are closely spaced as shown
in Fig. 9 and the photograph of Fig. 10. The spacers serve a dual pur-
pose; to hold the disks in alignment and to provide loss for the spurious
modes. The circular disks provide the necessary continuity to support the
TEoi and TE02 modes and the gaps introduce high resistivity to the longi-
tudinal currents of the other modes. The spaced-disk filters, which were
arbitrarily designed to provide a 10 db loss to the TMn wave, were 1 %"
and 3 }/i" long for the Ke" ^i^d 14," waveguide sizes, respectively. In the
experiments to be described, a mode filter was inserted at each joint of
the line, at approximately 12-ft. intervals. ,
The measured attenuation data with mode filters at each joint of the
various fines are indicated by the dashed lines of Fig. 8. As shown the
effect of the mode filters is to reduce the TEoi loss variation by a factor
of at least two.
The average attenuation is, however, generally somewhat higher than
for the unfiltered lines. This higher loss is partly due to spurious mode
power which is absorbed by the mode filter and is not reconverted to
TEoi power and to a slight degree to the increased TEoi loss introduced
by the mode filters. These results are shown in tabular form in Table II,
where the nomenclature is the same as in Table I. Because of the ex-
cellent performance of the 14" ^•^- hi^e (OFHC copper) by itself no meas-
urements with mode filters were performed on this line.
CONCLUSIONS
The measured data presented above indicate the feasibility of realizing
transmission losses as low as 0.5 db/100 ft. with the TEoi mode over dis-
tances up to several hundred feet. The transmission variations which
occur over the frequency band are a function of the circularity or tol-
erances of the waveguide. In a particular line the variations can be re-
duced considerably by adding mode filters along the line. It is reasonable
to expect that these variations can be reduced further by adding longer
mode filters at the joints or adding more mode filters at shorter intervals
along the line. Oxygen must be excluded from the line if the losses are to
be a minimum.
ACKNOWLEDGMENT
The author wishes to thank J. W. Bell and W. E. Whitacre for their
help in the measurements.
This study was carried out at Holmdel and was sponsored in part by a
Joint Service Contract administered by the Office of Naval Research,
Contract Nonr-687(00).
Automatic Testing in Telephone
Manufacture
By D. T. ROBB
(Manuscript received May 8, 1956)
A general discussion is given on the philosophy behind the development of
automatic test facilities and the relationship of this activity to product design
and manufacturing engineering. A brief historical discussion of early auto-
matic test machines used by the Western Electric Company leads to a sum-
mary of design considerations. These considerations are then illustrated by
descriptions of the specific techniques used in three automatic facilities of
considerable diversity.
INTRODUCTION
Many of the parts used in the telephone plant are made in such num-
bers that automatic shop testing of them is desirable. The cost of manual
testing by suitable personnel is high, and its nature so repetitive and dull
that accuracy suffers. Fortunately, in many cases the complexity of the
test requirements has matched the state of the art and the business pic-
ture well enough to warrant the development of machine methods. It is
our purpose in these articles to review the art as it has evolved in the
Manufacturing Division of the Western Electric Company, and to de-
scribe some of the techniques. This is done with the hope that improve-
ments or extensions to other testing or manufacturing problems may be
suggested.
It should be emphasized that the developments treated here and in
the other papers^ '^ have required cooperation among testing and manu-
facturing engineers in the Western and product design engineers in the
Bell Telephone Laboratories. Modifications of design for Western's con-
venience, changed methods for translating basic requirements into man-
ufacturing test requirements, informal Laboratories suggestions of ap-
proaches to manufacturing and testing problems, all are commonplace.
The boundaries of the specialists' domains are readily crossed.
Testing is a process for proving something such as quality of a prod-
1129
1130 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
uct or accuracy of a computation. In one form or another, testing is essen-
tial in manufacture. It insures against further investment of effort in
product found bad. More importantly, it provides information for the
manual or automatic correction of earlier processes, to prevent manufac-
ture of additional faulty product. Also, its techniques and devices are
used in many applications where testing is not the object. Table I gives a
listing of functions, with examples of some of our automatic means, that
illustrates this. Of these, la, 4, and 5a are testing functions. The remain-
der are manufacturing processes.
Table I
Function Example
1. Sorting, either
a. sorting good from bad or A network testing machine at Indian-
polis.'
A relay coil test set at Kearny. ^
b. sorting into cells for selective as- A capacitor test machine at Haw-
sembly thorne.^
2. Adjusting: An adjusting machine for flat type
resistors at Haverhill.*
3. Calibrating: " A calibrating machine for oscillator
film scales at Kearny.^
4. Plotting data: Continuous thickness test systems for
alpeth and stalpeth cable sheath at
Hawthorne and Kearny."- ^
5. Operation of wired equipment, Cardomatic and tape-o-matic test sets
a. to verify accuracy of wiring or ful- for key telephone equipments and
fillment of purpose, and wired relay units at Hawthorne and
b. to enable prompt location and Kearny.^- '
correction of faults.
GENERAL
The fundamental steps necessary to any testing operation are:
1 . Putting the item to be tested in location ;
2. Subjecting the item to a specified set of conditions;
3. Observing the results or the reaction of the item to the conditions;
4. Comparing the observed results to required results;
5. Deciding on the basis of the comparison what disposition to make
of the item;
6. Indicating the disposition;
7. Making the disposition. (This may mean transportation, repair or
adjustment.)
In purely manual testing all of these steps would be initiated by human
AUTOMATIC TESTING IN TELEPHONE MANUFACTUEE 1131
operators. In many cases it is feasible for all steps to be taken automat-
ically. The bulk of our accomplishment in automatic testing, however,
has been in steps 2 through 6. We do not ordinarily use "automatic" to
describe rudimentary automaticity in combinations among steps 3, 4,
and 5.
The present models of many of our machines have evolved from earlier
models, either because of changed product or test requirements or
through improved designs worked out for plant expansion or cost reduc-
tion. The names of engineers associated with the various developments
mentioned are included in the references. About 1927 there were put in
use at Hawthorne two machines, one for gaging a number of critical
dimensions and performing a breakdown test on carbon protector
blocks,^" and the other for heat coils.^^ In the protector block machine
the blocks follow a linear course drawn by an indexing chain conveyor
through a number of positions where the various checks are performed.
Failure of any block at a position causes a jet of air to blow the block
into the opening of a chute which conducts it to a reject pan. Good blocks
are delivered into a pan at the end of the run. The heat coil machine has
an indexing turret over a ring of ports which open selectively to permit
good or rejected coils to fall into chutes. The test parameters are three
,<!;aged dimensions and dc resistance.
In 1929 a machine with an indexing turret was put in use, testing paper
capacitors for dielectric strength and leakage resistance,^^ and sorting
them into 13 cells for capacitance grouped around a nominal 1 mf. The
13 cells correspond to 13 segments in a commutator disposed along the
scale of a microfarad meter. For a given test capacitor, when the meter
needle reaches its deflection a bow depresses it against the nearest seg-
ment, establishing a circuit through a relay. A system of relays then
locks up and serves as a memory to operate a solenoid later when the
turret has brought the capacitor to the point of disposition. Action of
the proper solenoid causes the capacitor to be deposited in its cell. The
cells are arranged as parallel files in a horizontal plane and, starting with
the cells empty, the machine will in effect produce a stovepipe distribu-
tion curve. Capacitors from the middle cell and its upper neighbors may
be used as 1 mf capacitors, and those from more remote cells combined,
large with small, to make 2-mf capacitors.
Also in 1929 a turret type machine was first used for sorting mica lam-
inations. ^^ The sorting parameter was ac dielectric strength, the criterion
being failure at 1760 volts r.m.s. The individual laminations were carried
from position to position by vacuum fingers mounted on a turret. Again
locking relays were used, in this case to operate a solenoid controlled
1132 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
valve in the vacuum line at the right time in the turret indexing cycle to
drop the laminations as class "A" or "B" mica.
Experience with these machines and with others that followed brought
into being a more or less orderly body of knowledge as to what features
are desirable and what constitutes good design in an automatic test ma-
chine.
If the machine is to have speed, reliability and long life, attention
should be paid to the following matters:
1. Reduction of the test process time to as low a figure as the capabilities
and use of the product will permit. Thus, if one of the requirements of a
capacitor is a maximum limit on its leakage current measured after a
charge time of 60 seconds, and if the material sand manufacturing process
are such that a unit is surely good or bad after a 25-second charge, then
the machine may be designed to charge for, say, 30 seconds. Frequently
the only limitation is the speed of the machine itself. When this is true,
it must be worked out so as to satisfy the needed production rate. Obvi-
ously the machine should satisfy the rate of the line it serves, or more
than one machine should be provided.
2. Rationalization of the number of test positions in the machine with the
production rate and the total test process time. This requires breaking the
test time down into bits equal to the desired output cycle. In the example
above, if the output needed is a capacitor every 5 seconds then the 30-sec-
ond charge will have to extend over 6 positions.
3. Ruggedness. This must be stressed, even at the expense of space,
power consumption, and dollars of first cost. If a project is large enough
to justify automatic test facilities, then any down time associated with
it will be expensive. A good mechanical design is essential.
4. Provision of self -stopping and alarm features to serve in the event of
certain types of failure. A limited torque clutch in the main drive will pre-
vent jamming and damage caused by parts getting into the wrong places,
or in certain applications overload cutouts will suffice. Gong and lamp
alarms are desirable to attract attention. The point is that allowance
must be made for mishaps which, without precautions, could result in
shutdowns of the equipment.
5. Provisions of adequate checking for accuracy. Accessible check points
and suitable easy-to-use standards are essential. Checking intervals are
determined by experience, but schedules should be laid out to cause as
Hi tic interference with use as possible. Where practicable there may be
means for self-checking in the regular operation of the machine. In this
case, periodic checking of the checking devices themselves is necessary.
6. Incorporation of features in the product and in the handling methods
AUTOMATIC TESTING IN TELEPHONE MANUFACTURE 1133
that will facilitate feed automatic testing. This requires the cooperation of
the product design and product manufacturing interests. It is almost
axiomatic that automation in manufacture requires special consideration
in product design. Automatic testing imposes the same requirement. A
notch or a lug may be needed for proper use of automatic feed devices,
or terminals may have to be properly chosen. Again, the method of trans-
port from the previous operation needs to be studied, rationalized, and
fully agreed upon. If continuous conveyor transportation can be justified,
so much the better. In the consideration of conveyor feed, the need for
time flexibility must not be overlooked. It is important that provision be
made for easy storage of product whenever the test machine is inopera-
tive, lest a breakdown of this machine shut down the entire line.
7. Arrangement of the events in the operating cycle in such a way that
their sequence is reliably self determined . This is comparatively straight-
forward when the programming is done by gear driven cams or other
mechanical means. It requires care when switching logic is used. Switch-
ing engineers are familiar with the phenomena known as "relay races"
and "sneak circuits." These have psychophysical analogies wherever
humans and machines work together. The prevention of both the switch-
ing errors and their analogs is essential in automatic test set design. Inter-
locks must be provided against any conceivable mishap.
8. Enough margin and design flexibility in electrical and mechanical
parameters to cope with reasonable variations in product design. Improve-
ments are constantly being made in telephone apparatus and equipment,
and these occasionally result in major redesigns or in entirely new sys-
tems. Also the need for adding new features to a historical complex of
existing telephone plant causes the generation of an endless variety of
special equipments. The product designer needs as much freedom as we
can afford. There has to be enough flexibility in the costly automatic
test sets to permit adaptation as new designs of product come along.
These considerations are in addition to the fundamental matters of
personnel safety and comfort, motion economy, quietness and appear-
ance.
While dealing with general considerations we must recognize one im-
portant difference between the product design and the facilities design
problems. In product design there is a premium on optimization of pa-
rameters, or striving toward perfection. There is generally also oppor-
tunity for winning this premium on later tries even though the rush for
first production may have denied it to us in the original design. In facili-
ties design there is no such premium and frequently no such opportunity.
While careful design is very important, the real premium here is on a
1134 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
a
o
■/3
a;
3
if
<u
AUTOMATIC TESTING IN TELEPHONE MANUFACTURE 1135
device that will do the required job and that can be put in use in time
for early production. Once the facility is in use it may be starting on a
productive life that will run thirt}^ years or longer. The designer may
think of countless ways to improve it or to redesign it completely. If his
improvements or redesign can be proved in on a business basis, they may
be undertaken. Sometimes the}^ cannot be proved in. The evolution that
has taken place in test set designs has been possible mainly because the
customers have wanted newer products, or products delivered at a greater
rate. Advancement has been attained under a compulsion to take each
step ciuickly and siu'ely. This has represented a real and continuing chal-
lenge to the test engineering force.
With these general considerations in mind the author has chosen three
automatic testing devices of diverse character to discuss in some detail.
The associated papers^' ^ cover additional machines. The machines de-
scribed illustrate in various ways the principles discussed above.
THE NETWORK TESTING MACHINE AT INDIANAPOLIS^
The 425B network^^ is used in the 500 series telephone sets to furnish
the transmission link between the handset and the line. Its shop testing
requires three tests for transmission, three for capacitance tolerance,
three for leakage current, two for ac dielectric strength, one for dc dielec-
tric strength and four for continuity. The rotating turret type test ma-
chine (Figs. 1 and 2) performs all these tests, applies a conditioning
"burnout" voltage and counts and date stamps the good networks.
Rejects from each test position are segregated in roller conveyors.
In the rotation of the turret an empty test fixture is presented to the
operator every 3^^ seconds moving from left to right. She must load each
position, taking networks from the pans at her right; good networks,
ejected automatically in a roller chute at the left, are hand loaded into
the carriage fixtures of the overhead storage type conveyor, which pass
within easy reach of the operator's left hand. The pans at the left are
used to store good networks when the accessible fixtures of the overhead
conveyor are full. The twelve roller conveyors for rejected networks are
arranged along the sides of the machine, six on each side.
The turret contains forty test fixtures (Fig. 3 and 4) and the machine
forty positions. The turret rotates continuously, causing eleven contact
brushes associated with each fixture to pass against fixed commutator
segments and a ground ring associated with the test positions. As each
fixture advances past one test position a gear connected cam shaft rotates
through a complete cycle. Seventeen switches are operated by the cams
1130 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
•- *•«!»' ■^J^TTT'
Fig. 2 — The network test machine.
to assure the proper sequence and timing of the conditioning and testing
events occurring at the various positions. Table II shows the order of the
positions and the approximate timing, with respect to cam rotation. The
result of the test at each test position is remembered by a self-locking
relay until the fixture comes just opposite the entrance to the correspond-
ing rejection chute. At that instant a cam switch closes and causes re-
jection if the test result was a failure. Unloading into the rejection chutes
is effected by compressed air operated cylinders as explained below.
The clamping movement of each fixture as it leaves the loading area
(entering position 7) is driven by a helical spring which lowers the con-
tact fixture over the terminals of the network, bringing spring loaded
plungers into contact with the terminals. (See Fig. 3) At a rejection loca-
tion a plunger rises, driven by an air (cylinder under the control of a sole-
noid operated valve. The rising of the plunger first forces the fixture to
AUTOMATIC TESTING IN TELEPHONE MANUFACTUKE
1137
unclamp against the compression of the helical spring, and then operates
an ejection arm which drives the network horizontally out of the fixture.
The top rollers of several of these ejection arms can be seen in the fixtures
at the front of the machine in Fig. 2.
The measuring circuits associated with the various test positions are
straightforward. If there is a dielectric failure in one of the breakdown
tests at position 8 or 9, the current through a relay coil in series with the
C>^
CABLE TO
BRUSHES
Fig. 3 — Test fixture, loaded.
1138 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
test exceeds a predetermined value. This causes another relay to lock up
and remember the faihu'e until the network reaches the reject location.
In a typical transmission test position (Position 10, 35 or 36) a fixed-
voltage, swept-frequency signal, 300 to 3,500 c.p.s., is impressed across
two terminals of the network. The three tests are for transmission and
short and long hne sidetone with suitable terminations connected as in
actual use. In each case the signal from two output terminals should be
less than or greater than a specified value. This signal is amplified and fed
Fig. 4 — Test fixture, unloaded.
AUTOMATIC TESTING IN TELEPHONE MANUFACTURE
1139
to a sensitrol relay, which is mechanically biased in amount and sense to
correspond to the limit. If the sensitrol operates it prevents rejection.
In the three capacitance test positions 12, 13, and 14, capacitors in
the networks are connected into a 60 c.p.s. comparison bridge. The out-
put signal from the bridge is amplified and rectified, and impressed on a
balanced dc amplifier which drives a sensitrol relay. If the bridge is out
of balance (that is if the capacitance is greater or less than nominal) cur-
rent flows in the relay, but always in the same sense. If the current in the
relay exceeds an amount corresponding to either capacitance limit, re-
jection occurs. Determination of which capacitance limit was violated is
done manually in a separate analysis of defects. It may be observed also
that any rejection at the capacitance positions could have been caused
by a loss unbalance of the bridge. If the conductance of the test capacitor
were such as to cause this it would so appear in the separate analysis,
mentioned above. The effect of any ordinary conductance deviation at
60 c.p.s. is neghgible. Quality is protected by the fact that a conductance
deviation could not cause an out-of -limit capacitor to be accepted.
Considerable pains are taken at each capacitance test position to pre-
vent damage to the equipment from various kinds of mishaps. The sen-
sitive winding of the sensitrol is short circuited at all times except for
about 0.2 second when the actual test is performed. This prevents dam-
age and erroneous rejections that would otherwise be caused by switching
Table II — Sequence of Events in Network Test Machine
CAM ROTATION —
(TWELFTHS OF A POSITION)
POSITION
PROCESS C
)
2
4
6
8
10
12
1 TO 6
LOAD
1
7
BURNOUT
DISCHGl
8
AC BKDN.
TEST-
'P
7KV)
O -
- Ill -
-»
UJ -
*
9
DC BKDN.
TEST-
10
TRANSMISSION 1
1 ,
TEST-
II
DISCHARGE
1
12
CAPACITANCE 1
^CIRCUIT SETUP-^
lESTJ^
M
iMORY 4
13
2
II
M
11
14
3
■1
H
II
15
BURNOUT
-CHA
R6E-
DISCHGl 1
16 TO 31
(1 MINUTE)
CHARGE FOR
LEAKAGE TEST
- C^Anuc
32
LEAKAGE 1
TEST
33
2
II
34
3
II
35
TRANSMISSION 2
II
36
3
M
37
CONTINUITY
>- TEST 4 CIRCUITS AT ONCE -
^
38
UNLOAD
—UNLOAD
39
RESET
40
LOAD
1
<l
1140 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
transients from this and other circuits. During the short interval of actual
test no other switching takes place in the machine.
A fixture that has no network because of rejection at an earlier test
position or because of operator failure to load it, would cause open circuit
in one bridge arm on capacitance test. Without intervention this would
cause a violent unbalancing of the bridge, overloading of the detector
system and possible damage to the sensitrol. Ordinary methods of limit-
ing the overload signal would be only partially effective and would de-
tract from the sensitivity. To forestall this trouble from empty fixtures,
each capacitance test position is equipped with a microswitch which is
operated by a dog at the bottom end of the ejection arm of any empy fix-
ture (Fig. 3). When the microswitch operates it causes the bridge to be
disconnected from the test leads and connected to a capacitor that is just
out of limits, several tenths of a second before the removal of the short
circuit from the sensitrol. Then w'hen the test is made it results in a re-
jection.
There is also an interlock circuit which will stop the machine if a failure
of the bridge and detector system causes an empty fixture not to show
rejection. This serves as a random occasional check on the functioning
of the circuit.
The conditioning of the three capacitors for the leakage current tests
l)egins at position 16. Because of charging and absorption currents ob-
scuring the effect of pure leakage, the test for leakage is made to an arbi-
trary current limit specified at one minute of charge. To insure that good
units pass the test, it is desirable to use the whole minute. But if the leak-
age current reading is taken after more than a minute of charge, quality
is jeopardized. Accordingly it is necessary to make sure that the charge
is for a minute and no longer on each capacitor. Therefore, at position 16
the first unit is put on charge, at 17 the second, and at 18 the third. Then
at position 32 the first unit is tested while the other two remain on charge.
At 33 the first unit is discharged, the second tested, and so on.
The leakage test itself is made by measuring the voltage across a large
resistor in series with the test capacitor and a dc voltage source. The
energy in this signal is small and must be amplified before there is enough
to operate a sensitrol. A dc amplifier with high input impedance is used
for this purpose. In addition the mechanical bias of the sensitrol is kept
small to increase sensitivity, and a carefully controlled dc biasing source
is used to insure accuracy and stability.
At position 37 three capacitors and a coil ^\•inding are given a final
check for contirmity. The test of the winding is made by connecting it in
series with a relay coil (say No. 1) and battery. If current passes, relay
AUTOMATIC TESTING IN TELEPHONE MANUFACTURE 1141
No. 1 operates. The three capacitors are tested simultaneously by con-
necting each of them in series with an 8,000 c.p.s. source and detectors.
The detectors consist of bridge type rectifiers and relays. If all of these
three relays operate, a series connection through their closed contacts
causes another relay to operate and lock up. Finallj^ this relay when
operated has open contacts in parallel with open contacts on relaj^ No. 1,
so that when the reject cam closes it finds an open circuit and rejection
does not occvu*.
The reader may question the necessity for continuity tests on capaci-
tors that have already been tested for capacitance. Perhaps the most
convincing answer is that there is an occasional failure on the continuity
test. Telephone apparatus is always exposed to more severe conditions
in test than it will encounter in ordinary use. The leakage resistance
charge and test operations and the transmission tests can on rare oc-
casions cause the metallized connections at the ends of the capacitors to
open. As the cost of making the final continuity test is vanishingly small,
the additional insurance is economical.
The detail list of checking standards for this machine contains some
twenty items. Most of them are modified 425B networks, specially ar-
ranged in one way or another to check certain functions of the machine.
These are used right in the individual fixtures.
It is interesting to reflect on the labor saving virtues of this machine.
The operator in one eight hour shift handles over five tons of networks.
She does it easily and without fatigue. The testing would not be even
attempted on a manual basis, because over and above multiple handlings,
the added human effort of closing fixtures, operating switches and the
like could not be tolerated.
In contrast to the multiposition set described above, it is instructive
to consider two single position sets of diverse character. They are a relay
coil test set and a film scale calibrating set.
THE RELAY COIL TEST SET AT KEARNY^
Coil assemblies for the U, Y and UA types of relays^^ are tested for dc
resistance, direction of winding and breakdown before assembly into
complete relays. INIany thousands of the relays are used in any crossbar
office. Minimum and maximum tolerance limits arc placed on their wind-
ing resistances, to control cinnulative current requirements and to insure
a proper margin of relay operation. Each coil assembly, as presented to
the test position, consists of a magnetic core, a solenoidal winding assem-
bly and a terminal assembly. A winding assembly may have one, two or
'ukI^hK^^
Fig. 5 — Relay coil test set control panel.
1142
AUTOMATIC TESTING IN TELEPHONE MANUFACTURE 1143
three windings (called primary, secondary and tertiary). The primary
and secondary are wired to corresponding pairs of terminals on the ter-
minal assembly, while the tertiary leads at this stage are not on terminals
and must be connected to the test contact fixture by hand.
Direction of winding is important in the multiwinding coils because of
external fields and the fact that the relays are required to respond to
currents in more than one winding and the proper direction of flow in
each, relative to the other, must be known. In some relays one or two
of the windings may be noninductively wound, to serve merely as resis-
tors. Also, many windings are wound part copper and part resistance
wire to obtain the desired resistance without unnecessary increase in
copper, inductance and response time. In such cases the percentages of
copper and resistance wire are known. This is important because of the
effect of temperature on the resistivity of copper. Resistance tolerances
on the test windings are specified at 68°F, but shop testing is done at any
value of room temperature. The effect of the difference on copper is seri-
ous enough to cause errors larger than some of the tolerances, and the
effect on resistance wire may be neglected. Therefore, it is necessary to
have the test set compensated for temperature in such a way as to allow
for the proportions of copper and reistance wire.
The coil test set (Fig. 5) tests all windings for resistance and direction
of winding and for breakdown to each other and the core. The maximum
total test time for three-winding coils is less than 3 seconds under normal
conditions. A borderline winding resistance will cause some delay. There
are lamps to indicate the type of failure on a rejection. Other lamps indi-
cate satisfaction of the requirements. At the completion of test on a good
coil an "OK" lamp lights on the test fixture, so that the operator need
look at the set itself only when there is a rejection.
Requirements data are stored in the set before a given code of coil is
tested. The codes come to the set in batches, so that one setup will serve
for a large number of coils. Three six-decade resistance standards are
set to the nominal values for the respective windings. If there are fewer
than three windings, a key is operated to disable bridges and furnish
substitute continuity paths. The percentage tolerances for the windings
are set on selector switches: ±1, 2, 5, 10 and 15 per cent tolerances are
available. Also, the known percentages of resistance wire in the windings
are set on selector switches in steps of 5 per cent from 0 to 100. Keys are
operated to warn the set of noninductive windings and bypass the direc-
tion of winding circuits as needed.
Once a coil is placed and connected in the test fixture and the fixture
closed by operation of a pedal, the test is automatic up to the point where
1144 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
the operator must make disposition. The sequence of events within the
set is controlled by a switching circuit containing thirty telephone relays,
a sensitrol relay and two electron tubes. The sensitrol is used in succession
to detect the existence and sense of unbalance of six dc bridge circuits
(high and low limit for each of three windings) . The operation sequence
for primary windings is shown in Table III.
Fig. 6(a), shows schematically a typical bridge arrangement for testing
a winding at one tolerance limit. A and B correspond to the ratio arms
of an ordinary Wheatstone bridge, and are nominally 1,000 ohms each.
The temperature compensation referred to above is obtained by including
the same resistance percentage (within 2.5 per cent) of copper in the A
arm of the bridge as there is known to be in the winding. Inspection of
the bridge balance equation in Fig. 6(a) will show that an error in X could
be compensated by a proportional error in either A or C. A is chosen as
the compensating arm because of its simplicity. It has available twenty
resistors of copper and twenty of low temperature coefficient resistance
wire. Each resistor is 50 ohms, measured at 68°F. The selector switch is
arranged so that the arm always has tw^enty resistors, the indicated per-
centage being resistance wire.
For proper compensation it is necessary that the A arm be as near am-
bient temperature and the temperature of the coils as possible. The di-
Table III — Sequence of Events in Test of Primary Winding
FOR High Limit Resistance
"ok" LAMP
STEP
DEFECT LAMP
POWER SWITCH CLOSED
SENSITROL RESETS AND HOLDS
OPERATOR CLOSES FIXTURE
FIXTURE START SWITCH CLOSES
CONTINUITY TEST - ALL WINDINGS
"P OPEN" ETC.
"HIGH" B ARM CONNECTED TO PRI. BRIDGE
SENSITROL RESET RELEASED
SENSITROL OPERATES
"HIGH"
"LOW"B ARM CONNECTED TO PRI. BRIDGE
BREAKDOWN TEST ON PRIMARY
"BREAKDOWN"
SENSITROL RESETS AND HOLDS
SENSITROL RESET RELEASED
"P RES. GOOD"
SENSITROL OPERATES
"LOW"
DIRECTION OF WINDING DETECTOR ENABLED
D.C. POWER DISCONNECTED FROM PRIMARY BRIDGE
INDUCED VOLTAGE IN PICKUP COIL
"P DIR. OF WDG. DEFECT"
("OK")
SENSITROL RESETS AND HOLDS
V
"HIGH"B ARM CONNECTED TO SEC. BRIDGE
\
(SECONDARY TEST PROCEEDS; SIMILAR TO
PRIMARY)
/FOR SINGLE -WINDING COILN
\LAMP ON FIXTURE LIGHTS/
AUTOMATIC TESTING IN TELEPHONE MANUFACTURE
1145
AT BALANCE:
BX = CA
A = I000^AT68°F
1000
I ±.OI(TOL.%)
C = NOM.RES. OF X
(2-^ TO 35K)
X= WINDING RES.
TO CIRCUITS
FOR FOLLOWING
TESTS
UNLOCK
(B)
Fig. 6 — Circuits used in Relay Coil Test Set. (a), resistance bridge, simpli-
fied schematic; (b) continuity, simplified schematic.
1146 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
vision into twenty resistors helps in this by maintaining high effectiveness
of dissipation. In addition, the automatic switching circuits are arranged
to keep the duty cycle of current in the bridge arms low.
The B arm of the bridge is selected by the setting of the percentage
tolerance switch. Each resistor is used alone and consists of low tempera-
ture coefficient resistance wire as in standard bridge practise. The value
of each resistor in ohms is 1 ,000 divided by one plus or minus the corre-
sponding tolerance fraction. Thus, for ±1 per cent tolerances the re-
sistors are 1,000/1.01 ( = 990.0) and 1,000/0.99 ( = 1010.1), respectively.
One setting of the switch indicates zero tolerance and is equipped with
1,000-ohm resistors to permit easy checking of the C arm precision.
The six-decade standard resistor in the C arm, which is set to the nom-
inal value of the test winding, is of a high quality commercial type with
a range of 0 to 40,000 ohms in steps of 0.1 ohm. Because the C and X arms
may contain values as low as 2 ohms, no relay contacts are used in them.
Relay switching is done in the A and B arms where the resistances are
always of the order of 1,000 ohms and small variations in contact resist-
ance are negligible. The more stable wiping contacts of selector switches
do appear in the X arm. These switches permit any contact in the test
fixture to be connected to any bridge terminal, to enhance flexibility.
A continuity test on all windings, before resistance test, is desirable
for two reasons. The effect on the sensitrol of the severe bridge unbalance
caused by an open winding would be life-shortening and is to be avoided
if possible. Also, the result of the resistance test would only show high
resistance, and separate analysis would be needed to reveal that a wind-
ing was open. The continuity test circuit in Fig. 6(b) was devised to prove
continuity for windings having resistance values as high as 35,000 ohms.
A relay (UA-104) was chosen which is sensitive enough to close a pair
of "preliminary make" contacts (m) on 0.005 ampere, and which pro-
vides the number of other contacts needed to satisfy circuit requirements.
When the test winding is connected at X, the currents through it and
the 100,000 ohms combine to equal 0.005 ampere or more. This closes m,
connecting the 20,000-ohm resistor in parallel with the 100,000 ohms,
thus locking the relay and assuring that all the other contacts operate.
In the act of proving continuity, the relay disconnects itself from the
test winding and remains locked. The make contacts shown at the right
end of the relay symbol are in series with similar contacts on the con-
tinuity relays for the other two test windings, and when all are closed
they pass operating current to a relay which initiates the first resistance
test (for primary high limit).
In the direction of winding circuit. Fig. 7(a), it is necessary to have a
negative pulse from the pickup coil, in the test fixture, cause the 313CA
AUTOMATIC TESTING IN TELEPHONE MANUFACTURE
1147
gas tube to fire and the relay to operate. The circuit is designed to handle
a wide range of pulse amplitudes. The VR tube Hmits negative pulses to
90 volts to protect the 6AK5. The varistor dissipates positive pulses and
prevents any false acceptance that might be caused by damped oscilla-
tions following a positive pulse. The 6AK5 furnishes the needed sensi-
tivity for small pulses.
Occasionally a winding will have a value of resistance just equal to
.5MEG
I— vw
+ 130
PICKUP COIL
30,000 TURNS
ON PERMALLOY
50 K
Mitt
QUENCH
CIRCUIT
FOR NEXT
TEST
UNLOCK
AAA/ M 55V. AC l^c.T. GROUNDED
/ONE SIDE OF IIOV. AC\
(A)
^;
SENSITROL
RESET <|_r
SOLENOID -• P
50MF-r
SLOW
RELEASE
3 SEC.
20 K
1
(B)
Fig. 7 — Circuits used in relay coil test set. (a), direction of winding, simpli-
fied schematic; (b) anti-stall, simplified schematic.
1148 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
its upper or lower tolerance limit. On the corresponding resistance test,
the sensitrol will balance and not operate either way. Without an anti-
stall device the test cycle would then be stalled until the balance failed.
Current flowing through the A arm would eventually heat it up and
vitiate the temperature compensation feature. The anti-stall circuit in
Fig. 7(b) is essentially a slow release device to which external energy is
interrupted at the same time as the sensitrol reset is released. Energy
stored in the 50-mf capacitor prevents release of the relay for about 3
seconds, long after the bridge test is ordinarily finished. If at release the
bridge is still balanced, a 50,000-ohm resistor is thrown in parallel with
that ratio arm which will make the sensitrol accept the test winding.
A prominent and hitherto valuable feature of this test set is its adapta-
bility to a large variety of coil assemblies. Some hundreds of distinct
designs of product are presently accommodated. In the Kearny relay
coil shop there are four sets of the design described here and four sets of
earlier designs. It is possible that future development, if justifiable, will
be directed toward greater automaticity for some of the simpler and
more numerous product codes, with less emphasis on universal applica-
tion.
THE CALIBRATING MACHINE FOR 56-A OSCILLATOR FILM SCALES^
Photographic films are used for the frequency scales of some oscillators
to afford scale length and enhance readability. There have been several
successive designs of film scale calibrators built and put in use at the
Bell Telephone Laboratories and at Kearny. Some have been described
in the hterature.^^' "■ ^^ One very early design is still in use on production
at the Marion Shops in Jersey City. In its use, a calibrating run requires
about an hour, and the possibility of frequency drift due to temperature
variations makes the use of an air conditioned room essential. All of those
used at Western, prior to the one described here, depended for accuracy
on the film scale of a standard prototype of the oscillator to be calibrated.
Using a frequency controlled servo linkage, the scale of the standard was
reproduced photographically on the film of the product. Some of the
prior art appears in the design of the new machine. In order to describe
the principle clearly, it seems necessary to discuss some features which
were previously covered, but which now are used in new ways.
The 56A is a heterodyne oscillator designed for use in the field testing
of L3 installations.*^ It has a usable range of 50 kc to 10 mc. One com-
ponent oscillator is fixed at or near 90 mc and the other may be varied
between 80 and 90 mc by means of a tunable cavity. The calibrated
portion of the 35-mm film scale geared to the cavity tuner is about 17
AUTOMATIC TESTING IN TELEPHONE MANUFACTURE
1149
Fig. 8 — Film scale calibrator,
feet long. It has sprocket holes and is moved by a standard movie
sprocket. The required precision of each calibration mark is ±2 kc. Two
resonant devices are included in the circuit to permit checking and ad-
justing two widely separated points on the scale, 100 kc and 7,266 kc.
Considering the output frequency as a function of scale setting, one of
the two adjustments controls the lateral displacement of the curve and
the other its average slope. By design the curve approaches linearity
but not closely enough to permit less than a uniciue calibration for each
oscillator manufactured.
Fig. 8 shows the machine which performs the calibration, with an
oscillator connected, and the control cabinet. The oscillator is shown in
its shipping frame. An unexposed photographic film to be calibrated is
mounted in a camera so that it can be driven by a sprocket. The sprocket
is connected by gears to a drive motor which also drives the take-up reel
and, through a flexible shaft, the cavity tuner and sprocket in the oscil-
lator itself. The gear arrangement is such that the peripheral speeds of
the two sprockets are the same.
A positive master film is provided which has a scale similar to the one
to be made for the product except that it is very precisely hnear. A por-
tion of the master is shown in Fig. 9(b). The master film passes over a
sprocket which is driven by a servo motor. A lamp illuminates and shines
through that portion of the master which is in front of an aperture at
1150 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
any instant. An optical system, Fig. 9(a), produces on the unexposed
film an image of the illuminated portion of the master. As the oscillator,
its film, and the master advance, the markings on the master can be re-
produced on the new film.
The problem in control is to cause each mark on the master film to
pass the slit just as the oscillator goes thru the corresponding value of
frequency. To do this we drive the oscillator and its scale together at a
constant linear speed. The oscillator frequency increases steadily but
not at a constant rate. Its rate of increase varies according to the law of
its particular cavity. So our problem reduces to causing the master film
to move according to that same law.
The method is to time the passage of known points in the oscillator
frequency spectrum, and then to pace the movement of the master film
to maintain precise correspondence. The pacing is done by detecting
small differences in times of arrival at corresponding points and correct-
ing the speed of the master film to keep successive differences small.
Fig. 10 is a block schematic of the automatic control system. The varying
oscillator output passes through multiples of 10 kc at a rate near five mul-
tiples per second. When it is compared in a balanced modulator with
APERTURE
sow. PROJECTION
LAMP
UNEXPOSED -
FILM
(A)
DQDai!
/aDaDDDDDDDDDDaDD
1.200
1,300
i I I I I I I I I I I I I I I I I I I I I I I
aDDaDDDDaDDDDDDDDDD
(B)
Fig. 9 — Film scale calibrator, (a), optical system schematic; (b) section of
master film.
AUTOMATIC TESTING IN TELEPHONE MANUFACTURE 1151
the fixed harmonics of a standard 10-kc signal, the first order difference
frequency in the modulator output varies back and forth between 0 and 5
kc. It passes through the 2500 c.p.s. point twice per period of variation,
or twice per 10-kc interval of the oscillator frequency.
The output of the modulator is sent through a narrow band amplifier
I which peaks at 2500 c.p.s. A burst of signal, therefore, leaves this ampli-
i fier twice per 10-kc interval. The bursts are further amplified and recti-
fied and become pulses which time the progress of the oscillator through
its spectrum. The pulses are impressed across the winding of a high speed
relay, causing its contacts to close momentarily twice per 10-kc interval.
During the instant when the contacts are closed they connect a particular
value from a sawtooth voltage wave to a 0.1 -mf capacitor.
The voltage of the capacitor biases the grid of a cathode follower tube,
and the output voltage from this tube is fed to a servo system and con-
trols the speed of its motor. Thus the motor runs at a speed determined
by the voltage of the sawtooth at the instant when the relay contacts
close. As the sawtooth itself is timed by the rotation of the servo motor,
its voltage-time relationship is the device for pacing the master film. The
sawtooth wave originates in the alternate shorting and charging of a
1-mf capacitor. Each tooth begins when a pair of shorting contacts is
closed momentarily by a cam geared to the servo motor. After a dis-
charge, the voltage on the 1-mf capacitor increases negatively as a prac-
tically linear function of time, with charging current flowing through a
one megohm resistor. Thus the value of voltage transmitted to the 0.1-mf
capacitor at the instant of closure of the relay contacts depends on the
time elapsed since the most recent shorting of the 1-mf capacitor. Twenty
volts at the input to the servo system corresponds to midvoltage of the
sawtooth and to 3,600 rpm of the motor, which is the same as the con-
stant speed of the motor driving the oscillator and undeveloped film.
If the characteristic of the oscillator causes a given 2,500-cycle point
to occur early, the contacts of the relay will close at a higher positive
voltage point on the corresponding sawtooth. The servo motor will start
to speed up to make subsequent sawteeth start earlier than they other-
wise would have. The motor will slow down if the 2,500-cycle points fall
later and lower on the teeth.
Several design features in the system are of interest. The servo system
was supplied by Industrial Control Company (SL-1035). It has a ta-
chometer feedback in inverse sense to enhance system stability. The cam
used to operate the shorting contactor and start the sawtooth is a small
permanent magnet mounted on a wheel. The moving field causes the
contactor to operate very briefly as the magnet swings past. The con-
tactor itself is a Western Electric 222- A mercury switch, which has a
1152 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
10 KC
STANDARD
OSCILLATOR
F= ( (t)
'
HARMONIC
GENERATOR
MODULATOR
2500 CPS
B.R FILTER
■300
COMPARISON
CIRCUIT
MASTER FILM
SPROCKET
0= f (t)
20 RPM
(NOM.)
NOM. SPEED
3600 RPM
I MEG
600 RPM
(NOM.)
600 RPM
(NOM.)
IMF
-|Vj^ -NN^ +250
)l r 1 VI
I MEG
Fig. 10 — Block diagram of film scale calibrator with schematic of comparison
circuit.
AUTOMATIC TESTING IN TELEPHONE MANUFACTURE 1153
hydrogen atmosphere, high speed capabihty and high current capacity.
The magnetic arrangement reduces shock torque loads on the servo
motor, which might result from mechanical operation. The high speed
relay which operates at the 2,500-cycle points is a Western Electric 275-B,
chosen because of the speed required (about 10 operations per second).
The time comparison circuit has a small amount of long time constant
positive feedback (shown at 1 in Fig. 10) to raise or lower the midvoltage
of the sawtooth wave in cases of extreme correction and prevent the
control point from slipping one or more teeth. In effect this supplies extra
acceleration to the master film when needed.
There is also incorporated in the design an arrangement which permits
an important variation in the method of use. A magnetic tape is driven
by a sprocket which is geared to the main drive motor and moves with
the oscillator drive. The magnetic head for recording on the tape receives
its signal in the form of 2,500 c.p.s. bursts through an amplifier. These are
the same bursts that time the progress of the oscillator through its spec-
trum. Thus it is possible to separate the function of calibration from
that of printing the film scale. The calibration data on the oscillator is
stored on the tape and may be checked for absence of abrupt departures
from linearity before it is used to drive the servo and master film in an
actual printing run. This eliminates some wastage of raw film. Also a
recording (or calibrating) run is made without the servo linkage and can
be made at twice the speed of a printing run. A 56A oscillator can be
driven through its spectrum, 50 to 10,000 kc, in 100 seconds, allowing
very little opportunity for temperature effects to change the check points.
In fact no particular effort need be made to control the temperature
beyond an ordinary warm up interval.
The control portion of the machine contains various circuits for con-
venience in setting up and starting the runs. For example one relay cir-
cuit under the control of a start button brings a fixed dc voltage into the
servo loop, and automatically disconnects after a period long enough for
the motor to reach approximately the right speed. A gear shift lever per-
mits changing the ratios between the speeds for the recording run and
the printing run.
It is doubtful that a calibration of the 56A oscillator could ho per-
formed by manual means. It has been estimated that even if possible,
such a task would require more than a week of the most painstaking
effort, under very carefully controlled conditions. By comparison, the
calibrator requires one minute forty seconds to obtain the data, and
three minutes twenty seconds to reproduce it. Development and checking
of the exposed film takes about a day. Accuracy of the scales has always
been well within the ±2-kc limit.
llo-t THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
CONCLUSION
111 this and the accompanying articles we have given a partial picture
of the facilities for automatic testing in the Western Electric Compaiw.
At this writing several new machines are under development, and modi-
fications are in progress extending the application of some of the present
machines. There is a continuing search for new fields in which to apply
these techniques. A staff portion of the manufacturing engineering force
now devotes its full attention to automation techniques in general, keeps
abreast of the field, bulletinizes important additions to the literature,
lends assistance in the solution of problems, and develops specific appli-
cations. It is likely that the near future will see important extensions in
the use of automatic test equipment.
ACKNOWLEDGMENTS
The author is indebted to the people cited in the references for informa-
tion used in this article, and particularly to A. L. Bennett, J. Lamont
and F. W. Schramm who furnished valuable comments on the early
drafts.
References
1. Developed bj- A. L. Bennett and C. R. Rasmussen.
2. The original design of automatic relay coil test set was developed at Haw-
thorne by R. W. Brown. The set discussed here is a Kearny modification
developed by J. Lamont.
3. C. C. Cole and H. R. Shillington, page 1179 of this issue.
4. Developed by G. H. Harmon and A. E. Rockwood.
5. Developed by F. W. Schramm based on suggestions by T. Slonczewski, Bell
Telephone Laboratories.
6. B. M. Wojciechowski, Continuous Incremental Thickness Measurements of
Non-Conductive Cable Sheath, B.S.T.J., p. 353, 1954.
7. W. T. Eppler, Thickness Measurement and Control in the Manufacture of
Polyethylene Sheath, B.S.T.J., p. 599, 1954.
8. A. N. Hanson, Automatic Testing of Wired Relay Circuits, A.LE.E. Techni-
cal Paper 53-407, Sept., 1953.
9. L. D. Hansen, Tape Control, Automation, p. 26, May, 1956. Also see page
1155 of this issue.
10. Developed by C. F. Dreyer and A. W. Schoof.
11. Develoi)ed by L. H. Brown and N. K. Engst.
12. Information was supplied by C. A. Purdy.
13. A. F. Bennett, An Improved Circuit for the Telephone Set, B.S.T.J., p. 611,
1953.
14. Improved U, UA, and Y Type Relays, Bell Lab. Record, p. 466, 1951.
15. J. O. Israel, Broadband Test Oscillator for the L-3 Coaxial Carrier Sj^stem,
Bell Lab. Record, p. 271, July, 1955.
16. W. J. Means and T. Slonczewski, Automatic Calibration of Oscillator Scales,
A.I.E.E. Miscellaneous Paper 50-80, Dec, 1949.
17. T. Slonczewski, A Servo System for Heterodyne Oscillators, A.I.E.E. Tech-
nical Paper 51-218, May, 1951.
18. F. W. Schramm, Calibrating Strip Type Dials, Electronics, pp. 102-3, May,
1950.
Automatic Manufacturing Testing of
Relay Switching Circuits
By L. D. HANSEN
(Manuscript received May 18, 1956)
The large variety and quantity of shop-wired relay switching equipments
produced by the Western Electric Company lead to the use of comprehensive
and flexible manufacturing testing facilities to insure quality of product and
to reduce costs. An older manual type test set is briefly described and used
to illustrate the functions and operation of two automatic test sets designated
as Card-0-Matic and Tape-0-Matic respectively.
INTRODUCTION
Early telephone central office installations were of the manual switch-
board type which were relatively simple and refjuired few relay circuits
other than those located in switchboards themselves. Installation effort,
in addition to actual erection of the switchboards, equipment frames,
fuse boards and the like consisted largely of running and terminating the
central office cabling. As the telephone art grew, both with the introduc-
tion of the dial telephones, and carrier and repeater equipments for long
distance calls and the consequent need for interconnection of these
various types of systems, a considerable variety of relay switching cir-
cuits was required.
To reduce the installation time and effort the practice of doing as
much circuit wiring in the factory as possible was introduced. Relay
switching units are now completely assembled, wired to terminal strips
and tested in the shop. Since these are in effect working circuits the in-
stallation testing effort, after the connection of office cabling, consists
largely of overall tests required to insure the proper functioning of the
entire office.
Due to the wide variety and complexity of these units, many of which
have optional circuit conditions that can be supplied on order and few
of which have sufficient demand to justify specially designed high pro-
1155
1156 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
duction test sets for their exclusive use, adaptable manually operated
test sets were first used. These sets required a high degree of flexibility
in interconnecting the terminals of the circuit under test to those of the
test set and in applying the proper potentials in sequence that would
insure putting the cii'cuit through its paces and checking that the switch-
ing functions are properly performed.
It should be stated here that since all apparatus components of these
circuits such as relays, transformers, capacitors, inductors and resistors
are tested and inspected for their respective electrical and mechanical
requirements when manufactured, except in the case of some types of
relays which require adjustment to meet their particular circuit recjuire-
ments, the testing of switching circuits is largely confined to verification
of the circuit wiring with normal voltages. Although marginal component
tests are not normally applied, operation tests will, of course, detect
defective apparatus components which cause malfunctioning of the
circuit.
MANUAL TEST SET
Fig. 1 shows a representative manual type test set that was extensively
used for wired relay vmit testing before the introduction of the automatic
test sets to be described later. On the left side is a pin jack field into which
the numbered wires of the connecting cable can be individually plugged
in order to connect the test set terminals to the proper terminals of the
relay unit under test. The other end (not shown) of the cable is equipped
with a contact fiixture arranged to give quick electrical connections to
the terminals of the wired relay unit. The plugging of the pins into the
proper pin jacks is a feature needed to provide flexibility in a test set
arranged to test many types of circuits and is a part of the setup opera-
tion for any one circuit. It is a slow and time-consuming operation since
each lead has to be identified and plugged into the proper pin jack. The
pin plug setup must be taken down and rearranged in order to test any
other type of relay circuit.
The test set is equipped with signal lamps for visual response indica-
tions and manually operated keys for the use of the tester in performing
the test operations. Separate power cords are plugged into power distri-
bution jacks which supply the various potentials commonly used in
telephone central oflSces.
After the initial setup the tester operates the numbered keys and ob-
serves the lamp signal responses in accordance with the chart clipi^ed
to the front of the test set. Failure to get a particular lamp indication
AUTOMATIC TESTING OF RELAY SWITCHING CIRCUITS
1157
Fig. 1 — Manual wired unit test set.
requires that he analyze the circuit conditions and locate the cause of
the trouble. Usually a circuit fault must be corrected before testing can
proceed.
Fig. 2 shows a small portion of a simplified circuit test arrangement
for such a manual test set. In this illustration a single key, when operated,
supplies battery and ground potentials to the winding of a relay in the
circuit under test. Assumption is made that the three relay contact
terminals are wired directly to the relay unit terminal strip so that
1158 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
thej'' can be connected to ground and to battery through lamps for cir-
cuit closure indications. The switching functions of the relay can then
be checked by operating the test key and observing that signal lamp (1)
extinguishes and that (2) lights.
While such an arrangement can adequately test most switching cir-
cuits of any complexity by further extension of the basic scheme, when
supplemented by internal circuit connections where necessary, the
SIGNAL
LAMPS
(2) (C
(I)
S:
^
X
>
MANUALLY OPERATED
TEST KEY
X
PIN
JACKS
PIN
PLUGS
CONTACT
FIXTURE
/
^
— ^
^
TEST CABLE-"
/Cl
CIRCUIT
TERMINALS
PORTION OF
RELAY CKT
UNDER TEST
Fig. 2 — Simplified circuit sketch for manual test operation.
WATCHING
1 RELAYS
SIGNAL
RELAYS
CONTACT
CROSS CONNECTING FIXTURE
DEVICE / CIRCUIT
> /TERMINALS
I I f
TEST CABLE
PORTION OF
RELAY CKT
UNDER TEST
Fig. 3 — Simplified circuit sketch for automatic test operation.
AUTOAIATIC TESTING OF RELAY SAVITCHING CIRCUITS 1159
system is at best a slow and laborious one which is subject to human
error. Wages for testers are determined not primarily on their ability
to operate keys and check the indications of lamps but on their skill in
analyzing and clearing trouble conditions. If some quick and automatic
means could be devised to make the initial cross connection setup, apply
the potentials in the proper sequence under control of some programing
device and check the circuit responses at each step a real advance in
speeding up tests and reducing human errors would be accomplished
Such an automatic set ideally should have improved response indications
to aid the the tester in locating circuit troubles when the test set stops
on the failure of meeting any test requirement.
THE AUTOMATIC TEST SET
The key and visual lamp indicating functions of the manual test set
can be replaced by relays in an automatic test set which perform these
operations if they are under control of suitable programing and advanc-
ing circuits as shown in Fig. 3. Here the "signal" relays operate through
the contacts of the relay under test and their operating positions are
checked by the "watching" relays whose contact closures must match
those of the signal relays. The series path through the contacts of all
signal and watching relays is called a chain lead. The program circuit
establishes the positions of the watching relays to meet the expected con-
ditions prior to operating the key relay and then any lack of continuity
through the chain lead caused by failure to satisfy test conditions halts
the progress of the tests under control of the advancing circuit. At this
point additional contacts (not shown) on the signal and watching relays
may be used to light signal lamps to convey information to the tester
as to which portion of the circuit failed to operate properly.
For quick setup a pre-wired multi-contact adapter plug may be used
as a cro?s-connection device to permit establishing the proper test con-
nections to the unit under test. One will be required for each type of
relay circuit to be tested. These, together with some means whereby
the sequential operation of the programing circuit can be controlled,
constitute the essential features of an elementary automatic relay switch-
ing circuit test set. How these basic features can be extended into prac-
tical embodiments will be explored further below.
THE CARD-O-MATIC TEST SET
Key equipment relay units are small switching circuits used as cir-
cuit building blocks to provide the desired optional features in conjunc-
tion with the key boxes or key-in-base telephones often seen in small
1160 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 195G
Fig. 4 — Card-0-Matic test set.
AUTOMATIC TESTING OF RELAY SWITCHING CIRCUITS 1161
)usines.s offices to furnish the flexibiHty needed in answering and trans-
ferring calls. These s3^stems are used where the number of telephones
served does not warrant the use of a regular PBX switchboard.
These circuits are relatively simple but their large scale pi'oduction
warrants the use of high speed automatic test sets to perform the test
functions and to indicate circuit trouble.
Fig. 4 shows the operating position of the Card-0-Matic* test set
which was developed to test such unit assemblies. The keys shown are
used to initiate and control the automatic operation of the test set and
in trouble shooting. They are not to be confused with those that per-
form the actual testing functions described previouslj^ for the manual
test set. The lamps pro^'ide indications of the progress of the tests and
of the positions of the watching relays which are also needed to aid in
determining the point of circuit failure. The meter type relay in the
upper left corner of the operating panel provides a sensiti\'e checking
de\'ice for audio freciuency tests through the \'oice transmission circuits.
The telephone dial affords a simple means of generating any recjuired
number of pulses for operating stepping selectors on some types of units.
The terminal field in the lower front of the cabinet gi\^es the tester access
to the circuit terminals of both the unit under test and the test set for
his use in analyzing and locating faults. The upper cabinet was a later
addition and contains the multi-contact rela3\s needed to permit testing
units with more than one circuit. The row of push buttons are used to
select the circuit to be tested.
Fig. 5 is a rear ^'iew of the set that shows the perforated insulating
card from which the set derives its name. The coded card controls the
sequence of test operations and is hung on pins over the field of 1,000
spring plungers (20 X 50) as a part of the setup operation for a particu-
lar relay unit. Closing the door and screwing up the hand wheel, which
is necessary to provide the force required to depress the plungers, will
ground those which coincide with holes in that particular card.
Cross-connection setup of the test leads is achieved by the use of a
plug-board such as is commonly used for quick change over on perforated
card type business machines. Fig. 6 shows the plug board being inserted
into the transport mechanism. The relatively large number of terminals
are retjuired because each of 60 test leads must be capable of being
patched in to an equi\'alent number of terminals on a maximum of ten
different circuits. Not all of our test sets are equipped with the upper
cabinet since most key units have only one circuit and on these a simpler
* Patent No. 2,329,491.
1162 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
Fig. 5 — Rear view of Card-0-Matic test set showing insertion of perforated card.
cross connection fixture is plugged into the location where the lower
end of the cable joining the two cabinets is shown terminated in Fig. 5.
A side view of the test set is shown in Fig. 7 to give an indication of
the amount of switching e([uipinent and wiring necessary for an auto-
matic test set of this sort. The set is powered from a r20-\'olt 60-cy('le
AUTOMATIC TESTING OF RELAY SWITCHING CIRCNITS 1163
source from which are derived the 24-volt dc, 90-volt 20-cycle ringing
current and 600-cycle audio tone supplies that are required. The test
circuit features mchide tone transmission checking, dial pulsing, 90-volt
20-cycle ringing and ground and batter}^ supplied either directly or under
relay control. Other battery and ground relays are available for checking
the response of the circuit under test.
These test features have been sufficient to perform operation tests on
most relay units associated with key telephone systems. The test cycle
is fast and the twenty test steps can be performed in approximately ten
seconds. The lamp indications given when the test is interrupted by an
open-circuited chain lead, convey information to the tester as to which
test step is involved and when any pairs of signal and watch relays fail
Fig. 6 — Insertion of cross-connection plug board into Card-0-Matic test set.
IKU TIIK BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBEE 1956
Fig, 7 — Interior of Card-0-Matic test set.
AUTOMATIC TESTING OF RELAY SWITCHING CIRCUITS 1165
to match each other. Simplified circuit sketches which show the inter-
connection of test set and wired unit circuits are provided to enal:)le the
1 ester to determine quickly the cause of the failure.
I Th(^ C'ard-(^-Matic test set, while performing admirably on the rela-
tively simple relay circuits within its range and capabilities, falls down
on the more complicated relay switching circuits used in telephone
central offices for several reasons. The most important of these are:
1. A fixed cycle within a maximum of twenty steps with any one
coded card.
2. No provision for alternate or optional circuit conditions on a card.
3. The only power supplies provided to operate relays are negative
24-volt dc and 90-volt 20-cycle ringing whereas telephone office units
frequently also require negative 48-volt and positive 130-volt dc as well
as positive or negative biased ringing currents for party line ringing.
4. The increase of either test steps or features would increase the
size of the perforated card beyond a practical size.
THE TAPE-O-MATIC TEST SET
The experience gained in the design and successful operation of the
Card-0-Matic test set led naturally to the exploration of ways and
means whereby a more versatile and comprehensive set could be devised.
The five hole coded perforated teletype tape was selected as a cheap
and flexible programing device. It afforded a means of providing a test
cycle of any required length and, since the perforating and reading
mechanisms were already available, it appeared to be nearly ideal for
its purpose.
Consideration was given to the following desirable features all of
which were incorporated in the design of the new set:
1. Provision for cross-connecting (under control of the coded tape)
any test set circuit to any terminal of the circuit under test for as long
as necessary and then disconnecting for reuse in later testing steps if
required. This A\'ould greatly extend the range and capabilities of the
set.
2. Provision for several power voltage sources which could be selected
as required to meet the normal telephone office voltage requirements
of the unit under test.
3. Provision for alternate or optional tests to be coded into the tape
to meet the various circuit arrangements that may be wired into the
unit as required by the Telephone Company who is our customer. Such
optional test arrangements could be applied by the test set under the
control of keys to be operated by the tester as part of the setup at the
start of the tests.
1166 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
4. Provision for stopping the test cycle to enable the tester to per-
form manual operations such as inserting a test plug in a jack on the
unit or insulating relay contacts in order to isolate portions of the cir-
cuit for test simplification and to obtain a more detailed test.
5. Provision of improved lamp indications to aid the tester in clearing
wiring faults or in locating defective apparatus. These would include
the necessary information as to which test set circuits are connected
to which unit terminals as well as which relays of the wired unit should
be operated at that stage of the test cycle.
6. Provision for connecting several terminals of the unit under test
together as a means of providing circuit continuity where required.
7. Provision for measuring resistance values of circuit components.
8. Provision for insertion of various resistors in battery or ground
leads to control currents to desired values.
9. Provision for checking voice transmission paths through non-
metallic circuits such as transformers or capacitors.
10. Provision for measuring circuit operating times in steps of ap-
proximately 100 milliseconds.
11. Provision for sending and receiving dial pulses.
12. Provision for a single code for releasing all test connections and
conditions previously established by the coded tape as a means of quick
disconnect. This is in addition to the release of individual connections
mentioned in (1) above.
13. Provision for audible and visual indications of completion of a
successful test cycle.
Through the use of two letters (each of which has its own combination
of the five holes) for each signal it was possible to obtain the over 500
codes required to control all test and switching functions even though
the teletype keyboard has only 32 keys. The only Teletype transmitter
(tape reader) available when the test set was first designed operated
at a speed of 368 operations per minute and was arranged for sequential
read out on two wires by means of a commutator. Conversion to five
wire operation and removing the commutator permitted reading each
row of holes simultaneously. The gearing was also changed to permit 600
operations per minute but even so the hole reading contact dwell time
was increased from approximately 20 milliseconds to 70 milliseconds for
more reliable operation with ordinary telephone relays.
The machine which was designated as the Tape-0-Matic* test set, is
shown in Fig. 8 in operation on a typical wired relay unit mounted in
its shipping frame. The contact fixture is attached to the unit terminal
* Patent No. 2,328,750.
AUTOMATIC TESTING OF RELAY SWITCHING CIRCUITS 1167
Fig. 8 — Tape-0-Matic test set in operation".
strip and cabled to a gang plug which in turn is plugged into a receptacle
behind the operator. These leads are extended through a duct to the
metal enclosure at the base of the set for entry to the test set proper.
The coded tape is dropped into the receptacle at the side of the key
shelf to which it returns after its traverse through the reader. A row of
circuit breakers on the end of the key shelf control the application of
1168 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
and provide protection for the various power supplies. Two of these
supplies are mounted on the top of the set.
The rows of vertical push button keys on the key shelf afford the
tester a means of determining (for trouble shooting purposes) the asso-
ciation (through lamp display signals) of the wired unit circuit terminals
with those of the test set and the corresponding test voltages which are
connected at that particular stage of the test. The lamp display panel
also indicates which test set circuits are in use and through fast or slow
(0.5 or 1 second) flashes whether the fault thus indicated is the result
of a failure to meet either an expected condition or the occurrence of an
unexpected condition. This feature is illustrated in Fig. 9 which shows
one link of the chain leads which extend through all pairs of signal and
watching relays for the check of satisfaction of all test conditions and
the application of steady or interrupted ground to the associated test
feature lamp. The operating condition of all test set key relays as pre-
viously established by the tape is also indicated by the display lamps.
xA.nother type of information obtained from the lamp display panel
which is valuable to the tester in trouble clearing is the indication of
the particular unit relays which should be operated at that part of the
test cycle. By checking the lamps against the operated or non-operated
position of the relays he can frequently localize the fault in a minimum
of time.
As mentioned above an important part of the test set flexibility is
the ability of the tester to set up the test set to test only those optional
circuit arrangments which are provided in any particular unit ordered
X
FAST
GROUND
PULSES
TO CKT.
UNDER _
TEST
ASSOCIATED FEATURE
SIGNAL LIGHT
(
cr
TO PRECEDI
WATCH RELAY
NG^
CHAIN
LEAD '
TO BATT OR
GRO.ASREQ'D.
"j-t.^"
SIG RELAY
c-^
SLOW
GROUND
PULSES
•- TO GROUND WHEN
REQUIRED FOR
EXPECTED
OPERATION
HI
^
CHAIN
T»^^
0 SUCCEEDING
SIGNAL RELAY
"watch" relay
Fig. 9 — Chain circuit showing watching rehiy function.
AUTOMATIC TESTING OF KEL.VY S^^ ITCHING CIKCUITS
1169
Fig. 10 — Lower portion of lamp display panel.
by the customer. Failure to provide this would result in fixed test cycles
and many more tapes, which might be similar but varying only in regard
to the options, would have to be prepared. Figure 10 shows the lower
portion of the lamp display panel with the push-pull option keys on
the bottom row. Directly above are the manual operation keys with
their associated lamps which the tester must operate to cause the test
set to resume the testing cycle after it has stopped for him to perform
a manual operation.
A side view of the interior of the set is shown in Fig. 11. Two bays
each facing the opposite direction from the other are housed within the
cabinet and are used for mounting the crossbar switches and telephone
type relays which are the principal circuit components. Two doors on
1170 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 195G
. M-f! x-t I ■! I .( •[ .r i
J- a* ■ > • I • 1 • r ( I f • > ' I n j
. ji -> -I t I ( ! I i t .r ^
M'-mf fi--«~^ f^** wfifr -wm ■*•
'|r||M|l||||4|fj
'i^rrrriTllHfiiil
ft "»
Fig. 11 — Interior of Tape-0-Matic test set.
each side give convenient access to all wiring and apparatus for mainte-
nance purposes.
A fairly large portion of the mounting space is occupied hy the cross-
bar switches which perform the functions of interconnecting the circuit
terminals of the unit under test and those of the test set. They also
connect the proper voltages to these circuits. The switching plan Fig. 12
AUTOMATIC TESTING OF RELAY SWITCHING CIRCUITS
1171
shows in abbreviated diagramatic form that the unit terminals 0-99
appear on the horizontal inputs of the two 10 X 20 and one 10 X 10
switches that comprise the primary group. The horizontal multiple of
these switches are split so that each section runs through five verticals
to afford connection to each of the hundred unit terminals.
The vertical outputs of the primary switches are connected to the
horizontal inputs of the two 10 X 20 secondary switches. The horizontal
multiple of these switches are split so that each section runs through
eight verticals. The verticals of the secondary switches are linked to
the horizontals of the two 10 X 20 tertiary switches which have their
tru-
tjj fr,
90
GROUP 0
'00
GROUP 0
9 Q
GROUP 0
,8
I
I
I 1
■o—
p A09
THROUGH
- GROUPS -
1-8
crui
uji-
\
THROUGH
-GROUPS -
1-3
THROUGH
-GROUPS -
1 8. 2
99
GROUP 9
'09
-o —
GROUP 4
0 0
0 0
GROUP 3
,30
39
PRIMARY
SWITCHES
2- 10 X 20
1 -10 X 10
SECONDARY
SWITCHES
2 -10 X 20
TERTIARY
SWITCHES
2 - 10 X 20
i|
QUJ
0.1-
28
THROUGH
FEATURES 0-9
-^-O-
00
09
THROUGH
FEATURES 10-29
THROUGH
FEATURES 30-39
CORRESPONDING
LEVELS MULTIPLED
30
39
TERMINATING
SWITCHES
■ 10X 20
Fig. 12 — Switching plan.
1172 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
multiple split into groups of ten. The 40 verticals of the latter are con-
nected directly to the 40 test set feature circuits designated 0-39.
Two additional 10 X 20 crossbar switches perform the function of
connecting any of the five power or five multiple terminations to any
of the forty test set features. These terminations are comprised of 5
loops and one each of ground, negative 24 volts, negative 48 volts, 90-
volt 20-cycle ringing current and positive 130 volts.
Thus it can be seen that, through proper operation of the primary,
secondary, tertiary and terminating crossbar switch cross points, a
path can be established from any circuit terminal to any test set feature
and supplied with any of the available power or loop terminations. It is
7 CROSSBAR
SWITCHES
RELAY
SWITCHING
TYPE CIRCUIT
UNDER TEST
MAX. 99
LEADS
AUTOMATIC
SWITCHING
OF CIRCUIT
TERMINALS TO
DESIRED TEST
FEATURES
QUICK CONNECT
CONTACT FIXTURES
TELETYPE TRANSMITTER
MODIFIED FOR 5-WIRE
OPERATION
40
LEADS
CONNECT «.
DISCONNECT
SIGNALS
TRANSMITTED
CODES
5 LEADS
TEST
FEATURES
CIRCUITS APPLY
DIFFERENT TESTS
AND CHECKING
CONDITIONS
40
LEADS
TEST
FEATURE
SIGNALS
TAPE
DECODING
CIRCUITS
10 KEYS
OPTIONAL
FEATURES
CIRCUITS
PERMITS VARIATION
OF TEST LISTED ON
STANDARD TAPES
TEST SIGNALS AND CHECK RESPONSE
2 CROSSBAR
SWITCHES
CONTROL
CIRCUITS
A SPECIAL CODE AT
END OF EACH TEST
STEP PERMITS THESE
CIRCUITS TO TRANS-
FER CONTROL OF THE
TRANSMITTER TO THE
CHAIN LEAD
RESET KEY
INDEXES TAPE i^
TO STARTING
POSITION i
TERMINATION
SWITCHING
OF POWER
8. SIGNALS
t130VDC GROUND
90V PO'^ RING 5 LOOPS
-48 V DC -24 V DC
TO TEST
FEATURES CIRCUITS
TERMINATION
SWITCHING
SIGNALS
TROUBLE
INDICATING
CIRCUITS
1. LAMPS INDICATE
PROGRESS OF TEST
AND ANY FAILURES
2. INDICATES FAILING
CIRCUITS
3. SHOWS POSITION OF
RELAYS IN TESTED
CIRCUITS
(-—CHAIN LEAD
CHECKS POSITION OF ALL TEST
FEATURE RELAYS WITH WATCH-
ING RELAYS. IF CHAIN IS
CLOSED, TAPE IS INDEXED TO
NEXT TEST CODE POSITION.
IF CHAIN IS OPEN, CONTROL
CIRCUIT WILL SWITCH TO
TROUBLE INDICATING CIRCUITS
START KEY
STARTS AUTOMATIC
PROGRESSION
OF TAPE
Fig. 13 — Block schematic.
AUTOMATIC TESTING OF RELAY SWITCHING CIRCUITS 1173
also apparent that several paths can be found that will satisfy any one
switched connection. Paths are assigned in sequence by a series relay
loop circuit. The entry point on this circuit is changed periodically to
distribute wear on the relays and switch cross points.
Although only one lead for the switched circuit is shown for each
cross point in Fig. 12 there are actually four leads through corresponding
pairs of contacts through each cross point. The remaining leads are
associated with the holding and signalling functions of the switch.
The block schematic (Fig. 13) shows the principal functions which
must be included in an automatic test set of this sort. A somewhat more
detailed schematic is presented in Fig. 14 in order to show the functions
of the forty test features 0-39. These are tabulated in Table I.
The coding of the two letter combinations in the tape must follow a
defuiite sequence in order that the machine may recognize and act on
the information it receives. This sequence is as follows:
1. Code FW to stop the tape at the end of the reset cycle after which
tests will proceed w^hen the start button is pressed. This is the first code
on all tapes.
2. Codes to set up crossbar switches to connect each circuit terminal
to its proper test set terminal and the proper termination. Knock down
or release codes may also be sent.
3. Codes to operate or release "Kej^" relays. These relays are shown
without windings in Fig. 14.
4. Codes to operate or release the watching relaj^s associated with
the "Signal" relays which are shown with windings in Fig. 14.
5. Codes to operate or release relays controlling the lamps associated
with relays in the circuit under test to aid in trouble shooting.
6. Codes to delay the timing out interval up to a maximum of ten
seconds.
7. Code FJ which checks the matching of all signal and watching
relays through the chain circuit for satisfaction of all test conditions
being applied.
In addition to the above, additional codes can be inserted after each
FJ test signal to stop progress of the test to permit the tester to perform
some required manual operation. After completion of this step he presses
a button associated with that operation and the test proceeds. Option
codes can also be inserted at the beginning and end of each testing step
to permit bypassing of that part of the tape if the corresponding option
keys are operated at the beginning of the test. A common knock down
code FR can be inserted at any time to release all connections and re-
lays for a quick disconnect and make all test set features available for
1174 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
03810038 SV SNOIiVNIWagj. Oi S3H0J.1MS dvassodD naHi
a.03d SV 66-0 uNwai j-ind Avnsy oi S3hoiims yvgssoyo Auvaaai qnv oas 'iHd ndHi
AUTOMATIC TESTING OF RELAY SWITCHING CIRCUITS
1175
reuse. A final code SC must be put in every tape to operate the OK
lamp and gong if a successful test cycle has been performed or conversely
to indicate that the tape should be re-run if trouble has been found
and cleared during the test cycle to be certain that no new faults have
been introduced.
Preparation for testing a particular wired relay unit requires only the
selection of a test cable one end of which is equipped with a suitable
contact fixture for attachment to the unit terminal strip and the other
with a gang plug for connection to the set. The proper tape is selected
from a nearby file cabinet and inserted in the gate of the tape reader
as shown in Fig. 15. The tape is stored in a cardboard carton 3^^ X 4
Table I
Feature Numbers
1 and 2
3 and 4
5 through 19
20
21 and 22
23 and 24
25 through 34
35
36 and 37
38 and 39
Description of Functions
High sensitivity relay circuit. Simulates 1,800-ohm sleeve
circuit for busy test and general continuity through high
resistance ciruits.
Simulates the distant tip and ring terminations of a subscriber
or exchange trunk. Provides for ringing, tone receival, dial
pulse sending, line resistance, high-low or reverse battery su-
pervision, pad control, continuity, and resistance verifica-
tion.
Auxiliary tip and ring circuit for holding, checking continu-
ity, receival of tone on four wire or hybrid coil circuits.
Loss range of less than 0.5 db, 0.5 to 1.5 db, 1.5 to 6 db and 6
to 15 db can be checked.
Direct connections for supplying any of the ten terminating
conditions.
Simulates low or medium resistance sleeve circuits for margi-
nal tests.
Simulates the local tip and ring terminations of a switch-
board or trunk circuit. Provides for ringing and dialing re-
ceival, high-low reverse battery supervision, transmission
pad control, tone transmission, continuity and resistance
check by balance.
An auxiliary tip and ring circuit for holding, checking con-
tinuity, tone transmission on four-wire hybrid coil circuits.
Low sensitivity relay circuits for general continuity checking.
A circuit for checking balance on the (M) lead of composite or
simplex signalling circuits and for checking receival of none,
one or two pulses.
Medium sensitivity relay circuits for continuity checking.
Direct connections for supplying any of the ten terminations.
1176 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
Fig. 15 — Perforated tape being inserted in reader.
inches in size, the label of Avhich carries all pertinent information required
for setup of the option keys, preliminary tests and manual operations
during test. A separate 12 conductor cable equipped with individual
test clips permits connection to internal parts of the circuit if needed
for adequate tests. No other information than that on the box label,
the circuit schematic and the lamp panel display is needed by the tester
to operate the test set and to analyze and locate circuit faults when
they occur.
With the tape inserted, the test connections established and am'-
preliminary operations pei-formed the tester has only to push the RESET
button to index the tape to the initial perforation on the tape and the
START button to initiate the test cycle. The set will continue to operate
until either a circuit trouble is encountered or a manual operation must
be performed. After a defect has been repaired, the automatic progres-
sion of the tape is again started by the momentary depression of the
STEP button. When a manual operation is performed the tape is re-
started by the momentary depression of the red button associated with
the lighted manual operation lamp signal.
AUTOMATIC TESTING OF RELAY SWITCHING CIRCUITS
1177
TEST-TIME PER CIRCUIT
HANDLING-TIME PER CIRCUIT
iv'AsSl SETUP-TIME PER CIRCUIT
START-UP-TIME PER CIRCUIT
LOCATING-TIME PER DEFECT
MANUAL TAPE
MANUAL TAPE
Fig. 16 — Comparison of manual and Tape-0-Matic test operation times.
As might be expected the easy setup, automatic testing and superior
trouble indicating features of the Tape-0-Matic test set have materially
improved the quality and reduced the testing time and effort required
for wired relay units as compared to the older manually operated sets.
The aA'erage time per circuit for six representative units are shown
graphically in Fig. 16. One time consuming operation on manual testing
is the start up time allowance for reading and understanding the written
test instructions which has no counterpart in the Tape-0-Matic tests
and this alone represents a sizeable gain. The handling time of the unit
itself is the only operation which is not reduced in automatic testing.
HISTORY
The initial Card-0-Matic test set was installed in 1938 in the Western
Electric, Kearny, New Jersey plant. Post war and subsequent expansions
of production levels have necessitated construction of six more sets of
improved design of the type described earlier in this article.
The first three Tape-0-Matic test sets were built in 1942 for the Wired
Relay Unit Shop and additional sets have since been constructed to
bring the number to twenty-six including six that are used in testing
trunk units in the Toll Crossbar Shop. They have performed admirably
with few changes from the initial design. They have been used to test
well over a million wired units with a minimum of maintenance. This
1178 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
may be accounted for, in part, by the fact that most of the component
parts are telephone type apparatus designed for heavy duty use.
A maintenance feature is the use of 18 specially coded tapes which,
together with a properly strapped input plug, permit the maintenance
technician to obtain indications on the lamp display panel of the per-
formance of the set.
Nearly three thousand tapes have been coded to date. Of these ap-
proximately two thousand are in active use on the many types of wired
relay units made at the Kearny plant. More tapes are being added
weekly as the Bell System telephone plant grows in size and complexity.
CONCLUSION
Automatic testing of wired relay switching circuits has been success-
fully applied to the manufacture of these equipments at the Kearny,
New Jersey, plant of the Western Electric Company for a number of
years. Even though the total production is large, manufacture is essen-
tially of a job lot nature due to large number of types made and is further
compounded by the optional circuit arrangments that may be ordered.
The solution to the problem was found through provision of flexibility
in programing and cross connection leading to quick setup, rapid testing
and improved transmittal of essential information to the tester to aid
him in clearing circuit faults.
Automatic Machine for Testing Capacitors
and Resistance-Capacitance Networks
By C. C. COLE and H. R. SHILLINGTON
(Manuscript received May 8, 1956)
The modern telephone system consists of a variety of electrical components
connected as a complex network. Each year, millions of relays, capacitors,
resistors, fuses, protectors, and other forms of apparatus are made for use in
telephone equipment for the Bell System. Each piece of apparatus must meet
its design requirements, if the system is to function properly. This article
describes an automatic machine developed hy the Western Electric Company
for testing paper capacitors and resistance-capacitance networks used in
central office switching equipment.
INTRODUCTION
The capacitors discussed in this article are the ordinary broad Hmit
units made ^^dth windings of paper and metal foil, packaged in a metal
case. They include both single and double units in a package, connected
to two, three, or four terminals. The networks consist of a capacitor of
this same type connected in series with a resistor.
The testing requirements for capacitors include dielectric strength,
capacitance, and insulation resistance. These same tests plus impedance
measurements are specified for networks. In general, requirements of
the kind involved here could be adequately verified by statistical sam-
pling inspection. However, in equipment as complex as automatic tele-
phone switching frames, even the minor number of dielectric failures
that would elude a properly designed sampling inspection would result
in an intolerable expense in the assembly and wiring operations. While
engineering considerations thus called for a detailed inspection for di-
electric breakdown, it was recognized that detailed inspection of the
other electrical requirements could be obtained at no additional expense
for labor with automatic testing machines.
1179
1180 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
DESIGN CONSIDERATIONS
In the development of this machine, the designer was faced with the
same problems that obtain in the conception and design of any unit of
complex equipment. These included the economic feasibility, reliability,
simplicity, and versatility of such a machine.
Economic Feasihilitij
This can be determined by comparing the cost of performing the opera-
tions to be made by the proposed machine with the cost by alternative
methods. Estimates indicated that the cost of the machines could be re-
covered within two years by the saving in labor that would be effected.
Reliability
Reliability has two connotations, (1) freedom from interruptions of
production because of mechanical or electrical failure and (2) consistent
reproducible performance. A rugged mechanical design combined with
the use of the most reliable electrical components available is necessary.
In addition, safeguards are required to protect the equipment from me-
chanical or electrical damage. To achieve consistent reproducible per-
formance, it is important that testing circuits of adequate stability be
used. Besides, it was recognized that each circuit should be so ar-
ranged that in case of a circuit failure, there would be immediate and
positive action by the machine to prevent acceptance of defective prod-
uct. All circuits are designed to provide positive acceptance. This means
that the machine must take action to accept each item of product at
each test position. In the case of the dielectric strength tests, a self-
checking feature is included.
Fig. 1 — Types of capacitors and networks tested.
AUTOMATIC MACHINE FOR TESTING CAPACITORS AND NETAVORKS 1181
SimTplicity
This type of equipment is operated by non-technical personnel. To
'minimize the possibility of improper operation of the equipment, it is
important that adjustments and judgment decisions by the operator be
minimized. From a production standpoint, it is important that the ma-
chine be designed to permit quick changes to handle the variety of prod-
uct to be tested. All "set-ups" are made by the operator and the switch-
ing of circuits and changing of contact fixtures are simply and easily
done.
Versatililij
The product tested by this machine includes a variety of physical
sizes and terminal arrangements with a wide range of electrical test
requirements (Fig. 1).
a. Physical Sizes. The aluminum containers for this type of capacitors
and R.C. Networks all have the same nominal length and width but are
made in three different thicknesses.
b. Terminals. The product is made with terminals of two different
lenths, two different spacings, and four different patterns connected in
eight combinations. It is necessary to provide contact fixtures and
switching facilities to handle all of these combinations.
c. Electrical Tests
(1) Dielectric strength tests are made between terminals, and between
terminals and can, on single unit packages. Two-unit packages require
an additional test between units.
(2) Capacitance: The capacitance of the product to be tested ranges
from 0.02 mf to 5.0 mf or any combination within this range in one- or
two-unit packages with no series resistance in the case of capacitors, but
with a series resistor from 100 ohms to 1,000 ohms in the case of net-
works. This problem is discussed in more detail in the description of the
capacitance test circuit.
(3) Insulation Resistance : The minimum requirements vary from 375
megohms to 3,000 megohms.
(4) Impedance: The RC networks have impedance requirements at
15 kc that range from 100 ohms to 1,000 ohms.
MECHANICAL ASPECTS OF TESTING MACHINE
Packaging of the product precludes a magazine type of feed because
the variety of terminal combinations associated with two-unit packages
necessitates orientation in the contact fixtures that can not be done by
1182 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
1. HANDWHEEL FOR POSITIONING TEST FIXTURES.
2. ROTARY FEED MECHANISM.
3. PRODUCT PASSING ALL TESTS EJECTED FROM FIXTURE.
4. INSULATION RESISTANCE TEST PANEL AND TERMINAL
COMBINATION "setup" SWITCHES.
5. CABINET HOUSING TEST CIRCUITS.
6. CONTAINERS FOR REJECTED PRODUCT.
Fig. 2 — Testing machine in operation.
mechanical means. A turret type construction is used to permit one
operator to perform both the loading and unloading operations.
Fig. 2 shows this machine in operation. The networks or capacitors
are fed into the fixtures by an operator and as the turret carries the fix-
tures past the feed mechanism, rollers on the feed mechanism are syn-
chronized with the fixtures and the roller forces the unit under test into
the contact fixture against a spring loaded plunger to make contact with
the fixture contact springs. Also, synchronized wdth the feed mechanism
is the closing of the gripper hook on the bottom end of the can contain-
ing the unit under test.
AUTOMATIC MACHINE FOR TESTING CAPACITORS AND NETWORKS 1183
REJECT
CHUTE
UPPER FIXTURE
FOR SHORT
TERMINAL PRODUCT.
PRODUCT ON TEST
GRIPPER HOOK
PIN FOR
SYNCHRONIZING
ROTARY FEED
MECHANISM.
gripper h00;<
follower arm
and roller.
"acceptance"
SOLENOID plunger
"acceptance"
solenoid.
Fig. 3 — View of rejection and acceptance mechanisms.
commutator brush assembly
and associated wiring.
UPPER CONTACT FIXTURE
FOR SHORT TERMINAL
PRODUCT.
OVERLOAD SLIP CLUTCH
AND OVERLOAD SHUT-OFF
SWITCH.
Fig. 4 — View of turret.
1184 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 195G
The acceptance or rejection of a unit under test at any one of the six'
test positions depends on whether the test on the unit energizes the i
"acceptance" solenoid associated with that test position. The gripper
hook, which locks the unit under test in the contact fixture, is con-
nected to a release shaft, follower arm, and roller (see Fig. 3). The roller
rides in a track in which the plunger of each "acceptance" solenoid hes,
unless removed by energizing the solenoid from its associated test cir-i
cuit. In the case of a defective unit, the acceptance solenoid is not ener- ■
gized and the roller in passing over the plunger of the "acceptance" »
solenoid trips the gripper hook and the spring loaded plunger in the 'H
contact fixture ejects the defective unit. Units that pass all tests are
ejected on a turntable to the left of the operator from which they are
stacked in handling trays by the operator.
The turret assembly includes the test fixtures, the gripper hooks and
associated release shaft, follower arm and I'oller, and the brush assembly
DIELECTRIC STRENGTH CONTROL
PANEL.
RESISTANCE STANDARDS FOR
IMPEDANCE TEST CIRCUIT.
SENSITROL RELAY FOR IMPEDANCE
TEST CIRCUIT.
5 KILO-CYCLE OSCILLATOR.
POWER SUPPLIES AND SWITCHING
PANELS.
Fig. 5 — Control panels for dielectric strength and impedance tests.
AUTOMATIC MACHINE FOR TESTING CAPACITORS AND NETWORKS 1185
connected to the test fixtures. The commutator is stationary and its
segments are connected to the test circuit through permanent wiring.
Fig. 4 shows the turret. Each fixture has two sections, one above the
other, with the contacts wired in parallel. The lower section is designed
for making contact to stud mounted units with long terminals and the
upper section for strap mounted units with short terminals. To change
the machine "set-up" from one fixture to the other, the turret assembly
i.s raised or lowered by means of the hand wheel, shown on Fig. 2, lo-
cated at the right of the operator. This feature was incorporated in this
machine to facilitate rapid "set-up" which is essential for testing small
lots. An overload clutch is incorporated in the driving mechanism to
prevent mechanical damage to the machine in case of a "jam".
Fig. 5 shows the control panels for dielectric strength and impedance
and Fig. 6 shows the control panels for the capacitance circuits.
* 'JSi. 'ii.
ij;; CAPACITANCE STANDARDS
FOR PADDING TEST
CIRCUIT ON UNIT NCI
-CAPACITANCE STANDARD
SERIES-PARALLEL
AND RANGE
SELECTOR SWITCHES.
CAPACITANCE STANDARDS
FOR PADDING TEST
CIRCUIT ON UNIT N0.2
Fig. 6 — Control panels for capacitance circuits.
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1186
> AUTOMATIC MACHINE FOR TESTING CAPACITORS AND NETWORKS 1187
ELECTRICAL ASPECTS OF TESTING MACHINES
Tests are applied to the product in sequence during one revolution of
the turret.
1. Dielectric strength test between terminals and can, and between
terminals and studs.
2. Dielectric strength test between units in the same can when the
can contains two units.
3. Dielectric strength test between terminals of each unit.
4. Impedance test.
5. Capacitance test.
6. Insulation resistance test.
Dielectric Strength Test Circuit Operation
Since the three dielectric strength tests are made on similar circuits,
the operation of one of these circuits is described using the nomenclature
and circuit designations shown in Fig. 7. A graphic interpretation of the
circuit operations shown in Fig. 7 is given in Fig. 8.
The "heart" of each circuit is a calibrated current sensitive relay K2
that operates on minute values of current resulting when a defective
unit under test attempts to charge on the "test" commutator position.
CAPACITOR ATTACHED TO INITIAL
ICHARGE COMMUTATOR SEGMENT
I
3 SECONDS
TEST
CAPACITOR
®
DEFECTIVE
PRODUCT
; CAPACITOR CHARGED
ACCEPTABLE /Os
PRODUCT W
K2
K3
K4
o-
CAPACITOR
ATTACHED
TO TEST
SEGMENT
OPENS K5
OPERATORS PATH
(PRODUCT REJECTED)
K2-
K3-
I-l
LAMP
TEST CIRCUIT
NORMAL
->
RESETS
TEST
CIRCUIT
T
■^
2 SECONDS
v;s2
CAM SWITCH
--K5
2| SECONDS
S4
CAM SWITCH
K9
CAPACITOR
DISCHARGED
--K7,K11
ACCEPTANCE
SOLENOID,
PRODUCT
ACCEPTED
wCAMMED TIME
■SWITCH
:k6
K2
K3
--*^^1 %^\
I-l
LAMP
Fig. 8 — Sequence chart for dielectric strength test circuit operation.
1188 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
Two commutator segments are required to make a dielectric strength
test. These segments are known as "initial charge" and "test". After
the unit under test has been charged at the test voltage for three sec-
onds on the "initial charge" segment, it passes to the "test" segment in'
which the unit is again connected to the test voltage through relay K2,'
current limiting and calibrating resistors R3 and R4 and the contacts;
on the preset terminal selecting relays KIO. ■.
One of the two conditions (under heading A and B below) may be^
encountered in making this test and the circuit operation for each will
be discussed separately.
A. Circuit Operation for AcceptaUe Product. An acceptable product
retains the charge received on the "initial charge" segments and when!
this unit reaches the "test" segment, no further charging current of a-
magnitude great enough to operate relay K2 will flow through the unit.
Two seconds after the unit under test has been connected to the test
segment, a cammed timing switch S4 closes to operate discharge relay K9
to discharge the unit under test to ground through R7. The "self-check-"
ing" feature mentioned earlier in this article under "Design Considera- :
tions" functions as follows: After the unit under test has been on the
"test" segment for approximately 2% seconds, a cammed timing switch ;
(not shown) closes the memory test relay K6 which in turn closes the \
"go" calibration indicator relay K5 and the "A" contacts on this relay;
grounds the high voltage test circuit through resistor R6. This resistor |
is of such a value as to permit sufficient current to operate relay K2. i
The contacts on relay K2 are not adequate to carry much current, so '
an auxiliary relay K3 is closed through contacts "A" on relay K2.
Contacts "B" on relay K3 closes the indicator light circuit II and oper-
ates relay Kll and the acceptance solenoid K7. Contacts "A" on the
same relay lock relay Kll. The circuit is reset for the next vmit to be
tested by momentarily opening the reset cammed switch S2. Relay Kll
was added to the circuit to eliminate a "sneak circuit" that occurred
occasionally following the reset when relay K5 opened faster than relay
K3. This would result in relay K4 operating to reject the next unit tested.
Relay Kl is controlled by switch SI operated by the manual control
Tl on the test voltage power supply. The function of this relay is to add
calibrating resistor R4 to the test circuit for voltages above 1,000 volts.
Resistor R5, relay K8, and switch S3 control the manual calibrating
"No Go" circuit for breakdown indicating relay K2.
B. Circuit Operation for Defective Product. Defective product will not
retain the charge it received on the "initial charge" segment and when
it reaches the "test" segment, current will flow through the breakdown
AUTOMATIC MACHINE FOR TESTING CAPACITORS AND NETWORKS 1189
indicating relay K2 in an attempt to charge the defective unit, l)ut this
current will close relay K2 which in turn closes relay K3. This completes
the circuit through the "B" contacts of relays K3, K5, and Kll to close
memory relay K4. The closure of relay K4 prevents the memory test
I relay KG from closing the "go" calibration indicator relay K5, thereby
heaving contact "C" open on relay K5 and no power is applied to the
"acceptance solenoid" K7 circuit, which rejects the unit under test.
IMPEDANCE — • TEST CIRCUIT OPERATION
The impedance test is made with a 15-kc circuit (see Fig. 9). One arm
of the circuit, composed of resistor R12 paralleled by capacitor C5 and
the imit under test, is compared with another arm, composed of resistor
Pvll, paralleled by capacitor C4 and either one of two resistance boxes,
R13 and R14 respectively, representing maximum and minimum im-
pedance limits. The detector consists of a balanced diode V2 with a 1-0-1
microampere sensitrol relay K24 connected between the diode cathodes.
If the impedance of the unit imder test falls within the limits for which
the resistance boxes were set, the acceptance solenoid will be energized
to accept the unit under test. A product outside the preset limits is re-
jected because the acceptance solenoid is not energized.
The circuit operation is discussed for the following four conditions
under A, B, C, and D.
A. Impedance Test on Dual Unit Capacitors
This test is made on capacitors to prevent shipment of resistance-
capacitance networks mislabeled as capacitors. Fig. 9 shows dual unit
networks connected to the test terminals. Capacitors to be tested are
connected to these same terminals. The greater than minimum test
cutout relay K18 is preset closed by the switching circuit K23. The
cammed memory reset timing switch S14 (normally closed) is opened
momentarily to clear relay K19, K20, and K21 at the start of the test.
The sensitrol relay reset switch S16 is cammed shut momentarily to
reset the contactor on the sensitrol relay K24. With relay K2(3 open, the
"less than maximum" resistance box R13 is connected to the test cir-
cuit. If unit "A" of the dual unit capacitor under test is acceptable
product, the contactor on sensitrol relay K24 will close on contact "A",
which applies power to close and lock test No. 1 "less than maximum"
memory relay K19. Cam operated switch S13 applies power to close
relay K26 to connect the "greater than minimum" resistance box R14
into the test circuit. This resistance box is set on zero ohms when capaci-
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1190
AUTOMATIC MACHINE FOR TESTING CAPACITORS AND NETWORKS 1191
tors are tested. Sensitrol relay reset switch S16 is cammed shut momen-
tarily to reset sensitrol relay K24, after which the sensitrol relay con-
tactor closes on its "B" contact, thereby applying power to close and
lock test No. 1 "greater than minimum" memory relay K21.
Switch S13 is cammed open which opens relay K26 and connects the
"less than maximum" resistance box R13 into the test circuit. At the
same time switch S12 is cammed shut to close relay K27 which discon-
nects unit "A" from test and connects unit "B" to the test circuit.
Switch S16 is cammed shut momentarily to reset the sensitrol relay con-
tactor. If the unit "B" on test is an acceptable product, the sensitrol relay
contactor will close on its "A" contacts and applies power to close and
lock test No. 2 "less than maximum" memory relay K20 through con-
tacts "B" of relay K27.
Switch S13 is cammed shut to close relay K26 and connect the "greater
than minimum" resistance box R14 into the test circuit. Switch S16 is
cammed shut momentarily to reset the sensitrol relay K24 after which
its contactor closes on the "B" contact for acceptable product. Mem-
ory circuit timing switch S15 is cammed shut and power from one side
of the 110 volt ac line flows through the acceptance solenoid, contacts
"A" on relay K19, contacts "A" on relay K20, the closed contacts on
relay K18 to the other side of the 110-volt ac line to close K25 and to
accept the dual unit capacitor under test. The failure of either relay K19
or K20 to operate because of defective product tested opens the ac-
ceptance solenoid circuit and rejects the capacitor tested.
B. Impedance Test on Single Unit Capacitors
The impedance test on a single unit capacitor is identical with the
testing of dual unit capacitors, except test No. 2 cutout relay K22 is
preset closed and test No. 2 "less than maximum" memory relay K20
is not operated since only a single unit is tested.
C. Impedance Test on Dual Unit Networks
The impedance test on dual unit networks is identical with the test
for dual unit capacitors, except the "greater than minimum" test cut-
out relay K18 is not preset closed and the resistance boxes R13 and R14
are set to represent maximum and minimum limits.
D. Impedance Test on Single Unit Networks
The impedance test on single unit networks is identical with the test
of dual unit networks except test No. 2 cutout relay K22 is preset closed
for the same reason given above for the test of single unit capacitors.
1192 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
1
Fig. 10 — Details of modified microfarad meter.
CAPACITANCE TEST CIRCUIT OPERATION
The wide range of capacitance values to be measured, both with and
without the series resistance in resistance-capacitance networks, and the
one and two-unit construction of the product imposed limitations on the
type of capacitance measuring circuits that could be used in this ma-
chine. The method selected consists of modified Weston Model 372
microfarad meters that automatically set up external circuits associated
with the meters to accept or reject the product as determined by limits
preset into the machine.
Two decade capacitance boxes, having a range from 0.001 to 1.0 mf
in steps of 0.001 mf are connected in series or parallel with the capacitoi'
on test to make the resultant capacitance fit the range of the meter and
control the maximum and minimum limits. This procedure increases the
number of capacitor codes that may be tested on a given meter. Capaci-
AUTOMATIC MACHINE FOR TESTING CAPACITORS AND NETWORKS 1193
tors from 0.02 to 5 microfarads are tested on this machine to an accuracy
of ±2 per cent.
The modified microfarad meters are equipped with two brass seg-
ments, covered with an overlay of silver (Fig. 10). These segments are
mounted end to end in a predetermined cutout portion of the meter
scale, representing maximum and minimum capacitance conditions. The
physical distance between the adjacent ends of these two segments is as
small as possible without the two segments touching. A small silver con-
tact is mounted on an insulated portion of the meter pointer, directly
at)Ove but not touching the segments while the meter pointer traverses
its arc of rotation. The armature of the relay, mounted on the meter,
i actuates a contactor arm which forces the silver contact on the pointer
I down against the silver overlay segment, thus closing external circuits
connected to the segments and contactor.
I The testing machine is equipped with three ranges of the special
microfarad meters as follows:
1. Suppressed scale from 1.2 to 1.8 mf, with the dividing point be-
tween the two segments at 1.60 mf.
2. Suppressed scale from 0.25 to 0.75 mf, with the dividing point be-
tween the two segments at 0.63 mf.
3. Suppressed scale from 0.051 to 0.075 mf with the dividing point
between the two segments at 0.062 mf.
Two meters for each of the above ranges are necessary in each testing
machine, one for each unit in a dual unit. Likewise, four capacitance
boxes are necessary, two for each unit in a dual unit.
The discussion that follows, which is divided into two headings, A
and B, is a detailed description of the capacitance test circuit. The cir-
cuit component designations are those shown in Fig. 11.
A . Capacitance Test on Dual Unit Capacitors or Networks
The cammed switch S5 is opened momentarily at the beginning of the
test to restore the test circuit to normal; following this, the cammed
switch S8 closes and operates relay K14, which applies power and closes
the power supply circuit through the microfarad meters and the capacitor
on test.
The capacitance decade box "less than maximum" C2 is shown in
series with test capacitor No. 1 by the preset series-parallel switch SIO,
and in a like manner a capacitance box is connected in series with test
capacitor No. 2.
1194 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
'im^
AUTOMATIC MACHINE FOR TESTING CAPACITORS AND NETWORKS 1195
Note: The capacitance decade box for Test No. 2 is not shown in Fig.
11. Also, only the segments for M2 Test No. 2 microfarad meter are
sliown.
If capacitor units No. 1 and No. 2 under test are acceptable product,
the pointer on the microfarad meters Ml and M2 will both swing to
segment "A". The cammed switch S7 will close and energize the relay
on the microfarad meters (not shown on meter M2) which will operate
the meter contactor and close the circuit through segments "A" of meters
Ml and M2 and apply 24 volts dc to close and lock the "less than maxi-
mum" memory relay K12.
The cammed switch S7 is opened to release the meter pointer from
segments "A" on Ml and M2. Cammed swdtch S8 is opened momen-
tarily to release relay K14 which removes the test voltage from the
capacitors on test and from meter Ml and M2. During this interval
cammed switch Sll is closed to energize relay K16 which connects the
"greater than minimum" capacitance box C3 in series with capacitor
unit No. 1 on test and meter Ml. In a like manner a second "greater
than minimum" capacitance decade box (not shown on Fig. 10) is con-
nected in series with capacitor unit No. 2 and microfarad meter No. 2.
If the capacitor units No. 1 and No. 2 under test are acceptable product,
the microfarad meter pointers will swing to segments "B". The cammed
switch S7 will close and energize the relay on the microfarad meters Ml
and M2 which will operate the contactor that depresses the Ml and M2
meter pointers against segments B and closes and locks the "greater than
minimum" memory relay K13. With relays K12 and K13 closed as
described above, the cammed switch S6 is closed which operates the
acceptance solenoid K17 through the "A" contacts on relays K12 and
K13 to accept the dual unit capacitor under test.
It may be readily observed that in case either or both of the capacitor
units on test are out of limits, the circuit will not close either or both
relays K12 and K13, w'hich would leave the acceptance solenoid K17
circuit open, and the product would be rejected.
B. Capacitance Test of Single Unit Capacitors or Networks
The capacitance test of single unit capacitors is the same as for dual
unit capacitors, except test No. 2 circuit and test No. 2 microfarad
meter M2 are not used. Test No. 2 cutout relay K15 is closed to apply
ground to its contacts B and D.
CURRENT LIMITING RESISTORS
R15
SWITCHING
CIRCUITS
S2I
TEST NO. 2
CUTOUT SWITCH
Fig. 12 — Simplified schematic of insulation resistance test circuits.
1196
AUTOMATIC MACHINE FOR TESTING CAPACITORS AND NETWORKS 1 197
IXSULATION RESISTANCE TEST CIRCUIT OPERATION
In general, the insulation resistance test consists of a charging period
and a test period. The charging of the unit inider test recjuires 10 posi-
tions or 30 seconds time to insure that the unit is thoroughly charged
before it reaches the test position. At the test position the capacitor or
network on test is connected to form part of a voltage divider in the
grid circuit of a sensitive balanced detector. This sets up relays to accept
or reject the unit vmder test depending on whether the unit meets the
limits for which the circuit was preset and calibrated. Two insulation
resistance circuits are rec^uired, one for each unit in a dual unit capacitor
or network. A calibrating circuit is provided by switch S23 and resistors
lUl, IU2, and R43.
The discussion that follows is a detailed description of the sequence of
operation of the insulation resistance test circuit. The component desig-
nations are those shown on Fig. 12. The discussion is divided into two
headings A and B as follows:
A . Insulation Resistance Test on Dual Unit Capacitors or Networks
The capacitor or network on test is automatically connected in suc-
cession to the INITIAL CHARGE POSITION, the LONG SOAK POSITION and
FIVE CONDITIONING POSITIONS which assures that the acceptable product
is thoroughly charged before it reaches the test position. The switching
circuits K28, K29, K30, K31 switch S18, and the temperature compen-
sating switch S17 are manual preset switch circuits for the particular
code on test.
For the sake of simplicity, the balanced detector and the reset solenoid
for sensitrol relay K3-1: for test circuit No. 2 are not shown. If the insula-
tion resistance of the imits on test meets the limits for which the circuit
was calibrated and preset, the contactor on K33 and K34 both close on
the "A" contacts. Switch S20 is then cammed closed to apply power
through the "A" contacts on the sensitrol relays to energize the accept-
ance solenoid K36 to accept the units on test. At the close of the test,
capacitor discharge timing switch S22 is cammed closed, thereby closing
the capacitor discharge relay K32 which discharges the imits on test
before they are ejected as acceptable product. It may be readily observed
from the schematic that a unit or units defective for insulation resistance
will fail to close either or both of the "A" contacts on the sensitrol relays
K33 and K34, which leaves the acceptance solenoid circuit K3G open,
thereby rejecting the units tested.
1198 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
B. Insulation Resistance Test on Single Unit Capacitors or Networks
The insulation resistance test on single unit capacitors or networks is ;
the same as for dual units, except the second test circuit is not required
and test No. 2 cutout switch S21 is closed to operate test No. 2 cutout '
relay K35 which eliminates the second test circuit and its sensitrol relay
K34.
CONCLUSION
This machine has been in successful operation on a multishift basis
for several years and has proven itself economically. Inspection of the
product tested shows that the machine's performance, quality wise, is
highly satisfactory. Difficulties that have been encountered were largely
those associated with product handling, contact fixtures, etc. Machines
of this type that are planned for the future will make use of circuitry
developed since this machine was built, but many of the features de-
scribed will be incorporated.
ACKNOWLEDGMENTS
The authors wish to acknowledge the contributions to the develop-
ment of this machine of G. E. Weeks of the Western Electric Company
S. V. Smith and S. E. Frisbee of the Electric Eye Company.
A 60-Foot Diameter Parabolic Antenna
for Propagation Stndies*
By A. B. CRAWFORD, H. T. FRIIS and W. C. JAKES, JR.
(Manuscript received February 2, 1956)
A solid-surface parabolic antenna, sixty feet in diameter and of alumi-
iium construction, has been erected on a hilltop near Holmdel, New Jersey.
This antenna can be steered in azimuth and elevation and was specially
ih signed for studies of beyond-the-horizon radio propagation at frequencies
of 460 mc and 4,000 mc.
The electrical properties of the antenna and the technique of measure-
ment are described; construction and mechanical details are discussed briefly.
IXTRODUCTION
Studies in recent years have demonstrated that transmission of useful
amounts of microwave energy is possible at distances considerably far-
ther than the horizon. ^ The exact mechanism responsible is not as yet
completely understood, although scattering by atmospheric irregularities
seems to play a significant part. A program to study the nature of these
effects has been started at the Holmdel Laboratory. An important and
necessary tool for this work is a steerable antenna having unusually high
gain and narrow beam width. Such an antenna has been built, and it is
the purpose of this paper to describe its design and the methods used to
measure its radiation properties.
DESCRIPTION OF THE ANTENNA
The antenna is a 60-foot diameter paraboloid made up of forty-eight
radial sectors, each constructed of sheet aluminum. Each sector is held
to the correct doubly-curved surface by reinforcing ribs, and all are
fastened to a central hub eight feet long and thirty inches in diameter.
During assembly, the axis of the paraboloid was vertical; thus no scaf-
* This work was supported in part by Contract AF 18(600)-572 with the U.S.
Air Force, Air Research and Development Command.
' Proc. I.R.E., October, 1955, contains many papers by workers in this field.
1199
1200 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
Fig. 1 — ■ Fastening the I'adial sectors to the hub.
folding was required. Figs. 1 to 5 illustrate the paraboloid construction
and support. The weight of the antenna is carried on a vertical column
which is mounted on bearings to permit movement in azimuth. The
column is held upright by a tripod structure. The central hub of the
paraboloid is fastened to a steel girder which extends to the rear along
the paraboloid axis and is pinned to a yoke carried by the vertical col-
umn, thus permitting movement in elevation. The antenna is scanned
by two motors mounted on an A-frame and connected to the end of the
axial girder by crank mechanisms. The total scanning range of the an-
tenna is about 3° in both azimuth and elevation.
The antenna is designed for use at frequencies of 460 mc and 4,000
mc. The tolerance on the parabolic reflecting surface is set by the higher
frequency and thus must be ±t6 i^^ch to meet the usual ±X/i6 criteria.
The focal length is 25 feet, so that the total angle intercepted by the
paraboloid as seen from the focal point is 124°. Design of a feed horn for
A 60-FOOT PARABOLIC ANTENNA FOR PROPAGATION STUDIES 1201
this angle so that the illumination is tapered to — 10 db at the edge of
the paraboloid is not difficult; the horn used is diagramed in Fig. 6, with
dimensions given in wave-lengths. The feed horn is mounted in a tripod
.support extending out from the front surface of the paraboloid. It is made
strong enough so that two 460 mc horns can be mounted side by side.
The paraboloid itself weighs approximately 53-^ tons; the frontal Avind
'load for a 100 mph wind is about 40 tons. It is expected that winds of
this force will be withstood.
The antenna is mounted atop Crawford Hill near Holmdel, New
Jersey, at an altitude of 370 feet. It is aimed towards Pharsalia, New
i York, a distance of about 171 miles.
I MEASUREMENT TECHNIQUE
I The two important properties of the antenna which had to be deter-
' mined before it could be put into use were its gain and radiation pattern
at the operating frequencies of 460 mc and 4 kmc. It was also hoped to
Fig. 2 — Assembling the sectors.
I
Fig. 3 — The completed antenna.
Fig. 4 — Front view of the paraboloid.
1202
A 60-FOOT PARABOLIC ANTENNA FOR PROPAGATION STUDIES 1203
Fig. 5 — Antenna scanning motors.
0-30^
Fig. 6 — Feed horn dimensions.
measure these properties at 9.4 kmc to get some idea of how good the
mechanical tolerances actually are.
The first requisite for making antenna measurements is a suffi-
ciently uniform incident field. The source producing this field must be
located at a distance of at least 2b VX, (b is the paraboloid diameter),
which means a distance of about 0.6 mile at 460 mc, six miles at 4 kmc,
and thirteen miles at 9.4 kmc. An obvious and convenient place for the
sources was at Murray Hill, 22.8 miles away, which is on the transmis-
sion path to Pharsalia. Having located the sources at a suitable distance
it was then necessary to test the incident field for uniformity. A 64-foot
1204 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
4KMC
9.4KMC
Fig. 7 — Height run tower with the three standard horns during preliminary
studies of the incident field.
tower was used for this purpose, and the variation of the incident field
with height w^as measured before the antenna was erected. Figs. 7 and
8 show a typical set up. Height runs were taken at intervals of 15 feet
along a line normal to the direction of transmission in the plane which
w^ould eventually contain the antenna aperture. The results of these
tests showed that the Murray Hill location was satisfactory for the 4
and 9.4 kmc sources, with ground reflections giving rise to ±1 db varia-
tions with height. In each case several complete cycles occurred in the
60-foot height run so that an average signal level could be established
Avith an accuracy of a few tenths of db.
However, at 460 mc the variation with height was about 5 db, and
only a portion of one cycle was available, so that the average signal could
not be determined. The solution was to bring the source to a location
as close as possible to the effective ground reflecting surface. Such a
location was found at the far edge of a large body of water lying in the
path, and the source antenna was placed in a mobile truck 10 feet above
the water and eight miles away. The resulting variation with height was
now only about 1 db.
In all cases the variation of field at right angles to the direction of
transmission w^as found to be no worse than ±1 db; thus it was felt that
suitable sources for test at all three frequencies were now ready.
A 60-FOOT PARABOLIC ANTENNA FOR PROPAGATION STUDIES 1205
The standard method of measuring the gain of a microwave antenna
is to compare the signal received from the antenna to that from another
antenna whose gain is accurately known. A pyramidal horn of about 20
db gain is usually used as the standard. Such horns are readily available
at 4 kmc and 9.4 kmc, and, in principle, also at 460 inc. Under the
present set up, however, the physical dimensions of the standard horn
were limited by the necessity of raising the horn on a carriage attached
to the 64-foot tower. The largest horn that could be so mounted had an
aperture of 4 feet X 4 feet, or 1.8X on a side at 460 mc. Since the gain of
a horn of this small aperture size cannot be accurately calculated by the
usual formulas a scale model was made and tested at 4 kmc. The result
of this test showed that the actual horn gain was 15.05 db, which is
about 0.4 db more than the calculated gain.
A typical gain measurement on the 60-foot paraboloid was thus made
as follows:
1. The feed position and antenna orientation were adjusted to obtain
maximum received signal level.
Fig. 8 — Position of height run tower during gain measurements.
1206 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
2. The average incident field was determined by a height run with a
standard horn.
3. The decibel gain of the antenna was then calculated by adding the
db gain of the standard horn to the db difference in the signal levels
determined in (1) and (2).
The problem of adjusting the 60-foot antenna for maximum received
signal at 4 kmc and 9.4 kmc was complicated by the scintillations of the
/■^'^:^\\^
Fi{ij. 9 -A view of the iuitennus at Crawl'uiU Hill used for beyund-t he-horizon
propagation studies and showing the 60-foot, a 28-foot and an 8-foot paraboliod,
the latter between the two larger ones.
A 60-FOOT PARABOLIC ANTENNA FOR PROPAGATION STUDIES 1207
Table I
Frequency
460 mc
3.89 kmc
9.40 kmc
Area
Gain,*
db
38.90
57.44
65.12
Gain, db Meas.
37.0 ± 0.1
54.6 ± 0.2
61.1 ± 0.5
Ratio of
Effective
Area to
Actual
Area
3 db beam
width
1st Minima
Calc.
Meas.
0.65
0.52
0.40
2.35°
0.28°
0.12°
2.45°
0.3°
0.14°
-33db
-25db
1st Minor
lobes
-23db
-18db
47r
* The area gain is defined as 10 log — — , where A is the paraboloid projected
area, 2,830 square feet.
incident field at these frequencies due to the remote location of the
source. Accordingly, instead of adjusting the feed position for maximum
signal level, it was adjusted to give vertical and horizontal radiation
patterns having the best possible symmetry, deepest minima, and lowest
minor lobes. It was then assumed that this was also the point of maxi-
mum gain. At 460 mc the scintillations were so small that the conven-
tional technique of adjusting for maximum output was effective.
A double detection receiver was used for making all measurements.
Signal level decibel differences were established by an attenuator in the
intermediate frequency (65 mc) channel, and could be determined to an
accuracy of dz0.02 db.
RESULTS
Carrying out the measuring procedure described above the results
given in Table I were obtained. At 460 mc the restricted scanning range
did not permit inspection of the minor lobes.
CONCLUDING REMARKS
The overall performance of this antenna is considered to be excellent.
In general the radiation patterns are clean with satisfactory minor lobe
structure. The good performance at 9.4 kmc (61 db gain) is particularly
gratifying, since the mechanical tolerance of zt^fe inch is equivalent to
itX/7 at this frequency.
As stated earlier, this antenna was designed to provide a research tool
for propagation studies and thus has some features which are neither
necessary nor desirable in an antenna intended primarily for communi-
cation use. A consideration of the problem of providing a sturdy 60-foot
1208 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER, 1956
antenna for fixed point-to-point service led to the square "bill-board"
design* and antennas of this type are now in production.
ACKNOWLEDGEMENTS
The construction of the antenna described in this paper was carried
out under the general direction of H. W. Anderson, Supervisor of the
Holmdel Shops Department. The paraboloid was assembled in place
by members of the Carpenter Shop supervised by C. P. Clausen. Daniel
Beaton, of Lorimer and Rose, served in an advisory capacity on some
features of the construction. Assistance in the design and testing of the
antenna was given by many members of the technical staff.
* A picture and short description of this antenna appeared in Bell Laboratories
Record, 34, p. 37, Jan., 1956.
^i
The Use of an Interference Microscope
for Measurement of Extremely
Thin Surface Layers
By. W. L. BOND and F. M. SMITS
(Manuscript received March 15, 1956)
A method is given for the thickness measurement of p-type or n-type sur-
face layers on semiconductors. This method requires the use of samples with
optically flat and reflecting surfaces. The surface is lapped at a small angle
in order to expose the p-n junction. After detecting and marking the p-n
junction, the thickness is measured by an interference microscope. Another
application of the equipment is the measurement of steps in a surface. The
thickness range ineasurahle is from 5 X 10^^ cm to 10~^ cm.
INTRODUCTION
Extremely thin p-type or n-type surface layers can be obtained on
semiconductors by recently developed diffusion techniques.^- - Layer
thicknesses of the order of 10~^ cm are currently used for making diffused
base transistors.^' ^ The thickness of the diffused layer is an important
parameter for the evaluation of such transistors. Its measurement is
facilitated by lapping a bevel on the original surface, thus exposing the
p-n junction within the bevel where the thickness appears in an enlarged
scale. With a sharp and well defined angle, one would obtain the thick-
ness by the measurement of the angle and of the distance between the
vertex and the p-n junction.
However, it is extremely difficult to obtain vertices sharp enough for
measurements of thicknesses of the order of 10~* cm. To avoid this diffi-
culty, an interferometric method was developed in which the depth is
measured directly by counting interference fringes of monochromatic
light. The method can also be used for the measurement of small steps
1 C. S. Fuller, Phys. Rev., 86, p. 136, 1952.
2 J. S. Saby and W. C. Dunlap, Jr., Phys. Rev., 90, p. 630, 1953.
' C. A. Lee, B.S.T.J., 35, p. 23, 1956.
* M. Tanenbaum and D. E. Thomas, B.S.T.J., 35, p. 1, 1956.
1209
I
1210 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
and similar problems occurring, for example, in the evaluation of con-
trolled etching and of evaporated layers.
PRINCIPLE^
A half-silvered mirror is brought into contact with a reflecting surface.
If this combination is illuminated with monochromatic light, one ob-
serves interference fringes. Dark lines appear where the distance between
mirror and surface is n X X/2, where n is an integer. Between two points
on adjacent fringes the difference in this distance is therefore X/2. Hence j
the fringes can be regarded as contour lines for the distance between
the mirror and the surface under consideration. Since the mirror is op-
tically flat, one can deduce the profile of the surface. Equidistant and
parallel fringes, for example, prove the surface to be flat. By taking the
profile across a bevel or a step, one is able to measure the depth of one
part of the surface with respect to another optically flat part of the sur-
face. The reflectivity of the crystal surface should be as high as possible,
and that of the mirror should be of the same order. The fringes are then
produced by the interference of several wave trains which make the
fringes very sharp, and one can measure fractions of X/2. With the equip-
ment described here, one is able to interpolate to 3^o of X/2 or less.
Since small linear dimensions are involved, this principle was adapted
for use under a microscope. Hence, it is possible to measure small linear
dimensions and the correlated depth simultaneously.
The measurement of small steps, or steps not too steep in an other-
wise flat surface, can be done without altering the sample. For measure-
ment on steep and high steps a bevel must be lapped on the sample.
For the measurement of p-type or n-type surface layers on semicon-
ductors, it is essential to lap a bevel on the original surface. The p-n
junction is thus exposed and can be found by an electrical method. After
marking its position within the bevel, it is then possible to measure its
depth with respect to the original surface by taking the profile across
the bevel. The marking has to be such that it will be visible in the fringe
pattern. By a proper adjustment of the optical flat, a fringe pattern can
be produced in which the profile is easily interpreted and the depth
measurement amounts to a counting of fringes.
PREPARATION OF THE SAMPLES 1
The method requires the use of samples with optically flat and highly
reflecting surfaces with respect to which a depth can be measured. It is
' S. Tolansky, Multiple-Beam Interferometry of Surfaces and Films, Oxford, at
at the Clarendon Press, 1948.
INTERFERENCE MEASUREMENT OF THIN SURFACE LAYERS 1211
also advisable to use plane-parallel samples to facilitate the lapping of a
l)Ovel at a small angle.
For lapping, the sample is waxed with its back side to the face of a
short steel cylinder. The face is cut at a small angle. Angles of 0.5° or
1.0° are practical. The cylinder is placed in a jig, in svich a position that
approximately half of the sample surface projects above the plane of
'the jig (Fig. 1). A short grind on a slightly rough glass plate using a
line abrasive with water gives usable bevels. For a shiny finish just the
light degree of roughness of the glass is important. The use of a lapping
machine with a vulcanized fiber plate and fine abrasive gives a better
surface finish, but the ridge is not as sharp. A 0.5° bevel could be obtained
only on a glass plate.
Fig. 1 — Jig for lapping a bevel.
MARKING OF p-TYPE OR n-TYPE SURFACE LAYERS
In a sample with a p-type or n-type surface layer the junction is ex-
posed within the bevel. The next step is to detect and mark the junc-
tion.
The sample is fixed on a microscope stage which allows a micrometer
controlled movement in two directions (Fig. 2 shows a Wilder microm-
eter cross slide). The sample is oriented in such a way that the ridge
is parallel to one direction of movement (y-direction). One or two lines
of aquadag are applied to the surface of the sample, perpendicular to
the ridge. The acjuadag should be diluted with water in such a proportion
as to achieve a thin film w^hich is non reflecting.
A needle is fixed to the base of the stage with a suitable linkage leav-
ing a vertical degree of freedom. The needle is brought into contact with
the surface of the sample outside the acjuadag. Thus, the sample can be
moved under the needle while the needle maintains contact. In a suitable
electrical circuit, the needle serves as detector of the junction. The sam-
ple is moved in the direction perpendicular to the ridge (x-direction)
1212 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
T:
Fig. 2 — Apparatus for locating and marking p-n junctions.
1
until the needle rests on the p-n junction as seen by the electrical detec-
tor. By moving the sample in the y-direction the same needle scrapes a
line through the aquadag. In this line, the reflecting sample surface is
bared and thus, a reflecting line is produced within a non-reflecting sur-
rounding and can be seen in the fringe pattern.
If the ridge of the sample is exactly lined up with the y-direction, the
needle moves along the junction and the line in the aquadag indicates
the position of the junction exactly. To minimize an error due to poor
alignment, it is advisable to locate the jimction close to the edge of the
aquadag. By doing this on two different sides of the coating, the average
INTERFERENCE MEASUREMENT OF THIN SURFACE LAYERS 1213
of both readings compensates the error. To obtain, however, the maxi-
mum of accuracy, one can locate the junction at any point. (See Fig. 3,
Point A). IVIoving the sample in the y-direction scribes a line through
the point at which the junction was found. A movement in the x-direc-
tion with the needle in the acjuadag marks a point B on this line. The
distance from this point to the junction can be obtained from the read-
ings on the micrometer. Thus, the exact point at which the junction was
located can be reproduced under the microscope.
DETECTION OF THE p-n JUNCTION
1. Thermoelectric Probe
The thermoelectric voltage^ occurring between a hot and a cold con-
tact to the sample, changes sign by crossing the junction with the hot
contact. The advantage of this probe is that it does not depend upon
the rectification properties of a p-n junction. The thermoelectric probe
is most suitable for germanium since lapping across a p-n junction nor-
mally produces a "short" between the two regions. However, it is likely
to give a p-reading on lightly doped n-material. It is therefore only
usable on heavily doped layers, where the nearly compensated zone is
very small. In the case of silicon, the junction normally maintains recti-
fying properties after lapping; thus, a photocurrent is present. This cur-
rent is superimposed upon the thermocurrent. Therefore, the thermo-
electric probe is only usable in the dark. The photoelectric method (see
below) is more convenient for these cases.
The thermoelectric probe used, consisted of a commercial phonograph
needle, which had a good hemispherical point and was surrounded by a
piece of ceramic tubing carrying a heating coil. Between needle and sam-
Fig. 3 — Schematic view of a scribed p-n junction.
« V. A. Johnson and K. Lark-Horowitz, Phys. Rev., 69, p. 259, 1946.
1214 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
pie a sensitive galvanometer is connected. It is unimportant whether the
contact is made to the p-type or to the n-type side of the sample. The
best results are obtained on freshly lapped and clean surfaces. It is,
therefore, advisable to keep the sample on the steel cylinder while ap-
plying the thermoelectric probe.
When applying the probe, the sample is moved in the x-direction to
the point of zero deflection on the galvanometer, whereby the point rests
on the junction.
2. Point Rectification on the Surface
This test is also usable on p-n junctions which are not rectifying. With
one fixed ohmic contact to the sample, the point rectification of the mov-
able needle can be displayed on an oscilloscope. By crossing the junction
with the needle, the characteristic changes from p-n to n-p. Thus, the
needle again can be placed on the junction.
This test was applied on lightly doped Ge-layers. The oscilloscope pat-
tern is not very definite, since on a lapped surface the point rectification
is poor. However, with some experience the junction can be located. It
is advisable to repeat the measurements several times. Boiling the sam-
ple in water before applying the probe improves the surface.
3. Photoelectric Probe
This method requires that the junction exhibit rectifying properties.
It is most successfully applied to silicon. Between the needle and a con-
tact to either the p-type side or the n-type side of the sample, a high
impedance voltmeter is connected. While the sample is strongly illumi-
nated, it is moved in the x-direction. When the needle crosses the junc-
n LAYER
P MATERIAL
Fig. 4 — ^ Arrangement for Cu-plating the p-tj^pe side of a p-n junction.
INTERFERENCE MEASUREMENT OF THIN SURFACE LAYERS 1215
tion, a change in the photoelectric voltage occurs. For more careful
measurements one might plot the photovoltage versus the x-coordinate
in units of the micrometer. Such a plot allows an accurate location of
the junction in these units. If the micrometer is set for this reading, the
needle will rest on the p-n junction.
4. Potential Prohe
This is another method for locating the junction where the junction
is at least slightly rectifying. One needs two contacts to the sample, one
on the p-type side and the other on the n-type side. When a current is
passed through the sample in the reverse direction, the voltage between
the needle and either contact shows a discontinuity at the junction. The
voltage can be plotted in a similar way as described for the previous
method, and thus the needle can be set on the p-n junction.
m
MONOCHROMATIC
LIGHT SOURCE
HALF-SILVERED
MICROSCOPE SLIDE
BEVELED CRYSTAL
Fig. 5 — Diagrammatic view of the light path in the interferometer.
1216 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
5. Plating the p-sidc of the p-ti Junction*
This method detects and marks the junction in one process without
using the micrometer arrangement, ^^oltages are applied in such a way
that only the p-type side is plated (See Fig. 4). Since the plating pro-
jects up and is not optically flat, it can be recognized under the interfer-
ometer. It has the advantage of showing the junction as a line. The dis-
advantage is that it is only convenient on rectifying p-n junctions
(silicon), with n-type layers since the plating ought to take place on the
body side of the p-n junction.
THE INTERFEROMETER
The main part of the interferometer is a microscope with illumination
through the objective. As a source of monochromatic light, a sodium
lamp for which X = 5.89 X 10~^ cm is most convenient. The use of a
Fig. 6 — Interferometer with light source.
This method was developed by N. Holonyak.
INTERFERENCE MEASUREMENT OF THIN SURFACE LAYERS 1217
shorter X would increase the resokition. However, a sodium lamp gives
enough light that one can easily work in daylight.
The microscope is mounted above a micrometer cross-slide of the same
kind as used in the procedure for marking the p-n junctions. The stage
carries a special sample support. Fig. 5 gives a diagrammatic view of
the light path in the interferometer. A normal microscope is used with
an attachment carrying a semi-transparent mirror. Fig. 6 shows a photo
of the complete arrangement, and Fig. 7 gives the details of the sample
support.
The prepared sample is waxed to a microscope slide and covered by
a half-silvered mirror. Both are placed on the adjustable lower jaw of
the sample support. The lower jaw is raised so that the upper jaw presses
against the mirror. In this position it is fixed by tightening the screw
in the back. Thus the mirror and sample are in contact, and the fringes
can be observed through the microscope. Three screws in the lower jaw
make it possible to change the relative position of mirror and sample.
Thus the fringe pattern can be adjusted to make it most suitable for the
particular case.
THE MEASUREMENTS
The measurement of a layer thickness was chosen to demonstrate the
principle of evaluating a fringe pattern. (See Fig. 8.) The first illustration
Fig. 7 — Sample support.
1218 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
AQUA DAG
"7^^
\
-ORIGINAL SURFACE
JUNCTION
BEVELED SURFACE
0.10
'^W
m
0.05
0
0.10
V
I
\
\
— («-
— 16-^^-
cr
m
1-
LU
I-
z
LU
U
z
X
0.05
0
0.10
1
/
I
i
1
I
\
V
1
- 17-
^-
0.05
V
\
\
-e--
-16.5-
^
10 20 30 40
n
Fig. 8 — Evaluation of the interference fringe pattern on a scribed 'p-n junction.
INTERFERENCE MEASUREMENT OF THIN SURFACE LAYERS 1219
COPPER-PLATED BODY
ORIGINAL
-SURFACE OF
GERMANIUM
BEVELED
SURFACE
Fig. 9 — Evaluation of the interference fringe pattern on a Cu-plated p-n junction.
"" • '*i«^^Nfciiir
Fig. 10 — Evaluation of the interference fringe pattern of a shallow step in a
surface.
1220 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
shows a sample with aquadag coating and the hnes marking the p-n
junction. Under this, three typical fringe patterns obtained on this sam-
ple are presented. As pointed out in the beginning, one can regard the
fringe pattern as contour lines for the distance between mirror and sam-
ple. The profile along any arbitrary straight line will show the structure
of the sample surface. The profiles along the marked x-axes are shown
to the right in each case. They were obtained by plotting the points of
intersection between the n-th fringe and the x-axis against n. The origi-
nal surface and the bevel (in this case 1°) are easily recognized. The
dashed line is an extrapolation of the original surface. The vertical line
marks the position of the p-n junction. The layer thickness is obtained
as the difference in n at this point between the extrapolated original
surface and the beveled surface. Note that the beveled surface need not
necessarily be flat.
.iii— i**-ir-*^
9
^S^WSIHpwSS?
jjpl^*.'
Fig. 11 ^ — Evaluation of the interference fringe pattern of a steep and high step
in a surface.
INTERFERENCE MEASUREMENT OF THIN SURFACE LAYERS 1221
In the second case the fringes turn liack. With a sUghtly different set-
ting of the mirror the fringes could be ahiiost parallel "wdth the turning
|)()int outside the field of sight. The fringe pattern then resembles the
lirst case, and therefore it might be easily misinterpreted.
The third case makes the plot unnecessary. The x-axis is chosen in
such a way that it coincides with a fringe in the original surface. Thus,
in the profile plot, the original surface is horizontal. Hence, the layer
thickness can be obtained by counting the number of intersecting fringes
between original surface and the p-n junction. This is, therefore, the most
convenient setting of the mirror.
The noted number gives in each case the layer thickness in "fringes."
All three cases are in essential agreement. The layer thickness in this
: case is
An X ^ = (16.5 ± 0.5) X ~ X 10"' cm
= (4.85 ± 0.15) X 10"' cm
j Fig. 9 gives the fringe pattern obtained with a silicon p-n junction
marked by the plating procedure.
The evaluation of steps in a surface is shown for two cases. The very
' shallow step in Fig. 10 is an example in which fractions of X.'2 are to be
measured. The step here is
^ X ^ = 0.195 X ^^ X 10"' cm = 5.75 X 10"' cm
a + 6 2 2
In Fig. 11 the step is so high and steep that it is impossible to correlate
the fringes crossing the step. But with the aid of the bevel, seen in the
lower part of Figure 11, a correlation is possible. The height of the step
along the drawn line is
*t)
(25 - 12) X ^ = 13 X ^ X 10"' cm = 3.8 X 10"' cm
The accuracy of the method depends mainlj^ on the (juality of the opti-
cally flat mirror since it serves as a plane of reference. A thin mirror is
likely to be slightly bent under the pressure of the clamp. Therefore, it
is advisable not to work with too high a pressure. For the measurement
of layer thicknesses the (juality of the original surface is also important.
An accuracy of 5 per cent is easily obtained using half-sih'ered micro-
scope slides for the mirror. These slides are essentially flat over the small
region covered by the microscope.
I
Bell System Technical Papers Not
Published in This Journal
Albrecht, E. G.,^ Dietz, A. E./ Christoferson, E. W.,® and Slot-
HOWER,, J. C.^
Co-ordinated Protection for Open-Wire Joint Use — Minneapolis
Tests, A.I.E.E. Commun. and Electronics, 24, pp. 217-223, May,
1956.
Anderson, P. W.^
Note on Ordering and Antiferromagnetism in Ferrites, Phys. Rev.,
102, pp. 1008-1013, May 15, 1956.
Atalla, M. M., see Preston, K., Jr.
Baker, W. O., see Winslow, F. H.
Benson, K. E., see Goss, A. J.
Bennett, W. R. ^
Techniques for Measuring Noise. Part III, Electronics, 29, pp. 162-
165, May, 1956.
Bennett, W. R.^
Electrical Noise, Part IV. Design of Low Noise Equipment, Electronics,
29, pp. 154-157, June, 1956.
Bennett, W. R.^
Electrical Noise. Part V. Noise Reduction in Communication Systems,
Electronics, 29, pp. 148-151, July, 1956.
Bennett, W. R.^
Methods of Solving Noise Problems, Proc. I.R.E., 44, pp. 609-638,
May, 1956.
* Bell Telephone Laboratories Inc.
^ Northwestern Bell Telephone Company,
^ Northern State Power Company, Minneapolis.
1223
1224 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
BOGERT, B. P.'
The VOBANC -A Two-to-One Bandwidth Reduction System. J.
Acous. Soc, 28, pp. 399-404, May, 1956.
Bonneville, S., see Noyes, J. W.
Boyd, R. C.^
Objectives and General Description of the Type-Pl Carrier System,
A.I.E.E. Commun. and Electronics, 24, pp. 188-191, May, 1956.
BoYET, H., see Weisbaum, S.
BuLLARD, W. R.,* and Weppler, H. E.-
Co-ordinated Protection for Open-Wire Joint Use — Present Trends,
A.I.E.E. Commun. and Electronics, 24, pp. 215-216, May, 1956.
Chynoweth, a. G.^
Surface Space Charge Layers in Barium Titanate, Phys. Rev., 102,
pp. 705-714, May 1, 1956.
Chynoweth, A. G.^
Spontaneous Polarization of Guanidine Aluminum Sulfate Hexahy-
drate at Low Temperatures, Phys. Rev., 102, pp. 1021-1023, May 15,
1956.
Chynoweth, A. G.^ and McKay, K. G.^
Photon Emission From Avalanche Breakdown in Silicon, Phys. Rev.
102, pp. 369-376, Apr. 15, 1956.
Dietz, A. E., see Albrecht, E. G.
Ditzenberger, J. A., see Fuller, C. S.
Dudley, H. W.^
Fundamentals of Speech Synthesis, J. Audio Engg. Soc, 3, pp. 170-
185, Oct., 1955.
Eberhart, E. K.,^ Hallenbeck, F. J.,^ and Perkins, E. H.^
Circuit and Equipment Descriptions of Type-Pl Carrier System,
A.I.E.E. Commun. and Electronics, 24, pp. 195-204, iMay, 1956.
'■ Bell Telephone Laboratories Inc. ^
2 American Telephone and Telegraph Companj^ Inc.
'' Ebasco Services, Inc., New York.
1
TECHNICAL PAPERS 1225
Ellis, H. M./ Phelps, J. W.,' Roach, G. L.,^ and Treen, R. EJ
Co-ordinated Protection for Open-Wire Joint Use — Ontario Tests,
A.I.E.E. Commun. and Electronics, 24, pp. 223-236, May, 1956.
Fuller, C. S.,^ and Ditzenberger, J. A.^
Diffusion of Donor and Acceptor Elements in Silicon, J. Appl. Phys.,
27, pp. 544-553, May, 1950.
Fuller, C. S.^
Some Analogies Between Semiconductors and Electrolyte Solutions,
Record of Chem. Progress, 17, pp. 75-93, No. 2, 1956.
Garrett, C. G. B., see Law, J. T.
Gaston, C. M.i
Stop Playing Hide-and-Seek with Engineering Drawings, Iron Age
Magazine, 177, pp. 100-101, May 17, 1956.
Gaudet, S., see Noyes, J. W.
Geller, S.^
The Crystal Structure of Gadolinium Orthoferrite, GdFeOs , J. Chem.
Phys., 24, pp. 1236-1239, June, 1956.
GiLLEO, M. A.i
Magnetic Properties of a Gadolinium Orthoferrite, GdFeOs Crystal,
J. Chem. Phys., 24, pp. 1239-1243, Jmie, 1956.
Giloth, p. K.i
A Simulator for Analysis of Sampled Data Control Systems, Proc.
Natl. Simulation Conf., pp. 21.1-21.8, Jan., 1956.
Goss, A. J.,1 Benson, K. E.,^ and Pfann, W. G. ^
Dislocations at Compositional Fluctuations in Germanium-Silicon Al-
loys, Acta Met., Letter to the Editor, 4, pp. 332-333, May, 1956.
Hallenbeck, F. J., see Eberhart, E. K.
Harrower, G. A.^
Auger Electron Emission in the Energy Spectra of Secondary Elec-
trons from Mo and W., Phys. Rev., 102, pp. 340-347, Apr. 15, 1956.
' Bell Telephone Laboratories Inc.
^ Hydro-Electric Power Commission of Ontario, Toronto, Ont., Canada.
* Bell Telephone Company of Canada, Montreal, Que., Canada.
1226 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
Harrower, G. A.^
Dependence of Electron Reflection on Contamination of the Reflect- I
ing Surface, Phys. Kev., 102, pp. 1288-1289, June 1, 1956.
Howard, J. D., Jr.^
Application of the Type-Pl Carrier System to Rural Telephone Lines,
A.I.E.E. Commun. and Electronics, 24, pp. 205-21-1, i\Iay, 1956.
HuTSON, A. R}
Effect of Water Vapor on Germanium Surface Potential, Phys. Rev.,
102, pp. 381-385, Apr. 15, 1956.
Katz, D.^
A Magnetic Amplifier Switching Matrix, A.I.E.E. Commun. and Elec-
tronics, 24, pp. 236-241, May, 1956.
KowALCHiK, M., see Trumbore, F. A.
Law, J. T.,1 and Garrett, C. G. B.^
Measurements of Surface Electrical Properties of Bombardment-
Cleaned Germanium, J. Appl. Phys., 27, p. 656, June, 1956.
Lewis, H. W.^
Two-Fluid Model of an "Energy-Gap" Superconductor, Phys. Rev.,
102, pp. 1508-1511, June 15, 1956.
Logan, R. A., see Thurmond, C. D.
LOZIER, J. C.^
A Study State Approach to the Theory of Saturable Servo Systems,
LR.E. Trans., PGAC, 1, pp. 19-39, 1956.
LuNDBERG, J. L.,^ and Zimm, B. H.^
Sorption of Vapors by High Polymers, J. Phys. Cheni., 60, pp. 425-
428, Apr. 16, 1956.
Matthias, B. T.,^ and Remeik.\, J. P.^
Ferroelectricity in Ammonium Sulfate, Phys. Rev., Letter to the
Editor, 103, p. 262, July 1, 1956.
^ Bell Telephone Laboratories Inc.
2 American Telephone and Telegraph Company, Inc.
* General Electrical Research Laboratories.
TECHNICAL PAPERS 1227
McKay, K. G., see Chynoweth, A. G.
I
McLean, D. A.i
ii '
Tantalum Solid Electrolytic Capacitors, Proc. Natl. Conf. Aeronauti-
cal Electronics, pp. 289-294, Alay, 1956.
McSkimin, H. J.i
Propagation of Longitudinal Waves and Shear Waves in Cylindrical
Rods at High Frequencies, J. Acous. See, 28, pp. 484-494, May, 1956.
Notes, J. W.,^ Gaudet, G.,^ and Bonneville, S.^
Development of Communications in Canada, Elec. Engg., 75, p. 539,
June, 1956.
O'Brien, J. A.i
Cyclic Decimal Codes for Analoge to Digital Converters, A.LE.E.
Commun. and Electronics, 24, pp. 120-122, May, 1956.
Owens, C. D.i
Stability Characteristics of Molybdenum Permalloy Powder Cores,
Elec. Engg., 75, pp. 252-256, Mar., 1956.
Pearson, G. L.^
Electricity from the Sun, Proc. World Symp. Appl. Solar Energy, pp.
281-288, Book.
Perkins, E. H., see Eberhart, E. K.
Pfann, W. G.i
Zone Melting: A Fresh Outlook for Fractional Crystallization, Chem.
& Engg. News, 34, pp. 1440-1443, Mar. 26, 1956.
Pfann, W. G., see Goss, A. J.
Phelps, J. W.^
Protection Problems in Telephone Distribution Systems, Wire and
Wire Products, 31, pp. 555-596, May, 1956.
Phelps, J. W., see Ellis, H. M.
' Bell Telephone Laboratories Inc.
* Bell Telephone Company of Canada, Montreal, Que., Canada.
1228 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
Pierce, J. R.^
Physical Sources of Noise, Pro. I.R.E., 44, pp. 601-608, May, 1956.
Pomeroy, a. F.,^ and Suarez, E. M.^
Determining Attenuation of Waveguide From Electrical Measure-
ments on Short Samples, I.R.E. Trans. MTT-4, pp. 122-129, Apr.,
1956.
PONDY, P. R.i
Dust-Lint Control in Tube Fabrication, Electronics, 29, pp. 246-250,
June, 1956.
Preston, K., Jr.^ and Atalla, M. M.^
Transient Temperature Rise in Semi-Infinite Solid Due to a Uniform
Disc Source, J. Appl. Mechanics, 23, p. 313, June, 1956.
Prince, E.^
Neutron Diffraction Observation of Heat Treatment in Cobalt Ferrite,
Phys. Rev., 102, pp. 674-676, May 1, 1956.
Remeika, J. P., see Matthias, B. T.
Reiss, H.^
p-n Junction Theory by the Method of Functions, J. Appl. Phys., 27,
pp. 530-537, May, 1956.
Rice, S. O.^
A First Look at Random Noise, A.I.E.E. Commun. and Electronics,
24, pp. 128-131, May, 1956.
Smith, D. H.^
Power Supplies for the Type-Pl Carrier System, A.I.E.E. Commun.
and Electronics, 24, pp. 191-195, May, 1956.
Suarez, E. M., see Pomeroy, A. F.
Theuerer, H. C.^
Purification of Germanium Tetrachloride by Extraction with Hydro-
chloric Acid and Chlorine, J. of Metals, 8, pp. 688-690, May, 1956.
' Bell Telephone Laboratories Inc.
N
TECHNICAL PAPERS 1229
Thurmond, C. D./ and Logan, R. A.^
The Distribution of Copper Between Germanium and Ternary Melts
Saturated with Germanium, J. Phys. Chem., 60, pp. 591-594, May,
1956.
Thurmond, C. D., see Trumbore, F. A.
Trumbore, F. A.,^ Thurmond, C. D.,^ and Kowalchik, M.^
The Germanium- Oxygen System, J. Chem. Phys., Letter to the
Editor, 24, p. 1112, May, 1950.
Weisbaum, S.' and Boyet, H.^
Broadbank Non-Reciprocal Phase Shifts - Analysis of Two Ferrite
Slabs in Rectangular Guide, J. Appl. Phys., 27, pp. 519-524, May,
1956.
Weppler, H. E., see Billiard, W. R.
WiNSLow, F. H.,1 Baker, W. 0.,^ and Yager, W. A.i
The Structure and Properties of Some Pyrolyzed Polymers, Proc.
Conf. on Carbon, pp. 93-102, 1956.
Wood, E. A. Mrs. i
The Question of a Phase Transition in Silicon, J. Phys. Chem., 60,
l)p. 508-509, Apr., 1956.
Yager, W. A., see Winslow, F. H.
1 Bell Telephone Laboratories Inc.
Recent Monographs of Bell System Technics
Papers Not Published in This Journal*
Bashkow, T. R.
DC Graphical Analysis of Junction Transistor Flip-Flops, Monograph
2615.
Becker, J. A., see Rose, D. J.
BiTTRicH, G., see Compton, K. G.
BoYET, H., see Weisbaum, S.
Brandes, R. G., see Rose, D. J.
Brattain, W. H., see Garrett, C. G. B.
Compton, K. G., Ehrhardt, R. A., and Bittrich, G.
Brass Plating, Monograph 2467.
Egerton, L., and Koonce, S. E.
Structure and Properties of Barium Titanate Ceramics, Monograph
2517.
Ehrhardt, R. A., see Compton, K. G.
EiGLER, J. H., see Sullivan, M. V.
Francois, E. E., see Law, J. T.
Fuller, C. S., see Reiss, H.
Garrett, C. G. B., and Brattain, W. H.
Some Experiments on, and a Theory of. Surface Breakdown, Mono-
graph 2589.
Hagelbarger, D. W.
SEER, A Sequence Extrapolating Robot, Monograph 2599.
* Copies of these monographs may be obtained on request to the Publication
Department, Bell Telephone Laboratories, Inc., 463 West Street, New York 14,
N. Y. The numbers of the monographs should be given in all requests.
1230
MONOGRAPHS 1231
[aynes, J. R., and Westphal, W. C.
Radiation Resulting from Recombination of Holes and Electrons in
Silicon, Monograph 2622.
[Ierring, C, and Vogt, E.
Transport and Deformation-Potential Theory for Many-Valley Semi-
conductors, Monograph 2596.
Ierring, C, see Vogel, F. L., Jr.
Xleimack, J. J., see Wahl, A. J.
KooNCE, S. E., see Egerton, L.
uAw, J. T., and Francois, E. E.
Adsorption of Gases on a Silicon Surface, Monograph 2600.
Lewis, H. W.
Superconductivity and Electronic Specific Heat, Monograph 2597.
jOGan, R. a.
Thermally Induced Acceptors in Germanium, Monograph 2601.
LuNDBERG, J. L., see Zimm, B. H.
May, J. E., Jr.
Low-Loss 1000-Microsecond Ultrasonic Delay Lines, Monograph
2584.
Mendel, J. T.
Microwave Detector, Monograph 2602.
Paterson, E. G. D.
An Over-all Quality Assurance Plan, Monograph 2630.
PoMEROY, A. F., and Suarez, E. M.
Attenuation of Waveguide from Electrical Measurements on Short
Samples, Monograph 2625.
Press, H., and Tukey, J. W.
Power Spectral Methods of Analysis and Application in Airplane Dy-
namics, Monograph 2606.
1232 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
Read, W. T., Jr., see Yogel, F. L., Jr.
Reiss, H., and Fuller, C. S.
Influence of Holes and Electrons on Solubility of Lithium in Silicon, ,
jMonograph 2603.
Rose, D. J., Becker, J. A., and Brandes, R. G.
On the Field Emission Electron Microscope, Monograph 2588.
Suarez, E. M., see Pomeroy, A. F.
Sullivan, M. V., and Eigler, J. H.
Electrolytic Stream Etching of Germanium, ]\'Ionograph 2595.
Thomas, D. E.
Tables of Phase of a Semi-Infinite Unit Attenuation Slope, Mono-
graph 2550.
TuKEY, J. W., see Press, H.
Van Uitert, L. G.
High -Resistivity Nickel Ferrites-Minor Additions of Manganese or
Cobalt, IMonograph 2594.
VoGT, E., see Herring, C.
VoGEL, F. L., Jr., Herring, C, and Read, W. T., Jr.
Dislocations in Plastic Deformation, Monograph 2616.
Wahl, a. J., and Kleimack, J. J.
Factors Affecting Reliability of Alloy Junction Transistors, Monograph
2604.
Westphal, W. C., see Haynes, J. R.
Weisbaum, S., and Boyet, H.
A Double-Slab Ferrite Field Displacement Isolator at 11 kmc, Mono-
grapli 2605.
ZiMM, B. H., and Lundberg, J. L.
Sorption of Vapors by High Polymers, Monograph 2573.
Contributors to This Issue
W. L. Bond, B.S. 1927 and M.S. 1928, Washington State College;
Bell Telephone Laboratories, 1928-. Mr. Bond has conducted investi-
gations in the mineral field including studies of the piezoelectric effect
in minerals and similar studies of synthetic crystals. He has designed
optical, X-ray, and mechanical tools and instruments for the orientation,
cutting and processing of crystals. Mr. Bond also served as consultant
on quartz crystals with the War Production Board. He is a member of
the American Physical Society, and of the American Crystallographic
Association.
Walter H. Brattain, B.S., Whitman College, 1924; M.A., Univer-
sity of Oregon, 1926; Ph.D., University of Minnesota, 1929. Honorary
D.Sc. Portland University, 1952, Whitman College and Union College,
1955. Radio section, Bureau of Standards, 1928-29. Bell Telephone
I Laboratories, 1929-. Co-inventor with Dr. John Bardeen of point contact
I transistor. Primary activity at Laboratories in semi-conductors. Re-
search in field of thermionics, particularly electronic emission from hot
surfaces. Frequency standards, magnetometers and infra-red phenom-
ena. Studied magnetic detection of submarines for National Defense
Research Committee at Columbia University, 1942-43. Visiting lecturer
at Harvard University, 1952-53. Author of numerous technical articles.
Recipient of John Scott Medal, 1955, and Stuart Ballantine Medal of
Franklin Institute, 1952. Fellow of American Physical Society, American
Academy of Arts and Sciences and American Association for the Ad-
vancement of Science. Member of Franklin Institute, Phi Beta Kappa
and Sigma Xi.
C. C. Cole, B.S. in E.E., State College of Washington, 1923; U. S.
Navy 1917-1919; Western Electric Company 1923-. His first assign-
ment was in manufacturing development on paper and mica capacitors.
Other assignments include manufacturing development on loading coils,
quality control, and inspection development laboratory. During World
War II he handled the design and construction of testing facilities for
various defense projects. Since World War II he has been engaged in
1233
1234 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956 i
•I
:t
inspection methods development and in the development and design of
testing facilities for telephone apparatus and cable. Member of Sigma i
Tau and A.I.E.E.
Arthur B. Crawford, B.S.E.E. 1928, Ohio State University; Bell]
Telephone Laboratories, 1928-. Mr. Crawford has been engaged in radio
research since he joined the Laboratories. He has worked on ultra short
wave apparatus, measuring techniques and propagation; microwave
apparatus, measuring techniques and radar, and microwave propagation
studies and microwave antenna research. He is author or co-author of
articles which appeared in The Bell System Technical Journal, Pro-
ceedings of the I.R.E., Nature, and the Bulletin of the American Me-
teorological Society. He is a Fellow of the LR.E. and a member of Sigma
Xi, Tau Beta Pi, Eta Kappa Nu, and Pi Mu Epsilon.
Harald T. Friis, E.E., 1916, D.Sc, 1938, Royal Technical College'
(Copenhagen); Engineering Department of the Western Electric Com-i
pany, 1919-1924. Bell Telephone Laboratories, 1925-. Dr. Friis, Di-i|
rector of Research in High Frequency and Electronics, has made im-i
portant contributions on ship-to-shore radio reception, short-wave i
studies, radio transmission (including methods of measuring signals and(
noise), a receiving system for reducing selective fading and noise inter-'
ference, microwave receivers and measuring equipment, and radar,
equipment. He has published numerous technical papers and is co-author
of a book on the theory and practice of antennas. The LR.E.'s Morris
Liebmann Memorial Prize, 1939, and Medal of Honor, 1954. Valdemar
Poulson Gold Medal by Danish Academy of Technical Sciences, 1954.
Danish "Knight of the Order of Dannebrog," 1954. Fellow of LR.E.
and A.I.E.E. Member of American Association for the Advancement of
Science, Danish Engineering Society and Danish Academy of Technical >
Sciences. Served on Panel for Basic Research of Research and Develop- '
ment Board, 1947-49, and Scientific Advisory Board of Army Air Force,
1946-47.
C. G. B. Garrett, B.A., Cambridge University (Trinity College),
1946; M.A., Cambridge, 1950; Ph.D., Cambridge, 1950. Instructor in
Physics, Harvard University, 1950-52. Bell Telephone Laboratories,
1952-. Before coming to the Laboratories, Dr. Garrett's principal re-
search was in the field of low-temperature physics. At the Laboratories
he has been engaged in research and exploratory development on semi-
conductor surfaces and, for the past year, has supervised a group work-
ing in this field. He is the author of "Magnetic Cooling" (Harvard
CONTRIBUTOES TO THIS ISSUE 1235
University Press, 1954). Senior Scholar of Trinity College, Cambridge,
1945. Twisden Student of Trinity College, 1949. Fellow of Physical
Society (London). Member of American Physical Society.
L. D. Hansen, B.S., Montana State College, 1924; Western Electric
Company, 1924-. Mr. Hansen joined the Equipment Engineering Or-
'ganization at the Hawthorne Plant of The Western Electric Company
in Chicago in 1924 where he was engaged in preparation of telephone
central office specifications. He transferred to the Kearny, N. J., Plant
in 1928 where he was promoted to section chief in 1929. He transferred
to the Engineer of Manufacture Organization in 1930 and worked on
carrier and repeater test development and methods until 1941 when he
was promoted to Department Chief in charge of wired switching ap-
paratus and equipment test set development and methods.
William C. Jakes, Jr., B.S.E.E., Northwestern University, 1944;
M.S., Northwestern, 1947; Ph.D., Northwestern, 1948. Bell Telephone
Laboratories, 1949-. Dr. Jakes is engaged in microwave antenna and
propagation studies and holds a patent in microwave antennas. He is
the author of chapter in antenna engineering handbook (McGraw-Hill).
Member of Sigma Xi, Pi Mu Epsilon, Eta Kappa Nu, LR.E. and Phi
Delta Theta.
Amos E. Joel, Jr., B.S., Massachusetts Institute of Technology, 1940;
M.S., M.I.T., 1942; Bell Telephone Laboratories, 1940-. Mr. Joel is
Switching Systems Development Engineer responsible for coordinating
the exploratory development of a trial electronic switching system.
Prior to his present position he worked on relay engineering, crossbar
test laboratory, fundamental development studies, circuits for relay com-
puters, preparation of a text and teaching switching design, designing
j AMA computer circuits and making fundamental engineering studies
on new switching systems. He holds some forty patents. Member of
A.I.E.E., LR.E., Sigma Xi and Association for Computing Machinery.
Archie P. King, B.S., California Listitute of Technology, 1927. After
three years with the Seismological Laboratory of the Carnegie Institu-
tion of Washington, Mr. King joined Bell Telephone Laboratories in
1930. Since then he has been engaged in ultra-high-frequency radio re-
search at the Holmdel Laboratory, particularly with waveguides. For the
I last ten years Mr. King has concentrated his efforts on waveguide trans-
mission and waveguide transducers and components for low-loss circular
1236 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1956
electric wave transmission. He holds at least a score of patents in the
waveguide field. Mr. King was cited by the Navy for his World War II
radar contributions. He is a Senior Member of the I.R.E. and is a Mem-
ber of the American Physical Society.
D. T. RoBB, B.S., University of Chicago, 1927; Western Electric
Company, 1927-. Mr. Robb has been concerned with measurement
and testing problems throughout his career. In the electrical laboratory ■
at Hawthorne Works, Chicago, he specialized in ac standardization.
Later he worked on the development of shop test methods and test sets. '
In 1944 he transferred to take charge of radar test engineering at the
Eleventh Avenue Plant of Western Electric in New York City. In 1946
he supervised the engineering of the standards laboratory at Chatham
Road Plant in Winston Salem, N. C. Currently, he has charge of trans-
mission test set development and test set design at Kearny Works, N. J.
Harry R. Shillington, B.S. in E.E. Iowa State College, 1937; Long
Lines Department of the American Telephone and Telegraph Company,
1928-1932; Western Electric Company, 1937-. Mr. Shillington's first
assignment was that of product engineering on panel dial equipment.
During World War II and the Korean War he was engaged in test engi-
neering on various defense projects. He is presently concerned with the
development of special test facilities for telephone apparatus. Member of
Eta Kappa Nu and Tau Beta Pi.
Friedolf M. Smits, Dipl.Phys. and Dr.Rer.Nat., University of Frei-
burg, Germany, 1950; research assistant, Physikalisches Institut, Uni-
versity of Freiburg, 1950-54; Bell Telephone Laboratories, 1954-. As a
member of the Solid State Electronics Research Department of the :
Laboratories, Dr. Smits has been concerned with diffusion studies of
germanium and silicon for semiconductor device applications. He is a
member of the American Physical Society and the German Physical
Society.
Frank H. Tendick, Jr., B.S.E.E., 1951, University of Michigan;
Bell Telephone Laboratories, 1951-. Mr. Tendick was first engaged ini
work pertaining to the synthesis of networks employed in the L3 coaxial i
cable system. Later he engaged in the design of transistor networks for
digital computers. More recently, he has been associated with exploratory
studies of submarine cable systems. He is a member of the I.R.E. Mr.
CONTRIBUTORS TO THIS ISSUE 1237
Tendick also belongs to four honor societies, Tau Beta Pi, Eta Kappa
iNu, Sigma Xi and Phi Kappa Phi.
Leishman R. Wrathall, B.S., 1927, University of Utah. Mr. Wrathall
did another year of graduate work at the University of Utah and joined
Bell Telephone Laboratories in 1929. For many years he was primarily
concerned with studies of the characteristics of non-linear coils and ca-
pacitors. During World War II non-linear coils were used extensively in
radar systems, and his work in this field was intensified. Later he was
occupied with general circuit research. He is now engaged in studies of
conductor problems, particularly digital repeaters, as a member of the
Transmission Research Department at Murray Hill.
!
HE BELL SY S^ E M
/
ecnnicm louma^
OTED TO THE SC I E N T I FIC^^^ AND ENGINEERING
•ECTS OF ELECTRICAL COMMUNICATION
UME XXXV NOVEMBER 1956 NUMBER 6
Ft
Nobel Prize in Physics Awarded to Transistor Inventors i
Theory of the Swept Intrinsic Structure w. t. bead, jbT. 1239
A Medium Power Traveling- Wave Tube for 6,000-Mc Radio Relay
J. p. LAico, H. L. Mcdowell and c. r. moster 1285
Helix Waveguide s. p. morgan and j. a. young 1347
Wafer-Type Millimeter Wave Rectifiers w. m. sharpless 1385
Frequency Conversion by Means of a Nonlinear Admittance
C. F. EDWARDS 1403
Minimization of Boolean Functions e. j. mccluskey, jr. 1417
Detection of Group Invariance or Total Symmetry of a Boolean
Function e. j. mccluskey, jr. 1445
Bell System Technical Papers Not Published in This Journal 1454
Recent Bell System Monographs 1461
Contributors to This Issue 1465
COPYRIGHT 1956 AMERICAN TELEPHONE AND TELEGRAPH COMPANY
THE BELL SYSTEM TECHNICAL JOURNAL
ADVISORY BOARD
A. B, GOETZE, President, Western Electric Company
M. J. KELLY, President, BeU Telephone Laboratories
E. J. McNEELY, Execviivc Vice President, American
Telephone and Telegraph Company
EDITORIAL COMMITTEE
B. McMillan, Chairman
S, E. BRILLHART E. I.GREEN
A. J. BUSCH R. K. HONAMAN
L. R. COOK H. R. HUNTLEY
A. C. DICKIE80N F. R. LACK
R. L. DIETZOLD J. R. PIERCE
K. E. GOULD G. N. THAYER
EDITORIAL STAFF
J. D. TEBO, Editor
R. L. SHEPHERD, Production Editor
THE BELL SYSTEM TECHNICAL JOURNAL is published six times a year
by the American Telephone and Telegraph Company, 195 Broadway, New York
7, N. Y. F. R. Kappel, President; S. Whitney Landon, Secretary; John J. Scan-
Ion, Treasurer. Subscriptions are accepted at $3.00 per year. Single copies are
75 cents each. The foreign postage is 65 cents per year or 11 cents per copy. Printed
in U. S. A.
Nobel Prize in Physics Awarded
to Transistor Inventors
The Swedish Royal Academy of Sciences announced on November 1
that a Nobel Prize in Physics, most highly coveted award in the world
of physics, had been awarded jointly to Dr. Walter H. Brattain of the
Laboratories Physical Research Department, with Dr. John Bardeen
and Dr. William Shockley, both former members of the Laboratories.
The prize was awarded for ''investigations on semiconductors and the
discovery of the transistor effect."
This marks the second time that Avork done at the Laboratories has
been recognized by a Nobel Prize. The previous recipient Avas Dr. C. J.
Davisson who shared in the 1937 prize for his discovery of electron dif-
fraction as a result of experiments carried out with Dr. L. H, Germer,
also of the Laboratories.
Each of the three Avinners of this year's prize Avill receive a gold medal,
a diploma and a share of the $38,633 prize money. When he Avas notified
that he Avas one of these Avinners, Dr. Brattain said, "I certainly ap-
preciate the honor. It is a great satisfaction to have done something
in life and to haA^e been recognized for it in this Avay. HoAvever, much of
my good fortune comes from being in the right place, at the right time,
and having the right sort of people to Avork Avith."
The principle of transistor action Avas discovered as a result of funda-
mental research directed toAA^ard gaining a better understanding of the
surface properties of semiconductors. Following World War II, intensiA^e
programs on the properties of germanium and silicon AA'ere undertaken
at the Laboratories under the direction of William Shockley and S. 0.
Morgan. One group in this program engaged in a study of the body
properties of semi-conductors, and another on the surface properties.
Dr. John Bardeen served as theoretical physicist and R. B. Gibney as
chemist for both groups. These iuA'estigations, Avhich resulted in the in-
\'ention of the transistor, made extensiA^e use of knoAvledge and tech-
niques developed by scientists here and elscAvhere, particularly by mem-
bers of the Laboratories — R. S. Ohl, J. H. Scaff and H. C. Theuerer.
Since the transistor Avas announced, little more than eight years ago,
it has become increasingly important in Avhat has been called the "neAv
11
THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 195G
The Nobel Prize winners in an historic photograph taken in 1948 when the
annonncement of the invention of the transistor icas made. Left to right,
John Bardccn, William Shockley and Walter H. Brattain.
electronics age." As new transistors and related semiconductor devices
are developed and improved, the possible fields of application for these
devices increase to such an extent that they may truly be said to have
"revolutionized the electronics art."
The invention of the transistor, basis for the Nobel Prize award,'
represents an outstanding example of the combination of research team-
work and individual achievement in the Bell System that has meant so;
much to the rapid development of modern communications systems.
Dr. Brattain received a B.S. degree from Whitman College in 1924, an
M.A. degree from the University of Oregon in 1926, and a Ph.D. degree
from the University of Minnesota in 1928. He joined Bell Telephone
Laboratories in 1929, and his early work was in the field of thermionics,
particularly the study of electron emission from hot surfaces. He also
studied frequency standards, magnetometers and infra-red phenomena.
NOBEL PRIZE IN PHYSICS 111
Subsequently, Mr. Brattain engaged in the study of electrical con-
ductivity and rectification phenomena in semiconductors. During World
War II, he was associated with the National Defense Research Com-
mittee at Columbia Fni\'ersity ^\■here he worked on magnetic detection
of submarines.
Mr. Brattain has received honorary Doctor of Science degrees from
Whitman College, Union College and Portland University. His many
awards include the John Scott Medal and the Stuart Ballantine INIedal,
both of which he received jointl^y with John Bardeen. Mr. Brattain is a
Fellow of the American Academy of Arts and Sciences.
Dr. Bardeen received the B.S. in E.E. and M.S. in E.E. degrees
from the University of Wisconsin in 1928 and 1929 respectively, and his
Ph.D. degree in Mathematics and Physics from Princeton University
in 1930. After serving as an Assistant Professor of Physics at the Uni-
versity of Minnesota from 1938 to 1941, he worked with the Naval Ord-
nance Laboratory as a physicist during World War II. In 1945 he joined
the Laboratories as a research physicist, and was primarily concerned
Clinton J . JJuvisson Previous Laburatories Nobel Laureate
In December, J 937, Di'. Clinton J. Davisson of the Laboratories was
awarded the Xobel Prize in Piiysics for his discovery of electron tliffrac-
tion and the wave properties of electrons.
He shared the jDrize with Professor G. P. Thompson of London, who
worked in the same field, though there was little in common between their
techniques. Dr. Davisson's work on electron diffraction started as an at-
tempt to understand the characteristics of secondary emission in multi-
grid electron tubes. In this work he discovered patterns of emission from
the surface of single crystals of nickel. By studying these patterns, Dr.
Davisson, with Dr. L. H. Germer and their associates, proved that reflected
electrons have the properties of trains of waves.
Dr. Davisson was awarded the B.S. degree in physics from the Univer-
sity of Chicago in 1908 and the Ph.D. degree from Princeton in 191L
From September, 1911, until June, 1917, he was an instructor m physics
at the Carnegie Institute of Technology, coming to the Laboratories on a
wartime leave of absence. He found the climate of the Laboratories
conducive to basic research, however, and remained until his retirement
in 1946. Besides his work on electron diffraction. Dr. Davisson did much
significant work in a varietj^ of fields, particularly electron optics, mag-
netrons, and crystal physics.
iv THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
with theoretical problems in solid state physics, including studies of
semiconductor materials.
Mr. Bardeen, whose honors include an honorary Doctor of Science
degree from Union College, the Stuart Ballantine Medal, the John
Scott Medal, and the Buckley Prize, is a member of the National Acad-
emy of Sciences. He joined the University of Ilhnois in 1951.
Dr. Shockley received a B.Sc. degree from the California Institute of
Technology in 1932, and a Ph.D. degree from the Massachusetts In-
stitute of Technology in 1936. He joined the staff of Bell Telephone
Laboratories in 1936. In addition to his many contributions to solid
state physics and semiconductors, Mr. Shockley has worked on electron
tube and electron multiplier design, studies of various physical phe-
nomena in alloys, radar development and magnetism.
His many awards include an honorary degree from the University of
Pennsylvania, the Morris Liebmann Memorial Prize, the Buckley Prize,
the Comstock Prize and membership in the National Academy of
Sciences. Dr. Shockley left the Laboratories to form the Shockley Semi-
conductor Laboratory at Beckman Instruments, Inc., in 1955.
THE BELL SYSTEM
TECHNICAL JOURNAL
VOLUME XXXV NOVEMBER 1956 number 6
Copyright 1966, American Telephone and Telegraph Company
Theory of the Swept Intrinsic Structure
By. W. T. READ, JR.
(Manuscript received March 4, 1956)
The electric field and the hole and electron concentrations are found for
reverse biased junctions in which one side is either intrinsic (!) or so weakly
doped that the space charge of the carriers cannot he neglected. The analysis
takes account of spare charge, drift, diffusion and non linear recombination.
A number of figures illustrate the penetration of the electric fii eld into a PIN
structure with increasing bias for various lengths of the I region. For the
junction between a highly doped and a weakly doped region, the reverse cur-
rent increases as the square root of the voltage at high voltages; and the space
charge in the weakly doped region approaches a constant value that depends
on the fixed charge and the intrinsic carrier concentration.
The mathematics is greatly simplified by expressing the equations in
terms of the electric field and the sum of the hole and electron densities.
i I. INTRODUCTION
Applications have been suggested for semiconductor structures having
j both extrinsic and intrinsic regions. Examples are the "swept intrinsic"
structure, in which a region of high resistivity is set up by an electric
[ field that sweeps out the mobile carriers, and the analogue transistors,
! where the intrinsic region is analogous to the vacuum in a vacuum tube.
However, the junction between an intrinsic region and an N or P region
1239
1240 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
is considerably less well understood than the simple NP junction. Most
of the assumptions that make the NP case relatively simple to deal with
do not apply to junctions where one side is intrinsic. Specifically, the
space charge is that of the mobile carriers; thus the flow and electrostatic
problems cannot be separated as they can in PN junction under reverse
bias. The following sections analyze the iV-intrinsic - P structure under
reverse bias.
For a given material with fairly highly doped extrinsic regions, the
problem is defined by the length of the intrinsic region and the applied
voltage. Taking the intrinsic region infinitely long gives the solution for
a simple A^-intrinsic or P-intrinsic structure. The results are given and
plotted in terms of the electric field distribution. From this the potential,
space charge and carrier concentrations can be found; so also can the
current-voltage curve. The final section considers the case where the
middle layer contains some fixed charge but where the carrier charge
cannot be neglected.
Qualitative Discussion of an N-intrinsic-P Structure
Consider an A^-intrinsic-P structure where the intrinsic, or /, region is
considerably wider than the zero bias, or built-in, space charge regions
at the junctions, so that there is normal intrinsic material between the
junctions. The field distribution at zero bias can be found exactly from
the zero-current analysis of Prim.' Throughout the intrinsic region, hole
and electron pairs are always being thermally generated and recombining
at a rate determined by the density and properties of the traps, or recom-
bination centers. Under zero bias the rates of generation and recombina-
tion are everywhere equal. Suppose now a reverse bias is applied causing
holes to flow to the right and electrons to the left. Some of the carriers
generated in the intrinsic region will be swept out before recombining. |
This depletes the carrier concentration in the intrinsic region and hence
raises the resistivity. It also produces a space charge extending into the
intrinsic layer. The electrons are displaced to the left and the holes, to ■
the right. Thus the space charge opposes the penetration of the field
into the intrinsic region; that is, the negative charge of the electrons on i
the left and positive charge of the holes on the right gives a field
distribution with a minimum somewhere in the interior of the intrinsic
region and maxima at the NI and IP junctions. If holes and electrons
had equal mobilities, the field distribution would be symmetrical with a
minimum in the center of the intrinsic region. Likewise, the total carrier
1 R. C. Prim, B. S. T. J., 32, p. 665, May, 1953.
THEORY OF THE SWEPT INTRINSIC STRUCTURE 1241
[concentration (holes plus electrons) would be symmetrical with a maxi-
[mum in the center. As the applied bias is increased the hole and electron
distributions are further displaced relative to one another and the space
charge increases. Finally, at high enough biases, so many of the carriers
are swept out immediately after being generated that few carriers are
left in the intrinsic region. Now the space charge decreases with increas-
ing bias until there is negligible space charge, and a relatively large and
constant electric field extends through the intrinsic region from junction
to junction. This may happen at biases that are still much too low to
appreciably affect the high fields right at the junction or in the extrinsic
layers, which remain approximately as they were for zero bias.
The current will increase with voltage until the total number of
carriers in the intrinsic region becomes small compared to its normal
value. After that, there is negligible further increase of current with
voltage. All the carriers generated in the intrinsic region are being sw^ept
out before recombining. In general, the current will saturate while the
minimum field in the intrinsic region is still small compared to the
average field.
Comparison with the NP Structure
The analysis is more difficult than in a simple reverse-biased NP
structure. In the NP case there is a well defined space charge region in
I which carrier concentration is negligible compared to the fixed charge of
i the chemical impurities; so the field and potential distributions are easily
found from the known distribution of fixed charge. Outside of the space
i charge region are the diffusion regions in which the minority carrier con-
j centration rises from a low value at the edge of the space charge region
; to its normal value deep in the extrinsic region. However, there is no
, space charge in this region because the majority carrier concentration,
I by a very small percentage variation, can compensate for the large per-
I centage variation in minority carrier density. The minority carriers flow
by diffusion. Since the disturbance in carrier density is small compared to
the majority density, the recombination follows a simple linear law
(being directly proportional to the excess of minority carriers). Thus
the minority carrier distribution is found by solving the simple diffusion
equation with linear recombination.
None of these simplifications extend to the NIP or NI or IP structure.
There is, in the intrinsic region, no fixed charge; hence the space charge
is that of the carriers. There is no majority carrier concentration to
maintain electrical neutrality outside of a limited space charge region.
1242 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
It is necessary to take account of (1) space charge, (2) carrier drift, (3)
carrier diffusion and (4) recombination according to a nonlinear bi-
molecular law. Of these four, only space charge and recombination are
never simultaneously important in practical cases. Nevertheless certain
simplifications can be made if the problem is formulated so as to take
advantage of them. The field and carrier distributions in the intrinsic
region are found by joining two solutions: one solution is for charge
neutrality; the other, which we shall call the no-recombination solution
is for the case where the recombination rate is negligible compared to the
rate of thermal generation of hole electron pairs. We shall show that in
practical cases the ranges of validity of the two solutions overlap; that
is, wherever recombination is important, we have charge neutrality.
Prim's Zero-Current Approximation
Prim* derived the field distribution in a reverse biased NIP structure;
on the assumption that the hole and electron currents are negligibly small
differences between their drift and diffusion terms, as in the zero- bias
case. He showed that the average diffusion current is large compared
to the average current. However, as it turns out, this is misleading.:
Throughout almost all of the intrinsic region (where the voltage drop
occurs in practical cases) the diffusion current is comparable to or
smaller than the total current. The larger average diffusion current comes
from the extremely large diffusion current in the small regions of high
space charge at the junctions. Prim's analysis, in effect, neglects the space
charge of the carriers generated in the intrinsic region. These may be
neglected in calculating the field distribution if the intrinsic region is
sufficiently narrow or the reverse bias sufficiently high. In the appendix
we derive the limits within which Prim's calculation of the field and
potential will be valid. The range will increase with both the Debye
length and the diffusion length in the intrinsic material. However, in
cases of practical interest the zero-current approximation may lead to
serious errors in the field distribution and give a misleading idea of the
penetration of the field into the intrinsic region. The present, more
general analysis, reduces to Prim's near the junctions where the zero-
current assumption remains valid. The zero current approximation was,
of course, not intended to give the hole and electron distributions in the
intrinsic region or to evaluate the effects of interacting drift, diffusion
and recombination.
Ibid.
THEORY OF THE SWEPT INTRINSIC STRUCTURE 1243
Outline of the Following Sections
Sections II through V deal with the ideal ease of equal hole and elec-
tron mobilities. Here the problem is somewhat simplified and the physics
easier to visualize because of the resulting symmetry. In Section VI,
the general case of arbitrary mobilities is solved by an extension of the
methods developed for solving the ideal case. The technique is to deal
not with the hole and electron flow densities but with two linear com-
binations of hole and electron flow densities that have a simple form.
Section II deals with the basic relations and in particular the formula
for recombination in an intrinsic region for large disturbances in carrier
density. The nature and range of validity of the various approximations
are discussed. Section III derives the field distribution in regions where
recombination is small compared to pair generation. Section IV treats
the recombination region and the smooth joining of the recombination
and no-recombination solutions. Section V considers the role of chffusion
in current flow and the situation at the junctions where the field and
carrier concentration abruptly become large. The change in form of
the solution near the junctions is shown to be represented by a basic in-
stability in the governing differential equation. Section VI extends the
results to the general case of unequal mobilities. Section VII deals with
the still more general case where there is some fixed charge in the "in-
trinsic" region. If the density of excess chemical impurities is small com-
pared to the intrinsic carrier density, the solution remains unchanged in
the range where recombination is important. In the no-recombination
region the solution is given b}'' a simple first order differentiatial equation
which can be solved in closed form in the range where the carrier flow is
by drift. The fixed charge may have a dominant effect on the space
charge even when the excess density of chemical impurities is small com-
pared to the density n, of electrons in intrinsic material. Consider, for
example, a junction between an extrinsic P region and a weakly doped
n region having an excess density N = Nd — Na oi donors. In the limit,
as the reverse bias is increased and the space charge penetrates many
difi"usion lengths into the n region, the field distribution becomes linear,
corresponding to a constant charge density equal to
m + Vn^ + 8 n.-^jeV^i']
where Li is the diffusion length in the weakly doped n type region and £
is the Debye length for intrinsic material. For germanium at room tem-
perature £,/Li is the order of 10~^ Thus, in this example, a donor density
as low as lO" cm~^ will have an appreciable effect on the space charge.
1244 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
II. BASIC RELATIONS
The problem can be stated in terms of the hole density p, the electron
density Ji, and the electric field E and their derivatives. Let the distance
.T be measured in the direction from N to P. The field will be taken as
positive when a hole tends to drift in the -{-x direction. The field in-
creases in going in the -fx direction when the space charge is positive.
Poisson's equation for intrinsic material is
f = a(p - «) (2.1)
where the constant a has the dimensions of volt cm and is given in terms
of the electronic charge q and the dielectric constant k by
■iirq
a = — -
K
For germanium a = 1.17 X 10~ volt cm.
The hole and electron flow densities Jp and J„ are^
Jp = nEv - d'^ = ^,Je -—^Inv
ax \ q dx
Jn = —hi nEn + D -^ j = —bun
E -\ -Inn
q dx
(2.2)
where n and D = n kT/q are the hole mobility and diffusion constant re-
spectively, k is Boltzmann's constant (8.63 X 10~^ cv per °C) and T is
the absolute temperature. The ratio b of electron mobility to hole mo-
bility we take to be unity. This makes the problem symmetrical in n and
p and consequently easier to understand. Section \T will extend the re-
sults to the general case of arbitrary b.
Charge and Particle Flow
For some purposes it helps to express the flow not in terms of Jp and
Jn but rather in terms of the current density / and the flow density
J = Jp -\- Jn oi particles, or carriers. The current density / = q{Jp —
Jn). Each carrier, hole or electron, gives a positive contribution to
J if it goes in the +.r direction and a negative contribution if it goes in
the —X direction. In other words, J is the net flow of carriers regardless
of their charge sign. The current / is constant throughout the intrinsic
^ See, for example, Electrons and Holes in Semiconductors, by W. Shockley.
D. Van Nostrand Co., New York, 1950.
THEORY OF THE SWEPT INTRINSIC STRUCTURE
1245
region. Particle flow is away from the center of the intrinsic region.
Carriers are generated in the intrinsic region and flow out at the two ends,
the electrons going out on the N side and holes on the F side. Thus J is
positive near the IP junction and negative near the NI junction.
From the definitions of / and J and equations (2.2)
- = nE{p -\- n) - D -J- {-p - 11)
q ax
J = m£'(p - n) - D^(p-\-n)
(2.3)
It is convenient to express the equations in terms of E and a dimen-
sionless variable
s =
n + p
2ni
(2.4)
I which measures how "swept" the region is. In normal intrinsic material
s = 1. In a completely swept region s = 0; at the junctions with highly
'' extrinsic material s ^ I. Using Poisson's equation to express p — n in
terms of E, equations (2.3) become
r J, qD ctE
1 = asE - ■ — -—
a ax-
J =
d_
dx
2a
- 27uDs
(2.5)
where a = 2 /x n,g is the conductivity of intrinsic material. The particle
flow J is thus seen to be the gradient of a flow potential that depends
only on E and s.
Equations (2.5) can be written in the form
[
a\ sE - £■
drE
dx^
(2.6)
(2.7)
where £ — \/kT/2aniq is the Debye length in intrinsic material and
V2kT
q&
(2.8)
is a field characteristic of the material and temperature. Specifically Ex
is \/2 times the field required to give a voltage drop kT/q in a Debye
1246 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
length. For germanium at room temperature £ = 6.8 10~* cm and Ei =
383 volts per cm.
Both / and / are the sum of a drift term and a diffusion term. For
charge neutrahty, where p — nis small compared to p + n, both charge
diffusion and particle drift can be neglected. We shall see later that,
except right at the junctions, charge diffusion is negligible.
The Equations of Continuity
The two equations of continuity are
I
(.ttJ p (J/fJ fi
dx dx
= g - r (2.9)
where g is the rate of pair generation and r the rate of recombination. In
terms of / and /, these become I
^ = 0 (2.10)
or / = constant and
^ = 2(^ - r) (2.11)
which says that the gradient of particle flow is equal to the net rate of
particle generation, that is, twice the net rate of pair generation.
To complete the statement of the problem it remains to express g and
r in terms of n and p.
Generation and Recombination
The direct generation and recombination of holes and electrons follows
the mass action law, in which g — r is proportional to w/ — np. The con-
stant of proportionality can be defined in terms of a lifetime t as fol-
lows: Let 8p = 871 <$C Ui be a small disturbance in carrier density. Then
defining T(g — r) = —8n, we see that the proportionality constant in
the mass action law is (2niT)~ . So
, _ , = !^ipi!£ (2.12)
and the generation rate
g = ^ (2.13)
is independent of carrier concentration.
THEORY OF THE SWEPT INTRINSIC STRUCTURE 1247
In actual semiconducting materials, recombination is not direct.
Rather it occurs through a trap, or recombination center. The statistics
of indirect recombination has been treated by Shockley and Read^ for a
recombination center having an arbitrary energy level &i somewhere in
the energy gap. At any temperature the trap level can be expressed by
the values rii and pi which n and p would have if, at that temperature,
the Fermi level were at the trap level. Shockley and Read showed that,
at a given temperature, the lifetime for small disturbances in carrier
density is a maximum in intrinsic material. It drops to limiting values
T„o and Tpo in highly extrinsic n and p material, respectively. The formula
for gr — r in terms of n and p is
g - r = — T— - — . , ^. . r (2.14)
Tpo(n + ni) + Tnoip + Pi)
For our purposes it is more convenient to define the hfetime r not by
'''(d ~ f) = — 6n « Wi , but rather as the proportionality factor in the
mass action law. Then r is not necessarily constant independent of carrier
density. From (2.12) and (2.14)
Tpo(n + Wi) + T„o(p + P\) i^ . re.
r = ~ (2.15)
We shall be interested in the hfetime in the region where 7i and p are
equal to or less than n, . r decreases as n and p decrease; that is, t is less
in a swept region than in normal intrinsic material. Let r = Tj for 7i =
p = 7ii and T = To for n = p = 0. The total range of variation of r is by
a factor of
II = 1 + ^^'(t'po + rpo) ,^ ^g.
TO PlTnO + rilTpO
Let the energy levels be measured relative to the intrinsic level, and
define a level 8o by
\ TpO
Then if &t = &o , niTpo = piTno • Now eq. (2.16) becomes
So = kT\n ..,
TpO
^^^sech(^i^) (2.17)
Thus the variation in r increases as the ratio of Tno to Zpo deviates from
unity and as the trap level moves away from the level 8o .
3 W. Shockley and W. T. Read, Jr., Phys. Rev., 87, p. 835, 1952.
1248 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
The data of Burton, Hull, Morin, and Severien* shows that a typical
value of the ratio of Tpo and r„o is about 10. This means that the varia-
tion in r with carrier concentration will be less than 10 per cent provided
St is about -ikT from So . In what follows we shall assume that this is so.
Then we have the mass action law (2.12) with r a constant, which could
be measured by one of the standard technicjues involving small dis-
turbances in carrier density. The general case of variable t is considered
briefly at the end of Section IV.
Outline of the Solution
To conclude this section, we discuss briefly the form of the equations
and the solution in different parts of the intrinsic region. First consider
(2.6) for the current in the ideal case of equal mobilities. In Sections III
and V we shall show that throughout almost all of the intrinsic region the
current flows mainly by pure drift so we can take I = asE. The reason
for this is as follows. The quantity £ is so small that the diffusion term
remains negligible unless the second derivative of E becomes large — so
large in fact that the E versus x curve bends sharply upward and both
the drift and diffusion terms become large compared to the current /.
This is the situation at the junction where / is the small chfference be-
tween large drift and diffusion terms. Thus (2.6) has two limiting forms:
(1) Except at the junctions the current is almost pure drift so 7 =
asE is a good approximation. In Section III we derive an upper limit
for the error introduced by this approximation and show how the
approximate solution can be corrected to take account of the diffusion
term.
(2) At the junction, the drift term becomes important and the
current rapidly becomes a small difference between its drift and diffusion
terms and the solution approaches the zero current solution, for which
sE = £^ (fE/dx^. In Section V we derive an approximate solution that
joins onto the I = asE solution near the junction and then turns con-
tinously and rapidly into the zero current solution. We shall call this the
junction solution.
The abrupt change in the solution from (1) to (2) near the junction
is shown to be related to a basic instability in the differential equation.
This makes it impractical to solve the equations on a machine.
When the applied bias is large compared to the built-in voltage drop,
the junction region will be of relatively little interest so the I = asE
solution can be used throughout.
In the region where / = <tsE there are two overlapping regions in
which the equations assume a simple form. These are the following: '
^ Burton, Hull, Morin and Severiens, J. Phys. Chem., 57, p. 853, 1953.
THEORY OF THE SWEPT INTRINSIC STRUCTURE 1249
The No-Recojnhination Solution
Here recombination is small compared to generation, r « g. This will
be so in at least part of the intrinsic region for reverse biases of more
than a few kT/q. The E versus x curve turns out to be given by a
simple, cubic algebraic equation.
The Recombination, or Charge Neutrality, Solution
Here 7i — ja is small compared to n + p, so the particle flow is by dif-
fusion. We shall find that the s versus x curve is given by a third degree
elliptic integral. As we move away from the center of the intrinsic
region and toward the junctions, recombination becomes small com-
pared to generation and the recombination solution goes into the no-
recombination solution. In the region where both solutions hold, the
solution has the simple form s = I/aE = A — x' where A is a constant
that must be less than f and the unit of length is twice the diffusion
length.
As the bias on an NIP structure is increased and the space charge
penetrates through the intrinsic region, the region where the recombina-
tion is important will shrink and eventually disappear.
Fig. 1 is a schematic plot of the field distribution for the case where
the applied bias is large compared to the built-in potential drop but not
large enough to sweep all the carriers out of the intrinsic region. As the
voltage is increased, the drop in field in the intrinsic region will become
less and finally the field distribution will be almost flat from junction to
junction. Only half of the intrinsic region is shown in Fig. 1. For equal
mobilities the field distribution will be symmetrical about the center
Xi of the intrinsic region.
The illustration shows the recombination solution (1), which holds
near the center of the intrinsic region and overlaps (2), the no-recom-
bination solution. The junction solution (3) joins continuously onto the
no-recombination solution at the point .To and rapidly breaks away and
approaches the zero-current solution at the junction. The figure is sche-
matic and has not been drawn to scale. In most cases of interest, the low
fields in the recombination region will be much lower and the junction
solution will hold over a smaller fraction of the intrinsic region.
It is convenient to take x = 0 not at the center .r, of the intrinsic
region but at the minimum on the no-recombination solution. As the
applied bias increases, x, approaches zero.
Unequal Mobilities
In the general case of unequal mobilities, it is no longer so that / is
pure drift except at the junctions. However we can define a linear com-
1250 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
--Ec
/
//
/L^
1
1 X
^ /■•
1
1
1 /
1 /
1 /
/
1 /
1 /
1 /
/
1 /
1/
/ZERO
/ BIAS
/
^^^_y
^
1
Fig. 1 — Schematic of the field distribution and the three overlapping solutions.
bination of Jp and J„ Avhich has the same form as / m (2.6) and in
which the diffusion term is neghgible except near the junction. As we
show in section VI, the effect of unequal mobiHties is (1) to introduce
some asymmetry into the curve in the region where the curvature is
upward and (2) to displace the curve toward the NI junction (for the
case where the electrons have the higher mobility). Thus the field is
higher on the side where the carrier mobility is lower, as would be ex-
pected.
III. THE NO-RECOMBINATION CASE
This section deals with the case where recombination can be neglected
in comparison with generation. This will be so where 7ip is small com-
pared to Hi .
The continuity equation for J now becomes
dJ „ ni
— = 2g = —
ax T
(3.1)
(
THEORY OF THE SWEPT INTRINSIC STRUCTURE 1251
Combining this with (2.7) gives
^(^-,) = JL (32)
where L/ = Z)r is the diffusion length in intrinsic material.
Equation (3.2) can be immediately integrated. There are two con-
'stants of integration, one of which can be made to vanish by choosing
[a; = 0 at the center of the intrinsic region, where the first derivatives of
E and s vanish. {E is a minimum here and s a maximum). The solution
obtained by two integrations is
r -^=(~] -A (3.3)
As we shall see later, the constant A is determined by the voltage drop
j across the unit.
I The exact procedure now would be to substitute s from (3.3) into (2.6).
The resulting second order differential equation could, in principle,
Ithen be solved for E versus x. The exact solution, however, would be
i quite difficult. We shall discuss it in Section V. Here we make the assump-
'tion that throughout the intrinsic region the charge flow is mainly by
'drift, so that we can neglect the diffusion term in (2.6) and take / =
asE, as discussed in Section IL Later in this section we find an upper
limit on the error due to this assumption and show how the cubic can be
i corrected to take account of the diffusion term.
1 Putting s = I/(tE in (3.3) gives a cubic equation
1 for E/Ei as a function of x/2Li . This equation contains two parameters
I / and A . A determines the voltage and / is determined by the length
i 2L of the intrinsic region. The relation is as follows: Let the applied
[ voltage drop across each junction be at least a few kT/q. Then the
minority carrier currents from the extrinsic regions will have reached
their saturation values. Call Is the sum of the hole current from the
A^ region and the electron current from the P region. Is comes from pairs
generated in the extrinsic regions near the junctions. 7s can be made
arbitrarily small by making the N and P regions sufficiently highly
doped (provided the diffusion length in the extrinsic material does not
decrease with doping faster than the majority carrier concentration in-
1252 THE BELL SYSTEM TECHJVICAL JOURNAL, NOVEMBER 1956
creases). The current generated in the intrinsic region is qg per unit
volume. So the density of current from pairs generated in the intrinsic
layer is 2Lqg = qniL/r. Hence
/ = /. + ^
r
In what follows we shall assume that Is is negligibly small compared to,
/. Then
r _ /^'^A J (qUiD
'-\-7)^-\-L-
Thus / is L/Li times a characteristic current equal to (1) the diffusion
current produced by a gradient rii/Li or (2) the drift current produced by ."
a field that gives the voltage drop kT/q in two diffusion lengths in normal
intrinsic material. In germanium this characteristic current is about 5
milliamperes per cm .
That the current / is proportional to L and independent of voltage
follows from the neglect of recombination. When recombination is small
compared to generation, then the current has reached its maximum, or
saturation, value. All the carriers generated in the intrinsic region are
swept out before recombining. It will sometimes be convenient to take
(jEi as the unit of current. From the above and (2.8)
/ „V2£L ^3_^^
In germanium aEi is about 7 amperes per cm*. In general we will be deal-
ing with currents that are small compared to this. For example, if L,
is 1 mm, we would have to sweep out an intrinsic region 3 meters long
in order to get a current this large. If we take Ei as the unit field, aEi as
the unit current and 2Li as the unit length then the cubic becomes E —
I/E = x^ - A.
For a given structure and temperature the field versus x curves form
a one parameter family. A determines both the field distribution and the
voltage. The voltage increases as A decreases. Fig. 2 is a plot of E/Ei
versus x/2Li for L/2Li =0.1 and several different values of A. Fig. 3
is for L = 2Li and Fig. 4 for L/2L, = 3.
There is an upper limit on A but not lower limit. The reason is as
follows: As A increases, the minimum value of E (at x = 0) decreases
and the maximum value of s increases. So if A is too large, the maxi-
mum 8 will be so large that we cannot neglect recombination, which
becomes important when np approaches n', or s approaches 1. Fre-
I
THEORY OF THE SWEPT INTRINSIC STRUCTURE
1253
quently recombination can be neglected over parts of the intrinsic
region but not near the center, where the field is a minimum and the car-
rier concentration a maximum. Then (3.4) will represent the field dis-
tribution over that part of the region where recombination is unimpor-
tant. The correct solution will join onto the cubic as we move away
fi'cjm the center of the intrinsic region, which will no longer be at the
x — 0 point on the cubic. In Section IV we solve the ecjuations for the
recombination region and show how the solution approaches the cubic.
^\e ^\•ill show that, as A increases, the distance from the center of the
intrinsic region to the x = 0 point on the cubic also increases. The
value A = % corresponds to an infinitely long intrinsic region. For a
larger A there exists no exact solution that could join onto the cubic
as recombination becomes negligible. In Figs. 3 and 4 the .4 = § curves
join onto recombination solutions at values of E which are too low to
show.
0.15
0 14
0.13
0.12
0.11
0.10
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
y
y
^
A=-0.01
^^
/
/
/
/
/
A=0.0025
/
/
>>
y
/
^
y
/^
/
'<
^
A=0.01
-<-
^
y
—
0.02
0.04 , 0.06
x/2Ll
0.08
0.10
Fig. 2 — Field Distributions for L = 0.2Li
1254 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
As A decreases and becomes negative the cubic approaches the form
E' = Eo' + Ei
(3.6)
where Eq = —AEi is the minimum value of E". This form of the solu-
tion will be valid when the minimum E is large compared to {lEi/a).
As Eq increases, the voltage increases and the curve becomes flatter.
This is because the increasing field sweeps the carriers out and reduces
the space charge; so the drop in field decreases.
If (3.4) for E/Ei versus x/2Li is extended to indefinitely large values
of x/2Li , it approaches the straight line of slope 1 going through the
origin. Since E is always positive the curve is above this straight line at
X = 0. li A is negative the curve is always above the straight line and
always concave upward. If A is positive, the curve crosses the straight
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
^
y
y
^^
^
/
A = -1
^^
^
^^
//
//
/
/
/
/
0 /
/
/
' >
/o.i y
/
/
/,
/
/'/3
/
/
/
/
/
f
/
/
/
/
/
Ia=2/3
y
/
/
/
^
J
_^
/
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1,0
X/2Ll
Fig. 3 — Field Distributions for L = 2L,-
THEORY OF THE SWEPT INTRINSIC STRUCTURE
1255
line at E/Ei = I/aEiA and thereafter remains under it approaching it
from below. For positive A the curvature, which is upward near the ori-
gin, changes to downward at about x/2Li = -y/A.
The carrier concentrations n and p can be found from the E versus x
curves with the aid of Poisson's equation p — n = 1/a dE/dx and the
definition s = (w + p)/2ni with s = I/aE. These relations and (3.4)
give
p — n _ X
p + n L
1
1 +
IE,''
(3.7)
From (3.4) and (3.7) we may distinguish the following two regions
on the cubic:
(1) When E^/Ei is smaller than I/aEi (which as we have seen is
usually smaller than unity), the E versus x curve is concave upward, the
hole and electron concentrations are almost equal (charge neutrality)
and the particle flow is by diffusion.
(2) When E^/E-^ is greater than I/aEi , in general there is space
charge and the particle flow, like the charge flow, is by drift. The curve
is concave downward for positive A.
Figure 6, which we will discuss in Section IV, shows the field and car-
rier distributions for L = 2Li and A = 0.665 plotted on a logarithmic
2.8
2.4
^
/
///
2.0
/
//
//
/
1-
/
y/
//
/
1.2
A
2
~~ 3
/
//
/
/
/
0.8
0.4
.
. n
/ /
/
V
/
/
y^
2
/
0
^
3
r
0 0.4 0.8 1.2 1.6 2.0 2.4 2 8 3 2
X/2Ll
Fig. 4 — Field Distributions for L = GL,- .
1256 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
scale to show the behavior at low values of field and carrier density.
In the region of no-recombination the field distribution is indistinguish-
able from that for A = ^, which is plotted in Fig. 3 on a linear scale. In
the region where recombination is important the solution is found from
the assimiption of charge neutrality as will be discussed in Section IV.
The cubic and charge neutrality solutions are each shown dashed outside
of their respective ranges of validity. For A = 0.665 the half length of
the intrinsic region is 2.098 X 2Li . Thus the length of the intrinsic re-
gion is more than twice the effective length 2L in which current is
generated. The effective length will be discussed in more detail in Section
IV and it will be shown that the effective length 2L of current generation
is equal to the twice the distance from the IP junction to the minimum on
the cubic. As explained earlier, it is convenient to take x = 0 at the mini-
mum on the cubic.
Inirinsic-Exirinsic Junction Under Large Bias
Consider the limiting case of an intrinsic-extrinsic junction as the
bias is increased and the space charge penetrates many diffusion lengths
into the intrinsic material. Then the field distribution approaches the
straight line E/Ei = x/2Li . This, by Poisson's equation, means that
there is a constant charge density of Ni where
2aLi Li
Thus in the limit, the field in the intrinsic region approaches that in a
completely swept extrinsic region having a fixed charge density of Ni .
In germanium at room temperature Ni is about 4.10^" cm~^ As the
field approaches the limiting form, the voltage V approaches EiL^/iLi .
Thus the limiting form of the current voltage curve is
aEi L, y 2EiL
So in the limit the current varies as the square root of the voltage. Typical
values for germanium at room temperature are a-Ei = 7 amps cm"""',
£/Li = 10"^ and 2EiLi = 50 volts.
Equivalent Generation Length for an Lntrinsic-Extrinsic Junction
It should be noted that for an IP structure the current is the same as
for an NIP structure with an infinite / i-egion, or at least an / region
that is long compared to the distance of penetration of the space charge.
THEORY OF THE SWEPT INTRINSIC STRUCTURE 1257
Thus the equivalent length of current generation is 2L even though the
current is actually being generated in an effective length L. The reason
is that for an NIP structure the holes entering the right hand half of the
/ region were generated in the left hand side. For an IP structure the
holes entering the space charge regions from the left were injected at the
external left hand contact to the / region.
Applied Voltage
In all cases the voltage can be found from the area under the E versus
X curve. In Figs. 2 to 4 the area under the curves gives the voltage ac-
curately; recombination becomes important only where the field is so
low as to have a negligible effect on the total voltage drop.
Correction of the Cubic
To conclude this section we consider the error introduced by using the
assumption / = asE. For simplicity take Ei as the unit field, 2Li as
the unit length and aEi as the unit current. Then the cubic becomes
E" — I IE = x" — A. The corresponding exact solution is E' — s =
x^ — A where the relation between s and E is given by equation (2.6)
which in dimensionless form is
^'%-^B-I (3.8)
where £ is of the order of 10~ .
Let bE and bs represent the difference between the cubic and the cor-
rect solution at a giv^en x. Assume that bE and its second derivative are
small compared to E and its second derivative respectively. Then bs =
2EbE and on the correct solution sE - I = (2lf -f I/E)bE. So (3.8)
becomes
bE ( £' \d'-E
E \2E^ + // dx'-
(3.9)
To obtain a first approximation to bE/E we use the cubic to evaluate
d E/dx . It is convenient to express the results in terms of a dimension-
less variable z = E/I^'^, or if E and / are measured in conventional units
z = E{a/Eilf'\ Then (3.9) becomes
bE __ 1 (L,£\-" ( z \- , ( X Y ^'(1 - z) (3 ^Q^
E 2\U / \z^ + hJ \2LJ {z^ + i)^
iV'hen the lengths are in conventional units.
1258 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
The first term has a maximum value of 0.35 (L,£/L^)^'^ at 2 = 0.6
and the second term a maximum value of 0.18 at 2 = 0.5 and x = L.
The dashed curve in Fig. 2 for ^ = ,01 is the corrected cubic. For
the other curves in Fig. 2, the correction is smaller. For the curves in
Figs. 3 and 4 the correction is too small to show.
Limits on the Solution
We now show that 8E as derived above is not only a first approxima-
tion but also upper limit on the correction necessary to take account of
charge diffusion. That is, an exact solution to (3.8) lies between the cubic
and the corrected cubic.
Consider the region where the second derivative of E is positive so
that the perturbed curve lies above the cubic as in Fig. 2. On the cubic
we have s£' — 7 = 0. As we move upward from the cubic and toward the
dashed curve, sE — I increases. The value oi sE — I on the dashed curve
just equals the value of £' d'E/dx' on the cubic. However, the dashed
curve has a smaller second derivative than the cubic. Thus in moving
upward from the cubic toward the dashed curve sE — I increases from
zero and £' d E/dx , which is positive, decreases; on the dashed curve
sE — I is actually greater. Therefore there is a curve lying just under
the dashed curve where the two sides of (3.8) are equal. The same argu-
ment applied to the region where the second derivative is negative shows
that the equation is satisfied by a curve lying just above the first per-
turbation of the cubic. Where the curvature changes sign, the cubic is
correct.
It should be emphasized again that the neglect of the diffusion term
in the current is justified only for the ideal case of equal hole and electron
mobilities. For unequal mobilities both drift and diffusion will be im-
portant in current flow. However, as we will discuss in section 5, we can
simplify the problem of unequal mobilities by defining a fictitious current
that has the same form as / in (2.6) and (3.8).
IV. RECOMBINATION
As discussed in Section III, when the voltage for a given current is re-
duced, s increases and near x = 0 becomes comparable to unity. Then
recombination becomes important and the cubic solution breaks down,
or rather joins onto a solution that takes account of recombination.
When recombination is important the center Xi of the intrinsic region is
no longer at the .r = 0 point on the cubic but to the left of it. That is, if
we want the same current with continually decreasing voltage, we even-
THEORY OF THE SWEPT INTRINSIC STRUCTURE 1259
tually get to the point where a longer intrinsic region is required. Finally
for a given current we reach a minimum voltage which corresponds to an
infinite length of intrinsic region. Another way of saying this is that,
when recombination becomes important, the length L defined in terms of
the current by / = qg2L = qrii/rL is no longer the half length of the
intrinsic region.
Equivalent Generation Length
We shall continue to define L by / = qnilrh. Thus L is an equivalent,
or effective, half length of current generation and not the half length of
the intrinsic region. By definition L is the length such that the amount
of generation alone in the length L is equal to the net amount of genera-
tion (generation minus recombination) in the total half length of the
intrinsic region. Hence
gL = [ \g - r)dx (4.1)
where Xi is at the center of the intrinsic region and Xp at the IP junction.
We shall for the most part deal with reverse biases of at least a few kT/g,
in which case recombination is negligible at the junctions. Then the exact
solution becomes the no- recombination solution before reaching the junc-
tions. We shall continue to take x = 0 at the point dE/dx = ds/dx = 0
on the no-recombination solution which the exact solution approaches
as recombination becomes negligible.
Simplifying Assumptions
The general differential equation with recombination will be the
same as for no-recombination except that g — r replaces g. From (3.1)
and (3.2)
From (2.12) and (2.13) and Poisson's equation
r = !^ = A^ + pY _ (^ - P)^ = s' - 9 (— —\ a '\)
g n? V 2n, / (2n,) ^ \E, dx ) "-^"^^
The following analysis will be based on the assumption of charge neu-
trality. That is we neglect terms m p — n in comparison with those in
p -\- n.\n particular this means:
(1) The charge flows by drift so / = asE. This is the same assumption
1260 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
made in the no-recombination case. It will be an even better approxima-
tion in the recombination region, where the second derivative of E is less.
(2) The particle flow is by diffusion. That is, E'^/E-C can be neglected
in comparison with s.
(3) The ratio of recombination rate r to generation rate g is propor-
tional to ^ — r; that is ^ — r = ^(1 — s~).
All of these simplifying assumptions can be justified by substituting
the resulting solution into the original expressions and showing that the
neglected terms are small when recombination is important. If the
solution is substituted into (4.3) and (2.6) the neglected terms will
turn out to be negligible — and therefore assumptions (1) and (3),
justified — when s^ is large compared to £/L, . Assumption (2) follows
from (1) and the fact that IjaEx is small compared to unity.
Assumptions (2) and (3) may also be justified by the discussion fol-
lowing (3.7) in the following way: Where recombination is important s
must be near unity. So the cubic will begin to break down when s =
II<jE becomes near to unity, or when E approaches I la. However, if
E is approximately I /a then cE^/IEi is approximately {I/aEif, which,
as we saw in the Section III, is small compared to unity in practical
cases. Thus recombination becomes important and the solution joins
onto the cubic in the range where E'^/Ei is small compared to I/aEi .
In this range the particle flow is by diffusion and p — n is small compared
to p -f n. As we move toward the center of the intrinsic region s increases
and E and dE/dx decrease. Therefore, since assumptions (2) and (3)
are good where the solution joins onto the cubic, they are good through-
out the region where recombination is important.
The Recombinafion Solution
The differential ecjuation (4.2) now takes the form
d's (1 - s')
dx" 2L,2
(4.4)
The solution for s in the recombination range is seen to be the same for
all values of the current. When s has been found E is found from E =
I/as.
For small disturbances in normal carrier concentration, s is only
slightly different from unit}' and (4.4) takes the familiar form
d' , . I - s
-r^ (1 - s) =
dx' L
2
THEORY OF THE SWEPT INTRINSIC STRUCTURE 1261
which says that the disturbance in carrier concentration varies expo-
nentially as .t/L, .
Equation (4.4) can be integrated once to give
where So is the value of s at the center of the intrinsic region where s is a
maximum.
As recombination becomes unimportant, s becomes small compared
to unity and (4.5) approaches the form
'dsY 1 /, So^^
(4.6)
\dx/ Lj"
and the solution joins onto the no-recombination solution.
Joining onto the Cubic.
We have seen that the solution joins onto the no recombination solu-
tion, in the region where particle flow is by diffusion so that the no
recombination solution has the form s = A — (.r/2L,:) . This is readily
transformed to the form (4.6) with
^ = So (l - ^) (4.7)
Thus the one arbitrary parameter so in the recombination solution
determines the parameter A in the cubic that the recombination solution
approaches. Since the maximum value of So under reverse bias is unity,
the maximum value of /I is f . Negative values of A correspond to solu-
tions where recombination is always negligible.
The s versus x Curve
To find s versus x we integrate (4.5). There is one constant of integra-
tion, which is fixed by the choice of x = 0. We have taken a: = 0 at the
point where dE/dx = ds/dx = 0 on the cubic. To make the recombina-
tion solution join the cubic we choose the constant of integration so that
the recombination solution extrapolates to s = 0 at {x/2Lif = A. Then
^ = Vl-^f /„, f , ,=^ (4.8)
2Li 2 Jo v3(so — s) — (so' — s^)
which can be expressed in terms of elliptic integrals.
12G2 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
^
"^
^
v,^
■"--'^
So=0.9 5
X
^
^
0.5
\
kk
^v
\
\
■
—
0.25
\
\
\
\,
\
\
\
\
\
\
V
-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
X/2Ll
Fig. 5 — Variation of s = -plni = n/n; in the range where recombination is
important.
Deep in an infinitely long intrinsic region the carrier densities ap-
proach their normal values n = 7? = n, , or s = 1. Putting So = 1 in
(4.8), we find that as s approaches So = \-,x becomes infinite. This will
be the solution for a simple intrinsic-extrinsic junction. Fig. 5 is a plot
of s versus x for various values of So . The dashed curves represent the
corresponding no-recombination solution s = ^ — {x/2LiY.
The IP Junction
It remains to find the position of the IP boundary. We now show that
if recombination is unimportant at the junction, so that the solution
joins onto a no-recombination solution, then the position of the junction
is at a; = L where L is the effective length of current generation and
a* = 0 is the point where dE/dx = ds/dx = 0 on the no-recombination
solution (which of course will not be valid at x = 0). The proof is as
follows: From the definition (4.1) of L and (4.2)
L = /;"(l-./,)rfx = 2L/£'|,(g-.)*-
= 2Lv
_dx \E{'
(4.9)
If the boundary comes where recombination is negligible so that
{E/Eif - s = (a-/2L,)' - A, then (4.9) gives Xj, = L. Physically
THEORY OF THE SWEPT INTRINSIC STRUCTURE 1263
this means that the amount of recombination in the interval from
X = 0 to a; = L is just equal to the excess amount of generation in the
interval from the center of the intrinsic region to x = 0.
If the applied reverse bias is less than a few kT/q then recombination is
important even at the junction and there is no joining onto a no-recom-
bination solution. In this case (4.9) says that for a given choice of cur-
rent (and hence of L) the boundary comes where
Example. Fig. 6, which we discussed briefly in Section III, is a plot
of the field and carrier distributions for L = 2Li and So = 0.95, for which
A = 0.665. The hole and electron densities were found from (3.7) and
p -{- 71 = 2niS where s is found from Fig. 5. When s approaches So (4.8)
for X versus s takes the simple form
•^ '^i So S /'lIlN
ZLi 1 — So^
This will be accurate when So — s is small compared to 1/so — So . We
have used (4.11) to evaluate the s versus x curve beyond the range of
the So = 0.95 curve in Fig. 5.
It is seen that the recombination solution in Fig. 6 joins the cubic
in the range where n and p are still almost equal.
Variable Lifetime.
Finally consider the general case where the variation in r with car-
rier density cannot be neglected. Then, with n = p = UiS, (2.15) be-
comes r = To + (tj — To)s and Li" in (4.4) is replaced by Dt[1 + (tj/tq —
l)s] where Tj/tq is given by (2.17). The more general form of (4.4) can
be solved graphically after one integration. The solution will join onto a
cubic if (ri/ro — l)s becomes small compared to unity before space
charge becomes important. This will be so if (t,/to — Vf'I/aEi is small
compared to unity.
V. THE JUNCTION SOLUTION
In this section we consider the solution near the junctions, where
the assumption / = usE breaks down. We shall deal with reverse biases
of at least a few kT/q so that recombination is negligible at the junctions.
The junction solution will therefore join onto the no-recombination
solution. We shall use the cubic solution in the no recombination region.
Again it is convenient to use dimensionless variables with Ei as the
1264 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
1.0
10
10
10
., .
1
8
-^=-=s
-^
CHARGE
NEUTRALITYy
\
f-
-1
\
8
6
4
2
-?
\
\
/
/
\
8
6
4
2
J
\
./
\
CENTER OF
•^^
CUBIC
^
,'V
7
pV
U-'
X = Xi.
)
'~~~~
;^
y
Pi
j
^ J
El
il
-3
n
1
-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0
x/2Li,
0.2 0.4 0.6 0.8 1.0
Fig. 6 — Field and carrier distributions for L = 2Lt and A = 0.665 (so = 0.95).
unit field, 2Lj as unit length and (tEi as unit current. Then on the cubic
s = //£", and E^ — I IE = x — A. The current is related to L by
/ = '\/2£L where the dimensionless £ is of the order^of 10~ for ger-
manium at room temperature. Substituting the exact no-recombination
solution E' — s = .r' — A into the solution (2.6), or (3.8), for the current
gives the second order differential equation
EJ
E{x' - A) - I
(5.1)
for E as a function of .t. The two boundary conditions are as follows: At
X = 0, clE/dx = 0 by symmetry. At the IP junction the carrier concen-
tration must rise and approach that in the normal P material. For a
strongly extrinsic P region the normal hole concentration P is large
compared to both iii and the electron concentration. Thus s must in-
crease and approach P/2w, » 1 as we approach the P region. Clearly
the cubic cannot satisfy this requirement. On the cubic the maximum
value of .s comes at x = 0 and is less than unity. As we approach the June-
THEORY OF THE SWEPT INTRINSIC STRUCTURE 1265
tion E increases so s = I/E must decrease. Thus the correct solution
must break away from the cubic near the junction.
Instability of the Solution
Equation (5.1) has two Hmiting forms and makes a rather abrupt
transition between them. Over most of the intrinsic region, the quantity
in brackets [£'s — /] = [E{E^ — x^ -\- A) — I] ahnost vanishes. It differs
from zero just enough that when multiplied by the very large factor
£^ ;^ 10*^ it gives the correct second derivative of E. In Section III we
derived an upper limit on the small deviation bE from the cubic required
to satisfy the differential equation. If E deviates from the cubic by more
than this small amount, then the second derivative of E becomes too
large. This increases the deviation from the cubic, which further in-
creases the second derivative and so on. E and s rapidly approach
infinity in a short distance. This, of course, is the reciuired behavior at
the junction. The rapid increase in s makes it possible for s to approach
P/2ni .
In Section III we showed that there is a solution to the differential
equation that lies within a small interval bE from the cubic. Suppose we
try to solve (5.1) graphically or on a machine starting at x = 0. There
are two boundary conditions: By symmetry dE/dx = 0 at x = 0. We
choose for E(0) a value somewhere in the interval 8E(0). The resulting
solution will not long remain in the interval 8E(x). In fact there is only
one choice of E(0) for which the solution remains close to the cubic
from .T = 0 to a; = oc . For any other E(0) the solution would remain
close to the cubic for a certain distance and then abruptly become un-
stable and both E and s approach infinity. £"(0) must be so chosen that
the solution becomes unstable and E and s become large at the junction.
However it is impractical to set E(0) on a machine with sufficient ac-
curacy to insure that the solution will remain stable for a reasonable
distance. A more practical procedure is to find a solution which holds
near the junction and joins the cubic to a solution in the adjacent
extrinsic region.
Zero Bias
It may be helpful to approach the junction solution by reviewing the
simple case of an IP junction under zero bias. Both charge and particle
flow vanish. The vanishing of particle flow means that in the intrinsic
region E' — s is constant, (2.7). Since E = 0 and s = 1 in the normal
intrinsic material, it follows that E^ — s = 1. With 7 = 0 the equation
1266 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
for current becomes
sE
£2
E^ + E
£2
(5.2)
This can be integrated at once. The boundary conditions are dE/dx = 01
when E = 0 and E = Ej at x = L; the field Ej at the IP junction will
be determined by joining the solutions for the / and P regions. The
solution can best be expressed by parametric equations giving x and the
potential V as functions of E.
L — X
£
J E
dE
= £
Vj - F = £
E
E Vl + E'-/2
dE 2kT
csch'
E
V2
— csch
-i^j
Vl + E-'/2
Q L
sinh"
1l
V2
sinh'
— 1
V2j
E -
V2_
(5.3) ,
(5.4)
where we have used the relation between dimensionless quantities
£ = ■\/2kT/q, which follows from (2.8) with Ei = 1. It will be more
convenient to express voltages in terms of kT/q rather than in terms of
the unit voltage 2EiLi ; then the ratio qV/kT is independent of the
units. For convenience we take the voltage as increasing in going toward
the IP junction with V = 0 in the normal P material. The voltage Vj
at the junction is found by joining solutions.
On the P side, let the excess acceptor density be P. Adding the term
— aP to the right hand side of Poisson's (2.1), and proceeding as before
we have, instead of (2.5)
— s
qT
'" kT,
= J = 0
where Sp = P/2ni . We shall assume that the P region is strongly ex-
trinsic so that n <K p. Then s = Sp in the normal p material, where
j^ = V = 0. Hence
E'
'qV
'"'"Vkr \
(5.5)
In the intrinsic material the corresponding solution is -E"" — s = — 1 .
Since both E and s are continuous at the junction, qVj/kT = 1 — 1/Sp
where l/sp can be neglected. Thus i?/ = Sj = Sp exp [ — (qVj/kT)] =
Sp/e where e = 2.72 is the base of the natural logarithms.
Knowing Ej we can find the field and potential distributions in the
intrinsic material from (5.3) and (5.4).
THEORY OF THE SWEPT INTRINSIC STRUCTURE 1267
Reverse Bias
Now in the intrinsic region, E^ — s = x"^ — A. Let Ec be the value
of E at the junction as given by the cubic, and let Sc = I/Ec be the
corresponding value of s. Then at the junction x^ — A = E^ — Sc . In
the P material equation (5.5) will still be a good approximation near
the junction, where the additional terms arising from the flow will be
negligible. Joining the solutions for the / and P regions and neglecting
Sc in comparison with Sp gives
^- = 1 + ^
fC i Sp
Again using sy = Sp exp [— {jqV j/kT)] we have
Ef = E; + Sp exp [- (1 + E^/sp)] (5.6)
■In most practical cases Ec will be small compared to Sp = P/2ni so
Ej will be the same as for zero bias.
Junction Solution
We now consider an approximate solution that joins smoothly onto
the cubic and has the required behavior at the junction. Let x = Xo
be the point where this solution is to join the cubic. Then in (5.1) x^
must lie between .To and L . We can obtain two limiting forms of the
solution by giving x the two constant values, Xo and L respectively.
It will be best to take x = Xo since in practical cases the x~ term is not
important except near the point where the junction solution joins the
cubic. In all cases the uncertainty due to taking x^ = constant can be
estimated by comparing the solutions for x = Xo and x = L.
With X constant, (5.1) can easily be integrated. The two boundary
conditions are (a) E = Ej at x = L, where Ej is given by (5.6), and (b)
to insure a smooth joining, the slope at x = Xo must be the same as that
of the cubic, namely
2a;o
\dx /o 2Eo + I/Eo'
The first integration of (5.1) with x = .To gives
(5.7)
'dEY ^ (cIEY 2^
,rf.T / \dx A £-
^ - ^ (Eo' - I/Eo) - IE
4 Z
(5.8)
where (dE/dx) is given by (5.7) and Ed^ — I/Eo = Xo — A. The E versus
12G8 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
X curve can now bo found from (5.8) and
X - Xo = I -r
L -
0 \dx/
=/:©"'-
(5.9)
In general we will be intrested in cases where the junction solution
holds over a length L — .To that is small compared to L, so we can take
.To = L in (5.7). It will also be valid to let Eo in (5.7) and (5.8) be the
value Ec on the cubic at x = L. Putting Ec = Eo in equation (5.6) then
gives Ej in terms of Eo and Sp = P/2ni , where P is the majority carrier
concentration in the extrinsic region. In what follows we shall use these
approximations. It will be convenient to express .To = L in (5.7) in
terms of / using / = \/2Z/<£. We continue to use dimensionless quan-
tities with El , 2Li and aEi as the units of field, length and current re-
spectively, and 2LiEi as the unit of voltage. In general however we can
express voltages in terms of kT/g.
When Eo^ is either large or small compared to /, the junction solution
takes a simple form and the field and potential distributions can be
found analytically. We next consider two approximations that hold in
those two cases respectively. Relatively good agreement between the
two solutions at Eo = I indicates that each solution may be used up to
this point.
Case of Eo Large Compared to I
From (5.7) to (5.9)
X — Xo = -x/ScC /
J E
0 l_
3\2
+ {E' - Eo')
-1/2
dE
(5.10)
This can be solved in the following two overlapping ranges where the
integrand has a simple form:
Range 1. Here E — Eo'is small compared to 2Eo , so (5.10) becomes
£
X — Xo =
\/2Ec
sinh
-1
\e - Eo) ?f-'j
(5.11)
Since E and Eo are almost equal, we have for the voltage drop in this
range
V - Vo = Eo(x - Xo) (5.12)
Range 2. Here E'^ — Eo' is large compared to 2(£L/Eof, so (5.10)
gives
THEORY OF THE SWEPT INTRINSIC STRUCTURE
1269
dE
L-x=V2S^r^
En
^2£ ^etnh- i - ctnh- i") (5.13)
£"0
En
En
From Eq ^ / it follows that Ranges 1 and 2 overlap. By joining the
two solutions in the overlap region, the solution in Range 2 can be
written as
£
X — Xq =
\/2Ec
(n
8En^ E — En
I E -\- Eo
(5.14)
Putting E = Ej in (5.14) gives the distance over which the junction
solution holds. In general we will be interested in cases where Ej is
large compared to Eq so (5.14) becomes
L — .To _ 3 (n2zQ
I 2 2o
(5.15)
where I = \^&/I^'^ and as before 2o = Eq/V^. In conventional units
I = 2L
L2
(5.16)
Fig. 7 is a plot of (L — Xd)/1 versus Zq . In germanium at room tempera-
ture £,Li will be around 10~ cm. Thus the junction solution will hold
over a region that is small compared to L if L is large compared to
3 X 10"^ cm.
Again it is convenient to use the relation & = '\/2kT/q to express
the voltage in terms of kT/q.
'") (3.17)
Je \dx/ q
Ej" — Eo
T?2 TP 2
By joining the two solutions in the overlap region, the voltage in Range
2 can be expressed as
kT
2Eo\ ^g>
e;-)
(5.18)
Setting V = V j and E = Ej in (5.18) gives the total voltage drop in
the region where the junction solution holds. Let AF be the difference
between Fy — Fo and the built in voltage drop at the junction. Then
substituting (5.6) with Ec — Eq into (5.18) and subtracting the built in
drop we have for AF,
AT = ^
9 L
(n
En
Eo_
s
p -i
(5.19)
1270 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
5
o
f< 0.5
0.2
O.I
0.05
'!
0.01
0.1
1.0
20
10
100
Fig. 7 — Variation of (L — Xo)/( with Zo .
I/Eo is equal to the value of s on the cubic at x = L. For positive values
of A the maximum value of E^/I is L/I = l/\/2£ as can be seen from
the cubic. In germanium at room temperature <£ is about 10~ (for
2Li = unit length) so the reverse bias produces an additional voltage
drop in the junction region equal to about IkT/q. For negative values
of A the additional voltage drop near the junction would be higher.
Comparing (5.3) and (5.13) we see that the junction solution reduces
to the zero bias solution when £"" is large compared to Eo" + 2. In this
case both solutions have the simple form
(5.20)
and
Vi- V
Q E
(5.21)
Case of Eo Small Compared to I
Now from (5.7) and (5.8) with xo = L = I\/2£, we have
£'
2Fj + {E- Eof (^ + ^'
(5.22)
THEORY OF THE SWEPT IXTRINSIC STRUCTURE 1271
Again there are t^^■o o\-erIapping ranges where the solution has a simple
form :
Range 1. Here E' is small compared to 21 /Ea . This will be so even
when E becomes large compared to Eq . Setting Ci = 2Eo/I and y =
E — Eo in equation (5.22) and integrating gives
X ^0 — ^ /\/ ~~r~
E, r^"^" dy
I X Vci^ + If
(5.23)
^ ,/Eo . , -1 /E - Eo\
and
V - Vo
IT /9F (5.24)
= ^ y Y (Vci^ + (^ - E,r- - ri) + 2Eo(x - .To)
Range 2. Here E is large compared to Eq . It follows from Eq « I
that E is also large compared to Ci . Setting ci = 21 /Eq we have
•^'- dE
L - X = V2£ / f
Jr e
E VWT~c?
Joining (5.21) and (5.23) where they overlap we have in range (2)
X — Xo = £ a/ ~ hi I ^3
'Mf.
E
C2
+ \/c.^ + E'
(5.26)
Putting X = L and /i" = Ej in (5.26) gives the length f, — .r„ in which
the junction solution holds. If Ej is lai'ge compared io c.> , then
^=y/|(«i (5.27)
where as before Zo = Eo/I^'^ and Z is given by (5.16). Fig. 7 is a plot of
(L — Xo)/l versus zo . The two approximations (5.15) and (5.27) for
Zn « 1 and Zo ^ I respectively are shown dashed. Both become inaccu-
rate as they are extended toward zo = I. The point at ^o = 1 was ob-
tained graphically. Each approximation is in error by about 28 per cent
here. The error will decrease as each approximation is (wtendod away
from 00 = 1 toward its range of validity.
The voltage in Range 2 is given by
1272 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 195G
Vj — V = Sinn — ^ — sinh - (o.28>
q L C2 C2J
or again joining (5.28) to the solutions in Range 1 we have in Range 2
V - 7o = -- sinh"' - + 2Eo{x - Xo) (5.29)1
q C2
The total voltage drop in the junction can be found by setting V = Vy'
and E = Ej in (5.29). The term 2Eo(L - xo) will be negligible. Wheni
E'^ is large compared to Co" + 2 the junction solution reduces to the
zero current solution as can be seen by comparing (5.3) and (5.25).
Then the solution has the simple form (5.20) and (5.21). Ej will always
be large compared to C2 . (Ef is appi'oximately Sp/e and Co" = 2so where 1
So is the value of s where the junction solution joins the cubic.) Thus the
difference AV between Vj — T^j and the built in voltage is
AF = --fn^ (5.30)
q I
Example. Fig. 8 shows the field distribution near the IP junction
for the case L = 2Li and /I = f , for which the intrinsic region is in-
finitely long. The field distribution near the junction, however, will he
indistinguishable from that for A = 0.6G5, or ,% = 0.95, for which the;
intrinsic region is about twice the effective length of current generation.
We have taken Ej = 30, which corresponds to an excess acceptor den-
sity P = 4.7 X 10' Ui in the P region. Over the range where the junc-
tion solution holds the cubic gives an almost constant field E = En = Ec .
The junction solution goes from the cubic to the zero bias solution in a ,
distance of the order of the Debye length. The sum of the built in volt-
age and the voltage derived from the cubic differ from the correct voltage
by the order of £Ei or about kT/q. The total voltage is about 0.3 EiLi ,
which would be about 11 volts in germanium at room temperature.
VI. GENERAL CASE, UNEQUAL MOBILITIES
This Section deals with the general case where the ratio of the hole
and electron mobilities is arbitrary. The procedure is similar to that
used in the preceding Sections. Many of the results for 6 = 1 are useful
in the present, more general, case. We shall deal first with the no-recom-
bination case and again find that E is given by a cubic. However, the
field distribution is no longer symmetrical and the coefficient of the I/E
term in the cubic is a linear function of x instead of a constant. The
differential equation foi' .s in the recombination region remains un-
THEORY OF THE SWEPT INTRINSIC STRUCTURE
30
20
10
8
6
5
1273
_E_
E,
1.0
0.8
0.6
0.5
0.4
0.3
0.2
0.1
E = E
J
-
-
ll
h
/
li
1 1
1
-
X = Xo
//
/
^
_^^^
^
1
;
/
-o—
SS=^.
.
———
-T"
f
-(
E-Ec-ho
CUBIC
1
1
1
1
t
/zero
/ BIAS
/
/
1
1
/
/
/
/
X-L
Fig. 8 ■ — Field Distribution near the IP Junction for L = 2L; and A = f.
changed. It is no longer so that charge diffusion can be neglected except
near the junctions. However, there is a linear combination of Jp and J„
in which the diffusion term is negligible except near the junctions.
Basic Relations
The equations are the two continuity (2.9) and Poisson's (2.1). The
formulas for g — r remain unchanged, since they involve only the
statistics of recombination and are independent of mobility. The hole
and electron currents are given by (2.2) with b arbitrary. Eciuation (2.2)
for Jp in terms of E, p and n remains unchanged. Now ./„/6 has the same
1274 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
form as J„ had for the b = 1 case. It is therefore desirable to deal with
the fictitious carrier flow J p + J„/b and the ficfitious current q{Jp —
Jn/b) since these have the same form in terms of E and s = (w + p)/2ni
as J and / had for b = 1. Thus
bj 1 + 6" L"" ™ dx
' dx^]
Es - £'~\ (6.2)
where Ei and £ have the same meaning as before and the conductivit}'
of intrinsic material is noAv a = qniij.(l + b). As before D and fj. are re-
spectively the diffusion constant and mobility for holes. Equations (6.1)
and (6.2) reduce respecti\Tly to (2.7) for ./ and (2.6) for I = cj{Jp — /„)
where 6=1.
When the flow is by pure diffusion, the holes and electrons diffuse "in
parallel" so the effective diffusion constant is the reciprocal of the average
of the reciprocal hole and electron diffusion constants. Hence the effective
diffusion length is given by
Lf = Dr ^^ (6.3)
We continue to let 2L = I/qg be the effective length of current genera-
tion; again it is the actual length for the no recombination case. Let x,,
and Xp be the coordinates of the AU and IP junctions respectively.
Since the problem is not symmetrical we will not take a' = 0 in the center
of the intrinsic I'ogion even for the no-recombination case.
No-Recoinbiualiun Case
Setting r = 0 we can immediately integrate the continuity equa+ '
dJp _ dJn _
dx dx
subject to the boundary conditions:
at the iV/ junction, x = rc„ , Jp = 0, Jn = ~Uq
at the IP junction, x = Xp , Jp = I/(j, Jn = 0
The result is Jp = g(x — .r„) and J„ = g{x — Xp). This agrees with / =
q(Jp — J„) = "^qgL since 2L = Xp — x„ is the length of the intrinsic
region, which, for no-recombjnation, is also the effective length of cur-
I THEORY OF THE SWEPT INTRINSIC STRUCTURE 1275
i| fent generation. It will be convenient to choose a; = 0 so that .t„ =
—Xp/h. Then the origin is nearer to the NI junction for 6 > 1. Now
from this and the boundary conditions (6.4) and I = 2qgL we have the
positions of the junctions:
L 1 + 6' L 1 + 6 ^^'^^
A.S before, the junctions are at .r = ± L for 6=1.
We can now find the fictitious carrier flow Jp + J„/6 and the fictitious
current q{Jp — Jn/i>) as functions of x.
■fp+T= (M^) !'^ (6.6)
where the dimensionless parameter j8 = (6^ — l)/46. Thus the fictitious
current q(Jp — J„/b) is equal to the actual current times a linear func-
tion of X. This function is always positive and varies from a minimum of
1/6 to a maximum of 1.
Combining (6.6) with (6.1) and integrating gives the equation
that we had before. Now, however, E is not a minimum at the same point
where s is a maximum. As before, when recombination is negligible
throughout all of the intrinsic region, A determines the voltage; and,
when recombination is important over part of the region, A determines
both the voltage and the length of the intrinsic region Xp — Xn > 2L =
\/o
' ibining (6.7) with (6.2) gives
(6.9)
which is similar to the previous (3.6) except that / is nuiltiplied by the
factor 1 + j3.r/L, which ^'aries from 1 + 1/6 to 1 + 6. The same argu-
ments used in Section V apply here and show that the second term in
brackets (the diffusion term) can be neglected except near the junctions.
In other words, although / is always part drift and pai't diflusion,
7(1 + ^x/L) is approximately pure drift except at the junctions.
Eliminating s between (6.9) and (6.8) and neglecting the diffusion
127G THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956 l!
term in (6.9) gives the cubic equation '
for the field distribution.
In germanium, where b = 2.1, /? = 0.406, Xp = 1.35L and x„ =
— 0.65L. The coefficient of I/aEi therefore varies from 1.47 to 3.10, or
by a factor of a Httle more than 2. This will introduce some asymmetry
into the E versus x curve in the low field region where the fictitious car-
rier flow Jp + Jn/b is by diffusion. It is evident that, as the voltage in-i
creases, the field versus x curve becomes increasingly symmetrical about
the x = 0 point; so the effect of having b 9^ 1 is simply to shift the
field distribution along the x axis.
Recombination -s
The arguments of section 4 again apply. Where recombination is im-
portant, n — p is small compared to n -\- p, so g — r = g(l — s^). The
diffusion term dominates in the fictitious particle flow Jp + Jn/b; that
is, E^/Ei is small compared to s, so (6.1) becomes
•^= -2n,D^
0 ax
Jp +-^= -^mD"^
The continuity equations give
So again we have
(fs^^ (1 - /)
dx^ 2Li2
(6.11)
The solution joins the no recombination solution where s = A —
{x/2Li)". Therefore A is again related to Sq , the maximum s, by ^ = :j
So(l — si/Z) and the s versus x curve is given by (4.8) and is symmetrica]
about the point where s is a maximum. When the recombination solu-
tion joins onto no-recombination solutions, there will be a difi'orent
no-recombination solution on each side of the recombination region.
The junctions will be at the points Xp and .r„ on the respective no-recom-
bination solutions. The length of the intrinsic region will not be Xp —
Xn = 2L since the x = 0 points are different on the two no-recombination
solutions and are separated by a region of maximimi recombination.
THEORY OF THE SWEPT INTRINSIC STRUCTURE 1277
To find E when s is known we express the current I = qiJp — Jn)
in terms of s and E. Since w — p is small compared to n + p, we set
/; = p = sUi in (2.2) and obtain
I =
[ j^ 1 - h kT dsl ,„ ,„v
Thus the current contains both a drift and a diffusion term. This is to be
expected for unequal mobilities. When holes and electrons have the
same concentration gradient, the electrons, which have the higher dif-
fusion constant, diffuse faster than the holes; hence the diffusion gives a
net current. It is seen that in the recombination region the total carrier
concentration has a symmetrical distribution about the point where it
is a maximum but the field remains unsymmetrical.
Junction Solution
When (Eo/Eif is large compared to I/cEi the junction solution is
independent of 6; so the solution obtained in Section V is valid. In all
cases the junction solution can be found using the method of Section V.
The effect of h will be small over most of the range where the junction
solution holds because the concentration of one type of carrier will be
negligible. To be exact, / in (5.8) should be multiplied by the factor
(1 + ^Xo/L), which can be taken to be (1 + b)/2b at the NI junction
and (1 -f b)/2 at the IP junction. Instead of equation (5.7) we have
as can be seen by differentiating (6.10) with Ei = 2Li = o- =1.
VII. EFFECT OF FIXED CHARGE
This section will deal briefly with the case where there is some fixed
charge but where the carrier charge cannot be neglected. For no recom-
bination, the field distribution is given by a first order differential equa-
tion. Solutions in closed form are obtained for the case of pure drift flow.
For recombination and charge neutrality the solution in Section IV is
valid provided the fixed charge is small compared to Ui . We have seen
that at large fields the E versus x curve becomes linear, correspond-
ing to a fixed charge density of A''; where Ni = \/2n{£/L,- . Thus
the fixed charge may have a dominant effect on the space charge while
having a negligible effect on the solution in the range where recombi-
nation is important.
1278 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Let the density of fixed charge he N = Nd — Na = excess density
of donors over acceptors. N may be either positive or negative. In what
follows we shall assume that N is positive. So the structure is NvP
where v means weakly doped n-type. Equations (2.2) for the hole and
electron currents remain unchanged. Poisson's equation becomes
^= aip-n-\- N) (7.1)
ax
We shall deal with the general case of arbitrary mobilities. As in Section
VI it is convenient to deal with a fictitious current q(Jp — Jn/b) and a
fictitious particle flow Jp + Jn/b. The extra term in (7.1) drops out by
differentiation when (7.1) is substituted into the equation for Jp —J„/'b
so (6.2) remains unchanged. However, instead of (6.1) we have
So the fictitious particle flow is no longer the gradient of a potential
involving only E and s.
No Recovibination
As in Section VI the continuity equations can be immediately inte-
grated to give (6.6) and (6.7). Again / is given by (6.9) where the dif-
fusion term on the right can be neglected except at the junctions; so
again we have asE = 1(1 -\- ^x/L). Substituting this into (7.2) and com-
bining (7.2) and (6.6) gives a first order differential equation for E versus
X. It is convenient to again use dimensionless quantities with Ei , 2L,
and aEi as the units of field, length and current respectively. Then the
differential eriuation becomes
!l
dx
where
= 2(.'c + aE) (7.3)
I
N
and as before Ni = \/2ni£/Li , which is around 4 X 10'" in germanium
at room temperature. The solution of (7.3) contains one arbitrary con-
stant (which corresponds to A in the V = 0 case). The lower limit on
the constant is determined by the necessity of joining onto a recombina-
tion solution \\hcre s approached unity. The positions of .r„ and Xp of
the Nv and vP junctions respectively are given by (6.5).
THEORY OF THE SWEPT INTRINSIC STRUCTURE 1279
In the region of low fields where E^ is comparable to or less than I,
(7.3) would have to be solved graphically or on a machine. At higher
fields the equation is easily integrated as discussed below.
Case of Pure Drift
When the flow is entirely by drift, E^ » / and (7.3) becomes
5^ = £ + " (^-^^
which is made integrable by the substitution E = yx. A family of solu-
tions for positive E throughout the v region is
{E - a,xT{E + a.xT- = Eo"'^"' (7.5)
where 2ai = \/4 + «' + « and 2a2 = -vZ-i -\- a- — a and Eo is the
value of E at x = 0. For an intrinsic region N = a = 0 and (7.5) reduces
to E^ = Eq' + x^, which is the same as (3.9) for negative .4. Fig. 9 shows
several curves for \'arious values of Eo . These remain above, and at
5 large distances approach, the asymptotic solutions E = aix on the
I right of the origin and E = —a2X on the left. These curves differ from the
corresponding curves for an intrinsic region in that the straight line
I asymptotes now have slopes of ai and — oo instead of ±1. Toward the P
I side the slope is greater because the positive change qN of the excess do-
I nors is added to the charge of holes. Toward the A^ side of the v re-
' gion the slope is reduced because A^ compensates to some extent for the
I electron charge. As a increases and the v region becomes more n type,
the solution approaches that for a simple NP junction, where E = ax
on the A^ side.
Another set of solutions of (7.4) are given by
(ai.r - EY^aox + E)"' = ai^'aa^V (7.6)
Several of these are shown in Fig. 9. They remain below the linear
asymptotes and go through zero field at x = ±:Xc . Actually these will
join onto solutions of the more general equation (7.3) when E becomes
small and the diffusion term becomes important.
Rccomhinaiion. When the fixed charge density is small compared to the
intrinsic hole and electron density the treatment of recombination in
Section IV remains \'alid. The recombination solution joins onto a solu-
tion of (7.3) at small fields. When N is comparable to ??» the recombina-
tion solution is difficult even with the assumption of charge neutrality.
1280 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
E.
E,
J a' Xf J
y' / X ' y
^J^ti \
-3.0 -2.5 -2.0 -1.5 -1.0 0.5 0 0.5 1.0 1.5 2.0 2.5 3.0
X/2LL
Fig. 9 — Field Distribution in the Range of Pure Drift for a fixed charge
N = N{ ,ora = 1 .
ACKNOWLEDGEMENTS
The author wishes to thank Miss M. M. Segrich for doing the exten-
sive computations and plotting the curves, and Miss M. C. Gray for
help with the calculations leading to Fig. 7.
APPENDIX A
Prim's Zero-Current Approximation
Prim's analysis is based on the assumption that the hole and electron
currents are negligibly small differences between their drift and diffusion
terms. Setting Jp = /„ = 0 then gives n and p as functions of the po-
tential, which is found by substituting n and p into Poisson's equation
and solving subject to the boundary conditions at the junctions. These
conditions involve the applied bias and the majority carrier densities in
the extrinsic regions. Since the current is assumed to vanish, the phe-
nomena of carrier generation and recombination do not enter the
problem and the results are independent of carrier mobility. The results
will be exact when there is no applied voltage; the potential drop across
the unit is then the built-in potential. In this appendix we use an internal
consistency check to see for what values of applied bias the analysis
THEORY OF THE SWEPT INTRINSIC STRUCTURE 1281
breaks down. First we find where the carrier concentration is in error by
finding the bias at which the minimum drift current as calculated from
qn(n + p)E becomes equal to the total current, as found from the excess
of generation over recombination in the intrinsic region. We then go on
to find where the error in carrier concentration gives a sufficient error in
space charge to affect the calculation of electric field. As we shall see, the
zero-current approximation gives too low a carrier concentration in the
interior of the intrinsic region. This will lead to serious errors in the field
distribution only if the space charge of the carriers is important. When
the bias is sufficiently high or the intrinsic region sufficiently narrow
that the intrinsic region is swept so clean that the carrier space charge is,
in fact, negligible, it will not matter that the calculated carrier density
is too low, even by orders of magnitude. In such cases, the electric field is
constant throughout most of the intrinsic region.
In the following we shall, for simplicity, take 6=1 and assume that
the extrinsic regions are ecjually doped so that the problem is symmetri-
cal.
Carrier Density
We now find where, on the zero current assumption, the drift current
becomes equal to the total current. This involves knowing only the
carrier concentrations and the field Ei in the center of the intrinsic
region, where the drift current qyi,{n -f- p)Ei is a minimum. By symmetry
n and y are equal here and n = p = 7ii exp ( — qVa/2kT) where Va is
the applied bias. The minimum field Ei is given by the total voltage
drop V and the field penetration parameter rj, which is the ratio of the
minimum field to the average field. Thus r) = 2LEi/V where 2L is the
width of the intrinsic regions. The difference between V and Va is the
built-in voltage {2kT/q)/ln{N /rii) where N is the majority carrier
concentration in the extrinsic regions. We now have for the drift current
in the center of the intrinsic region
,.(,. + p)£ = , ,0(1;)^ exp (-1^) (Al)
We next find the total current from the excess of generation over re-
combination in the intrinsic region. From the zero current assumption,
np = Ui exp ( — qVa/kT) is constant throughout the intrinsic region.
Hence g — r is constant. So the current / = q(g — r)2L = qL{ni — np)/
TUi is
qLrii
1 — exp
(A2)
1282 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Equating this to the drift current (Al) in the center of the intrinsic
region gives
The error in carrier concentration is less for narrower intrinsic regions
and lower biases. Thus (A3) gives a curve of L versus Va such that the
zero current solution gives a good approximation to carrier concentration
for points in the VaL plane lying well below the curve. As expected, for
zero bias, the solution is good for any value of L. However, for a bias of \
several kT/q, the solution for carrier concentration breaks down unless ^
L is a very small fraction of a diffusion length.
Carrier Space Charge.
In Prim's analysis the carrier space charge is so low throughout most
of the intrinsic region that the field remains approximately constant
and equal to Ei . However there must be enough carriers present that
the drift currents of holes and electrons can remove the carriers as fast
as they are generated. In this section we ask where the space charge of
the necessary carriers becomes large enough that its effect on the field
can no longer be neglected. Let i^E be the change in field due to the
space charge in the intrinsic region (not counting the high field regions
near the junctions). Unless LE is small compared to Ei the neglect of
carrier space charge will not be justified. We shall find the ratio of AE
to Ei .
If the field is to be approximately constant, then the hole and electron
concentrations can easily be found from the hole and electrons currents.
We shall deal with applied biases of at least a few kT/q, for which
recombination is negligible and the total current I = qg2L = qUiLlr.
Since g — r = g\s> constant, the hole and electron currents are linear in
X and, for constant field, are proportional to the hole and electron con-
centrations respectively. Thus the net space charge of the moving
carriers q{'p — n) is proportional to x and varies from zero in the center i
of the intrinsic region to qp near the IP junction, where n is small
compared to p and the current flows by hole drift, so / = q^ipEi . Thus
the maximum charge is I/iiEi and the total positive charge of the car-
riers on the P side of the center is IL/2iJ.Ei . This gives a drop in field
„ _ alL _ arii kT L
" 2qiJ.Ei ~ 'YqEiL}
THEORY OF THE SWEPT II
"JTRINSI
Dividing by Ei = 7]V/2L gives
AE L'
(kTV
Ei £'L,'
\mvj
1283
(A4)
Setting AE equal to some fraction, say 20 per cent of E^ gives a family
of curves for V versus L with ?? as a parameter. Prim has plotted such
curves in Fig. 11 of his paper. His curves will be good approximations
when V for a given L and 77 lies above the V given by (A4).
Prim's results are expressed in terms of the parameters U =
qV/2kT and L = 2L/£e where £e is the Debye length in the extrinsic
material. £e is given by the same formula as £ except that A'' replaces n» .
Substituting these into (A4) and setting AE = Ei/5 gives
L = 3.57 — '■ r,U (A5)
ni£
Prim's U versus L curves will be accurate up to the point where they
intersect the corresponding curves from (A5). For germanium a reason-
able value of NLi/ni£ is about 10 . This says that Prim's curves go bad
at about L = 10 , which would be about 2.1 X 10~^ cm in germanium
at 300°C.
Branching of the V versus L Curves
An effect which does not emerge from the zero-current analysis is
that V may have several values for the same L and 7/. In other words
the V versus L curve for given ?? will have more than one branch. Specifi-
cally, there will be a single V versus L curve up to a certain L at which
the curve splits into three branches that diverge as L increases. This
may be seen as follows: Consider an intrinsic region that is long compared
to the diffusion length. Suppose a bias is applied that is low enough not
to appreciably affect the space charge and potential drop at the junc-
tions. A current will flow and a proportional, ohmic voltage drop will be
developed across the intrinsic region. If the intrinsic region is long
enough, this ohmic voltage may become large compared to the built-in
voltage before the voltage drop at the junctions has changed appre-
ciably. In this range the field penetration parameter will be rising from
zero to about unity as V increases from the built-in voltage and ap-
proaches the ohmic voltage. As the voltage continues to increase, the
space charge begins to penetrate the intrinsic region and a majority of
the voltage drop comes in the space charge regions. Let L be the ef-
fective length of current generation. When L is larger than a diffusion
1284 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
length but small compared to the length of the intrinsic region, then the
voltage drop at the ends of the intrinsic region will be proportional to
L while the current, and consequently the minimum field, will be propor-
tional to L. Thus r? will be proportional to 1/L and will decrease as V
increases and the region becomes more swept. Finally the two space
charge regions meet; then ?? rises again with V and approaches unity.
Hence, for a given -q and length of intrinsic region, there will be three
different values of V. For lower L the dip in the i] versus V curve will be
less, and there will be only one V for some values of 77. Since -q starts
from zero at the built-in voltage and approaches unity for infinite volt-
age, there must be either one or three values of V for every r?. Thus
when the V versus L curve (or in Prim's notation the U versus L curve)
branches, it branches at once into three curves. Prim's plot gives the
upper branch in cases where all three are present.
A Medium Power Traveling-Wave Tube
for 6,000-Mc Radio Relay
By J. P. LAICO, H. L. McDOWELL and C. R. MOSTER
(Manuscript received May 15, 1956)
This paper discusses a traveling-wave amplifier which gives 30 dh of gain
at 5 watts output in the 5,925- to 6,425-nic common carrier hand. A descrip-
tion of the tube and detailed performance data are given.
TABLE OF CONTENTS Page
I. Introduction 1285
II. Design Considerations 1288
III. Description of the Tube 1291
3.1 General Description 1291
3.2 Tlie Electron Gun and Electron Beam Focusing 1295
3.3 The Helix 1302
3.4 The Collector 1311
IV. Performance Characteristics 1314
4.1 Method of Approach 1314
4.2 Operation Under Nominal Conditions 1315
4.3 Operation Over an Extended Range 1325
4.4 Noise Performance 1333
4.5 Intermodulation 1336
V. Life Tests 1342
VI. Acknowledgements 1343
I. INTRODUCTION
During the past ten years traveling-wave tubes have received con-
siderable attention in vacuum tube laboratories, both in this country
and abroad. So far their use in operating systems has been somewhat
limited, the most notable exceptions being in radio relay service in France,
Great Britain, and Japan. However, it appears that sufficient progress
in both tube and system design has been made so that traveling-wave
tubes may see widespread application in the near future.
This paper describes an experimental helix type traveling-wave tube
representative of a class which may see extensive use as a power amplifier
in radio relay systems. The tube is designated as the Bell Laboratories
type MI789. Stated briefly, the performance characteristics under
nominal operating conditions arc:
1285
1286 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Frequency Range 5,925-6,425 mc
Power Output 5 watts
Gain at 5 watts output 31-35 db
Noise Figure < 30 db
The tube is designed for use with w-aveguide input and output circuits.
The input voltage standing wave ratio (VSWR) is less than 1.1 and the
output VSWR is less than 1.4 over the 500-mc band when the tube is
delivering 5 watts of output. Fig. 1 shows a photograph of an MI789
and of an experimental permanent-magnet focusing circuit.
In developing this tube we have endeavored to produce an amplifier
which could be considered "practical" for use in a transcontinental radio
relay system. Because such an application requires a high degree of
reliability and refinement in performance, the tube was rather con-
servatively designed. This made it possible to obtain the desired gain
and power output without difficulty. On the other hand, the contem-
Fig. 1 — The M1789 traveling-wave tube and an experimental permanent mag-
netic circuit used to focus it. The circuit contains two specially shaped bar mag-
nets l)et\veen which the tube is mounted. The magnetic flux density obtained is
600 gauss, and the overall circuit weight is about 25 pounds.
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY 1287
plated system application made it necessary to investigate in detail the
problems associated with band flatness, matching, noise output, certain
signal distortions, reproducibility, and long life.
The solution of some of these problems required the development of a
precisely constructed helix assembly in which the helix winding is bonded
to ceramic support rods by glaze. Others required the initiation of a life
test program. Early results indicate that life exceeding 10,000 hours
can be obtained. This, in no small measure, is a result of a dc potential
profile which minimizes the ion bombardment of the cathode. Since
power consumed by focusing solenoids seriously degrades the o\'erall
efficiency of a traveling-wave amplifier, permanent magnet focusing cir-
cuits such as the one shown in Fig. 1 have been designed. Finally, to
further improve efficiency, a collector which can be operated at abcut
half the helix voltage was developed.
The major difficulties encountered in the course of the MI789 develop-
ment were: excessive noise output, ripples in the gain-frequency char-
acteristic, and lack of reproducibility of gain. There is evidence that a
growing noise current wave on the electron stream was the source of the
high noise output. This phenomenon has been observed by a number of
experimenters but is not yet fully explained. By allowing a small amount
of the magnetic focusing flux to link the cathode, the growing noise wave
was eliminated, and the noise reduced to a reasonable level for a power
amplifier. Reflections caused by slight non-uniformities in the helix pitch
were the source of the gain ripples. Precise helix winding techniques re-
duced these reflections so that the ripples are now less than ±0.1 db.
The lack of reproducibility in gain was caused by variations in helix
attenuation. Here, too, careful construction techniques alleviated the
problem so that in a recent group of tubes the range of gain variation at
five watts output was ±2 db.
We have divided this paper into four main parts. The next section
discusses some of the factors affecting the design of the traveling-w-ave
tube. (We will henceforth use the abbreviation TWT.) Section III
describes the tube itself. Certain performance data are included there
when closely related to a particular portion of the tube. Section IV
considers the rf performance in detail. There comparisons are made
lietween the performance predicted from TWT theory and that actually
observed. Finally Section V summarizes our life test experience.
This paper is written primarily for workers in the vacuum tube field
and assumes knowledge of TWT theory. However, we believe that
readers interested in TWT's from an application standpoint may also
benefit from the discussion of the rf performance in Section IV. Much of
that section can be understood w'ithout detailed knowledge of TWT's.
1288 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
II. DESIGN CONSIDERATIONS
While TWT theory served as a general guide in the development of
the MI789, a number of important tube parameters had to be determined
either by experimentation or by judgement based on past experience.
The most important of these were :
Saturation power output 12 watts
Mean helix diameter 90 mils
7a --^ 1.6
Magnetic flux density 600 gauss
Cathode current density '^ 200 ma/cm^
These quantities and the requirement of 30-db gain at five watts output
largely determined the TWT design.
The saturation output of 12 watts was found necessary to obtain the
desired linearity at five watts output and the 7a value of 1.6 to obtain the
flattest frequency response over the desired band.
The choice of helix diameter and magnetic flux density represented a
compromise. For the highest gain per unit length, best efficiency, and
lowest operating voltage, a small helix diameter was called for. On the
other hand, a large helix diameter was desirable in order to ease the
problem of beam focusing and to facilitate the design of a light-weight
permanent magnet focusing circuit. In particular, the design of such a
circuit can be greatly simplified if the field strength required is less than
the coercive force of available magnetic materials. This allows the use of
straight bar magnets instead of much heavier horseshoe magnets. More-
over, the size and weight of the magnetic circuit is minimized by employ-
ing a high energy product material. These considerations led us to choose
a flux density of 600 gauss, thereby permitting us to design a magnetic
circuit using Alnico bar magnets.
To obtain long tube life we felt it desirable to limit the helix intercep-
tion to about one per cent of the beam current. On the basis of past
results we estimated that this could be done with a magnetic flux density
2.6 times the Brillouin value for a beam entirely filling the helix. With
this restriction, Fig. 2 shows how the TWT design is affected by varying
the helix diameter. A choice of 600 gauss is seen to result in a mean helix
diameter of 90 mils.
In the selection of cathode current density, a compromise between
long life and ease of focusing had to be made. To obtain long life, the
current density should be minimized. However, this calls for a highly
convergent gun which in turn complicates the focusing problem. We
decided to use a sprayed oxide cathode operating at about 200 ma/cm^.
Experience with the Western Electric 41 6B microwave triode had shown
bOUO
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Fig. 2 — Alternate designs for the M1789. These curves are an estimate of how
the TWT design would be affected by changing the helix diameter. They represent
essentially a scaling of the M1789 design. In all cases the expected maximum
power output is 12 watts and the low-level gain is 33 db. The line at 90 mils mean
diameter in the curves represents the present M1789 design. In these calculations
it was assumed that :
a. 7a = 1.6
b. power output = 2.1 CIoVo = 12 watts
c. the magnetic flux density is 2.6 times the Brillouin flux density for a beam
entirely filling the helix.
d. the ratio of wire diameter to pitch is 0.34.
e. the dielectric loading factor is 0.79.
f . the ratio of effective beam diameter to mean helix diameter is 0.5.
1289
1290 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Table I — Summary of M1789 Design
I. Helix Dimensions
Mean Diameter
Inside Diameter
Wire Diameter
Turns per Inch
Pitch
Wire Diameter/Pitch
Active Length
II. Voltages and Currents
Electrode
III.
IV,
V.
90 mils
80 mils
10 mils
34
29.4 mils
0.34
5^ inches
Voltage
(volts)
Cathode 0
Beam Forming Electrode 0
Accelerator 2600
Helix 2400
Collector 1200
Heater Power
TWT Parameters at Midband (6175 mc)
6 watts
Current
(ma)
40
0
< 0.1
<0.4
>39.5
ka
C
QC
1.58
0.148
0.058
0.29
30
As defined by Tien'
N (number of X's on helix)
Dielectric Loading factor 0.79
Impedance Reduction factor 0.4
Electron Gun
Gun type — Converging Pierce Gun
Cathode type — Spraj'ed oxide
Cathode Current Density 213 ma/cm^ (for/x = 40 ma)
Cathode diameter — 192 mils
Convergence half angle 12° 40'_
Cathode radius of curvature (r^) 438 mils
Anode radius of curvature (/•„) 190 mils
It^c/n, 2.3
Pervernce 0.3 X 10~^ amps/volts^'z
VVa/Tk = 1.61 for Tk = 720°C
At the beam minimum in absence of magnetic field:
rmin (from Pierce^")
from Danielson, Rosenfeld & Saloom^
r9i
Tt/a-
a
Brillouin flux density for 80 mil helix ID
Actual focusing flux density required
Beam transmission from cathode to collector at 5 watts
output
11.5
mils
0.220
20.5
mils
3.50
4.80
mils
240
gauss
600
gauss
99%
RF Performance
Frequency range
5925-6425 mc
Saturation power output
12
watts
Nominal power output
5
watts
Gain at 5 watts
31-35
db
Noise figure
<30
db
Input VSWR
<1.1
"I impedance match to WR 159
/ waveguide
Output VSWR (at 5 watts)
<1.4
For an explanation of symbols see page 1345.
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY 1291
that tube life in excess of 10,000 hours was possible with such a cathode.
Moreover, an electron gun of the required convergence (about 13° half
angle) could be designed using standard techniques.
The various dimensions, parameters, voltages and currents involved
in the design of the MI789 are summarized in Table I. For the sake of
completeness, some rf performance data are also included.
III. DESCRIPTION OF THE TUBE
3.1 General Description
This section describes the mechanical structure of the MI789 and
presents some performance data closely associated with particular
portions of the tube. The overall rf performance is reserved for considera-
tion in the next section. In the MI789 we have tried to achieve a design
which could be easily modified for experimental purposes and which
would also be adapted to quantity production. To assist in obtaining low
gas pressure, a rather "open" structure is used, thereby minimizing the
pumping impedance. In addition, all parts are designed to withstand
comparatively high temperatures during outgassing, both when the tube
is pumped and, in the case of the helix and gun assemblies, during a
vacuum firing treatment prior to final assembly. Fig. 3 shows an MI789
and its subassemblies. Fig. 4 shows a simplified drawing of the whole
tube and Fig. 5 shows how the tube is mounted with respect to the perma-
nent magnet circuit and to the waveguides. The permanent magnets are
shown schematically in Fig. 5. In actual practice they are shaped so as
to produce a uniform field between the pole pieces. The means of doing
this was discussed by M. S. Glass at the Second Annual Meeting of the
I.R.E. Professional Group on Electron Devices, Washington, D. C.,
October 26, 1956.
Control of Positive Ions
Our experience with previous TWT's has indicated that an improve-
ment in life by as much as a factor of ten is obtained by arranging the
dc potential profile so that positive ion bombardment of the cathode is
minimized. This improvement has been observed even in tubes in which
all reasonable steps have been taken toward minimizing the residual
gas pressure. From Table I it is seen that the relative values of ac-
celerator, helix, and collector voltage are arranged to drain positive ions
formed in the helix region toward the collector. These ions are thereby
kept from reaching the cathode. Spurious ion modulation which can
result from accumulation of ions in the helix is also prevented.^
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1294 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
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TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY 1295
The effect that ions can have on cathode life was clearly demonstrated
in a TWT which was in many aspects a prototype of the MI789. This
tube operated with the accelerator, helix and collector at successively
higher voltages, with consequent ion draining toward the cathode. Severe
ion bombardment of the cathode brought about failure of most of
these tubes in from 500 to 2,000 hours. In contrast to this the average
life of the M1789 is in excess of 10,000 hours in spite of a cathode current
density about twice that in the prototype tube. Moreover, failure of the
M1789 comes about from exhaustion of coating material rather than as a
result of ion bombardment. During the course of the work of the proto-
type tube, an experiment was performed to determine how much the
ion bombardment would be affected by changing the potential dif-
ference between tube electrodes. In this experiment a small hole was
drilled in the center of the cathode and an ion current monitoring elec-
trode placed behind it. The ion monitor current was then investigated as
a function of electrode voltages. Fig. 6 shows the results. We see that
comparatively small potential differences are adequate to control the
flow of positive ions.
3.2 The Electron Gun and Electron Beam Focusing
The electron gun used in the MI789 is a converging Pierce gun. The
values of the gun parameters are summarized in Table I. Included are
both the original parameters introduced by Pierce as well as those defined
in a recent paper by Danielson, Rosenfeld and Saloom- in which the
effects of thermal velocities are considered. Fig. 7 shows a drawing of
the electrically significant contours of the J\II789 gun. Fig. 8 shows the
completed electron gun assembly. The method of constructing the gun is
a modification of a procedure used in oscilloscope and television picture
tubes. The electrodes are drawn parts made of molybdenum or, in the
case of the cathode, of nickel. They are supported by rods which are in
turn svipported from a ceramic platform to which these rods are glazed.
The whole gun structure is supported from the end of the helix by the
helix connector detail. Since this part must operate at helix potential,
it is insulated from the remainder of the gun by a ceramic cylinder which
is glazed both to it and to the accelerator.
To obtain good focusing, the cathode must be accurately aligned with
respect to the other electrodes. However, it must be omitted from the
gun during the glazing process and during a subsequent vacuum out-
gassing because the cathode coating cannot withstand the temperatures
involved. To insure proper placement of the cathode in the gun assembly
1296 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
ION
COLLECTOR
-20 VOLTS
BEAM-FORMING
^ ELECTRODE
0 VOLTS
COLLECTOR
1600,1800 OR
2000 VOLTS
^^S9W<R)W^''- timmmifMF- ■
T
CATHODE
0 VOLTS
ACCELERATOR
1800 VOLTS
HELIX
l.U
0.9
1
0.8
0.7
r\
0.6
^
0.5
0.4
0.3
0.2
XL
_-,/
ir"
¥ N
— i
lA
f
N
k >
\ 1
\\
/ 1
/ 1
1 1
\
/(;= 18(
DO V
f 1
O.IO
0.09
0.08
0.07
0.06
0.05
0.04
0.03
/j
.^^
1 \
.-^"'
r 1
'"2000 V
^ ^
A
a^
0.02
— • — r
16C
1 "
)0V .
1 1
, .-
-300
-200 -100 0 100
POTENTIAL DIFFERENCE BETWEEN HELIX
AND ACCELERATOR IN VOLTS
200
Fig. 6 — Effect of electrode voltages on ion bombardment of the cathode in a
prototype of the M1789. In this e.xperiment the helix voltage was varied while the
positive ion current to a monitor electrode behind a hole in the cathode was meas-
ured. Curves are shown for the collector voltage greater than, equal to, and less
than the accelerator voltage. During this experiment the accelerator voltage was
held constant at 1800 volts with a resulting beam current of 40 ma. The experi-
ment was performed on a continuously pumped sj'stem with the pressure main-
tained at 2 X 10-' mm Hg. The helix ID was 80 mils, the cathode diameter 300
mils, and the cathode hole diameter 20 mils. These curves show that the ion
bombardment of the cathode can be reduced by as much as a factor of 20 by prop-
erly arranging the voltage profile.
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY
1297
at a later stage, an alignment cylinder is included in the gun at the time
of glazing (outer cathode alignment cylinder in Fig. 8) . When the gun is
ready to receive the cathode, the subassembly shown in Fig. 9 is slid
into the outer alignment cylinder. The cathode to beam forming electrode
spacing is set using a toolmakers microscope, and welds are made be-
tween the inner and outer aligmnent cylinders.
Initially, we thought that the cathode should l)e completely shielded
from the magnetic field, and that the field should be introduced in the
region between the accelerator and the point at which the beam would
reach its minimum diameter in the absence of magnetic field. This ar-
//
/ra=l9i
/ /
/ /
ACCELERATOR ; / >
y//////////////////////////////^///^//y
CATHODE
\er r^ =192 >j
(COATED DIAMETER)
Fig. 7 — The electricall.y significant contours of the M1789 gun. All dimensions
are in mils. These contours were determined using an electrolytic tank and follow-
ing the procedure originated by Pierce. The measured potential at the beam boun-
dary in the tank was made to match the calculated value within ±j per cent of
the accelerator voltage to within 10 mils of the anode plane. The aperture in the
accelerator was made sufficiently large so that substantially no beam current is
intercepted on it. The significant parameters of this gun are:
P = 0.3 X 10-« amps/volts3/2 rel<y
fc/l-a =2.30 tr
e = 12.67° 7-95
VvIrFk = lM{Tk = 720°C) J
= 3.50 lAt the beam mini-
= 4.80 mils [mum in absence of
= 20.5 milsj magnetic field
= 213 ma/cm2
1298 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
HELIX
CONNECTOR
TUBE
HELIX LEAD
INSULATOR
\
BEAM FORMING
ELECTRODE
^- GLAZE BOND
-ACCELERATOR
1.64"
CATHODE
SUPPORT WIRES,
THREE AT 120° ~
SPACING
i
HELIX LEAD-
GLAZE BONDS
METAL RIBBON HAS THREE TABS
AT 120° SPACING WHICH ARE
LATER WELDED TO COUPLER ON
HELIX ASSEMBLY
SUPPORT WIRES, THREE
CONNECTED TO EACH
ELECTRODE
AT 120° SPACING
-^ GLAZE BONDS
CERAMIC
SUPPORT PLATFORM
HEATER
CATHODE
OUTER CATHODE
ALIGNMENT CYLINDER
- — INSULATOR
---__ INNER CATHODE
ALIGNMENT CYLINDER |
Fig. 8 — M1789 electron gun assembly. In constructing the gun, all the parts
with the exception of the cathode, heater, and inner support cylinder are mounted
on a mandrel which fixes their relative positions. Glass powder is applied to the
areas where glazed joints are desired. The unit is then heated in forming gas
(85% No ,15% H2) to 1.00°C to melt the glass and form the glazed bonds. With
this technique the precision required for alignment and spacing of the electrodes
resides entirely in the tools. The helix connector tube later slides into the coupler
detail of Fig. 14 to align gun and helix assemblies. The inner and outer cathode
alignment cylinders are welded together at two points at the end remote from the
cathode. Optical comparator inspection shows that the significant dimensions of
these guns are held to a tolerance of less than ±2 mils.
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY
1299
rangement did result in the best beam transmission to the collector.
We later discovered, however, that the noise on the electron stream be-
came extremely high when there was no magnetic flux at the cathode.
This effect will be discussed further in Section IV. We found that by
having a flux density of about 20 gauss at the cathode, the noise figure
could be considerably reduced with the only penalty being a slight in-
crease in interception on the helix. The penalt^y results from the fact that
the flux linking the cathode causes a reduction in the angular velocity of
the electrons in the helix region (from Busch's theorem), and this in
turn diminishes the magnetic focusing force.
Fig. 10 shows the distribution of axial magnetic field in the gun region.
The curve represents a compromise between that which gives best fo-
cusing (zero flux density at the cathode) and that which gives best
noise performance (about 25 gauss flux density at the cathode). This
flux density variation was arrived at by empirical methods.
CATHODE
SUPPORT LEGS
THREE AT 120°
SEPARATION
HEATER T
HEATER LEAD
INSULATOR
CATHODE
INNER CATHODE
- ALIGNMENT
CYLINDER
METAL TABS
TO HOLD
HEATER IN
PLACE
Fig. 9 — The cathode subassembly. In this unit the cathode is connected to
the inner alignment cylinder by three legs. These legs are first welded to the cath-
ode and then oven brazed to the alignment cylinder. During the brazing, a jig
holds the cathode accurately concentric with this cylinder. The cathode is then
coated and the unit is ready for assembly into the gun. The heater power required
to raise the cathode to its operating temperature of 720°C is about si.x watts.
1300 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Meaiirements of beam interception as a function of magnetic flux
density are sfiown for several beam currents in Fig. 1 1 . These measure-
ments were obtained without any rf input to the TWT. An interesting
way of normalizing these data is shown in Fig. 12. Here the magnetic
ACCELERATOR--. , /
/
/
CATHODE ^ /
^
MAGNET
POLE PIECE
, HELIX CONNECTOR
^
_fou 0 tFffWwi)'
BEAM-
FORMING
ELECTRODE
in
\///^////////A
MAGNETIC
M SHIELD
y////////////////////////////.
800
600
^^^^^^^^^^^^^
-
y
H^
400
200
-
/
f-
/
100
80
/
-
i
/
_
/
60
/
/
40
/
/
20
y
f
/^
^"^
in
/
-0.4 0 0.4 0.8 1,2
DISTANCE FROM CATHODE IN INCHES
1.6
Fig. 10 — Variation in magnetic flux density as a function of distance from the
cathode. A schematic representation of the gun electrodes and of the magnetic
parts which have been used to control the flux is also shown. All the elements in-
side the tube are non-magnetic so that the flux density variation is determined
entirely by magnetic parts external to the tube envelope. The flux density at the
cathode is built up (i.e., the step is put into the curve) by having the magnetic
shield end near the cathode. The flux which leaves the shield at this point increases
the flux density at the cathode over what it would be if the shield extended well
behind the cathode.
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY
1301
flux density has been divided by the Brillouin flux density for a beam
entirely filling the helix. This quantity is the minimum flux density
which could theoretically be used to focus the beam. This normalization
tends to bring all of the curves together. Thus we see that, although
the conditions in the IMI789 are far from those of ideal Brillouin flow
(because of transverse thermal velocities, aberrations in the gun, and
magnetic field at the cathode), the concept of the Brillouin flux density
still retains meaning, i.e., it appears that the flux density required main-
tains a fLxed ratio to the Brillouin value.
Applying sufficient rf input to the MI789 to drive it into non-linear
operation, results in defocusing caused by the high rf fields (both from
the helix wave and from space charge) near its output end. Fig. 13 shows
how the beam interception for different magnetic flux densities varies as
a function of the power output of the TWT. From these curves we see
that an output level of five watts can be maintained with about one per
cent interception with a flux density of 600 gauss.
6.(
x
_J
m
I 4.1
z
o
a
LU
4.0
3.5
3.0
I-
z 2.5
LU
cr
tr
D
U
2.0
5
<
LU
OD
U.
O
LU
1.5
1.0
O 0.5
tr
UJ
Q- n
1
i
40MA
Va= variable
Vh = 2400 VOLTS
Vc= 1200 VOLTS
20 MaI
\"
DMA
\ 1
1 \
30M/1
\
1 1
c
\ \
\\
\ '
\
\\
\
\
\
\
I \
\
\
i \
\
\]
^
\
kl
,N
\
V
\
^
1^
1
fe^
w
^
^
^— — i
^-,-
200
300
400 500 600
MAGNETIC FLUX DENSITY IN GAUSS
700
600
Fig. 11 — Per cent intercej^tion on the helix as a function of magnetic flux
density. These measurements were taken using a precision solenoid to focus the
TWT. The component of field perpendicular to the TWT axis was less than 0.1
per cent of the longitudinal field. During these measurements there was no rf
input to the TWT and there was substantiallj- no (<0.1 ma) interception on the
accelerator electrode.
1302 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
3.3 The Helix
The MI789 helix assembly is a rigid self-supporting structure com-
posed of three ceramic support rods bonded with glaze to the helix wind-
ing. A drawing of the helix assembly is shown in Fig. 1-4. The support
rods are made from Bell Laboratories F-66 steatite ceramic. This material
was chosen because of its low rf losses and because these losses do not
increase rapidly with temperature. Fig. 15 shows an enlarged photograph
of the glaze bonds between the winding and one of the support rods.
Attenuation is applied over a length of two inches starting li-^ inches
from the input end by spraying the helix assembly with aquadag (carbon
in water suspension) and then baking it.
Supporting the winding by glazing it to ceramic support rods has the
following advantages :
4.5
V 20 MA
n 30 MA
O 40 MA
A 50 MA
Va = VARIABLE
Vh = 2400 volts
Vc= 1200 VOLTS
0.5
(.0 1.5 2.0 2.5 3.0
MAGNETIC FLUX DENSITY
3.5
4.0
BRILLOUIN FLUX DENSITY FOR BEAM FILLING HELIX
Fig. 12 ^ The measurements of Fig. 11 normalized in terms of the Brillouin
flux density for a beam entirely filling the helix. The fact that the curves tend to
come together indicates that the concept of the Brillouin flux density retains some
meaning in the M1789. Because of the additional defocusing effects encountered
when the M1789 is driven to high output levels, the tube is usually used with
about 2.6 times the Brillouin flux density.
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY
1303
(1) The dielectric loading and intrinsic attenuation of the helix are
comparatively low because the amount of supporting structure in the rf
fields is small.
(2) High loss per unit length in the helix attenuator is made possible.
The reason for this will be discussed further below.
(3) The heat dissipation capability of the helix is greatly increased
because the glaze provides an intimate thermal contact between winding
and support rods. This is illustrated by Fig. 16 which compares the heat
dissipation properties of glazed and non-glazed helices.
(4) Mechanical rigidity is realized and therefore the helix can be
handled without risk of disturbing the pitch or diameter of the winding.
On the other hand, use of the ceramic rods in the j\II789 has a signifi-
cant disadvantage in that it makes the outside radius of the vacuum
envelope large compared to the helix radius, thus making coupled helix
matching out of the question. However, since the MI789 is required to
match over less than a 10 per cent band, this is not particularly serious.
To obtain reproducibihty of performance in the MI789, the helix
must be precisely constructed. Together, the pitch of the helix and the
amount of dielectric loading determine the synchronous voltage. A
pitch variation of ±1 per cent results in a voltage variation of about
±50 volts, and a loading variation of it 1 per cent results in a variation
»-
ir -■
m
U
LU
CL
y/sOO GAUSS
/^
6
/
r
i
V
y
/
600
y
^
^
^
• 700
2.5 5.0 7.5 10.0 12.5 15.0
POWER OUTPUT IN WATTS
17.5 20.0
Fig. 13 — Per cent interception on the helix a.s a function of rf power output.
These measurements were made u.sing permanent magnet circuit.s charged to
different field strengths. The magnetic field variation as a function of distance
from the cathode was as shown in Fig. 10. The component of magnetic field per-
pendicular to the tube axis in these circuits was less than 0.2 per cent of the longi-
tudinal field. All measurements were taken with a beam current of 40 ma and with
the helix voltage adjusted to maximize the power output.
1304 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1950
0) 03 (3 ro
^ -C --^ ■'^
mo
faC« " O „ -
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1_x gS =-«
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TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY 1305
of about ±25 volts. It is not difficult to hold the average pitch variations
to less than d=l per cent. The loading, however, is a more difficult prob-
lem for not only must the dielectric properties of the support rods and of
the glaze material be closely controlled, but attention must also be paid
to the size and density of the glaze fillets. The gain of the tube is affected
by the amount of loss in the helix attenuator. For the particular loss
distribution used in the MI789 a variation of ±5 db out of a total
attenuation of 70 db results in a gain variation of about ±1 db. The
helix attenuator depends to a large extent on a conducting "bridge"
between helix turns and therefore the amount of attenuation is sensitive
to the size and the surface condition of the glaze fillets. Thus, the glazing
process must be in good control in order to minimize variations in both
gain and operating voltage. With our present techniques, we are able to
hold the voltage for maximum gain to within ±50 ^'olts of the nominal
value. The gain is held to ±2 db — about half of the spread we believe
to be caused by variations in loss distribution and about half by differ-
ences in beam size.
Fig. 15 — Enlarged photograph of part of an M1789 helix. Two of the ceramic
support rods can be seen. The other is directly opposite the camera behind the
lielix and is out of focus. The fillets of glaze which bind the helix to the rods can
he seen along the upper rod. This section of helix was free from applied loss.
1306 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Helix-to-Waveguide Matching
In the helix-to-waveguide transducer the hehx passes through the
center of the broad face of the waveguide and energy is coupled between
helix and waveguide by an antenna and matching taper. A capacitive
coupler on the helix and an rf choke on the waveguide place an effective
ground plane at the waveguide end of the antenna. The rf choke also
assists in minimizing leakage of rf power. Details of this transducer are
shown in Figs. 5 and 14.
600
Hi
Q
<
a.
\-
z
o
<n
UJ
HI
o
550
500
450
400
- 350
LU
300
O
liJ
LU
cc
D
<
cc
Q-
LLI
1-
250
200
150
iOO
10 15 20 25
POWER INPUT TO HELIX IN WATTS
Fig. 16 — Comparison of heat dissipation properties of different helix struc-
tures. In this experiment, the helices were heated by passing dc current through
them while they were mounted in a vacuum. The temperature was determined
from the change in helix wire resistance.
Along with the results for glazed and non-glazed helices in a normal round
envelope, this figure shows results on a structure consisting of a glazed helix in an
envelope which has been shrunk around the helix support rods. This technique
produces a structure which, l)y virtue of the good thermal contact between the
support rods and the envelope, can dissipate more power than the conventional
structure. The additional complication of shrinking the envelope is not necessary
for the power levels used in the IM1789. However, this method could be used if it
were necessary to extend the tube's output range to higher power levels.
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY 1307
ij The dimensions of this transducer were determined empirically. It
j was found that the antenna length affects mainly the conductive com-
! ponent of the admittance referred to the plane of the helix. The length of
the matching taper affects mainly the susceptive component, and the
distance from helix to a shorting plunger, which closes off one end of the
waveguide, affects both components. If for each tube, the position of the
I waveguides along the axis of the TWT and the position of the shorting
plunger are optimized, the VSWR of the transducers will be less than 1.1
I (~26 db return loss) over the entire 500-mc frequency band. With these
j positions fixed at their best average value, the VSWR will be less than
I about 1.3 (--^IS db return loss).
Internal Reiiections
A problem that has required considerable effort has been that of
"internal reflections." By this we mean reflections of the rf signal from
various points along the helix as contrasted with reflections from helix-
to-waveguide transducers. The principal sources of internal reflections
are the edge of the helix attenuator and small variations in pitch along
the helix. In the MI789 the pitch variations are the main source of
difficulty.
The type of performance degradation caused by small internal reflec-
tions can be illustrated by the following. Consider a signal incident on
the TWT output as a result of a reflection from a radio relay antenna.
Except for a small reflection at the transducer, energy incident on the
TWT output will be transferred to the helix, propagated back toward the
input, and for the most part be absorbed in the helix attenuator. How-
ever, if there are reflection points along the helix, reflected signals will be
returned to the output having been amplified in the process by the TWT
interaction. Because of this amplification, even a small reflection of the
backward traveling wave can result in a large reflected signal at the TWT
output. In the MI789, these amplified internal reflections are con-
siderably larger than the reflection from the output transducer. They
limit the overall output VSWR to about 1.4, whereas the transducer
alone has a VSWR of about 1.1.
If there is a long length of waveguide between the TWT and the an-
tenna, the echo signal resulting from a reflection at the antenna and
a second reflection at the TWT will vary in phase with respect to the
primary signal as frequency is changed. This will cause ripples in both
the gain and in the phase delay of the system as functions of frequency.
Suppose the VSWR of the antenna is 1.2 and that of the TWT is 1.4
and the two are separated by 100 feet of w^aveguide. The amplitude of
1308 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
-a
-4
0
t
V
i
\
:3
5 4
^
\
I
\
/
\
/
\
lij
" 8
Z
/
\
/
\
/n
i
1
\
/
[
f
\
LOSS
i
\
/
/
\
/
I
/
/
\
i t6
(-
UJ
/
\
y
/
\
/
\
/
/
\
20
(5
t)
J
/
\
V
J
i
r
\
24
V
y
/
\
if
\
28
v/
4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4
FREQUENCY IN KILOMEGACYCLES PER SECOND
6.6
6.8
7.0
PERIOD OF PITCH DEVIATIONS
0.450" »+« 0.445"
■^-
0.455"
■-^
NOMINAL TPI= 40
EACH POINT REPRESENTS ONE TURN
DISTANCE ALONG HELIX >
Fig. 17 — Pitch deviations and internal reflections in an early M1789 TWT. ■
The ordinate of the pitch deviation curve is the difference between the measured
spacing between heli.v turns and the nominal value, which for this particular
helix was 25 mils. (The tube operated at 1,600 volts.) Each point represents a helix
turn. It is seen that the pitch deviations are periodic in nature, repeating about
every 0.450 inch.
The internal reflections were measured by matching the TWT with beam off '
at each individual frequency with a tuner to a VSWR of less than 1.01 (return
loss greater than 40 db). The beam was then turned on and the resulting reflection
taken as an approximate measure of the internal reflection. There appeared to be
no appreciable change in the helix-to-waveguide transducer reflection as a result
of turning th(! beam on. Evidence for this is the fact that when the beam was
turned on with the lielix voltage adjusted so that the TWT did not amplify, there
was little change in the reflection.
The peaks of the internal reflection curve occur at five, six and seven half wave-
lengths i)er i)eriod of the helix pitch deviations, indicating that the reflections
from each period arc adding in phase at these frequencies. At the 5,800-mc peak
the return loss is positive. This indicates a reflected signal larger than the incident
signal. Shorting the TWT output caused the tube to oscillate at this frequency.
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY 1309
the gain fluctuations will be about 0.25 db, the amplitude of the phase
I fluctuations will be about 0.9 degree and the periodicity of the fluctua-
tions will be about six mc. This effect may be eliminated by using an
I isolator between the TWT and the antenna to eliminate the echo signal.
I In addition to echo signals that occur between the TWT and the
1 antenna there are echoes which occur wholly within the TWT as a result
of a reflection of the signal from the output transducer and a second
reflection from some point along the helix. Thus even if a TWT is operat-
ing into a matched load it may have ripples in gain or phase characteris-
tics. These ripples may be controlled by minimizing the internal re-
flections. In the MI789 they are less than ±0.1 db in gain and one-half
degree in phase. Their periodicity is about 100 mc.
In addition to causing transmission distortions, internal reflections
can seriously reduce the margin of a TWT against oscillation. Outside
of the frequency band of interest, the helix-to-waveguide transducer
may be a poor match or the TWT may even be operating into a short
circuit in the form of a reflection type bandpass filter. At such fre-
quencies, the internal reflections must not be large enough so that an
echo between transducer or filter and an internal reflection point will
see any net gain, or else the TWT will oscillate.
With many types of helix winding equipment, variations in helix
pitch are periodic in nature. This causes the helix to exhibit a filter-like
behavior with respect to internal reflections. At frequencies at which
the period of the pitch variations is an integral number of half-wave
lengths, the resultant reflections from each individual period will add in
phase, thereby causing the helix to be strongly reflecting at these fre-
quencies. This effect can perhaps best be illustrated by considering some
results obtained in an early stage of the MI789 development. Fig. 17
shows measurements of the spacing between turns of an early helix.
Also shown is the return loss as a function of frequency that a signal
incident on the output of an operating TWT would see as a result of
internal reflections alone. Helix-to-waveguide transducer reflections were
eliminated with waveguide tuners during this experiment. The deviations
in helix pitch from nominal are rather large and are markedly periodic
in nature. The resulting internal reflections show strong peaks at fre-
quencies corresponding to five, six and seven half-wavelengths per
period of the pitch deviations.
In the present M1789 this situation has been considerably improved
b}^ increased precision in helix winding and by insuring that the re-
maining periodicity does not produce a major reflection peak in the band.
Fig. 18 shows pitch measurements and internal reflections for a recently
constructed tube.
1310 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
(6
cc ~
30
/^^
\
\
\,
/
\
/
\
s^
^
J\
VJ
/
v„
5.0
5.5
FREQUENCY
IN
6.0 6.5
KILOMEGACYCLES PER SECOND
7.0
7.5
01
Z
o
>
ai
o
-1
t -2
NOMINAL TPI = 34
\ /
k^
kj
■V
S.
.^\v-
A,
/\
A ,
^,^/XM
^
\ ^
\.^
^0^
s.
V
V
Twy*-
1
V
\jf
V^
DISTANCE ALONG HELIX (EACH POINT REPRESENTS ONE TURN)
Fig. 18 — Pitch deviations and internal reflections in a recent M1789 TWT.
By precise helix winding techniques the pitch deviations have been reduced by a i
factor of about 10 over those occurring in early tubes. The resulting internal re-
flections have been improved by about 25 db although there is still a residual
periodicity remaining.
For return losses greater than about 25 db, we begin to see internal reflections
originating from the edge of the heli.\ attenuator. At these values of return loss,
the measurements also begin to be in appreciable error as a result of the residual
transducer reflections.
Helix Attenuator
Attenuation is applied to the helix by spraying aquadag directly on
the heUx assembly and then baking it. The result is a deposit of carbon on
the ceramic rods and on the glaze fillets. The attenuation is held between
65 and 80 db and is distributed as shown in Fig. 19. Evidently most of
the loss is caused by a conducting bridge which is built up between
helix turns. This was indicated by one experiment in which we cleaned
the deposit off the rods of a helix by rubbing them with emery paper.
Only the carbon directly between helix turns then remained. This de-
creased the total attenuation by less than 20 per cent. Having the helix
glazed to the support rods is apparently necessary in order to get good
contact between the winding and the carbon "bridge." We have been
able to obtain about four times as much loss per unit length with glazed
hehces as with non-glazed ones. Using our method of applying attenua-
tion we can add in excess of 80 db/inch to a glazed helix. The ability to
obtain such high rates of attenuation allows us to concentrate the loss
along the helix thereby minimizing the TWT length.
The machine used for spraying aquadag on the helix is shown in Fig.
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY 1311
20. A glass cylinder and photocell arrangement is used to monitor the
amount of carbon deposited. In this manner the attenuation added is
made independent of both the aquadag mixture and the nozzle setting
of the spray gun. This machine has been checked alone by using it to
spray glass slides which are then made into attenuator vanes. Over a
two-year period we have found that a gi\'en light transmission through
the monitor slide results in the same vane attenuation within ±2 db out
of 40 db.
After a helix has been sprayed, it is vacuum fired at 800°C for thirty
minutes and then the loss is measured. About 60 per cent of the helices
fall within the desired range of 65-80 db. The principal cause of the
differences in attenuation is believed to be variation in the condition of
the glaze fillets. Helices not meeting specifications are sprayed and fired
a second time (after cleaning off excess acpadag if necessary) . This second
treatment, brings the attenuation of almost all helices to within the
desired range.
3.4 The Collector
It is desirable to operate the collector at the lowest possible voltage
in order to minimize the dc power input to the TWT. This increases the
overall efficiency and simplifies the collector cooling problem. On the
-J- lUU
u
z
S 75
Q.
to
i 50
u
LU
Q
2 25
10
f)
o
-J 0
1
j
\
\
\
0.5 1.0
1.5 2.0 2.5 3.0 3.5
DISTANCE FROM INPUT
HELIX INPUT
4.0 4.5 5.0
HEL
5.5
t
X OUTPUT
Fig. 19 — Distribution of helix attenuation. The attenuation pattern has a
gradually slanting edge facing the output to provide a smooth transition into the
loss for any signals traveling backwards toward the input. Reflections of these
signals must be \evy small since the reflected signals will be amplified in the
process of returning toward the output. Cold measurements (i.e., measurements
on the heli.x without electron beam) made by moving a sliding termination inside
the helix, indicate that the return loss from the attenuator output is better than
45 db, the limiting sensitivity of our measurement. The input side of the helix
attenuator is also tapered to minimize reflections but this taper is much sharper
than that on the output side because there is comparatively little gain lietween
input and attenuator. Cold measurements with a sliding termination showed a
return loss for this taper of about 40 db. (Surprisingly, even a sharp edge pro-
duces a reflection with a return loss of almost 30 db.)
1312 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
other hand, if there is appreciable potential difference between helix
and collector, we must insure that few secondary or reflected electrons
return from the collector to bombard the helix and accelerator, or else
we may overheat these electrodes. Fig. 21 shows a drawing of the col--
lector used in the M1789. It takes the form of a long hollow cylinder
shielded from the magnetic field. Inside of the collector the beam is
allowed to gradually diverge and the electrons strike the walls at a graz-
ing angle. This design reduces secondary electrons returned from the
collector to almost negligible proportions.
^CYLINDRICAL
' GLASS SLIDE
PHOTOCELL
Fig. 20 — Schematic diagram of the machine used for .spra.ying aquadag attenu-
ation on the helix. In this machine the helix is rotated rapidly to insure uniform
exposure to the spray. At the same time the masking drum rotates at a slower
speed and the spra}- gun traverses back and forth along the masking drum. The
drum therefore acts as a revolving shutter between the helix and the spray gun
and its degree of opening serves to control the amount of aquadag reaching the
helix. From a knowledge of the rate of attenuation increase as a function of the
amount of carbon deposited (empirically determined) the shape of the drum open-
ing can he calculated so as to give any desired attenuation pattern.
The spray gun also passes over a glass cylinder at one end of the masking drum
so that it receives a sample of the aquadag spray. A photocell is used to monitor
light transmitted through the cylinder. Before starting to spray, the glass is
cleaned and the photocell reading is taken as 100 j)er cent light transmission.
The helix is then sprayed until the light transmission has decreased to the proper
value. The photoelectric monitoring techniciue makes the attenuation added in-
sensitive to the aquadag composition and to the spray gun nozzle opening.
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY
1313
O QJ 03 <B
- cc Oj S
o o o c
o o o
n (\j —
SSnVO Nl AIISNHQ xn~id
II
1314 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Fig. 22 shows the total accelerator and helix interception as functions
of collector voltage at various output levels. When there is no rf drive,
the intercepted current remains low to a collector voltage of about 200
volts at which point it suddenly increases to a high value. This appears
to be caused by the phenomenon of space charge blocking. As the col-
lector voltage is progressively lowered, the space charge density at the
mouth of the collector increases because of the decrease in electron
velocity at this point. Increasing the charge density causes the potential
depression in the beam to increase until at some collector voltage the
potential on the axis is reduced to cathode potential. At collector voltages
lower than this, some of the beam is blocked, i.e., it is turned back by the
space charge fields.
When the TWT is operated at appreciable rf output levels, the col-
lector voltage must be increased to permit collection of all electrons
which have been slowed down by the rf interaction. Unfortunately, some
electrons are slowed far more than is the average, so that we must supply
to the TWT several times more dc power than we can take from it in the
form of rf power. However, as seen from Fig. 22, there is still an apprecia-
ble advantage to be gained by operating the collector at lower than helix
potential. These curves should not be taken as an accurate measure of
the velocity distribution because there are undoubtedly space charge
blocking effects which even at higher collector voltages have some in-
fluence on the number of electrons returned from the collector. This
arises from the fact that the rf interaction causes an axial bunching of
the electrons, thereby causing the space charge density in an electron
bunch to be much higher than it is in an unmodulated beam. Thus, as a
bunch enters the collector, the local space charge density may be high
enough to return some electrons.
IV. PERFORMANCE CHARACTERISTICS
4.1 Method of Approach
In this section we will consider the overall rf performance of the
Ml 789 and make some comparisons between theory and observed re-
sults. The following TWT parameters can be varied: input level; helix
voltage; beam current; frequency; and magnetic field. Our approach
here will be to first consider the operation of the tube under what might
be called nominal conditions. This will be followed by a discussion of the
variations in low-level gain and in maximum output over an extended
range of beam current, frequency, and magnetic field. By this procedure
we are able to obtain a description of tube performance without presenta-
tion of a formidable number of curves. Two topics, noise and inter-
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY 1315
20
18
16
14
12
10
<
HI
CD
LL
O
I-
z
LU
u
a.
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Q.
1
?
1
\ 10 WATTS
\ OUTPUT
\
lj
1
\
1
NO RF !
OUTPUT
\
V
\
1
\
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1
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r _-;
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
COLLECTOR VOLTAGE IN KILOVOLTS
1.8
2.0
2.2
Fig. 22 — Intercepted current as a function of collector voltage with helix and
accelerator voltages held constant at their nominal values. Below the knee of the
curves about three quarters of the total intercepted current goes to the heli.x and
about one quarter is focused all the way back to the accelerator. Curves are shown
for no rf input and for output levels of 1, 5, and 10 watts. With no input, the lowest
permissible collector voltage is determined by the phenomenon of space charge
blocking. With rf input, it is determined mainly b3' the velocity spread of the
electrons. In all cases it was found that the alignment of the TWT with respect
to the magnetic circuit becomes more critical as the knee of the curve is ap-
proached. For this reason the M1789 is usually operated with a collector voltage
about 200 volts above the knee.
modulation, will be divorced from the discussion as outlined above and
treated separately in Sections 4.4 and 4.5.
4.2 Operation Under Nominal Conditions
Basic Characteristics
By nominal conditions for the Ml 789 we mean the following:
frequency 6175 mc (band center)
beam current 40 ma
magnetic flux density 600 gauss
collector voltage 1200 volts
1316 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Fig. 23(a) shows representative curves of output power as a function of
input power for several values of helix voltage. This information is re
plotted in Fig. 23(b) in terms of gain as a function of output power. We
see that the TWT operates as a linear amplifier for low output levels.
As the output level is increased, the tube goes into compression and*
finally a saturation level is reached. The maximum gain at low input
levels is obtained with a helix voltage of 2,400 volts (about 10 per cent
higher than the synchronous voltage because of space charge effects).
2
a
3
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35
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(a)
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40 35 30 25
GAIN IN DECIBFt S
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f=^
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(e)
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POWER INPUT IN DBM
20
25
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(f)
/
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Pi
-^
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30 32 34 36 38
POWER OUTPUT IN DBM
Fig. 23 — See opposite page for caption
TRAVELING WAVE TUBE FOR G,000-MC RADIO RELAY 1317
The maximum output at saturation is obtained at a higher helix voltage
as is common in TWT's. The helix voltage also affects the shape of the
input-output curves — linear operation being maintained to higher
output levels at higher helix voltages.
As a measure of the efficiency of electronic interaction in a TWT, we
use an "electronic efficiency" which is defined as the ratio of the rf out-
put power to the beam power (product of helix voltage and beam cur-
rent). The "over-all efficiency" we define as the ratio of the rf output
power to the total dc power (exclusive of heater power) delivered to
the tube. With the collector operated at 1,200 volts, it is about twice the
electronic efficiency. For the M1789, maximum efficiency occurs at the
saturation level with a helix voltage of 2,600 volts. The electronic and
over-all efficiencies there are equal to about 14 per cent and 28 per cent,
respectively.
The curves of Figs. 23(a) and (b) were taken with sufficient time al-
lowed for the tube to stabilize at each power level. If the TWT is driven
to a high output level after having been operated for several minutes
' with no input signal, the output will be somewhat greater than is shown
' in the curves. It will gradually decrease until it reaches a stable level in a
period of about two minutes. This "fade" is caused by an increase in the
intrinsic attenuation of the helix near the output end. The increase is a
result of heating from rf power dissipation. At maximum output the
fade is about 0.6 db (about 15 per cent decrease in output power). At
the five-watt output level the fade is about 0.1 db (about 2 per cent
.( — — ■ '
Fig. 33 — See opposite page
j -c: (a) Output power as a function of input power. Both ordinate and abscissa are
in dbm (db with respect to a reference level of one milliwatt). A straight line at
45° represents a constant gain. A gain scale is included along the top of the figure.
For this tube a helix voltage of 2,400 volts gives maximum gain at low signal levels
and a voltage of about 2,600 gives maximum output at saturation.
(b) Gain as a function of output power. This is an alternate way of presenting
the information shown in (a).
(c) Compression as a function of input power. Three regions are shown in the
figure. The "compression" region is that in which there is less than one db change
in output level for a db change in input level. The "expansion" region is that in
which there is more than one db change in output level for a db change in input
level. The "inversion" region is that in which the output level decreases when
the input level increases (or vice versa). It occurs for input levels greater than
that necessarj^ to drive the TWT to saturation. In this region the change in out-
put is of opposite sign to the change in input. Using the definition in the text this
gives rise to compression values in excess of 100 per cent.
(d) Compression as a function of output power.
(e) Conversion of amplitude modulation to phase modulation as a function of
input power. This conversion arises because the electrical length of the TWT is a
function of the input level. The effect can cause rather serious difficulties in cer-
tain types of low index FM systems.
(f) Conversion of amplitude modulation to phase modulation as a function of
output power.
1318 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
decrease in output power). We will present some additional data on this
effect in Section 4.3.
Distortion of the Modulation Envelope
The curves of Figs. 23(a) and (b) tell what happens when a single
frequency carrier signal is passed through the TWT. In addition we
would like to know the effect on modulation which may be present on
the signal. In particular, it is desirable to know the compression of the
envelope of an AM signal and the amount of phase modulation generated
in the output signal as a result of amplitude modulation of the input
signal, (an effect commonly known as A]\I-to-PM conversion). As a
measure of compression of an AM signal the quantity per cent com-
pression will be used. This is defined as
% Compression
AV,/V,_
100
where Vo is the voltage of the output wave, Vi is the voltage of the
input wave, and AYo is the change in output voltage for a small change
AVi in the input voltage. When AF/F is small it can be expressed in db
as 8.68 AF/F = AF/F in db. From this it follows that
% Compression
1 =- > ni do
APi
100
where APo is the change in output power for a change APi in input power,
and the two powers are measured on a db scale. When the per cent
compression is zero the TWT is operating as a linear amplifier; when it
is 100 per cent the TWT is operating as a limiter.
From the above expression it may appear that the per cent compres-
sion could be determined directly from the slopes of the input-output
curves. This would be the case were it not for fading effects. Since there
is fading, however, the slope for rapid input level changes is different at
high levels from the slope of the static curves. Thus it is necessary to
determine compression from the resulting effect on an AM signal.
The electrical length of a TWT operated in the non-linear region is 1 1 >
some extent dependent on the input level. Therefore, an AM signal ap-
plied to the input of the TWT will produce phase modulation (PM) of
the output signal. This effect ma}^ be of particular concern when a TWT
operating at high output levels is used to amplify a low-index FM signal.
If such a signal contains residual amplitude modulation, the TWT
generates phase modulation with phase deviation proportional to the
input amplitude variation. Under certain circumstances this can cause
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY
1319
severe interference with the signal being transmitted. We wU discuss a
particular example after consideration of the compression and AM-to-
PM conversion characteristics of the M1789.
As in the case of compression, we must measure AM-to-PM conversion
dynamically. This is necessary because point-by-point measurements of
the shift in output phase as input level is changed include a component of
phase shift caused by changes in temperature of the ceramic support
rods and a consequent change in their dielectric constant. However,
this thermal effect does not follow AM rates of interest and therefore
does not produce AM-to-PM conversion.
Fig. 24 shows a simplified block diagram of the test set used to measure
compression and AM-to-PM conversion. This equipment amplitude
modulates the input signal to the TWT under test by a known amount
and detects the AM in the output signal with a crystal monitor and the
PM with a phase bridge. A more complete discussion of this measurement
is given by Augustine and Slocum.^
Compression is given as a function of power input in Fig. 23(c) and
as a function of power output in Fig. 23(d). We see that compression
sets in more suddenly at higher helix voltages. Above about 2,500 volts
REFERENCE
PHASE
PHASE SHIFTER
SIGNAL
SOURCE
.1
H
AMPLITUDE
MODULATOR
HYBRID
JUNCTION
PHASE
BRIDGE
OSCILLO-
SCOPE
TRAVELING-
WAVE TUBE
Fig. 24 — Simplified block diagram of test set used to measure compression and
conversion of amplitude to phase modulation. A ferrite modulator introduces one
db of 60 cps amplitude modulation into the test signal. The 60 cps rate is much
higher than that which can be followed by thermal changes in the TWT. Half of
the modulated signal serves as input to the TWT under test and half serves as a
reference phase for a phase detector. The signals at the phase detector input are
maintained equal and at constant level and nominally in phase quadrature. The
detector is essentially a bridge circuit, the output of which is a dc voltage propor-
tional to the phase difference of the two inputs. When operated with inputs in
quadrature it is not sensitive to amplitude changes of as much as two db in either
or both inputs. Phase modulation introduced by the amplitude modulator appears
at both inputs and thus does not produce an indication. The output of the de-
tector is therefore a direct measure of the phase modulation created in the TWT.
Compression is determined by comparing the percentage amplitude modulation
at the input and output crystal monitors.
1320 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
35.0
Z
g
m
a 12.50
UJ
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2
q 11.25
2
Q. 10.00
I
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r
(b)
GAIN^
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1
1
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CONVERSION
k
compression\
N
i
J
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1
f\
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r
1
^*v.^
1
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' 1
N
^
2300 2400 2500 2600
HELIX VOLTAGE IN VOLTS
2700
100 9
in
LU
75 Q:
Q.
50 8
I-
25 5
O
o5
2800 II-
Fig. 25 — Gain, compression and amplitude to phase conversion as a function
of heli.x voltage with the output power maintained constant at a level of five
watts (a) and ten watts (b).
there is expansion for some values of power input. Figs. 23 (e) and 23(f)
give the AM-to-PM conversion, as functions of input and output power
respectively. These data indicate that the conversion is very much less
if the tube is operated at lower helix voltages. For example, the con-
version at the saturation level of the 2, 700- volt curve is about 2^ times
that for the 2, 400- volt curve.
A final method of plotting gain, compression, and AM-to-PM con-
version data is shown in Fig. 25. The abcissa here is the helix voltage.
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY 1321
For these measurements power output was held constant by adjusting
input level at each voltage. The figure shows that as helix voltage is
increased, the compression decreases but the AM-to-PM conversion
increases. The choice of a helix voltage at which to operate the tube
must therefore represent a compromise between these quantities.
Phase Modulation Sensitivity
The equipment of Fig. 24 was also used to measure the phase modula-
tion sensitivity of various electrodes by omitting the amplitude modula-
OSCILLO-
SCOPE
SWEPT VIDEO
SIGNAL SOURCE
0-10 MC
FM
TRANSMITTING
TERMINAL
o
FM
RECEIVING
TERMINAL
-■Z.
^
X
SOURCE
OF ONE DB
OF AM
TRAVELING-
WAVE TUBE
UJ
O
UJ
Q
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^^
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234 56789
VIDEO FREQUENCY IN MEGACYCLES PER SECOND
10
Fig. 26 — Example of frequency response shaping caused bj' AM-to-PM con-
version. This figure shows the calcuhited frequency response viewed between
FM terminals for the system shown in the block diagram. Curves are given for the
case in which the phase modulation generated in the TWT both adds to and sub-
tracts from that of the transmitted signal. Inclusion of a limiter at point A would
result in a flat frequency response.
1322 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
-20
-15
0 5 10
INPUT IN DBM
Fig. 27 — Output power as a function of input power at various beam currents.
Tliese curves were all taken with the helix voltage adjusted to give the maximum
gain at low signal levels. At low beam currents (<20 ma) there is insufficient gain
between the attenuator and the output so that at these currents the attenuator
section is limiting the power output. This accounts for some of the difference in
shape of the curves near maximum output.
tor and introducing small changes in electrode voltages. The modulation
sensitivity of the helix is about two degrees per volt and that of the
accelerator about 0.1 degree per volt with the TWT operating under
nominal conditions.
Significance of AM-to-PM Conversion
Let us return briefly to a discussion of some consequences of AM-to-
PM conversion. As an example, we will consider the case of a low -index
FM signal. Assume the frequency deviation is ±5 mc peak to peak.
This gives a phase deviation of ±0.5 radian for a 10 mc modulating
signal. These values are typical of what might be found in a radio relay
system. Let us also assume that there is a residual amplitude modulation
of one db (about 13 per cent) in this signal and suppose further that the
signal is amplified by a TWT having a value of AM-to-PM conversion of
10 degrees per db. The phase modulation thus created in the TWT can
either add to or subtract from that of the original FM signal, thus chang-
ing its modulation index. At low modulation signal frequencies the phase
deviation of the FM signal will be large compared to that of the PM
interference and the interference will be of little consequence. At high
modulation signal frequencies the phase deviation of the original FM
and of the interfering PM signals will be comparable and the interference
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY
1323
can considerably change the net phase deviation of the overall signal.
For the example we are considering the frequency responses in Fig. 26
show what would be seen at the output FM terminal. Curves are given
both for the PM interference adding to and subtracting from the original
FM signal. We see that a gain-frequency slope of about 4 db over 10
mc is introduced by AM-to-PM conversion. To prevent such an effect,
a limiter should be used prior to the TWT in applications of this nature so
as to remove the offending AM from the input signal.
The fact that compression and amplitude-to-phase conversion vary
with input level means that in addition to the first order distortion just
described, higher order distortions of the modulation envelope will
occur. If, for example, the input signal is amplitude modulated at fre-
quency /i , the output modulation envelope will contain amplitude and
phase modulation both at /i and at harmonics of /i . The amount of
higher order distortion can be estimated by expanding the compression
and amplitude-to-phase conversion curves as a function of power input
in a Taylor series about the operating point. Such an expansion shows
that the greater the slope of these curves the greater will be the higher
order distortions.
40
35
30
25
20
15
10
0
.X
A
y^"
A
."'■'
HELIX
VOLTAGE
J
w
Y
/
\A
V
>
/
V
;ain
/
7
/
/
2450
2400
l5LU
io
o>,
2350 li.^
2300
2250
IU_|
I<
2200
10 20 30 40 50 60
BEAM CURRENT IN MILLIAMPERES
70
Fig. 28 — Low-level gain as a function of beam current. The helix voltage was
adjusted for maximum gain at each current.
1324 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Reproducibility
The curves presented in this section are all for the same tube, one
which is representative of a group of 50 which were built at the conclusion
of the Ml 789 development program. The tubes in this group had char-
acteristics falling within the following ranges. The numbers represent
the range containing 90 per cent of the tubes tested.
Accelerator Voltage for 40 ma 2,500-2,700
Helix Voltage for maximum low-level gain 2,350-2,450
Low-level gain 33-37 db
Gain at 5 watts output 31-35 db
Maximum power output J 40.5-42 dbm
\(1 1.2-15.8 watts)
/
/
45
/
y
/
/
^ 1
,70 MA
40
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/ /
y^
/
^^s-l
Nl \
// /
Y
/
/
^^^0
N
\
k
^ 30
LU
m
u
UJ
a 25
z
/
V/i
r^
/
/
^>^
i N
L N
\
lj[/ /
/
/
'--^
k
\
\ ^
M
^
/
/
^
k
\ 1
K \
\
z
<
O 20
15
10
X
1
K
\
\
\ ^
\^ \
L
WA
Y
1
1
1
1
1
i \
A
y
i/^
1
1
>^o
1
\
\
\
\ T
m/
1
1
1
L
N
i
*^ y
5
juj/l
A
^
\
\
\ 1
\ \
^
/
1
N
<5 MA
N
1
\
\
\l
0
/f
\
\
\
2000 2100 2200 2300 2400 2500 2600 2700
HELIX VOLTAGE IN VOLTS
2800 2900
3000
Fig. 29 — Low-level gain as a function of helix voltage for various beam cur-
rents. The dotted line represents the locus of the maxima of the curves.
TRAVELING WAVE TUBE FOR O-OOO-MC RADIO RELAY 1325
4.5
5.0 5.5 6.0 6.5 7.0 7.5
FREQUENCY IN KILOM EGACYCLES PER SECOND
8.0
Fig. 30 — Low-level gain and helix voltage for maximum gain as functions of
frequenc}' for several beam currents. The TWT was matched to the waveguide
(with tuners where necessary outside of the 5,925 to 6,425-mc range) at each fre-
(luency. The solid curves show the gain-frequency characteristic with the helix
voltage adjusted for maximum gain at 6,000 mc for each beam current and then
held constant as frequency was changed. Experimental points correspond to this
condition. The dotted curves show how the characteristics change when helix
voltage is optimized at each frequency. The optimum helix voltage increases by
about 100 volts in going from 6,000 down to 4,500 mc because of slight dispersion in
the phase velocity of the helix.
4.3 Operation Over an Extended Range
We now turn to a consideration of tj^pical Ml 789 characteristics over
an extended range of beam current, frequency, and magnetic field.* We
shall concentrate on two items, the low-level gain and the maximum
power output. From variations in these quantities the complete compres-
sion ctirves can be roughly deduced. This situation is illustrated in Fig. 27
which sho^vs output as a function of input at different beam currents.
While the shapes of these curves are slightly different, for the most part
they can be derived from the 40-ma curve by shifting it along the abcissa
* The characteristics of the tuV)e used for the low-level gain measurements
in this Section were slightly different from those of the tube used for the maxi-
mum output measurements and both were slightly different from those of the
tube used for the measurements of Section 4.2. All tubes, however, had charac-
teristics falling within the ranges listed above.
1326 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
(
by the amount the low-level gain changes, and along the ordinate by the
amount the maximum output changes as beam current is varied. A
similar procedure can be followed for variations Avith frequency and
magnetic field. In all figures in this Section, parameters not being pur-
posely varied were held at the nominal values given on page 1315.
Low-level Gain
Fig. 28 shows the variation in low-level gain with beam current and
Fig. 29 shows its variation with helix voltage for several different beam
currents. Fig. 30 shows the variation with frequency and Fig. 31 the
variation with magnetic field.
X
Hz
lUO 0.8
ujq:
0.4 -
Ol
2400 I-
O
>
2380
H 2360
OJ
I
2340 1
6
JO
01
_l
UJ
m 36
c
r^
~ .
o
UJ
Q
Z
■" 34
Z
<
19
^
32
500 550 600 650
MAGNETIC FLUX DENSITY IN GAUSS
700
750
Fig. .31 — Low-level gain, helix voltage for maximvim gain and helix intercep-
tion at low signal level as functions of magnetic flux density. These measurements
were made using different strength permanent magnet circuits. The gain varies
with magnetic flux density mainly as a result of its effect on l)eam size and there-
fore on the degree of coupling l)etween electron stream and lielix. The helix voltage
varies because of the effect of beam size on QC and therefore on the ratio of the
optimum gain voltage to the helix synchronous voltage.
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY 1327
70
65
60
55
50
45
IT)
LU
40
OJ
o
UJ
Q
35
z
z
30
<
15
25
20
10
o-
■-0 EXPERIMENTAL
, r-
ALCULATED
b/b =0.6
f
/
/
/
/
}
/.
V
^0.4
/
''A
/
/
/
0
^
A
/
/
/
^/
y
t
//
f
/'
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
r/3-(MA)'/^
Fig. 32 — Measured and calculated low-level gain as a function of the one-third
power of beam current. The parameter b/a is the ratio of effective beam diameter
to mean helix diameter.
40.0
37.5
35.0
32.5
Q 30.0
Z 27.5
<
25.0
22.5
20.0
^
"^
^
1 = 0.6
^
^
[>»•''"
? —
^—1
'"
>- — ..
3 .J
?
r""-
\
,^'''
5'-'
y"
^,
'■--,
-.
V^
"\
\
^
^v
s.
^^
X
4 = 0.4^
\
^v
'^^
N,
CALCULATED
EXPERIMENTAL
N
\
o — — O
\
•v
4.5
5.0 5.5 6.0 6.5 7.0 7.5
FREQUENCY IN KILOMEGACYCLES PER SECOND
8.0
Fig. 33 — Measured and calculated frequency response for a current of 40 ma.
1328 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
The observed gain compares well with that calculated from low-level
TWT theory provided that we properly consider the effect of the helix
attenuator and provided that we assume a hi a of one-half. The method
we have used in calculating the Ml 789 gain is discussed further in
Appendix I. Fig. 32 compares the measured and calculated gain as a
function of beam current and Fig. 33 compares them as a function of
frequency. Fig. 34 shows measured and calculated ratios of voltage for
maximum gain to synchronous voltage as a function of beam current.
In all these figures calculations are shown for several values of the ratio
of effective beam diameter to mean helix diameter (6/a). We see that
the effective value of 6/a appears to be about one-half. On the basis of
measurements made by probing the beam of a scaled up version of a
1.26
1.24
1.22
1.20
1.18
1.16
1.14
V/Vs
1.12
1.10
1.08
1.06
1.04
1.02
1.00
y
<•
^/^
y
b/a = o.2^
y
y
/
/
0.4^
^
-^
/
^
\
(
**
-•"^
/
^^
fe
,"""
-"^
'^
/
^
x^
<^
"^
0^8^
,<f
^
^
^
^
""XZ
^^
/ ^
'^ ^
-^
^^
A//
r
:^
1 •/ J
^
10 15 20 25 30 35 40 45 50
BEAM CURRENT IN MILLIAMPERES
55
60
65
70
Fig. 34 — Measured and calculated ratio of voltage for maximum gain to syn-
chronous voltage as a function of beam current. The calculated curves are shown
for several values of the ratio of effective beam radius to mean helix radius (b/a).
The location of the measured curve among the calculated ones is taken as an
indication of the effective value of b/a in the M1789. At 40 ma it is about 0.5.
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY 1329
z
tr
LU
5
o
Q.
CL
32.5
30.0
27.5
25.0
22.5
20.0
17.5
15.0
12.5
10.0
7.5
5.0
2.5
0
2800
2700
LU
O 2600
> 2500
liJ 2400
I
3
o
r
V
FORE FADE
TER FADE
HELIX VOLTAGE
SET FOR
MAXIMUM OUTPUT,
/
/
•
^
- AF
/
A
\
(
/
y,
/ \
A
/
/
/
/
A
t
^ >
r
•
V
y
^X
/ /
•
A
/^^ HELIX VOLTAGE
^ SET FOR
A
/
f
.^'
r
MAXIMUM GAIN
AT LOW LEVEL
A
{'
/'
Y
^
A
/
J,
v>
^^
^'^
.^
#^^
2300
2200
^^
^
^
"^
,y
X^^OLTAGE FOR
MAXIMUM OUTPUT
y'
A
)
__,
'
^
>
> VOL
TAGE FOR MAXIMUM
LOW LEVEL GAIN
^
10 15 20 25 30 35 40 45 50 55 60 65 70
BEAM CURRENT IN MILLIAMPERES
Fig. 35 — Maximum power output and heli.x voltage as functions of beam cur-
rent. Curves are shown for before and after fading, and for tlie helix voltage ad-
justed for the ma.ximum gain at low-level and for maximum output.
1330 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
4.0
4.5 5.0 5.5 6.0 6.5 7.0 7.5
FREQUENCY IN KILOMEGACYCLES PER SECOND
Fig. 36 — Maximum power output after fading as a function of frequency for
several beam currents; in (a) with the helix voltage adjusted for maximum gain
at low-level and in (b) with the helix voltage adjusted for maximum power output.
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY 1331
b
Z
^-
Q.
UJ
U
a.
LU
1- 3
z
X
_i
^2
t-
Z
UJ
u
\
k
1
\
\
\
\
\
\
tr '
UJ
Q.
^
P
0
500 550 600 650 700
MAGNETIC FLUX DENSITY IN GAUSS
750
Fig. 37 — Maximum power output after fading, voltage for maximum output,
and helix interception at maximum output as functions of magnetic flux density.
These measurements were made using magnetic circuits charged to different
strengths. Helix interception above about one per cent is undesirable if long tube
life is required.
1332
THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
focusing system similar to that employed in the M1789, we estimate the
actual beam diameter (for 99 per cent of the current) to be about 65
mils (Jb/a = 0.7). However, the current density distribution is peaked
at the center of the beam because of the effect of thermal velocities of
the electrons. Thus an effective h/a of 0.5 is not unreasonable.
Maximum Power Output '
Fig. 35 shows the maximum power output as a function of beam cur-
rent both immediately after rf drive is applied and after the tube has
had time to stabilize. We see that at high rf power outputs the fading
3.0
2.5
iJ 2.0
>
u
z
ly 1.5
o
u.
H] '-0
0.5
0
4.0
3.5
3.0
^2.5
U
z
y 2.0
u
IL
li 1.5
1.0
0.5
THEORETICAL
60 MA
20 MA
O 6
a 4
r
0 MA
0 MA
L—
3
-^
'^
\;
— -<
— ^
1
t —
20 MA
I
\
(a)
^^
60 MA
—
—
—
S
y***"*.^
THEORETI
60 MA
CAL
—
—
40 MA
20 MA
^
)
1
}■
-r:'
J .
1^
F^— P
""
I
20MA
i
I
k
I
1
'
' '
'
(b)
4.0
4.5 5.0 5.5 6.0 6.5
FREQUENCY IN KILOMEGACYCLES PER SECOND
7.0
7.5
Fig. 38 — Ratio of electronic efficiency to gain parameter C as a function of
frequency. The efficiencies used for this comparison are all before fading. The dot-
ted line.s are estimated from the Tien theory corrected for the intrinsic loss of the
helix. The curves in (a) are for the case of the heli.x voltage adjusted for the maxi-
mum low-level gain and those in (b) for the case of the helix voltage adjusted for
maximum power output.
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY 1333
becomes very serious and eventually limits the TWT output to about 30
watts. If it were necessary to reduce this fading, the envelope shrinking
technicjue illustrated in Fig. 16 could be used. The maximum power
output after fading is shown as a function of frequency for several beam
currents in Fig. 36 and as a function of magnetic flux density in Fig. 37.
The theory of the high level behavior of a TWT** predicts that the ratio
of electronic efficiency (i.e., E = power output/beam power) to the gain
parameter C should be a function of C, QC and 7b (where h is the beam
diameter). However, with the range of parameters encountered in the
M1789, the variation in E/C should be small. Fig. 38(a) shows E/C as a
function of frequency when the TWT is operating at the voltage for
maximum gain at low signal levels. Fig. 38(b) shows the maximum value
of E/C obtainable at elevated helix voltage. In both figures we show the
efficiency as estimated using the results of Tien^ corrected for the effect
of intrinsic loss following the procedure of Cutler and Brangaccio.^
All etticiencies in these two figures are the electronic efficiency before
fading. It would be quite difficult to compare the efficiency after fading
with theory because the intrinsic attenuation in this case varies along
the helix in an unknown manner so that we cannot properly take it into
account. From the figures we see that the calculated value of E/C at
6,000 mc and 40 ma is not far from the experimental value but the ex-
perimental points show more variation with frequency than is predicted
by theory. The low efficiency at 20 ma results from the fact that there
is insufficient gain between the helix attenuator and the output. As a
result, the TWT "overloads in the attenuation."
4.4 Noise Perjormance
A new and important noise phenomenon was observed in the course of
the Ml 789 development. It was found that the noise figure is strongly
dependent on the magnetic flux linking the cathode and on the rf output
level of the TWT. For example, with the TWT operating near maximum
output and with a cathode completely shielded from the magnetic field,
noise figures of about 50 db were observed. By allowing 20 gauss at the
cathode, the noise figure was reduced to 30 db. Fig. 39 shows the noise
figure as a function of magnetic flux density at the cathode for several
values of rf power output. We see that there is a peak of noise figure
roughly symmetrical about zero flux at the cathode, and that the magni-
tude of this peak is considerably increased by operating the TWT at
high output levels.
Some additional observed properties of the noise peak are:
(1) The magnitude depends on the synchronous voltage of the helix.
For a 1,600-volt helix it is about 10 db higher than shown in Fig. 39 and
1334 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
for a 2,600-volt helix it is about 5 db lower. The noise figure for 25 gauss
at the cathode remains constant, however.
(2) There appears to be a threshold level of about 15-ma beam current
below which the peak does not occur. Between 15 and 25 ma the peak
increases. Above 25 ma it is roughly constant in magnitude.
(3) The peak can be considerably reduced by intercepting some of
the edge electrons before they reach the helix region.
For this discussion it has been necessary to extend the concept of
noise figure to the case of non-linear operation of the TWT. Essentially
this noise figure is defined by the means we use to determine it. A block
diagram of the equipment is shown in Fig. 40. The outputs of a calibrated
broad band noise source and a signal oscillator are combined and used
for the input to the TWT under test. The noise output from the TWT is
passed through a filter tuned about 100 mc away from the signal so as to
reject the carrier. It is then detected by a receiver tuned to the filter
frequency. The noise figure is measured by turning the noise source off
and on, noting the change in receiver output level and calculating the
noise figure in the conventional manner. This procedure reduces to an
ordinary noise figure measurement in the absence of input signal.
There are other ways that could be used to measure noise figure of a
non-linear amplifier. A method more closely related to the use of the
50
45
<n
_I
UJ
o
^40
UJ
cc
35
111
in
o
z
30
/
^
T
/
/^
^7DBM
\
/
/
X
\
\
//
/
LOw\
LEVEL
^
\\
V
^^<:>
-20 -15 -10 -5 0 5 10 15
MAGNETIC FLUX DENSITY AT THE CATHODE IN GAUSS
20
Fig. 39 — Noise figure as a function of magnetic flux density at the cathode
for several values of rf power output. The flux density was varied by using an in-
ductive heater through which ac current was passed. The present ]\I1789 uses 19
gauss at the cathode, all of which is obtained from the focusing magnet — the
heater now being non-inductive.
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY
1335
TWT in an FM radio relay was investigated briefly. In this measurement
an FM receiver tuned to the carrier frequency was used to detect the
noise modulation present in the TWT output. The noise figure was deter-
mined in the usual manner from the ratio of receiver outputs with the
noise source turned off and on. When the TWT was operated in the
linear region, this measurement gave the same result that our first
method did. With the TWT operated in the non-linear region it gave
a value within a few db of that obtained from the first method.
The cause of the high noise output observed for low magnetic flux
densities at the cathode is at the present time not clearly understood.
Fried at MIT and Ashkin and Rigrod at Bell Laboratories have all
probed the beam formed by guns of the M1789 type and have found
certain anomalous efl"ects. Normally one would expect to find a standing
wave of noise current along the electron beam. For the M1789 gun they
find instead that after about two minima of the standing wave pattern,
the noise current on the beam begins to grow and continues to do so
until a saturation value is reached. The noise current at this saturation
LOW NOISE
TRAVELING-
WAVE TUBE
SIGNAL
POWER
MONITOR
NOISE
LAMP
SIGNAL
SOURCE
RECEIVER
y/C
FILTER
HYBRID
H
GK-r
SIGNAL
6000 MC
X
TRAVELING-
WAVE TUBE
UNDER TEST
RECEIVER LOCAL
OSCILLATOR
6170 MC
FILTER
6080
BAND
6100
20 MC
Fig. 40 — Block diagram of noise measuring equipment. Tiie noise source con-
sists of a fluorescent lamp the output of which is amplified by a low-noise TWT so
as to bring the noise level to about 35 db above kTB at the M1789 input. The out-
put from the M1789 is passed through a 20-mc bandpass filter which eliminates
both the single frequency test signal and the noise in the image band of the re-
ceiver. The noise figure is measured by noting the difference in noise level at the
receiver output with the noise source off and on, in a manner similar to that used
in a conventional noise figure measurement.
1336 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
value may be considerably higher than the original average noise level.
As is the case with the noise figure in the M1789, the growing noise
current has been found to be very sensitive to magnetic field at the
cathode. By allowing sufficient field to link the cathode, the growing
noise current can be eliminated leaving the normal noise current standing
wave pattern on the beam. This phenomenon is not peculiar to the
M1789 gun. It has been observed by various workers at MIT^ and else-
where on other guns producing beams with comparable current densities.
A satisfactory explanation for it has not, at the time of this writing, been
arrived at. It seems safe to say, however, that the growing noise current
on the beam is the source of the high noise figures obtained in the M1789
when the cathode is completely shielded from the magnetic field.
4.5 Inter modulation
It has been found that certain intermodulation effects in the Ml 789
can be predicted from a knowledge of the compression and AM-to-PM
conversion. Alternatively, these effects can be used to determine com-
pression and AM-to-PM conversion. The procedure to be described has
the advantage of being simple to implement as compared with the phase
bridge arrangement of Fig. 24.
UNIT VECTOR--. .^ — ■
ROTATING AT /
ANGULAR /
VELOCITY 1^
2 7rAf \
UNIT
AMPLITUDE
-Af — >|
FREQUENCY
(a)
(b)
4^ 4*
4^
AM
VECTORS
PM
VECTORS
(C)
Fig. 41
(a) Spectrum of input signal to amplifier.
(b) Vector diagram of two input signals and the resultant signal (R) in a frame
of reference rotating at an angular velocity 2irAf . Dotted line is the locus of the re-
sultant signal.
(c) The rotating vector of the proceeding diagram can be broken down into a set
of two vectors representing amplitude modulation and a set of two vectors rep-
resenting frequency or phase modulation.
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY 1337
Intermodulation effects are ordinarily complicated and results are
jvery hard to predict from single frequency measurements on an amplifier,
i'or a TWT, however, one case — that in which two signals of very
[different amplitude are passed through the tube — can be treated simply,
IConsider an input to a TWT consisting of two signals at frequencies
l/i and /i + A/ with the signal at/i being very much larger in amplitude.
The composite signal applied to the amplifier will then be a signal at
frequency /i which is amplitude and phase modulated at a rate A/ in an
amount proportional to the relative magnitudes of the two signals.
This can be represented vectorially as shown in Fig. 41(a) and b. In this
figure the amplitude of the signal /i + A/ has been normalized to unity.
"A" thus represents the ratio of the larger to the smaller signal. The
locus of the resultant signal is shown by the dotted line. The single
rotating vector can be considered as the sum of vectors at /i + A/ and
/i — A/ as shown in Fig. 41(c). One set of vectors produces PM and the
other AM. The AM and PM vectors cancel at /i — A/ and add at /i +
A/.
Suppose this signal is put through an amplifier operating in com-
pression. For the time being let us assume this amplifier has no AM-to-
PM conversion. The compression in the amplifier will operate on the
AM sidebands of the signal but will leave the PM sidebands unaffected.
Let us define the quantity c as a measure of compression in the amplifier
by
' = '- AVW< ^'^
where Vo is the output voltage, Vi input voltage, and AFo is the change
in output voltage for a change AVi in the input voltage. This quantity is
the per cent compression used in Section 4.2 divided by 100. If the signal
in Fig. 41 is put through the amplifier while it is in compression, and the
level of the signal at /i is subsequently brought back to amplitude A,
we would then expect to have the situation shown in Fig. 42. Each AM
sideband component has been multiplied by the factor (1-c). The locus
of the composite signal is now elliptical. Let Si and S2 be the magnitude
of the sidebands at /i + A/ and /i — A/ respectively. From Fig. 42 it is
seen that
^1 = K + Hd - c) =1- c/2 (2)
S9 = y2- Hil - c) = c/2 (3)
When c = 0, the amplifier is operating in the linear region and *Si = 1,
1338 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
^2 = 0. This is the condition in Fig. 41. When the amphfier is operating \
as a perfect Umiter, c = 1 and Si = S2 = 0.5. Thus, in this case, the side- 1
band *Si is down 6 db from its value when the amplifier is operating in
the linear region.
When there is conversion of AM-to-PM in the amplifier, the situation
becomes somewhat more complex. Suppose an AM signal is fed into the
amplifier and that its voltage is given by
V = Vi{l -\- a sin wj) sin Uct
where coc and oom are the carrier and modulating radian frequencies and
V\ and a are constants. The outputs will be given by
V = KVi[l + «(1 — c) sin oo,nt] sin {coct + kpa sin co^O (5)
Here K is the amplification, c is the compression factor and kp is a factor
which is a measure of the AM-to-PM conversion. It is seen that kp is
the output phase change for a given fractional input change a. Thus
rCp —
A^
a
(6)
where AO is the phase change in radians caused by a fractional input
change a. Later on it will be desired to express kp in terms of degrees
phase shift per db change in input amplitude. To express a in db we
i(i-c) ^
AM
VECTORS
4^
PM
VECTORS
(a)
(4) '
Fig. 42
(a) After passing through an amplifier in compression tlie AM sidebands are
reduced in amplitude but the PM sidebands are unaffected. The lower two side-
bands which represent a signal at frequency fi — Af no longer cancel and so there
is a net signal at that frequency.
(b) The locus of the resultant signal now assumes an elliptical shape.
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY 1339
lust evaluate 20 logio ( 1 + a). The quantity loge (1 + a) can be ex-
)anded in a series to give
loge (1 + a) =a — -a-\--a+ • • • .
A.S long as a <3C 1, we can approximate it by taking only the first term of
the above expression. Converting to the base ten and converting Ad
Prom radians as it appears in (6) to degrees, we find that
k.
0.152
Ad (in degrees)
A input level (in db)
(7)
Now let us consider the case in which the signal of Fig. 41 is put
through an amplifier having AM-to-PM conversion. Fig. 43 shows the
vector picture of the resulting signal after the level of the signal at /i
has been brought back to amplitude A. In this case the original PM
sidebands and the compressed AM sidebands are the same as in Fig. 42,
but there is now an additional set of PM sidebands as a result of the AM-
to-PM conversion. Since the peak deviation of output phase due to this
latter set of sidebands comes when the instantaneous amplitude is either
a maximum or a minimum, they are 90 degrees out of phase with the
other two sets of sidebands. From Fig. 43 it is seen that we can write
PM VECTORS
GENERATED BY
AMPLIFIER
AM
VECTORS
PM
VECTORS
(a)
o j » o ) »
ys.
Fig. 43
(a) After passing through an amplifier having both compression and amplitude
to phase conversion, the AM vectors are reduced in magnitude and a new set of
PM vectors have appeared.
(b) The locus of the resultant signal of the vectors shown above is elliptical but
the axis is tilted with respect to vector A.
1340 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
1.2
a
z
<
in
LU
Q
3
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-15
32 = 2400 VOLTS
::--Y
-ZS'-'^^
.^
-p-
/
-^
/S2 = 2600 VOLTS
•10
0 5 10
POWER INPUT IN DBM
15
20
25
Fig. 44 — Relative side band amplitudes Si and S2 for the M1789 as a function
of power input for two values of helix voltage.
for the sideband amplitudes &\ and >S^2 at/i + A/and/i — A/ respectively
^" = [M + M(i - c)f +
I-/,. -12
= (1 - c/2f + (^
S2' = [3^ - Vzil - c)f +
"A^
i
= {c/2r +
Solving for c and kp we obtain
c = 1 - {Si - S2)
K = 2[s.' - (i^
.s:
2\ 2-
1/2
(8) ;
(9)
(10)
(11)
Thus we see that from a measurement of the amplitudes Si and S2 the
values of c and kp can be determined.
To check the validity of this approach to intermodulation, we deter-
mined the values of compression and AM-to-PM conversion for an
M1789 from an intermodulation measurement and compared them with
values obtained using the phase bridge set-up described in Section 4.2.
In the intermodulation measurement the two signals were 100 mc apart
J
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY
1341
150
125
I/)
LU 100
CE
a.
o
o
75
50
25
r
7
^^
kJ
D
,^
^y/^
^600 VOLTS
/
2400 VOLTS^
^
/
J
^
y
/
^ —
A>-^
^
J2
r-^
-tf^
x^
-10
-5
5 10
POWER INPUT IN DBM
15
20
25
Fig. 45 — Compression as a function of input level for two values of helix volt-
age. Triangles represent data obtained with the test set of Fig. 24. Circles and
squares represent data obtained by the two signal intermodulation measurement.
in frequency and 30 db different in level. From measurements of signal
strength at the various frequencies involved, the magnitudes of S>\ and
*S2 were determined with the results shown in Fig. 44. From these re-
sults the values of c and h^ were calculated and then converted to %
compression and degrees per db in order to compare with the results of
_l
10.00
UJ
m
o
8.75
111
Q
rr
7.50
LU
Q.
01
6.25
LU
LU
ct
(J
5.00
LU
O
z
3.75
z
n
(0
2.50
cr
LU
>
7
1.25
O
O
?
0
Q-
O
1-
-1.25
5
<
-2.60
D
2600 VOLTS/
r
\
/
\
/
1
J^
/-
n
k
t
\
A
^
\
A
V
f
2400 VOLTs\
D --
^
!>
'
■J
i
-15
-10
-5
0 5 10
POWER INPUT IN DBM
15
20
25
Fig. 46 — Conversioia of amplitude modulation to phase modulation as a func-
tion of input level for two values of heli.x voltage. Triangles represent data ob-
tained with the test set of Fig. 24. Circles and squares represent data obtained by
the two signal intermodulation measurement.
1342 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
20
cr 18
O
^ 16
u.
o
(0 14
Q
Z
^ 12
O
f 10
UJ
o
z
I-
<
a
o
TUBE
TUBES
FAILURES
TEST
—
^
—
—
—
—
—
—
Fig. 47 — Life test results. The open bars indicate tubes that have failed; the
solid bars tubes that were operating as of May 1, 1956. These tubes were operated
with cathode temperatures between 720° and 760°C.
Figs. 23(c) and 23(e). The latter curves are repeated as Figs, 45 and
46 with the experimental points calculated from Si and S2 shown. It is
seen that the results of the two types of measurements compare remark-
ably well considering that the calculations of c and kp both require the
subtraction of nearly equal quantities. Thus we may conclude that our
method of considering the intermodulation is substantially correct and
that we can obtain compression and AM-to-PM conversion from an
intermodulation measurement .
V. LIFE TESTS
We feel that sufficient data have been accumulated to indicate that
tube life in excess of 10,000 hours can be expected. Fig. 47 summarizes
our life test experience. All tube failures were caused by cathode failure
and these were evidently the result of exhaustion of coating. End of life
for these tubes comes comparatively suddenly i.e., in a few hundred
hours after the cathode current begins to drop. At this time the emission
becomes non-uniform over the cathode surface with consequent beam
defocusing and helix interception. This in turn causes gas to be released
into the tube which then accelerates the cathode failure through cathode
poisoning. The rf performance remained good over the tube life — the
gain and output power actually increasing slightly near the end of life
as the beam started to defocus.
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY 1343
VI. ACKNOWLEDGMENTS
The M1789 TWT is the outcome of an intensive efTort which has
included many individuals in addition to the authors. R. Angle, J. S.
Gellatly, E. G. Olson, and R. G. Voss all have contributed to the me-
chanical design of the tube and to its reduction to practice. R. W.
DeVido has materially assisted with the electrical testing. M. G. Bodmer
and J. F. Riley have been responsible for setting up the life test program
and J. C. Irwin and J. A. Saloom contributed importantly to the design
work on the electron gun. P. P. Cioffi and M. S. Glass have been largely
responsible for the design of the magnetic circuits and P. I. Sandsmark
for the helix-to-waveguide transducers. D. 0. Melroy studied the
effects of positive ions and performed the experiments on ion bombard-
ment referred to in Section III. D. R. Jordan contributed to the studies
on noise. In addition to the above, the authors would like to thank
E. D. Reed for his very helpful criticism of this manuscript.
Appendix I — Gain Calculations
The gain calculations for the M1789 follow the procedure outlined
by Pierce"^ with some minor modifications. The steps involved in the
gain calculations for the loss free region of the helix are as follows:
- (1) The experimental synchronous voltage is used to determine
ya and the dielectric loading factor as defined by Tien.^
(2) From 7a the value of helix impedance K is obtained from Ap-
pendix VI of Pierce.^
(3) The value of K is corrected using Tien's^ results and C is then
calculated in the usual manner.
(4) The number of wavelengths Ni per inch of helix is obtained using
the experimentally determined (from synchronous voltage) wave-
length.
(5) The value of cog/w is determined. In this calculation the curves
for cop/cog from Watkins^ are employed.
(6) QC is determined from
QC =
(7) From QC, B is determined from Fig. 8.10 of Pierce'^ and the gain
BCNi in the loss free region is calculated.
In calculating the effect of the attenuator section, we have had to
make some rather gross assumptions. Fortunately, it turns out that the
134-4 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
gain in the attenuator is a small fraction of the total gain in the tube so
that the over-all gain is not particularly sensitive to the means we use
for treating the attenuator. Essentially what we have done is to con-
sider the high loss part of the attenuator as a severed helix region and
the low loss part of the attenuator as a lossy helix region.
Fig. 48 shows the value of the growing wave parameter as a function
of the loss parameter d for various values of QC as calculated from theory.
Because of discontinuity losses to the growing wave as it propagates in
a region of gradually increasing loss, the actual gain will be less than
that calculated from Fig. 48. Some rather crude probe measurements
have indicated that the effective x vs. d curve can be approximated by
a straight line through the d = 0 and d = 1 points — the dotted line in
Fig. 48.
Since the helix is effectively severed by the high loss portion of the
attenuator we must subtract some discontinuity loss from the gain in
the attenuator region. The effective drift length in the severed region
is unknown so this discontinuity loss cannot be accurately calculated
from the low-level theory. The discussion in chapter nine of Pierce^
indicates that an average value of about 6 db is reasonable.
An alternate method of treating the attenuator was also tried. In this
calculation, the x vs. d curves in Fig. 48 were assumed to be correct to
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
\
N,
\s
v
v^
^-^^
V
^^•.
"""---
QC = 0
^
S^^
V^
^sN
^> '
^
%
....,,0^5
^^N
— ^
0.5
—
V
^N
0.4
0.8
1.2
1.6
2.0
d
2.4
2.8
3.2
3.6
4.0
Fig. 48 — Curves of growing wave parameter x as a function of loss parameter
d showing approximation (dotted lines) used in gain calculations for the M1789.
TRAVELING WAVE TUBE FOR 6,000-MC RADIO RELAY 1345
(/ = 1. The region for which d > 1 was considered as a severed helix
region with 6-db discontinuity loss. Calculations using this procedure
gave total gains for the TWT within a couple of db of the first method.
The remaining steps in calculating the gain of the TWT are therefore:
(8) The quantity a is determined from the slope of the dotted lines
in Fig. 48.
(9) The length of helix, 4 in the attenuator for which x > 0 is
determined by using Fig. 48.
(10) The total attenuation L, in the section of the attenuator effective
in producing gain is calculated.
(11) The initial loss parameter A is obtained from Fig. 94 of Pierce J
(12) The gain is calculated from
Gain = A -6dh +aL + BCNi (3.5 + /«)
where the six db is the discontinuity loss in the attenuator section and the
3.5 inches is the length of loss free helix.
Glossary of Symbols
a loss factor from Pierce^
A discontinuity loss parameter at input of helix from Pierce^
B magnetic flux density or the space charge parameter from Pierce
Bb Brillouin flux density for a beam entirely filling the helix
C gain parameter from Pierce^
a helix radius
b beam radius
d loss parameter from Pierce'^
/ frequency
Ik cathode current
la accelerator current
Ih helix current
Ic collector current
k 2ir/Xo where Xo is the free space wavelength
fe length of helix attenuator in which gain is possible
L loss in the part of the attenuator section which is capable of pro-
ducing gain.
A'' number of wavelengths in TWT
Ni number of wavelengths on the helix per inch
QC space charge parameter from Pierce^
Ta anode radius of curvature of gun
Tc cathode radius of curvature of gun
Tmin minimum beam radius from Pierce'"
1346 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Tc cathode radius
r95 radius at the beam minimum through which 95 per cent of t
current flows
(7 standard deviation of electron trajectory
Tk cathode temperature
Va accelerator voltage
Vn helix voltage
Vc collector voltage
X growng wave parameter from Pierce
CO radian frequency
oic carrier radian frequency
ojm modulating signal radian frequency
ojp radian plasma frequency
cog corrected radian plasma frequency
c compression factor
kp AM-to-PM conversion factor
7 radial propagation constant
References
1. Cutler, C. C, Spurious Modulation of Electron Beams, Proc. I.R.E., 44, ,
pp. 61-64, Jan., 1956.
2. Danielson, W. E., Rosenfeld, J. L., and Saloom, J. A., A Detailed Analysis of "
Beam Formation with Electron Guns of the Pierce Type, B. S.T.J. 35, pp.
375-420, March, 1956.
3. Augustine, C. F., and Slocum, A., 6KMC Phase Measurement System For
Traveling-Wave Tubes, I.R.E. Trans. PGI-4, Oct., 1955.
4. Tien, P. K., A Large Signal Theory of Traveling-Wave Amplifiers, B.S.T.J.,
35, pp. 349-374, March, 1956.
5. Brangaccio, D. J., and Cutler, C. C, Factors Affecting Traveling-Wave Tube
Power Capacity, I.R.E. Trans. PGED-3, June, 1953.
6. Smullin, L. D., and Fried, C, Microwave Noise Measurements on Electron
Beams, I.R.E. Trans., PGED-4, Dec, 1954.
7. Pierce, J. R., Traveling-Wave Tubes, D. Van Nostrand, Inc., 1950.
8. Tien, F*. K., Traveling-Wave Tube Helix Impedance, Proc. I.R.E., 41, pp.
1617-1623, Nov., 1953.
9. Watkins, D. A., Traveling-Wave Tube Noise Figure, Proc. I.R.E., 40, pp.
65-70, Jan., 1952.
10. Pierce, J. R., Theory and Design of Electron Beams, D. Van Nostrand, Inc.,
1949.
Helix Waveguide
By S. P. MORGAN and J. A. YOUNG
(Manuscript received July 23, 1956)
Helix waveguide, composed of closely wound turns of insulated copper
wire covered with a lossy jacket, shows great promise for use as a communi-
cation medium. The properties of this type of waveguide have been investi-
gated using the sheath helix model. Modes whose wall currents follow the
highly conducting helix have attenuation constants which are essentially
the same as for copper pipe. The other modes have very large attenuation
constants which depend upon the helix pitch angle and the electrical proper-
ties of the jacket. Approximate formidas are given for the propagation con-
stants of the lossy modes. The circular electric mode important for long-
distance communication has low loss for zero-pitch helices. The propagation
constants of sotne of the lossy modes in helix waveguide of zero pitch have
been calculated numerically, as functions of the jacket parameters and the
guide size, in regions where the approximate formulas are no longer valid.
Under certain conditions the attenuation constant of a particular mode may
pass through a maximum as the jacket conductivity is varied.
Glossary of symbols
a Inner radius of waveguide
h = 13 — ia Complex phase constant
n Angular mode index
p Denotes p„„, or pnm' according to context
Pnm in^^ zero of Jn{x)
Pnm' w*^ zero of Jn{x)
r, d, z Right-handed cylindrical coordinates
a Attenuation constant
/? Phase constant
/?o = 27r/Xo = wifxoeoY'^ Free-space phase constant
€o Permittivity of interior medium
€ Permittivity of exterior medium
e e/eo
1347
e"
13-48 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
.. r 2 / / • //\ 7 2il/2
§2 L<^ Mo€o(.e — te ) — ll \
Xo Free-space wavelength
Xc = 2-Kaf'p Cutoff wavelength
juo Permeability of interior and exterior media
V = Xo/Xc = p\o/2ira Cutoff ratio
[e - I + V - te )
^ + IT]
e' - ie"
n Electric Hertz vector
n* Magnetic Hertz vector
0" Conductivity of exterior medium
rj/ Pitch angle of helix
CO Angular frequency
e" Harmonic time dependence assumed throughout
J nix) Bessel function of the first kind
Jn(x) dJn{x)/dx
Hn'^ix) Hankel function of the second kind
Hn^'^'ix) dHS-\x)/dx
MKS rationalized units are employed throughout. Superscripts i and e
are used to indicate the interior and exterior regions.
I. INTRODUCTION AND SUMMARY
Propagation of the lowest circular electric mode (TEoi) in cylindrical
pipe waveguide holds great promise for low-loss long distance communi-
cation.^' ^ For example, the TEoi mode has a theoretical heat loss of 2
db/mile in waveguide of diameter 6 inches at a frequency of 5.5 kmc/s,
and the loss decreases with increasing frequency. Increased transmission
bandwidth, reduced delay distortion, and reduced waveguide size for a
given attenuation are factors favoring use of the highest practical fre-
quency of operation. An increased number of freely propagating modes
and smaller mechanical tolerances are the associated penalties. Any
deviation of the waveguide from a straight circular cylinder gives rise to
signal distortions because of mode conversion-reconversion effects.
One solution to mode conversion-reconversion problems is to obtain a
waveguide having the desired low attenuation properties of the TEoi
mode in metallic cylindrical waveguide and very large attenuation for
all other modes, the unwanted modes.^' ^ The low loss of the circular
electric modes in ordinary round guide is the result of having only cir-
1 S. E. Miller, B.S.T.J., 33, pp. 1209-1265, 1954.
2 S. E. Miller and A. C. Beck, Proc. I.R.E., 41, pp. 348-358, 1953.
3 S. E. Miller, Proc. I.R.E., 40, pp. 1104-1113, 1952.
HELIX WAVEGUIDE 1349
cumferential current flow at the boundary wall. All other modes in round
guide have a longitudinal current present at the wall. Thus the desired
attenuation properties can be obtained by providing a highly conducting
circumferential path and a resistive longitudinal path for the wall cur-
rents. This is done in the spaced-disk line by sandwiching lossy layers
between coaxially arranged annular copper disks. ^ Another possibility
which has been suggested is a helix having a small pitch.
Helix waveguide, formed by winding insulated wire on a removable
mandrel and coating the helix with lossy material, has been made at the
Holmdel Radio Research Laboratory. Wires of various cross sections
and sizes have been used to wind helices varying from 3^ to 5 inches in
diameter, which have been tested at frequencies from 9 to 60 kmc/s.
Pitch angles of from nearly 0° (wire in a plane perpendicular to the axis
of propagation) to 90° (wire parallel to the axis of propagation) have
been used. The helices having the highest attenuation for the unwanted
modes while maintaining low loss for the TEoi mode are those wound
with the smallest pitch from insulated wire of diameter 10 to 3 mils
(American Wire Gauge Nos. 30 to 40). The high attenuation properties
for unwanted modes also depend markedly on the electrical properties
of the jacket surrounding the helix.
In this paper the normal modes of helix waveguide are determined
using the sheath helix approximation, a mathematical model in which
the helical winding is replaced by an anisotropic conducting sheath. A
brief formulation of the boundary value problem leads to an equation
which determines the propagation constants of modes in the helix guide.
Since the equation is not easy to solve numerically, approximations are
presented which show the effects of the pitch angle, the diameter, the
conductivity and dielectric constant of the jacket, and the wavelength,
when the conductivity of the jacket is sufficiently high.
By proper choice of the pitch angle and, in some instances, of the
polarization, a helix waveguide can be made to propagate any mode of
ordinary round guide, with an attenuation constant which should be
essentially the same as in solid copper pipe. The pitch is chosen so that
the wall currents associated with the desired mode follow the direction
of the conducting wires. The losses to the other modes are in general
much higher, and are determined by both the pitch angle and the jacket
material.
Special attention is given in the present work to the limiting case of a
helix of zero pitch, since the attenuation constant of the TEoi mode will
be smallest when the pitch angle is as small as possible. To explore the
^ Reference 3, p. 1111.
1350 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
region where the approximate formulas for the propagation constants
of the lossy modes break down, some numerical results have been ob
tained for helices of zero pitch using an IBM 650 magnetic drum calcu
lator. Tables and curves are given showing the propagation constants of
various modes in such a waveguide, as functions of the electrical proper-
ties of the jacket and for three different ratios of radius/ wavelength. In
many cases it is found that the attenuation constant of a given mode
passes through a maximum as the jacket conductivity is varied, the
other parameters remaining fixed. The numerical calculations indicate
that it is possible to get unwanted mode attenuations several hundred
to several hundred thousand times greater than the TEoi attenuation
for the size Avaveguide that looks most promising for low-loss communi-
cation.
US
J,"
Fig. 1 — Schematic diagrams of the helical sheath and the helical sheath de-
veloped, showing the unit vectors and the periodicity.
HELIX WAVEGUIDE 1351
II. SHEATH HELIX BOUNDARY VALUE PROBLEM
Ordinary cylindrical waveguide consists of a circular cylinder of radius
a, infinite length, and zero (or very small) conductivity, imbedded in an
infinite* homogeneous conducting medium. The sheath helix waveguide
has the same configuration plus the additional property that at radius a
dividing the tAvo media, there is an anisotropic conducting sheath which
conducts perfectly in the helical direction and does not conduct in the
perpendicular direction. The attenuation and phase constants are deter-
mined by solving Maxwell's equations in cylindrical coordinates and
matching the electric and magnetic fields at the wall of the guide.
The helix of radius a and pitch angle \J/ = tan~^ s/2ira is shown in the
upper part of Fig. 1. The developed helix as viewed from the inside when
cut by a plane of constant 6 and unrolled is shown in the lower part of
the illustration. A new set of unit vectors e^ and Cj. parallel and perpen-
dicular respectively to the helix direction is introduced. These are re-
lated to er , ee , and Cz by
er X e\\ — ex
e\\ = ez sin t^ + ee cos rp
fij. = ez cos \p — e$ sin xj/
The boundary conditions at r = a are
K = E{ = 0
Ej = E/
where the superscript i refers to the interior region, 0 ^ r ^ a, and the
superscript e refers to the exterior region, a '^ r -^ co . An equivalent set
of boundary conditions in terms of the original unit vectors is
E; tan ^p + Ee' = 0
E," tan rp + Ee' = Q
(1)
e: = e:
H; tan ,A -f He' = Hf tan ^p + ///
We are looking for solutions which are similar to the modes of or-
* The assumption of an infinite external medium is made to simplify the mathe-
matics. The results will be the same as for a finite conducting jacket which is thick
enough so that the fields at its outer surface are negligible.
1352 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
dinary waveguide, i.e., "fast" modes as contrasted with the well-known
"slow" modes used in traveling- wave tubes. ^' ^ To solve the problem we
follow the procedure set up by Stratton^ for the ordinary cylindrical
waveguide boundary problem. The fields E and H are derived from an
electric Hertz vector IT and a magnetic Hertz vector 11* by
^ = vxvxn- ^■w/xV X n*
H= {a + iwe)'^ X ii + V X V xn*
(2)
where
(3)
(4)
n = ezU,
n* = Ln*
and, assuming a time dependence exp (iwt),
00
ni V~^ i 7" / V N —ihz—inB
z = 2^ anJn{tir)e
n=— 00
00
ne V"* ejr (2)/ 5, \ —ihz—inB
n=— 00
00
n*i V~^ 7 i T / <, \ —ihz—inB
z = 2^ OnJn{hr)e
n=— 00
Jl= — 00
In these expressions
5-2 2 7,2
f 1 = CO )Ltoeo — h
5-2 2 / / ■ ,/\ 7 2
e — ie" = e/eo — ia/weo
where the interior region is assumed to have permittivity eo and perme-
ability ^0 , while the exterior region has permittivity e, permeability no ,
and conductivity a. The superscripts i and e refer to the interior and ex-
terior regions respectively, and the a's and 6's are amplitude coefficients.
6 J. R. Pierce, Proc. I.R.E., 35, pp. 111-123, 1947.
* S. Sensiper, Electromagnetic Wave Propagation on Helical Conductors, Sc.D.
thesis, M.I.T., 1951. In Appendix B of this reference, Sensiper shows that when
the interior and exterior media are the same, only slow waves will exist except in
special cases. Fast guided waves become possible if the conductivity of the exterior
medium is sufficiently high.
'J. A. Stratton, Electromagnetic Theory, McGraw-Hill, New York, 1941, pp.
524-527. Note that Stratton uses the time dependence exp (—icot).
HELIX WAVEGUIDE
1353
Attention is restricted to waves traveling in the positive ^-direction,
which are represented by the factor exp { — ihz), where /i ( = /3 — ia) is
the complex phase constant. However it is necessary to consider both
right and left circularly polarized waves; this accounts for the use of
both positive and negative values of n.
Substitution of (2), (3), and (4) into the boundary conditions (1)
leads to the following set of equations:
V 2 , , hn
fi tan \l/ — —
a
Jn(^ia)an + i(^iJ.(ihJn'{tia)hn = 0
^2 tan yp — —
a
(5)
•to;eofiJ«'(fia)a„* +
. 2 . , hn
fi tan yp — —
a
Jn(^ia)hn
(2)',
+ (o- + icoe)^2Hn ' {^2a)an
[
> 2 + , hn
ti tan \l/ — —
a
Hr.''\ha)h: = 0
If the conductivity of the exterior region is infinite, it is possible to
satisfy the boundary conditions with only one of the amplitude coeffi-
cients different from zero; for example
hn = a«' = 6„* = 0
a„
0
or
dn — CLn = bn = 0
bj 9^ 0
Jni^xO) = 0 Jn'iria) = 0
The first case corresponds to TM modes and the second to TE modes
in a perfectly conducting circular guide. Linearlj^ polarized modes may
be represented as combinations of terms in a,/ and a-n\ or bn and 6_„*.
If the exterior region is not perfectly conducting, one can still find
solutions having the fields confined to the interior region by propedy
choosing the angle of the perfectly conducting helical sheath. For exam-
ple, it is easy to verify that equations (5) are satisfied under the follow-
ing conditions:
ttn
an = bn = 0
bj 9^ 0
tan yp =
hn
Jn'i^ia) = 0
1354 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
li n 9^ 0, these conditions correspond to circularly polarized TE„
waves, in which the wall currents follow the direction of the conducting
sheath. If n = 0, then i^ = 0, and one has TEom modes with circum-
ferential currents only. \
The equations can also be satisfied with
bn = ttn = bn = 0
ttn 9^ 0
yl^ = 90°
Jnitia) = 0
corresponding to the TM„m modes (either circularly or linearly polarized)
of a perfectly conducting pipe, which are associated with longitudinal
wall currents only.
In the general case when the jacket is not perfectly conducting and
the helix pitch angle is not restricted to special values, it is necessary to
solve (5) simultaneously for the field amplitudes. The equations admit a
nontrivial solution if and only if the determinant of the coefficients of
the a's and b's vanishes. The transcendental equation which results from
equating the determinant of the coefficients to zero is
f:
f 1 tan V — r— ) r it^ \ ~ ^ Moeo
= t.
(6)
(2)//
f 2 tan 1^ - -— I , — CO MoeoCe - te ) , -
f2ay H^V'{^2a) Hr.^"\^2a) J
The solution of this equation determines the propagation constant ih
and therefore the attenuation and phase constants a and /3. When ih
has been obtained, it is a straightforward matter to determine the a and
b coefficients from equations (5) and the electric and magnetic fields
from (2), (3), and (4).
"It is well known^ that the only pure TE or TM modes that can exist
in a circular waveguide with walls of finite conductivity are the circularly
symmetric TEom and TMom modes. The other modes are all mixed modes
Avhose fields are not transverse with respect to either the electric or the
magnetic vector. In general the modes of helix waveguide are also mixed
modes, and no entirely satisfactory scheme for labeling them has been
proposed. In the present paper we shall call the modes TE„m or TM„m
according to the limits which they approach as the jacket conductivity
becomes infinite, even though they are no longer transverse and their
8 Reference 7, p. 526.
HELIX WAVEGUIDE 1355
field patterns may be quite different when the jacket is lossy. This sys-
tem is not completely unambiguous, because as will appear in Section
IV the mode designations thus obtained are not always unique. However
it is a satisfactory way to identify the modes so long as the jacket con-
ductivity is high enough for the loss to be treated as a perturbation.
Approximations derived on this basis are presented in the next section.
III. APPROXIMATE EXPRESSIONS FOR PROPAGATION CONSTANTS
If the jacket were perfectly conducting, the helix waveguide modes
would be the same as in an ideal circular waveguide, with propagation
constants given by
where
V = Xo/Xc = p\o/2Tra
p = ??i*^ zero of Jnix) for TM„m mode, or rn^^ zero of Jn(x) for TE„m
mode
If the jacket conductivity is sufficiently large, approximate solutions
of (6) may be found by replacing Hn'\^2a) and Hn'^'i^iO) with their
asymptotic expressions, and expanding Jni^ia) or Jn'(^ia) in a Taylor
series near a particular zero. This calculation is carried out in the ap-
pendix. The propagation constant may be written in the form
ih = a + i{^nm + A|S)
where to first order the perturbation terms are
TM„„ modes
a + m = ,\ ^ \„ rXT-^r-, (7a)
a(l — v-y^ 1 -\- tan^ \p
TE„TO modes
a 4- i\B - ^ + ''^ ^V" [tan ^ - n(l - vyVyvf . , .
^'^^~a(l -, 2)1/2 ^^^7^2 1 -f tan^ ^ ^'^^
and
? + ^> = (e' - ie'T'"
e = e/eo , e = cr/coeo
The approximations made in deriving (7) are discussed in the appen-
1356 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
dix. In practice, the range of validity of these expressions is usually
limited by the criterion
/1 2\l/2
^^^"^^ \a + iA^\«l (8)
V
The numerical calculations described in Section IV indicate that the
approximations are good so long as the left-hand side of (8) is less than
about 0.1, and that they break down a little sooner for TE modes than
for TM modes.
Inspection of (7) reveals three cases of particular interest, namely
^ = 0°,\p = tan~^ w(l — v^f^/pp, and i/- = 90°. These cases, which were
mentioned in Section II and are discussed again below, correspond to
preferential propagation of certain modes, in which the wall currents
follow the direction of the conducting helix. The preferred modes have
zero attenuation in the present treatment because the helical sheath is
assumed to be perfectly conducting. In practical helices wound from
insulated copper wire the loss should be only slightly greater than in
round copper pipe of the same diameter. The slight increase (of magni-
tude 10 per cent to 30 per cent) is due to the slightly nonuniform cur-
rent distribution in the wires, an effect that can be kept small by keeping
the gaps between the wires of the helix small. In general the attenuation
constants of modes whose wall currents do not follow the helix are orders
of magnitude larger than the attenuation constants of the preferred
modes.
iA = 0°
The circular electric (TEom) modes have attenuation constants sub-
stantially the same as in solid copper pipe. The additional TEom loss if
the pitch angle is not quite zero is proportional to tan^ \{/. This added loss
can be made very small by using fine wire for winding the helix.
The losses for the unwanted modes can be made large by a proper
choice of jacket material. When ^ = 0, equations (7) yield
TM„„j modes
a(l — v^y^
TE„m modes
a + iA/3 = i^ 'J- -^^ (^ + iv) (9b)
a p^ — n^
HELIX WAVEGUIDE 1357
It may be of interest to compare the attenuation constants given by
(9) with the results obtained by calculating the power dissipated in the
walls of a pipe' which has different resistances in the circumferential and
longitudinal directions. If the wall resistance for circumferential currents
is represented by Re and for longitudinal currents by Rz , the expressions
for a are
TM nm modes
Rz
a
TE„TO modes
a =
{(xo/eoY'-aa - I'V
Rev' + Rz{n/v)\l - v') p'
(Mo/€o)^/-a(l - i/'Y'^ p2 _ ^2
The results for ordinary metallic pipe are obtained by setting
Re = Rz — R = (co^o/2cr)
[f Re = 0, the expressions above agree with (9), inasmuch as
I = R(eo/ixo) '" when the jacket conductivity is large.
4/ — tan~^ n(l — v')^''/vv, n ^ 0
For this value of rp the circularly polarized TE„^ mode which varies as
exp(—in9) has low attenuation. (We assume 7i 9^ 0, since the case
n = 0 has been treated above.) One of the properties of helix waveguide
is the difference in propagation between right and left circularly polarized
TE„m modes. By properly designing the helix angle for the frequency,
mode, and size of guide, the loss to one of the polarizations can be made
very low. If the jacket is lossy enough the attenuation of the other
polarization should be quite high. Thus only one of the circularly polar-
ized modes should be propagated through a long pipe. Such a helix has
features analogous to the optical properties of levulose and dextrose
solutions, which distinguish between left and right circularly polarized
light.
Let an be the attenuation constant of the mode which varies as
exp{ — i7i9), and a_„ the attenuation constant of the mode which varies
^ S. A. Schelkunoff, Electromagnetic Waves, van Nostrand, New York, 1943,
pp. 385-387.
1358 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
as exp (-{-ind). Then from (7b), for any pitch angle t/',
^ p' v' [tan ^ + 7i(l - vflvvf
a -n = -
i
CXn =
a
-n — a„ = 4
a p2 _ ^2 (1 - v'yi' 1 + tan2 yf,
^ p V [tan \p — n{l — v^Y' /pvf
ap^ - n'' {1 - v2)i/2 1 + tan- rp
^ np V tan ip
ap"^ — 'n? 1 -\- tan^ yp
The mode which varies as exp( — zn0) has lower loss if \p and n have the
same sign.
The TM„m attenuation constants are independent of polarization and
are given by (7a).
yp = 90°
These "helices," with wires parallel to the axis of the waveguide,
should propagate TM„m modes with losses approximately the same as
in copper pipe. For the TE„„i modes, (7b) gives
TEnm modes
2 2
a + iA(3 = " -T^—2 (^ + ^■'?)
a(l — j'-)^'- p^ — v}
IV. NUMERICAL SOLUTIONS FOR ZERO-PITCH HELICES
The main interest in helix waveguide is for small pitch angles where
the TEoi attenuation is very low. The propagation constants of various
lossy modes in helix guides of zero pitch have been calculated by solving
the characteristic equation (6) numerically. These calculations will now
be described.
Equation (6) is first simplified by setting yp — Q and replacing the
Hankel functions with their asymptotic expressions. The condition for
validity of the asymptotic expressions, namely
I r2a I » I {^n - l)/8 I
is well satisfied in all cases to be treated here. Equation (6) may then be
rearranged in the dimensionless form
Fni^a) = i^oaf [{nhafJn\Ua) - (/5ca)'(fia)V„''(ria)]
- i{^,af [{nhaf -f (^oa)^(e' - Z6")(^a)V/(fia)/n(fia) (10)
= 0
There is no difference between the propagation constants of right and
HELIX WAVEGUIDE 1359
left circularly polarized waves when xp = 0. Using the relationships
ha = KM' + (M' (e' - ie" - l)f\ Im^a < 0
ha = {%af - (rla)T'^ Im /la < 0
it is clear that Fni^a) is an even function of ^a, involving the parame-
ters Pott (= 27ra/Xo), e', e", and n.
When specific values have been assigned to /3oa, e', and e", roots of
(10) can be found numerically by the straightforward procedure of
evaluating Fni^a) at a regular network of points in the plane of the
complex variable ^a, plotting the families of curves Re F„ = 0 and
Im Fn = 0, and reading off the values of ^a corresponding to the inter-
sections of curves of the two families.
The procedure just outlined has been applied to the cases n = 0 and
n = 1. When n = 0 one can take out of Fo(fia) the factor Jo'(fia), whose
roots correspond to the TEom modes; the roots of the other factor are
the TMom-limit modes. When n = 1 the function Fi(ha) does not factor,
and its roots correspond to both TEi^-limit and TMi^-limit modes. If
the jacket conductivity is high it is easy to identify the various limit
modes, and a given mode can be traced continuously if the conductivity
is decreased in sufficently small steps.
The numerical calculations were set up, more or less arbitrarily, to
cover the region 0 ^ Re ^a ^ 10, —10 ^ Im ^a ^ 10, for each set
of parameter values. A few plots of Re Fn and Im Fn made it apparent
that for propagating modes the roots in this region are all in the first
quadrant and usually near the real axis. The entire process of solution
was then programmed by Mrs. F. M. Laurent for automatic execution
on an IBM 650 magnetic drum calculator. The calculator first evaluated
Fni^ci) at a network of points spaced half a unit apart in both directions,
then examined the sign changes of Re F„ and Im Fn around each ele-
mentary square. If it appeared that a particular square might contain
a root of Fn , the values of Fn at the four corner points were fitted by an
interpolating cubic polynomial ° which was then solved. If the cubic
had a root inside the given square, this was recorded as an approximate
root of Fn . The normalized propagation constant iha = aa -{- i(3a was
also recorded for each root.
The calculated roots ^a and the normalized propagation constants
are summarized in Tables 1(a) to 1(f), which relate to the following cases:
Table 1(a)— /3oa = 29.554, e' = 4, e" variable
Table 1(b) —/3oa = 29.554, e' = 100, e" variable
Table 1(c) —/3oa = 29.554, e = e", both variable
10 A. N. Lowan and H. E. Salzer, Jour. Math, and Phys., 23, p. 157, 1944.
1360 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Table 1(d) — M = 12.930, e' = 4, e" variable
Table 1(e) — fi.a = 12.930, e' = e", both variable
Table 1(f) — fi^a = 6.465, e' = 4, e" variable j
The three values of ^oa correspond to waveguides of diameter 2 inches,
I inch, and ye inch at Xo = 5.4 mm. The jacket materials (mostly carbon-
loaded resins) which have been tested to date show a range of relative
permittivities roughly from 4 to 100. There is some indication that the
permittivity of a carbon-loaded resin increases as its conductivity in-
creases; this suggested consideration of the case e = e .
The tables cover the range from e" = 1000 down to e" = 1 at small
enough intervals so that the general course of each mode can be followed.
It is worth noting that at 5.4 mm a resistivity (l/o-) of 1 ohm cm cor-
responds to e' =32. Copper at this frequency has an e of approxi-
mately 2 X 10^
In general the tables include the modes derived from Fo(^ia) whose
limits are TMoi , TM02 , and TM03 , and the modes derived from /^i(fia)
whose limits are TEu , TMn , TE12 , TM12 , and TE13 (except that in
the i^-inch guide TM03, TM12 , and TE13 are cut off). Some results are
given for the TMis-limit mode, namely those which satisfy the arbitrary
criterion Re fia ^ 10; but these results are incomplete because for large
e" the corresponding root of Fi(^ia) approaches 10.173. Furthermore for
small values of e" the attenuation constants of a few of the TM-limit
modes become quite large and the corresponding values of ^la move far
away from the origin. Since our object was to make a general survey
rather than to investigate any particular mode exhaustively, we did not
attempt to pursue these modes outside the region originally proposed
for study.
The results of the IBM calculations are recorded in Table I to three
decimal places. Since the roots f la were obtained by cubic interpolation
in a square of side 0.5, the last place is not entirely reliable; but spot
checks on a few of the roots by successive approximations indicate that
it is probably not off by more than one or two units. The propagation
constants of some of the relatively low-loss modes (especially TE12 and
TE13 , whose wall currents are largely circumferential) were calculated
from the approximate formulas,* as noted in the tables. The attenuation
(Text continued on page 1375)
* The formulas used were (A9) and (AlO) of the appendix, which are slightly
more accurate than (7) of the text.
Table 1(a) —
2-INCH Guide at Xq = c
).4 MM (/3oa = 29.554)
WITH e' = 4 AND t" Variable
Limit Mode
€"
fia
aa + t/3o
TMoi
00
2.405
29.4561
1000
2.154 + 0.384i
0.028 + 29.4781
250
2.094 + 0.974i
0.069 + 29.4961
100
2.408 + 1.679i
0.137 + 29.5041
90
2.482 + 1.772i
0.149 + 29.5031
SO
2.579 + 1.878i
0.164 + 29.5021
64
2.804 + 2.083i
0.198 + 29.4951
40
3.519 + 2.547i
0.304 + 29.4561
25
4.604 + 3.165i
0.496 + 29.3691
16
5.870 + 3.763i
0.756 + 29.2191
10
7.564 + 4.131i
1.082 + 28.8871
8
8.464 + 4.158i
1.229 + 28.6461
TM02
00
5.520
29.0341
1000
5.399 + 0.127i
0.024 + 29.0571
250
5.274 + 0.268i
0.049 + 29.0811
100
5.109 + 0.445i
0.078 + 29.1131
90
5.081 + 0.472i
0.082 + 29.1181
80
5.047 + 0.504i
0.087 + 29.1251
64
4.968 + 0.569i
0.097 + 29.1391
40
4.716 + 0.701i
0.113 + 29.1841
25
4.375 + 0.677i
0.101 + 29.2371
16
4.172 + 0.551i
0.079 + 29.2641
10
4.047 + 0.448i
0.062 + 29.2791
8
4.004 + 0.412i
0.056 + 29.2851
4
3.905 + 0.344i
0.046 + 29.2971
1
3.820 + 0.310i
0.040 + 29.3081
TM03
00
8.654
28.2591
1000
8.577 + 0.078i
0.024 + 28.2821
250
8.500 + 0.1601
0.048 + 28.3061
100
8.408 + 0.260i
0.077 + 28.3341
90
8.395 + 0.275i
0.081 + 28.3381
80
8.378 + 0.293i
0.086 + 28.3431
64
8.344 + 0.330i
0.097 + 28.3541
40
8.253 + 0.424i
0.123 + 28.3821
25
8.125 -t- 0.545i
0.156 + 28.4211
16
7.943 + 0.678i
0.189 + 28.4751
10
7.658 + 0.779i
0.209 + 28.5561
8
7.511 + 0.780i
0.205 + 28.5951
4
7.200 + 0.693i
0.174 + 28.6731
1
6.986 + 0.612i
0.149 + 28.7241
TEii
00
1.841
29.4971
1000
1.703 + 0.234i
0.014 + 29.5061
250
1.764 + 0.630i
0.038 + 29.5081
100
2.465 + 0.963i
0.081 + 29.4671
90
2.660 + 0.748i
0.068 + 29.4441
80
2.633 + 0.604i
0.054 + 29.4431
64
2.594 + 0.464i
0.041 + 29.4441
40
2.546 + 0.312i
0.027 + 29.4461
25
2.508 + 0.226i
0.019 + 29.4481
16
2.481 + 0.176i
0.015 + 29.4501
10
2.455 + 0.140i
0.012 + 29.4521
8
2.445 + 0.129i
0.011 + 29.4531
4
2.418 + 0.106i
0.009 + 29.4551
1
2.394 + 0.095i
0.008 + 29.4571
1361
Table 1(a) — Continued
Limit Mode
t"
rw
aa + i/3o
TMn
00
3.832
29.305i
1000
3.652 + 0.197i
0.024 + 29.328i
250
3.457 + 0.440i
0.052 + 29.355i
100
2.978 + 0.880i
0.089 + 29.417i
90
2.821 + 1.215i
0.116 + 29.445i
80
2.945 + 1.476i
0.148 + 29.444i
64
3.146 + 1.868i
0.200 + 29.446i
40
3.728 + 2.564i
0.325 + 29.432i
25
4.659 + 3.175i
0.504 + 29.361i
16
5.921 + 3.727i
0.756 + 29.204i
10
7.613 + 4.135i
1.090 + 28.875i
8
8.487 + 4.153i
1.231 + 28.639i
TE.2
00
5.331
29.069i
1000
0.0008 + 29.070i*
250
0.0016 + 29.071i*
100
0.0026 + 29.072i*
64
0.0033 + 29.072i*
40
0.0042 + 29.073i*
25
0.0055 + 29.074i*
10
0.0092 + 29.075i*
4
5.297 f 0.072i
0.013 + 29.076i
1
5.322 + 0.096i
0.018 + 29.071i
TMi2
00
7.016
28.710i
1000
6.918 + 0.099i
0.024 + 28.733i
250
6.821 + 0.203i
0.048 + 28.757i
100
6.701 + 0.330i
0.077 + 28.786i
90
6.683 + 0.349i
0.081 + 28.791i
80
6.660 + 0.372i
0.0S6 + 28.796i
64
6.612 + 0.419i
0.096 + 28.808i
40
6.475 + 0.535i
0.120 +28.8411
25
6.253 + 0.655i
0.142 +28.8931
16
5.965 + 0.682i
0.141 +28.9541
10
5.719 + 0.590i
0.116 +29.0021
8
5.641 + 0.541i
0.105 +29.0161
4
5.471 + 0.419i
0.079 + 29.0471
1
5.317 + 0.347i
0.063 + 29.0741
TEi3
00
8.536
28.2951
1000
0.0003 + 28.2951*
250
0.0006 + 28.2951*
100
0.0010 + 28.2961*
64
0.0012 + 28.2961*
40
0.0016 + 28.2961*
25
0.0020 + 28.2961*
10
0.0034 + 28.2971*
4
0.0050 + 28.2961*
1
0.0058 + 28.2951*
TM„
00
10.173
27.7481
100
9.963 4- 0.219i
0.078 + 27.8251
90
9.952 + 0.231i
0.083 + 27.8291
80
9.938 + 0.246i
0.088 + 27.8341
64
9.911 + 0.277i
0.098 + 27.8451
40
9.840 + 0.356i
0.126 + 27.8701
25
9.746 + 0.460i
0.101 +27.9051
16
9.625 + 0.591i
0.204 + 27.9501
10
9.433 + 0.757i
0.255 + 28.0201
8
9.305 + 0.837i
0.278 + 28.0651
4
8.836 + 0.898i
0.281 + 28.2181
1
8.485 + 0.781i
0.234 + 28.3221
Approximate formula.
1362
HELIX WAVEGUIDE
1363
Table 1(b) — 2-inch Guide at Xo = 5.4 mm (/Soa = 29.554)
WITH e' = 100 AND e" Variable
Limit Mode
t"
fia
aa + i^a
TMe.
00
2.405
29.456i
1000
2.178 + 0.391i
0.029 + 29.4761
250
2.291 + 0.885i
0.069 + 29.4791
100
2.677 + 1.062i
0.097 + 29.4521
80
2.764 + 1.047i
0.098 + 29.4431
64
2.834 + 1.0191
0.098 + 29.4361
40
2.928 + 0.950i
0.094 + 29.4241
25
2.973 + 0.893i
0.090 + 29.4181
10
3.004 + 0.831i
0.085 + 29.4131
4
3.013 + 0.806i
0.083 + 29.4111
1
3.016 + 0.793i
0.081 + 29.4111
TMo2
00
5.520
29.0341
1000
5.406 + 0.133i
0.025 + 29.0561
250
5.339 + 0.298i
0.055 + 29.0691
100
5.372 + 0.473i
0.087 + 29.0661
SO
5.398 + 0.508i
0.094 + 29.0621
64
5.429 + 0.535i
0.100 + 29.0561
40
5.492 + 0.566i
0.107 + 29.0451
25
5.540 + 0.573i
0.109 + 29.0361
10
5.589 + 0.569i
0.109 + 29.0271
4
5.608 + 0.563i
0.109 +29.0231
1
5.617 + 0.560i
0.108 + 29.0211
TMo3
00
8.654
28.2591
1000
8.581 + 0.082i
0.025 + 28.2811
250
8.537 + 0.179i
0.054 + 28.2951
100
8.548 + 0.279i
0.084 + 28.2921
80
8.561 + 0.300i
0.091 + 28.2891
64
8.575 + 0.317i
0.096 + 28.2851
40
8.606 + 0.339i
0.103 +28.2761
25
8.630 + 0.348i
0.106 + 28.2681
10
8.658 + 0.352i
0.108 + 28.2601
4
8.669 + 0.352i
0.108 + 28.2571
1
8.675 + 0.351i
0.108 + 28.2551
TEn
00
1.841
29.4971
1000
1.719 + 0.236i
0.014 + 29.5051
250
1.871 + 0.504i
0.032 + 29.4991
100
2.132 + 0.484i
0.035 + 29.4811
80
2.161 + 0.451i
0.033 + 29.4791
64
2.178 + 0.420i
0.031 + 29.4771
40
2.191 + 0.372i
0.028 + 29.4751
25
2.192 + 0.343i
0.026 + 29.4751
10
2.190 + 0.316i
0.023 + 29.4751
4
2.188 + 0.306i
0.023 + 29.4751
1
2.187 + 0.301i
0.022 + 29.4751
1364 THE BELL SYSTEM TECHNICAL
JOURNAL, NOVEMBER 1956
Table 1(b) —
Continued
Limit Mode
«"
fia
aa + i^a
TMa
00
3.832
29.305i
1000
3.663 + 0.204
I 0.026 + 29.3271
250
3.579 + 0.485
I 0.059 + 29.341i
100
3.715 + 0.788
I 0.100 + 29.331i
80
3.787 + 0.826
I 0.107 + 29.322i
64
3.856 + 0.843
1 0.111 + 29.3141
40
3.969 + 0.836
I 0.113 + 29.299i
25
4.043 + 0.817
I 0.113 + 29.288i
10
4.100 + 0.777
I 0.109 + 29.279i
4
4.119 + 0.759
I 0.107 +29.2761
1
4.128 + 0.749
I 0.106 + 29.2741
TE12
00
5.331
29.0691
1000
0.0008 + 29.070i*
250
0.0018 + 29.0711*
100
0.0028 + 29.0711*
64
0.0032 + 29.0701*
40
0.0034 + 29.0701*
25
0.0035 + 29.0701*
10
0.0036 + 29.0701*
4
0.0036 + 29.0701*
1
0.0036 + 29.0691*
TM12
00
7.016
28.7101
1000
6.923 + 0.103
I 0.025 + 28.7321 1
250
6.868 + 0.226
I 0.054 + 28.746i \
100
6.885 + 0.355
I 0.085 + 28.7431 1
80
6.902 + 0.381
I 0.092 + 28.7401 {
64
6.922 + 0.403
1 0.097 + 28.7351 ^
40
6.965 + 0.429
I 0.104 + 28.7251
25
7.000 + 0.440
I 0.107 +28.7171 ;
10
7.037 + 0.443
I 0.109 + 28.7081
4
7.051 + 0.441
L 0.108 + 28.7041
1
7.058 + 0.440
I 0.108 + 28.7031
TEx3
00
8.536
28.2951
1000
0.0003 + 28.2951* !
250
0.0007 + 28.2951*
100
0.0010 + 28.2951*
64
0.0012 + 28.2951*
40
0.0013 + 28.2951*
25
0.0013 + 28.2951*
10
0.0013 + 28.2951*
4
0.0013 + 28.2951*
1
0.0013 + 28.2951*
Approximate formula.
Table 1(c) —
2-INCH Guide at Xq = 5
WITH e = e
.4 MM (I3,a = 29.554)
Limit Mode
e' and e"
fia
aa + i0a
TMoi
CO
1000
250
100
64
40
32
25
16
12
10
4
2
1
2.405
2.338 + 0.341i
2.418 + 0.707i
2.677 + 1.062i
2.925 + 1.226i
3.309 + 1.324i
3.540 + 1.299i
3.787 + 1.162i
3.946 + 0.800i
3.950 + 0.647i
3.946 + 0.573i
3.905 + 0.344i
3.869 + 0.252i
3.820 + 0.185i
29.4561
0.027 + 29.4641
0.058 + 29.4641
0.097 + 29.4521
0.122 + 29.4351
0.149 + 29.3991
0.156 + 29.3711
0.150 + 29.3341
0.108 + 29.3011
0.087 + 29.2961
0.077 + 29.2951
0.046 + 29.2971
0.033 + 29.3011
0.024 + 29.3071
TM02
00
1000
250
100
64
40
32
25
16
12
10
5.520
5.469 + 0.136i
5.423 + 0.282i
5.372 + 0.473i
5.337 + 0.624i
5.294 + 0.874i
5.279 + 1.0611
5.319 + 1.367i
5.852 + 1.969i
6.472 + 2.1781
7.026 + 2.1981
29.0341
0.026 + 29.0441
0.053 + 29.0541
0.087 + 29.0661
0.115 + 29.0751
0.159 +29.0901
0.193 + 29.0991
0.250 + 29.1051
0.397 + 29.0391
0.4S7 + 28.9231
0.536 + 28.7961
TM03
00
1000
250
100
64
40
32
25
16
12
10
4
2
1
8.654
8.620 + 0.0851
8.587 + 0.1731
8.548 + 0.2791
8.521 + 0.3551
8.483 + 0.4611
8.458 + 0.5261
8.425 + 0.6111
8.330 + 0.8241
8.206 + 1.0371
8.034 + 1.2401
7.200 + 0.6931
7.098 + 0.4831
6.998 + 0.3491
28.2591
0.026 + 28.2691
0.052 + 28.2801
0.084 + 28.2921
0.107 + 28.3021
0.138 + 28.3151
0.157 +28.3231
0.182 + 28.3351
0.242 + 28.3691
0.300 + 28.4131
0.350 + 28.4711
0.174 + 28.6731
0.120 + 28.6941
0.085 + 28.7161
TEu
1000
250
100
64
40
32
25
16
12
10
4
2
1
1.841
1.810 + 0.1901
1.911 + 0.3841
2.132 + 0.4841
2.270 + 0.4531
2.365 + 0.3661
2.389 + 0.3241
2.406 + 0.2811
2.420 + 0.2191
2.424 + 0.1871
2.424 + 0.1691
2.418 + 0.1061
2.409 + 0.0781
2.394 + 0.0561
29.4971
0.012 + 29.4991
0.025 + 29.4951
0.035 + 29.4811
0.035 + 29.4701
0.029 + 29.4621
0.026 + 29.4591
0.023 + 29.4571
0.018 + 29.4561
0.015 + 29.4551
0.014 + 29.4551
0.009 + 29.4551
0.006 + 29.4561
0.005 + 29.4571
1365
Table 1(c) — Continued
'V
Limit Mode
«' and e"
ria
aa + i/3a I
TMu
oo
3.832
29.3051
1000
3.759 + 0.203i
0.026 + 29.3151
250
3.714 + 0.439i
0.056 + 29.3231
100
3.715 + 0.788i
0.100 + 29.3311
64
3.797 + 1.070i
0.139 + 29.3291
40
4.080 + 1.400i
0.195 + 29.3051
32
4.276 + 1.550i
0.226 + 29.2851
25
4.586 + 1.661i
0.260 + 29.2451
16
5.359 + 1.579i
0.291 +29.1091
1
12
5.587 + 1.043i
0.201 + 29.0411
10
5.560 + 0.859i
0.164 + 29.0401
4
5.471 + 0.419i
0.079 + 29.0471
2
5.438 + 0.249i
0.047 + 29.0511
1
5.444 + 0.131i
0.025 + 29.0491
TEi2
1000
250
100
64
40
25
10
5.331
29.0691
0.0009 + 29.0701*
0.0018 + 29.0701*
0.0028 + 29.0711*
0.0035 + 29.0711*
0.0044 + 29.0711*
0.0055 + 29.0721*
0.0087 + 29.0731*
4
5.297 + 0.072i
0.013 + 29.0761
2
5.272 + 0.108i
0.020 + 29.0801
1
5.198 + 0.132i
0.023 + 29.0941
TMio
oo
7.016
28.7101
1000
6.971 + 0.107i
0.026 + 28.7211
250
6.931 + 0.217i
0.052 + 28.7311
100
6.885 + 0.355i
0.085 + 28.7431
64
6.852 + 0.457i
0.109 + 28.7531
40
6.801 + 0.6101
0.144 + 28.7681
32
6.768 + 0.708i
0.167 + 28.7781
25
6.720 + 0.850i
0.198 + 28.7931
16
6.562 + 1.359i
0.309 + 28.8501
12
6.869 + 2.095i
0.499 + 28.8251
10
7.322 + 2. 3741
0.605 + 28.7371
TE,3
00
1000
250
100
64
40
25
10
4
1
8.536
28.2951
0.0003 + 28.2951*
0.0007 + 28.2951*
0.0010 + 28.2951*
0.0013 + 28.2951*
0.0016 + 28.2951*
0.0021 + 28.2951*
0.0032 + 28.2961*
0.0050 + 28.2961*
0.0094 + 28.2951*
TMu
00
10.173
27.7481
25
9.981 + 0.4971
0.178 + 27.8231
16
9.910 + 0.6521
0.232 + 27.8521
12
9.841 + 0.7851
0.277 + 27.8801
10
9.776 + 0.8931
0.313 + 27.9071
4
8.836 + 0.8981
0.281 + 28.2181
2
8.656 + 0.5961
0.183 + 28.2651
1
8.523 + 0.4091
0.123 + 28.3021
Approximate formula.
1366
HELIX WAVEGUIDE
1367
Table 1(d)— |-inch Guide at Xq = 5.4 mm {^oa = 12.930)
WITH e' = 4 AND e" VARIABLE
Limit Mode
e"
no
aa + ij3o
TMoi
1000
250
100
64
40
25
10
6.4
4.0
2.5
1.0
2.405
2.286 + 0.1401
2.183 + 0.3241
2.113 + 0.5951
2.114 + 0.8001
2.185 + 1.0721
2.377 + 1.3691
3.212 + 1.6991
3.694 + 1.4401
3.765 + 1.0291
3.700 + 0.8531
3.624 + 0.7331
12.7041
0.025 + 12.7271
0.056 + 12.7491
0.098 + 12.7711
0.132 + 12.7821
0.183 + 12.7901
0.255 + 12.7861
0.431 + 12.6471
0.426 + 12.4821
0.312 + 12.4161
0.254 + 12.4211
0.214 + 12.4351
TMo2
1000
250
100
64
40
25
10
6.4
4.0
2.5
1.0
5.520
5.468 + 0.0541
5.416 + 0.1111
5.356 + 0.1831
5.317 + 0.2351
5.266 + 0.3081
5.206 + 0.4101
5.073 + 0.7721
5.095 + 1.137i
5.486 + 1.4291
5.818 + 1.3791
6.041 + 1.1881
11.6921
0.025 + 11.7171
0.051 + 11.7421
(V083 + 11.7701
0.106 + 11.7891
0.137 + 11.8141
0.180 + 11.8441
0.328 + 11.9231
0.485 + 11.9481
0.664 + 11.8141
0.689 + 11.6501
0.624 + 11.5111
TMo3
CO
1000
250
100
64
40
25
10
6.4
4.0
2.5
1.0
8.654
8.620 + 0.0341
8.587 + 0.0691
8.550 + 0.1111
8.525 + 0.1411
8.494 + 0.1831
8.459 + 0.2391
8.393 + 0.4111
8.386 + 0.5321
8.426 + 0.6681
8.515 + 0.7691
8.676 + 0.8241
9.6071
0.030 + 9.6371
0.061 + 9.6671
0.098 + 9.7011
0.124 + 9.7231
0.160 + 9.7521
0.207 + 9.7851
0.350 + 9.8511
0.452 + 9.8661
0.571 + 9.8471
0.669 + 9.7841
0.741 + 9.6511
TEu
00
1000
250
100
64
40
25
10
6.4
4.0
2.5
1.0
1.841
1.767 + 0.0741
1.717 + 0.1911
1.706 + 0.3681
1.734 + 0.5001
1.857 + 0.6561
2.126 + 0.7731
2.436 + 0.4111
2.413 + 0.3161
2.386 + 0.2621
2.364 + 0.2341
2.341 + 0.2121
12.7981
0.010 + 12.8091
0.026 + 12.8171
0.049 + 12.8221
0.068 + 12.8231
0.095 + 12.8131
0.129 + 12.7781
0.079 + 12.7061
0.060 + 12.7071
0.049 + 12.7111
0.043 + 12.7141
0.039 + 12.7181
1368 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Table 1(d) — Continued
Limit Mode
f"
ria
aa + ij3a
TMii
00
1000
250
100
64
40
25
10
6.4
4.0
2.5
1.0
3.832
3.750 + 0.081i
3.676 + 0.171i
3.588 + 0.290i
3.530 + 0.382i
3.447 + 0.516i
3.329 + 0.757i
3.749 + 1.664i
4.275 + 1.750i
4.701 + 1.553i
4.843 + 1.274i
4.844 + 1.031i
12.349i
0.025 + 12.375i
0.051 + 12.398i
0.084 + 12.426i
0.108 + 12.445i
0.143 + 12.474i
0.201 + 12.519i
0.499 + 12.496i
0.606 + 12.343i
0.600 + 12.160i
0.511 + 12.067i
0.415 + 12.040i
TE12
1000
250
100
64
40
25
10
4
1
5.331
11.780i
0.0007 + 11.780i*
0.0015 + 11.781i*
0.0024 + 11.782i*
0.0030 + 11.782i*
0.0039 + 11.783i*
0.0051 + 11.784i*
0.0085 + 11.785i*
0.0125 + 11.784i*
0.0146 + 11.781i*
TMu
00
1000
250
100
64
40
25
10
6.4
4.0
2.5
1.0
7.016
6.972 + 0.043i
6.930 + 0.087i
6.883 + 0.141i
6.853 + 0.179i
6.814 + 0.233i
6.769 + 0.305i
6.679 + 0.541i
6.670 + 0.718i
6.755 + 0.935i
6.942 + l.Oeii
7.193 + 1.054i
10.861i
0.027 + 10.889i
0.055 + 10.917i
0.088 + 10.947i
0.112 + 10.967i
0.144 + 10.992i
0.187 + 11.023i
0.326 + 11.090i
0.431 + 11.109i
0.570 + 11.080i
0.671 + 10.981i
0.700 + 10.819i
TEi,
CO
1000
250
100
64
40
25
10
4
1
8.536
9.712i
0.0002+ 9.712i*
0.0005 + 9.712i*
0.0008 + 9.712i*
0.0010 + 9.713i*
0.0012 + 9.713i*
0.0016 + 9.713i*
0.0027 + 9.713i*
0.0040 + 9.713i*
0.0048 + 9.712i*
TM,3
CO
10
6.4
4.0
10.173
9.949 + 0.340i
9.943 + 0.436i
9.970 + 0.543i
7.980i
0.409 + 8.276i
0.523 + 8.293i
0.655 + 8.277i
Approximate formula.
HELIX WAVEGUIDE
1369
Table 1(e) — |-inch Guide at Xq = 5.4 mm (jSoa = 12.930) with
e = €
Limit Mode
e' and e"
fia
aa + t/3a
TMoi
00
2.405
12.704i
1000
2.360 + 0.141i
0.026 + 12.714i
250
2.339 + 0.295i
0.054 + 12.720i
100
2.351 + 0.482i
0.089 + 12.724i
64
2.382 + 0.608i
0.114 + 12.724i
40
2.450 + 0.766i
0.148 + 12.720i
25
2.573 + 0.942i
0.191 + 12.708i
10
3.052 + 1.244i
0.301 + 12.630i
4
3.765 + 1.029i
0.312 + 12.416i
2
3.841 + 0.653i
0.203 + 12.366i
1
3.768 + 0.438i
0.133 + 12.378i
TMo2
00
5.520
11.692i
1000
5.497 + 0.058i
0.027 + 11.704i
250
5.475 + 0.118i
0.055 + 11.715i
100
5.451 + 0.190i
0.088 + 11.727i
64
5.435 + 0.241i
0.111 + 11.735i
40
5.416 + 0.310i
0.143 + 11.746i
25
5.393 + 0.402i
0.184 + 11.760i
10
5.338 + 0.701i
0.317 + 11.802i
4
5.486 + 1.429i
0.664 + 11.814i
2
6.389 + 1.780i
0.996 + 11.425i
1
6.901 + 1.040i
0.652 + 11.003i
TMo3
00
8.654
9.607i
1000
8.639 + 0.0.37i
0.033 + 9.621i
250
8.624 + 0.074i
0.067 + 9.635i
100
8.607 + 0.118i
0.105 + 9.650i
64
8.596 + 0.148i
0.132 + 9.661i
40
8.581 + 0.189i
0.168 + 9.675i
25
8.563 + 0.241i
0.213 + 9.694i
10
8.512 + 0.393i
0.344 + 9.747i
4
8.426 + 0.668i
0.571 + 9.847i
2
8.320 + 1.094i
0.910 + 9.999i
1
8.812 + 1.915i
1.721 + 9.806i
TEii
oo
1.841
12.798i
1000
1.810 + 0.072i
0.010 + 12.803i
250
1.807 + 0.161i
0.023 + 12.804i
100
1.833 + 0.265i
0.038 + 12.802i
64
1.870 + 0.330i
0.048 + 12.799i
40
1.939 + 0.401i
0.061 + 12.790i
25
2.047 + 0.459i
0.074 + 12.776i
10
2.295 + 0.414i
0.075 + 12.732i
4
2.386 + 0.262i
0.049 + 12.711i
2
2.389 + 0.186i
0.035 + 12.709i
1
2.369 + 0.129i
0.024 + 12.712i
1370 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Table 1(e) — Continued
Limit Mode
e' and «"
fio
aa + ij3a
TMu
00
3.832
12.349i
1000
3.794 + 0.086i
0.026 + 12.361i
250
3.766 + 0.176i
0.054 + 12.371i
100
3.739 + 0.288i
0.087 + 12.381i
64
3.725 + 0.369i
0.111 + 12.388i
40
3.711 + 0.485i
0.145 + 12.396i
25
3.708 + 0.651i
0.195 + 12.406i
10
3.893 + 1.161i
0.365 + 12.390i
4
4.701 + 1.553i
0.600 + 12.160i
2
5.319 + 1.062i
0.477 + 11.843i
1
5.241 + 0.614i
0.272 + 11.840i
TE12
00
5.331
11.780i
1000
0.0008 + 11.780i*
250
0.0016 + 11.780i*
100
0.0026 + 11.781i*
64
0.0032 + 11.781i*
40
0.0041 + 11.781i*
25
0.0051 + 11.782i*
10
0.0081 + 11.783i*
4
0.0125 + 11.784i*
1
0.0236 + 11.782i*
TM12
00
7.016
10.861i
1000
6.996 + 0.047i
0.030 + 10.874i
250
6.976 + 0.094i
0.060 + 10.887i
100
6.955 + 0.149i
0.095 + 10.902i
64
6.942 + 0.187i
0.119 + lO.Olli
40
6.924 + 0.238i
0.151 + 10.923i
25
6.903 + 0.305i
0.192 + 10.939i
10
6.841 + 0.509i
0.317 + 10.988i
4
6.755 + 0.935i
0.570 + ll.OSOi
2
7.053 + 1.730i
1.106 + 11.030i
1
8.138 + 1.672i
1.325 + 10.272i
TE,3
00
8.536
9.712i
1000
0.0003 + 9.712i*
250
0.0005 + 9. 7121*
100
0.0008 + 9.712i*
64
0.0010 + 9.712i*
40
0.0013 + 9.712i*
25
0.0016 + 9.712i*
10
0.0025 + 9.713i*
4
0.0040 + 9.713i*
1
0.0076 + 9. 7131*
TM13
00
10.173
7. 9801
4
9.970 + 0.543i
0.655 + 8. 2771
2
9.863 + 0.826i
0.963 + 8. 4571
1
9.698 + 1.418i
1.561 + 8. 8081
Approximate formula.
HELIX WAVEGUIDE
1371
^1 Table 1(f)— t^
-INCH Guide at Xq = 5.4 mm %a = 6.465) with
e' = 4 AND e" Variable
Limit Mode
t"
fia
aa + i/3o
Moi
1000
250
100
64
40
25
10
4
1
2.405
2.287 + 0.141i
2.228 + 0.244i
2.197 + 0.324i
2.170 + 0.439i
2.169 + 0.594i
2.355 + 0.943i
2.740 + 1.040i
2.961 + 0.878i
e.ooii
0.024 + 6.0251*
0.053 + 6.0491
0.090 + 6.0741
0.117 + 6.0901
0.156 + 6.1071
0.210 + 6.1231
0.364 + 6.1051
0.478 + 5.9661
0.446 + 5.8301
rMo2
00
1000
250
100
64
40
25
10
4
1
5.520
5.468 + 0.054i
5.439 + 0.088i
5.420 + 0.112i
5.396 + 0.146i
5.370 + 0.191i
5.327 + 0.328i
5.369 + 0.512i
5.539 + 0.614i
3.3651
0.043 + 3.4081*
0.086 + 3. 4501
0.137 + 3.4991
0.172 + 3.5301
0.221 + 3.5701
0.284 + 3.6161
0.471 + 3.7071
0.740 + 3.7121
0.965 + 3.5241
TEn
00
1000
250
100
64
40
25
10
4
1
1.841
1.772 + 0.069i
1.744 + 0.129i
1.731 + 0.176i
1.726 + 0.244i
1.744 + 0.334i
1.925 + 0.493i
2.121 + 0.425i
2.152 + 0.319i
6.1971
0.009 + 6.2061*
0.020 + 6.2181
0.036 + 6.2271
0.049 + 6.2311
0.068 + 6.2351
0.093 + 6.2351
0.153 + 6.1931
0.147 + 6.1231
0.112 + 6.1061
TMii
00
1000
250
100
64
40
25
10
4
1
3.832
3.751 + 0.082i
3.710 + 0.134i
3.683 + 0.173i
3.650 + 0.227i
3.615 + 0.303i
3.581 + 0.546i
3.763 + 0.810i
4.038 + 0.816i
5.2071
0.028 + 5.2351*
0.058 + 5.2661
0.094 + 5.2971
0.119 + 5.3171
0.155 + 5.3431
0.204 + 5.3721
0.360 + 5.4221
0.570 + 5.3501
0.639 + 5.1541
TE12
00
1000
250
100
64
40
25
10
4
1
5.331
3.6571
0.0005 + 3.6571*
0.0009 + 3.6581*
0.0015 + 3.6581*
0.0019 + 3.6591*
0.0024 + 3.6591*
0.0031 + 3.6591*
0.0052 + 3.6601*
0.0079 + 3. 6601*
0.0097 + 3.6581*
Approximate formula.
29.6
oca
0 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40
29.4
29.2
29.0
/3a
28.8
26,6
28.4
2 8.2
28.0
1000 TEii
TMqi
1000 K")
1000
TE
12
1000
TE
13
1000
"^
TM„
TMc
TM,2
TM,
03
W~^,
(b)
/3oa =29.554
f'=100
0 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40
aa
Fig. 2(a) and (b)
Fig. 2 — Plots of phase constant versus attenuation constant for modes in
various helix waveguides. Representative values of «" are shown on the curves. ,
1372
HELIX WAVEGUIDE
1373
0.04 0.08 O.I
aa
0.20 0.24 0.28 0.32 0.36 0.40
11.4
yOa
11.0
10.6
10.2
9.8
9.4
TM
12
TMr
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
aa
Fig. 2(c) and (d)
1374 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
13.
12.6
12.2
11.8 J
11 .4
caa
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
/3a
11.0
10.6
10.2
9.8
9.4
6.4
6.0
5.6
5.2
/3a
4.8
4.4
4.0
3.6
3.2
.TE,2
01
TM
-TM11
TM02
0.1 0.2 0.3 0.4
0.5
aa
(f)
/3oa =6.465
f'=4
0.6 0.7 0.8 0.9 1.0
Fig. 2(e) and (f)
HELIX WAVEGUIDE 1375
constants calculated from the approximate formulas are given to four
decimal places, i.e., usually two significant figures.
The contents of Table I are displayed graphically in Figs. 2(a) through
(f), which show plots of (3a vs aa for all modes except TM13 . Repre-
sentative values of e are indicated on the curves. Note that the scales
are different for the different guide sizes, and that the jSa-scale is com-
pressed in all cases. If aa and jSa were plotted on the same scale, the
curves would make an initial angle of 45° with the aa-axis when e =
constant, or 22.5° when e — e".
Figs. 3(a) to (f) show the normalized attenuation constants aa of
various modes plotted against e" on a log-log scale. In Fig. 3(b) the
curves for all TM modes would be similar to the two shown, and in
Fig. 3(d) the TM03 curve is like TM12 . Although for some modes the
attenuation constant increases steadily as the conductivity decreases
over the range of our calculations, in many cases the attenuation passes
through a maximum and then decreases as the conductivity is further
decreased. This phenomenon will be discussed in Section V.
It may be noticed that in some instances the limit modes are not
unique. For example, Tables 1(a), with e' = 4, and 1(c), with e' = e",
for the large guide have in common the case e' = 4, e" = 4. For this
case consider the circular magnetic mode corresponding to fia =
3.905 -1- 0.344t. If e' is constant (=4) while e" tends to infinity, this
mode approaches the TM02 mode in a perfectly conducting guide; but
if e' and e tend to infinity while remaining equal to each other, the same
mode approaches TMoi in a perfectly conducting guide. Presumably the
TMoi-limit mode in the former case coincides with the TMo2-limit mode
in the latter case ; but the value of f la for this mode is outside the range
of our calculations at e' = e = 4. A similar interchange occurs between
the TMii-limit and TMi2-limit modes in the large guide, depending on
whether e' is constant or e' tends to infinity with e". There is no evidence
of any such phenomenon in the smaller guide of Tables 1(d) and 1(e);
but the fact that it can occur means that the limit-mode designations of
modes in a lossy waveguide are not entirely unambiguous. The phen-
omenon is not due to the presence of the helix, since a helix of zero pitch
has no effect on circular magnetic modes.
Finally it is of interest to compare the propagation constants given
by the approximate formula with those obtained by numerical solution
of the characteristic equation. A reasonably typical case is provided by
the TMo2-limit mode in a 2-inch guide at Xo = 5.4 mm with e = 4, as
in Table 1(a). Exact and approximate results for ^a vs aa and aa vs e"
are plotted in Fig. 4. As the conductivity decreases, the attenuation con-
2.0
I .0
0.5
0.2
0.10
0.05
aa 0.02
0.010
0.005
0:002
o.ooto
0.0005
0.0002
1.0
0.5
0.2
0. I 0
0.05
(a)
-/3oa = 29.564
f'=4
/"
J
/
/
TMoy
^"^^^
TMo3
^
■V
\
■^
K.^J^^
^
N^
TMo2
^
\
■ T^
^
^ir^
y^
/-
^
^,3
^
^
^
^
^
^
^
y^
aa
0.02
0.010
0.005
0.002
0.0010
0.0005
0.0002
2
1.0
0.5
0.2
0.10
0.05
(C)
r^
V3oa = 29.55 4
TMo2
^
k
vTMoj
^
^
^
s
k
^
9^
V
\J\rMi, ^
^
X^
^
1 _^_^
/"
"
\
^
^
^
' V
<
^
'TE,2
^
^
,^
^
TE,3
^
^
^
«a
0.02
0.010
0.005
0.002
0-0010
0.0005
0.0002
/\
(e)
f'=f"
^J^^
.yi
^
\
^
X
^^
^
r^ J
^
^
^
^^
■^
>
y
^
->
^.^■^^
E,2
y^
^
<X
^
y'
^
^3
^
^
y^
^
^
^
--'
(b)
-/3oa =29.554
f'= 100
TM„
.^
^
^
"
1
TMq,
^
>^
TE„
/
TE,2
^
/
TE,3
y
^
(d)
TMo2^ TM|2
/3oa =12.930
f'= 4
.^'^
^
K. TK
rMoi_
^
^^
^
y
N
^
y
TE^"
~
/^
^
-y*
TE,2
^
^
X
^^
^
,^
TE,3
^
,^
^
y
^
^
y^
y
^
(f)
-/3oa = 6.465
f'= 4
TMo2
.<<
TMll
y^
^
'y-
TMoi
,^
y
t>^
—-
j:eh_
.
'^^
\y
y
^
^
>
y
y
^y
y
^
^
-TEiT
-X'
y
y
y^
1000 200 100 50 20 10 5 2 1 1000 200 100 50 20 10 5 2 1
e" e"
Fig. 3 — Attenuation constant as a function of jacket conductivity for modes
in various helix waveguides.
HELIX WAVEGUIDE
1377
29.32
29.28
29.24
29.20
/3a
29. 16
29.1 2
29.08
29.04
29.00
It
k
N
\
APPROXIMATE
\
■
)
.'
,-'-'
^^^
. — - O —
10
^-N.
,oJ
/
y
\
N
\
/
Y
0
\
\
\
\
\
100^
•noc
0
(a)
l<
0 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44
aa
0.5
0.4
0.2
0.10
0.08
0.06
0.04
0.02
-
EXACT
APPROXIMATE
,.'-'
^-'
--'•
,---
*
,.-"'
x'
-
<<
^
>
Ss,^^
-
X<^
-
^
f"'
""
"--.
^
^
^
^
(b)
I
1
1
1
1
\
1
1
1
1
1
1000 600 400 200 100 60 40 20 10 8 6 4 2 1
e"
Fig. 4 — Comparison of exact and approximate formula.s for the propagation
constant of a typical mode (TM02- limit in a guide with/3oa = 29.554 and «' = 4).
staiit first becomes larger, in all cases, than predicted by the approximate
formula. For still lower conductivities the attenuation constant may pass
through a maximum, as in the present example, and decrease again. The
existence of a maximum in the attenuation vs conductivity curve is not
indicated by the approximate formula.
1378 THE BELL SYSTEM TECHNICAL JOUKNAL, NOVEMBER 1956
V. DISCUSSION OF RESULTS
«ai
The dimensioiiless results of Section IV may easily be scaled to any >. \\
desired operating wavelength, and the attenuation constants and guides
wavelengths expressed in conventional units. If Xo is the free-space wave-
length in centimeters, then the guide diameter d in inches, the attenua-
tion constant a in db/meter, and the guide wavelength X^ in centimeters
are given by the following formulas:
din = 0.12532 (M(Xo)cn.
«db/m =
vAgjcm —
5457.5 (aa)
(|8oa)(Xo)cm
(i8oa)(Xo)cm
,<
ta
Table II lists the guide diameters and the conversion factors for a and
Xg for the three values of /Soa used in Section IV, at frequencies corre-
sponding to free-space wavelengths of 3.33 and 0.54 cm. The table also
lists the number of propagating modes in a perfectly conducting guide
as a function of jSoa (different polarizations are not counted separately).
When helix waveguide is used to reduce mode conversions, an im-
portant parameter is the ratio of the attenuation constant of any given
unwanted mode to the attenuation constant of the TEoi mode. The
theoretical attenuation constants of the TEoi mode at Xo = 5.4 mm in
copper guides of various sizes are listed below:
Diameter
aa
adb/m ^!
2"
2.77 X 10"'
9.47 X 10"'
nti
8
1.50 X 10"'
1.17 X 10"' i
7 //
16
7.11 X 10"'
1.11 X 10"' :
1l
Table II — Conversion Factors for Attenuation Constants and
Guide Wavelengths in Various Waveguides \
Propa-
gating
modes
Xo = 3.33 cm
Xo = 0.54 cm
Poa
Diameter
(inches)
a db/meter
\g cm
Diameter
(inches)
a db/meter
\g cm
29.554
12.930
6.465
227
44
12
12.33
5.40
2.70
55.5 aa
127 aa
253 aa
98.41/^a
43.06/^a
21.53//3a
2.000
0.875
0.4375
342 aa
782 aa
1563 aa
15.959/;8a
6.982//3a
3.491//3a
HELIX WAVEGUIDE 1379
Referring to the values of aa listed in Table I, we see that the un-
Iwanted mode attenuations can be made to exceed the TEoi attenuation
[by factors of from several hundred to several hundred thousand in the
[large helix guide. The attenuation ratios are somewhat smaller in the
[smaller guide sizes.
The attenuation versus conductivity plots of Fig. 3 show that for
I many of the modes there is a value of jacket conductivity, depending on
■the mode, the value of ;Soa, and the jacket permittivity, which maximizes
the attenuation constant. Since one is accustomed to think of the at-
tenuation constant of a waveguide as an increasing function of frequency
for all sufficiently high frec^uencies (except for circular electric waves),
or as an increasing function of wall resistance, it is worth while to see
why one should really expect the attenuation constant to pass through
a maximum as the frequency is increased indefinitely in an ordinary
metallic guide, or as the wall resistance is increased at a fixed frequency.
The argument runs as follows:
Guided waves inside a cylindrical pipe may be expressed as bundles of
plane waves repeatedly reflected from the cylindrical boundary." The
angle which the wave normals make with the guide axis decreases as the
frequency increases farther above cutoff; and the complementary angle,
which is the angle of incidence of the waves upon the boundary, ap-
proaches 90°. If the walls are imperfectly conducting, the guided wave is
attenuated because the reflection coefficient of the component waves at
the boundary is less than unity. The theory of reflection at an imper-
fectly conducting surface shows that the reflection coefficient of a plane
wave polarized with its electric vector in the plane of incidence first
decreases with increasing angle of incidence, then passes through a deep
minimum, and finally increases to unity at strictly grazing incidence. ^^
For a metallic reflector, the angle of incidence corresponding to minimum
reflection is very near 90°. Inasmuch as all modes in circular guide except
for the circular electric family have a component of E in the plane of
incidence (the plane 6 = constant), one would expect the attenuation
constant of each mode to pass through a maximum at a sufficiently high
frequency. For example, the TMoi mode in a 2-inch copper guide should
have maximum attenuation at a free-space wavelength in the neighbor-
hood of 0.1 mm (100 microns), assuming the dc value for the conductivity
of copper. To find the actual maximum, of course, would require the
solution of a transcendental equation as in Section IV.
The circular electric waves all have E normal to the plane of incidence.
" Reference 9, pp. 411-412.
12 Reference 7, pp. 507-509.
1380 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
For this polarization the reflection coefficient increases steadily from its
value at normal incidence to unity at grazing incidence. Thus one has an
optical interpretation of the anomalous attenuation-frequency behavior
of circular electric waves.
If instead of varying the frequency one imagines the wall resistance
varied at a fixed frequency, he can easily convince himself that there
usually exists a finite value of resistance which maximizes the attenua-
tion constant of a given mode. An idealized illustrative example has been
worked out by Schelkunoff. He considers the propagation of transverse
magnetic waves between parallel resistance sheets, and shows that if the
sheets are far enough apart the attenuation constant increases from zero
to a maximum and then falls again to zero, as the wall resistance is made
to increase from zero to infinity. It may be instructive to consider that
maximum power is dissipated in the lossy walls when their impedance is
matched as well as possible to the wave impedance, looking normal to
the walls, of the fields inside the guide.
In conclusion we mention a couple of theoretical questions which are
suggested by the numerical results of Section IV.
(1) Limit modes. It has been seen that the limit which a given lossy
mode approaches as the jacket conductivity becomes infinite may not
be unique. Can rules be given for determining limit modes when the
manner in which | e' — ?'e | approaches infinity is specified?
(2) Behavior of modes as a — ^ 0. It is known^^ that the number of true
guided waves (i.e., exponentially propagating waves whose fields vanish
at large radial distances from the guide axis) possible in a cylindrical
waveguide is finite if the conductivity of the exterior medium is finite.
The number is enormously large if the exterior medium is a metal; but
the modes presumably disappear one by one as the conductivity is de-
creased. If the conductivity of the exterior medium is low enough and if
its permittivity is not less than the permittivity of the interior medium,
no true guided waves can exist. At what values of conductivity do the
first few modes appear in a guide of given size, and how do their propa-
gation constants behave at very low conductivities?
The complete theory of lossy -wall waveguide would appear to present
quite a challenge to the applied mathematician. Fortunately the en-
gineering usefulness of helix waveguide does not depend upon getting
immediate answers to such difficult analytical questions.
13 Reference 9, pp. 484-489.
" G. M. Roe, The Theory of Acoustic and Electromagnetic Wave Guides and
Cavity Resonators, Ph.D. thesis, U. of Minn., 1947, Section 2.
HELIX WAVEGUIDE 1381
APPENDIX
APPROXIMATE SOLUTION OF THE CHARACTERISTIC EQUATION
The characteristic equation (6) of the heUx guide may be written in
the dimensionless form
[i^a tan ^ - -^ ^^.^ - (fta) -j-^^
fia tan ^ - -^ ] J^,,^ . — (M'
(Al)
If I e' — «" I is sufficiently large, the right side of the equation is large
and either J„(fia) or Jn'itio,) is near zero. Let p denote a particular root
of Jn or Jn', then to zero order,
Tia = p
ha = finma = i8oa(l - v')''' (A2)
Ua = iSoaie' - U" - 1 - vy
where
V = p/^oa
Henceforth assume that
I r2a 1 » I (4n' - l)/8 I (A3a)
and
I r2a I » I n I (A3b)
It is convenient to postulate both inequalities, even though the first is
more restrictive than the second unless \ n \ = lor|nl =2.
If (A3a) is satisfied, the Hankel functions may be replaced by the
first terms of their asymptotic expressions, and
Eq. (Al) becomes
A , , 7ihaY Jniha) /« n2 ^n'(fia)
ijia
2
Ua tan ^p — —- j + (M'U - 'i^")
1382 THE BELL SYSTEM TECHNICAL JOURN.IL, NOVEMBER 1956
It follows from (A3b), using the zero-order approximations (A2), that
1 nha/r2a \ « \ I3,a{e' - ie'f'^ \
so the characteristic equation finally takes the approximate form
m
(A4)
f2a
[(fsa tan 4^)' + (MV - ie')]
Now let
f itt = p + .r, I a; I <<C 1
h\
where a: is a small complex number. The normalized propagation con-
stant becomes, to first order,
iha = [(fia)' - (MT
= 2M(1 - vy" - ivx{l - vT'"
= aa + i(l3nma + A^a)
where /3„„i is the phase constant of the mode in a perfectly conducting
guide, and the perturbation terms are
aa + iA^a = —
ivx
(1 - v2)l/2
(A5)
For the TM„„i mode, let p be the //;*'' root of J„ ; then from Tajdor's
series, to first order in x.
Jni^ia) = J nip + .r) = .Vjn(p)
(A6)
Substituting (A6) into (A4), neglecting the first term on the left side of
(A4), and replacing everything on the right side by its zero approxima-
tion according to (A2), one obtains
(/3oa)^ ipMU — ■2"e" - 1 + i'^) tan" \p + (e — ie')]
X
{e' - ie" - 1 + v'~y
12
or
i{^ + iyi)
X =
v\\ +|l - ] ~ ^Itan^V-
L I e - le ] J
(A7)
HELIX WAVEGUIDE
1383
where
^ + iv =
1 -
1 -
2 -]
ie"
1/2
It follows from (A5) and (A7) that for TM modes,
a + iA^ =
a(l - u')
2 \ 1 2
1+1
___| tan V_
where ^ + irj is given by (A8).
For the TE„„ mode, let p be the m*^ root of J,/ ; then
/n'(fia) = Jn'iV + X) = ^""^ ~/^'' Mp)
y
Equation (A4) yields
X
ip V
tan rp
nil - v')
pv
2\l/2-|2
(^ + irj)
(p^ — n^)
1+ i-e^' r^"'*
and, using (A5), we have for TE modes,
a + 2A/3
V
tan \p —
n(l - /)
2\l/2-12
(^ + t^)
(p- - 71^) a(l - 1^2)1/2
1+1
7>^tan lA
t€
where ^ + z?? is given by (AS).
In view of (A5), the condition that | a; | <3C 1 is equivalent to
^^ I aa + lA^a \ « 1
(AS)
(A9)
(AlO)
(All)
In all the numerical cases treated in the present paper, the approximate
formulas agree well with the exact ones provided that the left side of
(All) is not greater than about 0.1.
A condition Avhich is usually satisfied in practice, although not strictly
a consequence of the assumptions (A3) or (All), is
1
«1
^e
1384 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956 |
This final approximation leads to the simple equations (7a) and (7b) of
Section III, namely:
TMnm modes
a + iA/3
a(l - vY'''[l + tanV]
TE„;„ modes
. . . ^ ^ (^ + iy) v'V [tan yp - n{l - vf^/yvf
" ^ ^^ a(l - v'^yi'' {f- - ^2) [1 + tanV]
where
i
Wafer-Type Millimeter Wave Rectifiers*
By W. M. SHARPLESS
(Manuscript received June 18, 1956)
A wafer-type silicon point-contact rectifier and holder designed pri-
marily for use as the first detector in millimeter wave receivers are described.
Measurements made on a pilot production group of one hundred wafer
rectifier units yielded the following average performance data at a wave-
length of 5.4 millimeters: conversion loss, 7£ dh; noise ratio, 2.2; interme-
diate frequency output impedance 34O ohms. Methods of estimating the
values of the circuit parameters of a point-contact rectifier are given in an
Appendix.
INTRODUCTION
Point-contact rectifiers for millimeter waves have been in experi-
mental use for several years. These units, for the most part, have been
coaxial cartridges which were inserted in a fixed position, usually cen-
tered, in the waveguide. Impedance matching was accomplished by
means of a series of matching screws preceding the rectifier and an adjust-
able waveguide piston following the rectifier. Tuning screws are gener-
ally undesirable l^ecause of the possibility of losses, narrow band widths
and instability.
It is the purpose of this paper to describe a new type millimeter-wave
rectifier and holder which were designed to eliminate the need for tuning
screws and to provide a readily interchangeable rectifier of the flat wafer
type. This wafer contains a short section of waveguide across which the
point contact rectifier is mounted. The necessary low frequency output
terminal (and the rectified current connection) together with the high-
frequency bypass capacitor, are also contained within each wafer. The
basic idea of the wafer-type rectifier is that the unit can be inserted in its
holder and moved transversely to the waveguide to obtain a resistive
match to the guide ; the reactive component of the rectifier impedance is
then tuned out by an adjustable waveguide plunger behind the rectifier.
* This work was supported in part by Contract Nonr-687(00) with the Office
of Naval Research, Department of the Navy.
1385
1386 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
The wafer unit and holder were developed primarily for use as the
first converter in double detection receivers operating in the 4- to 7-mil-
limeter wavelength range. In order to check the practicability of the
design and to supply rectifiers for laboratory use, a pilot production
group of one hundred units was processed and measured. Performance
data obtained with this group are presented. A balanced converter using
wafer rectifiers is also described.
Methods of estimating the values of the various circuit parameters of a
point-contact rectifier are outlined in an appendix. These calculations
proved useful in the design of the wafer unit and in predicting the broad-
band performance of the converter.
DESCRIPTION OF WAFER UNIT AND HOLDER
Fig. 1 is a drawing of the wafer type rectifier. The unit is made from
stock steel iV-inch thick and is gold plated after the milling, drilling and
soldering operations are completed. To allow for the transverse impe-
dance matching adjustment, the section of waveguide contained in the
wafer is made wider than the RG98U input guide to the holder. By
making the wafer thin {-^ inch), the short sections of unused guide on
either side will remain "cut-off" over the operating range of the recti-
fiers. The silicon end of the rectifier consists of a copper pin on which the
silicon is press mounted, the assembly held in place with Araldite ce-
ment which also serves as the insulating material for a quarter-wave-
length long high frequency bypass capacitor. The pin serving as the inter-
mediate frequency and direct current output lead is also cemented in
place with Araldite cement. A soft solder connection is made between this
pin and the pin holding the silicon wafer. A nickel pin with a conical end
on which a pointed tungsten contact spring is welded is pressed into
place from the opposite side of the guide at the time of final assembly.
DC AND IF
OUTPUT
0.031 "x 0.234^
WAVEGUIDE
0.063" "BRIGHT GOLD"
STEEL WAFER
BORON- doped/
SILICON
-CONTACT SPRING
Fig. 1 — Millimeter-wave wafer unit.
WAFER TYPE MILLIMETER WAVE RECTIFIERS
1387
?^^^^^^^^
"ARALDITE"
BONDING
RESIN
WELD
0.014" SILICON
SQUARES
0.0065" THICK
0.0009" DIA
TUNGSTEN
WIRE
WAVEGUIDE
Fig. 2 — Millimeter-wave point-contact assembly.
The region of the wafer unit containing the silicon and point contact is
shown in Fig. 2. The methods used in preparing the silicon wafer and
the spring contact point are similar in many respects to the standard
techniques used in the manufacture of rectifiers for longer wavelengths.
Some modifications and refinements in technique are called for by a
decrease in size and the increased frequency of operation.
A single-crystal ingot, grown from high purity DuPont silicon doped
with 0.02 per cent boron, furnishes the material for the silicon squares
used in the wafer unit. Slices cut from the ingot are polished and heat
treated. Gold is evaporated on the back surface and the slices are diced
into squares approximately 0.014-inch square and 0.0065-inch thick.
These squares are pressed into indentations formed in the ends of the
0.030-inch copper pins which have previously been tin-plated. The rods
are then cemented in place in the wafer. The spring contact points are
made of pure tungsten wire that has been sized to 0.9 mil in diameter by
an electrolytic etching process. A short length of this wire is spot welded
on the conical end of the 0.031 -inch nickel rod. The wire is then bent into
1388 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Fig. 3 — ■ Micro-photograph showing successive stages in the formation of the
contact spring. The posts are 3*0 inch in diameter.
(a)
(b)
Fig. 4 — Cathode-raj^ oscilloscope display of wafer unit static characteristic:
(a) before and (b) after tapping.
the "S" configuration in a forming jig. By an electrolytic process the
spring is then cut to the proper length and pointed. The niicro-photo-
graphs in Fig. 3 show successive stages in the formation of the contact
spring.
In the final assembly of the unit the nickel rod with the contact spring
is pressed into place until contact is made with the silicon. It is then
advanced a half mil to obtain the proper contact pressure. The voltage-
current characteristics as viewed at 60 cycles on a cathode-ray oscillo-
scope will then appear as shown in Fig. 4(a). The unit is "tapped" into
final adjustment. This is done by clamping the unit in a holder and
rapping it sharply on the top of a hard wood bench. This procedure re-
quires experience as excessive "tapping" will impair the performance
of the unit. Usually one vigorous "tap" is sufficient to produce the
desired effect and the voltage-current characteristic will appear as
WAFER TYPE MILLIMETER WAVE RECTIFIERS
1389
shown in Fig. 4(b). The static characteristic of a typical unit is shown in
Fig. 5.
The conversion loss of each unit is measured before the end of the
nickel rod carrying the contact point is cut off flush with the wafer. In
the event that this initial measurement shows that the conversion loss
exceeds an arbitrarily chosen upper limit (8.5 db), it is possible at this
stage to withdraw the point and replace it with a new one. This pro-
cedure, w^hich was necessary on only a few of the units processed, always
resulted in an acceptable unit. The final operation is to cut off the pro-
truding end of the nickel rod flush with the wafer.
A holder designed to use the wafer units is shown in Figs. 6 and 7. At
the input end of the converter block is a short waveguide taper section
to match from standard RG98U waveguide to the ^-inch high wave-
guide used in the wafer unit. As the wafer unit is moved in and out to
match the conductance of the crystal to the waveguide, the output pin
of the wafer unit slides in a chuck on the inner conductor of the coaxial
6.0
5.5
5.0
4.5
(O 4.0
111
a:
ai
Q- 3.5
<
J 3.0
?2.5
I 2.0
cr
^ 1.5
1.0
0.5
-0.5
•0.4
-0.2
0 0.2
VOLTS
0.4
0.6
Fig. 5 — • Static characteristic of typical millimeter-wave wafer unit.
1390 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
output jack. The unit may be clamped in position after matching adjust-
ments are made by tightening the knurled thumb screw which pushes a
cylindrical slug containing an adjustable piston against the wafer unit.
The piston is a short septum which slides in shallow grooves in the top
and bottom of the ya-inch high waveguide, thus dividing the waveguide
into two guides which are beyond cut-off. This septum is made of two
pieces of thin beryllium copper bowed in opposite directions so that good
contact is made to the sides of the grooves in the top and bottom of the
waveguide. Since the piston with its connecting rod is very light in weight
and is held firmly in place by the spring action of the bowed septum, no
additional locking mechanism need be provided. Since the rectifier is
essentially broadband by design, the adjustment of the piston is not
critical and is readily made by hand. The piston rod is protected by a
cap which is snapped in place over the thumb screw when all tuning
adjustments are completed.
B
n
L,
3
"0 or
2
^
-
1
£
1^^:: — l|
J
SECTION B-B
SECTION A -A
Fig. 6 — Assembly drawing of millimeter-wave converter.
WAFER TYPE MILLIMETER WAVE RECTIFIERS
1391
'" ^^H****-^
\
\
Fig. 7 — Explosed view of millimeter-wave converter.
With the converter fixed-tuned at 5.4 millimeters, a shift in wave-
length to 6.3 millimeters (17 per cent change) produces a mismatch loss
of from 1.6 to 4.0 db depending on the rectifier used.
PERFORMANCE DATA FOR WAFER-TYPE RECTIFIER UNIT
A pilot group of one hundred wafer units was processed and measured.
Figs. 8, 9 and 10 are bar graphs of the distribution of the conversion loss
L, and noise ratio A^r*, and the 60 megacycle intermediate frequency
output impedance Zip , for the hundred rectifiers measured in the
* Nu is the ratio of the noise power available from the rectifier to the noise
power available from an equivalent resistor at room temperature.
1392 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
mixer of Fig. 7 at a wavelength of 5.4 millimeters. In order that the
measurements might be more readily compared with those made on
commercially available rectifiers used at longer wavelengths, the avail-
able beating oscillator power was maintained at a level of one milliwatt
for all measurements.* Further, in the case of the conversion loss, a
35
30
25
20
15
10
6.2
T
^
'"" !1
^^S"'
1
6.6 7.0 7.4 7.8 8.2
CONVERSION LOSS IN DECIBELS
8.6
Fig. 8 — Conversion loss (L) of 100 wafer units at a wavelength of 5.4 railli-
meters with one-milliwatt beating oscillator drive (average 7.2 db).
50
45
40
35
(f)
Z 30
D
"25
LU
2 20
Z
15
to
'
1
1
1
1
1.2 1.6 2.0 2.4 2.8 3.2
NOISE RATIO Nr times
3.6
4.0
Fig. 9 — Noise Ratio (jVr) for 100 wafer units at a wavelength of 5.4 milli-
meters with a one-milliwatt beating oscillator drive (average 2.21 times).
* Power levels were determined by the use of a calorimeter. See, A Calorimeter
for Power Measurements at Millimeter Wavelengths, I. R. E. Trans., MTT-2,
pp. 45-47, Sept., 1954.
WAFER TYPE MILLIMETER WAVE RECTIFIERS
1393
40
35
12 30
2
3
u. 25
O
N
5"" ■
s,
1
1"
£20
m
5
10
■
J.
5
^^
""vwpp
0
150 200 250 300 350 400 450 500
60-MC INTERMEDIATE FREQUENCY IMPEDANCE, Z|p, IN OHMS
Fig. 10 — Sixty-megacj'cle intermediate-frequency output impedance (Zif)
for 100 wafer units with one milliwatt beating oscillator drive (average 338 ohms)
limit of 8.5 db was arbitrarily adopted. This required the readjustment
of eleven units, with a new point inserted in each case. No units were
rejected because of high noise and none of the hundred units processed
was lost.
From the bar graphs it may be seen that the wafer units have the
average characteristics shown in the accompanying table at a wave-
length of 5.4 millimeters.*
Conversion Loss L 7 . 2 db
(5.3 times)
Noise Ratio A^r 2.2 times
IF Impedance (60 mc) Zj-p 338 ohms
Knowing the noise figure, Nif , of the IF amplifier intended for use
with the rectifiers, the overall receiver noise figure, A^rec > may be cal-
culated by the following formula (using numerical ratios) :
NnKc = L(N,, - 1 + A^if)
Assuming an IF amplifier noise figure of 4.0 db (2| times) and the
average values of "L" and 'Wr" given above for the millimeter wafer
units, we have for the case of a noiseless beating oscillator;
ATrec = 5.3 (2.2 - 1 + 2.5) ^ 20 (13 db)
* A few wafer units have also been measured at a wavelength of 4.16 millimeters.
The conversion losses averaged about 1.6 db greater than those measured at a
wavelength of 5.4 millimeters.
1394 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Table I — Comparison of Low-Power Characteristics of
Cartridge-Type and Wafer-Type Rectifiers
Test Conditions
power
Frequency
Beating oscillator
level
Noise reference resistor
Conversion loss
Noise ratio
Nominal IF impedance
range
JAN Specifications for Cartridge-Type
Rectifiers
IN26
23984 mc
1.0 milliwatts
300 ohms
8.5 db (max)
2.5 (ma.x)
300 to 600 ohms
IN53
34860 mc
1 .0 milliwatts
300 ohms
8.5 db (max)
2.5 (max)
400 to 800 ohms
Performance of
Wafer-Type
Rectifiers
55500 mc
1.0 milliwatts
300 ohms
8.5 db (max)*
2.2 (average) t
250 to 500 ohms
* Limit arbitrarily set on basis of 100 per cent yield as explained in the text,
t Limit not set. Actually in more recent production A'^r has averaged 1.7 times.
In practice, the beating oscillator noise sidebands can be eliminated
by the use of a matched pair of rectifiers in a balanced converter ar-
rangement described later. The resulting overall noise figure of 13 db
on an average compares quite favorably with the figures obtained at
longer wavelengths.
In Table I it is seen that a high percentage of the group of one hundred
units would be able to pass low-power JAN specifications similar to those
set down for the commercially available IN26 and IN53 rectifiers used
at longer wavelengths.
effect of VARYING THE BEATING OSCILLATOR POWER
When the optimum over-all receiver noise figure is desired, it may
well turn out that a beating oscillator drive of one milliwatt (correspond-
ing to a dc rectified current for different wafers of from jq to Ij milli-
amperes) is too large. Fig. 11 shows the effect on the performance of a
typical unit as the beating oscillator drive is varied above and below the
one milliwatt level as indicated by the change in the dc rectified current.
It is seen that the value of N^. tends to increase rapidly for a beating
oscillator drive much in excess of one milliwatt; with reduced drive, the
over-all noise figure of the receiver, A^'rec for the example taken, im-
proves, reaching a minimum value near a rectified current of about ^u
m.illiampere corresponding to a drive of about f of a milliwatt.
A BALANCED CONVERTER FOR WAFER UNITS
A broad-band balanced first converter has been developed which makes
use of a pair of wafer- type millimeter-wave rectifiers. This converter
WAFER TYPE MILLIMETER WAVE RECTIFIERS
1395
14. Or
-I 13.5
o
HI 13.0
Q
12.5
d:
2 12.0
LU
5 11.5
11.0
ai
to
O 10.5
cc
^10.0
LU
o
^ 9.5
Q
< 9.0
ID
I/)
O 8.5
_i
2
O 8.0
CO
cc
HI
> 7.5
z
o
u
7.0
6.5
note:
this curve was calculated using
an assumed value of 5.5db for the
noise figure of the if amplifier "^^
3.5
(0
-3.0
(/)
h ^2.5
2.0
O '-^
t-
<
°^ 1.0
LU
If)
O 0.5
STANDARD UNIT NO. 46
•
\
\
HI
>
CC
Q
O
CD
5
111
z
o
^^
^
.^^^
"«^,
_
Nrec
s
N
N
.Z,F
^>
X.
\
N
N
s.
^x^
^
'x
^x
<
>
k--
^^
^
Nr
r
-^
^L
—
—
—
—
380
360
340
320
300
280
260
240
>-
O
111 o
cr I
U- (J
I- 9
< <o
5
LU
LU
:^ Q.
N
0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
RECTIFIED CURRENT IN MILLIAMPERES
Fig. 11 — Typical performance curves for wafer-type rectifiers.
was designed to operate over the 4- to 7-millimeter band and is pic-
tured in Fig. 12. A compact arrangement has been achieved which
makes use of a waveguide finline-to-coaxial input circuit for the beating
oscillator while the signal is introduced through a separate impedance-
matched waveguide "Tee" section. Return loss measurements show that
with a matched pair of Avafer units, fixed-tuned in the center of the 5- to
6-millimeter band, an excess loss of about 1 db may be expected at the
edges of a 15 per cent band. At midband, an improvement of 5 db in
over-all receiver noise figure was obtained by substituting the balanced
converter for an unbalanced one in a test receiver using an M1805 milli-
1396 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
2
Fig. 12 — Balanced converter with wafer-type rectifiers.
meter-wave reflex klystron* as the beating oscillator and a 60-mc
intermediate frequency amplifier with a 5-db noise figure.
REVERSED POLARITY WAFER UNIT
When using crystal rectifiers in a balanced converter arrangement,
there is a distinct advantage, circuit-wise, in using two units of opposite
polarity. For this reason, a reversed-polarity wafer type rectifier has
also been developed. This was done by interchanging the silicon and the
* E. D. Reed, A Tunable, Low-Voltage Reflex Klystron for Operation in the
50 to 60 kmc Band, B. S. T. J., 34, pp. 563-599, May, 1955.
WAFER TYPE MILLIMETER WAVE RECTIFIERS 1397
point contact spring in a standard unit. The standard and reverse-
polarity wafer have the same outer physical dimensions and thus they
may be used interchangeably in the holders as dictated by the specific
problems at hand.
CONCLUDING REMARKS
Aside from their intended use as first detectors in double detection
receivers, wafer units have been used for single detection measurements
at freauencies as high as 107 kmc.
It is felt that the pilot production group of one hundred units is a
sample of sufficient size to yield representative data and to demonstrate
the practicability of the design. It should be pointed out that the units
have not been filled with protective waxes and hsive not been subjected
to temperature-humidity cycling tests. However, a few reference units
have been in use in the laboratory for over a year and have shown no
measurable deterioration. No attempt has been made to establish a
burn-out rating for the rectifier, but units have withstood available cw
input powers of the order of 15 milliwatts and narrow pulse discharges
of the order of xV ^rg without causing noticeable changes in the con-
version loss or noise ratio.
ACKNOWLEDGMENTS
The author wishes to express his gratitude to H. T. Friis and A. B.
Crawford for their helpful suggestions and guidance during the course
of this work. Extensive use has also been made of the experience and
techniques of R. S. Ohl. E. F. Elbert participated in the development
of the wafer unit, being particularly concerned with the techniques of
fabrication. H. W. Anderson and S. E. Reed were most helpful in solving
mechanical problems encountered in the production of wafer units and
holders.
APPENDIX
This section describes some calculations that were made for the pur-
pose of estimating the values of the various parameters involved in the
design of a high frequency point contact rectifier. These parameters are
the barrier resistance, the spreading resistance, the capacitance of the
barrier layer and the inductance of the contact spring. Knowing the ap-
proximate values of these parameters one can, by an equivalent circuit
analysis, arrive at a simple parallel circuit for the rectifier which may
1398 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
be used in designing an appropriate holder. Also, using this equivalent
circuit, one may calculate the bandwidth expected for the converter.
Fig. 13 shows the point contact rectifiers under consideration and an
enlarged view of the point contact region. On the right of the figure are
shown equivalent circuits of the rectifier. Circuit I is the generally ac-
cepted circuit of a point contact rectifier. The true circuit for a rectifier
operating at millimeter wavelengths is probably more complicated than
that shown in the figure but, for an approximate analysis, the simplified
circuit has been found to yield useful results. In the folloAving para-
graphs, values are derived for the parameters of this equivalent circuit.
MKS units are used and values appropriate to the millimeter wave
wafer unit are used as examples.
Spreading Resistance
The spreading resistance, Rs , may be calculated if we know the re-
sistivity of the silicon used for the rectifier and the radius of the contact
area formed when the units are assembled. For DuPont high-purity
silicon, doped with 0.02 per cent boron by weight, W. Shockley* gives
the resistivity, p, as 0.90 X 10~ ohm meters. From numerous measure-
ments on millimeter wave contact areas, R. S. Ohl finds the contact
radius, n , to be about 1.25 X 10" meters. The spreading resistance,
RECTIFIER
UNIT
-SPRING
ENLARGED
POINT
CONTACT
EQUIVALENT CIRCUITS
BARRIER
SL+0.02%B
RESISTIVITY p
L = INDUCTANCE OF SPRING
C= CAPACITANCE OF BARRIER LAYER
R = RESISTANCE OF BARRIER LAYER
Rs= SPREADING RESISTANCE
a>C,
wC
^(^^)
R,=
1 + (a)CR)'
COL;
R2=Rs+Ri +
KM
Rs + R,
Fig. 13 — Point contact rectifier and equivalent circuits.
* W. Shockley, Electrons and Holes in Semiconductors, New York: D. Van
Nostrand Co., Inc., 1950, p. 284.
WAFER TYPE MILLIMETER WAVE RECTIFIERS 1399
itf Rs , assuming a circular contact area, may be calculated from the for-
mula, Rs = p/4ri .* For the above example, Rs = 18 ohms.
Barrier Resistance
The approximate operating value of the barrier resistance, /?, may be
determined from a knowledge of the intermediate frequency impedance
of a typical rectifier. A. B. Cra^^^ord has sho-wn that the optimum inter-
mediate frequency output impedance of a crystal mixer rectifier is a
function of the exponent of the static characteristic of the rectifier and
the impedance presented to the rectifier at the image and signal fre-
quencies. This information is presented in Fig. 12.3-6 in G. C. South-
worth's book.f In the millimeter wave case it is a good assumption that
the impedances for the signal and image frequencies are equal; for this
case and for matched conditions, the magnitude of the high frequency
impedance is seen to be a simple multiple of the intermediate frequency
impedance Rif •
From numerous measurements on mixer rectifiers operating at differ-
ent frequencies it is known that the intermediate frequency impedance
of an average rectifier is very nearly 400 ohms. We also know from the
DC static characteristics of our millimeter wave type rectifiers that the
average exponent is about four. With this information, and the curves
in Southworth's book, it is found that R ^ Rif/1.5. Thus, the barrier
resistance R is about 250 ohms.|
Capacitance of Barrier Layer
From a knowledge of the point contact area, the barrier layer thick-
ness, and the dielectric constant of the silicon, the capacitance of the
point contact may be calculated. The radius of the contact point area is
the same as that used for the calculation of the spreading resistance. The
barrier layer thickness, h, for the heat treated silicon used for millimeter
waves has been measured by R. S. Ohl to be about 10' meters. The
dielectric constant of sihcon is fr = 13. The capacitance is given by the
following formula
^&
2
* J. H. Jeans, Mathematical Theory of Electricity and Magnetism, 5th Ed.,
Cambridge University Press, 1925.
t G. C. Southworth, Principles and Applications of Waveguide Transmission,
New York: D. Van Nostrand Co., Inc., 1950.
t This resistance cannot be readily measured directly at millimeter waves.
1400 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
For the above case C = 5.7 X 10" farads or l/coC at 5.4 millimeters
is about 50 ohms.
The accuracy of this capacitance calculation can be verified later
when a completed rectifier is measured for its high frequency conversion
loss. This is possible because we know the calculated low frequency
conversion loss of the rectifier, for the case of zero spreading resistance
from Southworth's book. Fig. 12.3-7. For an exponent of four this loss
is given as 4.4 db. The additional loss at high frequency due to the
capacitance, C, may be calculated (see Equivalent Circuit II) by the
formula :
Additional Loss
10 logic :?L+_?f db
/ti
(2)
From the text (Fig. 8), it is seen that the average wafer rectifier unit
has a conversion loss at 5.4 millimeters of 7.2 db; thus, the difference
between the low and high frequency conversion losses is very nearly 3 db.
This means that about one-half the signal power is lost in the spreading
resistance; hence Ri and i?, are about equal. By transferring back to
Equivalent Circuit I, the average value of the capacitance is found to be
4.1 X 10 farads, which is a reasonable check with the calculated value
given by (1).
Inductance of the Contact Spring
The remaining parameter of the equivalent circuit to be determined
is the inductance of the contact spring. The value of the equivalent
parallel resistance, i?2 , depends on the inductance L (the other param-
eters being fixed), or conversely, for a given value of R2 , the appropriate
value for L may be calculated from the formula for Equivalent Circuit
III. For an off-center match of the rectifier to the waveguide, R2 must
equal the guide impedance, Zd , at the rectifier location. Also, for a
match, the distance, I, from the rectifier to the waveguide piston must
'/////////////////////////////J///////////////////^///////A
'R'.
I
PISTON
V////////////////////////////^///////////////////////>////////.
WAVEGUIDE B| J
T
I
b
I
I
I
i_
V///y^////y'y'//J///////////////77777y
I
V///////////f////y/////////y/y7/77/A
k
. -A
Fig. 14 — Mulching circuit for rectifier offset in waveguide.
WAFER TYPE MILLIMETER WAVE RECTIFIERS
1401
satisfy the relation, Zd tan 2-Ki/\g = — coLa . (See Fig. 14.) The imped-
ance of the guide as a function of d/a is given by,
Zd = 2407r -
'/RU
sni
xd
a
(3)
As a compromise between electrical and mechanical requirements, a
waveguide height, 6, of -5^ inch was chosen for the wafer unit ; the width
of the guide was taken to be the same as RG9SU. For b = 7.88 X 10~*,
a = 3.76 X 10"', d/a = | and X = 5.4 X 10~', (3) gives a value of 113
ohms for Zd (and R2). The appropriate value for L then becomes 3.38 X
10"^" henries.
An estimate of the size of a contact spring having the inductance
given above can be made from the formula below which gives the in-
ductance of a straight thin wire of length *S as a function of its sidewise
position in the waveguide.* (See Fig. 15.)
2S log,
. ird
2a sm —
a
r2«d
\-y
X 10 henries
(4)
For d/a = I and 2r2 = 2.28 X 10 ^ (0.9 X 10 ' inches), the length, S,
is found to be about 3.38 X 10" meters or about 0.013 inches.
Since the spring must be so very small, the circuit from the base of
the spring to the waveguide wall is completed with a large low induc-
tance conical post as shown in Fig. 2 of the text.
Bandwidth Calculation
Having assigned values to all the parameters of the equivalent cir-
cuit, it is now possible to calculate the mismatch loss of a fixed-tune
Y-
a
i
'/////////////////////////////7777.
I fSTRAIGHTA
•"V WIRE ]
-ZT2
V///////////}//////////////77777yA
U-d-J
I
s
I
I
JL
Fig. 15 — Thin wire in waveguide.
* Private communication from S. A. Schelkunoff.
1402 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
converter for a given change in operating wavelength. This loss is given
by the following formula:
Mismatch loss
= 10 log
4Zd
10
R2
1 +
R2
+
+
wLo tan 2iri/\g,
db (5)
For the wafer miit, calculation shows that the rectifier is matched to the
waveguide at a wavelength of 5.4 X 10"^ meters for d/a = j and ^ =
3.14 X 10^ . If now the wavelength is changed to 6.3 X 10~^ meters,
without re tuning (17 per cent change) the mismatch loss calculated by
(5) is 1.6 db. It was stated in the text that a number of wafer units gave
measured mismatch losses of from 1.6 to 4.0 db for a 17 per cent change
in wavelength without retuning. This is considered to be a reasonable
correlation between calculations and measurements.
Frequency Conversion by Means of a
Nonlinear Admittance
C. F. EDWARDS
(Manuscript received June 20, 1956)
This paper gives a mathematical analysis of a heterodyne conversion
transducer in which the nonlinear element is made up of a nonlinear re-
sistor and a nonlinear capacitor in parallel. Curves are given, showing the
change in admittance and gain as the characteristics of the nonlinear ele-
ments are varied. The case where a conjugate match exists at the terminals is
treated.
It is shown that when the output frequency is greater than the input fre-
quency, modulators having substantial gain and bandwidth are possible,
but when the output frequency is less than the input frequency, the con-
verter loss is greater than unity and is little affected by the nonlinear ca-
pacitor. The conditions under which a conjugate match is possible are
specified and it is concluded that a nonlinear capacitor alone is the pre-
ferred element for modidators and that a nonlinear resistor alone gives the
best performance in converters.
INTRODUCTION
Point contact rectifiers using either silicon or germanium are used as
the nonlinear element in microwave modulators to change an inter-
mediate frequency signal to an outgoing microwave signal and in re-
ceiving converters to change an incoming microwave signal to a lower
intermediate frequency. Most point contact rectifiers now in use behave
as pure nonlinear resistors as evidenced by the fact that in either of the
above uses the conversion loss is the same. In recent experiments with
heterodyne conversion transducers* using point contact rectifiers made
with ion bombarded silicon this was found to be no longer true. The
conversion loss of the modulator was found to be unusually low and
* This term is defined in American Standard Definitions of Electrical Terms
— ASA C42 — as "a conversion transducer in which the useful output frequency
is the sum or difference of the input frequency and an integral multiple of the
frequency of another wave".
1403
1404 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
that of the converter was several decibels greater. In one instance the
loss in a modulator used to convert a 70 mc signal to one at 11,130 mc
was found to be only 2.3 db but when the direction of transmission
through it was reversed and it was used as a converter, the loss was 7.8
decibels.
h Similar effects were observed several years ago in conversion trans-
ducers using welded contact germanium rectifiers. In these early experi-
ments substantial converter gain and negative conductance at the inter-
mediate frequency terminals were also observed. These results were
accounted for by assuming the presence of a nonlinear capacitance at the
point contact in parallel with the nonlinear resistance. At that time at-
tention was devoted mainly to the behavior of converters where noise
is a vital factor. It was found that although the conversion loss could
be reduced, the noise temperature increased and no improvement in
noise figure resulted. However, the noise temperature requirements in
modulators are much less severe and the nonlinear capacitance effect is
useful and can substantially improve the performance.
THEORY
The mathematical analysis given here was undertaken in order to
clarify the effect of the nonlinear capacitance in the frequency conversion
process and to obtain an estimate of the usefulness of modulators ex-
hibiting gain. The analysis is restricted to the simplest case in which
signal voltages are allowed to develop across the nonlinear elements at
the input and output frequencies only. This is not an unrealistic restric-
tion since the conversion transducers used in microwave relay systems
have filters associated with them which suppress the modulation products
outside the signal band. The final results will be given only for those con-
ditions which permit a conjugate match at the input and output of the
transducer.
The procedure used to obtain expressions for the admittance and
gain of conversion transducers utilizing a nonlinear element made up
of a nonlinear resistance and a nonlinear capacitance in parallel follows
the commonly used method of treating the nonlinear elements as local
oscillator controlled linear time varying elements. The current through
the nonlinear resistor is a function of the applied voltage. The derivative
of this function is the conductance as a function of the applied voltage.
Thus when the local oscillator is applied, the conductance varies at the
local oscillator frequency and the conductance as a function of time
may be obtained. This is periodic and may be expressed as a Fourier
series. The conductance is real and if we make the usual assumption that
FREQUENCY CONVERSION BY A NONLINEAR ADMITTANCE 1405
it may be expressed as an even function of time, we may write
7 =
(1)
where coo/27r is the local oscillator frequency /o and the Fourier coeffi-
cients Gn are real. Similarly the charge on the nonlinear capacitor is a
function of the applied voltage. The derivative of this function is the
capacitance as a function of the applied voltage. The application of the
local oscillator thus causes the capacitance to vary at the local oscillator
frequency so that it also may be expressed as a Fourier series. The ca-
pacitance K is real, and assuming it may be expressed as an even function
of time, we have
+ Cae"''""' + Cre~'"'' + Co + Cie^""' + C^e'^"'' +
(2)
It is assumed that the current and charge functions are single valued and
that their derivatives are always positive.
When a small signal voltage v is apphed to the nonlinear resistor, the
signal current through the resistor is given by yv. When it is applied to
the nonlinear capacitor the charge on the capacitor is kv. The total cur-
rent i which flows through the two nonlinear elements connected in
parallel thus becomes
(3)
V of course must be small and not affect the value of 7 and k.
Fig. 1 shows a heterodyne conversion transducer made up of a non-
linear resistor and a nonlinear capacitor in parallel driven by an internal
local oscillator, /i is the signal frequency at the terminals 1-2, and 7/1 is
the external admittance connected to these terminals. The signal fre-
quency at the terminals 3-4 is /2 , and y2 is the external admittance.
I,
>
1
+ v-
3
h*
^ (
'
+
yi
+
V,
A
B
m
ys
r^ *.«
2
4
L<^>_i
y/////////////////////////m///////m//////////////////////,//////^^^^^
Fig. 1 — Heterodyne conversion transducer.
140G THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
A, B and C are ideal frequency selective networks whose admittances
are zero at /i , f^ and /o respectively, and infinite at all other frequencies.
This circuit permits the application of the local oscillator voltage to the
nonlinear elements but permits signal voltages to develop across them
at /i and f^ only. Similarly, signal currents at frequencies other than /i
and /2 encounter no external impedance, so they cannot alter the signal
voltage or contribute to the external power. This, of course, assumes that
if the nonlinear element is a point contact rectifier the spreading resist-
ance normally present is negligible.
If /i is a frequency less than half the local oscillator frequency /o (it is
generally very much less), the network B can be selected to make /2
either /o + /i , or fo — fi ■ To distinguish between the two cases, we will
call the former a noninverting conversion transducer since an increase
in one signal frequency causes an increase in the other. The latter will
be called an inverting conversion transducer since an increase in one
signal frequency results in a decrease in the other. When yi contains
the generator and 2/2 the load, the device becomes a modulator. When 2/2
contains the generator and yi the load, it is a converter.
The real part of the signal voltage may be written
V = Vie''^'' + Vi*e~'"'' + V^e'"'' + ¥2*6-'"'' (4)
where V* is the complex conjugate of V and w = 27r/, Similarly, the real
part of the signal current may be written
• ^ j^^J-it _|. /^*e-i"i« + 72gi"2t ^ /2*e~'"=^' (5)
If we multiply equations (1) and (4) and retain only those terms con-
taining /i and /2 we obtain, in the case of the non-inverting conversion
transducer where /2 = /o + /i ,
(6)
+ [GoV,* -f G,V2*]e~'"'' -f [GiFi* + GoV2*]e~'"''
Similarly, if we multiply (2) and (4) we get an expression like (6) with
the G's replaced by C's. If we differentiate this expression we get
~ M = jcci [CoVi + CV^le'"'' + MiCiVi + C0V2W''''
at (7)
- jcoiiCoFi* -f CiF2*]e-^"^ ' - icoslCiFi* + C,V2*]e
■joi2 t
When we perform the addition indicated by (3) and compare the result
with (5) we obtain
/i = [Go + icoiColFi -f [G, -f jmCi]V2
(8)
h = [Gi + ic^CJFi + [Go + JCC2C0W2
FREQUENCY CONVERSION BY A NONLINEAR ADMITTANCE 1407
Going through the same steps for the hivertmg conversion transducer
where /2 = /o — /i we obtain
/i = [Go + icoiCo]Fi + [G, + iciCilFo*
h* = [G, - jwoCiW, + [Go - MC0W2*
Equations (8) and (9) are in the form
/i = FnFi + F12F2
I2 = ^21'''l ~l~ F22F2
(9)
(10)
A heterodyne conversion transducer may thus be represented by a
linear 4-pole, and the admittance and gain of the 4-pole may be expressed
in terms of the admittance coefficients. In Fig. 1 we see that the admit-
tance of the 4-pole yi at the terminals 1-2 is eciual to Ii/Vi and the
admittance 2/2 connected to terminals 3-4 is — /2/l^ . Putting these in
(10) we find
YuY,, (11)
yi
Yn
F22 + Vi
Similarly the admittance of the 4-pole 2/2' at the terminals 3-4 is 72/ F2
and the admittance yi connected to terminals 1-2 is —Ii/Vi . Putting
these in (10) gives
2/2
F
22
i 12^ 21
Yn + 2/1
(12)
To compute the gain of the 4-pole when 7/1 contains the generator and
y-i the load, it is convenient to assume a current source connected across
?/i . If the current from this source is Jo we have Ii = lo — yiVi . I2
equals —y2V2 as before. Putting these in (10) gives
-'0 _ T^
(Fn + 2/l)(F22 + ?/2)
F
(13)
21
If we let yi = Qi -{- jbi and ?/2 = ^2 + i&2 , the power in the load isF2 ^2
and the power available from the generator is /oV4^i . Therefore the
transducer gain ri2 defined as the ratio of the power in y2 to that avail-
able from 2/1 becomes
F2'
Tu =4gig2j-^ = "igig
1 n"
21
(14)
F12F21 - (Fn + 2/1) (F22 + 2/2)
When ?/2 contains the generator and yi the load, we may proceed in the
same way (letting 7o flow in terminal 4) and obtain
2
r2i = 4^-1^2
F
12
F12F21 - (Fu + ?/0(F22 + 2/2)
(15)
1408 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
We may now obtain expressions for the admittance and gain of the
4-pole when the nonhnear element consists of a nonUnear resistor and
a nonlinear capacitor in parallel. We shall do this for the case where a
conjugate match exists at the terminals by letting ?// = ^i* and y^ =
1)1*. Equations (11) and (12) may thus be written
(Fii - 2/i*)(F22 + ?/2) = (Fn + VxWii - y2*) = F12F21 (16)
When this is multiplied out, letting ¥„,„ = Gmn + jBmn , and the real
and imaginary parts set equal as indicated by the first equality we ob-
tain Gng2 = G-iigx and giiBn + &i) = QiiB-n + 62). In (8) and (9) it is
seen that Gn = (722 = (?o and that ^22 is positive in equations (8) and
negative in equations (9). We thus obtain
gi = g2 bi + wiCo = 62 ± C02C0 (17)
where the upper symbol of the ± sign is used in the noninverting case
and the lower symbol in the inverting case. When the real and imaginary
parts are set equal as indicated by the second equality in (16) we obtain,
using the results in (17),
g' = Go' - Gi ± C01C02C1' - B' (18)
where
g = gi = g2 (19)
and
B = bl + COiCo = 62 ± COsCo = ± ^ (C02 ± C0l)(7l (20)
2G-0
These results may be put in (14) to obtain the modulator gain. Since a
conjugate match exists at the terminals of the 4-pole, this is the maxi-
mum available gain. The result is
MAO. = ,^::^^% (2.)
For the converter, using equation (15) we obtain
These results are valid only when a conjugate match exists at the ter-
minals. For this to be possible, the right side of (18) must be positive.
If it is negative no combination of values of gi and ^2 will result in a
match.
FREQUENCY CONVERSION BY A NONLINEAR ADMITTANCE 1409
It may be shown that if the slope of the voltage-current characteristic
of the nonlinear resistor is always positive, then Gi/Go can never be
greater than unity. (Reference 1, p. 410.) It is therefore convenient to
normalize the above results with respect to Go . If we let
— = p,
CO-)
COlCl
= px,
CO'
2C1
Go Go
equations (18) through (22) become
= X,
Gi
Go
7T = y,
Go _
Gx ^
If ± px- -
XIJ
(l±p)i^
Go
= ±
:i±p)f
pxz.
MAG12 =
MAGn =
62 ^
Jf + X-
XIJ
±(1 ± p) '-^ ± xz
1 +
Go
+
(1 ±p)
xii_
y' + {9xY
1 +
Q_
Go
+
(1±P)^
(23)
(24)
(25)
(26)
(27)
In these equations, p is less than \ in the noninverting case and less than 1
in the inverting case. Ordinarily it will be very much less than 1. The
value of z will be determined by the shape of the nonlinear capacitor
characteristic. However z appears only in (25) where it influences the
values of the matching susceptances so that it does not affect the con-
ductance or gain. While we can be certain that y will have values be-
tween 0 and 1, limitations on the value of x will depend on the particular
device used. We will therefore assume that x may have any value.
EFFECT OF NONLINEAR CAPACITOR
We may now examine, in a general way, the manner in A\hich the non-
linear capacitor influences the behavior of the 4-pole. Consider first the
case where the nonlinear capacitor is absent. It is well known, and can
be seen in the above equations by letting Go = Gi = 0, that the non-
inverting and inverting cases are alike, that the 4-pole can always be
matched and that the gain is the same in both directions and can never
be greater than unity. In addition, the matching susceptances are zero
and the gain is independent of frequency so that there is no limitation
to the bandwidth. When the nonlinear capacitor is added, all but one of
these conditions are changed. Equations (8) and (9) show that the non-
1410 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
inverting and inverting cases are different, (24) may become negative
so that the 4-pole cannot ahvays be matched and (26) and (27) are dif-
ferent so that the gains through the 4-pole are not the same in the two
directions. Furthermore, (26) can be greater than unity so that modula-
tors may have gain. However, as will be shown, the converter gain
given by (27) is still restricted to values less than unity. It is also seen
that the matching susceptances are no longer zero and that the gain
varies with frequency so that the bandwidth is limited.
If we remove the restriction that a conjugate match exists and operate
the 4-pole between arbitrary admittances, it may be shown in (11) and
(12) that the conductance of the 4-pole may become negative, and in (14)
and (15) that the gain may have any value, however large. This is true
for both noninverting and inverting modulators and converters. How-
ever, we see in (14) and (15) that the ratio of the modulator gain to the
converter gain is | F21/F12 1". This is greater than unity, so that for the
same operating conditions the modulator gain will be greater than the
converter gain. Although increased gain is possible, it is obtained at the
expense of reduced bandwidth and increased sensitivity to changes in the
terminating admittances, particularly in the case of converters. The
present analysis will therefore be restricted to the case where a conjugate
match exists.
1.0
0.9
0.8
0.7
0 6
0.5
0.4
0.3
0.2
0.1
\
N^
yv Go 1
\^
O.J
\
0 sV
v
i
\s
V^
\
\
^
^
x
^.9
V
X^
^
^
^
^^
^
^
^
==
=
^^^
1.0
|-^
/
1.1
y^""^
^
■'^
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
X
Fig. 2 — Conductance contours of noninverting transducer.
FREQUENCY CONVERSION BY A NONLINEAR ADMITTANCE 1411
1.0
0.9
0.8
0 7
0.6
0.5
0.4
I 0.3
0.2
0 1
\
N^
\
V
\\
\
\ >
s^
\
\^
!bv
\
\^
^
V
^
\
\
\;
^
"^^
0.3
k
\?
ES
X
07^
05^
^
^-«^^
0.9\
\
X
'
^
X
7
X
10 11 12 13 14
Fig. 3 — Conductance contours for inverting transducer.
CONDUCTANCE AND GAIN VERSUS X AND y
By assigning a value to p, curves may be plotted showing how the
conductance and gain of the 4-pole change as the characteristics of the
nonlinear resistor and nonlinear capacitor are varied. The particular case
when /2 is about 160 times /i will be treated. This corresponds, for ex-
ample, to an intermediate frequency of 70 mc and a local oscillator f re-
fluency of 11,200 mc.
Figs. 2 and 3 show the normalized conductance contours as functions
of .T and y as given by (24) for the noninverting and inverting cases re-
spectively. It wall be seen that in most instances, increasing the value of
X causes g/Go to decrease. An exception occurs in the noninverting case
(Fig. 2) when y is less than 2-\/p/(p + 1) or 0.157 where it is seen that
increasing x causes g/Go to increase. When x and y have values corre-
sponding to points above the g/Go = 0 curve, the 4-pole cannot be
matched and (23) through (27) are not applicable. However, it will
be noted that connecting a resistor across either the nonlinear elements
or across the input and output terminals has the effect of increasing Go .
By this means the 4-pole can always be reduced to the condition w^here
it can be matched.
Figs. 4 and 5 show the modulator gain contours as functions of x and y
1412 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
1 .u
0.9
0 8
0.7
0.6
0.5
0.4
0.3
\
V
x^
\
\ \
\ \
\
\
\
\i
\
\
\
\
\
-5 I
\
N
\^
'
0
\^
^^.
"-^.
\
^
I
"""* —
^^
_,
0.2
0.1
0
^*-^v^
— — ^.
V
\,
15DB\
1 \
3 4 5 6 7 B
X
9 to \\ 12 13 14
Fig. 4 — Gain contours for noninverting modulators.
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
\
V
\
\
I \
\ \
\
\ \
\ \
\ \
\ \
\
\"
\ \
1
V
-5 1
\
\
\
>
\
C
3
\
\
X,
\
. "^^
'^-'^.
^^
\l(
3
N
^-
"^--.
'•«*^
A
15DB
^.
--^
-s.
3 4 5 6
7 6 9 10 11 12 13 14
X
Fig. 5 — Gain contours for inverting modulator.
FREQUENCY CONVERSION BY A NONLINEAR ADMITTANCE 1413
■--,
\.
-5DB
X
\
.^>
-10[
3B
^
^-<
NONINVERTING
/
^<s
INVERTING^^^
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4,0 4.5 5.0
X
Fig. 6 — Gain contours for converter.
as given by (26) . Here it is seen that increasing the value of x causes the
gain to increase. For values of x less than about 3, the gains in the non-
inverting and inverting cases are the same. In the nonin verting case, x
may increase indefinitely, provided y is less than 0.157, and a gain equal
to the ratio of the output frequency to the input frequency eventually
reached, 22.1 db in this case. In the inverting case, the maximum gain
obtainable is 19.3 db, and it occurs when y is zero.
Fig. 6 shows the converter gain contours as given by equation (27).
Here we see that increasing x causes a decrease in the loss, but the de-
crease is small and in no case can the gain be greater than 0 db. This oc-
curs when X is zero. The nonlinear capacitor is thus of small benefit in
the converter case. About the most benefit that can be obtained is a de-
crease in loss of perhaps 1 db. For example, if the nonlinear resistor alone
has a loss of 6 db {y = 0.8), this could be reduced to 5 db by adding a
nonlinear capacitor of such value as to make x = 1.3.
BANDWIDTH
Since both the admittance and gain of the 4-pole vary with frequency,
the bandwidth over which it can be used is limited. Figs. 7 and 8 show
the modulator gain as a function of x for input frequencies of 50, 70 and
90 mc, and a local oscillator frequency of 11,200 mc. These curves were
1414 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 195G
22
20
18
16
14
'^ 12
ffl
^ 10
LLI
Q
Z 8
Z
< «
-4
■^
y
50 UZy
y
--
^^"
70
/>
-.^"
^^^
--'
'fo
/
.'--
//
r"^
/f ^
/
//
■V
//
/
'/
/
/
/
0 - 2 4 6 a 10 12 14 16 18 20 22
X
Fig. 7 — Gain of noninverting modulator, q/Gq = 0.3.
computed using values of y which make qIG^ = 0.3 at midband. They
are thus near the largest gains obtainable for a given value of x. The
matching susceptances were assumed to be a single inductance or capaci-
tance connected across the terminating resistors. Co/Ci was arbitrarily
assumed to have a value of 2. The procedure used was to compute y,
hi/ Go , ho/ Go and the maximum available gain at midband using (24),
(25) and (26); hi/Go and hi/Go were then multiplied by the appropriate
frequency ratio to obtain the terminating susceptances at 50 and 90 mc
and the gain at these frequencies was then computed using (14).
Figs. 7 and 8 show that with the simple matching susceptances used,
the gain variation across the band increases as the gain increases. For
the same midband gain, the variation in the inverting case is somewhat
greater than in the noninverting case. The gain is thus limited by the
bandwidth requirements .
When the gain at 50, 70 and 90 mc is calculated using larger values
of g/Go it is found that as g/Go increases the gain variation across the
band decreases. In the limit the least variation is obtained when y is
FREQUENCY CONVERSION BY A NONLINEAR ADMITTANCE
24
22
20
18
16
1415
14
^t2
u
LU
Q
10
Z 8
<
(J
2
0
-2
-4
./
y
90 MC ,/
yA .
^
/
:^
,-'-'
y^
-y
^-^
<o'
/
V
.-"'
A
/,
,'-'
y
/
//
A/"
• /
t
r
//
y
/
6
X
10
12
Fig. 8 — Gain of inverting modulator, glG^ = 0.3.
zero. When the midband gain is 15 db, Figs. 7 and 8 show that the gain
variation is 2.0 db in the nonin verting case and 2.7 db in the inverting
case. When y is zero these variations are reduced to 0.8 db and 1.0 db
respectively for the same midband gain. The nonlinear resistor therefore
degrades the performance and, assuming complete freedom in the choice
of X, a greater bandwidth can be obtained if it is absent.
PREFERRED NONLINEAR ELEMENTS
Thus we see that, under the requirement that a conjugate match exist
at the terminals of the 4-pole, the nonlinear resistor contributes little
to the gain of a nonlinear capacitor modulator while the nonlinear capaci-
tor is of little benefit in a nonlinear resistor converter. In a modulator
having appreciable gain, the degree of nonlinearity permissible in the
nonlinear resistor is quite small. For gains exceeding 15 db, y must be
less than 0.2. Such a nonlinear resistor used alone would have a con-
1416 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
version loss exceeding 20 db. We thus find that, for the greatest band-
width, the preferred nonhnear element for modulators is a nonlinear;
capacitor while the preferred nonlinear element for converters is a non- ■
linear resistor. In modulators, the nonlinear capacitor device should !
have as little resistance as possible, so that an external resistor could
be used to control the value of x. It could be connected across the non-
linear capacitor or across the input and output terminals.
CONCLUSIONS
The results given above show that the preferred nonlinear element
for use in modulators is a pure nonlinear capacitor while the preferred
nonlinear element for use in converters is a pure nonlinear resistor. By
shunting the nonlinear capacitor or the terminals of a nonlinear capacitor
modulator with an appropriate resistance, an impedance match, ade-
quate bandwidth, and a performance superior to that of a nonhnear
resistor modulator can be obtained. Nonlinear capacitance effects are
not useful in converters because of stability and bandwidth limitations
and also because there is no evidence that an improved noise figure would
result from a reduction in conversion loss.
ACKNOWLEDGMENT
The writer is indebted to H. E. Rowe for many helpful suggestions in
the mathematical analysis and to R. S. Ohl for supplying the bombarded
silicon rectifiers used in the experiments which lead to the ideas presented
here.
REFERENCES
1. H. C. Torrey and C. A. Whitmer, Crystal Rectifiers, 15, Radiation Laboratory
Series, McGraw-Hill, New York, 1948, Chapter 13.
2. L. C. Peterson and F. B. Llewellyn, The Performance and Measurement of
Mixers in Terms of Linear Network Theory, Proc. I.R.E., 33, July, 1945.
Minimization of Boolean Functions*
E. J. McCLUSKEY, Jr.
(Manuscript received June 26, 1956)
A systematic procedure is presented for writing a Boolean function as
a minimum sum of products. This procedure is a simplification and exten-
sion of the method presented hy W. V. Quine. Specific attention is given to
terms which can be included in the function solely for the designer's con-
venience.
1 INTRODUCTION
In designing switching circuits such as digital computers, telephone
central offices, and digital machine tool controls, it is common practice
to make use of Boolean algebra notation.^- 2.3.4 'pj-^g performance of a
single-output circuit is specified by means of a Boolean function of the
input variables. This function, which is called the circuit transmission,
is equal to 1 when an output is present and equals 0 when there is no
output. A convenient means of specifying a transmission is a table of
combinations such as that given in Table I. This table lists, in the column
under T, the output condition for each combination of input conditions.
If there are some combinations of input conditions for which the output
is not specified (perhaps because these combinations can never occur),
d-entries are placed in the T-column of the corresponding rows of the
table of combinations. The actual values (0 or 1) assigned to these rows
are usually chosen so as to simplify the circuit which is designed to
satisfy the requirements specified in the table of combinations.
For each row of the table of combinations a transmission can be written
which equals "one" only when the variables have the values listed in
that row of the table. These transmissions will be called elementary
product terms (or more simply, p-terms) since any transmission can
always be written as a sum of these p-terms. Table I (b) lists the p-terms
for Table 1(a). Note that every variable appears in each p-term. The
* This paper is derived from a thesis submitted to the Massachusetts Institute
of Technology in partial fulfillment of the requirements for the degree of Doctor
of Science on April 30, 1956.
1417
Xi
X2
X3
T
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
Xl
X2
X3
Xi'
X2'
X3
Xl'
X2
Xz'
Xl'
Xl
X3
Xl
Xt'
Xz'
Xl
a-2'
Xz
Xl
Xi
Xz'
Xl
X2
Xz
1418 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Table I — Circuit Specifications
(a) Table of Combinations (b) p-terms
0
1
2
3
4
5
6
7
(c) Canonical Expansion
T = Xx'Xt'Xz + Xi'XtXz + Xi'XtXz + XxXi'Xz' + XiXt'Xz + XiXiXz
p-term corresponding to a given row of a table of combinations is formed
by priming any variables which have a "zero" entry in that row of the
table and by leaving unprimed those variables which have "one" entries.
It is possible to write an algebraic expression for the over-all circuit
transmission directly from the table of combinations. This over-all
transmission, T", is the smn of the p-terms corresponding to those rows
of the table of combinations for which T is to have the value "one."
See Table 1(c). Any transmission which is a sum of p-terms is called a
canonical expansion.
The decimal numbers in the first column of Table 1(a) are the decimal
equivalents of the binary numbers formed by the entries of the table
of combinations. A concise method for specifying a transmission function
is to list the decimal numbers of those rows of the table of combinations
for which the function is to have the value one. Thus the function of
Table I can be specified as ^(1, 2, 3, 4, 5, 6).
One of the most basic problems of switching circuit theory is that of
writing a Boolean function in a simpler form than the canonical expan-
sion. It is frequently possible to realize savings in equipment by writing
a circuit transmission in simplified form. Methods for expressing a
Boolean function in the "simplest" sum of products form were published
by Karnaugh,^ Aiken, ^ and Quine.® These methods have the common
property that they all fail when the function to be simplified is reason-
ably complex. The following sections present a method for simplifying
functions which can be applied to more complex functions than previous
methods, is systematic, and can be easily programmed on a digital com-
puter.
2 the minimum sum
By use of the Boolean algebra theorem a;ia:;2 + a;/a;2 = Xo it is possible
to obtain from the canonical expansion other equivalent sum functions;
MINIMIZATION OF BOOLEAN FUNCTIONS 1419
that is, other sum functions which correspond to the same table of com-
binations. These functions are still siuiis of products of variables but
not all of the variables appear in each term. For example, the transmis-
sion of Table 1, T = xix-Zx^ + X1X2X3 + XiXiX-s + aia-2'a;3' -f a-i.t;2'a;3 +
.Tia;2.r3' = (xiXz'Xi + X1X2X5) -f (aTi'a;2a;3' + a-ia,-2i-3') + (a;i.r2'ar3' + .t-ia-2'a;3) =
(.ri'a:2'.i'3 + X1X2X3) + (.<■/.^•2.^■3' + .r/.r2a;3) + (.-»ia;2'a;3' + a;i.T2a:;3') can be
written as either T = .r/.rs + .r2.r3' + xix-/ or T = x^x^ -f a;i'x2 + XiX^' .
A literal is defined as a variable with or without the associated prime
{xi , x-i are literals) . The sum functions which have the fewest terms of
all equivalent sum functions will be called minimum sums unless these
functions having fewest terms do not all involve the same number of
literals. In such cases, only those functions which involve the fewest
literals will be called minimum sums. For example, the function
T = E(7, 9, 10, 12, 13, 14, 15)
can be written as either
T = XiXoXi' + .r;i.r2.ri + .r4.r2'.ri + .r4.r3.r1'
or as
T = Xi^XiXx -f .r3a-2.ri + Xi^ci'xx + Xi\,x%
Only the second expression is a minimum sum since it involves 11 literals
while the first expression involves 12 literals.
The minimum sum defined here is not necessarily the expression con-
taining the fewest total literals, or the expression leading to the most
economical two-stage diode logic circuit,^ even though these three ex-
pressions are identical for many transmissions. The definition adopted
here lends itself well to computation and results in a form which is useful
in the design of contact networks. A method is presented in Section 9
for obtaining directly the expressions corresponding to the optimum
two-stage diode logic circuit or the e.xpressions containing fewest literals.
In principle it is possible to obtain a minimum sum for any given
transmission by enumerating all possible eciuivalent sum functions then
selecting those functions which have the fewest terms, and finally select-
ing from these the functions which contain fewest literals. Since the
number of equivalent sum functions may be c^uite large, this procedure
is not generally practical. The following sections present a practical
method for obtaining a ixiinimum sum without resorting to an enumera-
tion of all eciuivalent sum functions.
3 PRIME IMPLICANTS
When the theorem XxXt + Xxx^ = x\ is used to replace by a single
term, two p-terms, which correspond to rows i and j of a table of combi-
1420 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
nations, the resulting term will equal "one" when the variables have
values corresponding to either row i or row j of the table. Similarly,
when this theorem is used to replace, by a single term, a term which
equals "one" for rows i and j and a term which equals "one" for rows
k and m, the resulting term will equal "one" for rows i, j, k and m of the
table of combinations. A method for obtaining a minimum sum by re-
peated application of this theorem (.Ti.r2' + .Ti.'C2 = Xi) was first pre-
sented by Quine.^ In this method, the theorem is applied to all possible
pairs of p-terms, then to all possible pairs of the terms obtained from
the p-terms, and so on, until no further applications of the theorem are
possible. It may be necessary to pair one term with several other terms
in applying this theorem. In Example 3.2 the theorem is applied to the
terms labeled 5 and 7 and also to the terms labeled 5 and 13. All terms
paired with other terms in applying the theorem are then discarded. The
remaining terms are called prime implicants. Finally a minimum sum is
formed as the sum of the fewest prime implicants which when taken to-
gether will equal "one" for all required rows of the table of combinations.
The terms in the minimum sum will be called minimum sum terms or
ms-terms.
Example 3.1
T = Z(3, 7, 8, 9, 12, 13)
Canonical Expansion:
T = x/xi'xsXi -{- Xi'xiXsXi + a:ia;2'a^3 Xt + XyXz Xs Xi
0 0 11
3
0 111
7
10 0 0
8
10 0 1
9
-f a:ia;2a;3'a;4' + XiX^Xs'xi
110 0
12
110 1
13
The bracketed binary and decimal numbers below the sum terms indi-
cate the rows of the table of combinations for which the corresponding
term will equal "one." A binary character in Avhich a dash appears
represents the two binary numbers which are formed by replacing the
dash by a "0" and then by a "1." Similarly a binary character in which
two dashes appear represents the four binary numbers formed by re-
placing the dashes by "0" and "1" entries, etc.
a;i'a;2 x^Xi + xi x^x^xt = xi x^xt
0 0 11
3
0
1 1 1
7
"O-l l1
_ 3,7 J
MINIMIZATION OF BOOLEAN FUNCTIONS
1421
XxX-lxzxl + X\X2XzXi = .T1.T2 X3
10 0 0
8
"10 0 1'
9
X1X2X3 Xi + 0:1X2X3 X4 = XiXzXz
[1100] fl 10 1I [110-1
L 12 J L 13 J L 12,13 J
XiXiXz + ^1X2X3 = Xi Xz
[10 0-1 [110-1 [1-0
L 8,9 J L 12,13 J [8,9,12
.12,13
Prime Implicants;
X\ Xz ,
1-0 -
_8,9,r2,13_
Xi XzXi
"0-
3
-111
:,7 J
Minimum Sum;
Example 3.2
T = XiXz + XiXzXi
T = 2:(5, 7, 12, 13)
Canonical Expansion:
T = x(xix{xi^ + xlx-iXzXi^ + X\XiXzxl + X\XiXz a;4
0'
[0 10 1I [0 1 1 1I [110
L 5 J L 7 J [ 12
X-lxixixii, + XxXiXzXi = X\ Xi Xi
XiXiXzXi + XiXiXzXi = .T2.T3 Xi
'110 01 [110 1I [110 -1
_ 12 J L 13 J L 12,13 J
110 1
13
Prime Implicants:
Xi X2 Xi ,
x^xz Xi , Xia:2X3
[0 1 - 1I [- 1 0 1I [110-1
L 5,7 J L 5,13 J L 12,13 J
1422 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Minimum Sum:
T = Xi'xzXi + xiXipcz
«
Quine's method, as illustrated in Examples 3.1 and 3.2, becomes
unwieldly for transmissions involving either many variables or many
p-terms. This difficulty is overcome by simplifying the notation and
making the procedure more systematic. The notation is simplified by
discarding the expressions invoh'ing literals and using only the binarj^
characters. This is permissible because the expressions in terms of literals
can always be regained from the binary characters. The theorem being
used to combine terms can be stated in terms of the binary characters
as follows: If two binary characters are identical in all positions except
one, and if neither character has a dash in the position in w^hich they
differ, then the two characters can be replaced by a single character
which has a dash in the position in which the original characters differ
and which is identical with the original characters in all other positions.
Table II — Determination of Prime Implicants for Transmission
T = X) (0> 2, 4, 6, 7, 8, 10, 11, 12, 13, 14, 16, 18, 19, 29, 30)
(a) I (b) II (c) III
XiXiXzX-iXi X^XiXzX-iXi X^XiXzXiXi
02 OOO-OV 0246 00--0V
04 00-00\/ 028 10 O-O-OV
08 0-OOOV 02 16 18 -00-0
0 16 -OOOOa/ 048 12 0--00V
0
0 0 0 0 0 V
2
4
8
16
0 0 0 1 0 v
0 0 1 0 0 V
0 1 0 0 0 V
1 0 0 0 0 a/
6
10
12
18
0 0 1 1 0 V
0 1 0 1 0 v
0 1 1 0 0 V
1 0 0 1 0 V
4 12 0 - 1 0 0 V
8 10 0 1 0 - 0 v
8 12 0 1 - 0 0 V
7 OOlllV 16 18 100-OV
11 0 1 0 1 1 V
13 01101a/ 67 0011-
14 01110a/ 6 14 0-llOv/
19 10 0 11a/ 10 U O 1 O 1 -
10 14 0 1 - 1 O V
29 1 1 1 0 1 V 12 13 0 110-
30 11110a/ 12 14 0 1 1 - 0 V
26 00-lOV 26 10 14 O-'lOV
2 10 0-010a/ 46 12 14 0-1-OV
2 18 -0010a/ 8 10 12 14 01--0\/
4 6 0 0 1 - 0 V
18 19
10 0 1-
13 29
14 30
- 1 1 0 1
- 1 1 1 0
(d) IV
XfiXiXzXiXl.
02468 10 12 14 0 0
MINIMIZATION OF BOOLEAN FUNCTIONS 1423
The first step in the revised method for determining prime implicants
is to list in a column, such as that shown in Table 11(a), the binary
equivalents of the decimal numbers which specify the function. It is
expedient to order these binary numbers so that any numbers which
contain no I's come first, followed by any numbers containing a single
1, etc. Lines should be drawn to divide the column into groups of binary
numbers which contain a given number of I's. The theorem stated above
is applied to these binary numbers by comparing each number with all
the numbers of the next lower group. Other pairs of numbers need not
be considered since any two numbers which are not from adjacent groups
must differ in more than one binary digit. For each number w^hich has
I's wherever the number (from the next upper group) with which it is
being compared has I's, a new character is formed according to the
theorem. A check mark is placed next to each number which is used in
forming a new character. The new characters are placed in a separate
column, such as Table 11(b), which is again divided into groups of char-
acters which have the same number of I's. The characters in this new
column will each contain one dash.
After each number in the first column has been considered, a similar
process is carried out for the characters of column two. Two characters
from adjacent groups can be combined if they both have their dashes
ill the same position and if the character from the lower group has I's
wherever the upper character has I's. If any combinations are possible
the resulting characters are placed in a third column such as Table 11(c),
and the Column II characters from which the new characters are formed
are checked. All the characters in this third column will have two dashes.
This procedure is repeated and new columns are formed, Table 11(d),
until no further combinations are possible. The unchecked characters,
which have not entered into any combinations, represent the prime
implicants.
Each binary character is labeled with the decimal equivalents of the
binary numbers which it represents (see note in Example 3.1). These
decimal numbers are arranged in increasing arithmetic order. For a
character having one dash this corresponds to the order of its formation :
When two binary numbers combine, the second number always contains
all the i's of the first number and one additional 1 so that the second
number is always greater than the first. Characters having two dashes
can be formed in two ways. For example, the character (0, 2, 4, 6) can
be formed either by combining (0, 2) and (4, 6) or by combining (0, 4)
and (2, 6) as given in Table III. Similarly, there are three ways in which
a character having three dashes can be formed (in Table II the 0, 2, 4,
1424 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Table III — Example of the Two Ways of Forming
A Character Having Two Dashes
0
0 0 0 0
2
4
0 0 10
0 10 0
0 2
0 4
0 0-0
0-00
0 2 4 6
(0426
0 -
0 -
- 0
-0)
2 6
4 6
0-10
0 1-0
0 110
6, 8, 10, 12, 14 character can be formed from theO, 2, 4, 6, and 8, 10, 12,
14 characters or the 0, 2, 8, 10, and 4, 6, 12, 14 characters or the 0, 4, 8,
12 and 2, 6, 10, 14 characters), four ways in which a character having
four dashes can be formed, etc.
In general, any character can be formed by combining two characters
whose labels form an increasing sequence of decimal numbers when
placed together. It is possible to shorten the process of determining
prime implicants by not considering the combination of any characters
whose labels do not satisfy this requirement. For example, in Table
11(b) the possibility of combining the (0, 4) character with either the
(2, 6), (2, 10) or the (2, 18) character need not be considered. If the
process is so shortened, it is not sufficient to place check marks next to
the two characters from which a new character is formed; each member
of all pairs of characters which would produce the same new character
w^hen combined must also receive check marks. More simply, when a
new character is formed a check mark is placed next to all characters
whose labels contain only decimal numbers which occur in the label of
the new character. In Table II, when the (0, 2, 4, 6) character is formed
by combining the (0, 2) and (4, 6) characters, check marks must be
placed next to the (0, 4) and (2, 6) characters as well as the (0, 2) and
(4, 6) characters. If the process is not shortened as just described, the
fact that a character can be formed in several ways can serve as a check
on the accuracy of the process.
It is possible to carry out the entire process of determining the prime
implicants solely in terms of the decimal labels without actually writing
the binary characters. If two binary characters can be combined as de-
scribed in this section, then the decimal label of one can be obtained
from the decimal label of the other character by adding some power of
two (corresponding to the position in which the two characters differ)
to each number in the character's label. For example, in Table lib the
label of the (4, G) (0 0 1 - 0) character can be obtained by adding 4 = (2^)
to the numbers of the label of the (0, 2) (0 0 0 - 0) character. By searching
for decimal labels which differ by a power of two, instead of binary char-
acters which differ in only one position, the prime implicants can be
MINIMIZATION OF BOOLEAN FUNCTIONS 1425
determined as described above without ever actually writing the binary
characters.
4 PRIME IMPLICANT TABLES
The minimum sum is formed by picking the fewest prime imphcants
whose sum will equal one for all rows of the table of combinations for
which the transmission is to equal one. In terms of the characters used
in Section 3 this means that each number in the decimal specification
of the function must appear in the label of at least one character which
corresponds to a ms-term (term of the minimum sum).
The ms-terms are selected from the prime implicants by means of a
prime implicant table,* Table IV. Each column of the prime implicant
table corresponds to a row of the table of combinations for which the
transmission is to have the value one. The decimal number at the top of
each column specifies the corresponding row of the table of combinations.
Thus the numbers which appear at the tops of the columns are the same
as those which specify the transmission. Each row of the prime implicant
table represents a prime implicant. If a prime implicant equals "one" for
a given row of the table of combinations, a cross is placed at the inter-
section of the corresponding row and column of the prime implicant
table. All other positions are left blank. The table can be written directly
from the characters obtained in Section 3 by identifying each row of the
table with a character and then placing a cross in each column whose
number appears in the label of the character.
It is convenient to arrange the rows in the order of the number of
crosses they contain, with those rows containing the most crosses at the
top of the table. Also, horizontal lines should be drawn partitioning the
table into groups of rows which contain the same number of crosses,
Table IV. If, in selecting the rows which are to correspond to ms-terms,
a choice between two equally appropriate rows is required, the row hav-
ing more crosses should be selected. The row with more crosses has
fewer literals in the corresponding prime implicant. This choice is more
obvious when the table is partitioned as suggested above.
A minimum sum is determined from the prime implicant table by
selecting the fewest rows such that each column has a cross in at least
one selected row. The selected rows are called basis roivs, and the prime
implicants corresponding to the basis rows are the ms-terms. If any
column has only one entry, the row in which this entry occurs must be a
basis row. Therefore the fir.st step in selecting the basis rows is to place
* This table was first discussed by Quine."' However, no sj'stematic procedure
for obtaining a minimum sum from the prime implicant table was presented.
1426 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Table IV — Prime Implicant Table for the
Transmission of Table II
0 2 4 8 16 6 10 12 18 7 11 13 14 19 29 30
B
C
D
E
F
G
H
X X X X
X X
XXX
X X
X X
X
X
an asterisk next to each row which contains the sole entry of any cohmm
(rows A, B, C, D, E, G, H, in Table IV). A line is then drawn through all
rows marked with an asterisk and through all columns in which these
rows have entries. This is done because the requirement that these col-
umns have entries in at least one basis row is satisfied by selecting the
rows marked with an asterisk as basis rows. When this is done for
Table IV, all columns are lined out and therefore the rows marked with
asterisks are the basis rows for this table. Since no alternative choice of
basis rows is possible, there is only one minimum sum for the transmis-
sion described in this table.
5 ROW covering
In general, after the appropriate rows have been marked with asterisks
and the corresponding columns have been lined out, there may remain
some columns which are not lined out; for example, column 7 in
Table V(b). When this happens, additional rows must be selected and
the columns in which these rows have entries must be lined out until
all columns of the table are lined out. For Table V(b), the selection of
either row B or row F as a basis row will cause column 7 to be lined out.
However, row B is the correct choice since it has more crosses than row
F. This is an example of the situation which was described earlier in
connection with the partitioning of prime implicant tables. Row B is
marked with two asterisks to indicate that it is a basis row even though
it does not contain the sole entry of any column.
The choice of basis rows to supplement the single asterisk rows be-
comes more complicated when several columns (such as columns 2, 3,
and 6 in Table VI (a)) remain to be lined out. The first step in choosing
these supplementary basis rows is to determine whether any pairs of
rows exist such that one row has crosses only in columns in which the
MINIMIZATION OF BOOLEAN FUNCTIONS
1427
31
Table V — Determination of the Minimum Sum for
5" = E (0. 1. 2, 3, 7, 14, 15, 22, 23, 29, 31)
(a) Determination of Prime Implicants
0 0 0 0 0 V
1
2
0 0 0 0 1 v/
0 0 0 1 0 >/
3
0 0 0 1 1 V
7
14
22
0 0 1 1 1 v/
0 1 1 1 0 v/
1 0 1 1 0 V
15
23
29
0 1 1 1 1 >/
1 0 1 1 1 v/
1 1 1 0 1 V
0
0
1
2
X5X4X3X2X1
X5X4X3X2X1
0 0 0 0 - v
0 0 0 - 0 v
0 12 3
7 15 23 31
0 0 0 - -
--111
1 3
2 3
0 0 0 - 1 V
0 0 0 1 - v
3 7
0 0-11
1 1 1 1 1 >/
7 15
0 - 1 1 1 V
7 23
- 0 1 1 1 V
14 15
0 111-
22 23
10 11-
15 31
- 1 1 1 1 V
23 31
1 - 1 1 1 V
29 31
111-1
(b) First Step in Selection of Basis Rows
1 2 3 7 14 22 15 23 29 31
A
B
C
D
E
F
1 1
i :
X
i
c
:
I
^
If
n
■%
r
1
t
X
*
*
(c) Minimum Sum
r = 2 ((0, 1, 2, 3), (7, 15, 23, 31), (29, 31), (22, 23), (14, 15)]
T — Xi'XtXi + X3X2X1 + X6X4X3X1 + X6X4'X3X2 + X6'X4X3X2
other member of the pair has crosses. Crosses in Hned-out cohimns are
not considered. In Table VI (a), rows A and B and rows B and C are
such pairs of rows since row B has crosses in columns 2, 3, and 6 and row
A has a cross in column 6 and row C has crosses in columns 2 and 3. A
convenient way to describe this situation is to say that row B covers
rows A and C, and to write B3A,BZ)C.If row i is selected as a sup-
plementary basis row and row i is covered by row j , which has the same
total number of crosses as row i, then it is possible to choose row j as a
basis row instead of row i since row j has a cross in each column in which
row i has a cross.
The next step is to hne out any rows which are covered by other rows
in the same partition of the table, rows A and C in Table VI (a). If any
1428 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 195G
Table VI — Prime Implicant Tables for
7" = Z (0. 1» 2, 3, 6, 7, 14, 22, 30, 33, 62, 64, 71, 78, 86)
(a) Prime Implicant Table with Single Asterisk Rows and
Corresponding Columns Lined Out
0 1 2 64 3 6 33 7 14 22 30 71 78 86 62
!i
A
B
C
D
E
F
G
H
I
A
B
C
D
E
F
G
H
I
■
c :
X
: X
X
X X
X
1 1 1
XXX
X
1
V
V
Y 1
1
*
^
r
1
3
C
X
1
■^
r
^
r
1
1
(b) Prime Implicant Table with Rows which are Covered
by Other Rows Lined Out
0 1
2 64 3 6 33 /
' 14 22 30 71 78 86 62
\
1 1
y V
1
f ■>
X
X X
V
J
c
^
:
c
1 ,
column now contains only one cross which is not lined out, columns 2
3, and 6 in Table VI (b), two asterisks are placed next to the row
in which this cross occurs, row B in Table VI (b), and this row and all
columns in which this row has crosses are lined out. The process of draw-
ing a line through any row which is covered by another row and selecting
each row which contains the only cross in a column is continued until it
terminates. Either all columns will be lined out, in which case the rows
marked with one or two asterisks are the basis rows, or each column will
contain more than one cross and no row will cover another row. The
latter situation is discussed in the following section.
6 PRIME implicant TABLES IN CYCLIC FORM
If the rows and columns of a table which are not lined out are such that
every column has more than one cross and no row covers another row, as
in Table VI 1(b), the table will be said to be in cyclic form, or, in short.
MINIMIZATION OF BOOLEAN FUNCTIONS
1429
Table VII — Determination of Basis Rows for a
Cyclic Prime Implicant Table
'a) Selection of Single Asterisk Rows
0 4 16 12 24 19 28 27 29 31
A.
B
C
D
E
F
G
H
(c) Selection of Row 1 as a Trial Basis
Row (Column 0)
X X
X X
X X
X X
X X
X X
X X
X I X
X X
X X
0 4 16 12 24 19 28 27 29 31
A
B
C
D
E
F
G
H
I
J
1
r
y-L,
y
*n
—
1
V
I
X
I
r 1
LT
^
■ X
'
t 1
'
**
**
(b) Selection of Double Asterisk Rows
0 4 16 12 24 19 28 27 29 31
A
B
C
D
E
F
G
H
I
J
(d) Selection of Row 2 as a Trial Basis
Row (Column 0)
X X
X X
X X
X X
X X
X X
V V
'
-'' 1
' 1
1
1 1
0 4 16 12 24 19 28 27 29 31
A
B
C
D
E
F
G
H
I
J
1 1
r^
\
" 1 '
y
,
^
' I '
^
:
■J
c
■(
c
.
'^
1 y I
1
*
to be cyclic. If any column has crosses in only two rows, at least one of
these rows must be included in any set of basis rows. Therefore, the
basis rows for a cyclic table can be discovered by first determining
whether any column contains only two crosses, and if such a column
exists, by then selecting as a trial basis row one of the rows in which the
crosses of this column occur. If no column contains only two crosses,
then a column which contains three crosses is selected, etc. All columns
in which the trial basis row has crosses are lined out and the process of
lining out rows which are covered by other rows and selecting each row
which contains the only cross of some column is carried out as described
above. Either all columns will be lined out or another cyclic table will
result. Whenever a cyclic table occurs, another trial row must be se-
lected. Eventually all columns will be lined out. However, there is no
guarantee that the selected rows are actually basis rows. The possibility
exists that a different choice of trial rows would have resulted in fewer
selected rows. In general, it is necessary to carry out the procedure of
selecting rows several times, choosing different trial rows each time, so
1430 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
CT
0
that all possible combinations of trial rows are considered. The set of
fewest selected rows is the actual set of basis rows. '| \\
Table VII illustrates the process of determining basis rows for a
cyclic prime implicant table. After rows G and J have been selected u| |et(
cyclic table results, Table VII (b). Rows A and B are then chosen as al
pair of trial basis rows since column 0 has crosses in only these two rows. ,
The selection of row A leads to the selection of rows D and E as given in ;
Table VII (c). Row A is marked with three asterisks to indicate that it
is a trial basis row. Table VII (d) illustrates the fact that the selection!
of rows C and F is brought about by the selection of row B. Since bothi
sets of selected rows have the same number of rows (5) they are both
sets of basis rows. Each set of basis rows corresponds to a different min-
imum sum so that there are two minimum sums for this function.
Sometimes it is not necessary to determine all minimum sums
for the transmission being considered. In such cases, it may be possible
to shorten the process of determining basis rows. Since each column
must have a cross in some basis row, the total number of crosses in all
of the basis rows is equal to or greater than the number of columns.
Therefore, the number of columns divided by the greatest number of
crosses in any row (or the next highest integer if this ratio is not an
integer) is equal to the fewest possible basis rows. For example, in Table
VII there are ten columns and two crosses in each row. Therefore,
there must be at least 10 divided by 2 or 5 rows in any set of basis rows.
The fact that there are only five rows selected in Table VII (c) guaran-
tees that the selected rows are basis rows and therefore Table VII (d) is
unnecessary if only one minimum sum is required. In general, the process
of trying different combinations of trial rows can be stopped as soon as
a set of selected rows which contains the fewest possible number of basis
rows has been found (providing that it is not necessary to discover all
minimum sums) . It should be pointed out that more than the minimum
number of basis rows may be required in some cases and in these
cases all combinations of trial rows must be considered. A more accurate
lower bound on the number of basis rows can be obtained by considering
the number of rows which have the most crosses. For example, in Table
VI there are 15 columns and 4 crosses, at most, in any row. A lower
bound of 4 {—- = 3f ) is a little too optimistic since there are only three
rows which contain four crosses. A more realistic lower bound of 5 is
obtained by noting that the rows which have 4 crosses can provide crosses
in at most 12 columns and that at least two additional rows containing
two crosses are necessary to provide crosses in the three remaining col-
umns.
MINIMIZATION OF BOOLEAN FUNCTIONS 1431
CYCLIC PRIME IMPLICANT TABLES AND GROUP INVARIANCE
It is not always necessary to resort to enumeration in order to deter-
ne all minimum sums for a cyclic prime implicant table. Often
here is a simple relation among the various minimum sums for a trans-
nission so that they can all be determined directly from any single
ninimum sum by simple interchanges of variables. The process of select-
ng basis rows for a cyclic table can be shortened by detecting before-
aand that the minimum sums are so related.
An example of a transmission for which this is true is given in Table
VIII. If the variables a'l and x-2 are interchanged, one of the minimum
sums is changed into the other. In the prime implicant table the inter-
change of Xi and Xz leads to the interchange of columns 1 and 2, 5 and 6,
9 and 10, 13 and 14, and rows A and B, C and D, E and F, G and H.
The transmission itself remains the same after the interchange.
In determining the basis rows for the prime imphcant table, Table
VIII (d), either row G or row H can be chosen as a trial basis row. If row
G is selected the i-set of basis rows will result and if row H is selected
the ii-set of basis rows will result. It is unnecessary to carry out the
procedure of determining both sets of basis rows. Once the i-set of basis
rows is known, the ii-set can be determined directly by interchanging
the Xi and X2 variables in the i-set. Thus no enumeration is necessary in
order to determine all minimum sums.
In general, the procedure for a complex prime implicant table is to
determine whether there are any pairs of variables which can be inter-
changed without effecting the transmission. If such pairs of variables
exist, the corresponding interchanges of pairs of rows are determined.
A trial basis row is then selected from a pair of rows which contain the
only two crosses of a column and which are interchanged when the varia-
bles are permuted. After the set of basis rows has been determined, the
other set of basis rows can be obtained by replacing each basis row by
the row with which it is interchanged w^hen variables are permuted. If
any step of this procedure is not possible, it is necessary to resort to
enumeration.
In the preceding discussion only simple interchanges of variables have
been mentioned. Actually all possible permutations of the contact varia-
bles should be considered. It is also possible that priming variables or
both priming and permuting them will leave the transmission unchanged.
For example, ii T = Xi Xs Xo Xi + x/ Xs x-/ xi , priming all the variables
leaves the function unchanged. Also, priming Xi and x^ and then inter-
changing X4 and x^ does not change the transmission. The general name
for this property is group invariance. This was discussed by Shannon.^
1432 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
A method for determining the group invariance for a specified trans^
mission is presented in "Detection of Group Invariance or Total Sym;
metry of a Boolean Function."*
8 AN APPROXIMATE SOLUTION FOR CYCLIC PRIME IMPLICANT TABLES
It has not been possible to prove in general that the procedure pre
sented in this section will always result in a minimum sum. However,
this procedure should be useful when a reasonable approximation to a
minimum sum is sufficient, or when it is possible to devise a proof to!
show that the procedure does lead to a minimum sum for a specific trans-
mission (such proofs were discussed in Section 6). Since this procedure
is much simpler than enumeration, it should generally be tested beforef
resorting to enumeration.
The first step of the procedure is to select from the prime implicant
table a set of rows such that (1) in each column of the table there is a
cross from at least one of the selected rows and (2) none of the selected
rows can be discarded without destroying property (1). Any set of rows
having these properties will be called a consistent row set. Each consistent
row set corresponds to a sum of products expression from which no
product term can be eliminated directly by any of the theorems of
Boolean Algebra. In particular, the consistent row sets having the fewest
members correspond to minimum sums. The first step of the procedure
to be described here is to select a consistent row-set. This is done by
choosing one of the columns, counting the total number of crosses in each
row which has a cross in this column, and then selecting the row with
the most crosses. If there is more than one such row, the topmost row is
arbitrarily selected. The selected row is marked with a check. In Table
IX, column 30 was chosen and then row A was selected since rows A and
Z each have a cross in column 30, but row A has 4 crosses while row Z
has only 2 crosses. The selected row and each column in which it has a
cross is then lined out. The process just described is repeated by selecting
another column (which is not lined out). Crosses in lined-out columns
are not counted in determining the total number of crosses in a row. The
procedure is repeated until all columns are lined out.
The table is now rearranged so that all of the selected rows are at the
top, and a line is drawn to separate the selected rows from the rest.
Table X results from always choosing the rightmost column in Table
IX. If any column contains only one cross from a selected row, the single
selected-row cross is circled. Any selected row which does not have any
See page 1445 of this issue.
MINIMIZATION OF BOOLEAN FUNCTIONS
1433
Table VIII — Determination of the Minimum Sums for
T = J2iO, 1, 2, 5, 6, 7, 9, 10, 11, 13, 14, 15)
(a) (c)
0:4X3X2X1
f 0
0 0 0 0 V
' 1
2
0 0 0 1 v
0 0 1 0 v
, 5
6
9
■ 10
0 1 0 1 V
0 1 1 0 V
1 0 0 1 V
1 0 1 0 V
7
0 1 1 1 V
11
1 0 1 1 V
13
1 1 0 1 V
14
1 1 1 0 v
15
1 1 1 1 v
(b)
1
X4X3X2X1
0
1
0 0 0-
: i 0
2
0 0
- 0
1
5
0
_
0 1 V
1
9
-
0
0 1 V
2
. 6
0
-
1 0 V
9
10
-
0
1 0 V
5
7
0
1
- 1 V
5
13
-
1
0 1 V
6
7
0
1
1 - V
6
14
-
1
1 0 V
9
11
1
0
-1 V
9
13
1
—
0 1 V
;10
11
1
0
1 - V
|10
14
1
-
1 0 V
7
15
_
1
1 1 V
11
15
1
-
1 1 V
13
15
1
1
-1 V
14
15
1
1
1 - V
A
B
C
D
E
F
G
H
1
2
5 9 13
6 10 14
X4X3X2X1
--01
--10
5
6
9
10
7 13 15
7 14 15
11 13 15
11 14 15
-1-1
- 1 1 -
1 - - 1
1 - 1 -
(d)
0
1
2
5
6
9
10
7
11
13
14
15
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
(e)
(i) (0, 1) + (2, 6, 10, 14) + (5, 7, 13, 15) + ( 9, 11, 13, 15)
(ii) (0, 2) + (1, 5, 9, 13) + (6, 7, 14, 15) + (10, 11, 14, 15)
Ti = X4'X3'X2' + X2X1' + X3X1 + X4X1
Tii = X4'x3'xi' + X1X2' + X3X2 + X4X2
of its crosses circled can be discarded without violating the requirement
that each column should have at least one cross from a selected row.
Rows with no circled entries are discarded (one by one, since removal of
one row may require more crosses to be circled) until each selected row
contains at least one circled cross. This completes the first step. The se-
lected rows now correspond to a first approximation to a minimum sum.
A check should be made to determine whether the number of selected
rows is equal to the minimum number of basis rows. In Table X there
are at most 4 crosses per row and 26 columns so that the minimum num-
1434 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Table IX — Table of Prime Implicants for Transmission
^ = Z (0> 1. 2, 4, 5, 6, 7, 8, 9, 11, 13, 14, 15, 16, 18, 19, 20,
21, 23, 24, 25, 26, 27, 28, 29, 30)
The selection of row A is shown
0 1 2 4 8 16 5 6 9 18 20 24 7 11 13 14 19 21 25 26 28 15 23 27 29 30
A
B
—
X
1
X
C
k
D
X
E
X
F
X
G
X
H
X
I
X
J
X
K
X
L
X
M
X
X X
N
X
X
X
0
X
X
X
P
X
X
X
Q
X
X X
R
X
X
X
S
X
X
X
X
T
X
X
X
X
U
X
X
X
X
V
X
X X
X
W
X
X
X
X
X
X
X
X
X
Y
Z
X
X
X
X
X
X
X
X
X
X
X — X
I
X
X
i
2'
ber of basis rows is [-^] + 1 = 7. Since the number of selected rows is
9 there is no guarantee that they correspond to a minimum sum.
If such an approximation to a minimum sum is not acceptable, then
further work is necessary in order to reduce the number of selected rows.
For each of the selected rows, a check is made of whether any of the rows
in the lower part of the table (non-selected rows) have crosses in all
columns in which the selected row has circled crosses. In Table X row
E has a circled cross only in column 19; since row Y also has a cross in
coluimi 19 rows E and Y are labeled "a". Other pairs of rows which have
the same relation are labeled with lower case letters, b, c, d, e in Table X.
It is possible to interchange pairs of rows which are labeled Avith the same
lower case letter without violating the requirement that each column
must contain a cross from at least one selected row. If a non-selected row
is labeled with two lower case letters then it may be possible to replace
two selected rows by this one non-selected row and thereby reduce the
MINIMIZATION OF BOOLEAN FUNCTIONS
1435
ej .O « T3 aj
o^
4j a
o
ec
05
c^
r^
(M
w
(M
>C
r-H
on
c^
«o
o
c^
"Z
NH
>«
z
(N
o
1— 1
1—1
p-^
H
tf
05
<
1— I
Ph
•^
«
1— t
w
£2
<
n
H
©
X
©
XXX
X X
X
©
X
®
X X
©
XX X
X X
X X
X X
XX X
©
XX X
®
X
©
X
©
XXX X
©
X
X X
X X
©
XX XXX X
©
X XX
X X
X
XX X
X XX
©
X X
®
XX XXX X
X X
XX X
©
X X
©
XX XX
©
X
©
X X
XXX
XXX
-jJWfeOH-iWH;::)^ moQW^ jS^OPiO'tf a5>X>^N
1436 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
o
CO
Q CO
<
^
Q
(M
«t^
►J
05
w
«
f-H
^
e«5
a
'4.
1-H
<
^
t>.
\^
^
•^
W
C^
cc o
is "^
H 05
X
»o
H
n CD
< ^
H
I 00
X
a IN
n
< -^
©
X
©
XXX
©
X X
©
X
©
X X
©
XX X
©
XX X
®
XXX X
®
XX X
©
X
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X
©
X XX X
©
X
©
XXX
®
XX XXX X
©
XXX
©
X X
©
X X
©
X X X X X X
G
XX X
X X
©
XX XX
©
X
(^ X X
XXX
XXX
<*^>^0>-^\^U'^ Wp^WP30QWH3S;z;OPHC?tf a!>Xts5
MINIMIZATION OF BOOLEAN FUNCTIONS 1437
total number of selected rows (a check must be made that the two
selected rows being removed do not contain the only two selected-row
crosses in a column). In Table X no such interchange is possible.
Next a check should be made as to whether two of the labeled non-
selected rows can be used to replace three selected rows, etc. In Table
X rows Y(a) and J(b) can replace rows E(a), F(b) and K or rows Y(a)
and P(d) can replace rows E(a), T(d) and K. The table which results
from replacing rows E, F and K by rows Y and J is given in Table XL
The number of selected rows is now 8 which is still greater than 7, the
minimum number possible. This table actually represents the minimum
sum for this transmission even though this cannot be proved rigorously
by the procedure being described.
If it is assumed that a minimum sum can always be obtained by ex-
changing pairs of selected and nonselected rows until it finally becomes
possible to replace two or more selected row^s by a single selected row,
then it is possible to show directly that the Table XI does represent a
minimum sum. The only interchange possible in Table XI is that of
rows T and P. If this replacement is made then a table results in which
only rows J and F can be interchanged. Interchanging rows J and F
does not lead to the possibility of interchanging any new pairs of rows
so that this process cannot be carried any further.
On the basis of experience with this method it seems that it is not
necessary to consider interchanges mvolving more than one non-selected
row. Such interchanges have only been necessary in order to obtain al-
ternate minimum sums; however, no proof for the fact that they are
never required in order to obtain a minimum sum has yet been dis-
covered.
9 AN ALTERNATE EXACT PROCEDURE
It is possible to represent the prime implicant table in an alternative
form such as that given in Table XII (b). From this form not only the
minimum sums but also all possible sum of products forms for the trans-
mission which correspond to consistent row sets can be obtained sys-
tematically. For concreteness, this representation will be explained in
terms of Table XII. Since column 0 has crosses only in rows B and C,
any consistent row set must contain either row B or row C (or both).
Similarly, column 3 requires that any consistent row set must contain
either row D or row E (or both). When both columns 0 and 3 are con-
sidered they require that any consistent row set must contain either
row B or row C (or both) and either row D or row E (or both). This
requirement can be expressed symbolically as (B -f C) (D -f E) where
1438 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Table XII — Derivation of the Minimum Sums
FOR the Transmission
T = E (0, 3, 4, 5, 6, 7, 8, 10, 11)
(a) Table of Prime Implicants
Xi Xi
XiX%X\
X3X2X1
Xi'XiXi
Xz'x^Xx
XiXa'Xi
A
B
C
D
E
F
0
3
4
5
6
7
8
10
11
X
X
X
X
X
X
X
X
X
X
X
X
X
X
(b) Boolean Representation of Table
(B + C)(D + E)(A + B)(A)(A)(A + D)(C)(F)(E + F)
(c) Consistent Row Sets
(A, C, F, D), (A, C, F, E)
T = Xi'xz + xz'xi'xi' + xaz'x2 + a;4'x2a;i
T = Xa'X3 + Xs'Xi'Xi' + X^Xz'Xi + Xi'XiXx
"or" (non-exclusive) and multiplication signifies
addition stands for
"and." This expression can be interpreted as a Boolean Algebra expres-
sion and the Boolean Algebra theorems used to simplify it. In particular
it can be "multiplied out":
(B + C) (D + E) = BD + BE + CD + CE
This form is equivalent to the statement that columns 0 and 3 require
that any consistent row set must contain either rows B and D, or rows
B and E, or rows C and D, or rows C and E.
The complete requirements for a consistent row set can be obtained
directly by providing a factor for each column of the table. Thus for
Table XII the requirements for a consistent row set can be written as:
(B + C)(D + E)(A + B)(A)(A)(A + D)(C)(F)(E + F)
By using the theorems that A-(A + D) = A and A- A = A, this can
be simplified to ACF(D + E). Thus the two consistent row sets for this
table are A, C, F, D and A, C, F, E and since they both contain the
same number of rows, they both represent minimum sums. This is true
only because rows D and E contain the same number of crosses. In
general, each row should be assigned a weight w = n — \og,2k, where
n is the number of variables in the transmission being considered and
MINIMIZATION OF BOOLEAN FUNCTIONS
1439
Table XIII — Determination of the Minimum Sums for the
Prime Implicant Table of Table VII by Means of
THE Boolean Representation
(a) Boolean representation of the Prime Implicant Table of Table VI
(A+B) (A+C) (B+D) (C+E) (D+F) (G) (E+F+H) (G+I) (H+J) (1+ J)
(b) The expression of (a) after multiplying out. (The terms in italic
correspond to minimum sums)
ADEJG + ACDFJG + ACDHJG + ADEHIG + ACDHIG + ABEFJG
+ ABEFHIG + BCDEJG + BCDHJG + BCDHIG + BCFJG + BCFHIG
-G-
A
(c) Tree circuit equivalent of (b)
J
B E---F-
---D
■--H-
--H-
--I
--J
--I
--J
-E---
-B---
-C
D-
-_F
---H
---J
"1
---E
---H
--I
--I
--J
---H 1
---J
5
6
5
5
5
5
4 V
5
5
5
5
4 V
k is the number of crosses in the row.* To select the minimum sums, the
sum of the weights of the rows should be calculated for each row set
containing the fewest rows. The row sets having the smallest total weight
correspond to minimum sums. If, instead of the minimum sum, the form
leading to the two-stage diode-logic circuit requiring fewest diodes is
desired, a slightly different procedure is appropriate. To each row set
is assigned a total weight equal to the sum of the weights of the rows
plus the number of rows in the set. The desired form then corresponds to
the row set having the smallest total weight.
The procedure for an arbitrary table is analogous. A more compli-
cated example is given in Table XIII. In this example the additional
* n-log2 k is the number of literals in the prime implicant coriesponding to
a row containing k crosses.
1440 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
theorem (A + B)(A + C) = (A + BC) is useful. This example shows
that for a general table the expressions described in this Section and
the multipHcation process can become very lengthy. However, this pro-
cedure is entirely systematic and may be suitable for mechanization.
Since the product of factors representation of a prime implicant
table is a Boolean expression, it can be interpreted as the transmission
of a contact network. Each consistent row set then corresponds to a
path through this equivalent network. By sketching the network directly
from the product of factors expression, it is possible to avoid the multi-
plication process. In particular the network should be sketched in the
form of a tree, as in Table XIII (c) and the Boolean Algebra theorems
used to simplify it as it is being drawn. For hand calculations, this
method is sometimes easier than direct multiplication.
I
10 d-TERMS
In Section 1 the possibility of having rf-entries in a table of combina-
tions was mentioned. Whenever there are combinations of the relay
conditions for which the transmission is not specified, f/-entries are placed
in the T-column of the corresponding rows of the table of combinations.
Table XIV — Determination of the Minimum
Sum for the Transmission
T = X)(5, 6, 13) + f/(9, 14) Where 9 and 14 are the cI-Terms,
(d)
(a) Determination of Prime Implicants
Xi Xs X2X1
5 0 1 0 1 V
6 0 1 1 0 V
9 1 0 0 1 V
5 13
6 14
9 13
13 1 1 0 1 V
(d) 14 1 1 1 0 V
(b) Prime Implicant Table
5 6 13
*
X
X
*
X
X
X4X3 ^"2X1
- 1 0 1
- 1 1 0
1-01
(c)
Basis rows: (5, 13), (6, 14)
(d)
T = XaXi'xi + Tso-oa-i'
MINIMIZATION OF BOOLEAN FUNCTIONS 1441
The actual values (0 or 1) of these d-entries are chosen so as to simplify
the form of the transmission. This section will describe how to modify
the method for obtaining a minimum sum when the table of combina-
|{ tions contains rf-entries.
The p-terms which correspond to rf-entries in the table of combinations
will be called d-terms. These d-terms should be included in the list of
p-terms which are used to form the prime implicants. See Table XIV.
However, in forming the prime implicant table, columns corresponding
to the d-terms should not be included. Table XlV(b). The d-terms are
used in forming the prime implicants in order to obtain prime impli-
cants containing the fewest possible literals. If columns corresponding
to the f/-terms were included in forming the prime implicant table this
would correspond to setting all the rf-entries in the table of combina-
tions equal to 1. This does not necessarily lead to the simplest minimum
sum. In the procedure just described, the rf-entries will automatically be
set equal to either 0 or 1 so as to produce the simplest minimum sum.
For the transmission of Table XIV the 14 d-entry has been set eciual to
I and the 9 c^-entry has been set equal to 0.
II NON-CANONICAL SPECIFICATIONS
A transmission is sometimes specified not by a table of combinations
or a canonical expansion, but as a sum of product terms (not necessarily
prime implicants). The method described in Section 3 is applicable to
such a transmission if the appropriate table of combinations (decimal
specification) is first obtained. However, it is possible to modify the
procedure to make use of the fact that the transmission is already partly
reduced. The first step is to express the transmission in a table of binary
characters such as Table XVa. Then each pair of characters is examined
to determine whether any different character could have been formed
from the characters used in forming the characters of the pair. For
example, in Table XV (a) a (1) (00 00 1) was used in forming the
(0, 1)(0000-) character and a (3) (000 1 1) was used in forming the
(3, 7)(0 0 - 1 1) character. These can be combined to form a new char-
acter (1, 3) (000- 1). The new characters formed by this process are
listed in another column such as Table XV (b). This process is continued
until no new characters are formed.
In examining a pair of characters, it is sufficient to determine whether
there is only one position where one character has a one and the other
character has a zero. If this is true a new character is formed which has
a dash in this position and any other position in which both characters
have dashes, and has a zero (one) in any position in which either charac-
1442 THE BELL SYSTEM TECHXICAL JOURNAL, NOVEMBER 1956
Table XV — Determination of the Prime Implicants for the
Transmission of Table XV Specified as a
Sum of Product Terms
(a) Specification
(b) Characters Derived from (a)
Xa Z4 Z3a;2 a:i
a;5 X4 3:3 a;2 a^i
0 1 0 0 0 0 - v/
0 2 0 0 0 - 0 V
3 7 0 0-11
14 15 0 111-
22 23 10 11-
29 31 111-1
1 3 0 0 0 - 1 V
2 3 0 0 0 1 - V
7 15 0 - 1 1 1 V
7 23 - 0 1 1 1 V
15 31 - 1 1 1 1 x/
23 31 1 - 1 1 1 \'
(c) Characters De
ivcd from (a) and (b)
XiX^XzX-iXi
0 12 3
7 15 23 31
0 0 0 - -
- - 1 1 1
ter has a zero (one). In Table X\'a the (0, 1) character has a zero in the
.r2-position while the (3, 7) character has a one in the .ro-position. A new
character is fornied (1, 3) which has a dash in ihe .<-2-p()sition.
This rule for constructing new characters is actually a generalization
of the rule used in Section 3 and corresponds to the theorem.
.ri.r2 + .r/.rii = XiX-s + .ri'.r;5 + .r2.r3 .
Repeated application of this rule will lead to the complete set of prime
implicants. As described in Section 3, any character which has all of the
numbers of its decimal label appearing in the label of another character
should be checked. The unchecked characters then represent the prime
implicants. The process described in this section was discussed fi'om a
slightly different point of view by Quine.^
12 summary and conclusions
In this paper a method has been presented for writing any transmis-
sion as a minimum sum. This method is similar to that of Quine; how-
ever, several significant improvements have been made. The notation
has been simplified by using the symbols 0, 1 and - instead of primed
and unprimed variables. While it is not completeh^ new in itself, this
notation is especially appropriate for the arrangement of terms used in
determining the prime implicants. Listing the terms in a column which
is partitioned so as to place terms containing the same number of 1 's in
the same partition reduces materially the labor involved in determining
the prime implicants. Such a list retains some of the advantage of the
arrangement of squares in the Karnaugh Chart without reciuiring a
geometrical representation of an n-dimensional hj^percube. Since the
MINIMIZATION OF BOOLEAN FUNCTIONS 1443
l)i-ocodure for determining the i)rinie iniplicants is completely systematic
it is capable of being programmed on a digital computer. The arrange-
ment of terms introduced here then results in a considerable saving in
both time and storage space over previous methods, making it possible
to solve larger problems on a given computer. It should be pointed out
that this procedure can be programmed on a decimal machine by using
the decimal labels instead of the binary characters introduced.
A method was presented for choosing the minimum sum terms from
the list of prime iniplicants by means of a table of prime implicants.
This is again similar to a method presented l:)y Quine. Howe\'er, Quine
did not give any systematic procedure for handling cyclic prime impli-
cant tables; that is, tables with more than one cross in each column. In
this paper a procedure is given for obtaining a minimum sum from a
cyclic prime implicant table. In general, this procedure requires enumera-
tion of several possible minimum sums. If a transmission has any non-
trivial group invariances it may be possible to avoid enumeration or to
reduce considerably^ the amount of enumeration necessary. A method
for doing this is given.
The process of enumeration used for selecting the terms of the mini-
mum sum from a cyclic prime implicant table is not completely satis-
factory since it can be quite lengthy. In seeking a procedure which does
not require enumeration, the method involving the group invariances of
a transmission was discovered. This method is an improvement over
complete enumeration, but still has two shortcomings. There are trans-
missions which have no nontrivial group invariances but which give
rise to cyclic prime implicant tables. For such transmissions it is still
necessary to resort to enumeration. Other transmissions which do possess
nontrivial group invariances still reciuire enumeration after the in-
variances have been used to simplify the process of selecting minimum
sum terms. More research is necessary to determine some procedure
which will not require any enumeration for cyclic prime implicant
tables. Perhaps the concept of group invariance can be generalized so
as to apply to all transmissions which result in cyclic prime implicant
tables.
13 ACKNOW'LEDGEMENTS
The author wishes to acknowledge his indebtedness to Professor S. H.
Caldwell, Professor D. A. Huffman, Professor W. K. Linvill, and S. H.
Unger with whom the author had many stimulating discussions. Thanks
are due also to W. J. Cadden, C. Y. Lee, and G. H. Mealy for their
helpful comments on the preparation of this paper.
1444 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
This research was supported in part by the Signal Corps; the Office
of Scientific Research, Air Research and Development Command; and
the Office of Naval Research.
BIBLIOGRAPHY
1. Karnaugh, M., The Map Method for Synthesis of Combinational Logic Cir-
cuits, Trans. A.I.E.E., 72, Part I pp. 593-598, 1953.
2. Keister, W., Ritchie, A. E., Washburn, S., The Design of Switching Circuits,
New York, D. Van Nostrand Company, Inc., 1951.
3. Shannon, C. E., A Sj^mbolic Analysis of Relay and Switching Circuits, Trans.
A.I.E.E., 57, pp. 713-723, 1938.
4. Shannon, C. E., The Synthesis of Two-Terminal Switching Circuits, B. S.T.J. ,
28, pp. 59-98, 1949.
5. Staff of the Harvard Computation Laboratory, Synthesis of Electronic Com-
puting and Control Circuits, Cambridge, Mass., 1951, Harvard University
Press.
6. Quine, W. V., The Problem of Simplifying Truth Functions, The American
Mathematical Monthly, 59, No. 8, pp." 521-531, Oct., 1952.
7. Quine, W. V., A Wav fo Simplify Truth Functions, The American Mathe-
matical Monthly, 62, pp. 627-631, Nov., 1955.
Detection of Group Invariance or Total
Symmetry of a Boolean Function*
By E. J. McCLUSKEY, Jr.
(Manuscript received June 26, 1956)
A method is presented for determining whether a Boolean function pos-
sesses any group invariance; that is, whether there are any permutations or
primings of the independent variables which leave the function unchanged.
This method is then extended to the detection of functions which are totally
symmetric.
1 GROUP INVARIANCE
For some Boolean transmission functions (transmissions, for short) it
is possible to permute the variables, or prime some of the variables, or
both permute and prime variables without changing the transmission.
The following material presents a method for determining, for any given
transmission, which of these operations (if any) can be carried out with-
out changing the transmission.
The permutation operations will be represented symbolically as fol-
lows:
Si2z...nT will represent the transmission T with no variables permuted
8213.. -nT will represent the transmission T with the xi and X2 variables
interchanged, etc.
Thus *Si432T(.x-i , X2 , xs , X4) = T(xi , Xi , Xs , X2')
The symbolic notation for the priming operation will be as follows:
Noooo-.-oT will represent the transmission T with no variables primed
A^ono. --oT will represent the transmission T with the .r2 and ;i;3 variables
primed, etc.
Thus NiowT(xi , :r2 , X3 , Xa) = T(xi, X2 , Xs, Xi).
The notation for the priming operator can be shortened by replacing
the binary subscript on N by its decimal equivalent. Thus N9T is equiv-
* This paper is derived from a thesis submitted to the Massachusetts Institute
of Technology in partial fulfillment of the requirements for the degree of Doctor
of Science on April 30, 1956.
1445 .
144G THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Table I — Transmission Matrices Showing Effect of
Interchanging or Priming Variables
(a) Tr
ansmission IVIatrix
(b) Transmission jNIatrix
with a-3 and x^ columns
interchanged
(c) Transmission Ma-
trix with entries of the
x% and Xi cokimns
primed
0
1
2
9
10
11
Xi X% Xz Xi
0 0 0 0
0 0 0 1
0 0 10
10 0 1
10 10
10 11
0
2
1
10
9
11
X\ Xi Xi Xz
0 0 0 0
0 0 10
0 0 0 1
10 10
10 0 1
10 11
3
2
1
10
9
8
X\ X2 Xz' Xi'
0 0 11
0 0 10
0 0 0 1
10 10
10 0 1
10 0 0
alent to NwoiT. The permutation and priming operators can be combined.
For example,
S2mN3T(xi , X2 , xs , Xi) = T{x2 , Xi , x^, Xi)
The symbols SiNj form a mathematical group, ^ hence the term group
invariance.
The problem considered here is that of determining which A^,- and Sj
satisfy the relation NiS/F = T for a given transmission T. Since there
are only a finite number of different Ni and Sj operators it is possible in
principle to compute NiSjT for all possible NiSj and then select those
NiSj for which NiSjJ' = T. If T is a function of n variables, there are
n! possible Sj operators and 2" .V, operators so that there are n!2" pos-
sible combinations of N'iSj . Actually, if NiSjT = T then NiT must
equal SjT''^^ so that it is only necessary to compute all NiT and all Sj7\
For /I = 4, n! = 24 and 2" = 16 so that the number of possibilities to
be considered is quite large even for functions of only four variables. It
is possible to avoid enumerating all NiT and SjT by taking into account
certain characteristics of the transmission being considered.
The first step in determining the group invariances of a transmission
is the same as that foi finding the prime implicants.* The binary equiva-
lents of the decimal numbers which specify the transmission are listed
as in Table 1(a). This list of binary numbers will be called the transmis-
sion matrix. When two variables are interchanged, the corresponding
columns of the transmission matrix are also interchanged, Table 1(b).
When a variable is primed, the entries in the corresponding column of
the transmission matrix are also primed, 0 replaced by 1 and 1 replaced
by 0, Table 1(c).
If an NiSj operation leaves a transmission unchanged then the cor-
* Minimization of Boolean Functions, see page 1417 of this issue.
GROUP INVAKIANCE OR TOTAL SYMMETRY
1447
responding matrix operations will not change the transmission matrix
aside from possibly reordering the rows. In other words, it should b^
possible to reorder the rows of the modified transmission matrix to re-
gain the original transmission matrix. The matrices of Table 1(a) and
(b) are identical except for the interchange of the 1 and 2 and the 9
and 10 rows. It is not possible to make the matrix of Table 1(c) identical
with that of Table 1(a) by reordering rows; therefore the operation of
priming the x^ and .r4 variables does not leave the transmission T =
J] (0, 1, 2, 9, 10, 11) michanged.
If interchanging two columns of a matrix does not change the matrix
aside from rearranging the rows, then the columns which were inter-
changed must both contain the same number of I's (and O's). This must
Table II — Partitioning of the Standard Matrix for
2^ = Z (4, 5, 7, 8, 9, 11, 30, 33, 49)
(a) Transmission Matrix
Xi
X2
Xs
Xi
Xi
X6
4
0
0
0
1
0
0
8
0
0
1
0
0
0
5
0
0
0
1
0
1
9
0
0
1
0
0
1
33
1
0
0
0
0
1
7
0
0
0
1
1
1
11
0
0
1
0
1
1
49
1
1
0
0
0
1
30
0
1
1
1
1
0
Number of O's
7
7
5
5
6
3
Number of I's
2
2
4
4
3
6
(b) Standard Matrix for (a) Matrix
Weight
1
1
1
Xi
Xi
Xs
Xi
Xs
xe'
4
0
0
0
1
0
0
8
0
0
1
0
0
0
32
1
0
0
0
0
0
5
0
0
0
1
0
1
6
0
0
0
1
1
0
9
0
0
1
0
0
1
10
0
0
1
0
1
0
48
1
1
0
0
0
0
31
0
1
1
1
1
1
7
7
5
5
6
6
2
2
4
4
3
3
2
2
2
2
2
(c) Second Partitioning of
rows for (b) matrix
(d) Final Partitioning
for (b) matrix
Xi Xi
0 0
0 0
a-3 Xi
0 1
1 0
Xi xe'
0 0
0 0
X\
0
0
X2
0
0
Xz Xi
0 1
1 0
Xi Xe'
0 0
0 0
1 0
0 0
0 0
1
0
0
0
0
1
0
0
0 0
0 0
oooo
oooo
0 1
0 1
1 0
1 0
0 1
1 0
0 1
1 0
0
0
0
0
1
1
0 1
0 1
1 0
1 0
0 1
1 0
0 1
1 0
1 1
0 0
0 0
0 0
0 0
0 1
1 1
1 1
1 1
1 1
1448 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
be true since rearranging the rows of a matrix does not change the total
jiumber of I's in each column. Similarly, if priming some columns of a
matrix leaves the rows unchanged, either each column must have an
equal number of I's and O's or else for each primed column which has an
unequal number of O's and I's there must be a second primed column
which has as many I's as the first primed column has O's and vice versa.
Such pairs of columns must also be interchanged to keep the total num-
ber of I's in each column invariant. For the matrix of Table 11(a) the
only operations that need be considered are either interchanging xi and
X2 or Xz and Xt or priming and interchanging x^ and .re .
For the present it will be assumed that no columns of the matrix have
an equal number of O's and I's. It is possible to determine all permuting
and priming operations which leave such a matrix unchanged by con-
sidering only permutation operations on a related matrix. This related
matrix, called the standard matrix, is formed by priming all the columns
of the original matrix which have more I's than O's, the Xq column in the
matrix of Table 11(a). Each column of a standard matrix must contain
more O's than I's, Table 11(b). The NiSj operations which leave the
original matrix unchanged can be determined directly from the oper-
ations that leave the corresponding standard matrix unchanged. It is
therefore only necessary to consider standard matrices.
Since no columns of a standard matrix have an equal number of I's
and O's and no columns have more I's than O's it is only necessary to
consider permuting operations. The number of I's in a column (or row)
will be called the weight of the column (or row). Only columns or rows
which have the same weights can be interchanged. The matrix should
be partitioned so that all columns (or rows) in the same partition have
the same weight. Table 11(b). It is now possible to interchange columns
in the same column partition and check whether pairs of rows from the
same row partition can then be interchanged to regain the original
matrix. This can usually be done by inspection. For example, in Table
11(b) if columns .r4 and .r3 are interchanged, then interchanging rows 4
and 8, 5 and 9, and 6 and 10 will regain the original matrix.
The process of inspection can be simplified by carrying the partition-
ing further. In the matrix of Table 11(b), row 32 cannot be interchanged
with either row 8 or row 4. This is because it is not possible to make
row 32 identical with either row 8 or row 4 by interchanging columns .ti
and X2 . Row 32 has weight 1 in these columns while rows 8 and 14 both
have weight 0. In general, only rows which have the same weight in each
submatrix can be interchanged. Permuting columns of the same partition
does not change the weight of the rows in the corresponding submatrices.
GROUP INVAUIANCE OU TOTAL SYMMETRY
1449
The matrix can therefore be further partitioned by separating the rows
into groups of rows which have the same weight in every cokmin parti-
lion, Table 11(c). Similar remarks hold for the columns so that it may
then be necessary to partition the columns again so that each column in
a partition has the same weight in each submatrix, Table 11 (d). Par-
titioning the columns may make it necessary to again partition the
rows, which in turn may make more column partitioning necessary. This
process should l)e carried out until a matrix results in which each row
(column) of each submatrix has the same weight. Inspection is then
used to determine which row and column permutations will leave the
matrix unchangetl. Only permutations among rows or columns in the
same partition need be considered.
From the matrix of Table 11(d) it can be seen that permuting either
columns .r^ and .r4 or columns x^ and x^' will not change the matrix aside
from reordering certain rows. This means that interchanging .T3 and X4
or priming and interchanging X5 and x^ in the original transmission will
leave the transmission unchanged. Interchanging x^ and .T5 means re-
placing X5 by xt and x^ by x^,' which is the same as interchanging x^ and
x% and then priming both Xi, and Xq . Thus for the transmission of Table
II 0124356-Z = T and A* 000011*^123465-^ = N^Sus^ebT = T.
A procedure has been presented for determining the group invariance
of any transmission matrix which does not have an equal number of I's
and O's in any column. This must now be extended to matrices which do
have equal numbers of O's and I's in some columns, Table Ill(a). For
such matrices the procedure is to prime appropriate columns so that
there are either more O's than I's or the same number of O's and I's in
each column, Tal)le Ill(a). This matrix is then partitioned as described
above and the permutations which leave the matrix unchanged are de-
termined. The matrix of Table Ill(a) is so partitioned. Interchanging
Table III — Transmission Matrices
FOR T
=
Z (0, 6, 9, 12)
(a) Transniission Matrix
(b) Tr
with
ansmission Matrix
Xi and X2 primed
0
Xi X2
0 0
Xz Xi
0 0
0
10
5
12
Xi'X2'
0 0
Xz Xi
0 0
6
9
0 1
1 0
1 0
0 1
1 0
0 1
1 0
0 1
12
1 1
0 0
1 1
0 0
Number of O's
Number of I's
2 2
2 2
3 3
1 1
2 2
2 2
3 3
1 1
1450 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
both xi and X2 , and .T3 and Xi leave this matrix unchanged so that
^21437" = T. The possibiHty of priming different combinations of the
columns which have an equal number of O's and I's must now be con-
sidered. Certain of the possible combinations can be excluded before-
hand. In Table III (a) the only possibility which must be considered is
that of priming both xi and X2 . If only xi or X2 is primed, there will be
no row which has all zeros. No permutation of the columns of this
matrix (with Xi or .1-2 primed) can produce a row with all zeros. Therefore
this matrix cannot possibly be made equal to the original matrix by re-
arranging rows and columns. Priming both Xi and X2 must be considered
since the 12-row will be converted into a row with all zeros. The opera-
tion of priming .Ti and X2 is written symbolical!}^ as A^ioo = A''i2 . In
general, if the matrix has a row consisting of all zeros, only those Ni
operations for which i is the number of some row in the matrix, need be
considered. If the row does not have an all-zero row, only those A'', for
which i is not the number of some row need be considered. Similarly, if
the matrix has a row consisting of all I's, only those A\- for which there
is some row of the matrix which will be convei'ted into an all-one row%
need be considered. This is equivalent to considering only those Ni for
which some row has a number /c = 2" — 1 — t* where n is the number
of columns. If the matrix does not have an all-one row, only those A^, for
which no row has a number A: = 2" — 1 — i should be considered.
Each priming operation which is not excluded by these rules is applied
to the transmission matrix. The matrices so formed are then partitioned
as described previously. Any of these matrices that have the same par-
titioning as the original matrix are then inspected to see if any row and
column permutations will convert them to the original matrix. For the
matrix of Table III (a) the operation of priming both Xi and X2 was not
excluded. The matrix which results when these columns are primed is
shown in Table Ill(b). Inspection of this figure shows that interchange
of either Xs and .T4 or Xi and X2 will convert the matrix back to the
matrix of Table III (a). Therefore, for the transmission of this table
SuizNimT = T and S2i3iNnmT = T.
2 TOTAL SYMMETRY
There are certain transmissions whose value depends not on which
relays are operated but only on how many relays are operated. For
* The number of the row which has all ones is 2" — 1 . If Ni operating on some
row, k, is to produce the all-one row, i must have I's wherever k has O's and vice
versa. This means that
i + k = 2"" - 1 or A; = 2" - 1 - i.
GROUP ixvakiaxcf: or total symmetry 1451
Table IV — Transmission Matrix for
T = S (3, 5, 6, 7) = S2,z(xi , X2 , .1-3)
X3 X2 Xi
3 Oil
5 10 1
6 110
7 111
example, the transmission of Table IV equals 1 whenever two or
three relays are operated. For such transmissions any permutation of
the variables leaves the transmission unchanged. These transmissions
are called totally symmetric. They are usually written in the form,
T = Soi , a«---a„X^i , X2 , ••• Xn), whcrc thc transmission is to equal
1 only ^^•ilen exactly ai or a-z or • • • or Um of the variables Xi , x^ • ■ • Xn
are equal to one. The transmission of Table IV can be written as
'S2,3(.i"i , x<i , Xz). This definition of symmetric transmissions can be gen-
eralized by allowing some of the variables {xi , X2 , ■ ■ • .r„) to be primed.
Thus the transmission S^ixi , X2 , Xz) will equal 1 only when Xi = X2 =
X:i = 1 or 0^1 = x-i = 1 and X2 = 0. It is useful to know when a trans-
mission is totally symmetric since special design techniques exist for
such functions.'*
It is possible to determine whether a transmission is totally symmetric
from its matrix. Unless all columns of the standard matrix derived from
the transmission matrix have the same weight, the transmission cannot
possibly be totally symmetric. If all columns do have equal weights, the
rows should be partitioned into groups of rows which all have the same
weight. Whether the transmission is totally symmetric can now be de-
termined by inspection. If there is a row of weight k; that is, a row which
contains k I's, then every possible row of weight k must also be included
in the matrix. This means that there must be nCk rows of weight k where
71 is the number of columns (variables).* If any possible row of weight k
was not included then the corresponding k literals could be set equal to
1 without the transmission being equal to 1. This contradicts the defi-
nition of a totally symmetric transmission. In Table V(b) there are 4
rows of weight 1 and 1 row of weight 4. Since 4C1 = 4 and 4C4 = 1 this
transmission is totally symmetric and can be written as Si,i(xi , X2', Xz ,
Xi). The number of rows of weight 1 in Table V(d) is 2 and since iCi = 4
this transmission is not totally symmetric.
A difficulty arises if all columns of a transmission matrix contain equal
* nCk is the binomial coefficient -. " ,, ,
(n — K)\li\
1452 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Table V — • Determination of Totally Symmetric Transmission
(a) Transmission Matrix for
T=T.{h 4, 7, 10, 13)
1
4
10
7
13
Number of O's
Number of I's
Xi Xi Xz Xi
0 0 0 1
0 10 0
10 10
0 111
110 1
3 2 3 2
2 3 2 3
(c) Transmission Matrix for
T = X(3,5, 10, 12, 13)
Xl
X2
^3
3-4
3
0
0
1
1
5
0
1
0
1
10
1
0
1
0
12
1
1
0
0
13
Number of O's
Number of I's
110 1
2 2 3 2
3 3 2 3
(b) Standard Matrix for
r = X (1> 4, 7, 10, 13)
showing that
T = Si, 4 {Xi , X-i , Z3 , x/)
1
Xl
0
X2
0
XsZ
0
- 4
1
2
0
0
1
0
4
0
1
0
0
8
1
0
0
0
15
1
1
1
1
3
3
3
3
2
2
2
2
(d) Standard Matrix for
T =
V (3, 5, 10, 12, 13)
showing
that it is not
totally symmetric
Xl'
X2'
X3 Xi'
0
0
0
0
0
1
0
0
0
1
8
1
0
0
0
7
0
1
1
1
14
1
1
1
0
3
3
3
3
2
2
2
2
Table VI — Determination of Total Symmetry for
^ = Z (0, 3, 5, 10, 12, 15)
(a) Transmission Matrix
for T{xi , X2
, 3-3 , Xi)
Xl X2 Xs
2-4
0
0 0 0
0
3
0 0 1
1
5
0 1 0
1
10
1 0 1
0
12
1 1 0
0
15
1 1 1
1
Number of O's
3 3 3
3
Number of I's
3 3 3
3
(b) Standard Matrix
for Til, X2 ,
Xz , Xi)
Xi Xz Xi
1 0 0
0 1 0
0 0 1
Number of O's
2 2 2
Number of I's
1 1 1
T{1, X2 , Xz , Xi) = SiiXi', Xz', Xi)
(c) Standard Matrix for T(0, x^ , Xz , Xi)
X2 Xz Xi'
0
0
1
0
1
0
1
0
0
Number of O's
2
2
2
Number of I's
1
1
1
T{0, X2 , Xz , Xi) = Sl{X2 , Xz , Xi') = ^2(^2', Xz', Xi)
GROUP INVARIANCE OR TOTAL SYMMETRY 1453
numbers of zeros and ones as in Table VI (a). For such a matrix it is not
clear which variables should be primed. It is possible to avoid considering
all possible primings by "expanding" the transmission about one of the
variables by means of the theorem
T{xi ,x.2, ■■■ Xn) = XiT{l, X,, ■■■ x„) + x,'T(0, x., , ■ ■ ■ XnY-'
and then making use of the relation:
*^ai 1 a-> 1 ' ' ' amv^'l ) •^''' ) " * ' "^n)
= Xik!)ai_i , a-z—l ) ao— 1 > ' ' ' a„— IV-^'s j ' ' ' X^J
4- XiSa^ , a-, , •••<!„ ^'2 , • ■ • Xn)^
This technique is illustrated in Table \1. The standard matrix for
^(l, Xo , Xz , .T4) has three rows each containing a single one so that
7X1, X2 , Xi , X4) = Siix2, X3, Xi)
The transmission 7'(0, X2 , Xs , Xi) has an identical standard matrix so
that
i (0, X2 , X3 , Xa) = 01 (.T2 , Xz , X\)
This can be written in terms of Xt\ x/, and Xi :
Sl{X2 , X3 , Xi) = S2iX2, Xs, Xi^.
Finally
T{Xi , X2 , X3 , Xi) = XiT{\, X2 , X; , Xi) + XiT{0, X2 , Xz , Xi)
= XiSi{X2, Xi, Xi) + XiS2{X2, Xz, Xi) = S2{Xi , X2, Xs, Xi).*
The method just presented for detecting total symmetry is more sys-
tematic than the only other available method'' and applies for transmis-
sions of any number of variables.
BIBLIOGRAPHY
1. Birkhoff, G., and MacLane, S., A Survej' of Modern Algebra, The MacMillan
Company, New York.
2. Shannon, C. E., The Synthesis of Two-Terminal Switching Circuits, B. S.T.J. ,
28, pp. 59-98, 1949.
3. Shannon, C. E., A Symbolic Analysis of Relay and Switching Circuits, Trans.
A.I.E.E., 57, pp. 713-723, 1938.
4. Keister, W., Ritchie, A. E., Washburn, S., The Design of Switching Circuits,
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Circuits, Trans. A.I.E.E., 73, Part I, pp. 142-146, 1954.
* This technique for transmission matricies having an equal number of zeros
and ones in all columns was brought to the author's attention bj' Wayne Kellner,
a student at the Massachusetts Institute of Technologj'.
Bell System Technical Papers Not
Published in This Jovirnal
Anderson, O. L.^
Effect of Pressure on Glass Structure, J. Appl. Phys., 27, pp. 943-949,
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Ordering and Antiferromagnetism in Ferrites, Phys. Rev., 102, pp.
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Filamentary Growths of Metals at Elevated Temperatures, J. Appl.
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Bridgers, H. E.^
The Formation of P N Junctions in Semiconductors by the Variation
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Magnetic Properties of Some Orthoferrites and Cyanides at Low
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Chase, F. H.^
Power Regulation by Semiconductors, Else. Engg., 75, pp. 818-822,
Sept., 1956.
Chen, W. H., see Lee, C. Y.
Bell Telephone Laboratories, Inc.
1454
TECHNICAL PAPERS 1455
Chynoweth, a. G.^
Spontaneous Polarization of Guanidine Aluminum Sulfate Hexa-
hydrate at Low Temperatures, Phys. Rev., 102, pp. 1021-1023, May
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Cook, R. K.^ and Wasilik, J. H.^
Anelasticity and Dielectric Loss of Quartz, J. Appl. Phys., 27, pp.
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Darrow, K. K,^
Electron Physics in America, Physics Today, 9, pp. 23-27, Aug., 1956
David, E. E., Jr.i
Naturalness and Distortion in Speech Processing Devices, J. Acous.
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David, E. E., Jr.,^ and McDonald, H. S.^
A Bit-Squeezing Technique Applied to Speech Signals, I.R.E. Con-
vention Record, 4, Part 4, pp. 118-153, July, 1956.
Dewald, J. F.^ and Lepoutre, G.^
I — The Thermoelectric Properties of Metal-Ammonia. II — The
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Embree, M. L.,^ and Williams, D. E.^
An Automatic Card Punching Transistor Test Set, Proc. 1956 Elec-
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Feher, G.^
Method of Polarizing Nuclei in Paramagnetic Substances, Phys.
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^ Bell Telephone Laboratories, Inc.
145G THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Feher, G.,^ and Gere, E.^
Polarization of Phosphorus Nuclei in Silicon, Phys. Rev., Letter to
the Editor, 103, pp. 501-503, July 15, 1956.
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563-568, July 10, 1956.
Gere, E., see Feher, G.
Gianola, U. F.,^ and James, D. B.'
Ferromagnetic Coupling Between Crossed Coils, J. Appl. Phys., 27»
pp. 608-609, June, 1956.
Gilbert, E. N.^
Enumeration of Labelled Graphs, Canadian J. of Math., 8, pp. 405-
•411, 1956.
Gohn, G. R.^
Fatigue and Its Relation to the Mechanical and Metallurgical Proper-
ties of Metals, SAE Trans., 64, pp. 31-40, 1956.
Gohn, G. R.,^ Freynik, H S.,* and Guerard, J. P.^
The Mechanical Properties of Wrought Phosphor Bronze Alloys,
A.S.T.M. Special Tech. Pub., STP 183, pp. 1-114, Jan., 1956.
Guerard, J. P., see Gohn G. R.
H ANN AY, N. B.^
Recent Advances in Silicon — -Progress in Semiconductors, Book, 1,
pp. 1-35, 1956. (Published by Heywood & Co., Ltd., London)
' Bell Telephone Laboratories, Inc.
* Riverside Metal Co., Div., H. K. Porter Co., Inc., Riverside, N. J.
TECHNICAL PAPERS 1457
IToLDEN, A. N.,* Matthias, B. T./ Anderson, P. W.,' and Lewis,
H. W.i
New Low-Temperature Ferromagnets, Phys. Rev., 102, p. 1463, June
15, 195G.
Huntley, H. R.^
The Present and Future of Telephone Transmission, Elec. Engg.,
75, pp. G8G-G92, Aug., 195G.
James, D. B., see Gianola, U. F.
Jones, H. L.^
A Blend of Operations Research and Quality Control in Balancing
Loads on Telephone Equipment, Trans. Am. Soe. Quality Control
(195G Montreal Convention).
Kaminow, L p., see Kircher, R. J.
KiRCHER, R. J.^ and Kaminow, L P.^
Super-Regenerative Transistor Oscillator, Electronics, 29, pp. 1G6-
167, July, 1956.
Kretzmer, E. R.^
Reduced-Alphabet Representation of TV Signals, LR.E. Convention
Recortl, 4, Part 4, pp. 140-147, 1956.
KooNCE, S. Eloise, see Arnold, S. M.
Lee, C. Y.,1 and Chen, W. H."
Several-Valued Combinational Switching Circuits, Commun. and
Electronics, 25, pp. 278-283, July, 1956.
LePoutre, G., see Dewald, J. F.
Lewis, H. W.^
Two-Fluid Model of an "Energy-Gap" Superconductor, Phys. Rev.,
102, pp. 1508-1511, June 15, 1956.
Lewis, P. W., see Holden, A. N,
^ Bell Telephone Laboratories, Inc.
2 American Telephone and Telegraph Company.
* Universit.y of Florida, Gainesville, Fla.
9 Illinois Bell Telephone Company, Chicago, 111.
1458 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Manley, J. M.,1 and Rowe, H. E.^
Some General Properties of Non-Linear Elements. Part 1 — Gen-
eral Energy Relations, Proc. I.R.E., 44, pp. 904-913, July, 1956.
Matthias, B. T., see Holden, A. N.; Wood, E. A.
Maxwell, J. L.,^ and Farrar, H. K.^
Automatic Dispatch System for Teletypewriter Lines, Elec. Engg.,
75, p. 705, Aug., 1956.
McDonald, H. S., see David E. E.
McClean, D. A.i and Power, F. S.^
Tantalum Solid Electrolytic Capacitors, Proc. I.R.E., 44, pp. 872-
878, July, 1956.
McMahon, W.i
Dielectric Effects Produced by Solidifying Certain Organic Compounds
in Electric or Magnetic Fields, J. Am. Chem. See, 78, pp. 3290-3294,
July 20, 1956.
Merz, W. J.i
Effect of Hydrostatic Pressure on the Hysteresis Loop of Guanidine
Aluminum Sulfate Hexahydrate, Phys. Rev., 103, pp. 565-566, Aug.
1, 1956.
Merz, W. J.^
Switching Time in Ferroelectric BaTiO^ and Its Dependence on
Crystal Thickness, J. Appl. Phys., 27, pp. 938-943, Aug. 1, 1956.
Nelson, L. S.^
Windowed Dewar Vessels for Use at Low Temperatures, Rev. Sci.
Instr., 27, pp. 655-656, Aug., 1956.
NoYES, J. W.,^ Gaudet, G.,^ and Bonneville, S.^
Development of Transcontinental Communications in Canada, Com-
mun. and Electronics, 25, pp. 342-352, July, 1956.
1 Bell Telephone Laboratories, Inc.
^ Bell Telephone Company of Canada, Ltd., Montreal, Que., Canada.
^ Pacific Telephone and Telegraph Co., San Francisco, Calif.
TECHNICAL PAPERS 1459
PiLLioD, J. J.-
Clinton R. Hanna 1955 Lamme Medalist — History of the Metal,
i Elec. Engg., 75, p. 706, Aug., 1956.
Power, F. S., see McLean, D. A.
Prince, IM. B., see Veloric, H. S.
RiNEY, T. D.i
On the Coefficients in Asymptotic Factorial Expansions, Proc. of Am.
Math. Soc, 7, pp. 245-249, Apr., 1956.
RowE, H. E., see Manley, J. M.
SlIULMAN, R. G.^
Hole Trapping in Germanium Bombarded by High-Energy Electrons,
Phys. Rev., 102, pp. 1451-1455, .June 15, 1956.
Shulman, R. G.,^ and Wyluda, B. J.'
Copper in Germanium; Recombination Center and Trapping Center,
Phys. Rev., 102, pp. 1455-1457, June 15, 1956.
Slighter, W. P.^
On the Morphology of Highly Crystalline Polyethylenes, J. Poly. Sci.,
21, pp. 141-143, July, 1956.
Tien, P. K.i
A Dip in the Minimum Noise Figure of Beam-Type Microwave
Amplifiers, Proc. I.R.E., Correspondence Sec, 44, p. 938, July, 1956.
Veloric, H. S.,i Eder, M. J.,i and Prince, M. B.^
Avalanche Breakdown in Silicon Diffused P-N Junctions as a Func-
tion of Impurity Gradient, J. Appl. Phys., 27, pp. 895-899, August,
1956.
Walsh, Dorothy E., see Bozorth, R. M.
Wasilik, J. H., see Cook, R. K.
^ Bell Telephone Laboratories, Inc.
^ American Telephone and Telegraph Company,
14G0 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 195G
Wernick, J. H.i
Determination of Diffusivities in Liquid Metals by Means of Tern
perature-Gradient Zone-Melting, J. Chem. Phys., 25, pp. 47-49
July, 1956.
Wilkinson, R. I.^
Beginnings of Switching Theory in the United States, Elec. Engg.,
75, pp. 796-802, Sept., 1956.
Williams, D. E., see Embree, M. L.
Williams, H. J., see Bozorth, R. M.
Wood, Mrs. E. A.^
Guanidinium Aluminum Sulfate Hexahydrate; Crystallographic Data,
Acta Crys., 9, pp. 618-619, July 10, 1956.
Wood, Mrs. E. A.^
The Question of a Phase Transition in Silicon, J. Phys. Chem., 60,
p. 508, 1956.
Wood, Mrs. E. A.,' and Matthias, B. T.'
Crystal Structures of NbAu and Vi^Au, Acta Crys., 9, pp. 534, June
10, 1956.
Wood, E. A., see Geller, S.
Wyluda, B. J., see Shulman, R. G.
1 Bell Telephone Laboratories Inc.
ecent Monographs of Bell System Technical
Papers Not Published in This Journal
I Albrecht, E. G., see Bullard, W. R.
Anderson, P. W.
Ordering and Antiferromagnetism in Ferrites, Monograph 2636.
Baker, W. O., see Winslow, F. H.
Bennett, W. R., see Pierce, J. R.
BOGERT, B. P.
The Vobanc — A Two-to-One Speech Bandwidth Reduction System,
Monograph 2643.
BoMMEL, H. E., Mason, W. P., and Warner, A. W.
Dislocations, Relaxations, and Anelasticity of Crystal Quartz, Mono-
graph 2618.
BoYET, H., see Weisbaum, S.
Bullard, W. R., Weppler, H. E., Albrecht, E. G., Dietz, A. E.,
Christoferson, E. W., Slothower, J. E., Ellis, H. M., Phelps, J.
W., Roach, C. L., and Treen, R. E.
Co-Ordinated Protection for Open-Wire Joint Use — Trends and
Tests, Monograph 2662.
Christoferson, E. W., see Bullard, W. R.
Chynoweth, a. G.
Spontaneous Polarization of Guanidine Aluminum Sulfate Hexa-
hydrate at Low Temperatures, Monograph 2645.
* Copies of these monographs ma_v be obtained on request to the Publication
Department, Bell Telephone Laboratories, Inc., 463 West Street, New York 14,
N. Y. The numbers of the monographs should be given in all requests.
1461
1462 the bell system technical journal, november 1956
Chynoweth, a. G.
Surface Space-Charge Layers in Barium Titanate, Monograph 2628.
Chynoweth, A. G., and McKay, K. G.
Photon Emission from Avalanche Breakdown in Silicon, Monograph'
2619.
Dacey, G. C., see Thomas, D. E.
Danielson, W. E., Rosenfeld, J. L., and Saloom, J. A.
Analysis of Beam Formation with Electron Guns of the Pierce Type,
]\Ionograph 2609.
Darlington, S.
A Survey of Network Realization Techniques, IMonograph 2620.
DiETZ, A. E., see Bullard, W. R.
Ditzenberger, J. A., see Fuller, C. S.
Dudley, H. W.
Fundamentals of Speech Synthesis, Monograph 2648.
Ellis, H. M., see Bullard, W. R.
Fuller, C. S., and Ditzenberger, J. A.
Diffusion of Donor and Acceptor Elements in SiHcon, Monograph
2651.
GiANOLA, U. F., and James, D. B.
Ferromagnetic Coupling Between Crossed Coils, Monograph 2653.
Harrower, G. a.
Auger Electrons in Energy Spectra of Secondary Electrons from Mo
and W, Monograph 2621 .
Heidenreich, R. D.
Thermionic Emission Microscopy of Metals, Monograph 2445.
HoLDEN, A. N., Merz, W. J., Remeik.\, J. P., and Matthias, B. T.
Properties of Guanidine Aluminum Sulfate Hexahydrate and Some
of Its Isomorphs, Monograph 2580.
MONOGRAPHS 1463
HuTsoN, A. E.
Effect of Water Vapor on Germanium Surface Potential, Monograph
2023.
James, D. B., see Gianola, U. F.
Kaminow, I. P., see Kircher, R. J.
IVATZ, D.
A Magnetic Amplifier Switching Matrix, Monograph 2654.
Kelly, M. J.
The Record of Profitable Research at Bell Telephone Laboratories,
Monograph 2663.
KiRCHNER, R. J., and Kaminow, I. P.
Superregenerative Transistor Oscillator, Monograph 2664.
Logan, R. A., see Thurmond, C. D.
Mason, W. P., see Bomniel, H. E.
Matthl\s, B. T., see Holden, A. N.
McKay, K. G., see Chynoweth, A. G.
McSkimin, H. J.
Propagation of Longitudinal and Shear Waves in Rods at High Fre-
quencies, Monograph 2637.
Merz, W. J., see Holden, A. N.
Pearson, G. L.
Electricity from the Sun, Monograph 2658.
Phelps, J. W.
Protection Problems on Telephone Distribution Systems, Monograph
2631.
Phelps, J. W., see Bullard, W. R.
Pierce, J. R., and Bennett, W. R.
Noise — Physical Sources; and Methods of Solving Problems, Mono-
graph 2624.
1464 the bell system technical journal, november 1956
Prince, E.
Neutron Diffraction Observation of Heat Treatment in Cobalt Fer-
rite, Monograph 2632.
Reiss, H.
P-N Junction Theory by the Method of 6-Functions, Monograph 2638
Remeika, J. P., see Holden, A. N.
Rice, S. 0.
A First Look at Random Noise, Monograph 2659.
Roach, C. L., see Bullard, W. R.
RosENFELD, J. L., 866 Danielson, W. E.
Saloom, J. A., see Danielson, W. E.
Slothower, J. E., see Bullard, W. R.
Theuerer, it. C.
Purification of Germanium Tetrachloride by Extraction with Hydro-
chloric Acid and Chlorine, Monograph 2639.
Thomas, D. E., and Dacey, G. C.
Application Aspects of Germanium Diffused Base Transistor, Mono-
graph 2660.
Thurmond, C. D., and Logan, R. A.
Copper Distribution Between Germanium and Ternary Melts Sat-
urated with Germanium, Monograph 2640.
Treen, R. E., See Bullard, W. R.
Warner, A. W., see Bommel, H. E.
Weisbaum, S., and Boyet, H.
Broadband Nonreciprocal Phase Shifts — Two Ferrite Slabs in
Rectangular Guide, Alonograph 2642.
Weppler, H. E., see Bullard, W. R.
Winslow, F. H., Baker, W. O., and Yager W. A.
The Structure and Properties of Some Pyrolyzed Polymers, Mono-
graph 2572.
Yager, W. A., see Winslow, F. H.
Contributors to This Issue
C. F. Edwards, B.A. 1929 and M.A. 1930, Ohio State University;
A. T. & T. Co. 1930-34; Bell Telephone Laboratories, 1935- Research
in transoceanic short wave transmission, transoceanic short wave trans-
mission using multiple unit steerable antenna receiving system, wave-
guide cii'cuit design, frequency converters for microwave radio relay
systems and time division multiplex telephone system. Author of articles
published in I.R.E. Proceedings. Member of I.R.E.
Joseph P. Laico, M.E., Brooklyn Polytechnic Institute, 1933; Gen-
eral Drafting Company, 1920-23; American Machine and Foundry Com-
pany, 1923-29; Bell Telephone Laboratories, 1929-. Supervision in the
field of mechanical design and development of electronic devices is Mr.
Laico's occupation at the Laboratories. He holds some twenty patents,
all in electronic devices, and is a member of Tau Beta Pi.
E. J. McCluskey, Jr., A.B., 1953, Bowdoin College, B.S. and M.S.
1953 and Sc.D. 1956, M.I.T.; Bell Telephone Laboratories, co-operative
student, 1950-52; M.LT. research assistant and instructor, 1953-55;
Bell Telephone Laboratories, 1955-. Research in connection with elec-
tronic switching systems. Non-resident instructor at M.I.T., summer
195G. Lecturer at C.C.N.Y., 1956. Member of I.R.E., Phi Beta Kappa,
Tau Beta Pi, Eta Kappa Nu and Sigma Xi.
Hunter L. McDowell, B.E.E., Cornell University, 1948; Bell Tele-
phone Laboratories, 1948-. At the Laboratories, Mr. McDowell has been
principally engaged in vacuum tube development, particularly traveling
wave amplifiers. He is a member of I.R.E.
Samuel P. Morgan, B.S. 1943, M.S. 1944 and Ph.D. 1947, Cali-
fornia Institute of Technology; Bell Telephone Laboratories, 1947-. A
research mathematician, Dr. Morgan specializes in electromagnetic
theory. Studies in problems of waveguide and coaxial cable transmission
and microwave antenna theory. Member of the American Physical
Society, Tau Beta Pi, Sigma Xi and I.R.E.
1465
1466 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956
Clarence R. Moster, B.E.E., Alabama Polytechnic Institute, 1942;
S.M., Massachusetts Institute of Technology, 1947; Naval Research'
Laboratory, 1942-45; Bell Telephone Laboratories, 1947-. Mr. Moster's
main work at the Laboratories has been in vacuum tube development,
specializing in microwave tubes. Member of Institute of Radio En-
gineers, Sigma Xi, Eta Kappa Nu and Phi Kappa Phi. I'
W. T. Read, Jr., B.S. 1944, Rutgers and M.S. 1948, Brown Uni- :
versity; National Defense Research Committee, 1943-46; Engaged in
air-blast and earth-shock tests at Princeton University Station and (
measurements of air blast at Bikini atom bomb tests; Bell Telephone
Laboratories, 1947-. Photoelastic and mathematical stress analysis. Dis- {
location theory and problems of plastic deformation were early studies.
Later involved with theory of flow and space charge of holes and elec-
trons and with electrical and mechanical effects of dislocations and other
imperfections in semiconductors. Author of "Dislocations in Crystals,"
McGraw-Hill, 1953. Member of Phi Beta Kappa.
William Merlin Sharpless, B.S. in E.E. 1928 and Professional En-
gineering in E.E. 1951, University of Minnesota; Bell Telephone Labora-
tories, 1928-. Studies of optical behaviors of the ground for short radio
waves, artificial ground systems for short wave reception, angle of arrival
of transatlantic short wave signals, multiple unit steerable antenna sys-
tem, microwave radio circuits, noise factors in microwave silicon recti-
fiers, broad band balanced and unbalanced crystal converters, radar,
propagation of microwaves over land paths, angle of arrival of micro-
waves, and antenna systems and artificial dielectrics for microwaves.
Several patents. Published papers on short radio waves and microwaves.
Member of American Physical Society and Scientific Research Society
of America. Senior member of I.R.E.
James A. Young, Jr., B.S. 1943, California Institute of Technology;
Radio Officer, U. S. Army Signal Corps, 1943-1946; Jet Propulsion Labo-
ratory of California Institute of Technology, 1946-1947; Ph.D. 1953,
University of Washington; Bell Telephone Laboratories, 1953-. Con-
cerned primarily with low loss circular electric mode waveguide. Member
of American Physical Society, Sigma Xi and I.R.E.
r
HE BELL SYSTEM
Uechnical ournal
[voted to the scientific^^^ and engineering
pects of electrical communication
ADVISORY BOARD
A. B. GoETZE M. J. Kelly
E. J. McNebly
EDITORIAL COMMITTEE
B. McMiLLAX, Chairman
S. E. Brillhart E. I. Green
A. J. BUSCH H. K. HONAMAN
L. R. Cook H. R. Huntley
A. C. DicKiEsoN F. R. Lack
R. L. DiETzoLD J. R. Pierce
K. E. Gould G. N. Thayer
EDITORIAL STAFF
J. D. Tebo, Editor R. L. Shepherd, Production Editor
KANSAS CITY, MO.
INDEX PUBl/- y
FFR 1 '^ 1Q57
VOLUME XXXV I i^u ±o \^ut
1956
AMERICAN TELEPHONE AND TELEGRAPH COMPANY
NEW YORK
LIST OF ISSUES IN VOLUME XXXV
No. 1 January Pages 1-248
2 March 249-534
3 May 535-766
4 July 767-990
5 September 991-1238
6 November i-iv, 1239-1466
Index to Volume XXXV
lM See Amplitude Modulation
idam, Armand ().
biographical material 531
Crossbar Tandem as a Lung Distance
Switching System 91-108
Adda, L. P.
zone leveler
development 660
[Adminstration Equipment
translator
magnetic drum 741-44; illus 740
block diagram 742
Admittance
nonlinear
frequency
conversion 1403-16
Akron, Ohio
toll traffic graph 429
Albany, New York
toll traffic graphs 427-28
Algebra See Boolean Algebra
Alloy
silicon
diode
announcement 661
Alloy Junction Transistor See Tran-
sistor: junction
Alphabet
signaling
binary
group 203-34
best 212-15
defined 207
properties 204-19
special features 203
Alternate Routing See Routing
American Telephone and Telegraph
Company
functions, primary 422-23
operating companies, see Operating
Companies
Amplifier
feedback, negative, design 296-308
pulse
regenerative
described 1085
transistorized 1085-1114
reliability 1085-86
signal
binary
transistorized 1059-84
summing 308-13
transistor
junction
tetrode
design 813-40
traveling wave See Electron Tube
Amplitude Modulation
electron tube
traveling wave
Ml 789 1321-22
Analog Systems
transistor
junction
applications 295-332
Anderson, H. W.
antenna
parabolic
design 1208
rectifier
wave
millimeter
wafer-tj^pe 1397
Angle, R.
electron tube
traveling wave
M1789 1343
Antenna
microwave
testing
pulses, millimicrosecond 45-48
parabolic
60-foot diameter 1199-1208; illus
THE BELL TELEPHONE SYSTEM TECHNICAL JOURNAL, 1956
Antenna, continued
pulse
millimicrosecond 45-48
Apparatus
reliability studies
experiment time
reduction, by statistical tech-
niques 179-202
Aqueous Solutions
semiconductors, analog}- 637
Atlantic Telephone Cable See
Transatlantic Telephone Cal)le
Attenuation
atmospheric
wavelengths
millimeter
measurement
radar 907-16
slope
unit, semi-infinite
phase, tables 747-49
wave
circular
pipes
medium-sized
5-6 mm 1115-28
small
5-6 mm 1115-28
waveguide
helix 1358
Attenuator
coupled helix 165-67
Automatic Machine for Testing Capacitors
and Resistance-Capacitance Net-
works (C. C. Cole, H. R. Shillington)
1179-98
Automatic Manufacturing Testing of Re-
lay Switching Circuits (L. D. Han-
sen) 1155-78
Automatic Testing in Telephone Manufac-
ture (D. T. Robb) 1129-54
Automatic Testing of Transmission and
Operational Functions of Intertoll
Trunks (H. H. Felder, A. J. Pas-
carella, H. F. Shoffstall) 927-54
B
Babcock, Wallace C.
biographical material 531
Crosstalk on Open-Wire Lines 515-18
Bardeen, John illus ii
biographical material iii-iv
Nobel Prize in Physics, 1956 i-iv
Base
diffused
high-frequency
transistor 'j
junction
p-n-p
germanium 23-34 I
Beam See Electron Beam
Beaton, Daniel
antenna
parabolic
design 1208
Beck, A. C.
biographical material 244
Waveguide Investigations with Milli-
microsecond Pulses 35-65
Bell, J. W.
wave
electric
circular
attenuation 1128
Bell Laboratories Type M1789 Tube
See Electron Tube: traveling wave
Bell System
intertoll trunks 423
outside plant, see Outside Plant De-
partment
Bell System Technical Journal
advisor}' board, see inside front cover
editorial committee, see inside front
cover
editorial staff, see inside front cover
Bell Telephone Laboratories
Nobel Prizes in Physics i-iv
Bennett, A. L.
testing
automatic 1154
Bennett, Donald C.
biographical material 762
Single Crystals of Exceptional Perfec-
tion and Uniformity by Zone Leveling
637-60
Bennett, W. R.
amplifier
transistor
junction
tetrode 840
INDEX
regenenitor
pulse
binary
transistor 1()S4
iBergwall, F. W.
zone leveler
development 660
BiFiLAR Helix See Helix: coupled
Binary Microwave Pulse See Pulse
Binary Pulse Transmission See
Transmission
Binary Signaling Alphabet See Al-
phabet
Blecher, Franklin H.
biographical material 531
Trnnsistor Circuits for AtiaUxj and
Digital Systems 295-332
Bloomsburg, Pennsylvania
automatic alternate routing
schematic 440
Bodmer, M. G.
electron tube
traveling wave
M1789 1343
Bond, W. L.
biographical material 1233
Use of an Interference Microscope for
Measurement of Extremely Thin Sur-
face Layers 1209-21
Boolean Algebra
circuits
switching
design 1417
invariance
group
detection 1445-53
symmetry
total
detection 1445-53
Bosworth, R. H.
amplifier
transistor
junction
tetrode 840
Brannen, Miss M. J.
isolator
field displacement 896
Brattain, Walter H. illus ii
biographical material ii-iii, 1233
Combined Measurements of Field Ef-
fect, Surface Photo-Voltage and Pho-
to-Conductivity 1019-40
Distribution and Cross-Sections of Fast
Slates on Gernianium Surfaces 1041-
58
Nobel Prize in Physics, 1956 i-iv
transistor
point-contact
experiments 770
Breakdown Voltage See Voltage
Brooks, C. E.
concentrator
line, remote controlled
development 293
Buffalo, New York
toll traffic graphs 427-28
Buhrendorf, F. G.
biographical material 762
Laboratory Model Magnetic Drum
Translator for Toll Suntching Offices
707-4
Burke, P. J.
toll traffic study 506
Cable
coaxial
equalization
phase, tables
tabulation 747-49
translatlantic See Transatlantic Tele-
phone Cable
Capacitor
nonlinear
frequency
conversion 1409-11
testing
machine
automatic 1179-98
Card-0-Matic Test Set See Test Set
Card Translator See Translator
Carthage, N.
transistor
point-contact
surface effects 810
Center See Wire Center
6
THE BELL TELEPHONE SYSTEM TECHNICAL JOURNAL, 1956
Central Office
concentrator
line
remote controlled
circuits 274-86
defined 250
Chapman, A. G.
transposition theory 515
Chemical Interactions among Defects in
Germanium and Silicon (C. S. Fuller,
F. J. Morin, H. Reiss) 535-636
Cioffi, P. P.
electron tube
traveling wave
Ml 789 1343
Circuit
concentrator
line
remote controlled 261-70
switching
design
Boolean algebra 1417
relay
testing
automatic 1155-78
transistor
junction
analog systems 295-332
digital systems 295-332
translator
magnetic drum 725-41
Circular Wave See Wave
Class of Binary Signaling Alphabets (D.
Slepian) 203-34
Clausen, C. P.
antenna
parabolic
design 1208
Clos, C.
toll traffic study 431, 470
Coaxial Cable See Cable
Coil
relay
tr-Type
C testing
automatic 1141-48
UA-type
testing
automatic 1141-48
I
Y-type
testing
automatic 1141-48
Cole, C. C.
Automatic Machine for Testing Capa'
citors and Resistance-Capacitance
Networks 1179-98
biographical material 1233
Collector
electron tube
traveling wave
M1789 1311-13
Combined Measurements of Field Effect,
Surface Photo-Voltage and Photo
Conductivity (W. H. Brattain, C. G.j.
B. Garrett) 1019^0
Comparator
voltage 320-27
Complex Ion See Ion
Component(s)
reliability studies
experiment time
reduction, bj' statistical lechni-
ques 179-202
Computer See Analog S3-stems: Digi-
tal Systems
Concentrator
line
remote controlled
experimental 249-93
illus 277, 287, 289
circuits 261-70
central office 274-86
economy 249-93
field trials 286-93
operation 270-74
power supply 269-70
relay
reed switch
traffic loading
Conductivity
modulation
rectifier
series resistance
See also Photoconductivity
Contact
transistor
point-contact
formed 770-83
unformed 783-96
Co-
f
252-53
249-93
666-70
INDEX
ON VERSION
frequency
admittance
nonlinear 1403-16
Cook, J. S.
biographical material 244
Coupled Helices 127-78
CnoNCE, H. E.
amplifier
pulse
regenerative
transistor 1114
Copper
plating
transistor
point-contact
surface 776-81
Copper Oxide Rectifier See Rectifier
Cost
concentrator, line 249-93
drums, magnetic 707
outside plant 249-93
switching 249-93
See also Economy
Coupled Helices (J. S. Cook, R. Kompf-
ner, C. F. Quate) 127-78
Coupled Helix See Helix
Coupled Helix Attenuator See At-
tenuator
Coupled Helix Transducer See
Transducer
Coupler
stepped
helices, coupled 158-59
tapered
helices, coupled 157-58
Crawford, Arthur B.
biographical material 985, 1234
Measiirement of Atmospheric Attenua-
tion at Millimeter Wavelengths 907-
16
rectifier
wave
millimeter
wafer-type 1397
60-Foot Diameter Parabolic Antenna for
Propagation Studies 1199-1208
Crossbar Systems
4-type
development 423
5-type
concentrator
line
remote 251-93
switching plan 257-61
tandem
switching system, long distance
major toll switching features 91
See also Switching Systems
Crossbar Tandem as a Long Distance
Switching System (A. O. Adam)
91-108
Crosstalk
coupling
types 515
measurement 516
Crosstalk on Open-Wire Lines (W. C.
Babcock, Miss E. Rentrop, C. S.
Thaeler) 515-18
Crystal
defects
interaction 535-636
diffusion Sec Diffusion
germanium
acceptor content
zone leveling 638-60
defects
interactions, chemical 535-636
donor content
zone-leveling 638-60
etched
field effect 1019-40
measurements
combined 1019^0
photoconductivity 1019-40
photo-voltage
surface 1019-40
semiconductor applications
requirements 641-55
shaping
electrolytic 333-47
surface
fast states
cross-sections 1041-58
distribution 1041-58
transistor forming, relation 796-
808
testing 642-43
lattice, see Lattice
8
THE BELL TELEPHONE SYSTEM TECHNICAL JOURNAL, 1956
Crystal, continued
silicon
defects
interactions, chemical 535-636
diffusion 664-66
rectifiers 661-84
diode, see Diode
shaping
electrolytic 333-47
shaping
electrolytic 333-47
Customer Direct Distance Dialing
See Dial Telephone: nationwide
Cutler, C. Chapin
biographical material 985
electron beam formation, theory 375
generator, pulse, regenerative, de-
velopment 36
Nature of Power Saturation in Travel-
ing Wave Tubes 841-76
Danielson, W. E.
biographical material 531
Detailed Analysis of Beam Formation
u'ith Electron Guns of the Pierce Type
375-420
Data System See Digital Systems
Davisson, Clinton J.
biographical material iii
Nobel Prize in Physics, 1937 i, iii
Defect
crystal
interaction 535-636
DeLange, O. E.
biographical material 244
Experiments on the Regeneration of
Binary Microwave Pulses 67-90
Delay
distortion
phase
tables
tabulation 747-49
I)elay Distortion Repeater See Re-
' J peater
Design
amplifier
transistor
junction
tetrode
circuit
switching
Boolean algebra 1417
electron gun
Pierce-type 378-79, 399, 402-13
418-20
electron tube
traveling wave 867-68
M1789 1289-91
isolator
field displacement 884-91
relays 991
switching systems
electronics in 991-1018
transistor
junction
n-p-n
base, diffused 14-21
emitter, diffused 14-21
point-contact 769
Design of Tetrode Transistor Amplifier
(J. G. Linvill, L. G. Schimpf) 813-
40
Detailed Analysis of Beam Formation with
Electron Gunds of the Pierce Type
(W. E. Danielson, J. L. Rosenfeld,
J. A. Saloom) 375-420
Detection of Group Invariance or Total '
1)
813-40
Symmetry of a Boolean Function (E.
J. McCluskey, Jr.) 1445-53
DeVido, R. W.
electron tube
traveling wave
M1789 1343
Dial Telephone, Dialing
crosstalk, see Crosstalk
direct distance 955-72
crossbar tandem systems 107-08
lines, see Transmission Lines
nationwide
aspects, general 93-94
crossbar tandem switching system
91-108
customer direct
crossbar tandem systems 107-08
expansion 423
routing, see Routing
service requirements 436-37
translator
card 716-19
INDEX
magnetic drum 707-45
trunks
intertoll
testing, automatic 927-54
operator distance 965-72
United States statistics 423
testing, automatic 1129-54
traffic, see Traffic
transmission lines, see Transmission
Lines
Dickten, E.
amplifier
transistor
junction
tetrode 840
Dielectrics
helices, coupled, between 148-50
Dietzold, R. L.
phase, tables
computation 749
Diffused Emitter and Base Silicon Tran-
sistors (IVI. Tanneiil)aum, 1). E.
Thomas) 1-22
Diffused Junction Silicon Diode See
Diode
I Diffused p-n Junction Silicon Rectifiers
(M. B. Prince) 661-84
Diffusion
crystal
silicon 664-66
rectifiers 661-85
Digital Systems
drums, magnetic 707-45
transistor
junction
applications 295-332
Digital Transmission »See Transmis-
sion
Diode
junction
germanium
large area
announcement 661
temperature 661
silicon
diffused
current-voltage characteristic
equations, basic 688-706
forward 685-706
silicon allo}^
announcement 661
temperature 661
PIN See Diode: junction: silicon:
diffused
voltage
breakdown 685
Diode Rectifier See Rectifier
Direct Distance Dialing See Dial
Telephone
Distortion
delay
phase
tables
tabulation 747-49
Distribution and Cross-Sections of Fast
States on Germanium Surfaces (W. H.
Brattain, C. G. B. Garrett) 1041-58
Dominant Mode Waveguide See
Waveguide
Drum
magnetic illus 1007
access time 707
applications 707, 745
digital -data storage 707
features 709-16
geography 712
memory imits 707
reading 713-16
speed 107
switching
toll
translator 707-45
writing 712-13
E
Economy
concentrator, line 249-93
outside plant 249-93
switching 249-93
See also Cost
Edwards, C. F.
biographical material 1465
Frequency Conversion by Means of a
Nonlinear Admittance 1403-16
Effect of Surface Treatments on Point-
Contact Transistors (J. H. Forster,
L. E. Miller) 767-811
10
THE BELL TELEPHONE SYSTEM TECHNICAL JOURNAL, 1956
Elbert, E. F.
rectifier
wave
millimeter
wafer-type 1397
Electric Field
helices, coupled 139-42, 144-46
junction
PIN
bias
reversed 1239-84
Electrolytic Etching See Etching
Electrolytic Shaping of Germanium and
Silicon (A. Uhlir, Jr.) 333-47
Electron (s) and Holes
chemical entities 537-46
interaction 537-57
junction
PIN
bias
reversed 1239-84
Electron Beam
amplifier
traveling wave
coupling, finite, effects 349-74
space charge, eflects 349-74
wave
backward 351-55
forward 351-55
electric field 859-63
electron tube
traveling wave
Ml 789 1298-1303
formation
electron gun
Pierce -type 375-420
size
electron tube
traveling wave 856-58
spent
electron tube
traveling wave 846-54
spreading 388-401
waves
growing, due to transverse veloci-
ties 109-25
Electron Flow
waves
growing, due to transverse veloci-
ties 109-25
Electron Gun
electron tube
traveling wave
M1789 1298-1303; illus 1296-97
Pierce -type
anode lens 379-88
beam
current densities 413-16
formation 375-420
spreading 388-401
design 378-79, 399, 402-13, 418-20
development 377
Electron Tube
gun, see Electron Gun
microwave
electron gun, see Electron Gun
traveling wave
M1789 1285-1346
illus 1286, 1292-93
AM to PM conversion 1321-22
collector 1311-13
description 1291-1313
design 1289-91
electron beam 1298-1303
electron gun 1298-1303; illus
1296-97
gain calculations 1343-44
helix 1303-11
intermodulation 1335-42
life expectancy 1342-43
noise 1328-35
performance 1313-42
relaj^ sj'stems
radio 1285-1346
amplifier
equations 355-59
non-linear behavior 349 74
signal, large, theory 349-74
applications 1285
circuit elements 129-30
design 867-68
dispersive
helices, coupled 159-61
efficiency 841
measurements 844-46
electron beam
spent 846-54
helices, coupled 127-78
operating characteristics
non-linear 841-76
INDEX
11
power saturation 841-76
research 1285
space charge 854-56
See also Amplifier
Electronics in Telephone Switching Sys-
tems (A. E. Joel, Jr.) 991-1018
Electroplating
transistor
point contact
surface
copper 776-81
]']mitter
transitor
junction
n-p-n
diffused 1-22
Encoder
voltage
transistor 327-29
Equalization
cable
coaxial
phase, tables
tabulation 747-49
dela.v distortion
pulses, milliniicrosecoiid 54-57
Equipment
administration, see Administration
l^Ajuipment
reliability studies
experiment time
reduction, by statistical techni-
ques 179-202
Erhart, D. L.
zone leveler
development 660
Etching
electrolytic
crystal
germanium 333-47
silicon 333-47
Experiment Time
reliability studies
reduction
statistical methods 179-202
Experimental Remote Controlled Line
Concentrator (A. E. Joel, Jr.) 249-93
Experiments on the Regeneration of
Binary Microwave Pulses (O. E.
DeLange) 67-90
4-Type Crossbar System See Crossbar
Systems
4A Toil Switching System See
Switching Systems
5-Type Crossbar Systems See Cross-
bar Systems
56A Oscillator See Oscillator
425B Network See Network
Fabrication
transistor
junction
n-p-n
silicon
base, diffused 2-6
emitter, diffused 2-6
p-n-p
germanium
base, diffused 23-24
Feedback Amplifier See Amplifier
Felder, Harry H.
Automatic Testing of Transmission and
Operational Functions of Intertoll
Trunks 927-54
biographical material 985
Intertoll Trunk Net Loss Maintenance
under Operator Distance and Direct
Distance Dialing 955-72
Feldman, C. B.
regenerator
pulse
binary
transistor 1084
Felker, J. H.
amplifier
pulse
regenerative
transistor 1114
Field See Electric Field
Field Displacement Isolator (H. Siedel,
S. Weisbaum) 877-98
Field Effect
germanium
etched
measurements
combined 1019-40
12 THE BELL TELEPHONE SYSTEM TECHNICAL JOURNAL, 1956
Finch, T. R.
amplifier
pulse
regenerative
transistor 1114
transistor circuit research 329
Fleming, C. C.
trunks
intertoll
testing
automatic 954
Flow of Electrons See Electron
Flow
Forster, J. H.
biographical material 985
Effect of Surface Treatments on Point-
Contact Transistors 767-811
Forward Characteristic of the PIN Diode
(D. A. Kleinman) 685-706
Foster, F. G.
semiconductors
defects
chemical interactions 613
Fox, A. G.
ferrite devices
nonreciprocal 877
Frequency
conversion
admittance
nonlinear
mathematical analysis 1403-16
helices, coupled
strength of coupling versus fre-
quency 142-44
microwave
pulses, binary
regeneration 67-90
Frequency Conversion by Means of a Non-
linear Admittance (C. F. Edwaixls)
1403-16
Friis, Harold T.
biographical material 1234
rectifier
wave
millimeter
wafer-type 1397
60-Foot Diameter Parabolic Antenna for
Propagation Studies 1199-1208
Frisbee, S. E.
testing machines 1198
Fuller, Calvin S.
biographical material 762
Chemical Interactions among Defects in
Germanium and Silicon 535-636
Function
Boolean
minimization 1417-44
prime implicants 1419-40
sum, minimum 1418-19
writing
products, sum of 1417-44
transmission
Boolean
invariance
group
detection 1445-53
symmetry
total
detection 1445-53
G
Garrett, C. G. B.
biographical material 1234
Combined Measurements of Field Ef-
fect, Surface Photo-Voltage and
Photo-Conductivity 1019-40
Distribution and Cross-Sections of Fast
States on Germanium Surfaces
1041-58
Gellatly, J. S.
electron tube
traveling wave
M1789 1343
Generator
pulse, regenerative
block diagram 37
development 36-38
See also Regenerator
Germanium
crystal, see Crystal
defects
interactions, chemical 535-636
diode, see Diode
zone leveling 638-68
apparatus 655-60
technique 655-60
zone refining 637
Germanium P-N-P Transistor See
Transistor: junction
Germer, L. H.
electron diffusion studies i
INDEX
13
Gibney, R. B.
semiconductor studies i
Glass, M. S.
electron tube
traveling wave
Ml 789 1343
Glezer, L. L.
trunks
intertoU
testing
automatic 954
Goeltz, Miss J. D.
phase, tables
tabulation 749
Graham, R. E.
information rate
interpretation 926
Grant, D. W.
magnettor, construction 329
Gray, Miss M. C.
semiconductors
defects
chemical interactions 613
Grossman, A. J.
amplifier
pulse
regenerative
transistor 1114
Group Alphabet See Alphabet
Growing Waves due to Transverse Veloci-
ties (J. R. Pierce, L. R. Walker) 109-
25
Gun See Electron Gun
H
Hall, W. J.
toll traffic study 506
Hamming, R. W.
phase, tables
tabulation 749
Hannay, N. B.
semiconductors
defects
chemical interactions 613
Hansen, L. D.
Automatic Manufacturing Testing of
Relay Switching Circuits 1155-78
biographical material 1235
Harris, J. R.
amplifier
pulse
regenerative
transistor 1114
Harris, W. B.
magnettor, construction 329
Haj'ward, W. S.
toll traffic study 506
Heilos, L. J.
electron tube
traveling wave
power saturation 867
Helix
coupled 127-78
applications. Bell System 154-67
attenuator 165-67
bifilar
dispersion 146-48
coupler
stepped 158-59
tapered 157-58
dielectrics between, eft'ect 148-50
field equations 169-73
fields 139-42, 144-46
power transfer, maximum 151-52
solutions, non-synchronous 137-39
strength of coupling versus fre-
quency 142-44
transducer 161-65
transmission line equations 133-37
electron tube
traveling wave
M1789 1303-11
Helix Transducer See Transducer
Helix Waveguide (S. B. Morgan, J. A.
Young) 1347-84
Henning, H. A.
biographical material 762
Laboratory Model Magnetic Drum
Translator for Toll Switching Offices
707-45
Herbert, N. J.
transistor
point-contact
surface effects 810
Heterodyne Conversion Transducer
See Transducer
High-Frequency Diffused Base Germa-
nium Transistor (C. A. Lee) 23-34
14
THE BELL TELEPHONE SYSTEM TECHNICAL JOURNAL, 1956
375
Hines, M. E.
electron beam formation, theory
Hogg, David C.
biographical material 986
Measurement of Atmospheric Attenua
tion at Millimeter Wavelengths 907-
16
Holder
rectifier
wave
millimeter 1385
Hole(s) See Electron (s) and Holes
Howard, L. F.
trunks
intertoll
testing
automatic
954
Impedance
helices, coupled
modes 152-54
Impttrity
semiconductors
diffusion into 1-34
Indianapolis Works (Western Elec-
tric)
network
425B
testing
automatic 1135-41
Information
storage
drums, magnetic 707-45
See also Digital Systems
Information Rate
interpretation
new 917-26
Insulation See Dielectric (s)
Integrator
transistor 313-20
Interconnecting Network <See Net-
work
Interference See Crosstalk: Noise
Interference Microscope See Micro-
scope
Intermodulation
electron tube
traveling wave
M1789 1335^2
Intertoll Trunk Xet Loss Maintenance
under Operator Distance and Direct
Distance Dialing (H. H. Felder,
E. N. Little) 955-72
Ion(s)
complex-
formation 557-65
pairing 565-636
calculations 578-82
carrier
mobility
effect 601-07
(by) diffusion 591-601
energy levels 610-11
relaxation time 582-91, 607-10
semiconductors
phenomena 575-78
solubility, effect 613-17
theories 567-75
Irwin, J. C.
electron tube
traveling wave
M1789 1343
Isolator
field displacement 877-98
illus 878, 890
design 884-91
Jakes, William C, Jr.
biographical material 1235
60-Foot Diameter Parabolic Antenna for
Propagation Studies 1199-1208
Joel, Amos E., Jr.
biographical material 532, 1235
Electronics in Telephone Switching
Systems 991-1018
Experimental Remote Controlled Line
Concentrator 249-93
Johnston, R. L.
rectifier
junction
p-n
silicon
development 684
Jones, M. S.
transistor
point-contact
surface effects 810
INDEX
15
Jordan, D. R.
electron tube
traveling wave
M17S9 1343
Junction
NP 1241-42
TIN
bias
reversed
electrons and holes 1239-84
Junction Diode See Diode
Junction Silicon Diode jSee Diode
Junction Tetrode Transistor See
Transistor
Junction Transistor See Transistor
Kearney Works (Western Electric)
coil
relay
testing
automatic 1141-48
Kell}', John L., Jr.
biographical material 986
Xew Interpretation of Information Rate
917-26
King, Archie P.
biographical material 986, 1235
Observed 5-6mm Attenuation for the Cir-
cular Electric Wave in Small and
Medium-Sized Pipes 1115-28
Transmission Loss Due to Resonance of
Loosely-Coupled Modes in a Multi-
Mode System 899-906
Kingsbury, B. A.
phase, tables
computation 749
Kleinman, David A.
biographical material 763
Forward Characteristic of the PIN
Diode 685-706
Kleinman, D. A.
rectifier
junction
p-n
silicon
development 684
Kompfer, R.
biographical material 244
Coupled Helices 127-78
Kosten, L.
toll traffic study
431
Laboratories See Bell Telephone
Laboratories
Laboratory Model Magnetic Drum Trans-
lator for Toll Switching Offices (F. J.
Buhrendorf, H. A. Henning, (). J.
Murphy) 707-45
Laico, Joseph P.
biographical material 1465
Medium Power Traveling-Wave Tube
for 6000-Mc Radio Relay 1285
1346
Lamont, J.
testing
automatic 1154
Large-Signal Theory of Traveling-Wave
Amplifiers (P. K. Tien) 349-74
Lattice
crystal
germanivmi
zone leveling 638
perfection
zone leveling 649-55
Leagus, Miss D. C.
amplifier, traveling wave
large signal theorj- 373
Lee, Charles A.
biographical material 245
High-Frequency Diffused Base Ger-
manium Transistor 23-34
Lennon, Miss C. A.
toll traffic study 506
Leveler See Zone Leveler
Life Expectancy
electron tube
traveling wave
M1789 1342-43
rectifier
junction
p-n
silicon 680-83
reliability studies
experiment time
reduction, by statistical tech-
niques 179-202
Line(s), transmission See Transmis-
sion Lines
16
THE BELL TELEPHONE SYSTEM TECHNICAL JOURNAL, 1956
Line Concentrator See Concentrator
Linvill, J. G.
biographical material 986
Design of Tetrode Transistor Amplifiers
813-40
Little, Edward N.
biographical material 987
Intertoll Trunk Net Loss Maintenance
under Operator Distance and Direct
Distance Dialing 955-72
Local Switching See Switching
Long Distance Traffic See Traffic:
toll
M
M1789 Electron Tube See Electron
Tube: traveling wave
McCluskey, E. J., Jr.
biographical material 1465
Detection of Group Invariance or Total
Synnnetry of a Boolean Function
1445-53
Minimization of Boolean Functions
1417-44
McDowell, Hunter L.
biographical material 1465
Medium Power Traveling -Wave Tube
for 6000-Mc Radio Relay 1285-1346
McKim, B.
trunks
intertoll
testing
automatic 954
Magnetic Drum See Drum
Magnetic Drum Translator See
Translator
]^ Iaintenance
switching systems 1014-16
trunks
intertoll
testing
automatic 927-54
Malta, J. P.
semiconductors
defects
chemical interactions 613
Marcatili, Enrique A. J.
biographical material 987
Transmission Loss due to Resonance of
Loosely-Coupled Modes in a Multi-
Mode System 899-906
Matrix
Boolean
transmission
invariance 1445-53
s.ymmetiy 1445-53
Mead, Mrs. Sallie P.
toll traffic study 506
Measurement of Atmospheric Attenua-
tion at Millimeter Wavelengths (A.
B. Crawford, D. C. Hogg) 907-16
Medium Power Traveling-Wave Tube for
6000-Mc Radio Relay (J. P. Laico,
H. L. McDowell, C. R. Moster)
1285-1346
Melroy, D. O.
electron tube
traveling wave
Ml 789 1343
Melting See Zone Melting
Miami, Florida
toll traffic 7nap 439
Microscope
interference
surface layers
measurement 1209-21
Microwave Antenna See Antenna
Microwave Modulator See Modu-
lator
Microwave Pulse See Pulse
Microwave Pulse Regenerator See
Regenerator
Microwave Transmission See Trans-
mission
Microwave Tube See Electron Tube
Military Applications
transistor
point-contact 768
Miller, Lewis E.
biographical material 987
Effect of Surface Treatments on Point-
Contact Transistors 767-811
Miller, S. E.
ferrite devices
nonreciprocal 877
Millimeter Wave See Wave
Millimicrosecond Pulse See Pulse
j!i«
If
INDEX
17
Minimization of Boolean Fiaictions (E.
J. McCluskey, Jr.) 1417 44
MlXXESOTA
intertoll trunk groups, principal map
424
Mode
loosely-coupled
resonance
transmission
loss 899-906
spurious
resonance 899-906
Modulation See Amplitude Modula-
tion; Intermodulation; Phase INIodu-
lation
Modulator
microwave
noise temperature requirements
1404
rectifier
point contact 1403-16
Molina, E. C.
toll traffic study 506
Moll, J. L.
rectifier
junction
p-n
silicon
development 684
Monographs, recent, of Bell System
Technical Papers not published in
this Journal 242-43, 527-30, 759-61,
979-84, 1230-32, 1461-64
Moore, H. R.
rectifier
junction
p-n
silicon
development 684
Morgan, S. O.
semiconductor studies i
Morgan, Samuel P.
biographical material 1465
Helix Waveguide 1347-84
Morin, F. J.
biographical material 763
Chemical Interactions among Defects in
Germanium and Silicon 535-636
Moster, Clarence R.
biographical material 1467
Medium Power Trapcling-W'ave Tube
for 6000-Mc Radio Relay 1285-1346
Multi-Mode Transmission System.
See Transmission S^ystems
Murphy, O. J.
biographical material 763
Laboratory Model Magnetic Drum
Translator for Toll Switching Offices
707-45
N
No. 4 Crossbar System See Crossbar
System
Xo. 4A Toll Savitching System See
Switching Systems
Xo. 5 Crossbar System See Crossbar
Sj'stems
No. 56A Oscillator See Oscillator
No. 425B Network See Network
X^P Junction See Junction
N-P-X" Transistor See Transistor:
junction
Nationwide Dialing See Dial Tele-
phone
Nationwide Switching See Switching
Nature of Power Saturation in Traveling
Wave Tubes (C. C. Cutler) 841-76
Xeely, T. H.
trunks
intertoll
testing
automatic 954
X'egative Feedback Amplifier See
Amplifier
Network
425B
testing
automatic 1135-41
interconnecting
switching sj^stems 994-98
resistance-capacitance
testing
machine
automatic 1179-98
New Interpretation of Information Rate
(J. L. Kelly, Jr.) 917-26
X"ew' York City
toll traffic graph 431
18
THE BELL TELEPHONE SYSTEM TECHNICAL JOURNAL, 1956
Newark, New Jersey
toll traffic graph 429
Nobel Prize in Physics
awards
1937
Davisson, Clinton J. i, iii
Thompson, G. P. iii
1956
Bardeen, John i-iv
Brattain, Walter H. i-iv
Shockley, William i-iv
Noise
electron tube
traveling wave
M1789 1328-35
modulator
microwave
temperature requirements 1404
Nonlinear Admittance See Admit-
tance
Nonlinear Capacitor See Capacitor
NoNRECiPROCAL Ferrite Device See
Isolator
Number 4 Crossbar System See
Crossbar System
Number 4A Toll Switchinc System
See Switching Systems
Number 5 Crossbar System See Cross-
bar System
Number 56 A Oscillator See Oscil-
lator
Number 425B Network See Network
Nyquist, H.
toll traffic study 506
Observed 5-6mm Attenuation for the
Circular Electric Wave in Small and
Medium-Sized Pipes (A. P. King)
1115-28
Office See Central office
Ohl, R. S.
frequency conversion 1416
rectifier
wave
millimeter
wafer-type 1397
semiconductor studies i
Ohmic Resistance See Resistance
Olsen, K. M.
zone leveler, design 655
Olson, E. G.
electron tube
traveling wave
M1789 1343
Open-Wire Lines See Transmission
Lines
Operate Speed
drum, magnetic 707
electronics 993
relays 995
Operating Companies
functions, primary 422-23
Operator Distance Dialing See Dial
Telephone
Oscillator
56A
film scales
calibration 1148-54
Outside Plant Department
costs 249
concentrator
line
remote controlled
economy 249-93
PIN Diode See Diode: junction: sili
con: diffused
PIN Junction See Junction
PM See Phage Modulation
P-N-P Transistor See Transistor:
junction
Pairing
ions 565-636
calculations 578-82
carrier
mobility
effect 601-07
(by) diffusion 591-601
energy levels 610-11
relaxation time 582-91, 607-10
semiconductors
phenomena 575-78
solubility, effect 613-17
theories 567-75
Parabolic Antenna See Antenna
INDEX
19
Parameter
design
transistor
junction
n-p-n
silicon
base, diffused
calculation 14-21
emitter, diffused
calculation 14-21
rectifier, millimeter wave
wafer-type 1397-1402
transistor
amplifier
performance, relation 815-26
Pascarella, A. J.
Automatic Testing of Transmission and
Operational Functions of JntertoU
Trunks 927-54
biographical material 988
Phase Modulation
electron tube
traveling wave
M1789 1321-22
Photoconductivity
germanium
etched
measurements
combined " 1019-40
Photo-Voltage
surface
germanium
etched
measurements
combined 1019-40
Physics Prize See Nobel Prize in
Physics
Pierce, John R.
amplifier, traveling wave
large signal theory 373
biographical material 245
Growing Waves due to Transverse
Velocities 109-25
Pierce-Type Electron Gun See Elec-
tron Gun
Pietruszkiewicz, A. J., Jr.
semiconductors
defects
chemical interactions 613
Pipe See Waveguide
Plant See Outside Plant Department
Plating See Electroplating
Point Contact Rectifier See Rectifier
Point Contact Transistor See Tran-
sistor
Power Supply
concentrator, line, remote controlled,
experimental 269-70
Prince, M. B.
biographical material 764
Diffused p-n Junction Silicon Rectifiers
661-84
diode
PIN 706
Prize See Nobel Prize in Physics
transmission
rate 917-26
Propagation
waveguide, helix 1355-58
Pulse
microwave
binary
regeneration 67-90
testing 69-73
millimicrosecond
antenna 45-48
generation 36-41
waveguide
dominant mode
testing 35-65
apparatus 36-43
regenerative
generator, see Generator
Pulse Regenerator See Regenerator
Pulse Transmission See Transmission
Quate, C. F.
biographical material 245
Coupled Helices 127-78
R
Rack, A. J.
regenerator
pulse
binary
transistor
1084
20
THE BELL TELEPHONE SYSTEM TECHNICAL JOURNAL, 1956
Radar
frequency-modulation
attenuation
atmospheric
wavelengths
millimeter
measurement 907-16
Radio
propagation
beyond-the-horizon
antenna
parabolic
60-foot diameter 1199-1208;
illus
relay systems
6000 mc
electron tube
traveling wave
M1789 1285-1346
Radio Detection and Ranging See
Radar
Raisbeck, Gordon
regenerator
pulse
binary
transistor 1084
Rate See Information Rate
Read, W.T.,Jr.
biographical material 1466
Theory of Swept Intrinsic Structure
1239-84
Reading
magnetic drum 713-16
Rectifier
characteristics, ideal 662-63
graph 662
copper oxide
introduction 661
development
problems 662-63
diode
junction
p-n
silicon
diffused 681-83
silicon
diffused 661-84; illus 671
design 678-80
electrical characteristics 671-
78
fabrication 670-71
life expectancy 680-83
reliability 680-83
point-contact
wafer-type
silicon
waves
millimeter 1385-1402
selenium
introduction 661
semiconductor
characteristics, ideal 662-63
graph 662
series resistance
control
conductivity
modulation 666-70
wave
millimeter
wafer-type 1385-1402
converter illus 1390, 1391, 1396
description 1386-91
parameters 1397-1402
performance 1391-94
wave-wafer unit illus 1386
Reed, E. F.
electron tube
traveling wave
Ml 789 1343
Reed, S. E.
rectifier
wave
millimeter
waver-t^-pe 1397
Reed Switch Relay See Relay
Refining See Zone Refining
Regenerative Pulse Generator See
Generator
Regenerative Repeater See Re-
peater
Regenerator
pulse
binary
transistorized 1059-84
microwave 73-82
description 83-89
signal
binary
transistorized 1059-84
INDEX
21
Reiss, Howard
biograpliical material 764
Chemical Interactions among Defects in
Germanium and Silicon 535-636
Relaxation Time
ions
pairing 582-91, 607-10
Relay
design 991
U-type
coils
testing
automatic 1141-48
UA-type
coils
testing
automatic 1141-48
Y-type
coils
testing
automatic 1141-48
reed switch ill us 253
concentrator
line
remote controlled 252-53
speed 995
Relay, Radio See Rsidio: relay sj^stems
Reliability
amplifier
pulse
regenerative
transistorized 1085-86
Bell System standards 708
rectifier
junction
p-n
silicon 680-83
switching sj'stems
electronic 1016
transistor 295, 1085
point-contact 768
Reliability Studies
experiment time, reduction
statistical methods 179-202
Rentrop, Esther M.
biographical material 532
Crosstalk on Open-Wire Lines 515-18
Repeater
delaj^ distortion
phase, tables
tabulation 747-49
regenerative
block diagram 68
Resistance
ohmic
diodes 685
Resistance-Capacitance Network
See Network
Resonance
modes
loosely-coupled 899-906
spurious 899-906
Richardson, P. H.
phase, tables
computation 749
Riley, J. F.
electron tube
traveling wave
:\I17S9 1343
Riordan, J.
toll traffic study 507
Robb, D. T.
Automatic Testing in Telephone Manu-
facture 1129-54
biographical material 1236
Rosenfeld, Jack L.
biographical material 532
Detailed Anahjsis of Beam Formation
ivith Electron Guns of the Pierce Type
375-420
Ross, I. M.
diode
PIN 706
rectifier
junction
p-n
silicon
development 684
Round Waveguide See Waveguide
Routing
alternate
toll
administration 441-42
economics 437-41
engineering 441-42
methods, practical 487-505
dialing, nationwide 97-99
majj, 1965, 96
22
THE BELL TELEPHONE SYSTEM TECHNICAL JOURNAL, 1956
Rowe, H. E.
frequency conversion 1416
RUGGEDNESS
Bell System standards 708
transistor
point-contact 768
Rulison, R.
rectifier
junction
p-n
silicon
development 684
Saloom, Joseph A., Jr.
biographical material 532
Saloom, J. A.
Detailed Analysis of Beam Formation
with Electron Guns of the Pierce Type
375-420
Saloom, J. A.
electron tube
traveling wave
M1789 1343
Sandsmark, P. I.
electron tube
traveling wave
M1789 1343
Sansalone, F. J.
isolator
field displacement 896
Sawyer, Baldwin
biographical material 764
Single Crystals of Exceptional Perfec-
tion and Uniformity by Zone Leveling
637-60
Scaff, J. H.
semiconductor studies i
Scattaglia, J. V.
regenerator
pulse
binary
transistor 1084
Scheideler, C. E.
amplifier
transistor
junction
tetrode 840
Schimpf, L. G.
biographical material 988
Design of Tetrode Transistor Amplifiers
813-40
Schramm, F. W.
testing
automatic 1154
Seidel, Harold
biographical material 988
Field Displacement Isolator 877-98
Selenium Rectifier See Rectifier
Semiconductor (s) , Semiconducting
Materials
aqueous solutions, analogy 537
impurities
diffusion into 1-34
ions
pairing
phenomena 575-78
leveling, see Zone Leveling
Xobcl Prize in Physics, 1056 i-iv
regions
extrinsic 1239-84
intrinsic 1239-84
shaping
electrolytic 333-47
mechanical 333
structure
swept intrinsic
theory 1239-84
surface
layers
measurement 1209-21
traps
cross sections 1041-58
distribution 1041-58
zone leveling, see Zone Leveling
See also Crj'stal; Diode; Junction
Semiconductor Rectifier See Recti-
fier
Series Resistance Rectifier See Rec-
tifier
Service IVIaintenance See Mainten-
ance
Shannon, C. E.
information rate
interpretation 926
Shaping
electrolytic
INDEX
23
crystal
germanium 333-47
silicon 333-47
semiconductors 333^7
Sharpless, William M.
biographical material 1466
Wafer-Type Millimeter Wave Rectifiers
1385-1402
Shillington, Harry R.
Automatic Machine for Testing Capaci-
tors and Resistance-Capacitance Net-
uwrks 1179-98
biographical material 1236
Shockley, William illus ii
biographical material iv
Nobel Prize in Phj'sics, 1956 i-iv
Shoffstall, H. F.
Automatic Testing of Transmission and
Operational Functions of JnteroU
Trunks 927-54
biographical material 988
Signal
binary
amplification
transistorized 1059-84
regeneration
transistorized 1059-84
Signaling Alphabet See Alphabet
Silicon
crystal, see Crystal
defects
interactions, chemical 535-636
Silicon Diode See Diode
Silicon N-P-N Transistor See Trans-
istor
Silicon Rectifier See Rectifier
Single Crystals of Exceptional Perfection
and Uniformity by Zone Leveling
(D. C. Bennett, B. Sawyer) 637-60
60-Foot Diameter Parabolic Antenna for
Propagation Studies (A. B. Craw-
ford, H. T. Friis, W. C. Jakes, Jr.)
1199-1208
Slepian, David
biographical material 245
Class of Binary Signaling Alphabets
203-34 '
Smith, K. D.
rectifier
junction
p-n
silicon
development 684
Smith, S. V.
testing machines 1198
Smits, Friedolf M.
biographical material 1236
Use of an Interference Microscope for
Measurement of Extremely Thin Sur-
face Layers 1209-21
Sobel, Milton
biographical material 246
Statistical Techniques for Reducing the
Experimental Time in Reliability
Studies 179-202
Solution See Aqueous Solutions
Speed See Operate Speed
Spent Beam See Electron Beam
Spurious Modes See Mode
Statistical Methods
reliability studies
experiment time, reduction 179-202
Statistical Techniques for Reducing the
Experiment Time in Reliability
Stiidies (M. Sobel) 179-202
Stepped Coupler See Coupler
Stiles, G. J.
electron tube
traveling wave
power saturation 867
Storage Systems See Digital Systems
Summing Amplifier See Amplifier
Surface
semiconductor
layers
measurement 1209-21
transistor
point-contact
treatments
effects 767-811
Surface Photo-Voltage See Photo-
Voltage
Swenson, R. C.
rectifier
junction
p-n
silicon
development 684
Swept Intrinsic Structure See Semj-
c9nductor(s) J structure
24 THE BELL TELEPHONE SYSTEM TECHNICAL JOURNAL, 1956
Switch
waveguide
structure illus 1121
Switching
background 991
concentrator
line
remote controlled
economy 249-93
knowledge 991
local
crossbar tandem
application 91-93
nationwide
crossbar tandem
application 94-97
toll
translator
card 716-19
magnetic drum 707^5
Switching Systems
4A toll
translation
card 716-19
magnetic drum 708-45
concentration 249
control 998-1012
defined 993
design
electronics in 991-1018
electronic
reliability 1016
electronics in 991-1018
equipment concepts 1012-14
interconnecting network 994-98
long distance
crossbar tandem as 91-108
maintenance 1014-16
See also Crossbar Systems
^ Syracuse, New York
toll traffic 7tiap 439
TWT See Electron Tube: traveling
wave
Tables of Phase of a Semi-Infinite Unit
Attenuation Slope (D. E. Thomas)
747-49
Tandem Crossbar See Crossbar Sys-
tems
Tannenbaum, Morris
biographical material 246
Diffused Emitter and Base Silicon
Transistors 1-22
Tape-0-Matic Test Set See Test Set
Tapered Coupler See Coupler
Technical Papers, Bell System, not
published in this Journal 235-41,
519-26, 751-58, 973-78, 1223-29,
1454-60
Telephone See Dial Telephone
Temperature
diode
junction
germanium 661
silicon alloy 661
modulator
microwave
noise 1404
Tendick, Frank H., Jr.
biographical material 1236
Transistor Pulse Regenerative Ampli-
fiers 1085-1114
Test(s), Testing
antenna
microwave
pulses, millimicrosecond 45-48
circuits
relay
switching
automatic 1155-78
crystal
germanium 642-43
defined 1129-30
dial telei)hone
(in) manufacture
automatic 1129-54
electron tube
traveling wave
M1789 1342-43
manual
cost 1129-54
network
425B
automatic 1135-41
oscillator
56A
film scales
calibration 1148-54
INDEX
25
pulse
microwave
Innarj'
regeneration 69-73
rectifier
diode
junction
p-n
silicon 681-83
relay
U-type
automatic 1141-48
UA-type
automatic 1 141-48
Y-type
automatic 1141-48
reliability studies
experiment time
reduction, by statistical tech-
niques 179-202
translator
magnetic tlrum 744-45
trunks
intertoll
automatic
operation 927-54
equipment 929-34; ill us 933
scheme, basic 937-52
transmission 927-54
equipment 929-34; ilhis 933
scheme, basic 937 52
waveguide
dominant mode
pulses, millimicrosecond 35-65
apparatus 36^3
See also Life expectancy; Reliability;
Ruggedness
Test Set
card-o-matic
relay circuits 1155-78
tape-o-matic
relay circuits 1155-78
Test Machines
capacitors 1179-98
development 1129-35
networks
resistance -capacitance 1179-98
requirements 1132-33
Tetrode Transistor See Transistor:
junction
Thaeler, Charles S.
biographical material 533
Crosstalk on Open-Wire Lines 515-18
Theories for Toll Traffic Engineering in
the U. S. A. (R. i. Wilkinson) 421-
514
Theory of Swept Intrinsic Structure (W.
T. Read, Jr.) 1239-84
Theurer, H. C.
semiconductor studies i
Thomas, Donald E.
biographical material 246, 765
Diffused Emitter and Base Silicon
Transistors 1-22
Tables of Phase of a Semi-Infinite Unit
Attenuation Slope 747-49
Thomas, L. C.
amplifier
pulse
regenerative
transistor 1114
Thompson, G. P.
Nobel Prize in Physics, 1937 iii
Tien, Ping King
biographical material 533
Large-Signal Theory of Traveling -Wave
Amplifiers 349-74
Toll Alternate Routing See Routing
Toll Switching See Switching
Toll Traffic See Traffic
Traffic
concentrator
line
remote controlled 249-93
routing, see Routing
toll
Clos, C, study 431,470
engineering
United States 421-514
expansion 423
Kosten, L., study 431
overflow
moments 507-11
peakedness 443-46; graph 444
Wyckoff, Miss E. V., study 445
t ranking 421-514
Transatlantic Telephone Cable
repeaters
delay distortion
phase, tables
tabulation 747-49
26
THE BELL TELEPHONE SYSTEM TECHNICAL JOURNAL, 1956
Transducer
helix
coupled 161-65
heterodyne conversion
nonlinear element
admittance 1403-16
gain 1403-16
Transistor
base, see Base
contacts, see Contact
high-frequency operation
base layers, thin 1
junction
alloy
germanium
concentrator, line
remote controlled 253
temperature, effect 253
analog systems, applications 295-
332
digital systems, applications 295-
332
n-p-n
silicon
base, diffused 1-22
design 14-21
electrical characteristics 6-
10
fabrication 2-6
parameters, design 14-21
structure 10-14
emitter, diffused 1-22
design 14-21
electrical characteristics 6-
10
fabrication 2-6
parameters, design 14 21
structure 10-14
p-n-p
germanium
base, diffused 23-34
electrical characteristics 26-
33
fabrication 23-24
physical characteristics 24-
26
properties 295
parameter, see Parameter
point-contact
applications 768
characteristics
surface treatments
effect 767-811
demand 768
dependal)ility 768
design 769
electrical characteristics 768
knowledge
empirical 769
military applications 768
physical properties 769-811
processing
surface effects 767-811
reliability 768
ruggedness 768
power consumption 295, 1085
reliability 295, 1085
size 295, 1085
surface, see Surface
Transistor Amplifier See Amplifier
Transistor Circuits for Analog and Digi-
tal Systems (F. H. Blecher) 295-332
Transistor Integrator See Inte-
grator
Transistor Pulse Regenerative Aviplifiers
(F. H. Tendick, Jr.) 1085-1114
Transistor Voltage Encoder See
Encoder
Transistorized Binary Pulse Regenerator
(L. R. Wrathall) 1059-84
Translator
card
4A illus 1006
magnetic drum alternative 707,
709
magnetic drum illus 710
administration equipment 741-44 ;
illus 740
block diagram 742
l)lock diagram 720-21
card translator
alternative 707, 709
circuit design 725-41
equipment 725-41
functions 719-25
interchangability 719
switching
toll 707-45
testing program 744-45
INDEX
27
Transmission
data, sec Digital Systems
digital
historj- 1059-84
loss
resonance
modes
loosely-coupled 899-906
1 runk
intertoll 955
dialing
direct distance 955-72
operator distance 955-72
microwave
pulse, binary
advantages 67-68
regeneration 67-90
rate 917
routing, see Routing
trunks
intertoll
testing
automatic 927-54
See also Information Rate
Transmission Lines
concentrator, see Concentrator
dispersion
helix, bifilar 146-48
helices, coupled
equations 133-37
open -wire
crosstalk 515-18
transpositions 515-18
Transmission Loss due to Resonance of
Loosely-Coupled Modes in a Multi-
Mode System (A. P. King, E. A. J
Marcatili) 899-906
Transmission Systems
multimode
loss
modes
loosely-coupled 899-906
Transposition
transmission lines
open-wire 515-18
Traveling-Wave Tube See Electron
Tube
Trunk(s), Trunking
intertoll
Bell System statistics 423
loss
net
maintenance
dialing
direct distance 955-72
operator distance 955-72
operation
testing
automatic 927-54
transmission
testing
automatic 937-54
routing, alternate 437-42
traffic engineering 421-514
Tube, Electronic See Electron Tube
Type M1789 Electron Tube See Elec
tron Tube: traveling wave
U
Ulilir, Arthur, Jr.
biographical material 533
Electrolytic Shaping of Germanium and
Silicon 333-47
United States
telephone statistics 423
Use of an Interference Microscope for
Measurement of Extremely Thin Sur-
face Layers (W. L. Bond, F. M.
Smits) 1209-21
Vacuum Tube See Electron Tube
Voltage
breakdown
diodes 685
photo, see Photo-Voltage
Voltage Comparator See Compa-
rator
Voltage Encoder See Encoder
Voss, R. G.
electron tube
traveling wave
M1789 1343
W
Wafer-Type Millimeter Wave Rectifiers
(W. M. Sharpless) 1385-1402
28
THE BELL TELEPHONE SYSTEM TECHNICAL JOURNAL, 1956
Walker, Laurence R.
amplifier, traveling wave
large signal theory 373
biographical material 247
Growing Waves due to Transverse
Velocities 109-25
Wallace, R. L., Jr.
amplifier
transistor
junction
tetrode 840
Wave
backward
amplifier, traveling wave 351-55
circular
attenuation
5-6mm
pipes
medium-sized 1115-28
small 1115-28
forward
amplifier, traveling wave 351-55
millimeter
rectifier
point-contact
wafer-type 1385-1402
slow
propagation
electron flow 109-25
Wave Coupler See Coupler
Wave Rectifier See Rectifier
Waveguide
coupler, see Coupler
dominant mode
testing
pulses
millimicrosecond 35-65
apparatus 36-43
helix 1347-84
attenuation 1358
boundary value problem 1351-55
composition 1347-84
equation 1381-84
formation 1348-50
propagation constants 1355-58
helices
zero-pitch 1358-78
mode, see Mode
round
attenuation
5-6mm 1115-28
medium-sized
wave
circular
attenuation
5-6mm 115-28
small
wave
circular
attenuation
5-6mm 115-28
switch, see Switch
transmission, see Transmission
Waveguide Investigations with Millimicro-
second Pulses (A. C. Beck) 35-65
Weeks, G. E.
testing machines 1198
Weisbaum, S.
biographical material 989
Field Displacement Isolater 877-98
Weiss, M. T.
ferrite devices
nonreciprocal 877
Weiss, Miss R. A.
phase, tables
tabulation 749
Western Electric
test machines 1129-54
testing
automatic
facilities 1154
Whit acre, W. E.
wave
electric
circular
attenuation 1128
Wilkinson, Roger I.
biographical material 533
Theories for Toll Traffic Engineering in
the U.S. A. 421-514
Wire Center
defined 250
Wisconsin
intertoll trunk groups, principal
timp 424
INDEX
29
Wolfertz, W. F.
amplifier
transistor
junction
tetrode 840
Wolontis.V.M.
amplifier, traveling wave
large signal theory 373
Wrathall, Leishman R.
biographical material 1237
Transistorized Binary Pulse Regener-
ator 1059-84
Writing
magnetic drum 712-13
Wyckoff, Miss E. V.
toll traffic study 445
Young, James A., Jr.
biographical material 1466
Helix Waveguide 1347-84
Zone Leveler illus 656
Zone Leveling
germanium
apparatus 655-60 illus 656
technique 655-60
principles, basic 638-41
Zone Melting
defined 637
Zone Refining
germanium 637
Printed in U. S. A.
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