CO
u< OU_1 58332 >m
CO
ELECTRICAL COUNTING
ELECTRICAL COUNTING
With special reference to counting
ALPHA AND BETA PARTICLES
by
W. B. LEWIS, M.A., Ph.D.
Fellow of Conftttf 8Wff?aius College^ CantbriJ^e
University Lecturer in the Cavendish Laboratory
CAMBRIDGE
AT THE UNIVERSITY PRESS
1948
First printed in Great Britain at the University Press, Cambridge
Reprinted by litho-offset
by Percy Lund Humphries & Co. Ltd.
and published by the Cambridge University Press
(Cambridge and Bentley House, London)
Agents for U.S.A., Canada and India: Macmillan
PRINTED IN GREAT BRITAIN
CONTENTS
Preface page vii
Chapter I. IONIZATION BY SINGLE PARTICLES i
II. COUNTING IONIZATION CHAMBERS 5
III. LIMITATIONS OF AMPLIFIERS 16
IV. DESIGN OF AMPLIFIERS 23
V. OSCILLOGRAPH RECORDING 43
VI. FEEDBACK AND StABiLizERS 47
VII. MIXING CIRCUITS, TRIGGERED CIR-
CUITS AND DISCRIMINATORS 61
VIII. RECORDING COUNTERS 77
IX. GEIGER-MULLER TUBE COUNTERS 98
X. STATISTICS OF RANDOM DISTRIBU-
TIONS 114
XL COINCIDENCE COUNTING 121
XII. ENERGY DETERMINATIONS FROM
RANGE MEASUREMENTS %.. 126
Appendix 140
References 142
PREFACE
The technique of electrical counting has grown as an essential
aid in research in nuclear physics and this book owes much to
those who have pursued this science at the Cavendish Labora-
tory.
The central chapters of this book, beginning with Chapter in,
will I hope be of interest to many who have occasion to use
valve circuits, but who may not be concerned with nuclear
physics. The application of the technique to nuclear physics is
unfortunately somewhat in abeyance owing to the war at the
time of publication. I must also plead the war as my excuse
for not having included references to work published since the
beginning of the war.
I wish to express my thanks to all those of the Cavendish
Laboratory who have assisted with the preparation of this book
and especially to Dr N. Feather and Mr J. A. Ratcliffe who
have read and made valuable contributions to the text, and to
Mr G. R. Crowe who has drawn a number of the figures. The
fast counting meter illustrated on page 80 owes much in design
and construction to Mr J. Fuller of the Cavendish Laboratory
workshops.
W. B. LEWIS
1942
Chapter I
IONIZATION BY SINGLE PARTICLES
Individual atomic and subatomic particles may be detected if they
are electrically charged and possess sufficient kinetic energy.
When such particles pass through matter the electric charge
produces mechanical forces sufficient to disrupt the electronic
configurations of the atoms through which they pass. A trail of
charged atoms or ions is therefore left in the wake of the swiftly
moving particle.
One method of observing this trail of ions is by its electrical
effect, and it is with this general method that this book is exclu-
sively concerned. Another important method of observation is
provided by the Wilson expansion chamber in which visible
water drops may be condensed on the ions of such a trail in a gas.
These two methods are the most valuable means of observation
known in nuclear physics. They are closely interdependent; ex-
pansion chamber observations facilitate and make more certain
the deductions from the electrical effects. The expansion chamber
is supreme for observations in three dimensions. The electrical
method, on the other hand, is unsurpassed for the rapid accumula-
tion of data and for exact energy measurements. Two further
methods are also of importance, namely, observation of the
photographic effect of the trail of ions in a sensitive photographic
emulsion, and of the luminous effect of the trail in certain crystals
such as zinc sulphide.
Electrical methods of counting the particles all depend <5n the
ionization of the trail. It is therefore important to know the
ionization per unit length, usually called the specific ionization,
produced by different particles in different media. This specific
ionization depends to a certain extent on the energy of the
particle. Except for high-energy particles of energy greater than
io 8 e.V., such as are encountered in cosmic rays, there exists
experimentally a sharp division between the light particles which
2 ELECTRICAL COUNTING
are positive and negative electrons (/?-rays), and the heavy
particles such as protons, a-particles and other atomic nuclei.
The latter produce such dense ionization that it is possible to
measure, at least roughly, the ionization in less than a millimetre
of a single track in air at atmospheric pressure. The total range in
air of a typical a-particle of high energy ( ~ 7 M.e.V.) from a radio-
active substance would be a few centimetres, and the trail would
contain more than a hundred thousand ions. The specific
ionization on an electron track, on the other hand, is so slight
(4-50 ions/mm, air) that only by some method such as amplifying
8000
0-2 04 0*6 0*8 1-0 1-2 1*4 1-6 l8 2-0 2 2 2 4 2 6 2-8 30
Range in air in cm. (760 mm. 15 C.)
Fig. i -i. Specific ionization. Range curves for different particles.
the ionization by collisions can the ionization on a single electron
track be measured. Though the ionization is not easily measured
it may readily be detected by a device in which it releases a
momentary electrical discharge. Such discharge counters, as
they are termed, may be so sensitive that a discharge is produced
by a single pair of ions.
Fig. i-i shows specific ionization-range curves for the com-
moner particles in air. Except for ranges of a few millimetres
these curves are approximately of the same shape but with the
scale of ranges proportional to Af/Z 2 , where M is the mass and
Z the charge number of the particle, and the ionization scale
proportional to Z 2 . At short ranges the phenomenon by which
IONIZATION BY SINGLE PARTICLES 3
the effective charge of an a-particle is reduced by capture of an
electron disturbs this relation. The curves shown are based on
experimental observations. For long ranges the ionization de-
creases approximately as ^i/R, where R is the range, and for still
longer ranges as %/i/R.
Knowledge of the specific ionization, besides being important
for a proper appreciation of electrical recording processes, has
also led to means of determining the energy of a particle with a
high degree of precision. The energy of such a subatomic pro-
jectile is always ultimately determined by the curvature of its
path in a magnetic field together with determinations of its mass
and charge. It is, however, found that the ionization accounts for
practically all of the energy lost by the projectile. Now if the
specific ionization and, also the energy loss in forming a pair of
ions were constant for a particle of any energy, it would follow
that the particles would travel a total distance or range dependent
only on the initial energy. This is found to be approximately true,
but observation shows that particles initially of the same energy
have ranges which are not exactly equal. This is explained as due
to the statistical nature of the ionization process. This straggling
of the ranges of particles of a given energy has been studied in
detail for a-particles. Consequently it is now possible to deter-
mine the initial energy of a group of a-particles with a very high
degree of precision by measuring the ranges.
In common with all accurate measurements such a-particle
range measurements require careful attention to many details.
These will be discussed further in the last chapter, but here it
may be stated that such measurements require the measurement
of the ionization over a certain small length of the track of in-
dividual particles. Chapter xn is included in the present account
just because a discussion of the means for measuring this ioniza-
tion will be one of our main concerns.
The tracks of the heavy particles through air are for the most
part straight, only occasional large-angle deflexions occurring.
These are most common in the last few millimetres of the range.
The last few centimetres of the track of an electron, on the other
1-2
4 ELECTRICAL COUNTING
hand, are so curved that measurements of individual ranges can
only be made with any certainty in an expansion chamber.
Measurements of electron ranges by electrical recording result in
limiting ranges from the source which are considerably shorter
than ranges measured along the track. Nevertheless, such mea-
surements are of value if made in some dense absorber such as
a solid so that the lateral deviation of the rays is minimized. It is,
moreover, possible to determine energies from the ranges with
some precision. For the high-energy electrons for which this
method is most suitable the range varies almost linearly with the
energy.
Chapter II
COUNTING IONIZAT1ON CHAMBERS
The function of a counting ionization chamber is to produce a
change of potential on the input grid of the first valve of the
amplifier from the ionized track in the chamber. Usually the
chamber is operating with such small total charges that the
maximum changes of potential are not many times greater than
the minimum it is possible to detect. It is therefore desirable to
collect as much of the charge as possible on an electrode having
a minimum of capacity. Little advantage will, however, be gained
by making this capacity much less than the inherent valve input
capacity which is generally of the order of a few centimetres.
The size and shape of the chamber is usually determined by its
particular function; before, however, discussing special designs
a few general considerations may be noted. One electronic charge
e on a capacity of C cm. produces a potential change 3000/0 V.
= o-144/C /*V. Under ordinary circumstances it is possible to
detect on a capacity of 10 cm. a charge of 5000, which produces
a change of potential of 7-2 /*V. Such a small change of potential
is only detectable if it takes place suddenly; this is explained at
the end of this chapter and in the next on the limitations of
amplifiers. It is found that the time of collection of the ions should
be as short as possible, but an alteration of the amplifier or
recording system may be required to take advantage of a very
short collecting time, and with a given amplifier it is possible that
no advantage will be gained by shortening the collecting time
beyond a certain point.
The insulation of the collecting electrode must be of the highest
order. Leakage across good insulators takes place mainly over
the surface. Currents flowing in thin surface films are liable to
be unsteady; this gives rise to fluctuations of charge which may
affect directly or by electrostatic induction the potential of the
6 ELECTRICAL COUNTING
collecting electrode. It is not the magnitude of the insulation
resistance which is important, but the nature of the path taken
by the leakage currents.
The collecting electrode should be supported by insulators
only of the highest grade, such as quartz, amber, sulphur or
sealing wax. The insulators need not be long, for a variable sur-
face charge cannot be tolerated. If the surface is bad the insulator
is useless. The fixed ends of the insulators should be attached to
metal which is as near as possible to the potential of the collecting
electrode. The insulators should preferably be placed so that no
charge is driven on to them from the ionization in the chamber ;
satisfactory chambers have, however, been made in which this
precaution has not been observed.
The insulation of the high-potential electrode need not be of
such a high order; rubber and ebonite are satisfactory. The
insulation should be placed so that a variable surface charge on
it does not induce charges on the collecting electrode. If the
high-potential electrode is not completely screened it is liable to
pick up stray electromagnetic disturbances. To minimize the
effect of this the electrode should have a large capacity to earth.
The condenser providing this capacity should be placed very
close to the high-potential electrode and the earth connexion
should be as short as possible because any length of wire has an
appreciable reactance for some sufficiently high frequency. Such
high-frequency disturbances are not in themselves harmful, but
when rectified by the valve input circuit they give rise to dis-
turbing low-frequency impulses.
When it is desired to have a very high potential difference across
the chamber, trouble may be experienced from small discharges
of the corona type occurring at the junctions between the solid
insulator and the metal. This phenomenon is caused by the
difference of dielectric constant between the insulator and the
gas in the chamber; it is therefore desirable to use an insulator
with as low a dielectric constant as possible. Sulphur and resin
waxes are good in this respect, with dielectric constants of 3-4.
The conductor should also be in intimate contact with the
CO UNTING IONIZA TION CHAMBERS 7
dielectric; sulphur and the waxes are again very suitable as they
may be melted on to the metal. For potentials over 2000 V. it may
be necessary or more satisfactory to subdivide the insulation,
using a number of metallic guard rings maintained at inter-
mediate potentials by resistances. The resistances must be very
constant unless bridged by condensers. The same considerations
apply to the insulation of the condenser connected across the
chamber to prevent electromagnetic pick-up.
It is sometimes necessary to mount the first valve at some
distance from the ionization chamber. This may happen when
the ionization chamber must operate in a strong magnetic field.
The most satisfactory means of connecting the collecting elec-
trode to the first valve is probably by a thin wire along the axis of
a wide metal tube. This keeps the capacity low but provides a
hrge volume from which ions may be collected. To avoid this
collection of ions the wire should be at the same potential as the
surrounding tube. Where a difference of potential of only a volt
or so occurs it has been found satisfactory to run the wire through
a piece of narrow quill glass tubing along the axis of the wide
metal tube. The insulation at the ends of the tube may be im-
proved with sealing wax to reduce the leakage of charge from the
glass to the collecting electrode. It is presumed that the outer
surface of the glass tube quickly takes up such a potential that
there is no further collection of charge. The quill tube by pre-
venting movement of the wire also minimizes microphonic
effects.
Ionization chambers are very liable to be microphonic; this
is one of the most important points to be considered in the
design.
For the accurate measurement of ranges the particles should
enter the chamber through a uniform or very thin metallic foil.
Ions must be collected from the space immediately adjacent to
the foil, so the foil is necessarily in a strong electric field. Slight
movements of the foil are therefore liable to induce charges on
the collecting electrode and the chamber is consequently micro-
phonic.
8
ELECTRICAL COUNTING
The design shown in Fig. 2-1 probably represents the simplest
chamber satisfactory for accurate range measurements. The
collection of ions from all tracks penetrating the same distance is
exactly similar, so the amount of the charge collected is a measure,
although ambiguous, of the depth of penetration. The ambiguity
arises because of the maximum in the ionization-range curve for
a single particle. An a-particle which passes right through the
chamber and still has a residual range of about 2 mm. after
reaching the back wall of the chamber will give most ionization.
A particle which does not penetrate so far, as also a swifter particle
which has still farther to go, will give less ionization.
High Potential SOOw/ts
Ebonite
Holes to allow free
passage of sound
Brass
Earthed cap
Fig. 2' i
The ions are separated by the electrostatic field in a direction
approximately along the track. The ions will not be all collected
at the same time. If the ionization along the track is approximately
uniform, the rate of collection of ions will be also approximately
uniform. The potential of the collecting electrode will not,
however, rise uniformly, because before the ions are collected
the potential will be altered by the induced charge. In an exact
calculation of this induced charge it would be necessary to con-
sider the infinite series of electrical images, the inhomogeneity
of the ionization, the different ionic mobilities, the negligible
change of potential of the guard ring, and the total capacity of the
collecting electrode. Here, however, a very simple consideration
must suffice. If Fig. 2-2 represents positive ions moving to the
right and negative ions to the left under the action of the field
CO UN TING IONIZA TION CHAMBERS 9
between the high-potential electrode and the collecting electrode,
and if the ions close to either electrode are assumed effectively
to have been collected, then it will be seen that the initial rate of
effective collection of ions is just double the rate of arrival of ions
at the electrode. When only a few ions are left in the chamber
these will all be close to one or other of the two electrodes and
the effective rate of collection will be zero.
It has been mentioned that the time of collection of the ions
should generally be as short as possible. This time may be obtained
from a knowledge of the electric field and the mobilities of the
ions. The mobility of positive ions in air at atmospheric pressure
is about 1-35 cm./sec./V./cm. ; the mobility of negative ions
I High Potential
I Electrode
Collecting
Electrode
Negative Ions
Fig. 2-2
depends on the moisture and may be taken as 1-5 in moist air
and 1*8 in dry air. Mobilities may be assumed to be inversely
proportional to the pressure, but at pressures less than about
one-tenth of an atmosphere the mobility of negative ions increases
much more rapidly as the pressure is reduced. The mobility of
ions in hydrogen at atmospheric pressure is approximately
6 cm./sec./V./cm.
Hydrogen may with advantage be used instead of air as the
gas in an ionization chamber, for the high mobilities of ions and
the relatively low stopping power make it possible to use deeper
chambers and thus diminish the effects of small movements of
the foils, so the chamber is less microphonic. If the chamber
cannot be sealed gas-tight, it has been found possible to work
with a steady stream of hydrogen flowing through.
10
ELECTRICAL COUNTING
Special chambers.
A chamber which is not affected by ordinary noises may be
made by making the high-potential cap of thick ( > i mm.) brass
and cutting a grid in this for the particles to pass through. The
mesh of the grid should not be greater than the thickness of the
brass ; the holes may be square to reduce the number of particles
stopped. The outer surface may then be covered with thin gold
or aluminium leaf (stopping power 0*4-1 mm.).
This type of chamber is unsatisfactory if the particles are
already passing through a grid, as usually happens when the
source must be in a vacuum, for then it is difficult to move the
chamber without altering the relative shadow ratio of the two
grids. The number of particles counted at a given tange is thus
variable.
Differential chamber.
For the highest accuracy in the measurement of ranges a
differential chamber (Fig. 2-3) is used. The collecting electrode
in this is a thin foil through which the particles pass. The electric
High Potential
300 volts- +300 volts
Holes to allow
free passage
of sound
<x rays
Foil
Sulphur
'Ebonite
Earthed cap*
Fig. 2*3. Differential chamber.
field on either side of this foil is in the same direction in space,
so that positive ions are collected on one side and negative ions
on the other. By suitably proportioning the depths of the two
chambers it may be arranged that a particle passing right through
the two chambers gives only a very small nett charge to the
COUNTING IONIZATION CHAMBERS 11
collecting electrode. The size of the impulse as a function of the
residual range of an a-particle entering the front chamber is
shown for a typical differential chamber in Fig. 2-4. It should be
realized that the form of this curve depends on the specific
ionization of the particle at points near the end of its range; this
-0-1
01 234567 8mm
Residual length of a-particle track
Fig. 2-4
is, unfortunately, not known with accuracy, as explained in
Chapter i.
It will be realized that a differential chamber is very micro-
phonic. If possible the source and chamber should be sealed
up in an airtight box to exclude sound, and the whole should be
mounted on rubber or some sound-absorbing material to avoid
the transmission of vibrations by contact. Where this is not
possible it has been found best to go to the other extreme and
make the chamber as much of an openwork structure as possible,
12 ELECTRICAL COUNTING
rings of large holes being drilled through the disks supporting
the foils, and through the sides of the tubes to which the disks
are fitted. The object is to prevent as far as possible differences
of pressure from existing between the two sides of the foil. It
should, however, be arranged that the forms of the collecting
and high-potential electrodes are not such that they would ring
even at a very high pitch when struck.
Discriminating chamber.
Alfvn(a) has shown that it is possible to -obtain a rough trace
of the distribution of ionization along the track in an ionization
chamber and thus to discriminate between a-particles, protons
and possibly deuterons, triplons and He 3 particles. For this it is
necessary to avoid the effect of the charge induced on the collecting
electrode before the actual collection of the ions. This is achieved
(Fig. 2-5) by placing the collecting electrode behind a grid which
First Valve
of Amplifier
Source of
Particles
Foil
Fig. 2-5
replaces the collecting electrode in an ordinary single chamber
such as has been described. The potentials are arranged so that
in the ionization chamber proper the drift velocity is smaller than
in the chamber behind the grid. A certain proportion of the ions
arriving at the grid pass through; these are quickly drawn to the
collecting electrode, so the rate of collection of ions is pro-
portional to the rate of arrival at the grid. This in turn is pro-
portional to the ionization density of that portion of the track
which is at that instant arriving at the grid.
COUNTING IONIZATION CHAMBERS 13
The writer has found that by a suitable design of coupling
circuit in the amplifier it is possible to obtain from such a chamber
an impulse of the form shown in Fig. 2-6. On an oscillograph
record with the paper running at a high speed this would have the
form shown at (a), and with the paper running slowly this has the
form (b). The height of the thick portion is a measure of the total
ionization, and the extra height of the thin portion is a measure
of the ionization density at the front of the chamber. This allows
a discrimination between a-particles and protons which is useful
when protons must be counted in the presence of large numbers of
a-particles. For the same total ionization the proton will give less
ionization at the front of the chamber.
Oscillograph A
Deflexion \
Time -* /\ Time
A similar discrimination between particles may be made by
using a deep chamber to avoid the ambiguity of the interpretation
of the size of an impulse as a measure of the penetration distance.
To avoid the slow collection of ions along the depth of a deep
chamber it is better to let the particles travel parallel to the
electrodes which may then be closer together. By measuring the
variation of the average size of impulse as the distance from the
source is altered, the ionization density along the track may be
determined and hence the particle identified.
Ionization chambers for recording a-particles and
protons in the presence of intense /?- and y-radia-
tion.
The simple chamber and the differential chamber already
described were developed primarily for the observation of
a-particles in the presence of a background of ionization much
more intense than the ionization due to the a-particles. It proved
possible to work with an ionization which on the average was
100,000 times the ionization due to the a-particles. Such dis-
i 4 ELECTRICAL COUNTING
crimination was possible because the ionization due to a single
a-particle was formed practically instantaneously and the charge
collected in about 2 x io~ 4 sec. The background ionization might
be the equivalent of that from io 5 a-particles per sec., so that
in 2 x icr 4 sec. it would be equivalent to 20 a-particles or say a
total of 400,000 ions from a chamber 3-5 mm. deep. This rate is,
however, continuous except for the statistical fluctuations which
would amount to *J(nAt) ions in a short time At, where n is the
average number of ions/sec. The probable fluctuation in 2 x io~ 4
sec. would thus be only ^(400,000) == 630 ions. The arrival of an
a-particle produces a charge of 20,000 ions, which could readily
be distinguished from the background fluctuations.
As explained in the next chapter this background is added to
by that arising in the amplifier. The relative importance of this
may be decreased by increasing the ionization collected by
allowing proportional amplification of the ionization by ionic
collisions, which takes place in strong electric fields. Such strong
electric fields also decrease the time of collection of the ions,
which enables the background to be further reduced. This
practice of obtaining proportional amplification by collision has
been successfully used in experiments where protons were to be
observed at a slow rate with a large background of y-ray ioniza-
tion, as in experiments on artificial disintegration produced by
the a-particles from thorium C and C', and radium C'.
Proportional amplifying chambers.
Geiger and Klempereru-o studied in detail the behaviour of
counters in which the negative electrode is a small polished
sphere. Many workers have since used this type of counter with
which it is possible to obtain a proportional amplification of the
charge up to about io 4 as a limit, but more usually an amplifica-
tion of about io 3 or less is employed, as such amplification is more
stable and consistent.
Zipprich(8z) has developed a chamber with parallel plane
electrodes, one of which is a grid through which the ions are
admitted to the main accelerating space. The electric field in this
COUNTING IONIZATION CHAMBERS 15
space penetrates to some extent through the meshes of the grid
so that ions are drawn to the grid and some pass through. A pro-
portional amplification of about 1000 was used.
When the voltage on a proportional counter is raised the
amplification tends to become unstable, and for an amplification
exceeding io 5 it is found that discharges are set up independent
of the initial ionization. This process has been developed and is
widely used for recording /?- and y-rays. The Geiger-Miiller
counter discussed in Chapter ix operates on this principle.
Chapter III
LIMITATIONS OF AMPLIFIERS
When the amplification or gain of an amplifier is made very
great a background is observed. On listening with earphones to
the output of a high-gain audio-frequency amplifier this back-
ground is heard as a rushing noise. Three main sources of this
background noise have been recognized. First, noise dependent
on the input circuit but independent of the current in it; this is
identified as an effect of thermal agitation. Secondly, noise which
increases with the anode current of the first amplifying valve;
one recognized cause of such noise is known as the shot effect.
Thirdly, when a current flows through certain types of conductor
it is presumed that the lines of current flow do not remain constant
in detail, and this gives rise to noise generally rather more irregular
than noise from the first two sources but sometimes difficult to
distinguish. For example, if the current is accompanied by
electrolysis which results in the formation of gas at the electrodes,
the lines of current flow will constantly be interrupted by the
bubbles of gas. A somewhat similar effect is produced when
current flows through thin films of metal or carbon. This depends
on the physical nature of the film, for carbon film resistances
which do not show this effect are made and marketed by Siemens-
Schuckertdi,*)), but the writer has found no single specimen of
any other of the many film resistances, commonly advertised as
silent, which is free from this effect. Carbon composition resist-
ances are similarly defective. Current-carrying contacts with
insufficient contact pressure similarly give rise to noise. The
cathodes of certain valves show a similar effect; one particular
phenomenon of this type has been named the " flicker" effect (36),
the emission from any particular point of a cathode appearing to
flicker though the emission of the whole may appear constant.
This effect is most apparent at frequencies below about 1000
c./sec.
LIMITATIONS OF AMPLIFIERS 17
The third source of noise may be eliminated by using only
well-made wire-wound resistances (or the Siemens-Schuckert
resistances) in the early stages of the amplifier, and by selection
of the first valve. All contacts must have sufficient contact pressure
and sufficient contact area for the current they have to carry.
The magnitude of the thermal agitation effect may be derived
directly from the principle of the equipartition of energy. The
idealized elementary circuit (Fig. 3-1) has only one natural or
characteristic frequency; it thus has only two degrees of freedom
and we may write \LP = \CV 2 = \kT, where i 2 is the mean
square current flowing and V 2 the mean
square voltage on the condenser, k is
Boltzmann's constant, T is the absolute
temperature. In order to apply this we
require to know the distribution of this
energy over the frequency spectrum. This
problem is exactly analogous to the de-
termination of the distribution of radiant energy in the black-
body spectrum. The calculation on these lines was first made
by Nyquist<53). Although this is very illuminating it is a little
too long to be included here, and we may just note the con-
clusions. First it is to be noted that the thermal energy is
communicated to the idealized circuit through its resistance
R. If then we inquire thd rate at which two equal resistances
interchange energy as a function of frequency, it is possible
to determine the thermal agitation e.m.f. existing between
the ends of a pure resistance as a function of frequency. This
resistance with its thermal e.m.f. may then be considered inserted
in the elementary oscillatory circuit ancl the resultant voltage
across the condenser may be calculated.
If E 2 is the mean square e.m.f. between frequencies v and
v -f dv existing between the ends of a resistance R at temperature T,
then it is found that E 2 = \RkTdv. Calculating V 2 from this and
integrating over all frequencies leads to the expected result
V 2 = kT/C, which we note is independent of R. The frequency
distribution does, however, depend on R.
i8 ELECTRICAL COUNTING
/*Vs*00
It may be noted that El for a pure resistance is infinite.
Ji>~0
This is the old impasse of the classical theory of the distribution
of energy in the black-body spectrum and is resolved, as in that
case, by the adoption of quantum principles of the partition of
energy at high frequencies. On the other hand, when the resist-
ance e.m.f. is applied to our idealized elementary circuit no
resultant voltage is found across the condenser at high frequencies.
This paradox is again resolved by noting that no real circuit has
only one characteristic mode of oscillation; it has 3, where n is
the number of atoms in the circuit (cf. Debye's (17) theory of the
specific heats of solids).
In the particular application to amplifiers for ionization pulses
we are concerned with thermal agitation in the input circuit at
low frequencies up to i or 2 x io 4 c./sec. At these frequencies the
circuit may be considered simply as a condenser C shunted by
a resistance R for which we have
.
* = -- "^ ' ~ ~~^ tan
^ D -|
toCR
JO
If C lo/e/iF. and R io l ohms, CR = o-i sec. Frequencies
higher than 10 c./sec. (o)CR>2n) contribute only 10% to
F 2 .
It is rarely necessary to amplify frequencies as low as 10 c./sec.,
and ordinarily thermal agitation in the input circuit may be
neglected.
Thermal agitation does, however, provide a convenient means
of calibrating amplifiers, for if R is reduced to io 5 ohms, then
CR = io~ 6 sec., so that the thermal agitation noise covers the
frequency range amplified, and the sensitivity of the amplifier
may be gauged by measuring with a thermo-couple or other
square law device the rushing noise in the output circuit when a
ioo,ooo-ohm resistance is connected between the first grid and
cathode. If the frequency range of the amplifier is known, this
may be made the basis of an absolute calibration of the amplifier.
Even without this knowledge the method is found useful for
LIMITATIONS OF AMPLIFIERS 19
comparing similar amplifiers and for keeping a check on amplifica-
tion and background level. .
As has already been stated the background due to thermal
agitation in the input circuit of a pulse amplifier should be
negligible. The main contribution to the background is provided
by the first valve itself. Many partial explanations of this back-
ground have been discovered, but it has not been found possible
to predict its magnitude from fundamental principles. Some of
the recognized contributory phenomena may be mentioned.
First the valve possesses an internal resistance, which means that
the energy dissipation in the volume distribution of charge within
the valve is controlled by the applied potentials. The statistical
thermal variations in this space charge conversely affect the
electrode potentials. This space charge is, however, very far from
thermal equilibrium. It is thus not possible in any simple way to
assign a magnitude to the thermal agitation voltage, but on general
grounds it might be supposed that the voltage would be greater
the higher the temperature of the cathode. Evidence in support
of this has been obtained, notably by Pearson (54). At low fre-
quencies, however, the flicker effect predominates.
Particularly at high frequencies a contribution from another
fundamental cause may predominate. This is known as the shot
effect and depends on the finite size of the electronic charge. It
must be emphasized that this effect is never fully operative in an
amplifying valve. Its magnitude may, however, be quite simply
derived for a valve worked under saturation conditions, under
which the arrival of electrons at the anode is independent of
small variations of anode potential, arid in which the time of
transit of an electron from cathode to anode is negligible compared
with the periodic times of the frequencies concerned. Let C be
the anode-cathode capacity and R the external anode circuit
resistance. Let Q be the instantaneous charge on the anode and
I the mean anode current. The energy E stored in C is then ^Q 2 /C 9
but only discrete changes of Q of amount e are possible, where
e is the electronic charge, so we have E+AE = (Q + e) 2 /2C or
eQ/C+e*/2C. If n electrons reach the anode in unit time
20 ELECTRICAL COUNTING
the total change of energy in unit time is nAE = neQ\C+ ne z /2C.
This energy is dissipated in /?, but the energy dissipated in R in
unit time is 1 2 R + *|/?, where i f = fluctuation current. But l ne\
therefore neQ/C = IQJC = PR. So we have i}R = m? 2 /2C, or
i* = te/zCR, which is the well-known shot effect equation. This
derivation is due to E. B. Moullin(49).
The mean square fluctuating voftage across R is therefore
proportional to e, the electronic charge, and f, the mean anode
current. As an example of the magnitude, the root mean square
voltage = 200 juV. for I - i mA., C = 20 pfiF., R = io s ohms.
The energy is then spread over frequencies of the order
i/CR = 500,000 radians/sec.
When as in an amplifying valve the anode current depends on
the anode potential, these fluctuations tend to be smoothed out,
for if in a certain interval too few electrons are received the anode
potential rises and thus increases the mean current. But this is
not the only effect operating to reduce the shot effect. The anode
current is limited by the presence of an electronic space charge
round the cathode; the transit of an electron from cathode to
anode cannot therefore be considered to occupy a negligible time.
An electron in the space between cathode and anode induces
charges on the electrodes which vary with the position of the
electron. The change of energy of the anode-cathode capacity
cannot therefore be considered as taking place abruptly by
amount e.
In practice the selection of the first valve and its operating
conditions are determined by experiment. A few general con-
clusions may be noted: an uncoated tungsten filament valve is
liable to give occasional clicks and the general noise level is
liable to be high; a thoriated filament may be satisfactory, but
valves with such filaments are now rare and are liable to be
microphonic; the grid insulation of modern valves with oxide-
coated cathodes is often unsatisfactory, particularly if the elec-
trodes are positioned by mica spacers the surface path over which
between electrodes is short; defective grid insulation may give
rise to noise even though the insulation resistance may be high ;
LIMITATIONS OF AMPLIFIERS 21
the noise level of most valves increases relative to impulses on the
grid when the anode potential is increased above about 15 V., this
being presumably due to ionization; there are some exceptions
to this rule.
No valve specially designed for the purpose appears to be on
the market yet. Perhaps the nearest to a special design is the
Osram A 537, designed as the input valve for working from a photo-
electric cell for reproducing sound from film. This is a simple
indirectly heated triode with an amplification factor of 15-5.
Special attention has been paid to the grid insulation, not for-
getting the avoidance of microphony. This is achieved by
bringing the grid lead out separately at the top of the valve and by
using steatite in place of mica spacers to hold the electrodes.
The input valve of an amplifier for ionization pulses receives
a certain charge on the grid, and it is desired that the resultant
change of grid potential should be large. For this to be so the
effective grid input capacity must be as low as possible. It is
explained in the next chapter that this is more easily reduced by
using a screen-grid construction, leading to a tetrode or pentode
instead of a triode.
Many screen-grid valves are now made with the grid lead
brought out separately at the top of the bulb, and in some of these
consideration has been given to the grid insulation, slots being
cut in the mica spacers to increase the surface path over the mica.
Selected specimens of these are as satisfactory or better than the
A 537, and as these valves are used in ordinary radio sets their
price is much lower. The best valve that the writer has yet
encountered is a Western Electric type 310 A tetrode. This,
however, has a filament rating 10 V. 0-3 amp. which is generally
inconvenient. The Mullard Type SP 4 B pentode has been used
successfully. All valves with oxide-coated cathodes are more
silent or not less silent if the cathodes are run at a lower tempera-
ture than that normally recommended by the makers, and the
filament voltage may generally with advantage be from 10 to
20 % lower than the maker's rating.
Some valves (particularly triodes) of very high amplification
22 ELECTRICAL COUNTING
factor, such as Osram H 42 or H 30, cannot be operated with the
grid isolated, since the grid charges up to such a negative potential
that the anode current at low-anode voltages is reduced to zero.
A leak resistance of about io 9 ohms may be connected from the
grid to cathode to avoid this without causing trouble except when
very low frequencies are to be amplified.
The Osram D.E.V. has been used a great deal in this work.
This is a small valve with a thoriated tungsten filament in which
the grid is of low capacity and supported from a glass stem well
away from the anode and filament supports. The disadvantage
of this valve is that it is microphonic. Its noise level is, however,
low, though not lower than that of some of the new valves such
as the Osram A 537. Microphonic trouble with the D.E.V. is
lessened up to a point by increasing the filament temperature.
Also it will generally be found that the filament is not quite con-
centric with the grid and anode. The valve is least microphonic
when mounted with the filament horizontal and in such a position
that the sag of the filament brings it nearest to the centre of the
electrode system.
It is necessary to consider how a given change of potential on
the grid of the first valve may be made to stand out above the
background fluctuations. The potential V of the grid of the first
valve is a continuous function of time, and its variation is brought
about by the statistical fluctuations of a large number of events.
The probability (if small) of a certain change A V taking place in
a time A T will be proportional to A T. If, therefore, an impulse
which is a given small change of V is to be distinguished from the
background it must take place in a short time. How such an
impulse may be separated from the background is discussed in
the chapter on the design of amplifiers, and further in the section
on discriminators.
Chapter IV
.DESIGN OF AMPLIFIERS
Simple theory,
The simplest element of a resistance-capacity coupled amplifier
is shown in Fig. 4-1. In this C c is the coupling condenser, R the
H.T.+
H.T.-
Fig. 4-1
anode circuit resistance, R g the grid-leak resistance. R a is the
internal slope resistance of the valve. AV a represents a change of
anode potential, AV Q a change of grid potential. Suffixes i and z
will be used to denote successive valves. It may be seen that
R a
or
where T = CJR g . From Fig. 4-2 it is apparent that AV g2 becomes
appreciably less than AV ar at frequencies for which axi/T.
The amplification therefore falls at low frequencies.
In practice, the amplification also falls at high frequencies, due
to the interelectrode capacities of the valves and stray capacities
in the circuit.
24 ELECTRICAL COUNTING
The effective input capacity of an amplifying valve may be
very different from that when the cathode is cold. This arises
because a change AV Q will produce a change of anode potential
where m is the magnification of the stage, and
R
Fig. 4-2
the negative sign indicates that the anode potential falls when
the grid potential rises. The resultant change of potential on the
grid-anode capacity C ga is then (i -f ni)AV g \ the charge required
to produce this change is (i+m)AV g C ga . The effective grid-
anode capacity as far as the grid
circuit is concerned is thus seen
to be (i+m)C ga , for a change of
grid potential AV g requires a charge
(*+m)AV g C aa (Fig. 4-3). The
effective input capacity of the valve
is therefore C 7 = ( i -f m) C ga -f C gf ,
where C yf is the grid-filament
capacity.
At high frequencies, for which
the effect of R g may be neglected,
C c
Fig. 4-3
we have AV 2 =
- r (Fig. 4-4), but generally C c >C /f
and the effective circuit reduces to Fig. 4*5. The anode circuit
DESIGN OF AMPLIFIERS
Fig. 4'4
R
Att,,
Fig. 4-5
(OT
Fig. 4-6
26 ELECTRICAL COUNTING
JD
load reduces to R paralleled by C/, i.e. r~ss~~D' so
--
n
stage magnification becomes m = u ^~, . -7=^ ~, which is
* 5 ^J? a (i +;<><?,#) + #'
complex. This affects the input capacity C z of the first valve.
The magnification, neglecting the phase change, is
tiR i
;r2^2^, where r
This is illustrated in Fig. 4-6. As has been seen, however, C/ is
not constant but is given by C + mC ga \ the effect of this is to
raise the curve somewhat at high frequencies.
Tetrode or triode.
Screen-grid tetrodes or pentodes offer some advantages when
compared with triodes for resistance-capacity coupled amplifiers.
These screen-grid valves have an extremely small C aa , so that
C l is much smaller and m may be very high. For example, R may
be 100,000 ohms and the mutual conductance fi/R a may be
4mA./V., so that an amplification of 400 per stage may be
obtained if R a ^>R. C r may be about 15 /i/^F., to which must be
added the anode to screen-grid capacity of the previous valve,
about io//*F., and the stray capacity of the coupling condenser
to earth, about 5 /*/<F., making a total of 3O/4//F. Hence
C t r=^ CjR = 3 x io~ 6 sec.,
and amplification will be maintained up to 50,000 c./sec.
If, however, R were reduced to 10,000 ohms the amplification
would be 40 times and would be maintained up to frequencies of
about 500,000 c./sec.
These figures may be compared with those for triodes. A valve
such as the OsramMH4i may have /i = 75, R a = 12,000 ohms.
With an anode resistance of 50,000 ohms the stage gain at medium
frequencies would be about 60. C ga is about 4/^/tF., so that
Cj = 61 x 44- incidental stray capacities = 260 /t/tF.,
Cjr =s= C t R a as 2-6 x io~ 6 sec.,
and amplification is maintained up to about 60,000 c./sec.
DESIGN OF AMPLIFIERS 27
It is thus evident that the tetrode may have an amplification
comparable with that of a triode over a wider range of frequencies.
Against this apparent superiority of the tetrode it must be
remembered that special construction of the amplifier must be
adopted with the screen-grid valve to avoid any external increase
of C ga , for it is upon the low value of this (about 0-002 /^F.) that
its superiority depends. Also in such a high-gain amplifier as is
considered it would be necessary to adopt separate decoupling
CHARACTERISTIC CURVES FOR MULLARD SP4B WITH 250.00O OHM
ANODE RESISTANCE AND HT. VOLTAGE 200.
0-8
1.
-3 -2 -| 2
GRID VOLTS
Fig. 4-7
for the screen grids. In view of these complications, and also
because triodes have proved perfectly satisfactory for the present
purpose, the screen-grid valve is not always adopted. In America
it is more commonly used, as the American screen-grid valves
have mutual conductances of about 1-5 mA./V., and the practice
has been to keep to a stage gain of not more than 100, and to use
the same number of stages as in the equivalent triode amplifier.
To obtain a satisfactory performance from an amplifier using
screen-grid valves the grid-bias voltage must be kept within
28 ELECTRICAL COUNTING
narrow limits. This is well illustrated by the family of curves
(Fig. 4-7) for a screen-grid pentode (the Mullard S?4B) with an
anode circuit resistance of 250,000 ohms and an anode supply
voltage 200. The amplification falls when the anode voltage
becomes very low, and also when the anode current becomes very
low. For a given screen-grid voltage the grid-bias voltage at
which the anode current is cut off is almost independent of the
anode voltage. Moreover, if the valve provides an amplification
of 400 and has an anode voltage of 200 a change of grid bias of
0-5 V. would cover the whole working range. This indicates the
limits within which the grid bias must be fixed. It is often con-
venient to arrange that the grid bias is controlled automatically
by the average cathode, anode or screen-grid currents. Control
by the cathode current is probably most commonly adopted. This
is illustrated in Fig. 4-10 (e), (/).
It is useful to note that the ratio of screen-grid to anode current
is almost constant for any particular valve. If the screen grid is
connected to the anode it is easily seen that the cathode current
will divide between the two in a ceitain ratio depending on the
geometry of the electrode structure. Moreover, the anode current
is almost independent of the anode voltage over the working
range, so this ratio is preserved.
Design of the ionization pulse amplifier.
Five magnifying stages are generally more than sufficient to
give all the amplification that can usefully be employed. With a
special design fewer stages could be made to give the same full
output, but this practice is not generally adopted. Only three
stages of the normal amplifier are used to give a very high voltage
gain. Amplification is sacrificed in the first stage in order to secure
as low a ratio of background to pulse as possible. The final stage
is generally designed to give the maximum output power and not
the maximum voltage gain.
The overall voltage amplification required is between io 6 and
io 7 (i.e. 120-140 db.). Both with triodes and with tetrodes it is
easy to exceed this amplification with the five stages. If the first
DESIGN OF AMPLIFIERS 29
and last stages give an amplification of 10 and the other three
stages a gain of 60 each, the overall amplification would be
2-16 x io 7 . Usually such a high amplification is not required, and
it is possible to secure a greater constancy of amplification by
adopting negative feed-back to remove the excess amplification;
this important principle is discussed in Chapter vi.
It is not required that an ionization-pulse amplifier should have
uniform amplification over a wide frequency range, but since
the response of any linear amplifier to a transient impulse is a
unique function of its amplification-frequency characteristic, the
form of this characteristic is very important. Consider how the
pulse amplifier is required to act. A positive charge is collected
in a time which may be from io~ 2 to ro~ 4 sec. on an electrode
connected to the control grid of the first valve. This charge leaks
away relatively slowly, the discharge time constant being between
i and io~ 3 sec. This impulse must be registered, and perhaps
measured, in a time as short as possible so that the recorder is left
free to register another impulse with a minimum of delay. If Fig.
4-8 (a) represents the voltage change on the first grid, (6), (c) y (d)
represent the impulse after passing through one, two and three
coupling stages of the amplifier. If the time constants C C R of
these stages were made smaller, the ripple following the impulse
would be larger in amplitude and shorter in time. As the base-line
must be preserved for measuring subsequent impulses, the ripple
should be kept small in amplitude, so that C c R g must clearly be
as large as possible. But even then a large amount of time is
wasted on the downslope of the impulse. Most of this time may
be recovered for use by letting one and only one of the coupling
stages have a small C c R g . The result of this is shown at e.
This may be regarded in two ways. By including one quick
stage the amplification at low frequencies is reduced so that the
steep upslope is still amplified but the slower downslope is less
amplified. Alternatively, we may say that by having a small C c R y
the voltage cannot be maintained on one side of the axis for a
time much longer than C c R g .
The reason why only one quick stage or short time-constant
30 ELECTRICAL COUNTING
coupling may be introduced may be noted. If two were introduced
the back pulse after, the impulse would be comparable in magni-
tude with the impulse itself. If more than two quick stages were
introduced the ripple after the impulse would also be large so
that every impulse would appear at least double. It is seen that
Fig. 4-8
the quick stage is only of advantage when the time of collection of
ions is short compared with the recovery time of the collecting
electrode and the grid of the first valve. If this recovery time
cannot be made long it is sometimes an advantage deliberately
to make it short and to use no other quick stage in the amplifier.
This procedure is, however, not generally to be recommended
DESIGN OF AMPLIFIERS 31
owing to its effect on the background. Most of the background
originates inside the first valve, and if all the coupling stages
following this valve have long time constants the low frequencies
in the background, which are usually large due to flicker effect
and imperfect grid insulation, are fully amplified, with the result
that the grid voltage of the penultimate or of the output valve may
be varying over such a wide range at low frequency that the
amplification of short impulses may not be constant. For this
reason also it is an advantage that the quick coupling stage should
be one of the early coupling stages in the amplifier.
As a typical example of the orders of magnitude of impulses
at the various stages of the amplifier (without negative feedback)
it may be taken that the original impulse on the grid of the first
valve is + loo/^V. On the grids of the second, third arid fourth
valves it may be - i mV., + 4omV., - 1-6 V. respectively. The
fourth valve, the penultimate valve, is usually followed by some
potentiometer device for controlling the size of the impulse
passed to the output stage. The amplification obtainable is con-
veniently such that 4- 10 fiV. on the first grid can produce 4- 10 V.
on the grid of the output valve, but for normal operation the
amplification is reduced below this level.
It is necessary to decide how the three supplies for anode
filament and grid bias are to be obtained. There is little difficulty
about the high-tension anode supply; whether a battery or
rectified a.c. is used it will be necessary to decouple the supply
to each stage in the well-known manner (Fig. 4-9), with decoup-
ling condenser C d and resistance R d . The time constant C d R d
should be long compared with the coupling time constant C c R g .
If rectified a.c. is used, it is usually desirable that the voltage
should be stabilized in some manner to prevent changes of
amplification with changes in the mains voltage. This may most
simply be done by neon lamp stabilizers (see Fig. 6-8), or more
effectively by a valve stabilizer circuit such as described in
Chapter vi. If very low frequencies are to be amplified, so
that it would be expensive to provide adequate decoupling,
the high-tension supply may be separated into two parts,
32 ELECTRICAL COUNTING
one for the earlier stages and one for the later stages of the
amplifier.
When the high-tension supply is derived from rectified a.c. it
must be adequately smoothed. It is necessary for the smoothing
to be more complete for an amplifier using screen-grid valves
than for one using triodes, for if a ripple voltage A V is introduced
in series with the anode resistance, the voltage appearing on the
R
grid of the following valve is propoitional to ^~^AV\ this
Fig. 4-9
voltage is therefore greater for the screen-grid valve for which
R a is large.
The question of filament supply has no such unique solution.
Undoubtedly the simplest is to use accumulators for heating at
least the first valves of the amplifier. It is possible to heat all the
valves with a.c. if the wiring is very carefully laid out, and the
transformer is designed with balanced secondary windings, the
exact mid-point of which is earthed. For a.c. heating the cathodes
of the earlier valves must be of a well-designed indirectly heated
type. Reliable quantitative information of the minimum hum
level practically obtainable does not appear to be available.
Alternatively, valves having indirectly heated cathodes may be
supplied with rectified a.c. perfectly satisfactorily. The writer
has experience of one such amplifier in which the filaments of
DESIGN OF AMPLIFIERS 33
the first two valves are heated in this way. The valves used take
0-3 amp. at 8-13 V. and are run in series, the current being
regulated by a baretter from a supply at 150 V. obtained from
rectified a.c. and generously smoothed. This method is extra-
vagant but safe; valves may be changed with confidence that hum
Fig. 4-10
will not be introduced. The heaters of indirectly heated cathode
valves used in later stages of the amplifier may be heated by a.c.
without difficulty.
Many methods, none of them ideal, may be adopted for obtaining
grid bias. Some of these are illustrated in Fig. 4-10. If the early
valves of the amplifier are 2 V. battery valves of the H type, grid
34 ELECTRICAL COUNTING
bias is unnecessary if the negative end of the filament is earthed
as shown in Fig. 4-10 (a). The only valve on which the input grid
swing is of the order of i V. receives negative impulses- so that
grid current is avoided. Grid bias is only required for the output
valve. An extremely simple amplifier is possible using battery
valves of this H type with an accumulator for filament heating;
such an amplifier is described in more detail later. The provision
of grid-bias cells for individual valves (shown in Fig. 4*10 (ft)) is
not to be recommended, though it ensures good stability of
amplification. The disadvantage is that when the amplifier
produces, as every amplifier does at some time or another, an
increased and irregular background the grid-bias cells may be
responsible, and in the design of practical amplifiers the number
of such possible sources of trouble must be kept to a minimum.
When an accumulator is used for heating the first valves grid
bias may often be derived from this if the voltage is greater than
required for heating the valves. This is shown in Fig. 4*10(0).
Often the first valve may require a 4 V. accumulator and the later
valves only 2 V. Fig. ^-io(d) shows a method applicable with
indirectly heated valves where an accumulator is used, grid bias
being obtained from potentiometers across this accumulator.
Again, with indirectly heated valves bias may be obtained as
in Fig. 4'io(tf), (/) from the cathode current flowing through a
resistor between the cathode and earth. In radio- and audio-
frequency amplifiers it is common to shunt such self-bias resistors
by large-capacity condensers. It is expensive, however, to make
the time constant of this combination sufficiently long, and such
electrolytic condensers are not sufficiently reliable to be included
in this position in amplifiers of the type under discussion. It is
better therefore to use no condenser across this bias resistor. The
feedback at low frequencies due to the bias resistor will be
negative, with the effect that the amplification of the stage is
reduced (see p. 47).
Fig. 4io(/) shows another method of applying grid bias. In
this CR is made large compared with the lowest frequencies to
be amplified. This is Unsatisfactory if grid current should happen
36 ELECTRICAL COUNTING
to flow momentarily during an abnormally large impulse, for
then the grid bias is increased until the charge has leaked off the
capacity C. A further modification is shown in Fig. ^-io(g), which
is liable to the same grid-choking effect. The general wiring of the
amplifier is also complicated by these systems.
Grid bias for the output stage may be obtained by the use of
a bias battery (Fig. 4-10(6)) or by some method such as Fig.
4-io(/),(*),(A).
It remains to discuss the layout of the amplifier. It is almost
always essential that the amplifier should be screened as com-
pletely as possible against stray electromagnetic fields in the
laboratory. It should therefore be completely enclosed in a metal
box, common tinplate being as good as anything. Further, the
amplification is so great that the input wiring of the amplifier
must be carefully screened from the output wiring.
The very simplest form of construction that can be adopted is
a long flat box, with the input at one end of the length and the
output at the other. By keeping the box shallow the capacity of
all the components is mainly to the box and interaction between
components is a minimum. The amplifier shown in Figs. 4-11 and
4-12 is made on this principle, which is highly recommended
where the circuit is without complications such as elaborate grid-
bias circuits, gain control potentiometers and bulky coupling
and decoupling condensers, which are required when very low
frequencies have to be amplified. Where this is required it is
perhaps better to depart from the two-dimensional layout and
construct a box with screening partitions. One such design is
shown in Figs. 4-13 and 4*14. Where screen-grid valves are used
a similar design must be adopted.
When planning the wiring it should be borne in mind that such
resistance-capacity coupled amplifiers are prone to three kinds
of parasitic oscillation. The simplest is a low-frequency oscillation
known, from the sound produced in telephones, as motor-
boating. This is always due to insufficient decoupling in the
high-tension circuits or in the grid-bias circuits if that of Fig.
4'io() is used. Motor-boating is unlikely to occur if the design
38 ELECTRICAL COUNTING
has been thought out on the lines indicated. On the other hand,
a type of oscillation difficult to distinguish by ear from motor-
boating is liable to be encountered. This consists of an oscillation
at a frequency above the audible range, which, due to the flow of
grid current, charges one of the grids so negative that a valve
ceases to amplify, thus removing the feedback which was main-
taining the oscillation. When the grid discharges, the oscillation
begins again and the process is cyclically repeated at a low
frequency. This phenomenon is known as an ''automatically
interrupted" "blocking" or "squegging" oscillation. To cure it
the feedback causing the supersonic oscillation must be removed.
Such a supersonic oscillation is not necessarily interrupted. It
may readily be produced by taking off part of the screening near
the input end of the amplifier and pushing in through the opening
a wire connected to the output. As the wire is approached closer
the frequency is lowered and becomes audible. The feedback in
this instance is capacitive, and it should be particularly noted
that this never fails to produce an oscillation, there being always
some frequency at which the feedback is in the correct phase. As
the feedback capacity is made larger the frequency at which this
phase relation is correct naturally moves to a lower frequency.
Such feedback can accidentally occur in the wiring of the
amplifier due to the common supply wires, particularly the fila-
ment and grid-bias wiring. Since the oscillation is at a high
frequency it is often possible to cure it by connecting a small
o-oi or 0*1 /^F. condenser between the responsible wire and the
screening.
The third type of oscillation which may be encountered occurs
at a frequency of about 50 or 100 Mc./sec. (6 to 3 metres wave-
length). The circuit shown in Fig. 4- 15 is one of the most effec-
tive for generating such frequencies, and it will be seen that such
a circuit might unintentionally occur in the wiring of a resistance-
capacity coupled amplifier. The oscillatory circuit is formed by
the wires A and J9, the stray capacity C, and the valve inter-
electrode capacity. If such an oscillation occurs it should be
possible by moving the wire A, or touching it at different points,
ELECTRICAL COUNTING
Front Elevation
Wire soldered to tinplate.
Junctions.
H Tinplate screening partitions.
Insulating bush through tinplate to back.
() Plug and socket to H.T. -f busbar.
Insulating bush through tinplate.
Fig. 4-14. Screened amplifier.
DESIGN OF AMPLIFIERS 4 1
to alter the amplitude of the oscillation and hence the anode
current of the valve. If the wires A and jB are very short (not more
than an inch from the valve pins) and the stray capacity C is
small, such an oscillation should not be encountered. If it is
inconvenient to alter the disposition of the
wiring the oscillation may be stopped by
making the wires A and B of thin-resistance
wire or by including a resistance of 100 ohms
of small self-capacity in series with one of the
wires close to the valve pins.
In wiring an amplifier it should be re-
membered that an electrical contact is
satisfactory if the contact pressure (force per
unit area) is sufficient. The contact area must
also be sufficient to avoid local heating which
may lead to oxidation at the contact, that is, it must be sufficient
for the current to be carried. It is quite possible to use plug-in
valve sockets throughout the amplifier, but this is not recom-
mended. The requirements of sufficient contact pressure and
contact area are likely to fail to be satisfied first for the filament
contacts. In practic*e every amplifier at some time gives rise to a
bad background ; when this occurs every spring contact carrying
current is to be suspected as a possible cause of the trouble.
For this reason spring contacts carrying current should be
avoided where possible; soldered joints are recommended.
The output stage.
The design of the output stage depends on the method adopted
for measuring and recording the impulses. If a record is to be
taken by photographing the trace of an electromechanical oscillo-
graph, the output stage should be capable of delivering j or 2 W.
at any frequency in the range of the amplifier. If merely a valve
or thyratron counter is to be operated, much less power is required
from the output stage. Whether the powerful output stage should
be regarded as part of the oscillograph equipment or part of the
amplifier equipment depends on circumstances. An output stage
42 ELECTRICAL COUNTING
capable of operating a mechanical oscillograph will also be
suitable for operating a valve or thyratron counter.
A pentode output valve is preferable to a triode for operating
an oscillograph, since the reactance of the oscillograph is mainly
inductive at frequencies to which it responds. The internal
anode-slope-resistance of a pentode is much higher than that of
a triode, so that the time constant L/R of the oscillograph in
series with the valve is much smaller for the pentode than for
the triode, and the response of the oscillograph is therefore better
maintained at high frequencies when a pentode is used.
Chapter V
OSCILLOGRAPH RECORDING
It is often desirable to have a permanent record of the impulses
from an amplifier. Photographic records from an electro-
mechanical oscillograph have been found very suitable.
The aim in the design of an electromechanical oscillograph is
to produce a mechanical movement which is an accurate repro-
duction of an electrical wave form. One type of oscillograph is a
form of galvanometer which has its lowest natural frequency
higher than the highest component frequency in the wave form
to be reproduced.
If the mechanical equation of motion of the moving part of
the oscillograph is 0" + 2kO' + w?6 = G/7, where k includes the
electromagnetic damping resulting from the reaction of the
moving part on the electrical circuit. / is the moment of inertia
about the axis of rotation and is the angular displacement about
the same axis; G is the torque acting due to the current in the
electrical circuit. If G is sinusoidal = G cospt, then
Then as long as p 2 <^a) 2 and 4& 2 < o> 2 the amplitude of 0, and i/r t
the relative phase of and G, tan^ = "--rr~ L is independent
of frequency. By a suitable choice of k y say o>< k < &>, these
conditions can be maintained up to frequencies p which are a
large fraction of a). Under these conditions d will be an accurate
reproduction of G and, since the equation of motion is linear,
the same is true for any form of G provided it does not contain
components of higher frequency.
It should perhaps be noted that between p = o and p = o> the
relative phase of d and G necessarily changes by %n, but this does
not imply that 6 is necessarily a distorted reproduction of G. If
44 ELECTRICAL COUNTING
the relative phase changes linearly with frequency, the form of
is an accurate reproduction of G but delayed in time.
In practice it is not difficult to make the frequency o>/27r as
high as 2000 c./sec., while retaining adequate sensitivity for
operation from an ordinary valve of 6 W. dissipation. The
moment of inertia / cannot be made very small, since it is neces-
sary for the moving element to carry a mirror of adequate size
for the photographic registration of its quickest movement. The
brightness of the mirror cannot exceed the brightness of the light
Scms..
Fig. 5-1. Wynn- Williams oscillograph.
source. A very intense source, such as a carbon arc or a high-
pressure mercury arc, is therefore desirable.
An excellent oscillograph of this type has been described by
Wynn-Williams(8i) (Fig. 5-1). The armature consists of a small
soft iron rod suspended by taut tungsten wires so as to lie along
the axis of the fixed oscillograph coil. The whole is placed be-
tween the poles of a strong magnet giving a field of about 2000
gauss. The armature thus occupies a position similar to that of
the armature in the balanced armature type of loud-speaker
movement, the main magnetic field being at right angles to the
length of the armature. A small mirror is attached to one end of
OSCILLOGRAPH RECORDING
45
the armature. The tungsten wires are tensioned so that the lowest
natural frequency of the system is about 3000 c./sec. The sen-
sitivity of this type of oscillograph is about i cm. deflexion at
i m. for 5 mA. in the coil which has an impedance of about
15,000 ohms at 1000 c./sec. In order that the time constant of the
electrical circuit shall be low, the oscillograph is operated in the
anode circuit of a pentode having a high-anode slope resistance.
An oscillograph of greater sensitivity, but rather lower natural
frequency, is on the market, being made by Muirhead.
A quite distinct method of attacking the problem is first to
differentiate the wave form with respect to time and then record
with an integrating device. For example, a transformer may be
used to perform the differentiation
and a fluxmeter of a type having
a negligible restoring torque
may be used to integrate the
resultant wave form. A very satis-
factory oscillograph operating
on this principle has been de-
signed by Shire (67) (Fig. 5-2).
The moving system is a light
aluminium single-turn loop. It is
suspended by a torsionless sus-
pension so as to be free to rotate
about an axis of symmetry in its plane. It is looped round the
laminated core of the transformer and lies between the poles of
a powerful magnet which produces a field at right angles to the
transformer core. Virtually the same principle has been applied
in the type of moving-coil loud-speaker movement known as the
Duode. The performance of this oscillograph is indicated by the
characteristics of one instrument, which in a field of 12,000 gauss
reached 95 % of its final deflexion in 1/5000 sec. after applying
a voltage suddenly. Its sensitivity was i cm. deflexion at i m. for
401*. in the primary which had an inductance less than i H.
Where it is necessary to delineate a wave form containing very
high frequencies the cathode-ray oscillograph must be used.
Fig. 5-3. Shire oscillograph.
46 ELECTRICAL COUNTING
A great deal has been written on the technique of operating
cathode-ray oscillographs, so this will not be discussed here. It
should, however, be remarked that the use of a small cathode-ray
oscillograph with a linear time base traversed in about 1/15 sec.
is very valuable for the visual monitoring of the output from an
impulse amplifier. A larger cathode-ray equipment providing a
linear horizontal time sweep with adjustable timing from about
1/15 to 1/10,000 sec., adjustable gain on the amplifier controlling
the vertical deflexion, and facilities for controlling the width of
the horizontal sweep, is also found invaluable for designing
circuits and setting up counting installations with any special
properties.
Chapter VI
FEEDBACK AND STABILIZERS
Owing to the fact that general practice in the application of valve
circuits at present falls far short of what is known to be possible,
in this chapter certain principles which are likely to become more
widely applied will be described.
The principle of feedback and in particular of negative feed-
back (8) is a most powerful tool in the hands of the circuit designer.
Consider the voltage amplifier circuit shown in Fig. 6-1. An input
v l
t
v g
AMPLIFIER
-f\ O-
1 i
, r"^
i
1
Fig. 6-1
voltage Vj gives rise to an output voltage V o . A fraction of this
fiV o is fed back to the input of the amplifier. The voltage V g
between the input terminals of the amplifier is therefore
V g = V f fiV . If M be the voltage magnification produced by
the amplifier, then V = M(J^-/?^), from which we obtain
Vo^MVjKi+Mf). (6-1)
We note in particular that if M/?>i then VQ^-^VJ and is
independent of the voltage amplification of the amplifier provided
this is sufficiently great. Now it is easy to arrange in practice that
ft is a constant quantity, so that the amplification is constant and
independent of changes in the amplifier itself. Take, for example,
an amplifier which has four stages having a gain of 40 per stage
giving a possible amplification M of 2,560,000 times, and suppose
that an amplification one-twentieth of this is all that is required.
4 8
ELECTRICAL COUNTING
If a fraction 8 = ~ ---- of the output is fed back in the
r 128,000 r
phase into the input circuit the amplification will be
i i _ 128,000
correct
1*05
_
___ I22,OOO
and if M changes by 20 % the amplification changes by only i %.
Negative feedback has a pronounced effect on the internal
resistance of the output circuit. We have
(6 ' 2)
where V g is the voltage between the input terminals of the
amplifier, Z =* output load, R a = effective internal resistance of
the output stage of the amplifier for Z^>R a . Substituting -^
J< a
for M in equation (6-1) leads to
Comparing this with equation (6-2) it appears that the effective
internal resistance of the output circuit is reduced by the feedback
D
THT.+
to
This is
for
example, in the circuit of Fig. 6-2,
which is called the cathode follower
circuit because the potential of the
cathode follows very closely the
potential of the control grid (10,46).
It will be noticed that /? = i , the
effective internal resistance of the
r>
valve is therefore - , where it is
r
Fig - 6 ' 2
the amplification factor. For example, if the valve has
R a 2400 ohms
FEEDBACK AND STABILIZERS 49
and ft = 15 the effective internal resistance is 150 ohms. It will
be noted that this effective internal resistance is approximately
the reciprocal of the mutual conductance p>/R a . The circuit is
extremely valuable since the input impedance is very high and
considerable power amplification is obtained, although the output
voltage is approximately equal to the input voltage, being given
M
by V o = V x . The same principle may be extended to more
than one valve, and the circuit of Fig. 6-3 has been found useful
H.T.-f
H.T-
Fig. 6-3
for following the voltage on a condenser from which no current
could be drawn. For such a circuit M might well be as great as
400, so that V is closely equal to V f and the effective internal
resistance of the output circuit may be a fraction of an ohm. It
has been assumed that the high-tension voltage is maintained
constant.
Feedback also has an effect on the frequency range over which
amplification is maintained. We have seen that at high frequencies
the amplification of a single-resistance capacity-coupled stage is
*/i? i
Write C x r = t and M = amplifica-
M =
tion at medium frequencies =
LEC
for a single stage. Then at
4
50 ELECTRICAL COUNTING
high frequencies for which w 2 / 2 ^ i the amplification reduces to
M = A/o/w/, For twb stages the amplification is M = A/ /fc> 2 /j/ 2
and for 5 stages M M /o/(f, f 2 . . . f x ), where / lf / 2 , etc. are the
time constants C t r of the successive stages.
With negative feedback the amplification becomes
M M
F
Without feedback the amplification is reduced to ~M at a
frequency for which ^ 8 (^/ 2 ... t a ) = w. With feedback it is
reduced to i/ of the amplification at medium frequencies, i.e.
i M
-- when <'**i*- + M /i = ni+Mfl, i.e.
<*/(/! / 2 ... /) = w(M /?-f i -fM /y/w). When M Q (i^> i and w> i,
this reduces to (^(t^... t 8 ) nM /J. The amplification is main-
tained above a given fraction i/n of the maximum up to a fre-
quency a) = / without feedback and to a frequency
7wA/ /?
_ w__ w ith feedback. It may be noted that i//?M is the
factor by which the amplification has been reduced by negative
feedback. If, for example, we have a two-stage amplifier and
/?M = 100, the amplification will remain uniform up to a fre-
quency range 10 times that without feedback. It must be
remembered that other properties of the negative feedback
amplifier such as the lowered output circuit impedance will not
be maintained over the extended frequency range.
The stability of amplifiers controlled by negative feedback
requires special consideration. This arises because at both
ends of the amplified frequency range the phase changes so
that the feedback becomes positive or regenerative, and, to
preserve stability, it must be ensured that the amplification
falls sufficiently low at frequencies where the feedback phase is
reversed.
The particular case of the resistance-capacity coupled multi-
stage amplifier may be considered. For low frequencies the
FEEDBACK AND STABILIZERS 51
effective coupling element is Fig. 6-4, from which it may be seen
that V - E - - - . Write tan ft = -1=. Then
.._.__
i j tan cos ft - j sin ft
So that at each coupling stage the voltage phase is turned through
an angle depending on the frequency <*> and the time constant
CR, and its magnitude is reduced by a factor cos ft.
INPUT K <*K V OUTPUT
.. i_
Fig. 6 4
Consider an amplifier having three resistance-capacity
couplings. Let the magnification where the phase change is
negligible be M. Then the output V () ~ J^Mcosftj cosft 2 cosft 3
and the phase shift is ft| + ft 2 -l-ft,. Suppose a negative feedback
voltage pV o is applied at all frequencies; then if ftj-hft.^-f ft 3 = TJ
the feedback will be positive and the amplifier will oscillate if
(1M cos ft t cos ft 2 cos ft 3 > i . If
so that fiM cannot exceed 8 without instability occurring. fiM
can be much larger, however, if one of the angles, say ft 3 , is
made larger. Suppose (CR)^ = (C/) a = ioo(C7f) 3 . Then when
ftj = a == 45 J tanft 3 icx> so ft 3 ~ 90 and ft t 4-ft 2 i-ft^ = 180,
but now cosftj cosft 2 cosft 3 = 1/200, so that JIM can have any
value less than 200 without oscillation occurring.
It may be recalled that i/flM is the factor by which the ampli-
fication is reduced by feedback. If M varies by a small amount,
the resulting change in amplification of the controlled amplifier
is ij/IM of the variation in M.
4-2
52 ELECTRICAL COUNTING
High-frequency stability may be treated in a similar manner
for a resistance-capacity coupled amplifier using pentodes if the
effective grid-anode capacity may be neglected. The effective
circuit is Fig. 6-5, from which we see that
R+R,
-
Write tantf = w c-. Then V = -Kcosfle-* Hence
\
>R V
I
again at each stage the voltage phase is turned through an angle
and reduced in magnitude by
a factor cos#, so the conditions
for stability at high frequency are
formally similar to those for low-
frequency stability.
It is generally too complicated to
take into account the effect of the Flg * 6 ' 5
grid-anode capacity, and in practice the amplifier is stabilized
by adjustment of the input capacity of one stage.
The frequency characteristic of an amplifier may also be
controlled by the feedback circuit if this is given a frequency-
dependent characteristic. In this connexion there is an important
principle which should be recognized, that a unique relation
exists between the form of the output impulse from a given input
impulse and the frequency characteristic of a linear amplifier.
If, therefore, by controlled feedback an amplifier is produced
with the same frequency characteristic as any other given
amplifier, the output from a given input impulse will have the
same transient form.
In Chapter iv the form of the output impulse from an amplifier
having a coupling stage of short time constant was derived. The
form of the amplification characteristic at low frequencies is con-
cerned; this (p. a 3 ) is M-^^^-^.^ where
T 2 , T 3 , etc. are much larger than 7^, so the essential term is
FEEDBACK AND STABILIZERS 53
P r duces the steep downslope on the output
/ 2T2\>
i/&> i jj
impulse, the other terms producing the subsequent slow ripples.
When o> 2 rf<^i, the term reduces to o)T v and the amplification
is thus directly proportional to frequency in the frequency range
<j)*T\<^i jPT\, etc. If two coupling stages had short-time
constants T v T 2 , the amplification would be proportional to
<y 2 7^7J. It was pointed out that such an amplifier produces a
large reversed pulse following each impulse.
The frequency characteristic of a feedback circuit which would
give an amplifier the desired characteristic must therefore be such
that i//?oc a) over a certain frequency range.
There exists, moreover, a definite relation between the ampli-
tude and phase characteristics of an amplifier. This relation is not,
however, unique, since any phase change proportional to fre-
quency which amounts simply to a time delay is independent of
the amplitude characteristic.
So far only feedback proportional to the output voltage has
been considered. If feedback proportional to the output current
is applied different characteristics are obtained. When feedback
is proportional to the output voltage, this output voltage tends
to be maintained irrespective of the load, that is, the output
impedance is reduced. On the other hand, when feedback is
proportional to the output current, this tends to be maintained
irrespective of the load, so the output impedance is increased.
This may be useful for mixing, for the outputs of such amplifiers
may be connected in parallel with a minimum of mutual inter-
action. A combination of both types of feedback may be employed
to give an output impedance unaffected by feedback, and feed-
back independent of the load; this has some advantages for
achieving stability against oscillation.
Stabilizers.
For many purposes it is required that the voltage of a
rectified supply should be independent of variations of the
load or of the a.c. supply. Sufficient stability may often be
54 ELECTRICAL COUNTING
obtained from quite simple devices; a few of these will be
described.
For the operation of Geiger-Miiller counters and similar
discharge devices a potential of the order of 1000-2000 V. is
required which is constant within a few volts. The current taken
by the counter is negligible, so that a device which maintains a
constant current through a fixed high resistance is satisfactory.
The simplest in principle is probably that described by Street
and Johnson (?0 (Fig. 6-6). The potential drop across the resist-
ance R due to the anode current flowing through it is balanced
Stabilized
Output
Voltage
Rectified
H '3 h ^^TL__J|
Voltage
Supply qlp
"T"
Fig. 6-6
against the voltage of the battery B which may be about 60-
100 V/The grid of the valve is thus maintained at a small voltage
negative with respect to the cathode. Since the screen-grid
voltage is fixed, the anode current is almost independent of the
anode voltage over the working range, and is determined solely
by the control-grid voltage. Any slight variation in the anode
current alters the voltage across /?, the resultant change in control-
grid voltage tending to minimize the change of anode current.
The change of anode current At produced by a change of the
supply voltage A V may be calculated as follows. The change of
grid voltage A V g RAi. The change of anode current is therefore
AVtiAV
Ai ~ R + R +R' f Ai ( R + R a + R ' + V R ) = AV. The change
% tt
FEEDBACK AND STABILIZERS
R'
of the stabilized voltage is AiR' =
55
,. If, for
example, the stabilized current is i mA. and the voltage 1000,
R' = i M, R a may be 0-5 MQ, R = o-i MQ and p = 1000. The
i AV
change of stabilized voltage is then AV , ^= . The
to & 1-6+ 100 100
anode voltage of the valve must not be less than the screen-grid
voltage and should never greatly exceed the maker's rating. This
usually allows a variation of about 200 V., so that variations of
100 V. in 1200 or nearly 10% in the supply will be coin-
H/jh
Voltage
Supply
Stabilized
R Output
_ Voltage
^vww I
J-
Fig. 67
pensated. The circuit has the disadvantage of requiring two high-
tension batteries from one of which a small current is drawn.
The output voltage is conveniently regulated over a small range
by the variable resistance R\ larger changes may be made, if
required, by tapping off across only a portion of R'.
A circuit which appears similar but which is fundamentally
different in action is that described by R. D. Evans (o (Fig. 67).
In this the anode and screen-grid currents are maintained exactly
constant by a balance method. The screen grid, control grid and
cathode form a triode, the anode current of which may be written
as f(AV so + nAV g ) + constant, where AV SQ , AV g are the voltage
changes on the screen grid and control grid and p is the amplifica-
tion factor of the triode. The ratio of the resistances XY/YZ ia
56 ELECTRICAL COUNTING
made equal to /*, so that a change of the supply voltage produces
changes of screen-grid and control-grid voltages of opposite sign
.and such that AV 8O = -/*AV g . The triode current and therefore
the anode current of the pentode are unchanged. The actual
stabilized current through R may be regulated by adjustment of
K or of the bias voltage. A slight change of the balance setting
will be found for large changes of current or operating voltages.
A slight disadvantage of this circuit is that its action must be
checked when it is first set up. The tapping point Y is adjusted
until the output voltage is independent of variations in the supply
voltage. In principle no advantage is gained by increasing the
voltage of the battery J5, but when the balance adjustment is not
quite correct a high-voltage battery B and a large resistance K
give increased stability, as the circuit is then similar to that of
Street and Johnson.
Stabilized voltages of a lower order are required for high-
tension and grid-bias supplies for amplifiers and similar devices.
The simplest stabilizer for this 9
purpose is the neon lamp. The
circuit is shown in Fig. 6'8.
Special tubes are made for the Rectified
purpose capable of carrying a Voltage
current of 50 mA. or more (52). Supply
The voltage across such a tube \vy Voltiwe
(about 100 V.) will not change
by more than about 2 V. when
the current changes from 10 to lg *
50 mA. From these figures it would appear that the slope resist-
ance of the neon tube is 50 ohms. A tube which has only a small
difference between its striking and its burning voltage is advan-
tageous. Suppose the burning voltage is V b and the striking voltage
V b + x. Let V be the supply voltage, R 8 the series resistance which
includes the effective internal resistance of the supply, and R be the
load resistance. Then in order that the neon discharge shall strike
LA. il J | if the series resistance R 8 is large, V must
R
FEEDBACK AND STABILIZERS 57
be high. If R 8 is small, then the current carried by the neon is
large and the device is again not economical. There may also be
a limit on the total current available. Suppose it is arranged that
the neon current i n is equal to the load current i/. When the neon
discharge strikes, the increase in the voltage drop across R 8 is x
and this must be less than i n R 8 , for the load current will fall
somewhat. It follows that, when in operation, the total voltage
drop across R s , viz. (in + ii)R 8 > is greater than 2X. Hence the
supply voltage V must exceed the burning voltage by at least 2x,
and must be greater if the current carried by the neon stabilizer
is to be less than the load current.
Neon stabilizers of this kind may be connected in series as
shown in Fig. 6-9. The voltage required to strike the two dis-
charges will be 2V b + x if the
pilot resistance R p ^R 8 . R p
may be very high, of the order of
a megohm. The supply voltage
must be greater than 2V b + 2X
unless the stabilizer current is
greater than the load current.
The voltage across R p is also
stabilized, but if an appreciable
current is drawn the supply
voltage must be increased to
ensure that the second stabilizer
strikes. This defect is minimized if the two discharge gaps
are in series in the same bulb ; tubes of this kind are on the
market.
Small variations of the burning voltage are liable to occur with
age and with temperature. The magnitude of these variations is
liable to differ between tubes of different manufacture. It is
important to allow a sufficient margin for such changes in the
design of the stabilizing unit.
Another simple stabilizer with the output voltage adjustable is
provided by a neon lamp and a valve connected as a cathode
follower (Fig. 6-10). The effective internal resistance of this
Rectified
Votia g e A
Supply
Stabilized
Voltage
Fig. 6-9
58 ELECTRICAL COUNTING
R 4- R
stabilized supply is *, which is rather greater than the
reciprocal of the mutual conductance of the valve if R s is com-
parable with the anode slope resistance R a . The output voltage
variations should be at most i/(i -f ft) of the supply variations if
the valve is worked with a normal anode current and no grid
current, and if the internal resistance of the supply is negligible
compared with the resistance of the neon-lamp circuit.
Very much better stabilization can be obtained from the use of
two valves, and many suitable circuits are available. Two different
modes of operation may be distinguished: in the first, variations
Rectified
Voltage
Supply
Internal
Resistance
Stabilized
Voltage
Fig. 6-10
in the output voltage? are amplified and applied to the control
valve; in the second, variations in the output voltage are balanced
out so that control is derived from variations of the supply voltage
and of the output current. This second principle might appear at
first sight to be preferable, but it is found that while variations of
the supply voltage may be compensated over a fair range, varia-
tions of load are only compensated over a small range. The
effective internal resistance of such a stabilizer may be positive,
zero or negative. Against this type of stabilizer it should be noted
that the two balances must be made by trial. Also it is difficult or
perhaps impossible to design a circuit of this type so that a
number of stabilizers operated from one supply have one common
output terminal.
The first type of stabilizer may be so efficient, having an
FEEDBACK AND STABILIZERS
59
effective internal resistance of only a few ohms, and stabilizing
over a wide range of supply and load variations without the
necessity for any balancing adjustment, that it is very often to be
preferred.
Examples of these two types of circuits are shown in Figs. 6* 1 1
and 6-12. The standard of reference with which the output
voltage is compared is provided in these circuits by neon tubes,
but batteries may of course be substituted for these.
Rectified
Supply
Stab/ /t zed
Output
Voltage
Fig. 6- 1 1. Performance with V lt Milliard S?4B; K 8 , Osram KT4i; Neon
Milliard 7475; P, 250,0000*; Q, 250,000 w; R, aMii; S, 40,000 co;
T, 50,000*0. Output voltage constant to 0*2% for current from 10 to
60 mA. Output current or voltage constant to 0-5% for A.C. inputs
from 200 to 250 V.
In the circuit of Fig. 6'ii a certain fraction of the output
voltage is selected by the potentiometer R and balanced against
the voltage across the neon tube in the grid circuit of the pentode.
The anode resistance Q of this may be high, so that the amplifica-
tion of any variation in the output voltage is as great as possible.
The pilot resistance P ensures that the neon lamp strikes and
passes sufficient current to maintain it in its stabilizing condition.
The output voltage may be adjusted by R from the burning
voltage of the neon tube up to about 200 V. greater than this
provided the supply voltage is sufficient. Typical performance
figures are given above, Fig. 6* 1 1 .
The grid bias of the amplifying valve V l in Fig. 6-12 is obtained
from a fraction of the supply voltage selected by the potentio-
6o
ELECTRICAL COUNTING
meter P, and a voltage dependent on the load current developed
across R. These together constitute a considerable positive
voltage which is offset by the voltage across the large cathode
resistance. Increase of the supply voltage or decrease of the load
current makes the grid potential more positive, thus lowering the
anode potential which increases the resistance of the control
valve V 2 , as is required to maintain the output voltage constant.
jupply
Rectified <-
Suppl y ~ ~^L \A^
u__y \__
Stabilized
Output
Voltage
It should be noted that the action of these stabilizers is very
rapid, so that they provide a very considerable smoothing of
ripple on the rectified supply. In the balanced circuit it may be
found that the setting of the potentiometer P for zero hum or
ripple is rather greater than that for the elimination of slow
fluctuations; this may be compensated by a condenser connected
as at C.
The circuit of Fig. 6*11 is almost identical with the valve
voltmeter circuit of Fig. 6-3 which was discussed from the
viewpoint of negative feedback.
Chapter VII
MIXING CIRCUITS, TRIGGERED CIRCUITS
AND DISCRIMINATORS
In the discussion of amplifiers, feedback controlled circuits and
stabilizers, valves have been considered as quasi-linear devices.
In many other uses the essentially non-linear characteristics of
valves are applied.
The mixing circuit of a coincidence counting system is an
example of this. A circuit is required such that a pulse is only
produced in the output when simultaneous impulses occur in
H.T.+
H.T.-
Fig.
each of a number of independent inputs. This is achieved with
the circuit of Fig. 7-1 (57). The anodes of the required number of
valves, two for double coincidences, three for triple, four for
quadruple and so on, are connected in parallel. The cathodes are
similarly connected together but the grids are independent. The
anodes are connected to the high-tension supply through a high
resistance. The potentials of the grids are such that the internal
resistances of the valves (not necessarily the anode slope resist-
ances) are low compared with this high resistance in the anode
circuit. Suppose each is a tenth of this, then under normal
conditions the common anode potential is ^, -^ , ^j, etc., of the
62 ELECTRICAL COUNTING
high-tension potential for i, 2, 3, etc. valves. Negative impulses
are applied to the grids of the valves of sufficient size to stop the
flow of anode current even if the anode potential were equal to
the high-tension potential. Now as long as one valve has not
received such an impulse, the potential of the anodes must remain
less than fo of that of the high-tension supply. If, however, this
last valve simultaneously receives such a negative impulse on its
grid, the potential of all the anodes rises to the high-tension
potential. The change of anode potential when this occurs must
be at least nine times that when all but one of the valves received
simultaneous negative impulses. This then is a remarkable circuit
which passes on a large impulse when all the grids simultaneously
receive a negative impulse, but only passes on a much smaller
impulse if even all but one of the grids simultaneously receive
a negative impulse. Further, the large impulses passed on are all
of the same voltage.
Some elaborated circuits have been used for mixing in coin-
cidence systems, but the properties of the simple circuit leave
little room for improvement. Although this simple mixing circuit
forms the basis of most coincidence counting systems, a complete
system may nevertheless be quite elaborate for reasons which are
discussed in Chapter xi.
Remembering that the special property of the mixing circuit
depends on the non-linear "anode bend" of the valve character-
istic, that is to say on the possibility of cutting off all anode
current by any voltage on the grid exceeding a certain minimum,
it will be realized that the impulses on the grids must be an
appreciable fraction of a volt. In order to obtain a good per-
formance with small impulses of this order, it is necessary to
choose the type of valve and the operating conditions with care.
If large impulses are available, any valve will do. To work with
small impulses the valves must have as high a magnification
factor ft as possible and must certainly not be of the variable-/^
type. It will also be an advantage to work with a high-tension
voltage not greater than about /* V. If a higher voltage is used, the
impulse applied to the grid will have to exceed about i V. if it
MIXING CIRCUITS 63
is to change over the valve from a state in which it passes anode
current when the anode voltage is a small fraction of the high-
tension voltage, to a state in which it passes no anode current for
an anode voltage equal to the high-tension voltage.
Certain high-magnification screen-grid or pentode valves may
show some advantage. The screen-grid potential is kept fixed and
the control grid is biased to within i V. of the point at which the
screen grid and anode currents are cut off. Under these con-
ditions a suitable valve will pass an appreciable anode current for
an anode voltage as low as 5 V., the high-tension voltage may be
much greater than the screen-grid voltage so that quite a large
impulse is obtainable in the anode circuit. With a good valve the
performance is well maintained up to quite high screen-grid and
high-tension voltages if the control grid bias is correspondingly
increased. The limit is set by defects caused by bad vacuum or
grid emission. A valve in which the secondary emission current
from the anode is large would not be suitable.
The power available in the anode circuit may be small, due
either to the effective internal resistance being high or to the
impulse being of very short duration. The output may be in-
adequate for operating certain types of counting circuit. The
mixing circuit may in these circumstances be followed by an
amplifying valve having sufficient output power or by an " im-
pulse-lengthening " stage. An amplifying valve reverses the sign
of an impulse; if this is undesirable a phase-reversing transformer
may be used or the cathode follower circuit, which does not
reverse the sign of the impulse, may be suitable.
Impulse lengtheners.
The three types of circuit commonly employed as impulse
lengtheners are illustrated in Figs. 7-2, 7-3, 7-4. When a positive
pulse is applied at the input of the circuit of Fig. 7^2 grid current
flows so that when the pulse is over the grid charges up negative
and stops the anode current for a time determined by the time
constant CR g of the grid circuit. A lengthened positive pulse
therefore appears on the anode of the valve.
6 4
ELECTRICAL COUNTING
The action of the rectifier circuit of Fig. 7-3 should be obvious.
The resistance R should be greater than the resistance of the
rectifier when conducting. The capacity C is then chosen to
make the time constant CR sufficiently long.
H.T.+
OUTPUT INPUT
INPUT
OUTPUT
>R
H.T.-
Fig. 7-2
Fig. 7'3
INPUT
H.T.i
OUTPUT
Fig. 7*4
In both these circuits a certain amount of power is required
in the input circuit. The circuit of Fig. 7*4, however, requires a
negligible power. The valve acts as a rectifier, the resistance of
which is controlled by the grid. The length of the pulse is deter-
PO
mined by the time constant CR', where R' = R+ p-~ . The
resistances P and Q form a potentiometer system to bias the
valve, so that in the normal state it passes no anode current.
TRIGGERED CIRCUITS 65
Triggered circuits.
The non-linear properties of valves give rise to the possibility
of circuits having more than one stable state for the same applied
voltages. The circuit may be changed from one stable state to the
other by an impulse which brings it to the unstable state which
must exist between the two stable states. Such an impulse there-
fore acts as a trigger. Such circuits find application as recording
counters and as discriminators or peak voltmeters. They may be
formed by combinations of two valves as in the multivibrator
circuit (i > and in the flip-flop or zero frequency multivibrator (69),
or with a single valve by employing the effects of secondary
emission from one or more of the electrodes as in the dynatron.
With regenerative coupling between the anode and grid circuits
a single valve may have two stable states, one a steady state and
the other in which an oscillation takes place for the same applied
d.c. potentials. This phenomenon is described as oscillation
hysteresis. The oscillation may also exhibit another property that
it is automatically interrupted or blocked; this phenomenon is
sometimes referred to as "squegging".
A gas discharge tube also possesses this property of two stable
states for the same applied d.c. potentials. The striking voltage
is higher than the burning voltage, so that at an intermediate
voltage two stable states are possible, one with a discharge and
the other with no discharge. A grid-controlled gas discharge tube
or so-called gas-filled relay, gas triode, or Thyratron (the word
Thyratron is a registered trade name (34)) has some advantages
over the simple two-electrode tube.
The principles of these devices will first be discussed, and
particular applications will be left for description fater,
The gas -filled triode and thyratron.
If the grid is at the filament potential and the anode voltage is
greater than the ionization potential, an arc is produced and a
large anode current may flow. The pressure is low and an electron
has a much longer free path than a positive ion. An electron has
in fact a chance of being accelerated in the field to a velocity
LEC 5
66 ELECTRICAL COUNTING
sufficient to ionize. If the anode voltage increased, this ionization,
and consequently also the current, would be greatly increased.
When there is no arc, if a negative voltage is applied to the grid,
it is necessary to apply a voltage much higher than the ionization
potential to the anode to produce a field at the filament which will
draw off electrons and thus strike an arc. Just as in a hard vacuum
valve if V a +fiV g <o no anode current flows, so with the gas-
filled triode if V a +/iV g <o no arc will strike. If now a positive
impulse is applied to the grid, the arc at oncestrikes (it is necessary
to limit the anode current to less than the filament emission by a
series resistance in the anode circuit). Then it happens that if
the grid returns negative it has no effect on the arc, in fact it has
lost control. The reason for this is that a positive ion sheath is
formed round the grid by the following mechanism.
When an electrode is put in a gas discharge and brought to a
negative potential it is found that the positive-ion current flowing
to it is independent of its potential; also it is covered by a non-
luminous sheath whose thickness increases as the potential is
increased negatively. This is explained as follows. When a current
is carried by ions moving across an otherwise vacuous space the
maximum current (i) which can flow is given by an expression of
the form i = Kv* \d, where K is a constant depending on the
charge and mass of the ion and includes a numerical constant
which may be determined from the geometry of the electrodes.
It is assumed that the ions have no velocity other than that due to
acceleration in the electric field, v is the potential difference
between the anode and cathode and d is the distance between
them. If then v is constant the maximum current passing depends
only on d. Applying these considerations to the electrode at a
negative potential placed in a gas discharge it is evident that the
positive ions close to the electrode are attracted to it, but the
maximum distance from which the ions can be drawn is given by
Kv*/i. In the equilibrium state the current i must be the rate at
which positive ions enter the sheath which is a function of the
discharge passing. Increasing v merely increases the distance
from which positive ions are drawn, without greatly affecting
TRIGGERED CIRCUITS 67
the magnitude of the current. The discharge will not be appreci-
ably affected beyond the limit of the sheath ; if then the current is
large v must be a very large negative potential to extinguish the
discharge by drawing off the positive ions.
For this reason the arc cannot readily be extinguished by
applying a negative potential to the grid ; it is therefore necessary
to interrupt the anode current for a time long enough to allow
all the positive ions to diffuse to the walls and electrodes. This
time may be shortened by putting a high negative potential on
both anode and grid ; it varies with these potentials, and according
to the type of gas-filled triode may lie in the range from about
IQ- 3 to IO" 5 sec.
An important characteristic of a thyratron is its control ratio
/*, which corresponds to the amplification factor of a hard vacuum
triode. This control ratio is measured as the ratio of the increase
of anode potential necessary to strike the arc to the increase (if
small) of grid potential which also allows the arc to strike. If the
grid is not uniform it is like several grids in parallel, that with the
lowest / will allow the arc to strike for the lowest potentials. This
smallest /i must therefore be high, so that the anode must be very
completely shielded by the grid. Thyratrons and gas-filled triodes
are available with control ratios from 20 to 100. It is possible with
certain gas-filled triodes to extinguish the arc by only a moderate
negative potential on the grid.
It has been mentioned that the anode current of a thyratron
must be kept considerably less than the emission from the
cathode. The reason for this is that the cathode surface cannot
withstand positive-ion bombardment and must be protected
from this by a considerable electronic space charge. Moreover,
it is important that the filament temperature should be main-
tained correctly as the emission varies rapidly with filament
temperature. The life of a gas-filled triode may be only a few
minutes if the filament temperature is too low.
The gas used is either mercury vapour or one of the inert
gases, argon, helium and neon, or s6me combination of these.
The mercury-vapour triode suffers from the disadvantage that
5-2
68 ELECTRICAL COUNTING
the vapour pressure and hence the operating characteristics are
sensitive to temperature,
The flip-flop circuit.
This is a symmetrical two-valve circuit which has two stable
states (Fig. 75). The symmetrical state in which the anode cur-
rents of both valves are equal may be,
shown to be unstable, for if from this
state the grid potential of one valve V l is
increased its anode potential falls, re-
ducing the grid potential of V% which
increases the anode potential of V%
thus increasing the grid potential of V l
further. This process continues until
the anode current of V 2 is reduced to
H.T.+
H.T.-
GridBias
Fig. 7'5
zero. But the circuit is symmetrical, so it possesses two stable
states in which the anode current of one or other valve is zero.
The multivibrator circuit.
The multivibrator circuit (Fig* 7-6) is somewhat similar to the
flip-flop circuit, but the coupling from the anode of one valve
H.T.-f
H.T.~
Multivibrator
Fig. 7-6
to the grid of the other is by a condenser only, so that the coupling
is not maintained in a steady state. The circuit therefore oscillates.
This oscillation may, however, be prevented by giving the two
TRIGGERED CIRCUITS 69
valves different grid potentials. It may be arranged that one
valve normally passes no anode current, but if it receives a posi-
tive impulse on its grid, its anode passes a negative pulse to the
grid of the other valve, and the rise of anode potential of this valve
reinforces the initial positive pulse on the grid of the first valve.
If the time constants C^R l9 C 2 R 2 are suitably chosen, this is
maintained positive until the negative charge leaks away from the
grid of the second valve. This is therefore a triggered impulse
producer.
The dy natron.
This is essentially a negative-resistance device (33), but it is
also non-linear and therefore may be used as a triggered device.
If an electrode of a valve is sufficiently positive, secondary
electrons may be liberated from it by the primary electrons
collected. If another electrode is maintained still more positive,
it may collect the secondary electrons thus emitted. If the
potential of the first electrode is increased, the secondary emission
is increased. This increase of secondary emission may more than
annul the increase of primary current. The nett current to this
electrode therefore diminishes when the potential is increased.
The slope resistance between the cathode and this electrode is
therefore negative. *
The transitron.
Another means of obtaining a negative slope resistance is
illustrated in Fig. 7-7 (31). If the screen grid and suppressor grid
~n
IT
HH---I I
Fig. 7-7
of a pentode are connected together by a battery D, the current
voltage characteristic between the points A and B is of the type
70 ELECTRICAL COUNTING
shown in Fig. 7*8. The negative resistance portion arises because
over this region the suppressor grid (grid 3) controls the division
of the total current between the anode and screen grid in such a
way that if it is made less negative the anode receives more current
100 150
Screen voltage relative to cathode
Fig. 7'8
and the screen grid therefore less. It may be noted that over the
negative resistance range the suppressor grid is negative with
respect to the cathode and therefore draws no current. The
battery D may be replaced by a condenser for a.c. operation; the
bias on the suppressor grid is then derived from the cathode
through a high resistance and a small battery if required.
Oscillation hysteresis*
If we have any ordinary valve oscillator and increase the
negative grid bias, it is possible to apply a bias which if the valve
TRIGGERED CIRCUITS 71
were not oscillating would stop all anode current, yet the oscilla-
tion is maintained. If then the oscillation is stopped, by, for
example, interrupting the anode circuit momentarily, it does not
start again until the grid has been made more positive. This
phenomenon is called "oscillation hysteresis".
Blocking oscillator or squegger.
%
It would, however, have been possible to stop the oscillation
by applying a larger negative grid bias, and it is possible, by con-
necting a condenser paralleled by a high resistance in the grid
circuit, to make the grid automatically charge up negatively by
the grid current it draws during portion of the oscillation cycle
so that the oscillation is stopped. The negative charge then leaks
off the condenser and the oscillation starts again.
Alternatively, the normal grid bias may be too great for the
oscillation to start again unless a positive impulse is applied
momentarily to the grid. It is possible for the oscillation to be
blocked during the first cycle of the oscillation.
This blocking oscillator is a very useful triggered impulse
producer, particularly as the power in the impulse which trips
it off may be negligible.
Discriminators.
Another non-linear application of valves is for discriminating
between impulses of different voltages in such a way that impulses
below a predetermined voltage are not passed on, whereas im-
pulses exceeding this voltage by even a small amount are passed
on as large impulses.
The simplest discriminator consists of a high-magnification
valve with a large negative grid bias or cut-off bias, perhaps
100 V. (Fig. 7-9). A high resistance, 50,000 ohms to i megohm,
is included in series with the grid to limit the grid current when
large positive impulses are applied. The variation of anode
voltage with the voltage applied at the input terminals is
shown in Fig. 7-10 which makes the action of the circuit as a
discriminator clear.
72 ELECTRICAL COUNTING
This circuit has four limitations:
( i ) If the anode resistance is high, a very sharp impulse smaller
than the cut-off bias may be passed to the anode circuit (via the
grid-anode capacity of the valve) without change of sign. If the
Counter following the discriminator responds to such sharp
impulses, this may be troublesome. A remedy would be to use a
screen-grid valve, though the defect may be reduced by suitable
choice of circuit constants where only slow impulses are to be
counted.
H.T.+
INPUT
Cut off bias
Fig. 7*9. Simple discriminator.
(2) It may be required to count slow impulses superimposed
on a background having rapid variations such as is shown in the
lower part of Fig. 7-10. If the counter has a very short resolving
time the impulse shown would be counted as two, since it twice
crosses the cut-off bias line from left to right. This defect cannot
be completely eliminated with this type of discriminator, and it
is probably most satisfactory to filter the input so that rapid
fluctuations are suppressed.
(3) Due to the input capacity of the valve and the high resist-
ance in series with the grid, very rapid impulses are diminished
at the grid. For a similar reason the resolving time of the dis-
criminator is limited.
(4) The flow of grid current also imposes a limitation. When
impulses are arriving very rapidly the grid current flowing through
DISCRIMINA TORS
73
the grid-series resistance increases the effective cut-off bias. The
discriminator is also not suitable for a resistance-capacity input
coupling, since, owing to the charge collected on the coupling
condenser, the effective cut-off bias is temporarily increased
after each impulse.
200
ANODE
VOLTS
TIME
Fig. 7-10. Action of simple discriminator.
The impulses from such a discriminator are negative. For
operating a thyratron counter it is convenient to follow the
discriminator valve by an amplifier which reverses the sign and
also produces impulses of a limited and constant size. There is
no particular difficulty in this, but when this procedure is adopted
the first-mentioned defect of the discriminator is aggravated and
it will be almost essential to use a screen-grid valve as dis-
74 ELECTRICAL COUNTING
eliminator. Preferably this should be a pentode of a type in
which the screen-grid voltage may be the full high-tension volt-
age, since it is unsatisfactory to supply the screen-grid voltage
from a high-resistance potentiometer, for in that case the mean
potential would depend on the rate of counting.
Many other discriminators have been used which obviate some
of these disadvantages, but it is only recently that a discriminator
has been developed which is almost perfect in performance.
It will operate with impulses as slow as desired or as short as a
microsecond without any readjustment. It will discriminate in-
oi^r.; C a , optional; C 8 , C 5 , o-ooo
AC/TP Mazda; F 3> MH 4 i Osram,
fallibly between pulses differing by only J V. Impulses may
exceed the cut-off bias by about half the high-tension voltage
(200 V.) without drawing grid current or in any way disturbing
the action. The output pulse may be controlled by the circuit
constants to have a minimum duration as desired from io~ 6 to
io~ a sec. or possibly a greater range.
The circuit of this discriminator is shown in Fig. yn. The
first triode section of the first valve is effectively a cathode follower
with the cathode normally maintained at a higher voltage than
the grid by the cut-off bias. The cathode potential is constant
until a voltage greater than the cut-off bias is applied across /? t .
DISCRIMINA TORS 75
Any further increase of this-voltage raises the cathode potential.
This renders the second triode section of the valve non-conducting ,
so the anode voltage rises to that of the negative high-tension line,
thus removing the bias from the control grid of the pentode
section of the next valve. This second valve is connected in a type
of flip-flop circuit. Normally the triode section is conducting, so
that its anode potential and consequently the screen-grid poten-
tial of the pentode section is low. A negligible anode current is
flowing in this pentode section due to this low screen-grid
potential and the bias on the control grid. The anode potential is
therefore high, and this through R& and /? 6 maintains the grid
bias on the triode at a low value. Under the action of a positive
impulse on the control grid of the pentode, the anode potential
falls, increasing the negative grid bias on the triode section and
thus raising the anode potential and the screen-grid potential of
the pentode section which further increases the current through
the pentode section. At a certain bias on the control grid of the
pentode section this change takes place abruptly, providing a
sharp output impulse even if the input impulse is extremely slow.
The reverse change does not take place until the input voltage
has fallen considerably below that which first triggered the
circuit, as the screen-grid voltage is now much higher. Con-
sequently, the circuit is immune from being triggered by small
fluctuations superimposed on an impulse.
If the negative impulse which occurs on the anode of the triode
when the reverse change takes place is undesirable, it may be
suppressed in the output or by a cathode follower valve biased
to be normally non-conducting.
Since R 5 may be a high resistance, it is bridged by the condenser
C 5 in order to retain the sensitivity for impulses of very short
duration.
Another facility provided by this discriminator is found very
convenient. It is very desirable that a high-speed counter should
also count accurately at very low speeds. Now it so happens that
conditions are often not very favourable, and when counting at
a very low speed a slight disturbance, such as microphonic trouble
76 ELECTRICAL COUNTING
in the ionization chamber, causes the counter to record a rapid
burst of impulses which necessitates cancelling the observation
and possibly leads to a considerable waste of time. It is therefore
desirable to have some control by which the resolving time may
be lengthened very considerably when counting at low speeds, so
that chance disturbances can only add to the count a small number
which may even be determined by maintaining a monitoring
watch by ear. This control is provided by adjustment of C 2 or,
if a very long resolving time is required, also by increasing R 2 ,
RZ and R u .
The original impulse on the grid C l charges up the condenser
C 2 through the valve; this charge can only leak away through R%
and /? 14 , so by making the time constant C 2 /? 2 large any impulse
on the cathode and hence on the anode A 2 must be long. A micro-
phonic disturbance is liable to cause the first triode section to
conduct repeatedly, but this only superimposes a fluctuation on
the output impulse which does not cause the triggered circuit
following to record more than one impulse. It should be noted
that if R% and R u are made large R 3 must also be made large to
limit the anode current of the second triode section which also
flows through R 2 and R u .
The resistances jR 12 , /? 18 form simply a potentiometer system
for maintaining the normal bias potential of G 2 . The resistance
J? 14 provides negative feedback to limit the amplification of this
triode section to about two. This preserves the discrimination of
the second valve against superposed background on an impulse.
In conclusion, it may be remarked that a thyratron counter
has often been used as its own discriminator. Many of the
cheaper gas-filled triodes now available are not very suitable for
this use, as they may be extinguished by a large negative grid
potential, so the discharge will only pass for a portion of the
duration of the impulse. In practice grid bias up to 20 or 30 V.
may usually be applied. The striking potential may be regarded
as constant within about 3 V., so that if the impulses to be counted
are well above the background and not very different in size, a
separate discriminator is unnecessary.
Chapter VIII
RECORDING COUNTERS
The problem of the mechanical recording counter is not essentially
difficult; it has been governed in the past and still is by what
is commercially available rather than by what is physically
possible. What is generally required is an electromechanical
device which counts up to 10,000, and which operates in the
shortest possible time on the power which is readily available in
the anode circuit of an ordinary valve. Probably no such device
which even approaches the mechanical limit has yet been con-
structed. Electromechanical devices responding up to fre-
quencies of the order of 20,000 c./sec. without depending on
resonance effects are to be found constructed on the lines of
certain loud-speakers; the amplitude of movement is, however,
rather microscopic at these frequencies. Electromechanical
relays have been made in which the operation is completed in
^Q^ sec. or less. These figures may give some indication of
where the limit may lie, but it may be significant also to note
that what is required of a recording counter is merely a visual
indication. A beam of light need add nothing to the inertia of the
device, and, moreover, microscopic movements are permissible.
It is probable that ease of observation, cheapness and reliability
will condition the practical limit.
Telephone -message registers and selector switches.
Probably the most commonly used device is the telephone-
message register, such as is used in telephone exchanges for
counting the number of calls put through by a subscriber. Quite
a number of patterns are available (68), and on the average they
operate in ^ ~fa sec. and require from 07 to 5 W. for operation;
the greater the power expended the shorter the time of operation
can be m^de. Resistance values from 300 to 4000 ohms are
available. '
78 ELECTRICAL COUNTING
A few years ago there appeared on the secondhand market
step-by-step selector switches electromagnetically operated, such
as are used in totalizators and automatic telephone exchanges.
Available thus cheaply they have been applied as electro-
mechanical recorders, for the time of operation may be reduced
to j!^ sec. In order to obtain this it is necessary to operate the
recorder in series with a relatively high resistance, as an electrical
limit to the speed of operation is encountered, namely, the time
constant LjR of the winding. The power required for the high
speed of operation is about 0-6 amp. at 200 V. These selector
switches have been designed for quick operation but are heavily
loaded by the switch arms; these should therefore be removed
for economy of power.
The limit to the speed of operation of telephone-message
registers is largely set by the moment of inertia of the armature
and the maximum force which can be developed on the armature.
This is limited by the magnetic leakage, the saturation of the
magnet core and the heating of the winding. The operating time
may be reduced to its minimum by stiffening the return spring
and limiting the travel of the armature as much as possible.
Many counters have a catch with a gravity control ; for high-speed
operation this should be replaced or augmented by a spring
control.
In many circuits the counter is required to release itself after
operation. This may be done by the armature breaking a contact
in series with the winding or making a contact which short-
circuits the winding. The momentum of the armature and the
inertia associated with the magnetic field usually makes a simple
device of this kind mechanically satisfactory. Electrically this
contact is liable to be troublesome, for it is in a highly inductive
circuit, of which the inductance varies with the position of the
armature. Sparks at make and break cannot therefore be com-
pletely suppressed and the counter is liable to give electro-
magnetic pick-up in other parts of the circuit. A condenser of
about i /iF. in series with a resistance of 100 ohms connected
between the contacts is generally found a fairly satisfactory
RECORDING COUNTERS 79
suppressor. Alternatively, this may be connected across the
winding of the counter and a smaller condenser, o*i-O'O2//F.,
may be connected across the contacts.
Sparks may also be suppressed by disks of silicon carbide
specially fired and sold under various trade names such as
Thyrite, Metrosil, Atmite. These disks have a very high resistance
for a low applied voltage, but as the voltage is raised the current
rises and this causes a very marked instantaneous decrease in
resistance so that the current increases very considerably. The
disks are usually connected in parallel across inductive windings.
Fast -counting meters.
There is one meter on the market which may be included in
the category of fast-counting meters. It is the Cencods) meter
which ordinarily operates in j^$ sec. but which may be made to
operate in ZWG sec. if a high- voltage impulse is applied (66). It
is not easy to read, since it records only up to 60 for one revolution
of the main pointer, and a small subsiduary pointer indicates the
total number of revolutions. A scale-of-ten counter operating a
telephone-message register costs little more to construct than the
Cenco meter together with its operating circuit. The latter,
though much inferior in performance, is, however, simpler.
A number of fast-counting meters have been made using the
mechanism of a watch with the escapement replaced by an
electrically operated release. Accounts of some of these have been
published (23, 43, 75). A minor objection to these is that they
require periodical winding up.
The fastest counting meter yet described is that of Neher(so).
This has been made to operate in ^^ sec. This achieves its
speed by the use of a very small ratchet and very light moving
parts. Fast-counting meters have also been made at the Cavendish
Laboratory which operate reliably in ^fa sec. and operate two
hands which allow direct readings up to 1000 without any com-
plicated conversions of scales. These meters also depend for
their speed on a very small ratchet and low moment of inertia
of the moving parts. A sketch drawing of one of these is shown in
8o
ELECTRICAL COUNTING
Fig. 8-1. The armature A is attracted by the electromagnet M.
The paul P advances the ratchet while Q slides over one tooth.
On the return stroke the paul Q continues the motion of the
ratchet while P slides over a tooth. The movement of the ratchet
Adjustment
for Magnet
Fig. 8-1. Full size.
is thus spread over the whole time of operation so as to minimize
the accelerations and decelerations. Stops X and Y are arranged
so that at no point of the stroke can the ratchet step on by an
extra tooth. The pauls slide past these stops until they drop over
a tooth; one of the pauls is therefore always sliding between one
tooth of the ratchet and a stop, so the ratchet cannot advance by
RECORDING COUNTERS 81
an extra tooth. The ratchet has fifty teeth. The pauls and the teeth
are of hardened steel, and are designed so that considerable wear
can be permitted. The limit of all such high-speed counters is
the compromise between permissible wear and lightness of the
moving parts. The hands are driven through a very light flexible
spring coupling so that the inertia of the hands and gearing is not
added to that of the ratchet. The main hand is of i J in. radius and
is geared by reduction gearing of ratio 20 : i to a concentric hand
of f in. radius. This hand therefore makes one revolution for
1000 impulses. The resistance of the winding is 800 ohms
having 5000 turns of 44 s.w.g. wire. The voltage impulsively
applied is about zoo.
High-speed counters.
It will be explained later that it is often desirable to have a
counter which is able to resolve, that is, to count separately,
impulses which are only lo* 4 sec. apart or even less. In view of
this, electrical recording circuits capable of such resolution have
been devised. These operate in such a way that only every tenth
or every eighth impulse is passed on to an electromechanical
recorder. The general principle most commonly employed is that
of the scale-of-two counter introduced by Wynn- Williams. Each
successive stage in such a counter divides the counting rate by
two. The second stage is operated by every second impulse, the
third stage by every fourth impulse; the electromechanical
recorder or a fourth stage is then operated by every eighth impulse.
In the original Wynn- Williams counter (80) the unit which
passes on one impulse for every two it receives is a simple sym-
metrical circuit employing two thyratrons (Fig. 8-2). An arc is
struck in one thyratron the grid of which therefore loses control;
a positive impulse applied at the input will, however, cause an
arc to strike in the other thyratron. Its anode voltage therefore
drops from the supply voltage (200 V.) to the arc voltage (15 V.).
This drop of potential is communicated to the anode of the first
thyratron which therefore drops from 15 V. to nearly 170 V.,
extinguishes the arc, and the anode potential then rises to the
LEG 6
H.T.+
82 ELECTRICAL COUNTING
supply voltage. The effect of the impulse has thus been to
transfer an arc from one thyratron to the other. The large rise of
voltage on the anode of one thyratron after the arc has been
extinguished is used as an impulse to supply the next unit.
It should be clearly under-
stood that no circuit yet
proposed for a scale-of-two
counter is infallible, and, al-
though in ordinary use possible
failings may be unimportant
and the counter may appear
reliable, a proper appreciation
of the peculiar limitations of
the counter in use is necessary
in any work in which the exact
operation of the counter is
relied upon. The following
H.T.-
Fig. 8-a
discussion of the limitations of different counting circuits is not
therefore to be taken as indicating that the counter is necessarily
troublesome or unreliable.
The original scale-of-two unit has the merit of simplicity and,
provided it is not worked near the permissible maximum speed
or with impulses of irregular form, may be considered quite
reliable. With a high rate of counting, however, a second impulse
may arrive before the anode potential of the thyratron just
extinguished has risen to the full value; the thyratron may,
nevertheless, strike. A similar effecit may occur with a single
impulse if it is protracted and irregular. This may upset the
normal action of the counter in two ways. In the first place it is
the rise of anode potential of one of the thyratrons which operates
the next unit. If then this rise is curtailed, the impulse passed on
may be insufficient, and in this way a close pair of impulses may
appear to have been missed by the counter. In the second place,
when one of the thyratrons strikes before its anode potential
has risen to the full value, the fall of anode potential communi-
cated to the other thyratron is less than the normal and may be
RECORDING COUNTERS 83
insufficient to extinguish the arc. Both thyratrons remain alight
and the counter is completely jammed.
These two defects were obviated (37), the first by providing a
stage of valve amplification between the first and second units so
that even a small impulse does not fail to operate the second unit ;
the second by the addition of condensers C AQ as shown in Fig. 8-3 .
The fall of anode potential when one thyratron strikes is com-
municated by this small condenser to the grid of the other. The
grid potential is thus made strongly negative, and the thyratron
C H.T.+
H.T.-
Fig. 8-3
is prevented from striking until the charge has leaked off its grid
condenser. In the meantime the anode potential of the same
thyratron rises to the full value. It is found with this circuit that
it is possible to use a much smaller extinguishing condenser C A ,
so that the anode potential rises more rapidly after extinction and
the resolving time is reduced. This is due to the fact that the
negative potential on the grid hastens the collection of positive
ions and thereby shortens the deionization time. The stage of
valve amplification between the units is essential with this circuit
to prevent impulses being fed back from the next unit.
6-2
84 ELECTRICAL COUNTING
Circuits using hard vacuum valves.
It is evidently possible to make the flip-flop circuit act as a
scale-of-two counter, as it has two stable states. It is only neces-
sary to provide some means of triggering the circuit alternately
from one stable state to the other. A number of circuits have now
been published in which this has been achieved. These must be
judged by their simplicity, performance, and reliability.
The circuit for which the greatest claims of performance and
INPUT
Fig. 8-4- Stevenson and Getting's scale-of-two unit. All valves Type 57.
<KI RI, #3. ^s #4, 100,00001; /? 2 , #2, 300,000 co; C 2 , Ca, o-ooo25/iF.;
C 4 , 0-000025 /iF. Resolving time less than 2 x io~ 6 sec.
reliability have been made is that of Stevenson and Getting (72)
(Fig. 8-4), but unfortunately this circuit uses four pentodes
per stage. The high cost of pentodes in this country hinders its
adoption. Apparently this circuit is capable of resolving impulses
only 2 x io~ 5 sec. apart, and retains this property over the whole
of the very large range of grid bias which is permissible.
The simplest of the circuits is that published by Alfvenca)
(Fig. 8-5, p. 85), and also independently by Lifschutz and
Lawsonuo. This circuit is perfectly satisfactory provided it
receives sharp impulses of controlled magnitude. It has not,
RECORDING COUNTERS 85
however, proved so satisfactory when the resolving time is
reduced to the minimum.
It has proved advisable to check the action of any counter
circuit in detail, before trusting its operation near its limit. That
is to say, tests should be made of the resolving time, the certainty
of passing on an impulse to the next stage or thyratron, when a
close pair of impulses is received, the range of impulse forms
which it can handle, and how these properties are retained over
the grid-bias range.
+130 volts
Positive
Impulses
To Next Stage
II
20 Volts
Fig. 8-5. Alfve*n's scale-of-two unit.
Valves I and II, Philips 62038 G* = 33 ^=3*35 mA./V.). All resistances
R = 0-2 MQ. Q , C , 1000 cm. ; C 2 , Ci* , 500 cm. For high-speed counting
smaller condensers are preferable.
The circuits published by the writer (38) (Fig. 8-6, p. 86) are
complicated by the inclusion of cuprous oxide rectifiers ( Westec-
tors) and double- wound chokes. The particular objection to these
chokes is that they are components which cannot be tested and
measured so readily as condensers and resistances by anyone
with restricted laboratory facilities. The writer has set up other
circuits avoiding the use of such components but has not found
any such circuit without some disadvantages. The ideal simple
circuit which can be set up by anyone from a simple written
specification using only two valves per stage of any make, the
86 ELECTRICAL COUNTING
other components being only resistances and condensers which
can be relied upon to work without fail, has yet to be devised(s6).
Grid biai
-38V {=?*: C
Fig. 8'6
Circuit (i). V = V* = Mazda L2; AB = AC = Westector, Type W6;
r=4o,ooow; wJR= 240,0000;; /?= 100,00001; ^j=ioo,oooo>; L = 6oHy;
Centre tapped; C f o-ooifiF. Counts impulses of duration > 2*5 x io~ 5
sec. < o-o i sec. Resolving time 2 x io~* sec.
Circuit (2). Valves Mullard 904 V and TV 4 (tuning indicator). R l =
R* - 250,000 w; RZ = JR 4 = ioo,oooo>; Rectifiers, Westectors Type WX 6.
<?i = C a = 0-0002 fiF. L= Two 2,000 w headphone bobbins on centre
limb of two E -shaped stampings of Laminic. Counts impulses of duration
up to o-o i sec. Resolving time io~ 4 sec.
These remarks show that the nature of the difficulty is not such
that it would trouble a manufacturer or anyone making a number
of counters. Research apparatus of this type must, however, be
virtually home constructed.
RECORDING COUNTERS 87
Indicators.
It is necessary in these circuits to provide some means of
indicating in which stable state the circuit is at any time. The
most attractive means of doing this is to use a cathode-ray tuning
indicator in place Of one of the valves of each pair. This, however,
imposes a restriction on the circuit, for the triode portion of
these indicators is usually limited to working with Arery small
currents and consequently high resistances in the circuit. This
makes the circuit unsuitable for a resolving time less than
2 x IO"" 5 sec. Apart from this limit, which in most cases is quite
unimportant, very satisfactory counters have been made using
such indicators.
Alternatively, small neon-lamp indicators may be used. It
must be remembered, however, that the ignition voltage of a neon
tube is likely to increase with age, and an ample reserve voltage
must be provided in the circuit. Also, if the applied voltage is
somewhat low the discharge may not strike immediately the
voltage is applied. The striking of the tube then produces another
impulse in the circuit and this must not be passed through to
operate the counter in any way.
A milliammeter in one of the anode circuits does not prove
quite so convenient an indicator, since the time lag in its operation
renders it useless for visual checking of the action of the counter
at high speed.
Action of the circuits*
The action of the various circuits may be briefly described.
In Stevenson and Getting's circuit (Fig. 8-4) positive impulses
are applied to the control grids of two pentodes connected
together. The common grid bias is normally such that no anode
current flows. Ah impulse causes both pentodes to pass anode
current. The two anodes are separate and connected directly to
the anodes of the second pair of pentodes which are connected
in a simple flip-flop circuit with the addition of condensers
88 ELECTRICAL COUNTING
bridging the anode-to-grid resistances as in the multivibrator.
The use of pentodes is necessary to maintain the very short
resolving time. The screen grids are all maintained at a steady
potential (90 V.).
One of the pentodes in the flip-flop circuit will be passing
anode current so that its anode potential will be low; the extra
current drawn by the impulsing pentode will not lower this
anode potential greatly. The other pentode in the flip-flop circuit
will be passing no anode current, so its anode potential will be
high until the impulsing pentode draws anode current. The
potential of the two anodes will then fall and a negative impulse is
communicated by a condenser C 2 to the grid of the other pentode,
thus causing the system to change to its other stable state. The
system is symmetrical, so that, after the steady state has been
reached, another impulse would again reverse the conditions.
The action would be upset by a prolonged impulse which would
maintain all the anodes simultaneously at a low potential. It is
arranged that only short impulses can be transmitted by making
the time constant of the input circuit C 4 /? 4 <C 2 1? 2 . The latter
time constant C 2 /? 2 approximately represents the time constant
for the system reaching its stable state after a transition.
In Alfven's circuit (Fig. 8-5) positive impulses are applied.
Suppose that the grid of valve i is positive so that the valve is
conductive, while the grid of valve 2 is negative so that valve 2 is
passing no anode current. The resistance of the grid-filament
path of valve i is small and the applied positive impulse has little
effect, therefore, on the grid voltage and hence on the anode
voltage. The grid input resistance of valve 2, on the other hand,
is very high, so that the positive impulse produces a large change
in grid voltage and produces a negative impulse on its anode.
This is transferred to the grid of valve i by the condenser C 2 and,
being larger than the applied positive impulse, puts the grid of
valve i negative. The resulting positive impulse on the anode of
valve i increases the positive impulse on the grid of valve 2
through the condenser C 2 . This change-over takes place just as
in the multivibrator circuit, the resistances cross-connecting the
RECORDING COUNTERS 89
anodes and grids act as in the flip-flop circuit to maintain the
stable state which has thus been reached
The circuit can also be triggered by large negative impulses;
such impulses must therefore not be allowed to occur in the input.
This may be done by a rectifier as in the output of the last dis-
criminator described in Chapter vii.
Two of the counting circuits described previously by the
writer (38) are shown in Fig. 8-6. In circuit (i) of Fig. 8-6 negative
impulses are applied at A. If, in the initial state, valve V% is
passing no anode current, A is almost at the same potential as C
and is positive with respect to B. The rectifier AB will therefore
be in a non-conducting state, and very little of a negative impulse
at A is passed on to J5, whereas a large fraction of the impulse will
be passed on to C through the rectifier AC across which there was
initially a negligible difference of potential. The negative impulse
thus reaching the grid C causes the anode current of V t to fall;
the potential of B therefore rises, and if the impulse is sufficiently
large B will reach the potential of C. In this state the currents in
the two symmetrical halves of the circuit are equal. This condition
is unstable, and from it the system may pass to either of its stable
states, but the inductance L is included to continue the change
of relative potential of B and C so that the stable state which
results is not that from which the system started.
The circuit (2) is slightly different in that the centre point of
the two rectifiers is left to find its own potential, which will be
approximately that of the more positive grid, so the mode of
operation of the circuit is still as has been described above.
The performance of the circuits is indicated briefly with the
specifications below the figures.
Three scale-of-two units followed by an electromechanical
counting meter has been found most generally useful. The
counting meter operates for every eighth impulse and, if an
ordinary telephone-message register is used, its change of reading
must be multiplied by 8 and the odd number up to 7 added in
from observation of the state of the counter. This may be read
, quite easily from the indicators in the three stages if they have
90 ELECTRICAL COUNTING
been set to zero before starting the count, for the first may be
labelled i, the second 2 and the third 4, the corresponding
numbers being added in to the count if indicated.
To avoid the multiplication by 8 the meter may be modified
to read directly in multiples of 8. This may be done by altering
the figures on the units drum from 0123456789 to 0864208642,
and by fitting additional teeth so that the tens drum is moved on
at every movement of the units drum except when this moves
from showing o to showing 8. The meter thus shows the sequence
008, 01 6, 024, 032, 040, 048, ....
Scale -of -ten counters.
It would be still more convenient if the electrical counter
operated on a scale of ten. Wynn- Williams devised a thyratron
ring counter which could have any number of thyratrons arranged
in a ring with an arc in one of them, but this proved difficult to
adjust. It has proved possible to extend the basic idea of the
flip-flop circuit to five valves, only one of which passes no anode
current. These may be linked in a ring by condensers, and
condensers and resistances, so that impulses cause the system to
pass to each of its five stable states in rotation. By using cathode-
ray tuning indicators instead of ordinary valves it is evident which
valve is passing no anode current. By placing this ring-of-five to
follow a scale-of-two unit, a scale-of-ten counting meter may be
operated directly to record tens, hundreds, and thousands, the
units being read directly from the ring-of-five and the scale-of-
two unit.
The circuit is shown in Fig. 8-7. Positive impulses are applied
simultaneously to all the grids via the separate small condensers.
The grid-filament resistance of those valves whose grids are
positive is, however, low, so that the impulse on the grid is small;
the negative impulse received from the anode of the previous valve
in the ring is also small except for that following the valve which
was passing no anode current. The positive impulse on the grid
of this latter valve is large and its anode potential falls. The
negative impulse passed to the next valve is sufficient to stop its
RECORDING COUNTERS
SI
1
I
*!
a?
af ^
Q
M
of
92 ELECTRICAL COUNTING
anode current. The flip-flop connexions make this new state
stable and it persists until another impulse is received.
Circuits for operating mechanical recorders.
The simplest circuit for operating a telephone-message register
is probably a single thyratron circuit (Fig. 8-8). A break contact
is fitted to the message register to interrupt the thyratron anode
circuit. The means adopted for suppressing sparking at this
contact have already been discussed. It may, however, be added
that the insulation of the condenser must be high or sufficient
leakage current may pass to maintain the arc in the thyratron.
THYRATRON
INPUT
o><IOO,000<y
Rust . 9 _- -r, ..
<" r \ ^ a' d
co^} mftzt.
H.T.+
H.T.-
Fig. 8-8. Thyratron counter.
With message registers requiring a small enough current, a
type of flip-flop valve output circuit may be used. One such
circuit is illustrated in Fig. 8-9. Again, the counting meter is
fitted with a break contact B, but in this circuit it interrupts only
a very small current, so the contact is not troublesome to keep
clean nor is there any need for special measures for spark sup-
pression.
Very satisfactory valve circuits may, however, be made which
avoid the need for any contact by providing only a pulse of
current. The magnitude of this pulse may be adjusted to be
sufficient to operate the counter without fail. A circuit which has
proved very generally satisfactory for operating all types of
RECORDING COUNTERS
93
+ 220 volt*
INPUT
Grid Bias 38 volts
Fig. 8-9. Flip-flop meter operating circuit. Contact K is opened
in the home position of the counting meter.
lOHy
D.C.+
220volts
0-0002/tF
{ Gr/dBia$ 15 volts
Fig. 8-10. Blocking oscillator.
94 ELECTRICAL COUNTING
counter, including fast-counting meters, is shown in Fig. 8'io.
This is a blocking oscillator circuit. The triode formed by the
cathode, control grid and screen grid is connected as an ordinary
oscillator with regenerative coupling provided by the transformer
between the screen-grid and control-grid circuits. A large
negative grid bias is, however, applied to the control grid which
stops all anode current. The circuit is triggered by a short positive
impulse which momentarily removes the negative bias. The
circuit would then maintain an oscillation, but the damping
resistance across the secondary of the transformer in the control-
grid circuit ensures that after one cycle of the oscillation the
control grid never returns sufficiently positive to permit another
cycle to occur. The pulse of current in the anode circuit is used to
operate the counter. The duration of this pulse is controlled by
adjusting the time constant L/R of the screen-grid circuit, and
by adjusting the damping resistance. The main control of the
pulse duration is, however, effected by suitable choice of the
transformer. For example, for pulses from ^ to ^ sec., suitable
for operating a telephone-message register, the transformer may
be a good-quality audio-frequency inter-valve transformer such
as the FerrantiA.F. 3 (primary inductance 220 H. (60 H. at
6mA. d.c.), step up ratio i :3*s). For pulses of T ^j sec. or less
an audio-frequency output transformer such as the Ferranti
O.P.M.5 (primary inductance 70 H. (6 H. at 50 mA. d.c.), step
down ratio 4:1) is suitable. The use of a Westector rectifier in
the grid circuit maintains a high input resistance while mini-
mizing the dead space or time interval after an impulse during
which the counter remains insensitive. This dead space should
not, however, be too short as the counter should be allowed
sufficient time to release. This may be tested by setting the rid
bias to zero: the counter should then operate repeatedly or
" run over" at nearly its maximum speed.
It will be noticed that in the circuits shown for operating
counting meters a " run-over " contact is shown ; this may be used
for running the counter on to the next hundred or thousand in
order to start each count from a round number. A contact operated
RECORDING COUNTERS 95
by the counter may be arranged to interrupt the run-over contact
circuit in this home position, that is, when the hundred or
thousand is reached. If the meter runs over somewhat slowly,
relay circuits may be arranged for this operation, but with the
fast-counting meters the run-over contact is simply a push button
which is pressed until the meter reaches its home position, when
it stops running over, the push button then being released.
Counting -rate meters.
For some purposes it is advantageous to have a direct indication
of the rate of arrival of particles. Owing to statistical variations
in the number arriving in any given time interval such an indicator
cannot be very quick acting unless the rate is very high. The
principle may, however, be quite simple. Impulses of strictly
the same amount are derived from the particles and are fed into
a condenser across which there is a constant leak resistance; the
average potential difference maintained across the condenser is
then a measure of the rate of arrival of the impulses.
One of the remarkable features of the technique of counting is
that it proves possible to derive results from rates as low as one
particle in a few minutes, and with the same apparatus to count
thousands of particles per minute. This range of tens of thousands
to one has proved invaluable in certain investigations, but for
many experiments a much smaller range such as could be read on
an ordinary direct-reading instrument is sufficient. A counting-
rate meter which can measure rates from 30 to 6000 particles per
minute finds much application.
Such a meter has been devised and applied by Gingrich, Evans
and Edgerton (27). Their apparatus consists essentially of two
parts: a uniform impulse producer and a resistance-capacity tank
circuit for averaging the number of impulses over a time of the
order of half a minute.
This capacity-resistance averaging circuit is connected in the
anode circuit of a pentode so that the magnitude of each pulse
supplied to the capacity is independent of the voltage across it.
The uniform impulses are supplied to the grid circuit of the
96 ELECTRICAL COUNTING
pentode. A microammeter in series with the resistance measures
the voltage across the condenser. Gingrich, Evans and Edgerton
use a condenser C * ioo/^F. and R = 3 x io 5 ohms and the meter
reads 0-200 pA. Alternatively, they suggest using a smaller
condenser with a valve voltmeter to measure the voltage. A con-
venient valve voltmeter circuit which the writer has used for
this purpose has been described in Chapter vi.
Two impulse generators were proposed by Gingrich, Evans
and Edgerton, one essentially the first stage of a thyratron scale-
of-two counter, the other an unbalanced multivibrator circuit.
No information is given of the uniformity of the pulses produced
nor of the dependence of this on the form and magnitude of the
input impulse nor how this uniformity depends on the resolving
time.
O. Viktorin and the writer (unpublished) have applied a
blocking oscillator circuit similar to that of Fig. 8- io for producing
uniform impulses which are supplied to a condenser (8/*F.)
shunted by a high resistance (2-5 megohms) connected in the
anode circuit. The transformer used is very small, so that the
duration of a pulse is only about 3 x lO" 4 sec. The voltage
developed across the condenser is read with a valve voltmeter
using the circuit of Fig. 6-j.
It should be pointed out that the counting-rate meter is of less
general application than a counting circuit. It possesses a decided
advantage for taking a continuous record of a slowly changing
rate, but for other purposes where the rate is frequently changed
the counting-rate meter necessarily requires a longer time to
obtain a result of a given statistical value.
Count integrators.
A recording counter which records with certainty any number
from one to several million if required cannot seriously be chal-
lenged on performance. For some purposes, however, it would be
an advantage to make simultaneously a large number of counts,
say twenty or more. An installation of twenty high-speed counters
would be somewhat elaborate and costly. In such circumstances
RECORDING COUNTERS 97
a device which may be described as a count integrator may prove
useful. The arrangement is similar to that of a counting-rate
meter except that the leak resistance across the storage con-
denser is omitted. Twenty separate circuits feeding twenty
storage condensers may readily be set up ; the charge accumulated
on each condenser during the counting time may subsequently
be discovered by testing the condensers in succession with a
single-valve voltmeter.
A similar principle has been applied to make a scale-of-ten
counting circuit. The condenser receives and stores nine im-
pulsive charges, then on receiving a tenth charge it triggers a
circuit which discharges the condenser. This might seem a
simpler system than the scale-of-two and scale-of-ten counters
previously described, but the electronic means of discharging
the condenser introduces complications which make the two
systems comparable.
Chapter IX
GEIGER-MULLER TUBE COUNTERS
The Geiger-Miiller tube counter operates by the production of
an electrical discharge in a gas. The counter is extremely sensitive,
and a discharge may be produced when a single pair of ions is
liberated almost anywhere within the tube. It is distinguished
from other discharge counters by this large volume over which
the formation of an ion pair will produce a discharge.
The counter in its usual fornr consists of a cylindrical metal
tube, along the axis of which a thin wire is stretched. The wire is
usually bare or slightly oxidized and is highly insulated from the
metal tube. The tube is customarily about 10 cm. long but may
be five or ten times longer or shorter. Most satisfactory operation
is secured when the length of the tube is greater than about twice
its diameter. The tube is filled with gas at a low pressure, most
commonly between 5 mm. and 20 cm. of mercury. The wire is
maintained at a positive potential with respect to the tube.
These counters are used in large numbers, particularly in
cosmic-ray work. It is still, however, impossible to guarantee
that a counter made up Carefully to any specification will be
satisfactory in all respects. The extreme sensitivity of the counter
renders it liable to apparently spontaneous discharges, the origin
of which is uncertain. The characteristics of the discharge are
also often found to change with time.
If no restriction is placed on the shape, size and material of the
counter, the nature and pressure of the gas, the operating voltage
and the diameter of the wire, it seems possible to produce counters
of which the great majority will operate at least qualitatively in
a satisfactory manner.
The varied nature of the discharges in Geiger-Miiller counters
made to different specifications and operated under different
conditions should be clearly recognized. Generalizations about
GEIGER-MVLLER TUBE COUNTERS 99
the behaviour of counters are of little value unless the operating
conditions and the type of the discharge are specified. In dis-
cussing the operation of counters it is necessary to make a clear
distinction between three processes occurring in the counter:
the initiation of the discharge, its growth, and its extinction.
Initiation of the discharge.
Suppose for the present the growth and subsequent extinction
of the discharge are taken for granted. Evidence about the
initiation of the discharge is mainly obtained from characteristic
curves of the type shown in Fig. 9-1, which shows the number of
Volts
Fig. 9*1. Geiger counter "ideal" characteristic.
discharges per minute plotted against the voltage applied to the
counter under the action of a constant weak source of ionization.
The various curves of Fig. 9*1 refer to ionization sources of
different strength. They have the form which is claimed to be
the ideal characteristic for a Geiger-Muller counter. As the
voltage is increased the number of counts is first zero, then rises
steeply to a flat portion where the rate of counting is independent
of the voltage. At a higher voltage the number of counts again
increases, this increase in the ideal case being independent of the
source of ionization.
On these curves only two causes for the initiation of the dis-
charge are indicated: initiation by ionization, and spontaneous
initiation which is always obtained at high voltages and sometimes
7-a
zoo ELECTRICAL COUNTING
also at the working voltages. Included in the initiation by
ionization is the "natural " of the counter, namely, the discharges
produced by radioactive contamination of the counter and by
cosmic rays. The spontaneous discharges are sometimes vaguely
attributed to the presence of irregularities in the surface of the
wire. Sharp points on the wire certainly lower the discharge
voltage and therefore produce spontaneous discharges at a lower
voltage. There is, however, no evidence that this is even a frequent
cause of the defect. The writer has had satisfactory counters in
which the wire, of iron, was covered with rust crystals. It is
possible that spontaneous discharges are initiated by the local
concentrations of electric field which occur at the junctions
between the conductors and solid insulating materials, as the field
at such points is liable to fluctuations.
An unfortunately common defect of Geiger counters is the
production of multiple discharges, a spurious discharge being
likely to occur immediately after any discharge. One possible
cause of this is that in the discharge, atoms are excited into
metastable states. A short time later these return to normal with
the emission of radiation which may liberate photoelectrons from
the wall of the counter, and thus initiate another discharge.
Duffendack, Lifschutz and Slawsky(iS) have advocated the use
of pure hydrogen as the gas, since this is free from metastable
states. Alternatively, a second gas may be mixed with the first to
bring about de-excitation by collisions of the second kind, in
which the energy of excitation is liberated as kinetic energy of the
colliding molecules.
In the present state of knowledge of the factors affecting the
initiation of the discharge each counter requires individual
experimental investigation; nothing should be taken for granted.
In particular, no assumption should be made as to the effective
counting volume. Nor should the counter be assumed to retain
constant characteristics for any great length of time. It is even
necessary to check at intervals that the counter is able to add up
correctly at a given operating voltage and temperature when
connected to a given circuit. That is to say, counts should first
GEIGER-MVLLER TUBE COUNTERS 101
be taken with no source of ionization, then with one source, then
with another and then with both together. If this test is passed
satisfactorily, it is not to be assumed that it will still hold if the
operating voltage, temperature, or circuit is in any way altered;
nor will it necessarily hold for a later time, the time interval being
comparable with the time since the counter was made or pre-
viously tested. If there is the possibility of there being anything
loose inside care should be taken in moving the counter, as it is
possible that if the wire is not taut, the behaviour of the counter
may change when it is turned over. It may also be noted that when
glass chips were deliberately sealed up in a counter and the
counter was shaken violently, it was found to acquire a high
"natural" which decayed within a period of a few minutes. This
effect was hypothetically ascribed to the re-formation of the
oxide layer on the surface of the counter wall. It is to be remem-
bered that all metal surfaces, including gold and stainless steel,
after exposure to the air are covered by an oxide layer.
It should be noted that the addition test is also a test of the
recording counting mechanism.
For satisfactory experiments with Geiger-Miiller counters it is
usually arranged that the results would not be affected by slight
changes in the characteristics of the counters or by a certain
number of spurious discharges. Experiments in which only
coincident discharges in two or more counters are recorded are
ideal in this respect, as the chance of spurious discharges coin-
ciding with discharges in other counters is usually very small. In
such experiments elaborate checks of the individual counters are
generally unnecessary.
Growth of the discharge.
The first stage in the growth of the discharge is explained as an
avalanche process. An electron is attracted towards the positively
charged wire, and over a small region of its path it is accelerated
between its collisions with atomic electron shells through more
than the ionization potential of the gas. It is thus able to release
a second electron from the next atom encountered. The two
ELECTRICAL COUNTING
electrons are again accelerated and produce further ionization.
The process may continue until a large charge is passing. It is
found, however, that the charge passed is much greater than can
be attributed to a single avalanche. Some process must therefore
occur by which further electrons are liberated at points sufficiently
far from the wire to initiate further avalanches. Two mechanisms
for this process have been suggested and discussedoe, 24,47);
these may be designated the photoelectric and the positive-ion
mechanisms. It is possible that both are simultaneously effective.
Other mechanisms may also be imagined.
On the photoelectric hypothesis the radiation arising from the
recombination of ions liberates photoelectrons from the wall of
the counter. This hypothesis finds considerable support from the
observed effect of the wall material on the form of the discharge.
On the positive-ion hypothesis a collision experienced by the
positive ion is assumed to have a certain small probability of
liberating an electron. The collision may occur either in the gas
or at the wall. Some uncertainty exists about the quantitative
aspect of this process; it is, however, to be noted that the magni-
tude of the photoelectric process is only known very roughly,
though it appears to be of the order of magnitude required to
explain the observed phenomena.
On both hypotheses the chance of maintenance of the discharge
is approximately proportional to the number of positive ions
formed. The discharge therefore grows indefinitely but, if the
maintenance process is sufficiently improbable, fluctuations are
to be expected in the mean current passing.
Extinction of the discharge.
In order that the discharge shall be extinguished the prob-
ability of the maintenance process must be progressively reduced,
and a number of mechanisms have been adopted to secure this.
First, the voltage applied to the counter may be progressively
reduced by some means depending on the discharge current ; this
reduces the number of electrons and positive ions produced in
each avalanche. Two modes of extinction, which will be dis-
GEIGER-MULLER TUBE COUNTERS 103
tinguished as resistance extinction and external extinction,
operate in this way. In a third method of extinction the discharge
is extinguished entirely by internal action.
Internal extinction.
The process of internal extinction depends on the low mobility
of the positive ions. The electrons liberated in the avalanche
process are quickly removed by passing to the wire. The positive
ions, however, move more slowly, so that an excess of positive
ions is left. There exists close to the external tube a potential
gradient due to this distribution of positive space charge. As-
suming that the electric field remains everywhere radial, this
potential gradient at a radius a may be written as
CT 27TCI
3 27irdrp
ZTTdJ o
by Gauss's law, where p is the density of positive charge. If it
is assumed that the potential difference between the wire and the
external tube, that is, the voltage externally maintained across the
tube, is cither reduced or unchanged, then, to compensate for
this added potential gradient close to the tube, the potential
gradient must be reduced elsewhere. In fact, the electric field
must be reduced close to the wire. The avalanche process is thus
checked. If this process is to be effective it is necessary that the
positive ions, at least near the tube, shall not be such that they are
able to liberate electrons by any mechanism. The nature of the
positive ion and the photoelectric character of the wall material
is therefore again important.
It is found that this process of internal extinction is satisfactory
and reliable if the vapour of some polar organic substance such
as alcohol or acetone is included in the gas (74). Presumably the
positive ions in such a mixture are rendered slow and have low
recombination potentials.
Satisfactory internally extinguished counters may be con-
structed by using a very thin wire (about $0/1 diameter) and not
too low a gas pressure ; 5-1 2 cm. of mercury is common. The inert
104 ELECTRICAL COUNTING
gases argon or helium are particularly satisfactory. The pressure
of alcohol vapour may be about i or 2 cm. Such counters have
also been made using acetone vapour with no added gas. If the
counter is to last long, wax, ebonite, and similar substances
which absorb the vapour must not be used for the insulation of
the wire from the tube. Glass or quartz may be used.
In order to detect the discharge it is usual to include a resistance
of the order of i megohm in series with the counter. The voltage
drop across this resistance when a discharge occurs plays no
essential part in the extinction. Moreover, the duration of the
voltage impulse across the resistance gives little indication of the
time interval before the electric field within the counter is
restored so that the counter is again sensitive.
With internal extinction the quantity of electricity passing in
the discharge is approximately constant for a given operating
voltage but increases rapidly with voltage over the normal
operating range. If a large capacity is connected across the
counter the voltage drop occurring with a discharge is reduced,
as would be expected; the recovery time is not, however, neces-
sarily lengthened, since the voltage drop may have been so small
that the counter remained on the operating portion of its char-
acteristic as far as the external circuit is concerned. The recovery
time is conditioned by the time required for the removal of the
space charge.
Resistance extinction.
The mode of action distinguished as resistance extinction is
quite different from internal extinction, although in the operation
of some counters both modes may occur simultaneously. The
process of resistance extinction has been investigated in detail
by Werner (77). He finds that in general there is a certain minimum
current which may be passed in a continuous discharge through
the counter; if the voltage across the counter is increased the
current increases, but if an attempt is made to reduce the current
below the minimum value by limiting the current or reducing
the voltage then the discharge is extinguished. Let the voltage
GEIGER-MVLLER TUBE COUNTERS 105
across the counter when the minimum current t^^ passes be
V miUt . If a higher voltage V a is applied a discharge is not neces-
sarily produced at once, but ionization within the counter initiates
V -V
the discharge. If a resistance R>.?^ is included in series
with the counter, then when the current i mln . passes, the voltage
across the counter will automatically be reduced to less than
^min. so the discharge will not be maintained.
Although wide variations in *' mln are possible, depending on
the gas, the pressure, and the dimensions, in general if a voltage
difference V a -V m{rit of about 100 V. is to be permitted R will
have to be about io 8 to io 9 ohms.
The process of extinction is again internal in the counter. As in
other modes of operation the discharge, after initiation by the
avalanche process, is maintained by a process depending on the
current density. This mechanism weuld lead to an indefinite
growth of the current for any voltage greater than l^ ln ., so that
in order to obtain a limiting current it is necessary to suppose
that an internal space charge builds up which lowers the electric
field. In this mode, however, this space charge does not lead to
the extinction of the discharge; it is necessary also to reduce the
voltage externally applied to the counter. It happens that the
voltage may fall slightly below F min . After this the voltage rises
again, but the rate of rise is limited by the capacity of the counter.
Some ions remain in the counter, but the number of ions must be
sufficiently small to render maintenance of the discharge im-
probable.
This mode of operating counters with a high series resistance
remained for Jong the commonest, though it suffers from severe
limitations in the maximum speed of counting. If the resistance
R is io 8 ohms and the capacity associated with the wire and the
recording apparatus connected to it is 30 fi/i. y then the time con-
stant for the recovery of the voltage on the counter is 3 x io~ 3 seq.
A second discharge occurring within about o-oi sec. of another
would produce only a diminished impulse.
The current through the counter ceases while the voltage is
106 ELECTRICAL COUNTING
low; after this there is no reason why the resistance should be
large. Neher and Harper (so have pointed out the advantages of
a circuit which had previously been applied by Wynn-Williams (79),
in which there is effectively a high resistance in series with the
counter while current greater than a certain minimum is passing,
but only a low resistance as soon as the current falls below this.
The recovery of voltage is therefore rapid.
With resistance extinction the voltage across the counter drops
to a certain point a little above the lowest operating voltage; the
magnitude of the voltage drop is approximately proportional to
the excess of the operating potential over this voltage and is
independent of the capacity across the counter. This condition
is rarely perfectly satisfied, since the process of internal extinction
is usually operative to some degree.
Duration of discharge.
It has been pointed out that the mechanism of internal extinc-
tion prevents determination of the effective duration of a dis-
charge from observation of the voltage change occurring across
the counter. The duration can only be derived indirectly. If a
recording counter is available with a resolving time less than the
duration of the discharge, the minimum time between two dis-
charges may be inferred from the results of the addition test at
high rates of counting (see Chapter x). The duration is likely to
be of the order of io~ 4 sec., and a recording counter with a suffi-
ciently short resolving time may not be available. In such a case
a method based on coincidence counting may be adopted; each
discharge renders the counter insensitive for the duration of the
discharge, and the relative time during which the counter is insensi-
tive may be inferred from the observed reduction of the number
of true coincidence counts between it and another counter, when
the counter under test is simultaneously exposed to a source of
ionization giving a large but measurable rate of counting.
External extinction.
It will have been observed that in the previously described
methods of extinction it is necessary that, in the process of re-
GEIGER-MULLER TUBE COUNTERS 107
moving the last of the ions from the counter, no free electrons
should be released. If the choice of gas and wall material is
restricted, it may happen that the liberation of free electrons is
quite probable and prolonged discharges result. If the voltage
across the counter is not restored until a predetermined time
interval has elapsed, sufficient for the collection of all the ions,
then such prolonged discharges are prevented. In a circuit
devised by Wynn-Williams (79) this is achieved. For a counter
to be suitable for external extinction in this manner it is only
required that the minimum discharge current shall be sufficiently
large to operate the extinguishing circuit. Very little systematic
investigation has been made on externally extinguished counters.
It may be possible to construct counters having valuable special
properties which are only suitable for external extinction. For
example, Wynn-Williams constructed counters which operate
satisfactorily with an applied potential of only 300 V.
Circuits.
Three circuit arrangements which are used for resistance
extinction are shown in Fig. 9-2. The first (a) requires no ex-
planation; (b) and (c) differ in that in (b) the tube of the counter
is at high potential with respect to earth, and in (c) it is at earth
High Vo/ts
Negative
High l/o/ts
Positive
(a) () ^ (<)
Fig. 9-2. Circuits for resistance extinguished counters.
R x extinguishing resistance io 7 to io 9 ohms.
R g = grid leak resistance. C = 2 to 20
io8 ELECTRICAL COUNTING
potential. When, as is quite common, the tube of the counter is
its outer wall, it is more convenient to be able to touch it without
fear of shock, so circuit (c) would be adopted. This requires a
condenser of rather special construction, as the insulation of the
plate connected to the wire of the counter must be high com-
pared with the counter series resistance, which may be io 9 ohms.
Further, if the condenser is simple the insulation between the
plates must be at least 1000 times the resistance in the grid circuit
of the valve if the high potential is not to alter the potential of the
grid. This necessity is avoided if the insulation of the condenser is
split with an earthed guard ring. The small condensers known
commercially as ceramic condensers and rated for a working
voltage of 750 usually have an insulation resistance greater than
io 10 ohms and are often satisfactory if kept clean and not fingered.
If the series resistance is io 8 ohms or greater, the wire of the
counter and the grid coupling condenser may also be touched
without fear of shock.
Valve amplifying circuits for resistance extinction are shown
in Fig. 9-3. In Fig. 9-3 (a) the grid of the valve is biased so that the
valve is inoperative until the discharge current passing through
R x is sufficient to develop at least an appreciable fraction of a
volt. When the valve is thus made to pass anode current the
potential drop across the anode resistance R A is added to that
across R x and the voltage on the counter is thus reduced. It
should be noted that the current with which the discharge was
formed was derived from the capacity of the counter together
with that added by the circuit. When the voltage becomes in-
sufficient to maintain the discharge this current rapidly falls,
and when it becomes less than that flowing through the resistance
R x the potential rises again. Up to this stage the effective resist-
ance in series with the counter may be shown by analysis to be
M times R Xy where M is the magnification of the valve circuit.
However, when the current through the counter ceases the valve
becomes inoperative and the recovery time constant is that
appropriate to the low resistance R x .
Fig. 9*3 (b) shows a modification of this circuit in which the
GEIGER-MVLLER TUBE COUNTERS 109
potentials applied to the valve are not above the normal rating.
The vacuum in an ordinary valve used in the circuit of Fig. 9*3 (a)
is liable to soften, due to the high anode voltage when the current
is small.
High Volts Positive
High Volts Positive
H.T.+
H.T.-
H.T.-
Fig. 9-3. Valve amplifying circuits for resistance extinction.
It should be particularly noted that it is the non-linear char-
acteristic of the valve which gives this circuit an advantage over
simple resistance extinction. Any modification of the circuit in
which the non-linear property of the valve is not used must
necessarily be equivalent to simple resistance extinction.
External extinction circuits.
One of the simplest circuits for external extinction is that of
Wym\- Williams (Fig. 9*4). This is a complete recording counter
circuit. The recorder is operated by the anode current of the
thyratron. The armature of the recorder at the end of its travel
breaks a contact which interrupts the anode circuit and ex-
tinguishes the arc in the thyratron. The armature is thus released
and the contact is made again, thus restoring the operating
potentials to the thyratron and Geiger-Miiller counter. The extra
battery for the Geiger-Miiller counter may be replaced by a
supply from a rectifier connected as in Fig. 9*3 (4). In this form
no ELECTRICAL COUNTING
the counter is not suitable for very rapid counting, due to the
inevitable slowness of the mechanical recorder.
The multivibrator circuit has been employed for external
extinction(26,48,59). A successful circuit devised by de Sousa
Santos (unpublished) is simply that of a multivibrator with the
wire of the counter connected to the anode of one of the valves
which is normally held in a non-conducting state by a high
negative gri4 bias. A modification of this circuit in which the full
Geiger counter potential is not applied to the anode of the valve is
shown in Fig. 9-5. As soon as a discharge passes in the counter the
wire of the counter drops slightly in potential; this drop of
Battery supplying
Extra Voltage for Geiger'Q-imiting
Counter as rcqwred <fi*s>*t*
Spark
Suppressor
Contort? -t-
High&t Vo/tage
Supply A vaulable
giving sufficient
Current to operate
recording counter
Fig. 9-4. Wynn-Williams external extinguishing circuit.
potential is amplified by the second valve and fed back to the
grid of the first valve reversed in sign. If this impulse is as great
as the applied negative cut-off bias the first valve passes current,
its anode potential consequently falls and the process continues
independent of what is occurring in the counter. The normal
potential is restored again at a later time determined by the time
constants of the coupling condensers and grid-leak resistances.
Many other circuits using thyratrons, the multivibrator or a
blocking oscillator would appear suitable.
Very little work appears to have been done on designing
counter tubes most suitable for external extinction.
GEIGER-MULLER TUBE COUNTERS in
High counting rates.
The question of the minimum time for the discharge in a
Geiger counter is important for a number of investigations.
Although the Neher and Harper circuit requires only a change
of potential of the order of a volt on the grid of the valve, it
nevertheless requires the passage of a considerable charge, since
the capacity to earth of the case of the counter is usually several
centimetres. The multivibrator circuit (Fig. 9-5) is free from this
High Volts Positive
H.T.+ Anodes
and Screen-Grids
H.T.
R c -^z* RA C large = 0* I itF minimum
Fig. 9-5. Multivibrator external extinguishing circuit.
limitation, since a change of potential on the wire of the counter
of less than a tenth of a volt causes the potential to be removed
from the counter in a time which may be less than a microsecond.
If only a single avalanche could produce sufficient potential
drop to operate the recording circuit, the discharge time would
be a minimum. This condition may be approached in two ways.
If the processes responsible for the maintenance of the discharge
can be suppressed, a sufficiently large avalanche may be produced
with a very small chance of originating another and so building
up the discharge. The change of potential produced by such an
avalanche will be very small, but if such avalanches of 10,000
ii2 ELECTRICAL COUNTING
electrons can be produced it should certainly be possible to
record them. The main difficulty in this line of approach is that
the potential required on the counter is very critical.
The second line of approach is to employ an externally ex-
tinguishing circuit which operates on a single avalanche, to which
the only restriction of size is that the potential on the counter
shall not be so large that spontaneous discharges occur. The
externally extinguishing circuit must operate in such a short time,
and for such a time, that any subsequent avalanche originated
by the first is so small that it would not contribute to the main-
tenance of a discharge.
Certain practical considerations should be noted. First, if
advantage is to be taken of discharge times of the order of a
microsecond the high-gain amplifier required must be designed
to operate up to frequencies of the order of a megacycle. Such
resistance-capacity coupled amplifiers are now technically pos-
sible and are employed in television systems. Secondly, it would
be necessary to employ complete electromagnetic screening of
the Geiger-Miiller counter, such as is necessary for ionization
chambers operating with linear amplifiers. Thirdly, the insulation
of the Geiger-Miiller counter would require the same considera-
tion as that for ionization chambers.
It is not therefore suggested that the operation of Geiger
counters in this simpler manner is any easier than the usual
operation where discharge times of io~ 4 sec. can be permitted,
and screening and insulation difficulties are at a minimum.
It may be noted that the single avalanche is confined to a certain
small region of the counter volume. The remainder of the counter
will remain sensitive even while an avalanche is taking place. So,
if the first method, of working without any externally extinguishing
circuit, is adopted, the resolving time may be less even than the
duration of a single avalanche.
Operated in these ways the Geiger counter is not necessarily
less efficient than in the normal condition, for although the
potential applied is less than that for the plateau in the normal
regime, an avalanche must follow every ion pair produced except
those very near the wire. Electrons produced far from the wire
GEIGER-MULLER TUBE COUNTERS 113
may also at high gas pressures be effectively lost by attachment
to form molecular negative ions. The loss of efficiency at the
low- voltage end of the plateau is, however, to be connected with
a failure of the mechanism of growth and maintenance rather
than the absence of avalanches.
The fundamental lower limit to the avalanche size required
should be considered. If the single avalanche is to operate a
valve amplifier, the limit is that imposed by thermal agitation
noise and valve noise in the input stage of the amplifier. This has
been discussed in Chapter m. It is common practice in amplifiers
used for television and for the reproduction of sound from film,
both of which are operated by photoelectric cells, to evade this
thermal agitation and valve noise limit by amplifying directly
the electrons liberated in the photocell either by ionization, by
collision or now more commonly by secondary electron emission.
The latter process is always adopted in television, where only
very short time delays can be allowed. In the normal operation
of the Geiger-Miiller counter the process of ionization by
collision is employed to amplify the discharge, and this introduces
the inevitable time delay. It would seem therefore that if very
short times are required the television technique of amplification
by secondary emission might be employed either directly in the
counter, in which case the best form of the counter would pro-
bably differ from that of the familiar wire along the axis of a
cylindrical tube, or alternatively by registering the initial avalanche
by the radiation which accompanies it with a photocell employing
amplification by secondary emission.
For the successful operation of secondary emission multipliers
with such very small currents it is necessary to ensure that the
thermionic emission from the secondary emitting surfaces is very
small. Z. Bay (5) has reported success with caesium electrodes
cooled in liquid air. Also, for use at ordinary temperatures, he has
found that surfaces coated with barium oxide activated in the
manner of dull emitting cathodes give satisfactory multiplication
by secondary emission with negligible thermionic emission.
W. H. Rann(ss) has also reported similar experiments with larger
primary ionization currents.
Chapter X
STATISTICS OF RANDOM
DISTRIBUTIONS
When the distribution in time of the particles arising from the
decay of a long-lived radioactive substance is examined it is
found to conform statistically with a purely random distribution.
The statistics of such a random distribution are therefore
important for the interpretation of counts of particles.
A purely Random distribution would arise from the condition
that the chance of a particle arriving in a small time dt is Ad/,
where A is a constant provided that Xdt^i. The arrival of a
particle is independent of any other influence, in particular the
chance is not influenced by the previous arrival of another
particle or by the absence of a previous particle.
A definition of the chance of a particle arriving may be given
as follows. If, in a very large number N of equal intervals dt, the
number of particles counted is n, then A is defined as such that
n = N\dt, when n->oo.
Let W n (t) be the chance that n particles and no more arrive in
a time t. The value of W n (t) may be derived by the following
process of mathematical induction due to Batemanu). The
chance that n+i particles arrive in t+dt is the sum of two
chances: (i) that n+ 1 particles arrive in time t, and none in the
extra time dt. This chance is (i - A<ft) W n ^(t)\ (2) that n particles
arrive in time /, and one in the extra time dt. This chance is
\dtW n (t). The chance that two or more particles arrive in the
extra time dt [(A<fc) a -(A<ft) 3 , etc O becomes negligible as dt is
reduced indefinitely. Hence
or
RANDOM DISTRIBUTIONS 115
Proceeding to the limit
Putting n = o, i, 2, . .. in succession, we have
~~df~
These equations may be solved by multiplying each by e** and
integrating. Then since W (o) i , we have in succession
W - er".
Then
or e^dW^dt+Xe^W^ .= A
,
-J- = A.
W l =
Hence W H
n\ " '
The average number of particles which arrive in time t is Xt.
Write Xt x. The chance that n particles arrive in t is W n =^ -7 <?-*.
This relation is known as Poisson's Law, and has been derived
in other ways from the assumption of a random distribution in
different forms (73).
The number of particles N counted in a large time T will in
ii6 ELECTRICAL COUNTING
general not be exactly AT 1 . The mean deviation D, defined as
^/[probable value of (N AT 1 ) 2 ], is given by
= S (N-
A/!
AT.
Hence D = </(Ar).
The numerical calculation of Poisson's Law distributions may
be carried out by observing that W^/W^_ t = jc/w. If the average
number is 10 and the chance of observing 10 is written as />,
60
6
140
14
160 180 200
16 18 20
80 100 120
8 10 12
NUMBER COUNTED (a)
Fig. lo-i. Poisson's Law distributions.
then the chance of observing 9 is also />. The chances of ob-
serving 8, 7, 6, etc. are successively o*9/>, o8 x o-qp = o-yap,
0*7 x o*72/> o*5O4/>, etc. Poisson's Law distributions for
x = 10 and x = 100 are shown in Fig. 10-1.
Loss at high rates of counting.
When particles arrive at random at a mean rate of p per sec.
some will arrive too close together to be counted separately.
RANDOM DISTRIBUTIONS 117
Suppose r per sec. are recorded and the minimum resolving time
of the counter is i/q sec. The counter is then effectively unable to
operate for rfa sec./sec., during which timepr/q particles arrive
and are not recorded. We therefore have
r=p-pr/q, or p(i-r/q) = r, p = r(i-r/q)-*. (10-1)
For example, suppose q = 25, i.e. the counter takes ^ sec. to
record, and suppose 25 particles are counted per minute, i.e.
r = ff, then p = fM 1 ""^)" 1 * or ^ e true rate f arriva ^ f
particles is 17 % greater than the measured rate. If 250 particles
per minute were counted, p = ^f (|), i.e. 300 per min. It seldom
happens with counting meters that the recording time is known or
constant to better than 10 %, so an uncertainty of at least 2 % is
added to this rate of 300 per min. This would in many cases be
unimportant, but sometimes a greater certainty is required.
A counter with a shorter resolving time must then be used.
If an electrical counter with a resolving time of ^^ sec. is
used the loss will amount to 2 % when counting 6000 per min.
It may be pointed out as a general relation that if the resolving
time is i/q second the loss is approximately 1*7 % when counting
q impulses per minute and 2 % when counting 1-29 impulses per
minute.
The above simple considerations do not always apply, for it is
to be noted that if the ionization chamber or discharge counter is
unable to produce two impulses within a time less than i/q sec.
the recording counter introduces no loss at all, and the correction
to obtain the true rate of arrival of particles must be determined
from the characteristics of the ionization chamber and its amplifier.
If, on the other hand, the resolving time of the recording counter
is slightly longer than that of the ionization chamber and its
amplifier, at high rates of counting both resolving times must be
taken into account. Let the resolving time of the ionization cham-
ber and amplifier be i/c sec. Again let r particles per sec. be
counted, the recording counter is then dead for r/q sec./sec.
After each recorded impulse the ionization chamber is dead for
i/c sec.; there is therefore a time rjq-rfc sec./sec. during which
ii8 ELECTRICAL COUNTING
the ionization chamber might produce an impulse which is not
recorded. The occurrence of impulses within this time may
extend the dead time of the ionization chamber beyond the limit
of the dead time of the counter.
A rigid calculation of the loss to be expected is complicated,
but if the simplifying assumption is made that each particle
produces a dead time of i/c sec., as far as the recording counter is
concerned, no matter whether it arrives within i/c sec. after
another or not, an upper limit to the correction may be obtained
as follows. After each recorded impulse the recording counter is
dead for ijq sec., and any particle arriving in the last i/c sec. of this
interval will extend the dead time on the average by i/2 sec.,
assuming the chance of two particles arriving in the interval to
be negligible. Thus we have the number of particles arriving in
r intervals of i/c sec. = />r/c. Each provides an extra dead time
= i/2c sec., therefore the extra dead time = />r/2 2 ; during this
time/> 2 r/2c 2 particles arrive and are missed. The number counted
is thus
r = p -pr[q -p*r/2c 2
Suppose q = 100, c = 200, r = 20 per sec. = 1200 per min. Then
P-r[* -ft* + A)]" 1 = if?' = 'Si* per min.
Without the extra correction p is found as 1500 per min. The
number 1512 is, however, an upper limit because the time added
for two particles arriving in any of the intervals of i/c sec. has
been 2 x i/2c sec., and this is too great; also it is unlikely that the
ionization chamber arrangements will be such that every particle
will produce a dead time i/c sec. whether it produces an impulse
or not.
This example indicates that great care is necessary in estimating
corrections in such complicated circumstances. One of the
commoner pitfalls is to write p' = number of impulses per sec.
from the ionization chamber and then apply equation (ioi)
with/)' substituted for/> to obtain p' from r the number counted.
RANDOM DISTRIBUTIONS 119
This is not admissible because equation (10-1) assumes that the
p particles are at random; the p f impulses from the ionization
chamber are certainly not at random, since no intervals shorter
than i/c sec. can occur.
Caution should be observed in applying any large correction
to a number counted, for many complicating circumstances may
exist. If the rate of arrival of particles is very great the recording
counter may cease to operate at all, it may record steadily at as
fast a rate as possible, or it may record steadily as fast as possible
up to a limit at which the ionization chamber and amplifier fail
to produce large enough impulses. For such and higher rates
few or no impulses are recorded. Each of these conditions requires
a different correction when counting at high speeds.
A complicated correction is sometimes necessary with a scale-
of-two counter. If the counting meter operates for every eighth
impulse and cannot operate twice in less than i/m sec. there is a
chance of loss if nine impulses occur within ijm sec. This occurs
when 8 particles follow a certain particle which trips the counting
meter ( of all the particles are in this category) within i/m sec.
Since 8 particles are lost each time this occurs the fraction lost
will be 8 x of the chance that 8 particles or more arrive in a
given interval of i/m sec., viz.
yfer* x w e~ x
___ ____ ...,
where x = p/m and p is the mean number of particles arriving
per sec. If, however, any of these 8, 9, 10, ... particles arrive
within i/q sec. after another it will not be recorded by the first
stage and will not therefore introduce loss by the counting meter.
This chance is n^mfq, where n = 8, 9, 10, . . .. The nett loss by the
counting meter is therefore
ioom\ t
~rt '
This must be added to the loss introduced by the resolving time
of the first stage of the counter. In normal practice the loss by
the other stages of the counter is negligible. A table is reproduced
I2O
ELECTRICAL COUNTING
below giving some illustrative figures for the special case where
the resolving time of the first stage is j^ sec. and the resolving
time of the counting meter is ^ sec.
Mean rate
no./min.
Loss by
first pair
%
Loss by
meter
%
Nett loss
%
1500
o-5
7 x io~*
*5
3000
I'O
0-07
1*1
4500
i'5
075
2'3
6000
2*O
3'2
5'2
7500
2'5
8-0
10-5
It should be pointed out that the above calculation is only
approximate, and applies only when the losses are so small that
in the correction terms it is unnecessary to distinguish between
/>, the mean rate of arrival of particles, and r, the mean rate of
impulses passed by the first pair.
Chapter XI
COINCIDENCE COUNTING
Coincidence counting has already been mentioned in the dis-
cussion of Geiger-Miiller counters in Chapter ix. The very
simple and highly satisfactory mixing circuit which is commonly
employed has also been discussed in Chapter vn dealing with
non-linear properties of valve circuits. The simplest coincidence
counting system consists of two internally extinguished or resist-
ance-extinguished Geiger-Muller counters feeding direct into
such a mixing circuit. For certain purposes a greater refinement
is necessary and the whole technique must be discussed in greater
detail
A swift ionizing particle such as might produce discharges in
two counters would have a velocity of at least about io 9 cm./sec.
If the counters are less than a metre apart the ionization will be
produced in both within io~ 7 sec. of each other. Such a small
time interval may generally be neglected. It so happens, however,
that the initiation of the discharge in a Geiger-Muller counter,
or the separation of the ions in an ionization chamber, occupies
a finite time, and it is found that we must allow impulses to be
regarded as coincident if they are timed within an interval which,
according to circumstances, amounts usually to one or a few
microseconds.
Suppose the duration of a discharge is lo^ 4 sec., then the two
impulses might appear as in Fig. n-i, in which the time scale
is very large. Such impulses must be counted as coincident, but
if two impulses produced by independent ionizing particles
occur as close together as shown in Fig. 1 1*2, they should not be
recorded as coincident.
It is quite practicable to make a coincidence-counting system
capable of distinguishing between these. It would not be practic-
able to do this with the simple mixing circuit already described.
122
ELECTRICAL COUNTING
If the size of the impulse on each grid were carefully regulated it
might be arranged that the valve was only rendered non-con-
ducting by an impulse exceeding say V b (Figs, ii-i, 11-2), but it
20 40 60 80"
Fig. 1 1 i . Coincident impulses.
Fig. 1 1 2, Close impulses.
will be seen from Fig. 11-2 that V b would have to be very close
to the peak of the impulse if the two impulses are not to exceed
V b coincidently.
The usual method of solving the problem is therefore to differ-
entiate the impulse with respect to time. This may be done by a
simple resistance-capacity filter (Fig. 1 1 -3) in which the time con-
HI-
INPUT
from
Low Impedance
OUTPUT
to
Very High Impedance
Fig. 11-3. Simple resistance-capacity filter.
stant CR is made short compared with the required resolving time.
After passing through such a filter the impulses of Fig. 1 1 -2 would
appear as in Fig. 11-4, the ordinates in which are proportional to
COINCIDENCE COUNTING
123
the slope of the curve of Fig. 11-2 averaged over a time of about
a microsecond. These impulses may with advantage again be
differentiated, producing impulses such as are shown in Fig. 11-5.
Fig. 11-4. Impulses of Fig. xi*a after differentiation.
60 80
Fig. 11*5. Impulses of Fig. 11-4 after differentiation.
p, sec.
Each process of differentiation reduces the size of the impulse,
so that it is usually necessary to amplify after each differentiation.
The impulses shown in Fig. 11-5 may be directly applied to the
mixing circuit. In practice, however, these twice differentiated
impulses are liable to vary considerably in size, so they may with
advantage be passed through a simple discriminator stage
(Chapter vn) to even up the impulses and discriminate against
the subsidiary peak which occurs 80 /4-sec. after the initiation of
the discharge (Fig. 11-5). It would even be possible to arrange
a discriminator to pass on a very short pulse just at the moment
when the impulse of Fig. 11-5 reaches its maximum, but this has
probably never been found necessary.
It should be remembered that, if the resolving time is of the
order of io~ 6 sec., the amplifier must amplify at frequencies from
io 4 or less to over io 8 c./sec.; the amplifier should therefore be
regarded as a radio-frequency wide-band amplifier in which the
layout of the wiring is as important as the circuit diagram.
124 ELECTRICAL COUNTING
The argument advanced in discussing the linear amplification
of ionization impulses that only one quick coupling-stage, and
that of not too short a time constant, may be used does not apply
in the present considerations as it is not required that the voltage
of the final impulse shall be proportional to that of the input
impulse. In fact, by these processes of successive differentiation,
the magnitude of the final impulse is proportional to the maximum
values of dV/dt, d 2 V/dt 2 , dWjdf, etc., where V is a function of
time representing the voltage of the initial impulse. The reduction
of the resolving time for coincidences depends on the fact that
these higher differential coefficients have their maxima very close
to the moment of initiation of the discharge.
With this knowledge of what is technically possible considera-
tion may be given to the conditions which it is likely to be neces-
sary to satisfy in the coincidence counting of yff-rays and y-rays.
Probably the chief reason for adopting coincidence counting
is to reduce the ratio of the natural effect to the effect under
observation. When a Geiger-Miiller counter with thin walls is
unshielded it will give about 2 impulses per minute per cm. 2 of
its maximum projected area. This is due to cosmic rays and
ordinary radioactive contamination. By surrounding the counter
with a thickness of 3 or 4 cm. of lead on all sides, the lead being
free from radioactive contamination, this number of impulses
will be reduced to about 0*5 per cm. 2 per min. With an average
counter 10 cm. long by 2 cm. diameter, this amounts to about 10
impulses per minute.
The efficiency of a Geiger-Miiller counter for recording /?-rays
is approximately unity, so that if a /ff-ray traverses two counters
the probability of coincident discharges is very high. The number
of coincidences would therefore be only slightly less than the
number of single counts. The yff-rays must, however, be limited to
directions which traverse both counters. The ionization produced
by cosmic rays is largely due to single tracks having an ionization
density equal to or greater than that of /#-ray tracks, but a majority
of these have their directions making an angle of less than 45
with the vertical. By placing two counters with their axes parallel
COINCIDENCE COUNTING 125
and horizontal just so far apart that only rays making angles of
less than 30 with the horizontal can traverse both counters the
number of coincident discharges due to cosmic rays will be about
one in 4 min., with the average size of counter, 8 cm. long x 2 cm.
diam.
In addition to this " natural" count of true coincidences, other
coincidences will occur due to two independent discharges
happening by chance within the time interval set as the limit of
resolution. This time interval may be reduced to a few micro-
seconds, but nevertheless, if the rate of discharges in the individual
counters is high, these chance coincidences may outnumber the
coincidences which are being studied. It would be impossible to
give a general discussion covering all cases and the experimenter
must be left responsible for investigating all sources of coinci-
dences effective in each experiment.
One paradoxical effect may however be noted. If other things
remain constant a reduction of the duration of the pulse in a
counter is liable to lead to an increase in the number of chance
coincidences. The number of chance coincidences N c per sec.
for a resolving time interval for coincidences of T sec. is zr^N^
where N v N% are the numbers of discharges per second in the
two counters. The factor 2 arises because the discharge in the
second counter may be either before or after that in the first by
an interval up to r sec. If the duration of the pulses is reduced
N! and N 2 will be increased for a given source of ionization (see
Chapter x).
The formula JV C = 2r/V 1 7V 2 is almost self-evident if the A^ and
N 2 discharges occupy a negligible fraction of the total counting
time, but the formula is not valid if this is not the case.
Chapter XII
ENERGY DETERMINATIONS FROM
RANGE MEASUREMENTS
The theory of the loss of energy of charged particles by the
ionization processes has now been brought into fairly satisfactory
agreement with the experimental observations (7,9, 19). The theory
for heavy particles may be summed up in the proportionality
where T, Z and v are the kinetic energy, charge number and
velocity of the projectile. N is the number of atoms per unit
volume. f(v*IE) is a numerical function of v 2 /E, where E approxi-
mately represents the energy loss per ion pair produced. Thus for
different particles having the same velocity the specific ionization
is proportional to Z 2 . For heavy particles for which T=^ \Mv*
(where M = mass of the projectile) having a given velocity v it
follows that the total range R is proportional to M/Z 2 .
It is thus seen that the form of the specific ionization-range
curves, such as are shown in Fig. i-i for different particles, are
of approximately the same shape but with the scale of ranges
proportional to M/Z 2 and the ionization scale proportional to Z 2 .
There is, however, a process which disturbs this simple
relation. When the particle is travelling relatively slowly it is
liable to capture an electron or even two if it is doubly charged;
it then travels for a space with a reduced effective charge before
again losing the captured electron. This phenomenon of capture
and loss was studied for a-particles first by G. H. Henderson (30)
and then in greater detail by Rutherford (&>>; a full summary of
these and later investigations is given in Radiations from Radio-
active Substances (**). The number of interchanges of charge
along the track was found to be very great, amounting to more
than a thousand. Except near the end of the range the mean free
EN ERG Y DE TERM IN A TIONS 127
path for loss is much smaller than the mean free path for capture,
so the particle carries a single charge for a relatively short part of
its range, but in the last 4 mm. of its range in standard air the
particle is more often singly charged than doubly. It was found
that the equilibrium ratio between singly and doubly charged
particles, which is a measure of the ratio of the mean free path for
loss to the mean free path for capture, for particles of a given
velocity was almost independent of the atomic weight of the
absorbing substance, the only marked departure being for high
velocities in hydrogen.
It must be pointed out that considerable uncertainty exists
about the form of the relation connecting the specific ionization
and the range for particles of low energy both theoretically and
experimentally (78). The related function connecting the rate of
energy loss and the range is similarly uncertain, and also the range
integral of this, which is the energy-range relation. Since it is
convenient to make measurements of ranges in order to deter-
mine energies, the uncertainty about the range-energy relation
for very short ranges is unfortunate. Means were, however,
devised by which energies might be determined from range
measurements in such a way that this uncertainty is immaterial.
While it is easy to measure the range of a homogeneous group of
a-particles approximately, precise measurements are very diffi-
cult and the probable error of the best determinations is 0-2 mm.
of standard air or more. On the other hand, the differences
between the mean ranges of a number of homogeneous a-particle
groups from radioactive substances have been measured with a
probable error of 0-03 mm., which represents an accuracy of
about 2000 e.V. in the corresponding energy. It has therefore
been necessary to fix a conventional scale of ranges to which
measurements may be referred. This convention also requires
an exact definition of the conditions of measurement.
To emphasize the distinction between this conventional scale
of ranges and the absolute scale it should be pointed out that the
energies of a-particle groups may be deduced from measurements
made on the conventional scale to about 2000 e.V. between about
128 ELECTRICAL COUNTING
5 and 10 Mle.V. Measurements attempted on the absolute scale
at present diverge by as much as i mm. of standard air or
100,000 e.V.
The techniques of measuring a-particle ranges and energies
depend on the fact that radioactive substances can be deposited
on surfaces in such a way that few of the emergent a-particles
lose any appreciable energy before escaping from the surface.
The energies of the a-particle groups from such sources have
been determined with great accuracy.
a
3
12
+a
.,1
0-8
0*4
0-2
:
Fig. 1 2- 1
The standard absolute energy determination has been made
by Briggs(i4), who measured by the method of magnetic deflexion
the energy of the group of a-particles from radium C'. The
absolute energy of a-particles in this group was found to be
y68o2Xio 6 e.V., with a probable error of only 7 in io 5 , i.e.
540 e.V.
This is actually determined from the measured Hp (p = radius
of curvature of path in magnetic field H) of the particle and the
value of EjM for the a-particle which is determined from the
Faraday and the ratio of M for the a-particle to the chemical unit
atomic mass. The measurement of H and the Faraday involves
EN ERG Y DETERMINA TIONS 129
the relation between the absolute and international electrical
units. There is at present a discrepancy of 8 or 9 in io 5 between
the determinations of this ratio at the different standardizing
laboratories. This accounts for part of the probable error in the
energy of the a-particle.
The relative velocities of the a-particles from a number of
radioactive substances have been determined with varying
accuracy from i in io 5 = 70 e.V. to i in io 3 = 7000 e.V. by
Briggsda), Rosenblum(s8), and Rutherford, Wynn- Williams,
Lewis and Bowden (39,64).
The definitions of ranges on the conventional and absolute
scales should therefore be made with sufficient precision to allow
the determination of energies to about 1000 e.V., should it 'be
possible to measure the ranges with the necessary accuracy.
The absolute range of a single particle is taken as the distance
travelled measured along the track from the source to the last
ion produced. The range of a particle of a given initial energy is
subject to a variation due to the statistical nature of the ionization
process. The average or mean range of a large 'number of particles
initially all of the same energy will however preserve a precise
meaning. The fact that the variation of the individual ranges or
straggling has a definite form enables other ranges to be exactly
defined. Two such other ranges have been extensively used, these
may be distinguished as the extrapolated ionization range and
the extrapolated numbers range.
The distribution of ranges has the symmetrical Gaussian form
Fig. 12' i (a). This maybe deduced from the well-known argument
that if after any given energy loss the distribution of distances
travelled is Gaussian, then since the probable distance of travel
depends only on the energy of the particle this Gaussian form will
be conserved. If then after a large number of collisions the in-
homogeneity is still small compared with the spread finally
produced, so that a negligible error would be introduced by
assuming the distribution at this stage to have the Gaussian form,
then the final distribution will conform very closely to the Gaussian
form, which may be represented by N R + r = JV^e"" 1 * 7 **; N R+r is
130 ELECTRICAL COUNTING
the number of particles with a range R+ r, and R is the mean or
average range. The quantity a will be referred to as the straggling
parameter, following Livingston and Betheto); it is the same as
p$x introduced by Briggsdi) and the quantity p used by Ruther-
ford, Ward and Wynn- Williams <6 3 ) and later writers in this group
and called somewhat loosely the straggling "coefficient". The
straggling parameter is usually expressed in millimetres of air.
If the a-particle ranges have this Gaussian distribution, then by
plotting the number of particles passing beyond a given range
against the range a curve of the form of Fig. 12-1 (b) is obtained.
The intersection of the tangent at the point of inflexion of this
curve with the axis of zero number is the extrapolated numbers
range. It is easy to calculate that this range exceeds the mean
i \l n
range by a - y ~~ .
In the early work on a-particle ranges, extrapolated ranges
having a different meaning were measured. This extrapolated
range should be distinguished as the extrapolated ionization range
and is obtained not by counting the a-particles but by measuring
the ionization produced in a short distance by a pencil of the rays.
This ionization plotted against the range is the well-known Bragg
ionization curve. If the tangent at the point of inflexion is ex-
tended to cut the scale of ranges, the range indicated is the
extrapolated ionization range. In practice it is usual to draw this
tangent on the assumption which is approximately correct that
the straight portion of this curve is long; this makes the range
slightly longer.
For the purpose of measuring ranges standard air is taken
to be dry air at I5C. and 760 mm. pressure measured under
standard barometric conditions, in which the mercury column
is reduced to the equivalent height at oC. at sea level at 45
latitude. The magnitude this correction is likely to assume does
not appear always to have been appreciated. If the mercury
column of the barometer is at a temperature of isC., the
equivalent height at oC. will be 0-25 % less, corresponding to
a correction in a range of 10 cm. of 0-25 mm. or 15,000 e.V. The
ENERGY DETERMINATIONS 131
height and latitude correction in Cambridge amounts to only
0-066 %, but may be much larger in other laboratories.
The approximate range in any medium other than air may be
obtained by dividing the range in standard air by an appropriate
factor termed the relative stopping power of the substance. ^For
example, an average value for the stopping power of water vapour
relative to that of air at the same temperature and pressure may
be taken as 0-74. Typical laboratory air in England may be taken
to have a humidity of 75 % at i6C. The corresponding water-
vapour pressure is i-o cm. Very considerable departures from
this, however, are likely to be encountered. For this example
the correction to dry air would be about 0-34 % or 20,000 e, V.
for 10 cm.
Stopping screens.
It is common practice to use uniform thin sheets of mica to
reduce the range of particles, and the distance by which the range
is thus reduced is then the "stopping power" of the mica sheet,
Caution is necessary in applying this conception of stopping
power, for accurate measurements show that it depends on the
initial velocity of the a-particle, and this variation is very great
if the atomic Weight of the substance is very different from that
of air. The general results obtained by GurneyCaS) and by
Marsden and Richardson (45) are shown in Fig. I2'2.
A mica sheet used in range measurements should be placed
so that the emergent range of the a-particles is the same as used
in the calibration of the sheet.
It is convenient in the laboratory to calculate the stopping
power of a mica sheet from its mass per cm. 2 or from its thickness.
Recent experiments by Bennett (6> have shown that this procedure
should not be relied on to an accuracy better than 2 or 3 %, even
for pieces of mica from the same batch. If, however, the mica is
thin, say of less than a centimetre stopping power, such un-
certainty is often negligible. It is by no means easy accurately to
measure the stopping power of a mica sheet. For mica known
as Green Madras the stopping power of a sheet weighing
9-2
132
ELECTRICAL COUNTING
i *43 mg./cm, 2 is i cm. of standard air with a probable uncertainty
of i %, and this applies only for a-particles having a residual range
after leaving the mica between 3-5 and 10 cm.
When mica is split for this work it should be very carefully
examined in reflected monochromatic light to ensure that the
0-2
Range 8
Ocm.
thickness is uniform. Non-uniformity shows up as a break in
the intensity of the reflected light caused by the change in the
interference between the light reflected at the two surfaces. These
changes of thickness may be very slight, amounting perhaps to
only -fa of a wave-length, so very careful examination from all
angles is called for.
ENERGY DETERMINATIONS 133
An optical lever device for measuring the thickness of mica
sheets is found very useful.
When protons are being observed mica-stopping screens are
generally to be avoided, because mica contains hydrogen which
may be projected as fast protons by other protons, a-particles,
neutrons or other heavy particles. Such protons knocked on by
a-particles may have a range four times that of the a-particles,
but are distinguished from the a-particles by their lower specific
ionization. The number of protons varies greatly with the angle
at which they are knocked on, but as a rough order of magnitude
if one proton for io 4 a-particles would be undesirable, an
estimate of the number should be made though it may be found
that there are 100 times fewer. The relevant information may be
found in Radiations from Radioactive Substances, pp. 2$2ctseq. (6O.
Where knocked-on protons are undesirable thin sheets of alu-
minium may be used as stopping screens; the uniformity of such
screens is, however, difficult to test.
Finally, in the measurement of ranges well defined and care-
fully planned geometrical conditions are essential.
The use of mica or aluminium absorbing screens enables the
ionization chamber to be brought much closer to the source.
Thus the ionization chamber subtends a greater solid angle at
the source and more particles are received. Some of the tracks
of these particles will consequently make an appreciable angle (0)
with the principal direction, and their range will be sec# times
their apparent range. This "secant effect may be considerable
if the range is long. For example, sec 10 = 1-015, making a change
of 8 mm. in a 50 cm. range which is not uncommon for protons.
Absolute measurements of range may be attempted directly
in the Wilson expansion chamber. In practice it has 'proved
difficult to measure ranges with great accuracy by this method ;
there is always the uncertainty of the exact composition, density
and temperature of the gas and vapour mixture. Then, owing to
the phenomenon of straggling it is necessary to measure some
thousands of tracks to eliminate error from the statistical varia-
tions of the mean range.
134 ELECTRICAL COUNTING
The old method of measuring the extrapolated ionization
ranges gives consistent results more readily, but the exact
interpretation of the results depends on the form of the specific
ionization-range relation for a single particle near the end of its
range.
In the counting method particles giving more than a certain
ionization beyond a certain range from the source are counted.
This method enables differences of mean ranges or extrapolated
number ranges to be determined with accuracy, but again the
uncertainty of the specific ionization-range relation near the end
of the range prevents the deduction of the exact absolute range.
The conventional range scale.
On the conventional scale of ranges, the mean range of the
a-particles from thorium C' is taken to be 8-533 cm - in standard
air, and other ranges are to be measured by differences from this
in standard air.*
It is of interest to consider how this conventional scale was
fixed. The only method which gives the absolute range indepen-
dent of the form of the specific ionization-range relation near the
end of the range is that of direct measurement in the Wilson
expansion chamber. The conventional range scale should there-
fore be made to agree as closely as possible with what would be
determined by expansion-chamber measurements. There are,
however, not many accurate range determinations made in
expansion chambers available. Measurements of extrapolated
ionization ranges may be related to expansion-chamber ranges
most directly by using an ionization-range relation determined
in expansion-chamber measurements.
Combining the ionization-range relation determined by
Feather and Nimmouz) from expansion-chamber measurements
with the appropriate straggling coefficients determined from
counting measurements, it is possible by numerical calculation
to find the difference between the extrapolated ionization range
Holloway and Livingston (32) have recently proposed a conventional scale
making the thorium C' range 8-570 cm.
ENERGY DETERMINATIONS 135
and the mean range. This was found to be o*8a 0-06 mm. for
ranges of a-particles between 3 and 12 cm., where a is the
straggling parameter in mm. It should be understood that this
value may have little absolute significance, but it is only required
in order to relate range measurements made in the expansion
chamber to determinations of extrapolated ionization ranges. The
mean range is the average range to the last drop condensed on the
track in an expansion chamber. Other determinations of the
ionization-range relation at short ranges have been reported made
by electrical measurements (32, 35, 65, 70 .76). These results differ
considerably, but they have no importance in this connexion as
they necessarily lack any point which can be identified as the
point at which the last drop is formed in an expansion chamber.
The best expansion-chamber measurements of mean ranges,
and the mean ranges derived from measurements of the extra-
polated ionization ranges by the relation mentioned above, were
then compared with the differences between the mean ranges
found by the counting method. Combining the data in this way
it appeared that the expansion-chamber value of the mean range
of the thorium C' particles was best given as 8*533 cm, (40,62).
The absolute accuracy of this figure is of no importance for the
experhnental determination of energies from ranges measured
on the conventional scale.
The standard determinations of the relative velocities of radio-
active a-particle groups fix the a-particle conventional range-
energy relation down to the range of polonium 3*805 cm.
(5-30 x io 6 e.V.). This has been extended to lower energies mainly
by the experiments of Mano(44). Theoretical extrapolations have
also been made by Duncansondg) and by Bethete). The relation
must, however, be considered rather less certain in this low-energy
region than in the range covered by the standard a-particle groups.
The most accurate measurements of ranges by the counting
method have been made with a differential chamber, which,
as explained in Chapter n, enables counts to be made only of
particles stopping in the chamber within narrow limits of range
which may be as little as 2 mm. This narrow band is referred to as
136 ELECTRICAL COUNTING
the effective slit width. The variation of the form of the number-
range curve as this effective slit width is altered is illustrated in
Fig. 12-3 for a homogeneous group of a-particles.
A common defect of radioactive sources is that they are dirty,
that is to say there is some foreign matter covering the radioactive
material. Some particles therefore leave the surface with a
reduced velocity due to their passage through this layer of matter.
The result of this is that the tail on the short-range side of a group
SLIT WIOTH
- 5-4oc-3-2ci-
DISTANCE OP CENTRC Of SLIT FROM Me AN RANQC
Fig. 12- 3
is increased. Allowance must be made for this in fitting a curve
of the correct shape for a clean source to the experimental points.
If the dirtiness is considerable it is difficult to know how to fit
the curve, and in such cases it is found that the apparent extra-
polated numbers range is much less reduced than the apparent
mean range.
When the a-particles originate from a process of artificial
transmutation it often happens that they are liberated at a con-
siderable depth below the surface. If we suppose that the
particles are liberated uniformly throughout the material of the
ENERG Y DETERMINA TIONS 137
target the resulting numbers-range curve (counting all particles
exceeding the range) is as shown in Fig. 12-4. It might be sup-
posed that extrapolation of the straight portion of this curve would
-3
-2
+1
Mean Range
Range in units of straggling parameter
Fig. 12-4
lead to the extrapolated numbers range, but that this is not the
case is evident from the other curve in Fig. 12-4, which shows the
form of the numbers-range curve obtained from a thin target.
No confusion between these two curves should arise for the
138 ELECTRICAL COUNTING
straggling parameter, for a given range is a definite quantity and
this accounts for the whole breadth of the sloping portion of the
thin-target curve. If the sloping portion is seen to extend over
a greater range than this, either the target must be thick or the
emitted particles are not homogeneous in velocity. This is of
course to be expected in artificial transmutations if particles
emerging at different angles with the incident beam are included
in the observations. Interpretation is only difficult if both the
target is thick and the particles are emitted with a continuous
distribution of velocities of unknown form. It should be noted
that a source is effectively thick if its thickness is comparable with
the straggling parameter of the particles under observation. For
this purpose the straggling parameter may be estimated as &
little greater than i % of the range for a-particles and 2 % for
protons. It proves in practice difficult to be certain that the exact
thickness of a source is known. The roughness of the surface
must be taken into account. The chance of scattering in the source
itself is also sometimes to be considered.
When a-ray tracks are observed in a Wilson expansion chamber
it is found that the ends of individual tracks are very often bent;
the range measured along the track is therefore not quite the
same as the range measured as the maximum distance from the
source reached by the particle. This effect is unimportant in the
ordinary methods of measuring a-particle ranges where the
range is judged from the ionization in the last few millimetres of
the track, but would have to be taken into account if some type
of discharge counter sensitive to a few ions were used to deter-
mine the limits of tracks. The effect should be. small, and while it
has been commented on by one or two authors no quantitative
information appears to have been published.
No conventional scale has been set up for particles other than
a-particles, measurements of proton ranges are made assuming
some ionization-range relation. An error as large as i mm. in a
proton range amounts to only 5500 e.V. for an 80 cm. range,
9000 e.V. for a 30 cm. range, 15,000 e.V. for a 10 cm. range,
30,000 e.V. for a 2 cm. range. The form of the ionization-range
ENERG Y DETERMINA TIONS 139
relation (Fig. i-i) is fairly certain up to within i mm. from the
end of the range Owa), errors should therefore be only of minor
importance. Geometrical considerations and the composition of
the stopping medium are of much greater importance in deter-
mining the longer proton ranges. There is still some uncertainty
about the range-energy relation for protons, as measurements of
path curvature in a magnetic field combined with range measure-
ments are wanting; the actual range-energy relation at present
adopted is a theoretical extrapolation, the constants in the
formula being derived from the experimental a-particle range-
energy relation. The extrapolation is probably accurate, but the
validity of the assumed constants appears less certain.
APPENDIX
It may be useful to give an example of the corrections applied to
experimental measurements of an a-particle range to deduce the
range on the conventional scale and hence the energy of the
particles. This will serve to illustrate the order of magnitude of
the several corrections.
Distance of ionization chamber from source corre-
sponding to extrapolated numbers range ... 4-00 cm.
Penetration of particles into the chamber for this
setting (determined in a separate experiment
with a standard source) 0-30 cm.
Stopping power of mica screen (calibrated for
emergent a-particle range of i*ocm.) ... 2-00 cm.
Correction for actual thickness of mica displacing
air o*ooicm.
Correction to stopping power of mica screen for
emergent range of 6 mm. Not known accu-
rately but probably not less than o-oi cm.
Room temperature 20 C. Barometer reading
750 mm.
Correction of 3 -02 % to air distance, viz. 4-0 cm. 0-121 cm.
(For the highest accuracy it is necessary to consider
the effect of atmospheric density on the chamber
characteristic, but usually it is sufficiently accurate
to neglect the penetration distance.)
Correction of mercury column to o C. (2*44 mm.
Hg) ~o-oi4cm.
Correction to sea level at latitude 45 (0*5 mm.). . . -f 0:003 cm.
Correction for 70 % htimidity at 20 C 0-017 cm.
Secant effect correction on 6-30 cm -f 0-025 cm *
Corrected extrapolated numbers range ... 6- 1 65 cm.
APPENDIX
Straggling parameter a 2 for air 6-3 cm. 0-922
of for mica 2*0 cm. 0*145
- of for air 2*0 cm. 0-117
Zot*
141
0-950
a = 0-974 mm.
Correction for mean range
o-886a
-0-086 cm.
Mean range on conventional scale 6-079 cm -
Having arrived at this final corrected mean range the corre-
sponding energy is obtained from the range-energy curve (32, 42)
if this can be read with sufficient accuracy. If not reference must
be made to the range velocity data (40). A convenient difference
curve may be constructed from these data (61,64).
To obtain the energy released in the disintegration allowance
must be made for the energy of recoil of the residual nucleus, and
if it is an artificial transmutation an appropriate correction for
the energy of the bombarding particle.
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