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THE BELL SYSTEM

TECHNICAL JOURNAL

A JOURNAL DEVOTED TO THE

SCIENTIFIC AND ENGINEERING

ASPECTS OF ELECTRICAL

COMMUNICATION

EDITORIAL BOARD

F. B. Jewett H. p. Charlesworth W. H. Harrison

A. F. Dixon O. E. Buckley O. B. Blackwell

S. Bracken M. J. Kelly G. Ireland

W. Wilson
R. W. King, Editor J. O. Perrine, Associate Editor

TABLE OF CONTENTS

AND

INDEX

VOLUME XVIII
1939

AMERICAN TELEPHONE AND TELEGRAPH COMPANY

NEW YORK

Bound

Periodirsl

PRINTED IN U. S. A.

J 001959

Ft 9 '^

THE BELL SYSTEM

TECHNICAL JOURNAL

VOLUME XVIII, 1939

Table of Contents
January, 1939

Electrostatic Electron-Optics — Frank Gray 1

Equivalent Modulator Circuits — E. Peterson and L. W. Hussey . . 32
An Improved Three-Channel Carrier Telephone System —

J. T. O'Leary, E. C. Blessing and J. W. Beyer 49
Crossbar Dial Telephone Switching System —

F. J. Scudder and J. N. Reynolds 76
A Twelve-Channel Carrier Telephone System for Open-Wire Lines

—B. W. Kendall and H. A. Affel 119
Recent Developments in the Measurement of Telegraph Trans-
mission— R. B. Shanck, F. A. Cowan and S. I. Cory 143

Contemporary Advances in Physics, XXXII. Particles of the

Cosmic Rays — Karl K. Darrow 190

Hurricane and Flood — September 1938 — W. H. Harrison 218

A Terrain Clearance Indicator —

Lloyd Espenschied and R. C. Newhouse 222
Transcontinental Telephone Lines — /. /. Pilliod 235

April, 1939

Some Ceramic Manufacturing Developments of the Western

Electric Company — A. G. Johnson and L. I. Shaw 255

The Production of Ultra-High-Frequency Oscillations by Means

of Diodes — F. B. Llewellyn and A . E. Bowen 280

A Representation of the Sunspot Cycle — C. N. Anderson 292

The Number of Impedances of an n Terminal Network —

John Rior dan 300
Copper Oxide Modulators in Carrier Telephone Systems —

R. S. Caruthers 315
3

,;•:•: .*'BEbLl SAS'1J^M\ 7UCUNICA

L JOURNAL

Some Applications /if S.l>i^ Type " J " Carrier System — ■

*•.•*•'•''. L. C. Starhird and J. D. Mathis 338

Line Problems in the Development of the Twelve-Channel Open-
Wire Carrier System —

L. M. Ilgenfritz, R. N. Hunter and A. L. Whitman 363

July, 1939

Frequency-Modulation : Theory of the Feedback Receiving Circuit

— John R. Carson 395
The Application of Negative Feedback to Frequency-Modulation

Systems—/. G. Chaffee 404

Survey of Magnetic Materials and Applications in the Telephone

System— F. E. Legg 438

Impedance Properties of Electron Streams — Liss C. Peterson .... 465
Plastic Materials in Telephone Use —

/. R. Towns end and W. J. Clarke 482
The Dielectric Properties of Insulating Materials —

E. J. Murphy and S. 0. Morgan 502

October, 1939

Experience in Applying Carrier Telephone Systems to Toll Cables

— W. B. Bedell, G. B. Ransom and W. A. Stevens 547
The Toronto-Barrie Toll Cable — M. J. Aykroyd and D. G. Geiger . 588
The Computation of the Composite Noise Resulting from Random

Variable Sources — E. Dietze and W. D. Goodale, Jr 605

Load Rating Theory for Multi-Channel Amplifiers —

B. D. Holbrook and J. T. Dixon 624
The Quantum Physics of Solids, I — The Energies of Electrons in

Crystals — W. Shockley 645

Dial Clutch of the Spring Type — C. F. Wiebusch 724

Index to Volume XVIII

Affel, H. A., and B. W. Kendall, A Twelve-Channel Carrier Telephone System for

Open-Wire Lines, page 119.
Altimeter: A Terrain Clearance Indicator, Lloyd Espenschied and R. C. Newhouse,

page 222.
Amplifiers, Multi-Channel, Load Rating Theory for, B. D. Holbrook and J. T. Dixon,

page 624.
Anderson, C. N., A Representation of the Sunspot Cycle, page 292.
Aykroyd, M. J. and D. G. Geiger, The Toronto-Barrie Toll Cable, page 588.

B

Bedell, W. B., G. B. Ransom and W. A. Stevens, Experience in Applying Carrier
Telephone Systems to Toll Cables, page 547.

Beyer, J. W., J. T. O'Leary a?rd E. C. Blessing, An Improved Three-Channel Carrier
Telephone System, page 49.

Blessing, E. C, J. T. O'Leary and J. W. Beyer, An Improved Three-Channel Carrier
Telephone System, page 49.

Bowen, A. E., and F. B. Llewellyn, The Production of Ultra-High-Frequency Oscilla-
tions by Means of Diodes, page 280.

Cable, Toll, The Toronto-Barrie, M. J. Aykroyd and D. G. Geiger, page 588.
Cables, Toll, Experience in Applying Carrier Telephone Systems to, W. B. Bedell,

G. B. Ransom and W. A. Stevens, page 547.
Carrier System, Type "J," Some Applications of the, L. C. Starbird and J. D. Matins,

page 338.
Carrier System, Twelve-Channel Open-Wire, Line Problems in the Development of

the, L. M. Ilgenfrilz, R. N. Hunter and A. L. Whitman, page 363.
Carrier Telephone System, An Improved Three-Channel, /. T. O'Leary, E. C. Blessing

and J. W. Beyer, page 49.
Carrier Telephone System, A Twelve-Channel, for Open- Wire Lines, B. W. Kendall

and H. A. Affel, page 119.
Carrier Telephone Systems, Copper Oxide Modulators in, R. S. Caruthers, page 315.
Carrier Telephone Systems, Experience in Applying to Toll Cables, W. B. Bedell,

G. B. Ransom- and W. A. Stevens, page 547.
Carson, John R., Frequency-Modulation: Theory of the Feedback Receiving Circuit,

page 395.
Caruthers, R. S., Copper Oxide Modulators in Carrier Telephone Systems, page 315.
Ceramic Manufacturing Developments of the Western Electric Company, Some.

A. G. Johnson and L. L Shaw, page 255.
Chaffee, J. G., The Application of Negative Feedback to Frequency-Modulation

Systems, page 404.
Clarke, W. J., and J. R. Townsend, Plastic Materials in Telephone Use, page 482,
Clearance Indicator, A Terrain, Lloyd Espenschied and R. C. Newhouse, page 222.
Clutch, Dial, of the Spring Type, C. F. Wiebusch, page 724.
Contemporary Advances in Physics, XXXII. Particles of the Cosmic Rays, Karl

K. Darrow, page 190.
Copper Oxide Modulators in Carrier Telephone Systems, R. S. Caruthers, page 315.
Cory, S. /., R. B. Shanck and F. A. Cowan, Recent Developments in the Measure-
ment of Telegraph Transmission, page 143.
Cosmic Rays, Particles of the. Contemporary Advances in Physics, XXXII, Karl

K. Darrow, page 190.
Cowan, F. A., R. B. Shanck and S. I. Cory, Recent Developments in the Measurement

of Telegraph Transmission, page 143.

5

BELL SYSTEM TECHNICAL JOURNAL

Crossbar Dial Telephone Switching System, F. J. Scudder and J. N. Reynolds, page 76.
Crystals, The Energies of Electrons in — The Quantum Physics of Solids, I, W.
Shockley, page 645.

D

Darrow, Karl K., Contemporary Advances in Physics, XXXII. Particles of the
Cosmic Rays, page 190.

Dial Clutch of the Spring Type, C. F. Wiebusch, page 724.

Dial Telephone Switching System, Crossbar, F. J. Scudder and J. N. Reynolds,
page 76.

Dielectric Properties of Insulating Materials, The, E. J. Murphy and S. O. Morgan,
page 502.

Dietze, E. and W. D. Goodale, Jr., The Computation of the Composite Noise Re-
sulting from Random Variable Sources, page 605.

Diodes, The Production of Ultra-High-Frequency Oscillations by Means of, F. B.
Llewellyn and A. E. Bowen, page 280.

Dixon, J. T. and B. D. Holbrook, Load Rating Theory for Multi-Channel Amplifiers,
page 624.

E

Electron-Optics, Electrostatic, Frank Gray, page 1.

Electron Streams, Impedance Properties of, Liss C. Peterson, page 465.

Electrons in Crystals, The Energies of — The Quantum Physics of Solids, I, W.

Shockley, page 645.
Espenschied, Lloyd and R. C. Newhouse, A Terrain Clearance Indicator, page 222.

F

Feedback, Negative, The Application of to Frequency-Modulation Systems, J. G.

Chaffee, page 404.
Feedback Receiving Circuit, Theory of the. Frequency-Modulation : John R. Carson,

page 395.
Flood, and Hurricane — September 1938, W. H. Harrison, page 218.
Frequency-Modulation: Theory of the Feedback Receiving Circuit, John R. Carson,

page 395.
Frequency- Modulation Systems, The Application of Negative Feedback to, J. G.

Chaffee, page 404.

G

Geiger, D. G., and M. J. Aykroyd, The Toronto-Barrie Toll Cable, page 588.
Goodale, W. D., Jr., and E. Dietze, The Computation of the Composite Noise Re-
sulting from Random Variable Sources, page 605.
Gray, Frank, Electrostatic Electron-Optics, page 1.

H

Harrison, W. H., Hurricane and Flood — September 1938, page 218.

Holbrook, B. D., and J. T. Dixon, Load Rating Theory for Multi-Channel Amplifiers,

page 645.
Hunter, R. N., L. M. Ilgenfritz and A. L. Whitman, Line Problems in the Development

of the Twelve-Channel Open-Wire Carrier System, page 363.
Hurricane and Flood — September 1938, W. H. Harrison, page 218.
Hussey, L. W. and E. Peterson, Equivalent Modulator Circuits, page 32.

I

Ilgenfritz, L. M., R. N. Hunter and A. L. Whitman, Line Problems in the Develop-
ment of the Twelve-Channel Open-Wire Carrier System, page 363.
Insulating Materials, The Dielectric Properties of, E. J. Murphy and S. O. Morgan,
page 502.

J
Johnson, A. G., and L. I. Shaw, Some Ceramic Manufacturing Developments of the
Western Electric Company, page 255.

6

BELL SYSTEM TECHNICAL JOURNAL

K

Kendall, B. W., and H. A. Affel, A Twelve-Channel Carrier Telephone System for
Open-Wire Lines, page 119.

L

Legg, V. E., Survey of Magnetic Materials and Applications in the Telephone System,
page 438.

Line Problems in the Development of the Twelve-Channel Open-Wire Carrier System,
L. M. Ilgenfritz, R. N. Hunter and A. L. Whitman, page 363.

Lines, Open-Wire, A Twelve-Channel Carrier Telephone System for, B. W. Kendall
and H. A. Affel, page 119.

Lines, Transcontinental Telephone, J. J. Pilliod, page 235.

Llewellyn, F. B., and A. E. Bowen, The Production of Ultra-High-Frequency Oscilla-
tions by Means of Diodes, page 280.

Load Rating Theory for Multi-Channel Amplifiers, B. D. Holbrook and J. T. Dixon,
page 624.

M

Magnetic Materials and Applications in the Telephone System, Survey of, V. E. Legg,

page 438.
Mathis, J. D., and L. C. Starbird, Some Applications of the Type " J " Carrier Systerii,

page 338.
Measurement of Telegraph Transmission, Recent Developments in the, R. B. Shanck,

F. A. Cowan and S. I. Cory, page 143. .
Modulation, Frequency: Theory of the Feedback Receiving Circuit, Joht R. Carson,

page 395.
Modulation Systems, Frequency — The Application of Negative Feedback to, J. G.

Chaffee, page 404.
Modulator Circuits, Equivalent, E. Peterson and L. W. Hussey, page 32.
Modulators, Copper Oxide, in Carrier Telephone Systems, R. S. Caruthers, page 315.
Morgan, S. O., and E. J. Murphy, The Dielectric Properties of Insulating Materials,

page 502.
Moulding: Plastic Materials in Telephone LIse, /. R. Townsend and W. J. Clark,

page 482.
Multi-Channel Amplifiers, Load Rating Theory for, B. D. Holbrook and J. T. Dixon,

page 624.
Murphy, E. J., and S. O. Morgan, The Dielectric Properties of Insulating Materials,

page 502.

N

Network, n Terminal, The Number of Impedances of an, John Riordan, page 300.
Newhouse, R. C, and Lloyd Espenschied, A Terrain Clearance Indicator, page 222.
Noise, the Composite, Resulting from Random Variable Sources, The Computation
of, E. Dietze and W. D. Goodale, Jr., page 605.

O

O'Leary, J. T., E. C. Blessing and J. W. Beyer, An Improved Three-Channel Carrier

Telephone System, page 49.
Open-Wire Carrier System, Twelve-Channel, Line Problems in the Development of

the, L. M. Ilgenfritz, R. N. Hunter and A. L. Whitman, page 363.
Open-Wire Lines, A Twelve-Channel Carrier Telephone System for, B. W. Kendall

and H. A. Affel, page 119.
Optics, Electrostatic Electron — Frank Gray, page 1.
Oscillations, Ultra-High-Frequency, The Production of by Means of Diodes, F. B.

Llewellyn and A. E. Bowen, page 280.

Peterson, E., and L. W. Hussey, Equivalent Modulator Circuits, page 32.
Peterson, Liss C, Impedance Properties of Electron Streams, page 465.
Physics, XXXII, Contemporary Advances in. Particles of the Cosmic Rays, Karl
K. D arrow, page 190.

7

BELL SYSTEM TECHNICAL JOURNAL

Physics, The Quantum, of Solids, I — The Energies of Electrons in Crystals, W.

Shockley, page 645.
Pilliod, J. J., Transcontinental Telephone Lines, page 235.
Plastic Materials in Telephone Use, J. R. Townsend and W. J. Clarke, page 482.

Q

Quantum Physics, The, of Solids, I — The Energies of Electrons in Crystals, W.
Shockley, page 645.

R

Ransom, G. B., W. B. Bedell and IT. A. Stevens, Experience in Applying Carrier

Telephone Systems to Toll Cables, page 547.
Reynolds, J. N., and F. J. Scudder, Crossbar Dial Telephone Switching System,

page 76.
Riordan, John, The Number of Impedances of an n Terminal Network, page 300.

Scudder, F. J., and J. N. Reynolds, Crossbar Dial Telephone Switching System,

page 76.
Shanck, R. B., F. A. Cowan and S. I. Cory, Recent Developments in the Measurement

of Telegraph Transmission, page 143.
Shaw, L. I., and A. G. Johnson, Some Ceramic Manufacturing Developments of the

Western Electric Company, page 255.
Shockley, W., The Quantum Physics of Solids, I — The Energies of Electrons in

Crystals, page 645.
Spring Type, Dial Clutch of the, C. F. Wiehusch, page 724.
Starbird, L. C, and J. D. Mathis, Some Applications of the Type "J " Carrier System,

page 338.
Stevens, W. A., W. B. Bedell and G. B. Ransom, Experience in Applying Carrier

Telephone Systems to Toll Cables, page 547.
Sunspot Cycle, A Representation of the, C. N. Anderson, page 292.
Switching System, Crossbar Dial Telephone, F. J. Scudder and J. N. Reynolds,

page 76.

T

Telegraph Transmission, Recent Developments in the Measurement of, R. B. Shanck,

F. A. Cowan and S. I. Cory, page 143.

Telephone Lines, Transcontinental, /. J. Pilliod, page 235.

Telephone System, An Improved Three-Channel Carrier, J. T. O'Leary, E. C.

Blessing and J. W. Beyer, page 49.
Telephone System for Open-Wire Lines, A Twelve-Channel Carrier, B. W. Kendall

and H. A. Affel, page 119.
Terrain Clearance Indicator, A, Lloyd Espenschied and R. C. Newhouse, page 222.
Toll Cable, The Toronto-Barrie, M. J. Aykroyd and D. G. Geiger, page 588.
Toll Cables, Experience in Applying Carrier Telephone Systems to, W. B. Bedell,

G. B. Ransom and W. A. Stevens, page 547.

Townsend, J. R., and W. J. Clarke, Plastic Materials in Telephone Use, page 482.
Transcontinental Telephone Lines, J. J. Pilliod, page 235.

U

Ultra-High-Frequency Oscillations by Means of Diodes, The Production of, F. B.
Llewellyn and A . E. Bowen, page 280.

W

Whitman, A.L., L. M. Ilgenfritz and R. N. Hunter, Line Problems in the Development

of the Twelve-Channel Open-Wire Carrier System, page 363.
Wiebusch, C. F., Dial Clutch of the Spring Type, page 724.

VOLUME XVm JANUARY, 1939 number 1

THE BELL SYSTEM

TECHNICAL JOURNAL

DEVOTED TO THE SCIENTinC AND ENGINEERING ASPECTS
OF ELECTRICAL COMMUNICATION

Electrostatic Electron-Optics — Frank Gray 1

Equivalent Modulator Circuits — E. Peterson and L, W, Hussey 32

An Improved Three-Channel Carrier Telephone System

—7. T. O'Leary, E, C. Blessing and J, W, Beyer 49

Crossbar Dial Telephone Switching System

— F. J. Scudder and J. N, Reynolds 76

A Twelve-Channel Carrier Telephone System for Open- Wire
Liaes—B,W, Kendall and H. A. Aff el 119

Recent Developments in the Meastirement of Telegraph
Transmission — R, B, Shanck, F, A, Cowan and S, L Cory 143

Contemporary Advances in Physics, XXXII. Particles of the
Cosmic Rays — Karl K, Darrow 190

Hurricane and Flood — September 1938 — W, H, Harrison . . 218

A Terrain Clearance Indicator

— Lloyd Espenschied and R. C. Newhouse 222

Transcontinental Telephone Lines — 7. J. Pilliod 235

Abstracts of Technical Papers 246

Contributors to this Issue 251

AMERICAN TELEPHONE AND, TELEGRAPH COMPANY

NEW YORK

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A. F. Dixon
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EDITORIAL BOARD

H. P. Charlesworth

O. E. Buckley

M. J. KeUy

W. Wilson

W. H. Harrison

O. B. Blackwell

H. S. Osborne

J. O. Perrine, Associate Editor

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American Telephone and Telegraph Company

PRINTED IN U. S. A.

The Bell System Technical Journal

Vol. XVIII January, 1939 No. 1

Electrostatic Electron-Optics

By FRANK GRAY

Certain types of electrostatic fields may be used as lenses to
focus electron beams. The theory of these lenses is developed
for electric fields that are symmetrical about a central axis. The
introduction of two velocity functions exactly reduces the partial
difTerential equations of electron motion to a series of ordinary
differential equations. The first equation describes the action of
a lens for electron paths near the axis; the remaining equations
determine the higher order aberration terms. Sections on the
following subjects are included: the general equations of electron-
optics, thin lenses, thick lenses, aberration, the reduction of aberra-
ration, apertured plates, and concentric tubes. A list of symbols
and lens equations is also included at the end of the article.

TN certain types of modern vacuum tubes, a beam of electrons is
-*■ brought to a focus by an electrostatic field whose action on the
beam is analogous to that of an optical lens on a beam of light. An
electrostatic field which acts in this manner is called an electron lens.
Such lenses are rapidly finding applications in amplifier tubes, tele-
vision and oscillograph tubes, electron microscopes, and various types
of experimental apparatus. As the extent of their application widens,
the theory of these lenses naturally assumes a corresponding
importance.

The first articles on the new science of electron-optics were published
by Bush ^ in 1926-1927, and the next important step in its develop-
ment was taken by Davisson and Calbick ^ and by Briiche and
Johannson ^ working independently in 1931-1932. The following
years marked an increased interest in the subject, with comprehensive
articles by various authors, and its literature expanded rapidly. An

1 H. Bush, Ann. d. Physik, 81, 974, 1926 and Arch. f. Elecktrotech., 18, 583, 1927.
2C. J. Davisson and C. J. Calbick, Phys. Rev., 38, 585, 1931 and Phys. Rev.,
42, 580, 1932.

^ E. Bruche and N. Johannson, Ann. d. Physik, 15, 145, 1932.

1

2 BELL SYSTEM TECHNICAL JOURNAL

excellent review of this literature and the history of electron-optics
are given in a symposium * of papers published in 1936, and the
various practical applications of electron lenses are well described in
the books on that subject.^

E, = 0

___:::::rE2

EQUIVALENT
LENSES

APERTURED PLATE

+ +

TUBES SAME SIZE

EQUIVALENT
LENSES

CONCENTRIC TUBES
Fig. 1 — Lines of force in typical electron lenses.

TUBES DIFFERENT SIZES

^Zeit.f. techn. Physik, 17, 584-645, 1936.

■> E. Briiche and O. Scherzer, Geometrische Eledronenoptik (Springer, 1934).
J. T. MacGregor- Morris and J. A. Henley, "Cathode Ray Oscillography " (Mono-
graphs on Electrical Engineering), 1936. Maloff and Epstein, "Electron Optics in
Television" (McGraw-Hill, 1938).

ELECTROSTATIC ELECTRON-OPTICS 3

The theory of electron-optics is thus well established and any
further attempts at the subject must lead to substantially the same
results. There is, however, a need for a precise development of the
theory in a simpler manner. With this need in mind, the present
article approaches the subject in a manner that appeals to the reader
who is more familiar with electrical theory than he is with the concepts
of geometrical optics, and this approach leads clearly to the various
approximations that are needed in the development of the theory.
With the aid of two velocity functions, the partial differential equations
of electron motion are briefly and exactly reduced to a series of ordinary
differential equations ; the theory is then developed in terms of their
approximate solutions.

Attention is confined to systems in which the electric fields are
symmetrical about a central axis. In such systems any field having
a radial component of electric intensity changes the radial velocity of
an electron passing through it, and thus behaves — to some extent at
least — as an electron lens. A uniform field parallel to the axis and
field-free space are the only regions in which there is no lens action.
Typical electron lenses are shown in the figures on the second page.
As illustrated by these examples, a practical electron lens is character-
ized by a short region in which there is an abrupt change in the electric
intensity parallel to the axis. Lines of force are continuous, and the
field parallel to the axis can change only by lines of force coming
into it, or going out from it, in a radial direction. In the region of
the abrupt change, there are consequently strong radial fields which
can deflect an electron in a radial direction. The region changes the
focus of an electron beam passing through it, and its action is analogous
to that of an optical lens.

Section I — The General Equations

In the present paper it is assumed that the initial electron source
has perfect symmetry of form about the central axis, and that the
electrons have no appreciable velocities of emission from the source.
An electron thus has no angular velocity about the axis, and its motion
may be described in terms of a coordinate z taken along the axis and
a radial coordinate r measured from the axis.

If an electron's velocity vector is projected at any point along its
path, it intersects the axis at some point p, as illustrated in Fig. 2,
and the electron may be regarded as instantaneously moving either
away from, or else toward, this point of intersection. The distance d
along the axis from the electron to the point of intersection is called

4 BELL SYSTEM TECHNICAL JOURNAL

the instantaneous focal distance.^ Defined in this manner, the focal
distance conforms with the optics of light ; it is positive when an
electron is moving toward a focal point ; and is negative when the

Fig. 2 — Focal distance.

electron is moving away from such a point. From the geometry of
the figure, it is seen that

rz

d = -

(1)

where r and i are the instantaneous components of electron velocity.
The focal distance of an electron varies continuously as the electron
moves along. The simplest variation occurs in field-free space, where
the electron travels in a straight line and the focal point remains
stationary; but even then the focal distance varies as the electron
moves; for the focal distance is measured from the moving electron
to the stationary focal point, as illustrated in Fig. 3. In an electron

Fig. 3 — Focal distances, field-free space.

lens, the focal point of an electron also shifts continuously as the
electron moves through the lens and the focal distance varies in a
complicated manner.

The values of d at the two sides ^ of an electron lens, for any elec-
tron path, are called conjugate focal distances of the lens, and are
usually designated as di and d2. The theory of electron-optics is
largely concerned with the derivation of an equation relating these
conjugate focal distances.

* The term is here used in a broad sense to include the distance to any intersection
point on the z-axis, even though the latter is not the point of convergence of an
electron beam.

' The value of d as an electron enters the non-uniform field of the lens, and the
value of d as it leaves the non-uniform field.

ELECTROSTATIC ELECTRON-OPTICS 5

Before passing on to such a derivation, it is well to introduce
another quantity, which is analogous to focal distance and very useful
in making approximations. Suppose that, from any point along its
path, an electron were to continue on with its instantaneous velocity
in a straight line. Its velocity along the axis would continue to have
the instantaneous value i, and the electron would travel over the
distance d and arrive at the focal point in a period of time T given by

T = djz (2)

or from equation 1

T = - r/r. (3)

This period of time is analogous to focal distance, and we therefore
call it focal time. The values of T at the two sides of an electron
lens, for any electron path, are in a corresponding manner called
conjugate focal times of the lens.

To obtain an equation relating the conjugate focal distances of a
lens, we must consider the path of an electron through the lens.
The path is determined by the initial velocity and coordinates of the
electron as it enters the lens and by its acceleration in the electric
field of the lens. By defining electrical units in the proper manner
the ratio e/m is eliminated from the equations of acceleration and they
assume the simple form

where $ is the potential at points in space. ^

The first solution of these equations gives the well known energy
relation

r^ -\- z^ = 2$, (6)

where the electron source is taken as zero potential.

With the exception of special cases, the equations are not further
soluble in the usual sense, and one resorts to solution in series.

As they stand, the two equations for acceleration are inconvenient;
they involve partial derivatives of potential with respect to space and
ordinary derivatives of velocity with respect to time, and the latter
cannot be transformed to partial derivatives with respect to space,
for the simple reason that the velocity of an electron does not exist

^ The final equations of electron-optics involve the potentials only in the form of
ratios which are independent of the electrical units.

6 BELL SYSTEM TECHNICAL JOURNAL

at points off its path. The equations may, however, be reduced to a
more convenient form by the introduction of two velocity functions ^
defined as follows.

Let u and w be any two functions of r and z that satisfy the equations

f^-5^=0, (7)

dz dr

u^ -\-w^ = 2$. (8)

Consider now an imaginary point moving with velocity components

f = u, z = w. (9)

The derivative of f with respect to time is

.. du . , du . du , du ,._.

r=^-r-\- — z=—u-\- — w (10)

dr dz dr dz

and from equations 7 and 8

du , dw d^ /,..

r=— i^+-r-w=— (11)

dr dr dr

the component f thus satisfies differential equation (4) for electron
motion. In a similar manner it may be shown that the velocity
component z satisfies equation (5) . The motion of the imaginary point
is thus the same as the motion of an electron, and the velocity functions
u and w are therefore the velocity components of electron motion.

The velocity functions are solutions of equations 7 and 8, one of
which is a simple algebraic equation and the other a partial differential
equation with respect to space alone. The inconvenient time deriva-
tives have been eliminated in these new equations for electron velocity.

The existence of a velocity function is not confined to a single
electron path ; it exists over the electric field in general. Any pair of
particular solutions for u and w thus corresponds to an infinite number
of possible electron paths. In the converse manner, there are an
infinite number of particular solutions for any electric field, and there
is a pair of particular solutions corresponding to any given electron
path through the field. ^°

^ These functions are the components of the generalized vector function described
in Appendix 4.

1" The existence of such solutions is proved by the existence of the series solutions,
which are derived in the following pages.

ELECTROSTATIC ELECTRON-OPTICS 7

Solutions for the velocity functions are obtained by expressing them
as power series in r.

u = Ar + Br^ + Cr^ -\- ■•-, (12)

w = a -\- br^ -{- cr* -i- " • , (13)

where the coefficients are functions of z alone. The above powers of
r are the ones required in a system symmetrical about the z-axis.
In such a system r reverses in sign with r and the w-series is odd ;
z does not reverse sign with r and the w-series is even. Aside from
such reasoning, the choice of the two series is justified provided they
lead to solutions of the differential equation in a form suitable for
the purposes of electron-optics.

The potential $ obeys the equation

_ a2<i> a2$ 1 a$ _

dz^ dr^ r dr ^ ^

and it may likewise be expressed as a power series in r. This well

known series is

v" v""

^ = ^-Y^r^+-(2^.''--'^ (15)

where v is the potential on the axis of the system, and the primes
indicate differentiation with respect to z.

On substituting the three series in equations 7 and 8 and equating
the coefficients of the various powers of r in each equation we obtain
a series of ordinary differential equations for the coefficients of the
w-series.

^vA' + A' - -~y (16)

^|YvB' + 4AB='^-^
lo 2

(17)

^vC -h6AC= -^-j^- SB' - 3/4A'B', (18)

and the coefficients of the w-series are

a = V2z;,

b = A' 12, (19)

c = B'lA.

8 BELL SYSTEM TECHNICAL JOURNAL

The solution of the partial differential equations for electron velocity
is thus reduced to the solution of a series of ordinary differential
equations, which in themselves contain no approximations.

From equation 1, the inverse focal distance is now obtained by
dividing uhy r and w, which gives

This is the general equation for focal distance as it is affected by
aberration. In using this equation, we are at liberty to set the higher
coefficients equal to zero at the incident side of the lens. This de-
termines the initial value of A in terms of the first conjugate focal
distance. The second conjugate focal distance is then determined by
solving for the coefficients at the exit side of the lens. Due to the
presence of the terms in r, this second focal distance varies slightly
with the radial distance at which an electron passes through the lens,
and the focus is therefore diffused along the axis. This diffusion of
the focus is called aberration.

The coefficient A is of particular importance in the theory of
electron-optics. For paraxial rays, that is, rays near the axis, the
higher terms in the two series are negligibly small compared to their
first terms, and for such rays

With the exception of aberration, the single coefficient A thus de-
termines the complete performance of a lens, and the principal con-
stants of a lens are determined by its differential equation alone.
In lenses where the rays are confined to a region near the axis with
proper diaphragms, the aberration terms are small and the coefficient
A describes the performance of a lens sufficiently well.

The next section is devoted to the derivation of the principal lens
equations from this coefficient. The aberration terms are considered
only in the last section of the paper.

Section II- — Rays Near the Axis

For rays near the axis the optical characteristics of an electric field
are determined by the differential equation for A alone,

^[2vA' + ^' = -y • (16)

ELECTROSTATIC ELECTRON-OPTICS 9

For such rays the higher terms in r may be neglected in the general
equations and we obtain the following useful relations

2v
d

A = r/r = —
z = V2i;,

T = d|^|2i = - ^ '

dt — dz/z = dzl^2v.

(22)
(23)
(24)

(25)

A Uniform Electric Field
A uniform electric field parallel to the axis is not usually regarded
as an electron lens,^^ but it does shift the focal point of a beam of
electrons passing through it. In a uniform field, v" is zero and the
differential equation for A may be written in the form

dA

^2

dz

\2v

(26)

An integration of this equation from any point Si to any other point Z2,
in the uniform field-, gives

J 1_ 2(22 - Si)

^2 Ai V2i;2 + A'2yi'

(27)

where Ai and A 2 are the values of A at Zi and Z2. On substituting
— -^^Id for A in this equation, it may be transformed to

1 +

^1 - 1 +

-')^2 = 2(s2-zi), (28)

V2

which is the equation relating the conjugate focal distances at any
two planes — located at Zi and Z2 — in the uniform field.

The shift in the focal point of an electron beam as it passes through
a uniform field is illustrated in Fig. 4.

-^

^1^

-P2

-^=0—

-d2-

Fig. 4 — Focal distances in a uniform field.

1^ Electron rays parallel to the axis are not bent by the field, and it does not
magnify an electron image.

10 BELL SYSTEM TECHNICAL JOURNAL

Thin Lenses
Approximate solutions of the differential equation 16 for A are
obtained more clearly by first changing the space variables to time
variables. This is done by using relations 24 and 25, which transform
the equation to

or

The new equation tells how the focal time T varies with time as an
electron moves along. ^^

A thin lens is defined as a region of non-uniform field extending
over such a short distance along the axis that an electron traverses
it in a period of time small compared to the focal times involved :
the thickness of the lens is small compared to the conjugate focal
distances. By taking the origin of time t at the middle of an electron's
period of transit through a lens, / in the lens is not greater than half
the period of transit, and / may therefore be neglected in comparison
to r in a thin lens. With this approximation in equation 31, it
reduces to

d /\\ v"

dt\TJ 2 (^^)

In integrating this equation through a lens we choose two points
Zi and Zi at the approximate boundaries of the non-uniform field, that
is, the points where v" substantially drops to zero as illustrated in
Fig. 5. Then, remembering that dt is dz/yJ2v, an integration from Zi

k

z

to Z2 gives

Fig. 5 — Conjugate focal distances, thin lens
11 1

T. T, F' ^^^^

" The period of time that a train requires to reach its terminal point also varies
with time as the train moves along.

ELECTROSTATIC ELECTRON-OPTICS

11

where the inverse focal term is

2 y'

2V2z;

dz

or on integration by parts

^ _ 1

F~ 2

\ V2z;/2

^^v

+

^ r(i'')H2i')-

.72

■'iHz.

(33)

(34)

The substitution in equation 32 of the values for Ti and T2 as given
by equation 24 now gives the lens equation

■yjlvi _ ^J2vi _ 1
~dr ~d7 ~ F'

(35)

This equation is analogous to the equation for a thin optical lens

M2
d2

di ~ f'

(36)

bounded on its two sides by media with different refractive indices
ixi and /X2, the ^2v corresponding to refractive index.

Electron rays parallel to the axis do not come to a focus at a distance
F from an electron lens ; in other words, F is not a principal focal
distance. There are, in general, two principal focal points on opposite
sides of an electron lens. Their principal focal distances /i and fi
are found by setting first dx, and then d^, equal to infinity in equation
35. This gives

fi= - V2^F, h = V2^^ (37)

as the two principal focal distances. It may be shown from equation
33 that these principal focal distances really involve the voltages
only in the form of the ratio i'2/f i- By substituting them in the lens
equation 35, it may be written in the convenient form

-+-= 1,
di d\

(38)

which likewise involves the voltages only in the form of a ratio.

There are two types of electron lenses that deserve special con-
sideration. The first is a small aperture in a thin plate separating
two uniform fields of different intensities — as a special case one of the
fields may be zero. An example of such a lens is illustrated in Fig. 6.

12

BELL SYSTEM TECHNICAL JOURNAL

In this type of lens, the non-uniform field at the aperture covers a
distance along the axis about equal to its diameter. ^^ If the diameter
is small compared to vjv', there is little change in potential throughout

Fig. 6 — An apertured plate.

the lens and the •V2y may be considered as a constant in the integration
32) for the inverse focal term. With this approximation,

F

4Tv J

(39)

when V is the potential of the plate and Vi and Vz' are the electric
intensities of the two uniform fields. The lens equation 35 is then

■\2v -xlv
di di 2

l\V2' - Vl'

21 42i

which may be written in the simpler form

V2' — Vl

dz

d,

4v

(40)

(41)

In this type of lens, the electrical refractive index -slv is the same on
both sides of the lens and the two principal focal distances are equal,
just as they are for a thin optical lens when it is bounded by air on
both sides. ^^

13 "Two Problems in Potential Theory," T. C. Fry, Bell Telephone System Mono-
graph B-671.

i"* A complete electron-optical system usually involves a combination of lenses.
The calculations for a combination are illustrated by the example in Appendix 1.

ELECTROSTATIC ELECTRON-OPTICS 13

The apertured plate between two uniform fields is the only lens
that permits such a simple calculation of focal distances. In all
other lens structures the potential varies appreciably throughout the
lens and the integration for the focal term is complicated. The
actual numerical calculations have been carried out for only a few of
these cases.

The second type of lens deserving special consideration is a lens
bounded on both sides by field-free space. For such boundaries the
first term in the last member of equation 34 vanishes, and \IF is
determined by the integral term alone. This integral in inherently
positive, and a lens bounded on both sides by field-free space is thus
always a convergent lens. The two concentric tubes of Fig. 7 give

Z7777//////^///M :V(///////////7777A

^/////////)/77fJ7777ZZ7/////////.
Fig. 7 — Concentric tubes — lines of force and electron paths.

a lens of this type, the electric field in each tube dropping to zero at
a short distance from its end. It is true that there is a divergent
field of the same intensity as the convergent field ; but an electron is
at a higher potential in the divergent field and traveling faster, so it
receives a smaller radial deflection in that field and the lens is con-
vergent. It is interesting to note that the lens is still positive even
when the potentials on the electrodes are reversed; in other words,
a lens of this type is positive irrespective of the direction of the electric
field.is

An Approximation j or Certain Thick Lenses

In certain electron lenses there is a short region of strong lens
action accompanied by more extended regions of weaker action ; the
large values of the derivative v" are confined to a short distance along
the axis, but the derivative does have appreciable values over a more
extended region. A lens of this type can be treated in the following
approximate manner, provided that there is but one maximum of
I v" I in the lens.

For this purpose, the differential equation 31 is rewritten in the form

cf(^)=y(l+|.)~'^/, dt = dzl^v (42)

" The principal focal distances of concentric tubes are calculated in Appendix 2.

14

BELL SYSTEM TECHNICAL JOURNAL

and the lens equation is derived by integrating it from a point Si to
a point 22, where the two points are taken at the substantial boundaries
of the non-uniform field. In carrying out this integration, the origin
of time is taken at the instant that the electron is at the maximum of
\v"\, as illustrated in Fig. 8, and for convenience the origin of z is

Fig. 8 — Coordinates for a thick lens.

also taken at that point. With this choice of the origin, the term
tIT in the second member of the equation is small compared to unity
in the region where v" is large and not very important in the regions
where v" is small. This term may therefore be neglected in lenses
when the time of transit is not too great a fraction of the focal times
involved. The integration of the equation then gives

1

1

when the inverse focal term is again

and

1 _ r«» v"

r'^ dz _ r

Jo ^l2v Jo

^ dz_

2v'

(43)

(44)

(45)

A transformation to space variables by means of equations 24 and 25
gives the lens equation in a form analogous to that for a thick optical
lens,

■^2v2 _ V2yi
di — a2 d\ — oi]

1

where

a2 = — V2»2^2 = — I ^^—dz,
ax = — ■42viti = — I -yA-^dz.

(46)

(47)

ELECTROSTATIC ELECTRON-OPTICS

15

A plane located at a distance ai from the point Zi is the approximate
first principal plane of the lens ; and a plane located at a distance a^
from the point Z2 is the approximate second principal plane of the lens.
In the lens equation, di — ai and di — a^ are the conjugate focal
distances measured from the principal planes. If the focal distances
measured in this manner are designated as Di and D2 respectively,
the lens equation assumes the simpler form

\hj% _ -shji _ 1
_,

D,

Dx

(48)

An electron lens frequently has both a positive and a negative
maximum of v" , and the preceding approximation cannot be applied
to the lens as a whole. There is, however, necessarily a point between
the two maxima where v" is zero and by taking this as a division
point, the lens can be separated into two components. The approxi-
mation can then be separately applied to each component, and the
whole lens treated as a combination of two lenses.

The General Theory of Thick Lenses ■
The equation for the coefficient A,

dA A^ = ^"

dz J2i

2V2y

is a Racciti equation and, with the exception of special cases, it has
no exact solution in the usual sense. Particular solutions can be
obtained only by integration in series. It is, however, possible to
express the general solution of a Racciti equation in terms of any two
particular solutions, and this property enables us to develop the
general theory of a thick lens in terms of its principal focal distances.

Fig. 9 — Paths corresponding to X and Y.

In considering a thick lens, two points Zi and S2 are again taken at
the substantial boundaries of the non-uniform field constituting the

16 BELL SYSTEM TECHNICAL JOURNAL

lens. The differential equation for A necessarily has a particular
solution equal to zero at Z\. This solution is designated as F, and it
corresponds to an electron ray entering the lens parallel to the axis.
At Z2 this solution is equal to — ■\[2v2lf2, where /2 is the second principal
focal distance measured from Z2. The path of such a ray is illustrated
in Fig. 9. This particular solution obeys the same differential equation
as A. By subtracting the differential equation of A from that of Y
and making a slight transformation, we obtain

^,„,(^_K)=-^, (49)

and it should be noted that

^/V2^=-^ = ^logr. (50)

r^2v dz

An integration from 2i to Z2 and a transformation to focal distances
then gives the relation

(/2-^2Mi^^ Jl^ls (51)

fidi \ V2 ^2

where k2 is a constant of the lens, given by

1/^2 = exp. r^. (52)

By proceeding in the same manner with a particular solution X for a
ray leaving the lens parallel to the axis, we obtain a second relation

(f^-ddd.^j^ jv^rj^ (53)

fidi \viri

where

The differential equations of X and Y may also be subtracted and
integrated, and this gives a third relation

f If - -^"^ S. (55)

A multiplication of the first two relations 51 and 53 gives

(/2 - ^2)(/i - d,) = -^1-^2/1/2, (56)

ELECTROSTATIC ELECTRON-OPTICS

17

which is one form of the equation relating the conjugate focal distances
of a lens. This equation may be converted into a more useful form
by the following considerations.

A combination of the three preceding relations gives

-J- {di — Q!2) = X (^1 ~ '^l)'
^2 CLl

where

a =/i(l - ^i),

^2 = /2(1 — ^2).

(57)

(58)

To interpret this equation, we erect two imaginary planes as shown
in Fig. 10. The first plane is located at a distance ai from Zi. If the

Fig. 10 — The principal planes.

path of the incident ray is projected it intersects this plane at some
radial distance R\. The second plane is erected at a distance 0:2 from
22. The path of the exit ray intersects it at a radial distance Ri.
The equation says — from simple geometry — that the two radial
distances Ri and R2 are equal. The path of an electron through the
lens is therefore the same as if the electron proceeded in a straight line
to the first plane, passed parallel to the axis to the second plane, and
then proceeded again in a straight line to the second conjugate focal
point. These two planes are called the first and second principal
planes of the lens. The action of a thick lens is the same as if the
space between the principal planes were non-existent, leaving them
in coincidence, and a thin lens were located at the plane of coincidence.

The principal planes of a lens may lie either inside or outside of
the lens. In most convergent lenses, ax is positive and a^ negative,
and the two planes both lie inside the lens.

The first conjugate focal distance measured from the first principal
plane is designated as Di, and the second conjugate focal distance
measured from the second principal plane is designated as D^. When
they are measured in this manner, the two conjugate distances are

Di = d,

Oil,

D2 — di — a2.

(59)

18 BELL SYSTEM TECHNICAL JOURNAL

The two principal focal distances measured from the principal planes
are, in a similar manner, designated as T^i and F^; then, from equation
58,

F\ = fi — Oil = kifi,

Fi = fi — Oi2 = kifi,

(60)

and, from equation 55,

^i/^2=-J^- (61)

2v:

Substitution of the new focal distances in the lens equation 56 now
gives

{Fi - D2){F, - DO = FxFi (62)

or

This is the general equation relating the conjugate focal distances in
any lens. With the aid of equation 61, it may be written in the more
familiar form •

^2v2 ^2^1 _ 1

~^~~d7 ~f'

where

1 V2iJ2 ^|2vl

Fy

(64)
(65)

The Principal Points of a Lens

The points locating the two principal planes on the axis of a lens
and its two principal focal points are called the cardinal points of the
lens. The preceding theory of a thick lens shows that its performance
is completely determined by the locations of these four points. ^^
The theory does not furnish a general method for calculating their
locations, but it does show that they can be determined from a knowl-
edge of two so-called principal rays. The first is a ray leaving the
lens parallel to the axis. If its entrance and exit paths are projected,
they intersect as shown in Fig. 11, and the intersection locates the
first principal plane. The projected incident ray also intersects the
axis, and this intersection locates the first principal focal point. The
second principal plane and the second principal focal point may be
located in a similar manner from the entrance and exit paths of a ray
entering the lens parallel to the axis.

1^ We are here speaking only of rays near the axis.

ELECTROSTATIC ELECTRON-OPTICS

19

The required paths of the two rays must in general be determined
either by a series or step-by-step integration of the differential equation
for A, or else by actual measurements on the physical lens.^^

FIRST
RAY

FIRST PRINCIPAL I FOCAL |POINTS

SECOND
RAY

SECOND
PLANE

Fig. 11 — The cardinal points of a lens.

Magnification

Electron object and electron image are defined as their optical
analogies. The electron object may be an actual source of electrons,
or the real image of such a source, or it may be a virtual image from
which the electrons are apparently coming as they enter a lens.

The magnification by an electron lens may be treated in the following
manner. Let Si be the size of an electron object located at a distance
Di from the first principal plane of a lens. Two electron rays from
the edge of the object are considered— as shown in Fig. 12. The ray

PRINCIPAL

PLANES

FIRST SECOND

Fig. 12 — Magnification.

entering the lens parallel to the axis may be regarded as passing on to
the second principal plane and then bending sharply to pass through
the second principal focal point ; the ray through the first principal
focal point may be considered as passing on to the first principal
plane and then proceeding parallel to the axis. The intersection of
the two rays locates the electron image and determines its size 52.
The magnification M is defined as S2/S1, and it follows from simple
geometry that

D2 - F2 Fi

M =

Di- Fx

(65)

^' Other step-by-step methods can be used when a map of the equipotential
surface is available.

20 BELL SYSTEM TECHNICAL JOURNAL

A more convenient expression for magnification is now obtained by
combining the two preceding expressions to give

and from equation 61

^=ftg-: (^^)

M = - xlTT^-Ff- (6/)

The magnification is not in general equal to the ratio of the image
distance to the object distance, as it is for an optical lens in air. It
is only equal to that ratio when the voltage is the same on both
sides of the lens.

Section III — Aberration in a Lens
Returning to the first section, we see that the general expression
for focal distance is

1 ^ + 5^2 + Cr* • • •

^ V2^ + ^',2+^V

(20)

The exact focal distance of an electron thus depends on its radial
coordinate r, and a ray passing through a lens at a distance from the
axis does not come to the same focus as a ray near the axis. A precise,
general theory for rays at a distance from the axis could — in theory
at least — be derived by solving the differential equations for as many
of the higher coefficients as desired and substituting them in the
above equation. Such a general solution would, however, be very
difficult indeed, and one is content — as he usually is in optics — to
treat the performance of a lens in a much more restricted manner.

The equation for focal distance can be simplified to some extent by
noting that its denominator is the velocity component z. With the
aid of the energy equation 6, this component can be written in the form

= 42v

^ + (!)?"•

In most lenses r is small compared to d, and the last factor in the
above equation may be approximately set equal to unity. This
approximation is accurate to one per cent even for a lens with an
angular aperture corresponding to F3.5 — an F2 lens is a very fast
camera lens. With this approximation the inverse focal distance is

1 A ^- Br'' + Cr^ + ■••

2-- VI (*'>

ELECTROSTATIC ELECTRON-OPTICS 21

The presence of the terms in f causes a diffusion of the focus in a
lens, and a clearer picture of this diffusion is obtained by expressing
it as lateral aberration. So we now proceed to derive an expression
for this aberration, and the meaning of the term becomes apparent
from the derivation. For this purpose we consider electrons entering
a lens as if they all came from a point source at a distance di from the
first side of the lens. We are at liberty to set the higher coefficients
equal to zero at that side of the lens, and this gives

Ai = --7—' ('0)

di

B,= Ci^ •■■ = 0.
At the exit side of the lens, the focal distance is

^ = - (^2 + Br~ + C.r' +•••), (71)

d2

where the coefficients are solutions of their differential equations
subject to the initial conditions 70. The focal distance do for rays
near the axis is given by

^'' = - A,. (72)

d.

The difference between the focal distance d2 of a ray leaving the lens
at a distance r from the axis and the focal distance do of a ray near
the axis is

d2-do^^ (B^r' + dr' +•••)• (73)

^I2V2

This difference is called the longitudinal aberration of the lens. It is
the distance that the focal point is diffused along the axis, when the
lens is limited by an exit diaphragm or radius r.

If a screen is placed at a distance do from the lens, rays near the
axis will come to a point focus on the screen ; but rays leaving the
lens at a distance r from the axis will strike the screen along a circular
line. The radius 5 of this circle is called the lateral aberration of the
lens. It follows rather simply, from the value of the longitudinal
aberration, that the lateral aberration is

(B2r' -\- C2r' ■•■). (74)

This is the radius of the diffuse image of a point source, when the lens
is limited by a diaphragm of radius r.

22 BELL SYSTEM TECHNICAL JOURNAL

The differential equations 17, 18 • • • for the aberration coefficients
are linear and subject to solution in the usual manner when A and v
are known functions of z. The solutions for the higher coefficients
would of course be quite involved. The higher terms are, however,
small compared to the second term, which causes most of the aberra-
tion, and the approximate distortion is given by the second term alone.
This term is called the second order aberration term.

The Reduction of A herration

The coefficient of any aberration term vanishes when conditions
are arranged so that the last member of its differential equation is zero,
for the coefficient may be arbitrarily set equal to zero at the first side
of the lens, and the solution of its linear equation is then zero through-
out the lens.

The important second order aberration term can thus be made to
vanish by arranging conditions so that

V"" {A'Y

16

= 0. (75)

In a lens that is not too thick compared to the focal distances involved,
we have seen that the term A"^ may be neglected in the differential
equation for A , and

The substitution of this value for A' in the above equation gives

(v"r

V —

= 0 (77)

as the differential equation for electric fields that are approximately
free from second order aberration, when the focal distances are reason-
ably large compared to the length of the field along the axis.

The general solution of this equation is a series solution, but several
particular solutions have been obtained in terms of known functions.
The potentials corresponding to these particular solutions are given
by the following equations :

$ = ae±"Vo(aj/'), (78)

$ = (a sin co2 -f 6 cos o)z)Jo{io:r), (79)

$ = (a sinh u)Z -{- b cosh cos)7o(wr), (80)

^ = 3az'''\ 4-4(7^V + i^ ' ^^

[3 4

2z ' 64\2z/

(81)

ELECTROSTA TIC ELECTRON-OPTICS

23

Any one of these electric fields can be produced by shaping and
positioning electrodes to correspond with two of its equipotential
surfaces. These fields are, however, in general not well adapted to
production with practical electrode structures. The one exception is
the field defined by equation 79, and electrodes for producing it in a
practical form are shown in Fig. 13. They are suitable for giving an

Figs. 13, 14 — Lenses with reduced aberration.

electron stream its initial acceleration. The electric field constitutes
a divergent lens, as do practically all initial accelerating fields.

As expressed by equation 79, this field is followed by a symmetrically
reversed field, and for some purposes it may be desirable to include
the reversed field. This is done by locating a low potential electrode
along its corresponding equipotential surface as shown in Fig. 14.
A small aperture may be cut in this electrode for the passage of
electrons. The aperture then acts as a lens to bring the beam to a
focus, but this lens has its own aberration, and the whole system is
then only partially free from first order aberration.

Appendix I — Calculations for a Complete System

The electrode arrangement of Fig. 15 is chosen for giving a simple
example of the calculations for a complete optical system. The final
focal distance is found by calculating the focal distances at the points
m, n, o, p in succession. Electrons leave the cathode and travel
parallel to the axis in the uniform field between the first and second
plates, so their focal distance is — oo when they arrive at the point m.
The electrons then pass through the aperture in the second plate,

24

BELL SYSTEM TECHNICAL JOURNAL

and their focal distance at n is calculated from the lens equation 41.
which gives

^ + ^ =

Vi

V2

I

-l]

(1)

Fig. 15 — Example of a complete system.
and the focal distance at n is

d„ =

41

i32 - 2

(2)

where /3 is -^v^jvi. The beam then passes through the uniform field
between the second and third plates, and the focal distance at 0 is
calculated from equation 28 for a uniform field, which becomes

and gives

(1 +i8Mn - (1 + 1/^Vo = 2/

4 + 2/3 - /32

2/3/

(1 +i8)(/32- 2)

(3)

(4)

The beam then passes through the aperture in the third plate into
field-free space, and the lens equation for this aperture is

(5)

1 1 1

0 -

V2

— Vi

dp do 4i'2

I J

Substitution for do now gives

1 1 +/3

r /32- 2

,1-/3]

dp 2/3/

[4 +

2/3-

P'

+ 2

^ J

(6)

which is the reciprocal of the final focal distance measured from the
last plate.

ELECTROSTATIC ELECTRON-OPTICS

25

In complete lens systems, where the symbolic calculations are
complicated, it is frequently simpler to introduce specific numerical
values and carry the successive steps of the calculation through in a
numerical manner. By doing this for a few suitably chosen numerical
values one can obtain the particular information that is desired.

Appendix II — Concentric Tubes
Two concentric tubes at different potentials form an electron lens
that is well adapted to practical tube construction. When the two
tubes are of the same diameter, the approximate constants of the
lens may be determined as follows. ^^

Fig. 16 — Concentric tubes.

In this type of lens, the electric intensity is symmetrical with
respect to an imaginary plane drawn between the two tubes — as
illustrated in Fig. 16 — and the plane is therefore an equipotential
surface. Its potential Vq is the mean potential of the two tubes.
This plane is regarded as a division plane separating the lens into two
component electric fields.

We first consider the component to the right of the plane. The
solution for the potential inside of the tube may be obtained in the
form of a Bessel Function series, and it follows from this series that
the potential on the axis is

2

V ^ V2 — (V2 — Vo)H

fxJiifJ.)

exp.

^JLZ
R

(1)

where R is the radius of the tubes, and lu. takes on discrete values
equal to the successive roots of

0.

(2)

We find that an approximation to the exponential series is given by

E

■;:' fiJi(n)

exp.

-^1=1
R '

tanh co2.

(3)

^^ We assume that the separation between their ends is negligibly small compared
to their diameter.

26

BELL SYSTEM TECHNICAL JOURNAL

where co is equal to 1,32/i?. The closeness of this approximation is
shown in Fig. 17. Its introduction gives

V = Vo -\- (v2 — vo) tanh cos.

(4)

A similar approximation is found for the potential on the axis to
the left of the division plane,

V = I'o — (vi — Vo) tanh coz,

(5)

and it turns out that the potential on the axis of both tubes can be
expressed by the single equation

V = f [(^2 + Vi) -\- {v2 — Vi) tanh wz].

(6)

3 0.6

^"•''•l^^m"-

H^R

-^

k

s

""

^^

---^

C= — r:<!

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

UJZ

Fig. 17 — An approximation for the exponential series.

With the potential on the axis expressed in terms of a known
function of z, various series methods may be used for locating the
principal planes and calculating the principal focal distances. They
are, however, complicated and it may be preferable to use the approxi-
mate lens equation obtained by treating the structure as a thin lens.

When treated in this manner, the expression 33 for the inverse focal
term can be exactly integrated, and the lens equation is

>V2

^1 3(-yjv2 -\- -yfvi)

(Vz^ — V^'l)^

= \,32IR. (7)

Division by either ^2v2 or V2i^— as desired — reduces this equation
to one that involves the voltages only in the form of a ratio. The
error in a focal distance d calculated from this equation is of the
order of R, when the focal distance is measured from the division
plane of the tubes.

ELECTROSTA TIC ELECTRON-OPTICS

27

\
\

\

V| V2

E3EB-

\

\
\

\

\

\

\
\

\

\
\

\
\

\

V

\

\
>

\

\

\
\
\

\

\

\

N

^

^

S

-F,-^'

'''-^.

.

-^ -

-- —

1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0

f 22.5

y

[^

y
y

r

^

/■

y
y

.'
y

-^ -y

,^— ^ ^

^^: -^^—

0.40
V2

Fig. 18 — Principal focal distances — concentric tubes.

28 BELL SYSTEM TECHNICAL JOURNAL

The principal focal distances for various voltage ratios are given in
terms of the tube diameter by the curves of Fig. 18. For rough
calculations, these plotted values may be used in the lens equation

^ + ^=1. (8)

where focal distances are again measured from the division plane of
the tubes.

The electric field of the concentric tubes has two maxima of \v"\
located symmetrically with respect to the division plane, as illustrated
in Fig. 16. Each maximum is located at a distance .SR from the
plane. The electron lens may therefore be treated in a somewhat
more exact manner by considering it as two thin lenses located at
these points. The inverse focal term of the equivalent lens to the
left of the plane is

1 C0V2

— I'l L

F vo -• ' ^

vo^i^ - Vi^'^

(9)

and the inverse focal term of the equivalent lens to the right of the
plane is

Vo

(VlJ2 — ^0) —

v^i-^ - z;o'/2

(10)

The final focal distance in any particular case is found by carrying
out the calculations for the two lenses in succession, with their separa-
tion taken equal to R.

Appendix III **

A Plane Electrode at the End of a Tube. — In addition to their above
application, the last two equations may be used for other purposes.
In electron devices, one frequently puts a plane electrode at the end
of another, tubular electrode. ^^ The approximate lens action of the
electric field between the plate and tube is then described by one or
the other of these equations. Equation 9 applies when the plane
follows the tube in the direction of electron motion ; and equation 10
applies when the plane precedes the tube.

In structures of this type, the plate is usually pierced with an
aperture for the passage of electrons. When the aperture is small
compared to the tube diameter, the lens system can be treated in the
following manner.

'* We assume the separation between the plate and the end of a tube to be negli-
gible compared to the tube diameter.

ELECTROSTATIC ELECTRON-OPTICS 29

We first consider the case of the plane preceding the tube. The
electric intensity at the plate is found by difTerentiating equation 4
with respect to z and then setting z equal to zero. A substitution of
this intensity in equation 41 of the text gives the lens equation of
the aperture. In addition to this lens there is an equivalent thin
lens located inside the tube at a distance .SR from the plate, and
having the inverse focal distance of equation 10. The system is
considered as a combination of the two lenses and the calculations
are carried through in the usual manner. When the plane follows
the tube, the constants of the two lenses are determined from equations
5 and 9, and the combination is treated in a similar manner.

Appendix IV — The Velocity Function
The auxiliary functions u and w are a special case of the components
of a generalized vector function that is useful in developing series
solutions for electron motion. The equations of this function are
equivalent to the Hamilton -Jacobi equation ; they are briefly outlined
in the present system of units as follows.

In a field that may comprise both an electric intensity E and a
magnetic intensity H, let v be any vector function of x, y, z that
satisfies the equations

curl i; = HIc, (1)

l/2|i;|2= 0 + T7, (2)

where PF is a constant equal to the energy of electron emission from
the source. Then u is a possible vector velocity for electron motion
in the field.

If the magnetic intensity is zero, the vector function v has a po-
tential ^p, which may be any solution of the equation

l/2lgrad^|2= c^-f TF (3)

and grad \p is then a possible vector velocity for electron motion in
the field.

The validity of these equations is established by transforming
them to the usual equations for electron acceleration.

A List of the More Important Symbols and Equations
In the present theory of electron-optics, all distances along the axis
are measured in the direction of motion, as they are in the optics
of light.

r, z — cylindrical coordinates
/ — time

30 BELL SYSTEM TECHNICAL JOURNAL

$ — potential at point in space, the electron source taken as zero
potential

V — potential on the axis

v' — derivative of v with respect to s

V — is also used for the voltage of electrodes
d — focal distance in general

T — focal time in general

A - — the important coefficient for rays near the axis, a function of

2 alone
u, w - — velocity functions corresponding to f and z
d\, di — conjugate focal distances measured from the two sides of a lens
fitfi — principal focal distances measured from the two sides of a lens

As an approximation in thin lenses, the focal distances are measured
either from the mid-point of the lens, or from the point where \v"\
is a maximum, provided that there is but one maximum in the lens.

ai, (X2 — location of the principal planes with respect to the sides of

a lens
Di, D2 — conjugate focal distances measured from the principal planes
7^1, F2 — principal focal distances measured from the principal planes
F — the focal term of a lens, not a focal distance

Equations for Rays Near the Axis

z = -yflv,

^ - _ ^ r/r,

^TvA' +A^ = ~ V

TUt^ ^ ^ 2

The important equations for a thin lens are :

V2z'i xlvi _ 1
di di ~ F'

h _ /2i'2

jr "V2^'
--+-=1,

di d\

\ _ r'i v"

dz.

ELECTROSTATIC ELECTRON-OPTICS 31

The following equations hold for any lens :

V2z;2 V2fi _ 1

di — oi2. di — ai F ^

^^2v2 V2yi _ 1
~D^ ~~D^ ~ F'

F2

F

2 _ _ I2V2

1 ~ V 2v, '

M - l^ - - l^£i
^^^ ~ F,Dr ~ y 2v, D, *

where M is magnification.

Equivalent Modulator Circuits

By E. PETERSON and L. W. HUSSEY

Equivalent modulator circuits are developed in the form of
linear resistance networks. They are equivalent in the sense that
the current magnitude in any mesh of the network is equal to the
current amplitude of a corresponding frequency component in the
modulator. The elements of the network are determined by the
properties of the modulator, while the terminating resistances are
those physically existent in the connected circuit.

With this correspondence demonstrated, the operating features
of the modulator may be deduced from the known properties of
linear networks. Among the properties considered are the trans-
fer efficiency from signal to sideband, and the input resistance to
signal as affected by the sideband load resistance.

Equivalent networks are worked out for a number of interesting
cases, involving different impedances to unwanted modulation
products, together with different non-linear characteristics. The
equivalents come out comparatively simple in form under the
restrictions noted and followed in the te.xt, which make the carrier
large compared to the signal, and the circuit elements purely
resistive.

CONSIDERED from the circuit standpoint, a number of modulator
performance features are important in any application. Among
these features might be mentioned the efificiency of power transfer
from signal input to sideband output, and associated with it the
question of how the signal input energy is distributed among the
different frequency components and dissipated in the modulator itself.
Then, too, we need to know how the impedance of the modulator to
any component depends upon the modulator structure and upon the
connected impedances to other products.

In attempting to get answers to these questions by mathematical
analysis, we encounter lengthy and cumbersome expressions in general
which do not lend themselves to ready physical interpretation. The
physical interpretation of these equations may be facilitated by intro-
ducing equivalent circuits of familiar form. One form commonly
used in the past replaces the non-linear system by a circuit including
a series of generators and linear impedances.

This may be illustrated by reference to a simple non-linear circuit,
in which carrier and signal generators are connected through an

32

EQUIVALENT MODULATOR CIRCUITS

33

external resistance to a two-terminal non-linear element such as a
diode, or a copper oxide rectifier. The effects of non-linearity show-
up in the change of modulator resistance with changes in applied
potentials and in the appearance of new frequency components.
These efifects may be reproduced quantitatively if we replace the
non-linear element by its equivalent consisting of a linear internal
resistance together with a series of internal generators — indicated at
the right of the dashed line of Fig. \-A. It is easy to see from this

Eq©

LINEAR
NETWORK

A B

Fig. 1 — {A) Equivalent modulator circuit in which the modulator is replaced
by a fixed internal resistance together with a series of generators. (5) Equivalent
modulator circuit replacing the modulator by a network of linear elements which
serves to couple the signal circuit into the paths followed by the modulation products.
In this circuit the mesh currents represent the amplitudes of the various frequency
components.

circuit^ what the amplitude of any current component should be;
for the general component

Despite the apparent simplicity of this relation, a difficulty arises as
soon as we attempt to state the internal generator e.m.f.'s explicitly,
since they are found to be tied up with the impressed potentials, the

' Here we denote the carrier frequency by />/2n and the signal frequency by g/2n ;
the corresponding generator potentials are Ep and Eq respectively, and the external
resistance is Rk where k indicates the frequency at which the resistance is effective.

The new frequencies are usually made up of sums and differences of integral
multiples of carrier and signal frequencies. In general, they may be represented
by {mp ± nq)/2ll, where m and n are integers or zero. It is advantageous to adopt
an abbreviated notation for the voltage component, say, of any frequency by which
the general component is indicated as £„,+„. Further when n is unity it is omitted
from the subscript, so that the generator e.m.f. of frequency (mp ± q)/2ll is indicated
as £m+. One of the restrictions mentioned further on results in limiting n to unity.

34 BELL SYSTEM TECHNICAL JOURNAL

modulator characteristics, and the external circuit impedances. For
this reason the equivalent circuit of Fig. X-A reveals only part of the
story, and in general the relation between the amplitudes of impressed
and generated components remains somewhat obscured.

In a number of cases of practical interest it is possible to represent
the connection between the amplitudes of various frequency compo-
nents by means of a different type of equivalent circuit. Figure \-B
is an illustration of this type, in which the paths of the current compo-
nents are shown individually. The connection between the various
circuits is effected by means of a linear network which contains no
internal generators. In this equivalent network the magnitude of
any mesh current is equal to the amplitude of a corresponding fre-
quency component in the modulator circuit. The purpose of this
paper is to demonstrate the validity of this representation, and to
show in detail what the linear network looks like when applied to
various types of modulating elements, in a variety of interesting cases.

In order to develop such equivalent networks in simple and useful
form, the following restrictions are imposed. The system includes
only one non-linear element.^ The terminating impedances are purely
resistive, although they may be functions of frequency. The signal
amplitude must be much smaller than that of the carrier. Finally,
the slope of the modulator current- voltage characteristic never becomes
negative. Under these conditions a number of modulating systems
can be treated, including variable resistance modulators with a
variety of current-voltage characteristics, and the variable resistance
microphone.

The section following deals with the modulator as a resistance
(or conductance) varying at carrier frequency. Succeeding sections
consider the behavior of such variable elements under different
circuit conditions.

I. Carrier Controlled Resistance
In setting up equations from which the equivalent networks are
obtained, the restriction on signal amplitude permits us to assume
the modulator to be a resistance or conductance varying at carrier
frequency. This commonly used assumption may be arrived at with
the aid of Fig. 2, which shows a typical non-linear current-voltage

2 Other cases are to be found in a paper by R. S. Caruthers on "Copper Oxide
Modulators in Carrier Telephone Systems," presented at the A.I.E.E. Winter Con-
vention, January 1939.

Modulators including a plurality of elements can frequently be replaced by an
equivalent structure with a single modulating element. This is true of the rectifier
type of modulator. In the double-balanced or ring type, however, under certain
conditions the equivalent circuit involves merely an ideal transformer connecting
signal and sideband circuits.

EQUIVALENT MODULATOR CIRCUITS

35

Fig. 2 — Non-linear current-voltage relation representative of certain types of
modulators. The impressed carrier voltage is large in comparison to the signal,
the variation of which is represented in the neighborhood of the potential reached
by the carrier wave at time to.

36 BELL SYSTEM TECHNICAL JOURNAL

curve. The variation with time of a large carrier voltage and a small
signal voltage are also indicated. Now if we consider the carrier to
provide a varying bias, then at any typical point /o we can consider
the signal voltage to sweep over a small segment (a, b) of the modulator
characteristic. The resistance is practically constant over this seg-
ment and of magnitude

^ = s' (')

the derivative being evaluated at the carrier voltage under considera-
tion. In general this resistance varies from point to point of the
carrier cycle. Thus the carrier enters the signal-sideband relation
only through the variation of a resistance facing the signal and modu-
lation products.

If the current-voltage characteristic is a smooth curve the resistance
varies smoothly over the carrier cycle. If the characteristic is made
up of two straight lines the resistance switches between two constant
values. This latter is approximated by most rectifiers, such as diode
and copper-oxide rectifiers with suitably large carrier amplitudes;
it is called by analogy a commutator modulator.

As a simple example of a variable resistance consider the char-
acteristic

i = av -\- bv^, (2)

from which

llR = ~ = a-\- 2bv. (3)

av

If the impressed carrier potential, v, is P cos pt, the conductance is

G = -1 = a + 2bPcos pt. (4)

K

More generally, the resistance or conductance for a given char-
acteristic can be expressed as a series

CO

R = ro -\- Y^lvn COS npl, (5a)

1

or

oo

G = g<i-\- Y^lgn COS npi. (56)

Here the coefficients depend only on the modulator characteristic and
the carrier amplitude. In special cases some of the coefficients vanish.

EQUIVALENT MODULATOR CIRCUITS 37

Thus an expansion for the Hnear rectifier includes only those coefficients
for which n is odd, whereas one for a modulator exhibiting odd sym-
metry in its current-voltage relation, such as thyrite, includes only
coefficients for which n is even.

The choice between (5a) and {Sh) in any given case is usually a
matter of convenience.^ This will be made clear by the forthcoming
examples. In every case use will be made of Ohm's law in one of
the two forms

V = Ri
or

i = Gv.

For simplicity, we select the relation which leads to the smallest
number of terms in the expansion. Thus if, from the form of the
terminating impedance, we know that i involves only a small number
of significant frequency components, whereas the voltage involves a
large number, (5a) will be used. If the potential, v, across the modu-
lating element is known to be the simpler, {5b) will be used.

In the practical application of modulators to carrier systems the
impedance characteristics of the connected selective circuits for taking
out the desired sideband energy provide, to a good approximation,
just such simplification. Thus a filter is substantially resistive in its
pass band and the suppression regions may be designed to have either
a very high or a very low impedance. If very high, no currents flow
in these frequency regions and (5a) applies ; if very low no potentials
appear across it in these frequency regions so that (5b) applies.

II. Single Sideband — High Impedance Outside Band
We will first consider a single sideband modulator involving any
variable resistance which can be expressed in the form (5a). The
terminating resistance is Rq to signal and Ri+ to the upper second
order sideband. Because of the high terminating impedance which
we assume to all other products, all current components other than
signal (Q) and sideband (/i+) are negligibly small.
The total current flowing in the circuit is then

i = Q cos qt -f /i+ cos (p + q)t. (6)

The potential across the non-linear element (v = Ri) is obtained
from (5a) and (6) as

fo + '^2rn. cos npt
1

[_Q cos qt + /i+ cos (p -f g)0. (7)

^ Except for those cases in which the occurrence of an infinity in any one of
these two quantities prohibits its use.

38

BELL SYSTEM TECHNICAL JOURNAL

After multiplying, and separating out the different frequency compo-
nents, each frequency component of v is equated to the corresponding
terminating generator e.m.f. minus the potential drop across the
external impedance. Carrying out this process for signal and side-
band, respectively,

£g = (i?, -f ro)(3 + ri/i+, (8)

0 = ri(2 + (i?i+ + ro)/i+.

If Q and /i+ are considered as mesh current amplitudes in a simple
linear circuit, it is evident that ri represents a mutual resistance, and
that Fig. 3 represents an equivalent network. In this system the

VV\A-

Fig. 3 — Equivalent modulator network connecting signal and sideband when other
modulation current components are suppressed by high circuit impedances.

signal source is connected to the sideband load by a simple T network.*
It will be found in subsequent cases similarly, that the connection
between signal and sideband circuits may be effected by a network
comparatively simple in form. Hence we can make our deductions
concerning the performance of modulator circuits by reference to the
well known properties of such equivalent networks. In the present
case, for example, we can draw the following conclusions.

1. The modulator loss becomes negligibly small if the series arm

resistance, r^ — ri, is very small and the shunt arm resistance,
ri, is relatively large.

2. Considering the modulator network as fixed, maximum power is

transferred when the signal and sideband resistances match
the characteristic resistance of the network, so that

R, = R,+ = V^o^ - n\ (9)

3. Under matched impedance conditions the power efficiency is

V

ro

+ Vro^ — ri^

(10)

^ While the results come out most simply in terms of a 7" network, the various
possible transformations (for example to a jt or to a lattice network) are of course
equally valid.

EQUIVALENT MODULATOR CIRCUITS

39

The term power efficiency — as used here — means the ratio of the power
delivered to the load resistance {Ri+) to that introduced at the input
side of the network by the signal source. The corresponding current
ratio of sideband to signal is the square root of r}. If the sideband
resistance is shorted the current ratio rises to its maximum. The
ratio of voltage at the network output to that at the network input
when the load resistance is made infinite coincides with this value

If we consider the various possible kinds of resistance variation with
time under the restrictions noted, it appears that the greatest attain-
able value of the power ratio is unity. It is evident from the equiva-
lent circuit that this limit corresponds to no loss from signal to side-
band. The closest approach to this no-loss condition is obtained in a
modulating element presenting a resistance which, over a carrier
cycle, varies between widely different resistances, taking on one
extreme value for a small fraction of the cycle and remaining near the
other extreme for the remainder of the cycle. Under these conditions
the series arm of the equivalent net tends to zero, the shunt arm to
infinity. There are practical limitations to the extent to which these
conditions can be approached in practical modulators. For example
the best attainable values of the two resistance extremes usually
depend upon the modulator characteristic, and upon the carrier
amplitude employed which may be limited by heat dissipation or by
voltage breakdown. Further limitation is imposed by parasitic
capacitances, which effectively limit the maximum attainable modu-
lator resistance.

The commutator modulator may be used to illustrate the results of
analysis above. Figure 4 shows the variation of the resistance of

■pn

B

1 1

ESISTANCE
>

a.

1

1 1 1

pn

2n

pt

Fig. 4 — Variation of resistance with time in a commutator modulator, in which
the resistance is switched from A to B, remaining at the higher value B for the
fraction /3 of the carrier cycle.

such a modulator over a carrier cycle. B and A are the two values
of the resistance {B > A) and j8 is the fraction of the carrier cycle

40

BELL SYSTEM TECHNICAL JOURNAL

over which the resistance is B. The coefficients of the resistance
expansion are readily shown to be

ro = /35 + (1 - /3M, (11)

r, = {B-A)'^^. (12)

V 35

/

^^

^

... 1

/

\

/

\

/

A =0.01

\

/ /
/ /
/ /

\
\

\

//

//

1 1

1

\
\
\

\
\
\

//
//

\

\
\
\

y

\
\
\

^

/

/

/

\

\

\

\

/ 0.1

/ ^
/ y

.-'""'

^^^^

\

\

\
\

\\

1 / '

/ /
/
/
/

t

'"-.

\

■\

\

0.5

r^r::^-

"^-;\

.^.^^

^

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

P>

Fig. 5 — Efficiency of a commutator modulator shown as a function of the pulse
fraction /3 with the ratio of the two commutator resistances as parameter. Here
the resistance terminations to signal and to sideband are optimum and the circuit
impedance is made high to unwanted components. Full line applies to double
sideband output, dashed line to single sideband output.

The efficiency (with optimum termination) depends only on /3 and the
ratio AlB. The dashed curves on Fig. 5 show the variation of effi-

EQUIVALENT MODULATOR CIRCUITS 41

ciency with these parameters. It is evident from the equivalent
circuit that best efficiency is obtained with r^ — ri small and ri large.
In this case ro increases linearly with /?, and ri varies sinusoidally
with /? — having its maximum at |8 = 0.5. The immediate conclusion
is that the optimum conditions are obtained when (3 is less than 0.5.
In fact the efficiency approaches the limiting value of 100 per cent
when j8 is very small and B is much greater than A, as may be seen
from (11) and (12).

III. Double Sideband — High Impedance Outside Band

In double sideband operation both upper and lower sideband
currents flow, but all other modulation products are suppressed as in
the previous case. Here the equations for signal and upper and
lower sideband respectively are

(ro + R,)Q + ri/i+ + rj,^ = E„
nQ + (ro + i?i+)/i+ + rJx- = 0, (13)

rxQ + rJx+ + (ro + Rx-)h- = 0.

Comparing (13) with the equations for a three-mesh circuit, we
obtain the equivalent network of Fig. 6. It is obvious from the
symmetry of this network that the two sidebands are equal when
Ri+ = 2?i_. Conditions for optimum efficiency may be put in form
permitting convenient comparison with the single sideband case when
we assume equal resistances to both sidebands.

Efficiency curves of a commutator modulator are shown on Fig. 5
for both single and double sideband cases. They differ primarily in
that the utilization of two sidebands gives greater efficiency, except in
limiting cases. The outstanding difference is that the unsymmetric
network has optimum signal and sideband resistances which are not
equal except at three values of /S equal to 0, 1/2 and 1. Modulators
are often operated with /3 approximately 1/2, so that in this case the
results here check with the common experience that the two terminating
resistances should be equal. It may be remarked that only in highly
efficient modulators would unequal terminations make an appreciable
difference in the efficiency of power transfer.

A comparison of Figs. 3 and 6 gives some light on the difference in
efficiency of the single and double sideband cases. The comparison
is made when Ri+ = i?i_. From the symmetry of the circuit of
Fig. 6, /]+ then equals /i_ and the mutual resistance (— ra) may be
eliminated, leaving a simple T network connecting the input and the
load. This is, with two exceptions, the T network of Fig. 3 with all

42

BELL SYSTEM TECHNICAL JOURNAL

elements doubled in magnitude. The input series arm is decreased
(ro — 2r\ instead of 2ro — 2ri) and the output series arm is increased
by an element Ir^. Since 2^2 is generally much smaller than ro there
is a net gain in efficiency.

O

1+

-AV-
-'"2

I i y^^

^0-^ + ^2

Fig. 6 — Equivalent modulator circuit showing the connection between signal
and two sideband circuits. All other modulation current components are suppressed
by means of high circuit impedances.

IV. Low Impedance Outside Band

The foregoing systems involved high impedances, suppressing the
flow of current at all but two or three frequencies. Circuits are as
readily obtained in the case of low impedance to all but two or three
of the modulation products. The physical systems this approximates
are the same as those previously discussed except that the terminating
filters must present a low impedance to frequencies outside the band.

All the external potential drops across the modulating element are
taken as negligible except components at the signal and one or two
sideband frequencies. The analysis, corresponding to that of the
previous sections, uses Ohm's law in the form i = Gv. Thus this
analysis, and the equivalent circuits, involve the expansion of a
conductance instead of a resistance. The equations corresponding
to (8) and (13) are equations in V q, V\+ and Fi_. In the single side-
band case a resulting equivalent circuit is that of Fig. 7. This is a
simple symmetric tt network. From its well known characteristics
the optimum terminating conductance and maximum efficiency are
immediately available :

Gi+ = -^ = W^^l?, (14)

R

1+

L go + Vgo^ - gi^ J

(15)

EQUIVALENT MODULATOR CIRCUITS

43

These expressions are identical in form with corresponding ones
obtained for the high-impedance single-sideband case, in which
conductance components replace resistance components. This con-

Fig. 7 — Equivalent modulator circuit showing connection between signal and a
single sideband. AH other modulation voltage components are suppressed by
means of low circuit impedances. The use of a 11 network and the specification
of element values as conductances are both matters of convenience.

firms what has been observed in several special cases : that there is no
theoretical advantage of either impedance extreme over the other in
the general case.^ Which one to use in any particular case depends
upon the special characteristics of the modulator or upon the practica-
bility of obtaining required impedance conditions.

The equivalent network for the corresponding double sideband
system is shown in Fig. 8. Similarly to the previous double sideband
case, the symmetry shows that when i?i+ = i?i_ the sideband current
amplitudes are equal and there is no potential across the coupling
resistance — (l/£2). Thus it may be shorted, reducing the circuit to
a simple unsymmetric tf. The matching resistances and maximum
efficiency may be obtained as before.

The results again are identical with the high-impedance case, if
resistances are replaced by conductances. The comment made on
the single-sideband case still holds — that there is no general theoretical
advantage of either a high- or low-impedance system over the other
as far as maximum possible efficiency is concerned.

The curves of Fig. 5 are evidently immediately applicable to the
low-impedance circuits provided all resistances are replaced by
conductances.

There are, of course, practical advantages of the high- or the low-
impedance circuit in particular cases. For example, it is commonly
easier to make the terminating impedance to unwanted frequency

* The form of the equations in corresponding high- and low-impedance cases
suggests that the impedance and efficiency relations for one case could be deduced
from those of the other through the principle of duality. See Guillemin, "Com-
munication Networks," Vol. 2.

44

BELL SYSTEM TECHNICAL JOURNAL

components very small rather than very large. The impedance
matching may be simpler in one case than in the other since, for the
same efficiency, the matching resistances are quite different in the
two cases.

vW^

Fig. 8 — Equivalent modulator circuit showing connection between signal and
two sidebands. All other modulation voltage components are suppressed by low
circuit impedances. When one of the sideband paths is shorted, the network reduces
to that of Fig. 7.

V. Finite Resistance to Distortion Products

One more extension may be made, without excessively complicating
the equivalent circuit. This is an extension to the case of a constant
resistance R to all unwanted products, which yields information
unobtainable from the limiting cases previously treated oi R — ^
and i? = 0.

This problem can be handled in a simple way by the artifice of
incorporating R within the modulator proper. In that case the
external impedances to signal and sideband must be reduced by R
to keep the total circuit resistance at its correct value, while the ex-
ternal resistance to any other modulation product then becomes zero.
This brings the situation down to that considered and solved in the
section immediately preceding.

By this manipulation the equivalent circuit is obtained as that of
Fig. 9 in the single sideband case. The primes indicate coefficients in
the expansion of the modified characteristic. These coefficients are
immediately available in the case of the commutator, since the sole
change there is an increase in both values of the variable resistance by
the amount R. Comparing the efficiency of transformation with that
obtained with extreme values of R as in the cases preceding, it appears

EQUIVALENT MODULATOR CIRCUITS

45

that the use of extreme values of R results in the maximum obtainable
power.

The impedance conditions specified above permit the flow of any
generated products, so that an infinite network would be required in

Fig. 9 — Equivalent modulator circuit showing connection between signal and
single-sideband circuits when a constant resistance R is effective to all other modu-
lation products. The primed coefficients {gk) apply to the conductance coefficients
when the series resistance R is included in the original modulator.

general to bring out the relation of any one product to the others.
Discussion was limited, however, to signal and upper sideband ; the
amplitudes of other components did not appear explicitly.

The section following deals with a different case involving an
infinite network in which individual meshes are treated explicitly.

VI. Equivalent Network for the Idealized

Resistance Microphone

Other variable resistance systems may be put into equivalent form.

For example, from the electrical side, an idealized variable resistance

microphone actuated by a sinusoidal acoustic wave can be represented

by the resistance

r = Rq -\- R cos qt.

This is exactly the form of the variable resistance already discussed,
with Tq = Ro, 2ri — R, and rn — 0 for n > I.

If one were interested in the modulation products with other
frequency components impressed electrically, the systems would be of
the same type as those of the previous section. In the case of the
microphone the d-c. voltage impressed leads to current components
which are d-c. and harmonics of the signal q. In this case, the equa-
tions are

= Rolo + RIil2,

= Roll + Rio + RI 2/2,

= Roh + R{Ii + h)/2,

Vo = Eo — Rblo
l\ = - R,h

Viq = — R'iql2

Vnq = — Rnqln = RqI n + R{I n-\ + In+l)l2,

(16)

46 BELL SYSTEM TECHNICAL JOURNAL

in which Rb represents the external d-c. resistance, and Rnq represents
the external resistance to the nth. harmonic.

Figure 10 shows the equivalent circuit for this system in the form
of an infinite ladder structure. From this circuit relative magnitudes

Fig. 10 — Equivalent circuit of idealized variable resistance microphone. Here
mesh currents represent amplitudes of the various frequency components. Ro
represents the fixed and R the variable internal microphone resistance, while Rnq
represents the external circuit resistance to the nth harmonic of the signal.

of the various frequency components are readily perceived ; evidently
the successive harmonic current components decrease progressively
in magnitude. A large value of Rnq makes the nth harmonic and all
successive harmonics small. A case in which quantitative information
is obtainable in simple form is that in which the resistances to all
harmonics are equal {Rnq = Rt, n > I) . In this case the equivalent
network beyond terminals (1) and (2) is a simple recurrent structure
and the resistance is obtainable by the customary methods of handling
infinite recurrent networks. The admittance looking in at the
terminals (1, 2) is the iterative admittance of the latter and is given by "^

L = l + ^ (17)

Ri R^ Ro - R -^ Rt -\- Ri ^ ^

Solving for Ri gives

Ri =

R

1+A 1 4

2R

Ro- R-\- Rt

As far as d-c. and fundamental current components are concerned,
the network beyond (1), (2) may be replaced by Ri and the system
reduces to a two-mesh circuit from which Q, Iq and power relations
are obtainable very simply. If harmonic current amplitudes are

^ In an infinite recurrent structure, the resistance Ri must be the same looking
in at successive point pairs (1, 2) (3, 4) etc. This is stated in (17).

EQUIVALENT MODULATOR CIRCUITS 47

desired, they may be obtained from equations (16), using the known
values of 7o and /i.

The two-mesh circuit for /o and Q can immediately be put in the
form of an unsymmetric T terminated at one end by the battery and
its internal impedance and at the other end by Rq. The optimum
terminating resistances and corresponding efficiencies are obtainable
as in previous cases but it is evident from the network, without further
computation, that losses are minimized (with suitable termination)
\i Rq — R and Ri are small compared with R. Ri is decreased by
decreasing Rnq (n > 1). These conditions mean that the best elec-
trical efficiency is obtained when the resistance variation is large and
the unwanted signal harmonics are short circuited.

VII. Extensions and Summary

Equivalent networks can be obtained in some cases when the
restrictions on the relative amplitudes of signal and carrier are re-
moved. It is evident from Fig. 2 that the value of the variable
resistance at any instant then depends not only on the carrier ampli-
tude but also on the signal amplitude. Thus the equivalent networks
are no longer made up of constant resistances, but depend upon the
magnitudes of both signal and sideband components. Further, new
components appear involving multiples of the signal frequency. The
equivalent for this case lacks the simplicity of those discussed here, a
simplicity which appears when one of the two input components is
much greater than the other.

The reason for the restriction to pure resistances becomes evident
when one attempts to generalize the results. The current components
will then have phase angles differing from zero in general. Consider-
ation of lower sidebands then shows that the phase angles must have
their signs reversed in certain circumstances, which leads to obvious
complexities. Again in purely resistive circuits it is possible to
determine the instantaneous current-voltage relation and hence to
specify the resistance variation as a function of time. In a reactive
circuit, however, additional difficulty arises in that the relations are
much more complex and in general impossible to specify in simple
terms.

To summarize, the presentation has been limited to the simplest
circuits used for modulation by means of a variable resistance. In
each example, the inter-relations between modulation product ampli-
tudes, terminating resistances, and types of modulator characteristics
are shown in terms of familiar linear resistance networks. From these,
qualitative information concerning the properties of the system is

48 BELL SYSTEM TECHNICAL JOURNAL

more readily obtained than from the equations and, in some cases,
the solutions for effective impedances and current and voltage ampli-
tudes are obtainable without further recourse to the equations.

ACKN OWLEDGMENT

The writers are indebted to several of their associates in the Bell
Telephone Laboratories for the use of unpublished material in this
paper. In particular, acknowledgment is due to Mr. R. S. Caruthers,
Mr. J. M. Manley, Dr. G. R. Stibitz, and Mr. R. O. Wise, who origi-
nally obtained some of the impedance and efficiency relations.

An Improved Three-Channel Carrier Telephone System

By J. T. O'LEARY, E. C. BLESSING and J. W. BEYER

This paper describes an improved three-channel carrier telephone
system for use on open-wire lines. It employs recent advances in the
telephone art to bring about many economies and circuit simplifica-
tions as compared with previous models of the three-channel sys-
tem. A new type of automatic regulating equipment is included.

Introduction

THERE are now in service in the Bell System approximately
750,000 miles of telephone circuit which are furnished by carrier
systems. Of this total, almost 90 per cent is provided by some 600
Type C systems, ranging from about 75 miles to over 2000 miles in
length. Basically designed to add three carrier channels to the normal
voice channel on open-wire lines, the Type C system has also been
used in special cases to provide additional circuits over deep sea
cables of moderate lengths.

The system was first described in this Journal in the July 1928 issue.'
Improved designs and the application of new circuit elements have
recently permitted a very extensive revision of the terminal and re-
peater equipment which results not only in striking reductions in
size and cost as compared with the older equipment, but also gives a
considerable improvement in transmission performance. A new type
of automatic regulating equipment has been provided for both the
terminal and repeater.

The improved system employs heater type pentode tubes, copper-
oxide modulators and demodulators and makes use of the negative feed-
back type of amplifier at both terminal and repeater points. The
terminal band filters are newly designed to give improved transmission
frequency characteristics on all channels. Each channel is arranged to
terminate on a four-wire basis in the same manner as the Type K
system for cables.^

An outstanding feature of the modified design is the large saving in
space in comparison with the previous equipment. As shown on
Fig. 1, the complete terminal with its regulating equipment occupies
a single bay, whereas the older system without regulating equipment
required two and one-half bays. The repeater space savings, while
not so large, are nevertheless substantial. The number of vacuum

49

50

BELL SYSTEM TECHNICAL JOURNAL

Fig. 1 — New and old type C carrier telephone terminals.

AN IMPROVED THREE-CHANNEL CARRIER TELEPHONE SYSTEM 51

tubes required in the system has been reduced, which results in a
material saving in power.

Certain features of the improved equipment, notably the automatic
regulation, can also be used on the older types of systems and the
design objectives were set up with this in view.

Frequency Allocation

The frequency range employed by the system and the allocation of
channel bands within that range are shown in Fig. 2. The allocations
used in the older systems are also shown for comparison.

6.3

Xl

: ic

NEW SYSTEMS

J .IZZ

7.6 10.6

r-TTi! c

1 20.7

3 tc

I32:

24.4

in

ARROWS DENOTE CARRIER
; - EAST TO WEST
f - WEST TO EAST

17.7 214

OLDER SYSTEMS

28.4
25.4

XZI c

nn

9.4

ic

Xi

19. S

24.4
4|—

r~5~i!

FREQUENCr- KILOCYCLES

Fig. 2 — Frequency allocation of the new systems relative to that of the older systems.

The original selection of the frequency range for the Type C system
was the result of many different factors. Foremost among these was
the desire to keep the frequencies low in order to minimize line crosstalk
and attenuation and changes in the latter due to weather and tempera-
ture. On the other hand was the greater filter cost that results from
crowding the channels close together. Different frequency bands
were used for transmitting in opposite directions in order to avoid
the problem of near-end crosstalk and to give the advantages of four-
wire transmission. Although consideration was given to the general
desirability of increasing the band of frequencies effectively transmitted
by the individual channels, the requirement for coordinated operation
with older systems already in use precluded any material increase in
the frequency space allocated to each channel of the new system.
Nevertheless, as will be seen from Fig. 4, the channels show very little
distortion within the transmitted band and represent a material
improvement over the older systems.

52 BELL SYSTEM TECHNICAL JOURNAL

Because the line crosstalk tends to be greater at the higher fre-
quencies, past experience has indicated the advantage of having
available two systems between which the crosstalk in the higher
frequency group will be unintelligible. Two allocations are provided
for this purpose, designated CS and CU. The channel bands are
identical in the lower frequency group (East to West) and in the
upper frequency group (West to East) differ only in that the carrier
frequencies are at opposite ends of the bands. In this group crosstalk
between similar bands will have the speech frequencies inverted and
will therefore be unintelligible.

This arrangement does not give as high a crosstalk advantage as
the arrangement used previously where the bands were not only
inverted but also displaced with respect to each other. However,
better line crosstalk conditions now prevail due to the application of
improved transposition designs and line configurations to the more
recently constructed lines and to the use of new methods of mitigating
crosstalk on the older lines. This permits the simplification of the
frequency allocation, as a result of which one system may be readily
converted into the other with fairly simple equipment changes. It
will also be possible to use the voice frequency circuit on all pairs as
a program circuit transmitting up to 5000 cycles. The advantages of
the greater plant flexibility resulting from these two factors are
obvious.

The new system may be used on suitably transposed lines with the
Type D ^ and Type H* single channel systems, whose frequency
bands are such that no serious near-end crosstalk problem will arise.

Overall System

A block diagram of a complete system, consisting of the two termi-
nals and a single intermediate repeater, is shown on Fig. 3. In
practice there might be as many as ten or more such repeaters. The
two terminals differ from each other only in the frequencies for which
their respective transmitting and receiving circuits are designed. The
west terminal transmits the high-frequency group of Fig. 2 and receives
the lower frequency group while the east terminal does the reverse.
The repeater is provided with means for separating the frequencies in
the two directions of transmission, amplifying the current to the
desired level, and passing them on to the next line section.

A typical overall frequency characteristic for one of the circuits
derived from the new system is shown on Fig. 4. This characteristic
illustrates the relative freedom from distortion in the transmitted
frequency range.

I 1 ujS^I 1

r^^^^

r^-^^^^

1 1*

1 t

< —

Ml t

t l^

Q- _J

TT

t I'

E

ii

^

a-tt —

gs

! 1

! I

t 1

t I

u.

1-^t:5-U

u

til

L_n::=:-U

54

BELL SYSTEM TECHNICAL JOURNAL

The carrier channels are separated from the voice frequency circuit
on the same pair of wires by means of a high-pass and low-pass filter
combination as shown on Fig. 3. Several different filter sets are
available for this purpose differing from each other in the frequency

10
9
8

7
6
5

3

2

\

\

/

0

1

^

J

Vx

"^

1

400

Fig. 4-

800

1200 1600 2000 2400

rREOUENCY -CYCLES
-Typical overall transmission-frequency characteristic

2800 3200

band which is desired in the voice circuit. Where the voice circuit is
an ordinary message circuit the filter will have a cutoff around 3 kc.
Where it may be used for program transmission a filter set having a
cutoff above 5 kc is provided. For still wider program bands there is
a filter set cutting off above 8 kc. The use of this latter filter would,
of course, require the sacrifice of the lowest carrier channel since it
would be overlapped by the program band.

An important feature of the system is the method of stabilizing
the overall transmission. Ahead of the terminal transmitting amplifier
in each direction of transmission there is connected to the circuit an
oscillator which generates a pilot current. This pilot current has a
frequency adjacent to the band of the middle channel. The oscillator
is designed to have a relatively high degree of stability with respect
to output and frequency. At the output of each repeater and at the
receiving terminal the pilot frequency is selected by a high-impedance
bridging filter, which has little effect on the through transmission,

AN IMPROVED THREE-CHANNEL CARRIER TELEPHONE SYSTEM 55

and is then used to actuate a regulating mechanism. Changes in the
Hne transmission at this frequency are indicative of the changes at
all frequencies and the regulator functions to maintain a nearly
constant output level in all three-channel bands.

LOW CHANNEL- 20. 7 KC. CARRIER

i i I ' I I I I 1 I I 1 L 1 1

zu

?^
u.
u
Ol-

5s:

TO

+ 7

+ 6
+ 5
+ 4
+ 3
+ 2
+ 1
0

^

^

\

[

1

<^

\

\

1

\

i

1

\

\

\

\

i

-

\

/

\

\

/

\

^

^

\

/

/

\

1

>

f

10 15

DAY or MONTH

20

25

30

Fig. 5 — Chart showing regulation for a period of one month on
system with one repeater.

56

BELL SYSTEM TECHNICAL JOURNAL

1

u2

(T >-

ZW

O^

<?

tru.

\j*n

o[e>

o£u

UJ-

0:1-

a:^

50

UJ .

•^.z

(L-*

^<

Oi>-

h^O

\.

/

Z

ui2

0—1

4-WIR
ERMINAT

OF
CARRIE
CHANNE

H

zd*

— (OQ

t-

u

Z I

?<..!i^z
^?oS^z

3 5<

AN IMPROVED THREE-CHANNEL CARRIER TELEPHONE SYSTEM 57

The pilot current is also used to indicate through an audible or
visual alarm any trouble which results in large sudden changes in
transmission such as would be occasioned by an open or short circuit
on the line itself.

The ability of the regulating mechanism to stabilize the transmission
over the system is shown on Fig. 5 which shows the deviations recorded
in daily measurements on all three channels of a 250-mile system over
a period of one month. The actual changes in line loss at the pilot
frequency are also shown for comparison. During this period various
conditions of temperature, rain and fog were experienced.

With the transmitting level that has been provided and for ordinary
line conditions it is found practicable to employ repeater spacings of
from 125 miles to over 250 miles. The exact distance in any par-
ticular case depends upon many factors, such as: wire size, length of
toll entrance or intermediate cables, location of existing offices and
the susceptibility of the line to sleet or frost. Where this latter
condition is prevalent conservative spacings are desirable.

"-pPj^l — \W-'

-Wv-

TO

MODULATOR

BAND

FILTtR

OSCILLATOR

7-

I I

\ ^ /

TO
HEATER
CURRENT
SUPPLY

Fig. 7 — Schematic of modulator.

Terminals

The general theory of operation of the terminal may be understood

from the block diagram shown in Fig. 3. On the voice-frequency side

each channel terminates as a four-wire circuit. The input to the

carrier system from the voice circuit is designed to operate at a level

58 BELL SYSTEM TECHNICAL JOURNAL

13 db below the transmitting toll switchboard which is the common
reference point. The output from the system is at a level 4 db above
that point. Equipment for coupling the system to both two-wire and
four-wire circuits has been designed. The circuits employed in each
case may be seen in Fig. 6.

The modulator circuit, shown in Fig. 7, uses copper-oxide varistors *
for converting the voice frequencies to the higher line frequencies.
The high degree of balance obtained in the copper-oxide varistors
has the important advantage of making carrier leak a practically
negligible factor. This is of particular importance in the case of that
channel to which the pilot current is adjacent in the frequency spec-
trum. The modulator circuit is also designed to limit the peaks of
very loud talkers which would otherwise overload the common ampli-
fiers. The effect of this limitation on the quality of the speech
transmitted is not noticeable.

The oscillator which supplies the carrier to the modulator is designed
to be stable in both output and frequency. When it is once adjusted
with the oscillator at the distant end, departures from synchronism
will be relatively small. Part of this stability is due to a new circuit
design employing coil and condenser elements having opposite temper-
ature coefficients so that changes in one will be compensated for by
changes in the other.

The band filters use coils wound on magnetic core material, having
improved modulation characteristics, instead of the solenoidal air
core coils previously used. This results in a considerable reduction
in the space which they occupy.

The transmitting and receiving filters associated with each channel
are identical as to band width. They are further characterized by a
more abrupt increase in discrimination immediately below and above
the pass-band frequencies than was realized in the channel filters for
the previous Type C systems and also by less distortion across the
pass band. Most of this distortion is in the form of higher loss in
the vicinity of the band limiting frequencies. It was deliberately
included in the design of the filters for the purpose of masking delay
distortion effects on overall transmission quality which might otherwise
become noticeable when four or five type C carrier telephone systems
are connected in tandem.

The uniformity and symmetry of the various filters are shown by
Fig. 8 which gives the characteristics of those in the upper frequency
group. This symmetry is required in this group in order to make
the CS allocation convertible into the CU by moving the carrier from
one end of the band to the other.

AN IMPROVED THREE-CHANNEL CARRIER TELEPHONE SYSTEM 59

/

y

c:

ziZ

N.

\
y

— •■

—

—

-

\

.

■■-

^

/

1

/

to

_l

u
z
z
<

X

o

—

y

c

:C

V

J

1

a-

)

__ —

-•-

^-

A

—

.

^■

1

'

— .

■>

e

—

-..

^

1

1

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\

_1

LJ

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z
<

X

u

,-•

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--.

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—

—

—r~

.

'

V

-~-

— -.

^__

^

/

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<

-~~-

^.

N
d

z
z
<

I

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__^_^

— •

—

—

*•

c^r

—

—

-~z

''1

s
\

\

i

a

60 BELL SYSTEM TECHNICAL JOURNAL

The transmitting amplifier is the same as that used on the receiving
side and in both directions of transmission in the repeater. This
ampHfier is capable of operating at a level 18 db above the transmitting
toll switchboard.

On the receiving side, following the directional filters, is the equip-
ment which makes up the system of equalization and regulation.
This is identical with that used at the repeaters and is described more
fully later. The regulator functions so as to maintain a nearly
constant level at the output of the receiving amplifier. The band
filters differ from those on the transmitting side only in the frequency
bands which are transmitted and are the same as those used at the
distant transmitting terminal. The demodulator circuit is of the
same general type as the modulator circuit and the oscillator which
supplies it with a carrier frequency is practically identical to that
used by the modulator. However, because of the low levels at which
these copper-oxide units are operated, an amplifier tube is necessary
to restore the level to the required value at the output. The gain of
this amplifier is continuously adjustable over a range of about 10 db
so that precise adjustments of the overall circuit net loss can be made
on each channel individually.

On very short non-repeatered systems the transmission variations
may not be great enough to require the automatic regulating equip-
ment. In such cases a manually operated potentiometer will be used
for controlling the gain.

Repeater

A block diagram of the repeater is shown in Fig. 9. Directional
filters on each side separate the two directions of transmission. As in
the case of the receiving terminal, the equalizing and regulating
equipment maintains all channels at the proper level at the amplifier
output. The high cut-off filter shown on the circuit in the west-to-
east direction limits the transmission to frequencies below 30 kc.
This may be desirable when a system employing still higher frequencies
is used on the same pair as the Type C system or on other pairs on
the same line.

The repeater provides a maximum gain of about 49 db at the
highest frequency in the upper group of the new system and about
43 db at the similar point in the lower group. The exact gains at
different points in the frequency range are adjusted by the regulator
so as to compensate for the attenuation of the line section preceding
the repeater.

A complete repeater with its regulating equipment is mounted on
a single equipment bay. A photograph of this bay is shown in Fig. 10,

AN IMPROVED THREE-CHANNEL CARRIER TELEPHONE SYSTEM 61

irn:

< J

St

I

a z
< J

3^

Q-ii.

I I

< UJ

rzi

ZTI

E

L.

iRc

b?

<

(-Z„,

62

BELL SYSTEM TECHNICAL] JOURNAL

I!|iiip|i|M

xn

Ff^

C»ii1fi'!

jLJ-LC *> I

"^-it.

Fig. 10 — New repeater for Type C systems.

AN IMPROVED THREE-CHANNEL CARRIER TELEPHONE SYSTEM 63

Regulation

At the transmitting terminal each channel is adjusted to the same
output level and in the operation of the system it is desirable to restore
this equality of levels at each repeater point and at the receiving
terminal. In each direction of transmission the line losses at the
upper end of the frequency range will be higher than at the lower

(0 l^

I-
cr
<

o
z
<

50
48
46
44
42
40
38
36
34-
32
30
28
26
24
22
20
18
16
14

LINE + VARIABLE ARTIFICIAL LINE + EQUALIZER - SCALE A |

v^

t^^

^\

v_

S0^

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BASIC
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FREQUENCY - KC

Fig. 11 — Theory of regulator.

64 BELL SYSTEM TECHNICAL JOURNAL

end and, furthermore, these losses change by varying amounts with
temperature and weather conditions. It is the function of the regu-
lating equipment to provide the needed adjustment and equalization
of levels over the wide range of line conditions.

The theory of the operation of the regulating system is shown in a
simplified manner in Fig. 11. The line circuit is connected at the end
of each repeater section to a line equalizer, which is in turn connected
to an artificial line unit designed to be continuously variable. The
slope of the line equalizer loss characteristic is the reverse of the line
slope and is as great as may be found in practice on any ordinary
length of line section except under conditions of severe ice or frost.
The artificial line slopes in the same direction as the line circuit itself.
In lining up a system the artificial line is adjusted so that when
added to the real line the slope of the combination neutralizes that of
the equalizer leaving the overall transmission very nearly uniform for
all frequencies in the range. Then as the loss and slope of the real
line change, the artificial line is made to change in the reverse direction
leaving the overall transmission still uniform. The action of this
artificial line is under the control of the pilot current, referred to
before, and the design of the equipment is such that in maintaining
the pilot at the proper level the other channels are also properly
adjusted.

In practice, the regulating unit must take care of a wide variety of
wire sizes, wire spacings and insulator types. It has been found,
however, that the change in slope for a given change in attenuation
at some reference frequency is very nearly the same for all combinations
of the above during ordinary weather conditions. As a result a single
unit can be made to serve all cases.

Where conservative repeater spacings are employed there is a large
amount of regulating range available to take care of sleet or frost
formations on the wires. For the particular use illustrated in Fig. 11
the total range is about twice that required for ordinary wet weather.
For shorter sections the available range would be still greater.

Some details of the regulating equipment are shown on Fig. 12.
The pilot frequency is selected from the other frequencies on the line
by a narrow band filter bridged across the output of the amplifier.
This filter has a high impedance so that the bridging loss is small and
does not interfere with regulation at succeeding stations.

A copper-oxide varistor is used to convert the selected pilot frequency
into direct current which in turn actuates two Weston Sensitrol
relays connected in series. The relays are equipped with meter scales
on which a needle attached to the armature serves as a pointer. One
of these relays controls the action of the regulator, the other functions

AN IMPROVED THREE-CHANNEL CARRIER TELEPHONE SYSTEM 65

TELECHRON Q, ^

MOTOR 3 (O)

[>

Fig. 12 — Regulator circuit.

in an alarm circuit described later. With normal current flowing,
corresponding to the proper pilot level at the output of the amplifier,
the pointers of these relays are on midscale with a reading of 0 db.
When the pilot level changes by more than .5 db in either direction,
contacts close on the relay controlling the regulator and cause power
to be supplied to a Telechron motor which controls the continuously
variable artificial line mentioned above. This will be driven inter-
mittently at a rate of about 1 db per minute until the output level
has been restored to within ± .5 db.

As will be seen from the sketch the variable line consists of three
sections connected in tandem. The ends of these sections are con-
nected to the four stators of a variable air condenser. The rotor of

66

BELL SYSTEM TECHNICAL JOURNAL

the condenser meshes with any stator or with parts of two adjacent
stators. The condenser, therefore, serves as a potential divider across
the regulating network sections, the loss introduced depending upon
the position of the rotor with respect to the stators. Basically these
artificial line sections consist of units having the same loss character-
istic. The first section, however, may be supplemented by additional
units which will be required on the shorter line sections in order to
build out the line slope as shown on Fig. 11. Since this section will
be the last one to be cut out by the regulator, the less accurate part
of the regulating range is thereby reserved for the periods of very
high line loss, such as during ice or frost formation which occurs only
infrequently.

The second sensitrol relay has contacts which close only on much
larger changes in the pilot level such as would result from a failure of
the line itself. When it operates it disables the regulating circuit and
through a slow operating mercury relay brings in an audible or visual
alarm indicating to the attendant that the system is in trouble.
The slow operating relay introduces a delay in the operation so that
short interruptions will not operate the alarm system.

The principal function of the regulating amplifier shown on Fig. 12
is to provide a high-impedance termination for the regulating network
and condenser combination. There is, however, a small amount of
gain available which may be useful in some cases.

New Line Anplifier

The amplifier which is used in the repeaters and in the transmitting
and receiving branches of each terminal is one of the outstanding
developments of the system. It was designed to have satisfactory
transmission characteristics over both upper and lower frequency
groups. It employs the principle of negative feedback ^ to achieve
a high degree of stability, freedom from modulation and stabilized
input and output impedances.

The advances made in the design of this amplifier can be seen by
the comparison in the following table with the push-pull amplifier
which was used in the older systems. In some cases the latter was
supplemented by an auxiliary amplifier where higher gains were
needed.

Push-Pull Amplifier

Push-PuU Amplifier Plus Auxiliary

Amplifier

New Feedback Amplifier

24-Volt
Power — -

Watts

52.8

76.1
16.4

130-Volt
Power —

Watts

15.1

17.2
6.3

Panel
Space —
Inches

12i

171
3i

Gain
db

32

50

No. of
Tubes

AN IMPROVED THREE-CHANNEL CARRIER TELEPHONE SYSTEM 67

There should be added to the comparison the fact that the new
ampUfier does not require selection of tubes to obtain satisfactory
modulation results. It is also more stable with variations of power
voltages and changes of vacuum tubes. The large space saving will
be evident from Fig. 13, which pictures the new amplifier with the
old push-pull amplifier and its auxiliary.

301"

Fig. 13 — New amplifier compared with the older t)pe which it replaces.

The circuit of the amplifier is shown in Fig. 14. It is a two-stage
circuit using pentode tubes. As will be seen from the circuit the
feedback connection is obtained through the use of input and output
transformers which are essentially hybrid coils. These coils are

68

BELL SYSTEM TECHNICAL JOURNAL

I— l-AAA.

" \/W

Hi'

AN IMPROVED THREE-CHANNEL CARRIER TELEPHONE SYSTEM 69

designed to have unequal ratios,f"minimizing the loss to through
transmission at the expense of greater loss in the feedback circuit.
Including the transformers in the feedback path makes them also
beneficiaries of the feedback with a resultant reduction in impedance
irregularities, transmission distortion and modulation products.

90

80

70

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FREQUENCY -KC

25

30

35

Fig. 15 — Gain frequency characteristic of amplifier.

The amplifier has a gain of 50 db with provision for increasing it to
52 db when used as a terminal transmitting amplifier. Gain-frequency
characteristics are shown in Fig. 15 for the 50-db gain condition with
and without the feedback connection. The effect of feedback on
transmission distortion is evident in this figure.

70

BELL SYSTEM TECHNICAL JOURNAL

The second and third harmonic products in the amphfier are illus-
trated in Fig. 16 which shows their relation to the fundamental for
different values of fundamental output. This harmonic production
is a good measure of the modulation performance. In this respect

80

70

60

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40

30

20

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Fig. 16 — Modulation in line amplifier.

30

the new amplifier is as good as or better than the push-pull amplifier

which was used in the older system when a periodic selection of tubes

was necessary to insure a satisfactory reduction of second harmonics.

A gain-load characteristic of the amplifier, with respect to a single-

AN IMPROVED THREE-CHANNEL CARRIER TELEPHONE SYSTEM 71

0 — -^ I -«^

-3

0 10 20 30

OUTPUT-DB ABOVE I MW
Fig. 17— Gain-load characteristic of amplifier at frequency of 15 kc.

frequency output, is shown in Fig. 17. Translated into terms of
three-channel operation this means a permissible level of 18 db above
the transmitting toll switchboard without noticeable distortion or
interference between channels due to modulation.

Power Supply

The new system is designed to operate at both terminals and
repeaters on standard telephone office battery supply of 24 and 130
volts. A dry-cell battery is required to supply grid bias to the output
tube of each amplifier. A small amount of UO-volt a-c power is also
required to drive the Telechron motor in the regulator circuit. The
total steady power consumption in a terminal is 88 watts and in a
repeater is 56 watts. These figures compare with 220 watts and 164
watts, respectively, in the older terminal and repeater.

Where regulated 24-volt battery is not available, tubes having a
slightly greater current consumption are used in combination with
ballast lamps. In this case the power used will be somewhat greater.

Provision has been made for a separate a-c power conversion unit
to be used with the system in offices where the usual d-c voltage is
not available. This should prove of great value where the provision
of a battery reserve is not warranted.

Signaling

Standard voice-frequency signaling equipment can be used with the

new terminals. There is also available a new type of ringer circuit

in which a single tube functions both as the source of power for an

outgoing signal and as a detector for an incoming signal. This

72 BELL SYSTEM TECHNICAL JOURNAL

circuit employs heater type tubes and will operate from the a-c power
conversion unit mentioned above. Since it also obviates the need for
a 1000-cycle generator as a source of signaling current it is particularly
well adapted to the small office type of installation.

Equipment Features

As mentioned before the new terminal is much more compact than
those previously used. Formerly 2| bays of standard size were
required for the terminal proper and an additional bay for the auto-
matic regulating equipment. Now a complete terminal including the
regulating equipment can be mounted in one such bay with some space
left for miscellaneous equipment.

The same degree of compactness has been applied to the new
repeater. A bay of standard size was formerly required for the
repeater proper with another bay for the automatic regulating equip-
ment when provided. Both are now provided in one bay and, as in
the terminal, some space is available for mounting other equipment.

The assembly of the equipment panels of the carrier terminal and
repeater generally follows conventional practices, the repeating coils,
condensers, vacuum tubes, etc., being mounted on the front of steel
panels with the electrical terminals projecting through and the wiring
placed on the rear. The filters are in sealed cans with soldering
terminals brought out on the rear for wiring connections.

In view of the wide field of use anticipated for the new system,
somewhat more than the usual flexibility of assembly and arrangement
of parts has been provided. In small terminal offices, that is, offices
having one or two systems, the four-wire terminating sets and asso-
ciated patching jacks and the carrier line equipment and associated
jacks may all be in one bay, using for this purpose the miscellaneous
bay space referred to above. Similarly, the line filter equipment may
be mounted on the repeater bay.

In the larger terminal offices, in order to facilitate operation and
maintenance, the four-wire voice-frequency patching jacks can be
located in a central patching bay with similar jacks from other carrier
channels. Testing and monitoring equipment provided at such a
point will, therefore, be common to many circuits. In the same
manner the carrier frequency patching jacks of a large number of
terminals or repeaters in an office can be grouped at a central point.

Line Considerations

Since the new system occupies practically the same frequency range
as its predecessor, it can be applied to open-wire routes in very much

AN IMPROVED THREE-CHANNEL CARRIER TELEPHONE SYSTEM 73

the same manner. Wire sizes of 104 mil, 128 mil and 165 mil are
commonly used in the Bell System plant, the particular size often
being governed by mechanical rather than by transmission considera-

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CS INSULATORS
8" SPACING

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FREQUENCY - KILOCYCLES

Fig. 18 — Attenuation characteristics of 104, 128 and 165 mil open-wire lines.

tions. These lines are carried into the terminal and repeater offices
through cables which are usually loaded to maintain smooth impedance
relations and reduce the transmission losses.

The control of crosstalk ^ is one of the major problems in the
application of carrier to open-wire lines. On short lines where only a

74

BELL SYSTEM TECHNICAL JOURNAL

AN IMPROVED THREE-CHANNEL CARRIER TELEPHONE SYSTEM 75

few systems are involved, the engineering solution may be quite
different from that on a long line on which it is desired to operate
many systems. Several different plans for transposing wires have
been developed which can be applied with various pole line configura-
tions so as to meet the necessary requirements in any practical case.
The more recently constructed carrier lines have, in general, employed
a spacing of 8 inches between the wires of a pair, with from 16 to
26 inches between horizontally adjacent pairs. Besides contributing
to the crosstalk reduction, the closer spacing is also less susceptible
to interference from outside sources, which is an advantage from a
noise standpoint.

Attenuation characteristics ^ for typical eight-inch spaced pairs
using the CS type of insulator are given in Fig. 18. Normal or dry
weather characteristics are shown, together with the losses that are
assumed for ordinary wet weather. Temperature changes also result
in sizable transmission changes. It is also important to note that the
losses when the wires are coated with sleet or frost may go far beyond
those indicated for the wet weather condition.

Conclusion
The widespread use that has been made of the Type C system up
to this time is pictured in Fig. 19, which shows the routes in the Bell
System over which systems are now operating. The new design with
its lower costs, improved performance and greater flexibility should
find increased application not only on these routes but on shorter lines
on which the system has hitherto not been economical.

References

1. "Carrier Systems on Long Distance Telephone Lines," H. A. Affel, C. S. Demarest

and C. W. Green, Bell Sys. Tech. Jour., volume 7, July 1928, pages 564-629;
A.I.E.E. Transactions, volume 47, October 1928, pages 1360-1386.

2. "Cable Carrier Telephone Terminals," R. W. Chesnut, L. M. Ilgenfritz and

A. Kenner, Bell Sys. Tech. Jour., volume 17, Jan. 1938, pages 106-124;
Electrical Engineering {A.I.E.E. Transactiotis) , volume 57, May 1938, pages
237-244.

3. " Carrier Telephone System for Short Toll Circuits," H. S. Black, M. L. Almquist

and L. M. Ilgenfritz, Electrical Engineering {A.I.E.E. Transactions), volume
48, January 1929, pages 117-140.

4. "A New Single-Channel Carrier Telephone System," H. J. Fisher, M. L. Almquist

and R. H. Mills, Bell Sys. Tech. Jour., volume 17, January 1938, pages 162-
183; Electrical Engineering {A.I.E.E. Transactions), volume 57, January 1938,
pages 25-33.

5. "Copper-Oxide Modulators," R. S. Caruthers, Presented at Winter Convention

of A.I.E.E., Januarv 1939.

6. "Stabilized Feedback Amplifiers," H. S. Black, Bell Sys. Tech. Jour., volume 13,

January 1934, pages 1-18; Electrical Engineering, volume 53, January 1934,
pages 114-120.

7. "Open-Wire Crosstalk," A. G. Chapman, Bell Sys. Tech. Jour., volume 13, Janu-

ary 1934, pages 19-58; April 1934, pages 195-238.

8. "The Transmission Characteristics of Open- Wire Telephone Lines," E. I. Green,

Bell Sys. Tech. Jour., volume 9, October 1930, pages 730-759; Electrical
Engineering {A.I.E.E. Transactions), volume 49, October 1930, pages 1524-
1535.

Crossbar Dial Telephone Switching System *

By F. J. SCUDDER and J. N. REYNOLDS

This paper describes the crossbar dial telephone switching system
recently adopted by the Bell System for large cities where the panel
system has been used for nearly twenty years. Central offices of
the crossbar type can be introduced in panel areas without changes
in existing offices and without changes in existing dial telephone
instruments. Crossbar offices and panel offices in the same build-
ing will operate on a common power plant and utilize other equip-
ment in common, such as "A" and " B " operator switchboards and
outgoing trunks.

The precious metal contact crossbar switches are used for all
switching purposes as contrasted with the base metal contact panel
switches. The switches operate with relay-like movements under
control of common control or marker circuits consisting primarily
of multi-contact, U and Y type relays. The control and marker
circuits, which are connected to the switch frames by means of
multi-contact relays, perform their operations in a fraction of a
second. The switches, the U and Y type relays and the multi-
contact relays are equipped with twin contacts of precious metal.
Senders similar to those of the panel system are employed.

The system will be used for new offices in larger cities as manu-
facturing and plant conditions permit.

Introduction
TT is the purpose of this paper to describe briefly the crossbar dial
^ telephone central office switching system which has recently been
developed by the Bell System for use in large cities. Sixteen years
ago, in February 1923, a paper was read before the Institute, by
Messrs. E. B. Craft, L. F. Morehouse and H. P. Charlesworth of the
Bell System which outlined the history and the problems involved in
telephone central office switching and described the panel dial central
office system which had just been developed and was being introduced
in the large cities. The first central office of this type was placed in
service in December 1921, and since that time 456 panel dial offices
serving nearly four and one-half million subscriber stations have been
installed in 26 different cities throughout the country. During these
years many improvements have been made in the panel system to
make it more serviceable to the telephone public and to meet the new

* Presented at Winter Convention of A.I.E.E., New York, N. Y., January 23-27,
1939.

76

CROSSBAR DIAL TELEPHONE SWITCHING SYSTEM 77

problems which have arisen, but in addition the engineers of the
Bell System have continued their search to find new and better means
for meeting telephone switching demands. This work has resulted in
the adoption of the crossbar type central office switching equipment.
Two offices of this type were placed in successful operation during
1938 and others are in process of manufacture and installation.

It will be appreciated that for large metropolitan areas, the develop-
ment and economic introduction of a central office switching system
which differs materially from the existing systems is a rather large
undertaking. The system must fit into the existing plant as a whole
without material change. Generally any important changes afifecting
the subscribers' use of the telephone or the methods used by switch-
board operators should be avoided. Existing numbering plans should
not be affected, existing classes of service should be continued, and
the addition of others made feasible in case they should be required.

All of these and many other factors have been taken into account
and all requirements have been met by the crossbar system which
offers important improvements in telephone switching, both in opera-
tion and maintenance. Its introduction does not make any of the
existing equipments obsolete in the sense that these equipments will
be less serviceable nor will it cause their replacement. Central offices
of the crossbar type can be installed in the same building with existing
penel central offices without loss in operating economies in either type
of office. Certain equipment, such as the existing and additional
outgoing trunks to other central offices, manually operated switchboard
positions, operating room and maintenance desks, power plant and
alarms, can be used in common by the two types of offices in the
same building.

General

Before describing the crossbar system it is desirable first to give a
brief outline of the principal functions of a dial central office equipment.
Such an office is capable of serving 10,000 subscriber line numbers,
and is provided with a sufficient number of connecting switches,
trunks and associated circuits so that under usual peak loads of traffic,
calls will be completed promptly.

The central office circuits, in response to the lifting of the receiver
by the calling subscriber, connect the subscriber line to the switching
equipment. This equipment then extends the calling line, "link by
link," through several switching stages to the called line as determined
by the called office code and line number dialed by the calling sub-
scriber. When the connection has been established to the called line,
the subscriber bell is rung and, when the subscriber answers, the

78 BELL SYSTEM TECHNICAL JOURNAL

talking connection is completed. During the conversational period
the connection is held under control of the calling telephone, and when
the telephone receivers are replaced, the central office equipment and
the telephones are released for use on other calls. The equipment,
of course, transmits the busy tone signal to the calling subscriber if
the called line is found busy, and automatically routes a call for a
discontinued or an unassigned line to an operator who informs the
subscriber of the status of such a line.

Operators and associated switchboards are provided in the dial
system to handle certain classes of calls and to render assistance to
subscribers when required. Calls to these operators are established
in response to the dialing of operators' codes in a manner similar to
the establishment of calls to other subscribers.

Operators are usually provided to complete calls terminating in a
dial office which are originated by subscribers served by manual
offices.

Prior to the introduction of the crossbar system, the Bell System
employed two general types of dial central offices. These are the
well known step-by-step and panel systems.

The step-by-step system has been used generally in the smaller
cities which are frequently served by a single central office or by a
relatively small number of offices and where the trunking problems
are consequently less complicated. The switches of the step-by-step
system are controlled directly by the impulses from the subscriber
dials and, necessarily in conformity with the dial, the system operates
on a decimal basis. The selectors of this system are first moved
under control of the dial to any one of ten vertical positions, corre-
sponding to the numeral of the digit dialed, and in the case of trunk
hunting switches is then automatically rotated over a row of ten trunk
terminals to find an idle trunk during the interdigital time of the dial.

The step-by-step switch thus has access to ten different groups of
trunk terminals with ten terminals each. The location of the trunk
groups on the switches is governed by the digits dialed and conse-
quently the relocation of a group necessitates directory changes.
These limitations in trunk access and flexibility are not material
handicaps in the smaller cities throughout the country where the
system is giving excellent service.

The panel system meets the complex service requirements of the
larger cities with their large volume of traffic and multiplicity of central
offices. In these cities the number of trunk groups is large and the
number of trunks in the groups varies widely. Further, the number of
groups and their sizes are frequently changed by the introduction of

CROSSBAR DIAL TELEPHONE SWITCHING SYSTEM 79

new ofiices and changes in the character or extent of existing central
office areas.

In the panel system, senders are provided which record and store
the dial pulses as they are dialed and then independently control the
operation of the switching units. The large panel type switches
provide access to large groups of trunks and to a large number of
groups, and at the same time permit considerable variation in the sizes
of the groups. The necessary flexibility in the size and location of the
trunk groups is obtained by flexibly wired routing equipment provided
in decoder circuits which are associated with the senders. These
facilities permit trunk group locations on the switches as dictated by
traffic regardless of the office codes listed in the directories and dialed
by the subscribers. The panel system also readily provides for the
routing of calls through intermediate or tandem offices where the
traffic between offices can be more economically handled in this
manner.

The crossbar system also makes use of the sender and decoder
method of operation and provides a still greater flexibility in the
trunking arrangements than is obtained by the panel system.

The Crossbar System

The two outstanding features of the crossbar system are the "cross-
bar switch" which is used for all major switching operations, and the
"marker" system of control which is used in the establishment of all
connections throughout the crossbar office.

The crossbar system is essentially a relay system employing simple
forms of relays and relay type structures for all switching operations.
The apparatus consists almost wholly of crossbar switches, multi-
contact relays and the usual small relays similar to those generally
employed in all telephone systems. The switching circuits are wired
to the contacting springs of the switches, and the connections through
the switches are made by pressing contacts together by means of
simple electromagnetic structures instead of the moving brushes and
associated fixed bank terminals of other systems.

The use of rela}^ type apparatus with its small, pressure type
contact surfaces economically permits the use of twin or double
contacts with thin layers of precious metal for all contact points.
Obviously, double precious metal contacts make for reliable operation,
especially with the low speech and signaling currents inherent to a
telephone system.

The short mechanical movements and the inherently small operating
time intervals of the "relay-like" crossbar switch permit the use of

80 BELL SYSTEM TECHNICAL JOURNAL

common circuits or "markers" to control the operation of the switches.
This has permitted the use of large assemblies of switches and asso-
ciated relays on unit frames which can be wired and completely tested
for operation in the factory before the units are shipped.

In the design of the switching frames and associated control circuits,
one of the objectives realized has been the standardization of a rela-
tively small number of different types of equipment units, thereby
simplifying manufacture and merchandizing. This also simplifies the
engineering of the equipment by the Telephone Companies in the
preparation of their specifications to meet the particular trafitic
requirements of the various central offices.

The marker system used for controlling the switching operations
has many advantages, the more important of which will be disclosed
later in the general description of the operation of the equipment.
It might be mentioned here, however, that the marker is an equipment
unit consisting almost entirely of relays, which completes its functional
operations in the establishment of a call in a fraction of a second.
This short operating time permits a few markers to handle the entire
traffic in the largest office. The markers are connected momentarily
by means of multi-contact relays to the various switching units of
the office to control the establishment of the calls through the crossbar
switches.

An outstanding advantage of the marker system of control is the
"second trial " feature, by means of which two or more attempts can be
made to establish a call over alternate switches and trunks when the
normally used paths are all busy. The markers are arranged to
detect short-circuited, crossed, grounded and open-circuit conditions
at all vital points, and before releasing from a connection they make
circuit checks to insure that the connection has been properly estab-
lished. When trouble conditions are detected, they make a second
attempt to complete the connection, after sounding an alarm and
recording the location and nature of the trouble encountered. The
marker system facilitates the introduction of new service features and
changes in operation, which may be found desirable from time to
time, due to the fact that the principal controlling features of the
entire system are vested in a small number of markers.

Apparatus
Crossbar Switch
The crossbar switch from which the system derives its name is the
basic switching unit of the system. Figure 1 shows the front view of
a 200-point crossbar switch.

CROSSBAR DIAL TELEPHONE SWITCHING SYSTEM

U

82 BELL SYSTEM TECHNICAL JOURNAL

Fundamentally this switch consists of three major functional parts:
(a) twenty separate vertical circuit paths, {h) ten separate horizontal
circuit paths, and (c) a mechanical means for connecting any one of
the twenty vertical circuit paths to any one of the ten horizontal
circuit paths by the operation of electromagnets. From a structural
viewpoint the switch is comprised of a rectangular welded frame on
which are mounted twenty vertical units and the selecting mechanism
consisting of five horizontal bars operated by ten selecting magnets.

Primarily the switch is a multiple relay structure with twenty
vertical relay-like units, each unit having an operating or "holding"
magnet and ten sets of contacts in a vertical row. The switch arrange-
ment provides a rectangular field of contacts in twenty vertical rows
and ten horizontal rows or a total of 200 sets of contacts, one set at
each "crosspoint." These crosspoint contacts are operated inde-
pendently of each other by a coordinate operation of the horizontal
and vertical bars. The horizontal bars are controlled by the ten
horizontal or "selecting" magnets and the vertical bars by twenty
vertical or "holding" magnets. Any set of contacts in any vertical
row may be operated by first operating the selecting magnet corre-
sponding to the horizontal row in which the set of contacts is located,
and then by operating the holding magnet associated with the vertical
row. Since the contacts are held operated by the holding magnet
alone, the selecting magnet is operated but momentarily and is
released as soon as the holding magnet is operated. After the selecting
magnet is released, other connections may be established through the
switch by the operation of other selecting and holding magnets. It is
thus apparent that ten connections can be established through the
switch, one for each of the horizontal paths.

From Fig. 2 the rather simple mechanical interlocking of the
horizontal and vertical bars which causes the operation of a set of
crosspoint contacts will be understood. The ten sets of contacts in a
vertical row are associated with the vertical or "holding" bar of the
row. Each horizontal or "selecting" bar is provided with twenty
selecting fingers which are made of flexible wire. These fingers are
mounted at right angles to the bar, one at each of the vertical rows of
contacts. Thus when a selecting bar is rotated through a small arc
by its magnet, the selecting fingers will move up or down into a
position so that when a holding bar is operated by its magnet, it will
engage the selecting finger at the crosspoint of the two bars and cause
the corresponding set of contacts to operate. The selecting bar and
the fingers not used will then be released when the selecting magnet
is released, but the selecting finger used to operate the selected set of

CROSSBAR DIAL TELEPHONE SWITCHING SYSTEM

83

crosspoint contacts will remain latched and the contacts held closed
by the holding bar until the holding magnet is released at the end of
the connection. The selecting fingers are each provided with a
damping spring to reduce vibration on the operation and release of
the fingers.

ADJUSTABLE
SUPPORT FOR
SELECTING
FINGER .

OPERATING
SPRING

CONTACT
MULTIPLE

Fig. 2 — Crossbar switch selecting mechanism.

It will be noted that the selection operation is performed by five
horizontal bars although there are ten horizontal rows of contacts.
This is accomplished by operating the bars in either of two directions.
As shown in Fig. 1, two magnets are associated with each bar, one
whose armature is on top of the bar, the operation of which causes
the selecting fingers to move in a downward direction, and the other
whose armature is below the bar causing the fingers to move upward.
The selecting bars are restored to the normal or mid-position by the
centering springs located on the end of the switch adjacent to the
magnets.

Figure 3 shows the vertical unit of the crossbar switch with its ten
sets of normally open ' ' make " type contact springs, the holding magnet
at the bottom, and the long vertical armature to which is attached

84

BELL SYSTEM TECHNICAL JOURNAL

Fig. 3 — Crossbar switch vertical unit.

the vertical holding bar. The vertical unit shown has six pairs of
contacts at each of its ten crosspoints. Other vertical units are
provided with ten sets of 3, 4 and 5 pairs of contacts per set. One
spring of each pair as shown is a fixed spring consisting of a projection
of an insulated vertical metal strip, made in the shape of a comb.
This strip extends from the top to the bottom set of contacts of a
vertical row. Wiring lugs are provided at the lower end of these
vertical strips facing the rear to which are wired the lines or trunks

I

CROSSBAR DIAL TELEPHONE SWITCHING SYSTEM 85

of the vertical circuit paths. At the lower end of these strips and
facing the front is another projection used by the maintenance force
for testing purposes. The mate or movable spring of each pair is
individually insulated from all other springs. These springs extend
to the rear of the switch for wiring purposes and may be strapped
horizontally to the corresponding springs of adjoining vertical units
to extend the horizontal circuit path through the switch.

The contacting ends of the thin movable contacting springs are
bifurcated to provide two flexible contacts in parallel. The con-
tacting surfaces on these springs as well as the mating fixed springs
are provided with a thin layer of palladium. The use of the double
precious metal contacts is an important feature of the crossbar system
in providing more reliable contacting surfaces. Experience has shown
that the chance of simultaneous failures of both contacts of a pair is
extremely small. The actual contacting surfaces of each pair of
springs consist of small bars of contact metal located at right angles
to each other. These bars are composed of a ribbon of nickel capped
with a thin layer of palladium. This crossbar arrangement of contacts
provides a rather large area over which the two springs can make
contact with each other, and thereby permits considerable tolerance
in the manufacture and adjustment of the contact spring assemblies

The switch may be equipped with "off normal" contact spring
assemblies. When these are furnished they are associated with each
selecting or holding magnet and are operated like relay contacts when
the associated magnet operates, regardless of which crosspoint contact
is closed. They are used to perform circuit functions as required in
the. various uses of the switch.

In the design of the switch special attention was given to the
problem of wiring and cabling. Figure 4 shows the wiring terminals
on the rear of the switch. These terminals are arranged for individual
wiring and also have staggered, notched projections so that the
terminals can be readily strapped together horizontally with bare
wire as shown. This is an important feature of the switch since it
permits a multiple of terminals to be easily soldered together and
reduces the wire congestion on the switch:

The 200-point crossbar switch is 9j inches in height and 30| inches
in length. In addition a 100-point switch 20| inches in length is
provided. This switch is similar to the 200-point switch but is
equipped with 10 vertical units.

BELL SYSTEM TECHNICAL JOURNAL

CROSSBAR DIAL TELEPHONE SWITCHING SYSTEM

87

Multi-Contact Relay

The multi-contact relay used in the crossbar system is shown in
Fie:. 5. It resembles in design the vertical unit of a crossbar switch.

%

Fig. 5 — Multi-contact relay.

The relay is provided in four sizes in respect to the number of contacts,
namely, in 30, 40, 50 and 60 sets of individually insulated contacts,
all of which are of the normally open type which are closed when the
magnets of the relay are operated. Each relay is provided with two
separate magnets, armatures and associated groups of springs, and
both magnets are energized in parallel in order to close all of the
contacts. By operating the two magnets independently the structures
can be used as two separate relays, each equipped with 15, 20, 25 or
30 sets of contacts. The relay occupies a mounting space approxi-
mately 2" X 11" and is provided with a cover.

All contact springs are equipped with twin contacting surfaces
similar to the contacts used on the crossbar switch except that they
are composed of solid bars of precious metal due to the heavy duty
requirements. To facilitate wiring, these relays are manufactured
with two types of wiring terminals. In one type the movable springs
are of graduated lengths and are provided with notched lugs for bare
wire strapping to permit the multipling of springs horizontally to
corresponding springs on other relays mounted adjacent. In the
second type the strapping lugs are omitted and all springs are of the

88 BELL SYSTEM TECHNICAL JOURNAL

same length and are provided with soldering eyelets for individual or
non-multiple wiring.

The multi-contact relay finds its chief use in the common connector
circuits where a large number of leads must be connected simultane-
ously to a common circuit.

U and Y Type Relays

New and improved general purpose small relays which have been
coded the "U" and " Y" type are used in this system. Figure 6 shows
a typical "U" type relay. Although somewhat similar to the E and
R type relays which have been in a common use in the telephone
systems for many years, it differs from them principally in that it
has a heavier and more efficient magnetic structure which permits
the use of a greater number of contact springs. These relays permit
the use of spring assemblies up to a maximum of 24 springs in various
combinations of springs, including transfer contacts, simple make-
and-break contacts. The relays are constructed of relatively simple
parts, most of which are blanked and formed in the desired shapes in
the same manner as the earlier E and R type relays. The cores are
made from round stock and are welded to the mounting bracket of
the relay. The structures of all of these relays are similar and differ
principally in their spring assemblies and windings.

In order to insure more reliable contact closures, the relays are
equipped with twin contacts. Various types of contact metal and
sizes of contacts are provided, depending upon the characteristics of
the circuit controlled by the contacts.

Improved methods of clamping the springs in their assemblies,
together with the design of the springs, provide stability and minimize
manufacturing and maintenance adjusting effort.

Contacts practically free from chatter on both the operation and
release of the relay have been obtained by the use of relatively heavy
stationary springs, short thin movable springs, and a pivoted arrange-
ment of the armature suspension. By reference to Fig. 6 it will be
seen that the rear ends of the armature are pivoted by two pins which
project through holes in the hinge bracket mounted on the rear spring
assembly. In the earlier flat type relays of the E and R type, the
armature was suspended at the rear by means of a reed type armature
hinge.

The Y type relays make use of the same manufacturing tools and
processes as the U type. Copper or aluminum sleeves are provided
over the cores beneath the windings to secure the slow-release char-
acteristics required on these relays. The relay armature is embossed

I

CROSSBAR DIAL TELEPHONE SWITCHING SYSTEM

89

SO that when the relay is operated satisfactory contact is made between
the metal surfaces of the magnetic circuit which insures uniform time
characteristics.

In both the U and Y type relays the cyhndrical cores permit the use
of form wound coils which are wound on special machines and slipped

Fig. 6 — "U" type relay.

over the cores when completed. In the manufacture of these coils a
removable mandrel is used. It is covered with a layer of sheet cellu-
lose acetate and accommodates several coils. These coils are then
automatically wound on the mandrel from different spools of insulated
wire. Separations are left between adjacent coils so that when the
winding operation has been completed the individual coils can be sepa-
rated. A very thin sheet of cellulose acetate is automatically inter-
leaved between successive layers of wire to hold the wire in place and to
provide insulation between layers. This general method of winding
coils also is used for the magnets of the crossbar switches and multi-
contact relays.

Functions of the Equipment Units

The general operation of the system as a whole may be more easily
understood by first describing the principal equipment units in the
system and their functions before proceeding with a description of the

90

BELL SYSTEM TECHNICAL JOURNAL

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CROSSBAR DIAL TELEPHONE SWITCHING SYSTEM 91

operation of the circuits. A simplified block diagram of the principal
equipment units of the system is shown in Fig. 7. It will be noted
that in general there are three types of equipment units:

1. The transmission battery supply and supervisory circuits consisting

of the "district junctors" and the "incoming trunks."

2. The crossbar switch frames.

3. The common "control" circuits, the "senders" and the "markers."

The "district junctor" and the "incoming trunk" circuits are
composed principally of small relays. The district junctors furnish
the talking battery for the calling subscribers and supervise the
originating end of connections. The incoming trunks control the
ringing of the called subscriber bells, furnish talking battery for the
called subscribers, and supervise the terminating end of connections.

The switch frames, which consist almost entirely of crossbar switches,
provide the means for switching between the subscriber lines, the
district junctors and the incoming trunks. Switch frames also are
used for switching the district junctors and the incoming trunks to
the senders.

The "senders" consist principally of small relays and their functions
are similar to those of the operators at a manual switchboard. The
"subscriber senders" register the called numbers from the subscriber
dials and transmit the necessary information to the "markers," to
the "terminating senders" and to the manual operator positions in
manual offices for completing connections to the called lines. The
subscriber senders also control the operation of the selectors in distant
panel offices. The "terminating senders" in the terminating end of
the crossbar office receive the numerical digits of the called numbers
from the subscriber senders of any dial office and transmit the required
information to the "terminating markers" for setting up the connec-
tions to the called lines.

The "markers" are the most important control circuits in the
system. They are composed of both small and multi-contact relays.
There are two types, one for originating traffic and one for terminating
traffic. The operating time of the markers is short, considerably less
than one second, and consequently only three or four markers of each
type are required in the average office.

The "originating markers" determine the proper trunk routes to
the called office. They have access to all outgoing trunk circuits and
all the crossbar switch frames that are used for establishing the
connections to the called office trunks. They test the trunk group
to find an idle trunk to the called office, and also test and find an idle

92 BELL SYSTEM TECHNICAL JOURNAL

channel through the switch frames, and finally operate the proper
selecting and holding magnets of the crossbar switches to establish
the connections from the subscriber line to the trunk circuit.

The "terminating markers" perform similar functions in the
terminating end of the office to set up the connection from the incoming
trunk circuit to the called subscriber line. They have access to all of
the subscriber lines terminating in the office, and to all crossbar
switch frames used for connecting to subscriber lines. 'They test the
called line to determine whether it is idle, and also test for and find an
idle channel through the switch frames and finally operate the proper
magnets of the crossbar switches and establish the connection to the
called subscriber line.

In addition there are common "control" circuits associated with
the "line link" and the "sender link" frames for controlling the
operation of the switches on these frames. There are also the common
"connector" circuits, consisting mainly of multi-contact relays, which
are used for connecting the markers to the senders, to the switch
frames and to the test terminals of the called subscriber lines.

It should be noted that the line link frames, although shown sepa-
rately, are used for both originating and terminating traffic.

After the talking connection has been established between two
subscribers, all of the common control units, such as the senders,
markers, connectors, line link control circuit, and the sender link
frames and their associated control circuits, will have been released,
and the talking connection will be maintained in this condition by
the holding magnets of the crossbar switches used on the line link,
district, office and incoming link switch frames. These switch
magnets are held operated under control of the supervisory relays in
the district junctor and the incoming trunk circuits and are released
when the subscribers replace the receivers.

Trunkinc; Arrangements

The fundamental method of using the crossbar switch for setting
up connections is illustrated in Fig. 8. This figure shows a 200-point
crossbar switch with twenty vertical units each wired to a subscriber
line and ten trunks strapped horizontally across the switch. With
such an arrangement, any one of the twenty lines may be connected
to any one of the ten trunks. The number of lines which can be
connected to the same ten trunks may be increased to forty by adding
a second 200-point crossbar switch with twenty difi^erent lines con-
nected to its verticals and by wiring the horizontal contact multiple
of this second switch to the horizontal multiple of the switch shown

CROSSBAR DIAL TELEPHONE SWITCHING SYSTEM

93

FROM 20 LINES

^

0 1 2 3 4 5 6 7 & 9 10 II 12 13 14 15 16 17 le 19

\,

■*■ 9
-»• 8
-^ 7
-»■ 6
-»• 5

TO TEN
TRUNKS

Fig. 8 — Simple trunking arrangement with a single 200-point crossbar switch.

in Fig. 8. By adding other switches in this manner, any number of
lines may be given access to the ten horizontal trunks.

To obtain greater trunking access, two groups of switches known as
"primary" and "secondary" are used. Figure 9 illustrates this
primary and secondary switch arrangement as used in the "line link"
switch frames and in various forms throughout the crossbar office.

SUBSCRIBER
LINES

t t

DISTRIBUTING
FRAME

FRAME SERVES
150 TO 700 LINES

^

TRAFFIC

/

/

FRAME HAS
ACCESS TO
100 DIST JUNCTORS
100 LINE JUNCTORS

PRIMARY SECONDARY

Fig. 9 — Primary-secondary trunking arrangement.

94 BELL SYSTEM TECHNICAL JOURNAL

The switches are arranged in two vertical files of ten primary switches
and ten secondary switches. There are twenty subscriber lines
connected to the verticals of each of the ten primary switches and
twenty trunk circuits are connected to the twenty verticals on each
secondary switch. The horizontal multiples on the primary switches
are connected to the horizontal terminals of the secondary switches,
each primary switch having one horizontal path connected to each of
the ten secondary switches. With this arrangement, the twenty lines
of any primary switch have access to all 200 trunks connected to the
secondary switches. Since all of the primary switches are wired in
this manner, that is, with their ten horizontal paths distributed over
the ten secondary switches, then all of the 200 lines on the primary
switches have access to the 200 trunks on the secondary switches.
It is evident that another vertical file of ten primary switches may be
added with twenty subscriber lines connected to the verticals of each
switch, and with the horizontal paths strapped and connected to the
horizontal paths of the primary switches shown. This would give
400 lines access to the 200 trunks on the secondary switches. In
actual practice on a line link frame, several files of primary switches
may be connected together in this manner depending upon the traffic
volume of the subscriber lines. The circuit paths connecting the
horizontal rows of terminals of the primary switches to the horizontal
rows of terminals of the secondary switches are called "line links."

To establish a path from a line circuit on a primary switch to a
trunk circuit on a secondary switch, the common "control" circuit
serving this line link frame locates the subscriber line to be served and
then simultaneously selects an idle "line link" on the primary switch
on which the subscriber line appears and a group of trunks wired to a
secondary switch in which there are one or more idle trunks. Thus
the selection of the line link is made contingent upon the availability
of trunks, and by means of this together with the primary-secondary
distribution of the links a very efficient usage of the links and trunks
is obtained.

In the "line link" frame shown in Fig. 9, it will be seen that the
trunks on the verticals of the secondary switches are split into groups
of 100 trunks each, one group being connected to the "district junc-
tors" and used for originating traffic and the other group of 100
trunks being connected to "line junctors" and used for terminating
traffic.

It will be noticed that there is but one crossbar switch appearance
of a subscriber line in the office. This is on a vertical unit of a primary
crossbar switch where both the originating and terminating calls are

CROSSBAR DIAL TELEPHONE SWITCHING SYSTEM

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completed by means of the same line link circuits. Thus all originating
traffic from any of the twenty lines on any primary switch flows
through the associated ten line links to the 100 district junctors and
all terminating traffic to these twenty lines flows through the same
ten line links from the 100 line junctors.

This single "primary and secondary" trunking arrangement also is
used at other points in the system, such as in the originating and
terminating sender link switch frames, where the circuits reached are
non-directional, that is, where any one of the selectable circuits wired
to the frame can be used for setting up a connection.

For the switch frames where the circuits reached are directional,
that is, where a particular called line or a particular group of trunks
must be used in order to complete a connection, the problem of trunking
becomes more complex and it is necessary to provide a trunking
arrangement using two "primary and secondary" switch frames
arranged in tandem.

Figure 10 shows a typical arrangement of this kind which is necessary
to secure the required trunking flexibility and efficiency. This figure
shows an "incoming link" frame to which incoming trunks are con-
nected and a "line link" frame to which subscriber lines are connected
as described above. These two frames are used in tandem for estab-
lishing the terminating connections between the incoming trunks and
the called subscriber lines. As is indicated, 100 incoming trunks are
connected to the 100 horizontal paths of the ten incoming link frame
primary switches, there being ten incoming trunks connected to each
of the primary switches. A total of 150 to 700 subscriber lines may
appear on the verticals of the primary switches of the line link frame;
however, only 200 lines or twenty on the verticals of each of the ten
primary switches are shown in the figure.

In order to connect a particular incoming trunk to a particular
called line, an idle channel is selected through these two switch frames,
consisting of an "incoming link" on the incoming link frame, a "line
junctor" between the two frames and a "line link" on the line link
frame, and all are connected in series as shown in the figure. It will
be noted that the incoming trunks on each of the primary switches
have access to twenty incoming links appearing on the twenty verticals
of the switch. These twenty incoming links are distributed over the
ten secondary switches of the frame, two links being connected to
each switch, one to each half switch. It will be observed that in
order to provide for the distribution of the twenty incoming links
over the ten secondary switches, the horizontal paths of the secondary
switches are separated between the tenth and eleventh verticals,

CROSSBAR DIAL TELEPHONE SWITCHING SYSTEM 97

thus taking advantage of the flexibiHty of the crossbar switch by pro-
viding twenty horizontal paths instead of ten on each switch. The
incoming links, on each half of these secondary switches, have access
to "line junctors" appearing on the verticals of these switches.
These line junctors are in turn distributed over the secondary switches
of all the line link frames in the office. There will be at least one
line junctor as shown, from each secondary switch on an incoming
link frame to a secondary switch on every line link frame in the office,
or a minimum of ten line junctor paths between any incoming link
frame and any line link frame. The number of the line junctors
between these frames will vary depending upon the number of frames
required in an office. The line junctors on the verticals of each of
the line link frame secondary switches in turn have access to ten
line links on the horizontal paths. These ten line links are, as described
above, distributed over the primary switches of the line link frame,
one to each primary switch. These line links then have access to the
called subscriber lines which appear on the verticals of the primary
switches. With this arrangement of switches and the three groups
of interconnecting link paths, any incoming trunk can be connected
to any called line on the line link frame shown, or by means of other
groups of line junctors, to a called line on any other line link frame
in the office.

Terminating markers are employed for selecting the paths through
these switches to connect an incoming trunk to a called subscriber
line. The marker, as will be explained later, records information
which permits it to connect to the test wire and holding magnet of a
called line and to the test wires and switch magnets of the groups
of incoming links, line junctors and line links through which the
incoming trunk may be connected to the called line. The marker
simultaneously tests these three groups of paths and "marks" an
incoming link, a line junctor and a line link which are idle and are
accessible to one another, and then operates the switch magnets to
connect these three paths and the incoming trunk and the called line
together. The paths are selected in an ordered arrangement, so that
the lowest numbered incoming links, line junctors and line links are
preferred and are used as long as they are available. This increases
the efficiency of the paths as compared with a random selection, since
it reduces the chance that one or two of them although idle cannot be
used because the third one is busy.

A double primary and secondary trunk arrangement similar to the
one shown in Fig. 10 is employed for connecting district junctors to
outgoing trunks in the originating end of the office.

98 BELL SYSTEM TECHNICAL JOURNAL

Brief Description of Circuit Operation
The operation of the system will be described by tracing the progress
of a call through the system. The establishment of a call from one
crossbar subscriber to another crossbar subscriber may be divided into
four stages: two in the originating end of a connection and two in
the terminating end.

1. The calling subscriber is connected to a sender for the purpose of
registering the called number which is dialed.

2. The subscriber sender is connected to an originating marker and
the marker selects the switch frames for establishing the connection to
an outgoing trunk.

3. The outgoing trunk circuit is connected to a sender in the termi-
nating end to register the called number.

4. The terminating sender is connected to a terminating marker and
the marker selects the switch frames for establishing the connection
to the called subscriber line.

The first stage in the progress of a call is illustrated in Fig. 11.
It will be seen that the line of a calling subscriber terminates on a
vertical unit of a primary crossbar switch located on a line link switch
frame. When the subscriber receiver is lifted from the telephone
preparatory to dialing, a line relay is operated, as in other systems, and
the circuits proceed with the establishment of the connection to an
idle subscriber sender which will register the called number when it
is dialed.

The circuit functions on this stage of the call are as follows:
1. The subscriber line is located by the "line link control" circuit
which is common to the line link frame, by a coordinate method of
testing. That is, the control circuit determines the primary crossbar
switch in which the line is located and the particular vertical unit in
the switch on which the line is terminated. This operation is similar
to the line finder operation in other dial systems, except that the
operation is accomplished by relay operations instead of by a mechani-
cally traveling brush.

2. The line link control circuit then simultaneously selects an idle
line link between the primary switch in which the line appears, and a
secondary switch on which a group of district junctors appears which
has at least one idle district junctor in the group and which has
access to idle senders and an idle sender link.

3. This will bring into operation the common "sender link control"
circuit of the sender link switch frame to which the selected group of
district junctors is connected. This control circuit will select an idle
district junctor in this group which appears on a primary switch on

CROSSBAR DIAL TELEPHONE SWITCHING SYSTEM

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the sender link frame. There are ten sender Hnks serving the selected
district junctor. These ten sender links and the ten sender groups to
which they have access on the secondary switches are then tested
simultaneously to find an idle sender link with access to a group of
senders in which there are one or more idle senders. When this
choice has been made an idle sender in the group is then selected.

4. The two control circuits in cooperation with each other first oper-
ate the selecting magnets and then the holding magnets associated
with the paths selected on the switches of both the line link and sender
link frames, and thereby establish the connection from the calling
subscriber to an idle subscriber sender.

This connection may be traced by referring to Fig. 11, from the
calling line on the vertical unit on a primary switch of the line link
frame, through a line link and a secondary switch, through a district
junctor circuit, to a vertical unit on a primary switch of the sender
link frame, through a sender link and a secondary switch to a subscriber
sender which is connected to a horizontal circuit path on the secondary
switch.

5. The two control circuits are then released and made available
for use on other calls. The connections through the switches to the
sender are held established by means of the holding magnets which
are held operated over a signal control lead, called the "sleeve" lead,
under control of the relays in the sender, which in turn are under
control of the subscriber telephone.

Upon completion of these operations which take but a fraction of a
second the subscriber sender transmits the dial tone to the calling
subscriber as an indication to dial the number. When the subscriber
dials, electrical impulses are transmitted to the sender, which receives
and registers them. When the sender has registered the office code,
which in New York City for example is contained in the first three
digits dialed, the sender will connect itself to an idle originating marker
by means of multi-contact relays of a marker connector circuit.

Before proceeding further it is desirable to mention several other
functions of the two common control circuits used for setting up this
part of the connection.

1. The control circuits signal to the sender the class of the calling
line, that is, for example, whether the line is a coin line or a non-
coin line.

2. The sender link control circuit signals to the sender the number
of the district link switch frame on which the selected district junctor
appears, since this identification will be used later in the establishment
of the connection.

CROSSBAR DIAL TELEPHONE SWITCHING SYSTEM 101

3. The sender link control circuit tests the circuit paths chosen
from the line circuit to the sender before disconnecting from the
connection, in order to insure the proper establishment of the con-
nection. In case of a failure the control circuits will make repeated
trials to establish the connection over different paths and give an alarm
to the maintenance force.

4. Emergency control circuits are provided for use in case the
regular control circuits are removed from service for maintenance
reasons.

The next stage in the progress of the call is illustrated in Fig. 12.
In this stage of the call the principal control unit is the originating
marker. Its major function is to control the switches in the establish-
ment of the connection to an idle outgoing trunk circuit to the called
office, which may terminate in a distant office or in the same office as
the calling subscriber.

When the subscriber sender connects to the originating marker
through the connector circuit, the sender transfers the called office
code indication and the district link frame identification to the marker
circuit. The called office code indication causes the operation of a
"route" relay in the marker corresponding to the particular office
called.

There are a number of "route" relays in each marker and one is
assigned to each called office routing. The route relay is connected
as required by the office code to which it is assigned, so that it will
direct the marker to the trunks of the called office and to the office
link switch frame on which these trunks appear and indicate the
number of trunks in the group. The route relay also is connected to
determine the type of the called office, such as Crossbar, Panel, or
Manual, and to set up the corresponding circuit conditions in the
subscriber sender to enable the sender to handle the connection
properly after the marker has been released. The connections of
the route relay contacts to the control relays in the marker are made
flexible so as to permit the assignment of any route relay to any
office code and to permit changes to be made from time to time in the
route information, changes in trunk group sizes and location, changes
in the type of terminating office, etc. The route relays and associated
flexible connection facilities represent a considerable portion of the
marker equipment, especially in large metropolitan offices where
several hundred central offices are involved.

When the route relay is operated, the marker proceeds with the
establishment of the connection as follows:

1. It connects to the office link frame on which the trunks to the

102

BELL SYSTEM TECHNICAL JOURNAL

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CROSSBAR DIAL TELEPHONE SWITCHING SYSTEM 103

called office appear. This connection is made through the office Hnk
frame connector circuit, one of which is provided for each office Hnk
frame. Through this connector the marker is extended to the test
leads of any desired trunk group on the office link frame and to the
crossbar switches of the frame. When so connected the marker has
exclusive control of the trunks and switches of the frame and other
markers which desire connection to the same frame are deprived of
access until the connected marker releases.

2. The marker next tests the outgoing trunks to the called office and
selects an idle one. If, as determined from the route relay, the trunks
are divided over more than one frame, the marker will connect to
the second group of trunks on the second office link frame in case the
first group of trunks is found to be busy..

3. The marker also connects by means of a connector circuit to
the district link frame associated with the district junctor to which
the calling line is connected. The identification of this frame was
obtained from the sender and the sender link control circuit as pre-
viously mentioned. Through the connector circuit of the district link
frame the marker is extended to the control leads of the district
junctor circuit and the crossbar switches of the district link frame.
As in the case of the office link frame, only one marker is connected to
a frame at a time.

4. The marker after selecting an idle trunk circuit which appears
in a horizontal circuit path on one of the secondary switches of the
office link frame, then proceeds with the selection of an idle channel
through the switches of the two switch frames. A number of these
connecting channels is provided between the district junctor and the
outgoing trunk. Each channel consists of a "district link" on the
district link frame, of an "office link" on the office link frame, and an
"office junctor" connecting the district Hnk frame to the office link
frame. The marker tests a group of these channels simultaneously
and selects an idle one. It then operates the switch magnets which
will connect these three paths of a channel, and the district junctor
and the outgoing trunk together, thereby establishing a connection
from the district junctor to the outgoing trunk.

5. When the marker has completed this operation it checks the
connection to insure that it has been properly established and that
it is capable of being held under control of the district junctor, before
releasing itself from the connection.

6. The marker performs these functions in approximately .5 second,
then releases and becomes available for use on other calls.

It will be observed that the three links involved in establishing the

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BELL SYSTEM TECHNICAL JOURNAL

connections between the district junctors and the outgoing trunks are
used in series and are chosen simultaneously. Generally in other
systems the establishment of a connection involving three such paths,
is made in three successive stages with a possibility that after a
selection has been made at one stage it will be found that the paths
accessible to it are all busy and, therefore, the connection cannot be
completed

Before describing the next stage in the establishment of a call,
it is desirable to point out other features and functions of the origi-
nating marker.

1. The marker permits wide variations in the sizes of trunk groups,
permitting trunk groups as small as two and as large groups as may
be required. This makes for an efficient use of the office link frame
terminals and thereby tends to reduce the office link frame equipment.

2. The marker makes a second trial to establish connections over
alternate trunk routes in case calls cannot be completed over the
normally used groups because of busy conditions.

3. The marker makes a continuity test of the circuits over which
the switches are controlled and tests them for short-circuits, crosses,
opens and grounds which would interfere with the proper establish-
ment of a call and where troubles are detected, it signals this condition
to a common "trouble indicator" where an indication of the trouble
and its location is recorded and a maintenance alarm given. The call
is then completed over another group of circuits.

The first stage in the progress of the call through the terminating
end of a crossbar office is illustrated in Fig. 13. It consists of con-
necting the incoming end of the selected trunk to a terminating sender
for the purpose of receiving the number of the called line from the
subscriber sender.

When the incoming trunk is selected by the originating end of the
office equipment, the "sender link control" circuit associated with the
terminating sender link frame on which the incoming trunk appears,
is called into action. The control circuit then proceeds with the
following functions:

1. To locate the incoming trunk circuit, which appears on one of
the ten horizontal paths of a primary switch.

2. It selects an idle sender link between this primary switch and a
secondary switch on which there is an idle terminating sender.

3. The control circuit selects one of the idle terminating senders
reached through the secondary switch and then operates the selecting
and holding magnets associated with the selected circuits, which will
establish the connection from the incoming trunk to the terminating
sender.

CROSSBAR DIAL TELEPHONE SWITCHING SYSTEM

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4. The control circuit will signal to the terminating sender the
number of the incoming link frame in which the incoming trunk
appears. This frame identification will be used later in establishing
the connection to the called line.

5. The control circuit will then disconnect after checking to insure
that the connection to the sender has been properly established and
that it will be held under control of the trunk and sender circuits after
the control circuit leaves the connection.

As soon as this operation has been completed, which takes but a
fraction of a second, the terminating sender will be in direct connection
with the subscriber sender in the originating end of the connection.
This path may be traced, by referring to Fig. 13, from the subscriber
sender through the sender link frame, through the district junctor,
through the district link and office link frames, over the outgoing
trunk to the incoming trunk, and through the terminating sender link
frame to the terminating sender.

At this stage of the connection the calling subscriber is still con-
nected with the subscriber sender, and dialing may be still in progress.
As the subscriber proceeds with the dialing of the digits of the called
number, the subscriber sender will transfer them to the terminating
sender. This is done by means of impulses transmitted over the
circuit paths between the two senders. When the subscriber sender
has completed the transfer of the called number to the terminating
sender, the subscriber sender will be released and the calling line
will then be connected through the district junctor to the incoming
trunk.

When the terminating sender has secured the record of the called
line number, the sender then connects to an idle terminating marker
by means of multi-contact relays of a connector circuit.

The next stage in the progress of the call is shown in Fig. 14. The
terminating marker is the principal control unit at this point in the
connection. Its principal function is to provide means for establishing
the connection from the incoming trunk to the called subscriber line.

When the terminating sender has connected to the terminating
marker, the sender will transfer both the called line number and the
incoming link frame identification to the marker. The terminating
marker then proceeds to establish the connection to the called line as
follows :

1. It connects itself to the particular "number group connector"
circuit including the "block relay" frame in which the called line
appears in its numerical sequence. All subscriber lines are provided
with a set of three test terminals which appear on the block relay

CROSSBAR DIAL TELEPHONE SWITCHING SYSTEM

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frame. These terminals correspond to the director number of the
subscriber Hne. A number group connector generally has access to
the test terminals of several hundred line numbers depending on the
terminating traffic to the lines.

2. The marker will obtain a connection through the number group
connector to the busy test terminal of the particular called line and
determine whether the line is busy or idle.

3. It will determine from the two other test terminals, the identifica-
tion of the line link frame where the called line appears, and the hori-
zontal group of line links which has access to the called line. In addi-
tion, it determines the type of ringing to be applied to the called line
from the circuit conditions on the test terminal.

4. Assuming that the called line is idle, the marker will connect,
through the line choice connector circuit, to the line link frame and to
the ten line links which have access to the called line.

5. It will then connect, through the connector circuit, to the in-
coming link frame associated with the incoming trunk to which the
calling subscriber line is now connected. The incoming link frame
identification was obtained from the sender link control circuit
through the sender as previously mentioned.

6. The marker will then select an idle channel through the incoming
link and line link frames as previously described. This channel will
consist of an "incoming link," a "line junctor," and a "line link" all
to be connected in series. The marker then operates the proper
selecting and holding magnets of the crossbar switches in each frame
which establishes the connection from the incoming trunk to the called
subscriber line.

7. The marker will then cause the incoming trunk to start the
proper ringing over the called subscriber line and to transmit the
ringing tone signal over the trunk to the calling subscriber.

8. At this point the terminating marker and the terminating sender
will have completed their functions and, together with the terminating
sender link frame, will be released. The complete connection will then
be established from the calling line to the called line and the con-
versational circuit completed when the called subscriber answers.

If the terminating marker finds the called line busy it will cause the
incoming trunk circuit to transmit a busy tone to the called subscriber.
The terminating marker has the following other important functions:
1. If the call is for a PBX (Private Branch Exchange) the condition
on one of the test terminals of the called line in the number group
connector will inform the marker that the line is one of a group of
lines. The marker will test all of the lines in the group, testing up to
as many as twenty simultaneously, and will select an idle one.

CROSSBAR DIAL TELEPHONE SWITCHING SYSTEM 109

The lines of a PBX may be assigned to non-consecutive numbers
within the usual 10,000 series, and with the exception of the numbers
dialed, they may be assigned to line numbers in a special group of
2500 outside of the 10,000 series. These features reduce the necessity
for number changes due to the growth of private branch exchanges,
and conserve subscriber line numbers in the office. The lines of a
PBX group can be distributed over several line link frames and over
two number group connectors to equalize the terminating traffic load
n the case of busy private branch exchanges.

2. The marker recognizes numbers dialed which are unassigned,
disconnected or changed numbers, and automatically routes such
calls to an operator who will inform the calling subscribers as to the
status of the numbers called.

3. In case the called number is on a party line, the marker deter-
mines from one of the test terminals which station of the line is to be
rung, and signals the incoming trunk to provide the proper ringing.

4. The marker tests the continuity of the circuit paths to be used
to the called line before establishing the connection, to insure that the
connection is properly set up and that it will be held under control
of the subscriber telephone after the marker disconnects. The marker
also tests for short-circuits, crosses and grounds, and in case of a
failure due to any inoperative condition it will connect itself to the
common trouble indicator and leave a record of the trouble and its
location and give an alarm to the maintenance force.

Figure 15 shows the complete talking connection through the various
trunks and switch frames as finally established after all of the common
control circuits have been released.

On a call to a subscriber served by a panel dial office, the connection
is routed through the district link and the office link frames in the
same manner as on a call terminating in a crossbar office, but in this
case the idle trunk chosen on the office link frame terminates in an
incoming panel switch in the distant panel dial office. The subscriber
sender of the crossbar office causes the incoming and final selectors in
the terminating panel office to select the called subscriber line without
the aid of any terminating senders in either office. When the sub-
scriber sender has completed these functions it will be released and
the connection will be established from the calling line over the inter-
office trunk circuit and through the terminating panel incoming and
final selectors to the called line. On this type of call the subscriber
sender operates in the same manner as though the called line were in a
crossbar office, and the selectors in the panel office operate in the same
manner as though the call had originated in another panel office.

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No changes are required in the panel selectors to function with the
crossbar office.

On a call for a subscriber in a manual office, the call would be routed
through the switches of the district link and the office link frames as
previously described and connected to a trunk circuit on the office
link frame which terminates in the "B" switchboard in the manual
office. The subscriber sender of the crossbar office then transfers the
called number by impulses transmitted over the interoffice trunk
circuit to the operator's position equipment in the manual office.
The called number appears in the form of visible numbers on the
operator's keyshelf. The operator completes the connection by
"plugging" the associated trunk circuit, which terminates on a cord
and plug, into the called subscriber line jack.

A call originating in a panel dial office for a subscriber line in a
crossbar office reaches the crossbar office through an incoming trunk
circuit as in the case where the call originated in a crossbar office.
The call from the panel office is then handled by the crossbar office
terminating sender and marker in exactly the same manner as described
for calls originating in the same crossbar office.

A call originating in a manual office for a line connected to the
crossbar office reaches the crossbar office over an incoming trunk
circuit from an "A" operator's position in the manual office. These
incoming trunks in the crossbar office are similar to the incoming
trunks previously described. In this case, however, the incoming
trunk is connected to a terminating "B" sender and by means of this
sender to a "B" board operator in the crossbar office. The "B"
operator will obtain the called number verbally from the distant
"A" operator and then, by means of the keyset on her position,
register the called number in the terminating sender. The terminating
sender will then select a terminating marker and the connection will
be established in exactly the same manner as described for a call
originating in a crossbar office.

Maintenance Facilities
Automatic routine testing circuits are provided for testing all the
principal circuit units, such as the district junctors, incoming trunks
and senders. These test circuits automatically put each circuit, one
after the other, through all of its functions on all classes of calls to
insure that it performs satisfactorily. It tests the important relays
of the circuits to insure that they have the proper adjustment to
handle the worst circuit conditions. In case any circuit fails to meet
the test conditions, the test is stopped and an alarm given to the
maintenance force.

112

BELL SYSTEM TECHNICAL JOURNAL

Trouble indicator circuits are provided for use in connection with
the test and maintenance of the marker circuits. These circuits are
arranged so that when trouble is encountered by a marker, the marker
will seize the trouble indicator and operate combinations of relays and
light small lamps which indicate the nature and the location of the
failure and give an alarm to the maintenance force.

Equipment

Figure 16 shows a typical switch frame used in the crossbar system.
This particular frame is a "line link" frame which serves a group of
subscribers for both originating and terminating traffic. The frame-
works on which the equipment is mounted are constructed of rolled

Fig. 16 — Line link frame.

CROSSBAR DIAL TELEPHONE SWITCHING SYSTEM 113

bulb angle iron sections with a sheet metal base. The bulb angle
construction provides a framework which is light in weight and has
the required strength, and permits an equipment mounting arrange-
ment which conserves space and facilitates the wiring of the apparatus.
The frames are welded and incorporate such features as sanitary base
construction, guards to protect the apparatus and wiring against
damage from the rolling ladders located between the rows of frames,
and a cable duct or runway for the A.-C. power service cables with
plug receptacle outlets for use with electric soldering irons, portable
lights, etc.

These frame equipments are built in standardized units, which
provide the required flexibility to satisfy the variations in telephone
traffic and classes of service encountered in the different telephone
areas. Where it has been necessary to divide an equipment assembly
into several units, due to the limitations of handling, shipping and to
care for different classes of service, the equipments have been designed
so that the installation effort required for interconnecting such units
has been reduced to a minimum.

The bays of equipment located at the right, in Fig. 16, equipped
with crossbar switches, are the primary line link bays. The vertical
units of these crossbar switches are wired to the subscriber lines.
These primary bays are made available in units of 100 and 200-line
capacities. As discussed previously the number of primary bays
provided in a line link frame may be varied to fit the traffic load of
the subscriber lines. The left-hand bay of this frame contains the
vertical file of crossbar switches, known as the secondary switches and
the vertical units of these switches are wired to district junctors and
line junctors. The line link control circuit apparatus, which is
common to the frame, is located at the bottom of this bay.

Figure 17 shows a group of three frame units, namely, the sub-
scriber sender link, the district junctor and the district link frames,
which are closely associated in the trunking network and have been
designed as a fixed equipment group. However, for shipping reasons
the group is divided into three separate equipment units. The
district junctor circuits, consisting primarily of relays, are mounted in
groups on the middle frame. These groups are provided in stand-
ardized units of various types, such as those required to serve coin and
non-coin subscribers lines. A similar arrangement of frames is used
for the combination of terminating sender link, the incoming trunk,
and the incoming link frames.

Figure 18 shows a row of subscriber sender frames and a frame of
"A" operator senders located at the extreme right. These frames

tl4

BELL SYSTEM TECHNICAL JOURNAL

CROSSBAR DIAL TELEPHONE SWITCHING SYSTEM 115

Fig. 18 — Sender frames.

116

BELL SYSTEM TECHNICAL JOURNAL

Fig. 19 — Originating marker frame.

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CROSSBAR DLAL TELEPHONE SWITCHING SYSTEM

117

Fig. 20 — Battery supply feeders, power wiring, fusing, etc.

accommodate five senders which may be of one type, or a combination
of both types. The crossbar switch shown on the right of each sub-
scriber sender unit, is a part of the sender circuit and is employed for
the purpose of registering the called numbers dialed by the subscribers.

118 BELL SYSTEM TECHNICAL JOURNAL

The "A" operator senders are associated with the "A" operator
switchboard equipment and are used for the completion of certain
classes of calls such as toll and assistance calls.

A view of the originating marker frame is shown in Fig. 19. There
will be a variation in the equipment on this frame for different cities
due to the variation in the number of route relays required, the number
depending upon the number of central office codes that may be dialed
by subscribers and operators. This variable feature is cared for by
providing the route relay equipment in bays of 100 codes as shown in
the right-hand bay. The terminal fields shown below the route
relays on the frame provide the flexible connecting facilities which
permit the use of any route relay for any office code and which readily
permit changes in routings, variations in trunk group sizes and other
features which are subject to change from time to time.

The power plant equipment provided for the crossbar offices is
similar to the equipment now being furnished for all large dial central
offices. The principal power supply arrangements provide 48- volt
direct current for the operation of practically all the signaling and
the telephone transmission circuits. Also several other sources of
direct current are provided for miscellaneous purposes as in other
standard dial systems. A new distribution scheme for the battery
feeders on the frames is employed which reduces the amount of
copper required. A common set of 48-volt battery feeders supplies
the signaling and talking current for all frames. Individual frame
filters are connected across the battery supply leads at the frames
where a noise-free battery supply is required for talking circuits.
Figure 20 shows a view of the overhead battery cables, conduits for
the A.-C. power leads, and the fuse cabinets for the fusing of the
battery supply to a row of frames.

Application

As mentioned in the first part of this paper, two crossbar dial central
offices were cut into service in 1938 and these have now been in com-
mercial operation for several months. One of these offices serves a
residential area in Brooklyn, while the other serves a congested business
area in the midtown Manhattan district of New York City. The
operation of these offices under actual service conditions has been
highly satisfactory and our expectations in regard to performance have
been fully realized.

This type of system will be used for new offices in large cities instead
of the panel system as rapidly as manufacturing and plant conditions
permit and the apparatus which was designed for this system will be
used in other fields of the telephone system.

A Twelve-Channel Carrier Telephone System for
Open- Wire Lines

By E. W. KENDALL and H. A. AFFEL

A new carrier telephone system is described, together with its
application in the long distance telephone plant. By its use, an
open-wire pair which already furnishes one voice circuit and three
carrier circuits may have twelve more telephone circuits added.
Thus in all sixteen telephone circuits are obtained on a single pair.
Several such systems may be operated on a pole line.

Various problems incident to the extension of the frequency
range, from about 30 kilocycles, the highest frequency previously
used, to above 140 kilocycles, are discussed. Among the more im-
portant of these are the control of crosstalk between several systems
on a pole line, arrangements for taking care of intermediate and
terminal cables, and automatic means for compensating for the
effects of weather variations on the transmission over this wide
frequency range.

Introduction

BARE wires supported on insulators, stretched between poles,
make up the pioneer electrical communication circuit, the open-
wire line. Although great advances have been made in the applica-
tion of cable structures, the open-wire lines still hold their own in some
sections of the country. This is because, to offset their physical
vulnerability, they have several unique virtues. They are flexible
and permit adding one pair of wires at a time. They are also com-
paratively economical where conditions favor their use. Furthermore,
they are low-attenuation circuits and for this reason were the first
to be used for high-frequency carrier systems.

The first carrier systems, beginning in 1918, added three or four
channels to the existing voice circuit on a pair. To keep pace with
this development, improvements in transposition systems were de-
vised so that many such carrier systems might be operated on the
same pole line. Such carrier systems, typified by the three-channel
type C ^ system, have seen continuous growth in use in the long dis-
tance plant. Now a twelve-channel system, the type J, is being made

^ "Carrier Systems on Long Distance Telephone Lines," H, A. Affel, C. S. Dema-
rest and C. W. Green, Bell System Technical Journal, July 1928, and A. I. E. E.
Transactions, Oct. 1928, pp. 1360-1387. "A New Three-Channel Carrier Telephone
System," J. T. O'Leary, E. C. Blessing and J. W. Beyer, Bell System Technical
Journal, this issue.

119

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BELL SYSTEM TECHNICAL JOURNAL

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A TWELVE-CHANNEL CARRIER TELEPHONE SYSTEM 121

available to add to the type C system, thus giving sixteen telephone
circuits on an open-wire pair in addition to the two telegraph circuits.
Since there are already about 60,000 miles of pole line equipped with
type C systems, the new type J system was developed to go in the
frequency range above the type C system rather than to supersede it
with more channels (Fig. 1).

The new system has been designed to meet high standards of trans-
mission and reliability for distances up to several thousand miles.
The frequency band transmitted by the individual derived circuits is
exceptionally wide, from about 100 to 3600 cycles for a single system
and has been previously discussed ^ in relation to the channel spacing
in this and other new broad-band devefopments.

An important feature of the work on the type J system has naturally
been that of making the line circuits suitable for carrying the higher
frequencies. The tendency of circuits to crosstalk into one another
increases rapidly with frequency. Advances in transposition design
and structural improvements have now made it possible to extend the
frequency range from 30,000 cycles to 140,000 cycles, which is about
the upper frequency of the type J system. The problem of incidental
cables in open-wire lines has also been serious, since the losses increase
with frequency, and what is usually more important, there may be sub-
stantial reflection effects at junctions of the open-wire line and cable.
These are serious, not only from the standpoint of the transmission
loss which they entail, but from their effect on crosstalk. The in-
crease in attenuation at the higher frequencies has also brought other
problems into the picture. For example, repeaters are needed at
more frequent intervals than with the lower frequency systems.
Attenuation variation with frequency due to weather changes is
greater than at the lower frequencies.

Figure 2 shows schematically the complete type J system, with its
different major circuit elements, resulting at the terminals in the
division of the single line circuit effectively into sixteen talking circuits.
In no recent development is the function of the wave filter in providing
essential units in a frequency dividing plan more forcefully illustrated
than in the application of this new system, in combination with the
type C and other facilities which exist. There are about sixty different
designs of filters and networks in the terminals and repeaters. Their
functions are varied, — as, for example, separating the individual
channel bands, separating the opposite directional groups of channels,
separating the type J frequency range as shown in Fig. 1 from the
type C and other ranges, separating the different carrier frequencies

^"Transmitted Frequency Range for Circuits in Broad Band Systems," H. A.
Affel, Bell System Technical Journal, October 1937.

122 BELL SYSTEM TECHNICAL JOURNAL

of a carrier supply system in which the carriers are all derived from a
common 4000-cycle source, etc.

The new system, as in the case of the type C, uses single sideband
transmission with carrier elimination. Copper-oxide units are em-
ployed as translator elements of various kinds, — modulators, de-
modulators, and harmonic producers. Methods of mounting the
equipment, and methods and apparatus for testing follow lines already
worked out for the type K cable carrier system, which was described a
year ago in two A. I. E. E. papers.^

Channel Terminals

A terminal of the type J system changes twelve independent voice
channels into a compact block of twelve carrier channels properly
allocated in frequency for transmission over the open-wire line. In-
versely, such a block received from the open-wire line is separated and
transformed into twelve independent voice channels. The first step
in transmitting the twelve voice channels is to modulate them on
twelve carrier frequencies 4 kilocycles apart from 64 to 108 kilocycles
and to select the lower sidebands by means of quartz crystal channel
band filters. The last step in the conversion from a received twelve-
channel block to the twelve independent voice channels consists in the
division of the block by twelve quartz crystal channel filters and the
demodulation of these messages to produce voice frequency transmis-
sions. These two frequency changes and separations are performed by
the same equipment that is used in the type K cable carrier system
terminals.

Figure 3 shows the circuit of a modulator and a demodulator for the
opposite directions of a single conversation with indicated connections
for the eleven others which make up this fundamental twelve-channel
block. The modulator consists of a bridge assembly of copper-oxide
varistors and is supplied with about 0.5 milliwatt of carrier power from
the carrier supply system which is described later. Of the two result-
ing sidebands, the lower is selected by the crystal band filter follow-
ing the modulator. The line sides of twelve modulator band filters
are joined in parallel and a compensating network is connected to
preserve the band characteristics of the upper and lower channels.

On the receiving side, after separation by one of the twelve parallel
filters the sideband is applied to a demodulator supplied with the

3 "A Carrier Telephone System for Toll Cables," C. W. Green and E. I. Green,
Bell System Technical Journal, January 1938 and Electrical Engineering, May 1938.
"Cable Carrier Telephone Terminals," R. W. Chesnut, L. M. Ilgenfritz and A.
Kenner, Bell System Technical Journal, January 1938 and Electrical Engineering,
May 1938.

r-EHI)— E> — 1> 1 EH

HD ' <i

-m-m-

MOCNJLATOfi - ^_

0- DEMODULATOR R - BECTIFIER

F -FILTER X - COMPOSITE" SET

E - EQUALIZER TG- D C. TELEGRAPH

C- REGULATOR

OS -OSCILLATOR

HG-HARMONtC GENERATOR

O-Q- HYBRID COIL AND NETWORK

Fig. 2 — Terminal and repeater layout.

-CD-CD-©— >j(ZJ-

TYPE C

-CaW^HD-CD-

V

122 BELL SYSTEM TECHNICAL JOURNAL

of a carrier supply system in which the carriers are all derived from a
common 4000-cycle source, etc.

The new system, as in the case of the type C, uses single sideband
transmission with carrier elimination. Copper-oxide units are em-
ployed as translator elements of various kinds, — modulators, de-
modulators, and harmonic producers. Methods of mounting the
equipment, and methods and apparatus for testing follow lines already
worked out for the type K cable carrier system, which was described a
year ago in two A. I. E. E. papers.^

Channel Terminals

A terminal of the type J system changes twelve independent voice
channels into a compact block of twelve carrier channels properly
allocated in frequency for transmission over the open-wire line. In-
versely, such a block received from the open-wire line is separated and
transformed into twelve independent voice channels. The first step
in transmitting the twelve voice channels is to modulate them on
twelve carrier frequencies 4 kilocycles apart from 64 to 108 kilocycles
and to select the lower sidebands by means of quartz crystal channel
band filters. The last step in the conversion from a received twelve-
channel block to the twelve independent voice channels consists in the
division of the block by twelve quartz crystal channel filters and the
demodulation of these messages to produce voice frequency transmis-
sions. These two frequency changes and separations are performed by
the same equipment that is used in the type K cable carrier system
terminals.

Figure 3 shows the circuit of a modulator and a demodulator for the
opposite directions of a single conversation with indicated connections
for the eleven others which make up this fundamental twelve-channel
block. The modulator consists of a bridge assembly of copper-oxide
varistors and is supplied with about 0.5 milliwatt of carrier power from
the carrier supply system which is described later. Of the two result-
ing sidebands, the lower is selected by the crystal band filter follow-
ing the modulator. The line sides of twelve modulator band filters
are joined in parallel and a compensating network is connected to
preserve the band characteristics of the upper and lower channels.

On the receiving side, after separation by one of the twelve parallel
filters the sideband is applied to a demodulator supplied with the

3 "A Carrier Telephone System for Toll Cables," C. W. Green and E. I. Green,
Bell System Technical Journal, January 1938 and Electrical Engineering, May 1938.
"Cable Carrier Telephone Terminals," R. W. Chesnut, L. M. Ilgenfritz and A.
Kenner, Bell System Technical Journal, January 1938 and Electrical Engineering,
May 1938.

5<S

,<^

A TWELVE-CHANNEL CARRIER TELEPHONE SYSTEM 123

proper carrier frequency to restore the voice frequency message. Be-
cause of the low level at which demodulation takes place, the demodu-
lator is followed by a single-stage amplifier to produce the level
desired in the voice frequency circuit. The gain of this amplifier is
adjustable over a moderate range.

MODULATOR

FROM
4-WIRE -
TERM SET

FROM
CARRIER
SUPPLY

FROM (-_

II OTHER J
MODULATOR 1_
CIRCUITS ^

TO
•GROUP
MODULATOR

COMP
FILTER

COMP

FILTER

TO

II OTHER

DEMODULATOR

CIRCUITS

± 5DBGAIN
ADJUSTMENT

DEMODULATOR

FROM

GROUP

DEMODULATOR

Fig. 3 — Channel modulator and demodulator.

The combination of a single modulator and a single demodulator
and associated equipment shown in Fig. 3 is called a "Modem" and
two of these are mounted on a single equipment panel. Nine of these
panels, sufficient for one and a half type J systems, or eighteen con-
versations, mount in a single relay rack bay of standard height.

Carrier Supply
The carrier frequencies 64-108 kilocycles are all derived as harmonics
of a 4-kc frequency produced by a tuning fork controlled oscillator.
This frequency is applied to an easily saturated coil to produce a
sharply peaked wave which is rich in odd harmonics. Even har-
monics of 4 kilocycles are obtained by rectification in a copper-oxide
unit of part of the odd harmonic output. Odd and even harmonics
appear in separate circuits from which each frequency desired is
separated by a quartz crystal filter. Frequencies as high as the 121st

124 BELL SYSTEM TECHNICAL JOURNAL

harmonic, that is, 484 kilocycles, are obtained in this way from the
carrier supply system. Because of the importance of the carrier
supply two sources are provided, with automatic equipment to transfer
rapidly from the regular to the emergency source.

Group Modulation

As shown in Fig. 1, the type J system uses a band of 36 to 84 kilo-
cycles for the west to east direction of transmission and 92 to 140 kilo-
cycles for the east to west direction. The output of the fundamental
twelve-channel unit consists of twelve lower sidebands from carriers of
64-108 kilocycles. This must, therefore, be translated to the two type
J directional groups for line transmission. Since the frequencies
in the fundamental unit overlap those in both directions of line
transmission, this transfer must be made in two steps. Figure 4 shows
these frequency translations. The first group modulation is the same
for both directions of transmission. By modulating the fundamental
unit with a carrier of 340 kilocycles there is obtained a block of lower
sidebands extending from 400 to 448 kilocycles. A second modulation
with a 484-kc carrier then gives, for transmission from west to east,
a twelve-channel block of upper sidebands extending from 36 to 84
kilocycles. For the east to west transmission the second modulation
uses a 308-kc carrier, producing a twelve-channel block of lower side-
bands between 92 and 140 kilocycles.

Frequencies as high as 308, 340 and 484 kilocycles are chosen for
group modulation in order that undesired products shall be well
separated from desired products to permit their elimination by simple
filter structures.

The same group modulation processes that have been described
above for adapting the twelve-channel group for line transmission are
used in the opposite sequence for receiving the block from the line and
preparing it for separation by the channel band filters of the receiving
terminal; thus, for instance, at an east terminal the block of upper
sidebands, extending from 36 to 84 kilocycles as received from the line,
is first modulated with 484 kilocycles producing lower sidebands be-
tween 400 and 448 kilocycles. These are next modulated with 340
kilocycles, which produces a block of twelve lower sidebands extending
from 60 to 108 kilocycles, which is the group that the fundamental
twelve-channel terminal unit is designed to handle.

Figure 5 shows the essential features of the group modulating and
group demodulating circuits. As in the type K system, group modula-
tion is performed at a very low level of the message material and with
a high level, about 25 milliwatts, of the group carrier supply, in order

A TWELVE-CHANNEL CARRIER TELEPHONE SYSTEM 125

oa

So

2°

ID
33

126

BELL SYSTEM TECHNICAL JOURNAL

ioOOr^OOo)

A TWELVE-CHANNEL CARRIER TELEPHONE SYSTEM 127

to minimize interchannel crosstalk. The group modulators are of the
doubly balanced bridge type which aids in suppressing some of the
unwanted modulation products. Following the first group modulator
and also following the first group demodulator are coil and condenser
type 400-448 kc band filters which reject the unwanted products and
pass the band of frequencies containing the twelve channels. Between
this filter and the second group modulator on the transmitting side of
the terminal, an intermediate amplifier is used in order to keep the
level of the group transmission above danger of noise. Following the
second group modulator and also following the second group demodu-
lator are low-pass filters which cut off frequencies above about 160
kilocycles, to suppress unwanted modulation products. From the
output of the receiving low-pass filter the twelve-channel group, 60-108
kilocycles, passes through a two-stage "auxiliary" amplifier to bring
it to the desired level.

The carrier frequencies for group modulation and for group de-
modulation are derived from the same 4-kc tuning fork controlled
oscillator that supplies carriers for the twelve-channel unit. From
the circuit in which appear the odd harmonics of 4 kilocycles, the 77th,
85th and 121st harmonics, that is, 308, 340 and 484 kilocycles, are
selected by carrier supply filters and separately amplified by two-stage
amplifiers to produce the powers required for group modulation.
Outputs from these amplifiers are fed to individual frequency busses
capable of supplying the group modulators and demodulators for ten
systems. An emergency carrier supply for these frequencies is also
provided, with arrangements for switching rapidly from the regular to
the emergency circuits.

Terminal Amplifiers

As indicated on Fig. 5, the transmitted twelve-channel group, now
transferred to the proper frequency range for line transmission, goes
from the low-pass filter at the output of the second group modulator
to a transmitting terminal amplifier which is similar in most essentials
to the amplifiers of the line repeaters. The twelve-channel group,
arriving from the line, passes through a regulating amplifier arranged
and controlled to compensate for variations in equivalent of the
adjacent line section before passing to the first group demodulator.
Similar regulating amplifiers are used at all repeater points.

Filters

At terminals and also at repeater points, two kinds of filter sets
are required. One kind is used in the line to separate the type J

128 BELL SYSTEM TECHNICAL JOURNAL

frequency range 36 to 140 kilocycles from the type C and other lower
frequencies on the line. The second kind is the directional filters of
the type J system itself. These separate a twelve-channel band of
frequencies lying below 84 kilocycles used for west to east transmission
from the twelve-channel group lying above 92 kilocycles which is
transmitted from east to west. These directional filter sets are care-
fully designed to equalize any non-uniformity of loss in both the
directional and the line filters. As this equalization involves a con-
siderable loss over a large part of the filter band it is provided entirely
in the receiving directional filters where the transmission is at a low
level and the loss can readily be made up by amplification. In this
way nearly the full energy output of the transmitting or repeater
amplifier is available for line transmission.

Line Crosstalk Problems

As noted previously, type J systems will, in general, be applied on
pairs on which type C systems are already operating. Such pairs
have already been arranged to transmit frequencies up to 30,000
cycles, and transposed in such a manner as to perform satisfactorily as
regards crosstalk to and from nearby pairs on which similar carrier
systems are operating. In addition, on most modern lines the spacing
between wires of a pair has been reduced from twelve to eight inches;
and, on many of the lines, in order further to reduce crosstalk by
increasing the spacing between pairs, the number of pairs on a cross-
arm has been limited to four instead of five, omitting the pole pair.
Now, by applying a new transposition system designed for type J
operation up to 140,000 cycles, an eight-inch spaced four-crossarm
line may be arranged to transmit type J frequencies on at least ten
pairs out of sixteen. Type C systems may, of course, be used on all
of the pairs. Finally by using the most advanced transposition de-
sign methods, and increasing the crossarm spacing, in addition to the
features noted above, a new line may be constructed to permit the
operation of sixteen channels on all pairs.

To make the pairs of wires good for type J systems, more than a four-
fold increase in frequency range, was difficult. The natural tendency
of the circuits to crosstalk is increased even more than the frequency
ratio, so that in addition to applying a new transposition design it is
necessary that the transposition poles be more accurately located, and
that the sags of the two wires of each pair be kept more nearly alike.
On lines which already have eight-inch spaced wires, no major struc-
tural changes are necessary. However, on lines which have only
twelve-inch spaced wires and where it is desired to make available a

A TWELVE-CHANNEL CARRIER TELEPHONE SYSTEM 129

number of pairs for type J transmission, structural changes, such as
respacing the wires of the pairs concerned to six inches, are necessary
in order to reduce the coupling.

One factor of extreme importance is that of reflected near-end cross-
talk. In the application of transposition systems it is usually not
possible to reduce the near-end crosstalk to a magnitude approximating
the far-end crosstalk. It is the latter with which the carrier systems
are chiefly concerned, since similar types of systems on different pairs
all transmit the same frequency range in the same direction. If,
however, the lines concerned do not have smooth impedance character-
istics, i.e., a high degree of freedom from reflection effects, near-end
crosstalk may be converted by reflection into far-end crosstalk of
sufficient magnitude to be controlling over the true far-end crosstalk.

This means that lines to be used for several type J systems must be
made unusually smooth electrically — impedance variations kept
within a few per cent. The achievement of such smoothness consists
chiefly in:

(1) Reducing the electromagnetic and electrostatic couplings to other

pairs so that there are no large energy interactions, with corre-
sponding impedance irregularities. Generally speaking, when
the pairs concerned have been transposed for reduced far-end
crosstalk up to the maximum frequency transmitted, this
condition is also satisfied.

(2) Minimizing the effect of intermediate and terminal cables. This

latter problem has caused considerable concern and is responsi-
ble for the development of several new techniques in the design
and treatment of such cables, where they appear in a long line
otherwise consisting chiefly of open wire.

Cable Treatment

As a means of overcoming the reflection and attenuation effects of
short pieces of terminal or intermediate cable, loading naturally sug-
gests itself, as applied in type C systems, where the cable pairs in-
volved are commonly equipped with carrier loading coils, spaced at
about 700-foot intervals. This compares with the 3000-foot or 6000-
foot spacings which are standard for voice-frequency loading. How-
ever, loading, pairs in existing cables satisfactorily up to 140,000
cycles would mean coils at approximately 200-foot intervals. Because
of physical limitations, existing manhole spacings, etc., this is highly
impractical. A reasonable solution has, however, been found in the
creation of a new form of low-capacitance high-frequency cable, —
a disc-insulated unit which has constructional features in common
with the coaxial cables and a capacitance of only .025 microfarad per

130

BELL SYSTEM TECHNICAL JOURNAL

mile as compared with about .062 microfarad for conventional cable
pairs. This permits more practical loading coil spacings. These
disc-insulated units are made up as spiral-fours, that is, two pairs
(.051" diameter wire) which form the diagonals of a square. When
these cables are loaded with small coils at intervals of approximately

Fig. 6 — Disc-insulated cable. Sheath diameter 2.3 inches.

600 feet, they present impedance characteristics substantially equiva-
lent to that of an open-wire pair over the desired frequency range.
Accordingly, they form a desirable, although somewhat expensive,
solution of the problem of intermediate or entrance cables. As shown
in Fig. 6, the spiral-four units are bound together in complements of
seven or less under a lead cable sheath similar to standard toll cables.
It should be noted that the low-capacity disc-insulated loaded cables
not only provide a satisfactory solution of the impedance matching

A TWELVE-CHANNEL CARRIER TELEPHONE SYSTEM 131

problem, but they also give a cable circuit of low attenuation, — ap-
proximately 1.2 db per mile at 140 kilocycles.

Nevertheless, where spare pairs exist in cables, it has often been
found economical to use them for type J transmission. It is possible
to use them only non-loaded, in which case the attenuation is very
high — 4 to 6 db per mile, depending on the gauge, at 140 kilocycles,
and impedance matching transformers are, of course, required at the
junction of the open wire and cable. There are cases where this higher
attenuation may be permitted and these pairs are used by separating
the type J range from the lower frequency range, which is transmitted
through pairs equipped with the older type C carrier loading. The
separation is accomplished by filters which are usually housed in
small filter huts at the junction of the open-wire line and cable.

In other cases it has been found economical to use the frequency
separation method with filters and to install new non-loaded cables of
lower attenuation to lead in the type J frequency band alone. Paper
insulated 10-gauge pairs or the disc-insulated spiral-four cable of the
type described above may be used for this purpose. In either case
transformers are used to match the cable impedance to that of the
open-wire line over the type J frequency range.

The reflection requirements are so severe and the effects of even
short lengths of cable at the high frequencies so serious, that even short
lead-in cables, where the open-wire line actually extends to the re-
peater or terminal building, — cables which are only 100 or 200 feet
long, must receive special treatment. This has also been accomplished
by the use of the disc-insulated spiral-four cables, loaded.

Interaction Crosstalk

Because of the higher attenuation there will be many repeater
points on a long line at which the type J system will be amplified but at
which the other systems and wires on the line will pass through the
station without amplification. In this case, evep though the type J
pairs are properly transposed to keep down crosstalk between them-
selves, there still remains the crosstalk between them and the other
pairs on the line, not only pair-to-pair crosstalk but crosstalk from
the type J pair to various circuit paths consisting of irregular wire
combinations.

Two difficulties arise in this case: The first is that the crosstalk from
the output of one J system into an irregular path may be retransferred
into the input of a repeater on another type J system. The second
is that the crosstalk from the irregular path may be returned to the
input of the same repeater and either influence the overall transmis-

132 BELL SYSTEM TECHNICAL JOURNAL

sion characteristic or, if sufficiently severe, actually cause the repeater
to sing. This general situation has made it necessary to introduce
in the circuits at such points "crosstalk suppression" filters in the
non-J pairs and longitudinal choke coils in all pairs.

Staggering
In addition to the various steps which are taken in order to reduce
crosstalk by improving the line conditions, the type J system may
include a feature which has been used in the type C system, — the
staggering of the channel bands used on neighboring pairs. The ad-
vantage of staggering results from the facts that (a) the sensitivity of
the ear and the power of the voice vary over the audible range, {b)
the efficiencies of transmitter and receiver also tend to vary over the
frequency range, (c) part of a channel band may lie opposite "dead"
frequency range on an adjacent pair, and (d) by controlling the arrange-
ment of the sidebands the crosstalk may be made unintelligible even
if not inaudible. The staggering feature is readily provided in the
type J system by a suitable choice of carrier frequency for the second
group modulator and first group demodulator. With the staggered
systems the highest frequency used would be about 143 kilocycles.

Attenuation Problem
In what has preceded in the discussion of line problems, the emphasis
has been confined chiefly to the question of the smoothness of a line
from an impedance standpoint in order to keep down reflection effects
and, correspondingly, to improve the operation from a system-to-
system crosstalk standpoint. There is also the problem of the higher
attenuation incident to the use of higher frequencies. Between
30,000 cycles and 140,000 cycles, the normal wet weather attenuation
for a 165-mil open-wire pair, for example, rises from about 0.13 to 0.28
db per mile, — an increase of approximately 2:1. Repeaters on the
type J system, if applied on the basis of approximately the same output
level and minimum level requirements, must be spaced at about one-
half the interval of the type C systems. Normal spacings for type J
systems would therefore be expected to range from 75 to perhaps
100 miles where no large amount of intermediate cable existed.

However, another problem, not present to a similar degree at the
lower frequencies, tends in many cases to have a controlling effect
on this spacing, that is, sleet or ice on the wires. With ice, frost, or
snow on the wires, the wet weather attenuation may be exceeded by
very large amounts. The additional attenuation is due primarily to
the coating on the wires themselves rather than the coating on the

A TWELVE-CHANNEL CARRIER TELEPHONE SYSTEM

133

insulators. It arises from the potential gradient through the ice
deposit in combination with the high dielectric loss characteristic of
the ice or snow coating. Figure 7 gives examples of the attenuation

0.8

0.6

D 0.4

0.2

r-

i<

/

/

/

/

/

/

,

/

/

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WET WEATHER

-

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,

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_

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k

"

DRY WEATHER

-

-

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25 50 75 100 125

FREQUENCY KILOCYCLES PER SECOND

150

Fig. 7 — Attenuation frequency characteristics of open wire lines.

frequency characteristics of open-wire lines, including certain measure-
ments with ice coating. The exact increase in attenuation due to
snow and ice naturally depends on the thickness and other character-
istics of the coating. Even very thin coatings of ice on the wires
tend to raise the attenuation at 140 kc from the normal wet weather
figure of about 0.28 db to about 1 db a mile, i.e., an increase of three or
four to one. Extremes up to 5 db per mile have been measured for
short lengths of line with ice nearly two inches in diameter. Such
heavy ice obviously approaches the mechanical breakdown conditions
for the line.

Where ice and sleet occur the repeater spacings may be reduced to
about fifty miles or less. The repeaters now being provided for the
type J systems have gains of approximately 45 db. Repeaters are
under development which are expected to raise the maximum available
gain to something like 75 db. The normal dry or wet weather opera-
tion of such repeaters would be limited to gains of perhaps 10 to 25
db depending upon the amounts of cable included. The problem of
obtaining automatic gain control over the extra wide range required
by the high sleet attenuations is a difficult one.

134 BELL SYSTEM TECHNICAL JOURNAL

Repeaters

At each repeater point line filters and directional filters are required
on both sides of the amplifying equipment to separate type J currents
from those of lower-frequency services on the line and to separate
oppositely directed groups for separate amplification in one-way line
amplifiers. These filters have been described in connection with the
terminals where they perform similar functions. Two regulating
amplifiers, one for each direction of transmission, properly controlled
to compensate for variations in the attenuation of the preceding line
section, are also needed at each repeater point. These are described
later under "Regulation."

Figure 8 shows the circuit of one of the line repeaters and indicates
the location of the directional filters, and certain supplementary
filters for suppressing frequencies outside the transmitted range; also
the regulating amplifier circuit, and the pick-off of the pilot channel
which controls the gain.

The line amplifier has three stages of pentodes. The first two
stages use single tubes of high voltage amplification and low power
capacity while the third stage has four power pentodes in parallel to
increase the output capacity. Because of considerable heat developed
by these power tubes, special precautions are necessary to dissipate the
heat and to protect condensers and other elements mounted near
them.

Negative feedback to improve the operation of the amplifier is
supplied over two paths. The inner feedback, from the plates of the
output tubes over a properly designed network to the grid of the input
tube, reduces the gain at frequencies outside the transmitted band and
so prevents singing at those frequencies. It has little effect at fre-
quencies within the type J range. The outer feedback path includes
the input and output transformers, which are made as hybrid coils.
In each of these one pair of the conjugate windings is connected to the
incoming or outgoing circuit of the amplifier while the other pair is
used for the feedback connection. By feeding back through the trans-
formers in this way, they benefit by feedback in much the same way
as the tubes, and the overall characteristic of the amplifier is practically
independent of the transformer characteristics. This feedback re-
duces the amplifier gain by over 40 db and correspondingly reduces
modulation effects within the amplifier, and gives exceptionally stable
transmission with respect to tube and voltage changes. It is also
designed to improve and stabilize the input and output impedances.

A TWELVE-CHANNEL CARRIER TELEPHONE SYSTEM

135

bo

136 BELL SYSTEM TECHNICAL JOURNAL

Equalization

Equalization is necessary in each direction of transmission at a
repeater point and in the receiving direction at a terminal, to compen-
sate for frequency distortion produced by the preceding section of line.
Fortunately, the attenuation frequency curves for the usual open-wire
circuits, that is, 104, 128 and 165-mil wire, have nearly the same shapes
for section lengths giving the same attenuation at the maximum fre-
quencies for the two directions of transmission, so that these various
circuits can be equalized alike.

As is well known, the transmission frequency characteristic of an
amplifier with large feedback is almost the inverse of that of the
feedback circuit itself, so that the insertion in the feedback circuit of a
network having the same characteristics as a line section will provide
equalized transmission over the amplifier and section combined. In
the outer feedback circuit of the line repeater is included an equalizer
which has a characteristic sloping with respect to frequency in the
same way as the variation in loss under wet weather conditions of the
longest open-wire section likely to be used. Thus, there is provided in
the repeater a basic equalization for this longest wet weather line.
At a receiving terminal a basic equalizer is provided which performs
this same compensation, but in this case the slope of the curve must
necessarily be opposite to that of the line attenuation and of the
equalizer in the feedback path of the line repeater.

Line sections, however, vary in length and in the amount of en-
trance cable included. In order that they may be properly corrected
by this basic equalization, they must be built out to equal this longest
wet weather section. For this purpose there are provided flat loss
pads and building-out networks whose losses have the same frequency
shapes as the losses of short lengths of open-wire circuit. These pads
and networks can be inserted or omitted by simple changes in strapping.
They suffice to build out the shortest section which is expected to be
used.

Pilot Currents

For a satisfactory system, arrangements must be provided to correct
automatically for the effects on line attenuation due to changes in
weather, by adjusting the amplification at each repeater point and in
the receiving terminal circuit. To permit measuring these effects
a pilot current of fixed frequency, near the middle of the transmitted
band, and of constant amplitude, is supplied from each terminal.
This is applied to the transmitting side of the terminal circuit between
the twelve-channel terminal and the first group modulator, where the

A TWELVE-CHANNEL CARRIER TELEPHONE SYSTEM 137

message band lies between 60 and 108 kilocycles. The pilot frequency
is 84.1 kilocycles which is obtained by modulation of 88 kilocycles,
from one of the output taps of the channel supply of that frequency,
with 3.9 kilocycles derived from a tuning fork oscillator. This modu-
lation is performed in a copper-oxide bridge similar to the channel
modulators and the desired product is selected by an 84-kc. carrier
supply filter. The output of 84.1 kilocycles is sufficient to supply
pilot current for ten terminals in the office. A sharply selective crystal
band elimination filter is inserted between the output of the twelve-
channel terminal and the point where the pilot source is bridged on the
circuit to eliminate any current near the pilot frequency which would
interfere with the small pilot current that is sent out to control the
system.

The two group modulation processes alter this pilot frequency of
84.1 kilocycles so that it appears on the line as 59.9 kilocycles in the
west to east directional band, and as 116.1 kilocycles in the east to
west band. Correction in accordance with the magnitudes of these
mid-group currents in the two directions is satisfactory over all twelve
channels under ordinary conditions. In the case of ice or snow the
channels at the edges of the directional frequency groups may not be
properly adjusted. Additional pilot frequencies will probably be
needed ultimately to care for such unusual conditions.

Regulating Amplifier
Figure 9 shows the circuit of the regulating amplifier, and above this,
the circuit of the pilot channel receiving equipment which controls it.
Current enters the regulating amplifier circuit from the left, coming
from the receiving directional filter through a shielded transformer and
the pads and building-out networks used for equalization. At the
terminals the circuit includes also the basic equalizer. Last in the
circuit leading from the line to the regulating amplifier is the regulating
network which consists of a series of three equal networks having a
total loss of 20 db at 140 kilocycles in the east to west direction and
15 db at 84 kilocycles in the west to east direction. The network
loss increases with frequency in the same way as the difference between
dry and wet weather attenuation of the line. The two terminals of
the regulating network and the two junction points between the three
networks are brought to four sets of stator plates on an adjustable
condenser. The rotor of this condenser, which has about the same
area as one set of stator plates, is connected to the grid in the first
stage of the regulating amplifier. Rotation of the condenser therefore
applies, to the grid of the first tube, a voltage which decreases con-
tinuously as the condenser rotates from left to right.

138

BELL SYSTEM TECHNICAL JOURNAL

n4n

5P 2u LvN^>i:

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A TWELVE-CHANNEL CARRIER TELEPHONE SYSTEM 139

The regulating amplifier has two stages of pentode tubes, a high
input impedance necessary for the proper operation of the condenser
potentiometer, and feedback to stabilize the gain and to prevent inter-
modulation of the channels. Its output goes to the line amplifier at
repeater stations, and to the first group demodulator at the terminals.
At a west terminal there is interposed a high cut-off filter to eliminate
frequencies above the upper band which may have been picked up on
the open-wire line.

Pilot Control

The setting of the condenser which controls the regulating network
is determined in accordance with the amount of pilot current flowing
in the circuit in the direction concerned. At repeater stations the
pilot current is picked off at the output of the line amplifier, being
separated from the message transmissions by a quartz filter which
has about a 30-cycle pass band. For control of transmission from west
to east at the repeater stations, this filter selects 59.9 kilocycles and
for control of the oppositely directed transmission, 116.1 kilocycles.
At the terminals the pilot channel selecting filter is connected across
the output of the auxiliary amplifier following the second group de-
modulator where the pilot frequency is 84.1 kilocycles. The pilot
current from the pick-off filter is amplified in a single-stage amplifier
which has feedback for constancy of operation and input and output
circuits tuned to the pilot frequency. After amplification the pilot
current is rectified by a temperature compensated copper-oxide
rectifier.

The resulting direct current passes through the operating windings
of the control and alarm relays. These Weston Sensitrol relays are,
in fact, microammeters with high and low contacts made by the point-
ers. The mechanical bias of the moving system is adjusted so that
with the normal pilot current the pointer will remain free in the middle
between the two contacts. A change of about 0.5 db in this current
will cause the pointer of the control relay to make contact with the
terminal at the corresponding end of its swing. As the limiting con-
tacts are magnetized and the pointer is of magnetic material, good
contact is insured. When contact is made on one side a 60-cycle
circuit is closed through the motor which controls the regulating con-
denser in such a direction as to cause the loss in the regulating network
to be increased. Closure of the other contact similarly causes the
loss in the regulating network to be decreased. Closure of either con-
tact also closes a circuit containing a slow-operate "pulse" relay to
release the Sensitrol relays after an interval of about four seconds.
During this time the gain of the regulating amplifier will have been

140

BELL SYSTEM TECHNICAL JOURNAL

Fig. 10 — Typical installations.

(A) Auxiliary repeater station.

(B) Cable hut.

(C) and (D) Terminal installations.

A TWELVE-CHANNEL CARRIER TELEPHONE SYSTEM 141

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142 BELL SYSTEM TECHNICAL JOURNAL

changed about 0.1 db. If now the pilot current level is within 0.5 db
of normal the operation is complete. If not, it is repeated and the
device keeps periodically testing the circuit so long as it is away from
satisfactory compensation. There are also alarm circuits for attracting
attention in cases of wide variations in equivalent. In severe ice
conditions where a single regulating repeater has not sufficient gain
to make up for the great loss in the line, the next succeeding repeater
will do its utmost to make up the deficiency.

Conclusion

In what has preceded, developments have been described which
are making it possible to provide a very substantial increase in circuits
on open-wire pole lines without additional wire stringing. Photo-
graphs showing typical office installations of type J carrier equipment,
unattended repeater stations, and filter huts are shown in Fig. 10.

Three stages in the development of the open-wire line over the past
twenty years, giving successive increases in circuit capacity, are shown
in Fig. 11. Prior to the application of carrier systems, a four-crossarm
pole line would yield thirty voice circuits. Now, on a new line 256
circuits are potentially obtainable. Thus it is probable that the open-
wire line will continue as an important factor in furnishing facilities
in moderate numbers, particularly in the less densely populated sec-
tions of the country and where climatic conditions are not unfavorable.
Installations of type J systems have already been made in various
parts of the country.

Recent Developments in the Measurement of
Telegraph Transmission

By R. B. SHANCK, F. A. COWAN and S. I. CORY

This paper describes the progress which has been made in re-
cent years in the development of methods and apparatus for the
measurement of telegraph transmission in the Bell System. Such
measurements pla^^ an important part in transmission maintenance
work in the field and are also necessary in development work. The
changes which have occurred in service requirements, particularly
the large commercial development of start-stop teletypewriter serv-
ice and the effect of these changes on the technique of telegraph
transmission measurement, are first discussed; then a description is
given of several new measuring devices and their use.

TN keeping with advances in the telegraph transmission art, note-
-'- worthy improvement has been made in measuring devices and
methods in the past few years. The faster, more accurate, and
generally more dependable telegraph service now available has been
made practicable not only by improvements in the telegraph systems
but also by the use of improved measuring apparatus and techniques.

In the early stages of development most transmission-measuring
systems were arranged to measure transmission on "looped" circuits,
that is, with sending and receiving terminals at the same point, so
that a comparison between the sent and received signals could be made.
Although such an arrangement is quite useful for laboratory testing,
it imposes serious limitations on field testing. Therefore, it is generally
desirable to make tests on a straightaway basis.

For straightaway tests it is necessary to have at the receiving end
certain information regarding the sent signals. This requires either
the use of signals of certain known characteristics or the determina-
tion of the important characteristics of the sent signals and the trans-
mission of this knowledge to the receiving end. The latter of these
alternatives is not frequently used since it requires another com-
munication channel, although in some instances, where tests on
working circuits are desired, it represents the only practicable ap-
proach. Straightaway measurements of telegraph transmission have
for this reason been generally confined to measurements in which the
important characteristics of the transmitted signals were known.

Fortunately, either synchronous or stop-start teletypewriter signals

143

144 BELL SYSTEM TECHNICAL JOURNAL

fall into the last-mentioned classification and the increased use in the
Bell System of stop-start teletypewriter transmission has afforded
the opportunity of making telegraph transmission tests on working
circuits without the need of transmitting information regarding
the character of the sent signals. Of course, when sectionalized
transmission measurements are desired it is necessary for proper
interpretation to transmit the results of the measurements to a single
point for analysis, but the communication of this information is not
at all burdensome.

Aside from the ability to measure on a straightaway basis, which is
primarily a field-maintenance requirement, testing equipment should
preferably be direct-reading without the need of measuring adjust-
ments on the part of the tester. Direct-reading devices in general effect
considerable reduction in the time required for measurement. This
feature is especially important in the field where a rapid test of possible
trouble conditions is desirable and in the laboratory where the large
numbers of tests which are necessary for thoroughly checking a
telegraph transmission system under all of the likely operating con-
ditions become even at best tedious and time-consuming.

The major development in telegraph transmission testing within
the past few years has been the provision of instrumentalities which
possess the desirable properties indicated above. They permit the
rapid and direct reading of signal distortion on working teletypewriter
circuits. The same instrumentalities when used with selected or
miscellaneous teletypewriter test signals also permit the rapid de-
termination of the capabilities of a telegraph circuit in the field or in
the laboratory.

A paper published in 1927 ^ discussed fundamental concepts relating
to signal distortion and described a number of measuring devices
which had been employed in the Bell System. Another paper ^
treated the design of telegraph circuits for distortionless transmission
from the standpoint of the steady-state characteristics. The funda-
mental ideas set forth in these papers have continued to form the
basis for development of the technique of measuring telegraph trans-
mission. However, it has been necessary better to adapt these ideas
to start-stop teletypewriter operation and changing field requirements.

Operation of telegraph circuits by means of start-stop teletype-
writers *• ^ using 7.4-unit code has become of much greater importance
in the Bell System in the past dozen years. The majority of private-
line service is now furnished on a teletypewriter basis; also teletype-
writer exchange (TWX) service,* inaugurated in 1931, has become an

1 References are listed at end of paper.

MEASUREMENT OF TELEGRAPH TRANSMISSION 145

important factor, having already grown to the point where the trunk-
circuit mileage employed is a large part of the total telegraph mileage.
Incidentally, there has been at the same time a general increase in
operating speeds, so that the majority of the circuits now operate at a
nominal speed of 60 words per minute (23 dots per second or 46 bauds).
As regards the requirements for measuring apparatus for field
transmission maintenance, the desired precision and convenience have
increased considerably in the last few years. This is due to several
causes, chief of which are the continuing desire to give better service
with greater freedom from interruptions and isolated errors, increase
in speeds of operation, and the use of more complicated circuit layouts
with more sections in tandem, particularly in Press and TWX service.
For complicated circuits it is very advantageous to employ mainte-
nance procedures in which each section is measured and adjusted
separately to close limits, to avoid the more costly and otherwise less
desirable overall line-up. Furthermore, a need has arisen for accurate
transmission measuring devices for other uses such as checking the
condition of receiving teletypewriters, transmitting keyboards and
regenerative repeaters,^ and use in "equalizing" of telegraph circuits,
that is, the application of wave-shaping arrangements for reducing
distortion. Finally, in line with improvements in main-line circuits
greater emphasis has been placed on maintaining loops and circuits
to outlying points so that they introduce but little distortion.

Adaptation of Measuring Technique to Teletypewriter Basis
The earlier types of measuring sets were arranged to measure the
total change in the duration of signal pulses, that is, the combination of
the displacements at the beginning and end of any given pulse. This
method of measuring gives results which are directly indicative of the
impairment for Morse operation since the interpretation of the signals
depends on the total duration of pulses. This method also gives
a moderately good indication of the effect of distortion for teletype-
writer operation.

In start-stop teletypewriter operation there are two ways in which
circuit imperfections may cause the transmission to be impaired. In
the first place, imperfections other than constant delay (known as line
lag), which may be neglected, may cause the start transition of any
character to be displaced with respect to the time at which it should
occur. This causes the starting of the receiving mechanism to be
advanced or retarded and effectively displaces the succeeding transi-
tions of the character. Secondly, other imperfections may also cause
any of the succeeding transitions to be displaced in either direction.
The combination of these two effects determines the effective distortion.

146 BELL SYSTEM TECHNICAL JOURNAL

It is of interest to consider the case of bias alone. With uniform
bias the displacement of mark-to-space transitions is in one direction
and that of the space-to-mark transitions is in the other direction with
respect to their positions in undistorted signals. Since the start
transition is mark-to-space the result is that the effective displacement
of subsequent mark-to-space transitions is zero and the efTective dis-
placement of space-to-mark transitions is numerically equal to the
bias. In practice bias is seldom uniform and may vary with the
signal combinations. In these cases there is an effective displacement
of mark-to-space as well as space-to-mark transitions.

From the foregoing, it will be seen that it is of considerable practical
value to be able to measure teletypewriter circuits on a start-stop
basis in terms of displacement of transitions with respect to the start
transition. (For a more complete explanation of the effect of dis-
tortion on teletypewriter operation, reference should be made to
published discussions.** ^' ^) In testing with miscellaneous signals,
bias may for convenience be taken as the average effective displace-
ment of space-to-mark transitions relative to mark-to-space transitions;
characteristic distortion will have the appearance of a combination
of fortuitous and bias effects; and the maximum total distortion will
be the sum of the average effect and the variation therefrom which
causes the greatest displacement.

Other Changes in Measuring Technique
In measuring with normal and inverted signals ^ on circuits of the
types commonly employed, the result obtained for the bias varies
somewhat from pulse to pulse of the test signal. A case in which this
variation is appreciable is that of carrier telegraph having level
compensators (automatic devices which correct for changes in the
magnitude of the received current). With these compensators, the
response is fairly rapid, the result being that the bias is to some extent
a function of the signal combinations of the transmitted material.
This bias variation is also noticeable with open-and-close d-c. telegraph
circuits having large bridged capacitance or series inductance.

On account of this bias variation, it is desirable to measure the
algebraic average of distortion of the individual pulses of miscellaneous
signals and take this as the bias. This may be conveniently done by
measuring on the start-stop basis mentioned above. In such measure-
ments the differences between the distortions of the individual pulses
and the average distortion may be considered as due to the combination
of characteristic and fortuitous effects; further measurement is
necessary in order to separate these effects. A measure of character-

MEASUREMENT OF TELEGRAPH TRANSMISSION 147

istic distortion may be obtained by determining the difference between
the systematic distortion measured with selected recurring signals and
the average distortion with miscellaneous signals. Fortuitous dis-
tortions may be taken as the difference between the total and sys-
tematic distortions obtained with recurring signals. In order to
distinguish between the variable bias and the true characteristic
distortion in the case of level-compensated circuits measurements
may be made with the compensator disabled and with it functioning.

For tests in the field where it is desired to measure systematic
distortion effects, as for instance in connection with equalizing, several
simple signals corresponding to certain especially selected teletype-
writer characters are employed. In each of these signal combinations
there are only two transitions; therefore it is convenient to observe
the effect of the remnants of one transition upon the next transition.
As discussed in the Appendix, the characteristic distortion obtained
for miscellaneous signals is a function of the distortion obtained with
the simplest characters; if there were no distortion on the simple
characters no characteristic distortion effects would be expected
when miscellaneous signals were transmitted. The process of equal-
ization, therefore, consists in adjusting the transmission characteristics
of the line circuit to reduce the characteristic distortion measured
on six special characters to a minimum. The teletypewriter char-
acters which are used for this purpose are Blank, T, 0, M, V and
Letters; the corresponding signals are shown in Fig. 1. The distortions
of these signals are observed at the receiving end on a measuring set
operating on the start-stop principle or a portable systematic-distortion
measuring set having an integrating meter, as will be described more
fully below.

In equalization testing, each of the six signals is sent repeatedly for
the time required to determine the total systematic distortion —
generally about 50 repetitions. In analyzing the results the bias
component is assumed to be substantially the same for all of these
signals and whatever difference is observed from one signal to another
is taken as being due to characteristic distortion. It is found generally
that the result for the O signals, which are practically unbiased six-
cycle reversals (see Fig. 1), is not radically different from the result
obtained for bias with reversals at 6 or 23 d.p.s. (shown in the lower
part of Fig. 1), the results being expressed, of course, in the same
terms, as for instance in per cent of a 23-cycle dot. The largest
distortion is usually found on either the Blank or Letters character,
this being reasonable because usually the remnants of transients
practically disappear within a few dot lengths. Sometimes it is

148

BELL SYSTEM TECHNICAL JOURNAL

SIGNAL

STOP

START 12 3 4 5

STOP

BLANK

T

0

i

1

M

V

LETTERS

UNIT

^

r

ei^-REVERSALS

23~ REVERSALS

TIME
BIAS- 7o

-61.7

-34 7

-7 8

-H9.2
+ 46.1

f730
-73 0

0
0

note; (I) TIME BIAS =

MARKING TIME -SPACING TIME
MARKING TIME-H SPACING TIME

Fig. 1 — Signals used in measuring systematic distortion. The first six signals and
the eighth signal are teletypewriter characters.

desirable to extend the test to include biased test signals, as described
below.

As an example, curves are given in Fig. 2 showing the results of
tests with the six characters on a d-c. metallic telegraph ^ circuit
operating on 112 miles (180 km.) of composited 19-gauge cable pair.
Curves 1 and 2 show the results before and after equalization respec-
tively; it will be noted that considerable improvement was effected.
On the basis of both experiment and theory, the slope of Curve 1 is
known to indicate that the received direct current is larger than it

Fig. 2 — Equalization test result for a 112-mile section of metallic telegraph; signalling
speed 23 d.p.s. Curve 1, before equalization; curve 2, after equalization.

MEASUREMENT OF TELEGRAPH TRANSMISSION 149

should be as compared to the higher-frequency components of the
received current waves. The required type of equaUzer in this case
is one which adds loss at frequencies in the vicinity of zero, without a
corresponding loss at the higher frequencies. If, however, the slope
had been in the opposite direction, an equalizer which would dis-
criminate against the higher frequencies would have been required.
As a check of the equalizer setting, the total distortion and bias are
usually measured using miscellaneous teletypewriter signals.

In addition to measuring with undistorted signals applied at the
sending end of a circuit, the measuring technique has been expanded
to include measuring with distorted signals and a device has been
made available for field use by means of which reversals or teletype-
writer characters may be distorted by known amounts. This kind of
test furnishes additional information in that it affords an examination
of the effect of signal combinations which are not included in perfect
telegraph signals. It is of value because in actual operation a given
telegraph section may not have perfect signals impressed at the
sending end due to distortion occurring in previous sections or at the
transmitter. Although such a test furnishes valuable information
for line testing, it has been used in the field up to the present mainly
in testing the distortion-tolerance of subscriber-station teletypewriters
with signals from the adjacent central office and in maintaining re-
generative repeaters.

It is necessary, of course, to make transmission measurements on
the manual Morse circuits which still constitute a considerable part of
the total mileage. Testing such circuits by the same methods as used
for teletypewriter circuits has been found to give good results. How-
ever, due to improvement of telegraph circuits, the transmission-
maintenance problem in this case consists mainly of keeping the bias
within reasonable limits for which purpose simple tests with reversals
can be used.

New Measuring Devices

In the following is given a description of a number of testing methods
and arrangements which have been found useful in recent years both
in the field and in development work.

A. Start- Stop Distortion- Measuring Set for Central-Office Use
A start-stop type of measuring set for testing teletypewriter circuits
has been developed and is now used generally in maintenance work
and special testing in the field and in laboratory work. This repre-
sents an outstanding advance in that it provides a quick and convenient
means for reading, directly from conventional-type milliameters as

150

BELL SYSTEM TECHNICAL JOURNAL

illustrated by Fig. 3, the distortion of miscellaneous teletypewriter
signals on working circuits. It has the distinct advantage of giving
immediate indication of the occasional isolated peaks as well as the
average distortion. In using this set, it is unnecessary to have a
knowledge of the transmitted text.

This set employs the condenser-charging principle in the measure-
ment of small time intervals corresponding to the distortion of the

Fig. 3 — Meters and control apparatus at telegraph board.

signals. The outstanding feature of this device is that the beginnings
of the condenser-charging intervals are timed with relation to the start
transition by a start-stop distributor which forms an integral part of the
set. The charging intervals are terminated by the occurrence of tran-
sitions in the characters, at which times the operation of a receiving
relay causes the condenser voltages to be compared to a reference volt-
age. The circuit is arranged to charge the condenser at a constant
rate; hence the voltage attained is determined by the duration of the
charging interval. In this way the displacements of the transitions

MEASUREMENT OF TELEGRAPH TRANSMISSION

151

in the received teletypewriter characters from their proper positions
are measured in terms of condenser voltages. Indications are afforded
of the average distortion and the peak value of the total distortion,
the latter being the sum of the bias, characteristic and fortuitous
effects.

SIGNAL

IN

LOOP

DISTRIBUTOR
SEGMENTS

-dh I — ®^

JM METER

TO LOOP

?=

REFC.E

Fig. 4 — Explanatory sketch of start-stop telegraph transmission
measuring set.

The general features of this set will be described in the following.
In Fig. 4 a condenser-charging circuit is shown with a distributor for
the purpose of timing the charging intervals in the measurement of
distortion occurring at transition B. Assume the distributor brush
to be traveling in the direction of the arrow after being released by the
mark-to-space transition at A by means of arrangements not shown.
This same transition causes the relay armature to move to the spacing
contact {S) and the condenser to begin to charge from the constant
current supply, but as soon as the brush touches the grounded segment
the condenser is discharged completely. After leaving the grounded
segment the brush travels over an open segment and during this
time the condenser accumulates a charge. At transition B, the arma-
ture of the relay moves to its marking contact {M) and the voltage
of the condenser is compared with the reference voltage (REFC. E)
which has been previously adjusted to such a value that if there is no
distortion the condenser voltage and the reference voltage will be
equal. However, if transition B does not occur at the proper time,
because of distortion, the condenser voltage will differ from the
reference voltage and a momentary current will flow through the
indicating meter {M) in proportion to the amount of distortion.

152

BELL SYSTEM TECHNICAL JOURNAL

Two condenser-charging circuits are provided, one for space-to-mark
transitions and the other for mark-to-space transitions as is indicated
in Fig. 5. Graph A of this figure shows an undistorted teletypewriter

UNDISTORTED
SIGNAL

VOLT -TIME CURVE
CONDENSER CI

VOLT-TIME CURVE
CONDENSER C2

SCHEMATIC
CIRCUIT

HE>

I

^AA/ * ^

RELAY
D

NOTE

IN (B38.CC) THE HEAVY
SLANTING PARTS OF THE
CURVES INDICATE CHARG-
ING INTERVALS USED IN
MEASUREMENTS.

LEGEND

TD- TOTAL DISTORTION METER (PEAK-
B - BIAS METER INDICATING)

CI - M-S MEASURING

CONDENSER

C2 - S-M MEASURING

CONDENSER

TO TELEG LOOP

Fig. 5 — Simplified diagram of start-stop telegraph
transmission-measuring circuit.

character having a stop pulse, start pulse, and five selecting pulses.
The segments of the distributor, laid out to show their relation to the
received signal, are indicated at the top of the schematic circuit {D).
It will be noted that there are seven short grounded segments, one
for each of the pulses of the character, for initiating the condenser-
charging intervals referred to above.

Assume the distributor brush to be at rest during the stop interval
as show^n. The measuring condenser CI is now charged to the refer-
ence voltage. As the brush leaves the stop position due to the mecha-

MEASUREMENT OF TELEGRAPH TRANSMISSION 153

nism controlled by the start pulse (not shown), it travels in the direction
of the arrow and the condenser charges vary as indicated by graphs
B and C. It will be seen on graph B that condenser CI is charged
during intervals between grounded segments and mark-to-space
transitions. Graph C shows that condenser C2 is charged between
the grounded segments and space-to-mark transitions. If there is
no transition while the brush is traveling between two adjacent
grounded segments the condenser continues to be charged until the
brush touches the second grounded segment at which time it is com-
pletely discharged. Therefore, the useful charging interval is that be-
tween a grounded segment and a transition occurring before the next
grounded segment is traversed by the brush. These intervals are
indicated by the heavy-lined portions of the graphs. They amount
to 37.5 per cent of a unit pulse as a maximum, i.e., the maximum
distortion which can be measured is about 37.5 per cent. The
currents flowing as a result of the comparison of the condenser voltages
with the reference voltage are indicated on a "Total-Distortion
Meter" TD which is, in reality, a peak-indicating voltmeter, and on
a "Bias Meter," B which is sufficiently sluggish to give an indication
corresponding to the average distortion. These meters are calibrated
to indicate directly the percentage distortion with miscellaneous
teletypewriter characters.

Good accuracy is obtained with these sets; when measuring distor-
tions of small or moderate amounts with a well-adjusted set, the
indication is accurate to within about 2 per cent distortion at 60 words
per minute. For occasional large distortions or for higher speeds,
the accuracy is not quite as good, and there are certain possible mutila-
tions of signals, such as the dropping out of pulses, which would not be
readily detected.

In addition to measuring miscellaneous teletypewriter characters
these sets may be used with recurring test signals in which the spacings
of the transitions are such that the maximum characteristic effects
will be obtained, and with signals which experience mostly bias and
fortuitous effects. In this way a measure of the components of
distortion may be obtained. Such tests are commonly made in
adjusting variable networks to minimize characteristic distortion, i.e.,
making the equalization tests, referred to above, with selected tele-
typewriter signals.

In special testing where it is desired to separate the total distortion
into its components, this may be done by measuring the systematic
distortion with the first 6 signals of Fig. 1 and then measuring the
bias and total distortion using the / character of Fig. 1 (which is sub-

154

BELL SYSTEM TECHNICAL JOURNAL

stantially the same as unbiased reversals at about 11 d.p.s.). The
bias component is simply the bias measured with / signals, the fortui-
tous component is taken as the difference between the total distortion
and the bias of / signals, and the characteristic component is obtained
by averaging the results for the 6 selected characters and then selecting
the result which shows the maximum departure from the average.

These sets also furnish a convenient means for the measurement of
mean-square values of distortion. The current impulses flowing
through the total distortion meter are proportional to the distortion
and it is practicable to insert in series a specially arranged meter
which is calibrated to indicate the mean-square values of the dis-
tortion. The circuit used is shown by Fig. 6, the heavy lines showing

LOOP
RELAY C

TOTAL

DISTORTION ::

(PEAK- indicating)

C2

copper-oxide
rectifiers

MEAN- SQUARE -
DISTORTION

Fig. 6 — Circuit of start-stop set for measurement of mean-square distortion.

the meter circuit which is inserted in series. It contains an integrating
meter whose characteristic is modified by a full-wave copper-oxide
rectifier, a large condenser for increasing the damping and resistances
for adjusting the amplitude and response characteristics. Measure-
ments of mean-square distortion have been found of value in con-
nection with producing transmission ratings of telegraph circuits,
these ratings being based on the assumption that the mean-square
values of distortion of component parts of a circuit may be added
directly to predict the total mean-square distortion.^

MEASUREMENT OF TELEGRAPH TRANSMISSION

155

In certain other special tests, where it is desired to obtain a record
of the variation in distortion, recording meters have been connected
in series with the meters of the set and a continuous record made using
either a recurring test message or the signals from the subscriber.

JHL

Fig. 7 — Start-stop telegraph transmission measuring seL.

An idea of the arrangement of the measuring set for central office
use may be obtained from the front and rear views which are shown
in Fig. 7. It is the practice to provide multiple appearances at
telegraph boards in order that one set may be used at any one of a

156

BELL SYSTEM TECHNICAL JOURNAL

number of positions. The unit containing the indicating meters and
associated controls for mounting at the telegraph board is illustrated
in Fig. 3. The set is also provided in portable form for temporary
use in cases where a permanent installation is not justified.

B. Telegraph Stability Test Set
Recording meters have been used for a number of years in the
measurement of the transmission stability of telegraph circuits.^ In
such a measurement a continuous graphic record is made over as long a
period as desired of the variations in the bias and of the number and
time of occurrence of fortuitous effects which would impair telegraph
service. For this purpose telegraph reversals are impressed at the
sending end and a recorder at the receiving end makes a record of the
bias of these reversals. This type of test was found to be of such
utility in field work that standard stability test sets were produced
for this purpose.

* GALVANOMETER RELAY
^(* RECORDING METER

Fig. 8 — Schematic circuit of telegraph stability test set.

The circuit of the telegraph stability test set is indicated in Fig. 8.
This is essentially a simple bias-measuring circuit combined with an
alarm circuit to indicate when given values of bias are exceeded.
Movement of the armature of loop relay A from M to S contact or
vice versa in response to the received signals causes a battery E to be
connected first to one arm (resistances 6 and 4) and then to the other

MEASUREMENT OF TELEGRAPH TRANSMISSION 157

arm (resistances 3 and 7) of a bridge type of circuit containing recording
meter M. The two arms of the bridge are balanced and the meter,
being bridged across them, receives positive and negative current
pulses of equal magnitude in response to the armature movements.
If these pulses are of equal duration, as for telegraph dots or reversals
having zero bias, the average meter current will be zero. Biased
reversals will cause the meter current to average at other than zero
by an amount directly proportional to the percentage bias. A center-
zero recording meter is used and this provides a running record of the
variation in bias. A damping condenser C is used to reduce the
width of the trace and the amount of unsteadiness of the indication
due to fortuitous effects.

The alarm circuit contains a galvanometer-relay bridged across equal
resistances 4 and 7. The needle of the galvanometer-relay moves to
one contact or the other when excessive values of bias are experienced,
the sensitivity being adjusted for response to different values of bias
by means of adjustable resistance 2. The response is made somewhat
sluggish to avoid alarms being given for interruptions of short duration
which are not of interest in connection with an investigation of bias
stability.

A sample chart obtained by means of one of these sets is shown in
Fig. 9. This chart shows slow variations in bias in the upper part
and in the lower part the change in the indication due to dropping
out or adding a single dot and momentary failures. Such charts do
not, of course, show the characteristic distortion, since this is not
present in the case of unbiased reversals.

These sets are now generally used in the field in routine checks on
telegraph circuits and in special checks on circuits which have de-
veloped faults in service. Usually these checks are made with the
idea of locating the cause of hits or swings which it is difficult to
locate otherwise ; in some cases sets are used simultaneously at several
repeater points to sectionalize trouble. Charts are run for long
periods, sometimes for several weeks in such tests. The stability test
sets are also used to obtain data for transmission ratings of circuits,
in which case it is desired to know the extent of the bias variations
over long periods and the number and frequency of occurrence of hits.

Figure 10 shows a view of the portable arrangement of the set
including the recording meter. The alarm buzzer and the receiving
relay are located on the panel along with a row of keys for adjusting
the alarm for operation on given values of bias. Jacks are provided
on the side of the box for connection to circuits, batteries and the

158

BELL SYSTEM TECHNICALZJOURNAL

NOON

MOMENTARY
SPACING
FAILURE

MOMENTARY
.MARKING
FAILURE

Fig. 9— Telegraph stability test— sample chart.

MEASUREMENT OF TELEGRAPH TRANSMISSION 159

Fig. 10 — Stability test set with recording meter.

recording meter. This set is also arranged for permanent mounting
on a relay rack in a central office.

C. Portable Measuring Set for Use at Outlying Stations
A new measuring set has been made available for commercial use
especially at outlying stations in either routine or special testing.
This set is arranged for the accurate measurement of the systematic
components (bias and characteristic) of distortion of recurring test
signals. In addition measurements may be made of peak values of
interference and of the effect of bias and variations in operating
currents on the distortion. Such measurements are desirable in
analyzing the causes of transmission troubles and in equalization
work. By properly interpreting the results of these measurements a
fair idea may be obtained of the maximum total distortion. In
addition the set is arranged for the convenient measurement of the
operating currents and voltages in various parts of the subscriber's
circuit and in external circuits. This set may be used on either
110-volt a-c. or d-c. commercial power supply. It is mounted in an
aluminum case, and weighs only about 28 lbs. (13 kg.).

The circuit employed for the measurement of systematic distortion
is indicated schematically by Fig. 11. This is a simple bridge type of
circuit similar to that generally used in a measurement of bias with
reversals but especially arranged to indicate directly the percentage
systematic distortion of the signals of Fig. 1 excepting " I " signal. The
meter circuit is highly damped to prevent undesirable vibration of the
meter needle in response to the 6-cycle fundamental frequency of the
60-speed teletypewriter characters. This entails the use of high
resistances R, and large capacitance C. Since the voltage in the power
supply is limited, a very sensitive meter M is required.

160

BELL SYSTEM TECHNICAL JOURNAL

To obtain a zero reading on the meter for each undistorted test
character the ratio of the marking to spacing currents is made inversely
proportional to the ratio of the marking to spacing time intervals.
This is accomplished by means of taps on a potentiometer as indicated
in Fig. 11. With the connection made to the middle or Reversals

im'tl pH receiving

RELAY

IhAA-

Fig. 11 — Outlying-station test set. Schematic circuit for measurement of systematic

distortion.

tap, equal and opposite currents flow through the meter when the
relay armature rests first on its marking and then on its spacing
contact. If the relay is repeating undistorted reversals, the time bias
in the signals is zero and the average meter indication will be at zero.
With a given undistorted recurring character such as Blank, and with
the potentiometer set at the Blank tap, the meter indication will again
average at zero. The meter circuit is arranged so that the systematic
distortion is indicated directly in percentage based on the duration of
a unit signal element of a teletypewriter character.

The circuit used in the measurement of interference is indicated by
Fig. 12. The interfering effect is measured by noting on the meter M
the biasing current which will just prevent the armature of the receiving
relay from responding to the interfering currents. Movement of the
armature from its contact is indicated by a response in a telephone
receiver connected in the armature circuit when the switch is operated
as indicated. The biasing current variation is effected by means of
potentiometer P and the biasing current may be reversed by means
of a switch (not shown).

The circuit of Fig. 12 may also be used to give an indication as to

MEASUREMENT OF TELEGRAPH TRANSMISSION

161

the amount of transmission degradation to be expected due to the
interference measured and to given changes in operating currents.
In this case the switch is operated to connect meter Ml in circuit
for the purpose of measuring bias. The effect on the bias of changes
in the biasing current for a given operating condition may then be

LINE

Fig. 12 — Outlying-station test set. Schematic circuit for interference measurement.

noted on this meter when receiving reversals or any of the selected
teletypewriter characters. The biasing current is varied by means of
potentiometer P as before.

This set has several interesting operating features. By inspection
of Fig. 13, which shows a view of the set, it will be seen that it contains
its own receiving relay located in the lower left corner. This relay
may be connected in series in a line circuit or in the local circuit of
the subscriber set using the line jacks 1 and 2 (located in the upper
right-hand corner of the set) or if desired convenient connection may
be made by means of the splecial plug and adapter shown in the lower
part of the figure. In the latter case the subscriber set relay is trans-
ferred to the measuring set and the special plug, and adapter if required,
is inserted into the relay connecting block of the subscriber set in place
of the relay. By operating the proper keys on the test set the currents
in different circuits of the subscriber set may then be measured conven-
iently. Distortion may also be measured with this connection but in
most cases it is desirable to measure with the receiving relay in its nor-
mal position in the subscriber set to obtain representative conditions.

Because of the advantages of the set, namely, the accuracy possible
in the measurement of distortion, the convenience afforded in the

162

BELL SYSTEM TECHNICAL JOURNAL

Fig. 13 — Outlying-station test set.

measurement of operating and interfering currents, and the portability
of the set, it is expected to be of considerable benefit in telegraph
transmission maintenance work at outlying subscriber stations.

D. Distortion-Distribution Recorder

A short test to determine the peak value of the distortion existing
on a circuit at any particular time is of great value but in development
work it is sometimes desired to know the frequency of occurrence of
different values of distortion ; in other words, to obtain data from which
a distribution curve of distortion may be plotted. Such distribution
curves were referred to in the earlier paper and it was stated there that,
in general, the distribution of distortion is in accordance with the normal
law. To check this on different types of circuits in connection with
work on transmission ratings of telegraph circuits and for other labora-
tory uses a "distortion-distribution recorder" has been devised.

The distortion-distribution recorder operates on a synchronous basis
and is suitable only for testing over looped-back circuits. It may be
used at any speed up to about 75 words per minute (28.5 dots per
second, 57 bauds). It indicates the distortion of the transition at
either end of a signal pulse, the indication being in terms of the dis-
placement of the transition from its correct time of occurrence in the

MEASUREMENT OF TELEGRAPH TRANSMISSION 163

signal combination. Records of the distortion are made on message
registers in ranges of one per cent for small distortions and greater
ranges for larger distortions.

As shown in Fig. 14, this device contains a sending distributor face
(a) to provide test signals and two receiving distributor faces {h)
and (c). Coupled to these and running five times as fast is a large
disc carrying a fine point from which a spark may be made to jump to
any one of a series of stationary segments. This is referred to as
"distortion-scanner" in the figure. Since the disc makes one-half
revolution while the sending distributor brush is traversing one seg-
ment, one-half revolution of the disc requires the same time as one
dot and is, therefore, equal to 100 per cent distortion. One hundred
segments are provided as indicated, each being equivalent to 1 per cent
distortion, so that this ring of segments forms a distortion scale
covering the range of ± 50 per cent distortion. Distortion indicators
are associated with these segments, each containing a gas-filled tube
and a message register. Only the first ten segments on either side of
zero are provided with individual indicating arrangements, the
succeeding segments being combined in successively larger groups as
shown in the figure; this affords adequate information for the usual
case.

Assume the switches associated with the sending distributor face {a)
to be operated to send the signal shown in note 2a. After traversing
the circuit to be tested this signal operates the receiving relays, one
of which is associated with a "lag-meter" and the other with a spark-
producing circuit. If the time of occurrence of transition X (note 2-a)
is to be used as a reference, the MS switch of the lag circuit is closed
and the sending segments oriented until transition A" occurs while
the brush of receiving distributor {b) is midway between segments 9
and 10, as is indicated by a lag-meter reading of zero. The positions
of the segments of the receiving faces {b) and {c) with respect to the
signal will now be as indicated in notes 2-h and 2-c, and the set is
ready to measure the occurrence of a transition between any two
segments of the sending face, for instance, transition Y or Z.

If for instance the displacement of transition Y with respect to
transition X is to be measured, the switch associated with face (c) is
set to connect to segment 4. When transition Y occurs the receiving
relays operate to marking, condenser C is discharged through the
primary of the induction coil and a spark jumps from the scanning
point to a stationary segment. If transition Y is not distorted the
spark will jump when the scanning point is opposite segment 0.
This will cause the gas tube associated with segment 0 to fire and

164

BELL SYSTEM TECHNICAL JOURNAL

^ r% ^

MEASUREMENT OF TELEGRAPH TRANSMISSION

165

operate the message register which in turn will extinguish the tube by
momentarily short-circuiting the anode potential. Other transitions
in the signal will not cause the condenser C to be discharged through
the coil because the brush of face (c) will not be traversing the proper
segment and there will be no path to ground.

The complete circuit of the device contains a selecting switch which
automatically changes the signal combination for each revolution of
the brush arm of face (a) and reversing switches to invert the signals
and the relay connections. These have been omitted for the sake of
briefness and clarity. It is thought, however, that the above descrip-
tion will give a good idea of how this device operates to make a record
of the frequency of occurrence of distortions. A sample of such a
record is plotted in Fig. 15, this being from data obtained over a

600

-10 -8

-6

-4-2 0+2+4

•7o DISTORTION

Fig. 15 — Typical curve obtained with distortion-distribution recorder.

short-wave radio link. The measurements covered a 15-minute period
and one transition of a repeated signal was observed continuously
during this period. By inspection it is seen that this circuit has bias
of — 1 per cent and the r.m.s. value of distortion is about ± 3 per cent.
With miscellaneous signals and with characteristic distortion present,
the curve would have several peaks and would be somewhat irregular,
but would have the general shape of a normal-law distribution curve.

166 BELL SYSTEM TECHNICAL JOURNAL

E. Sources of Test Signals
Bell System telegraph circuits are tested at present with both
substantially perfect and distorted test signals. The quality of the
test signals is, of course, of prime importance because the measurements
are generally made on a straightaway basis and it is not practicable
to make correction for accidental distortion in the test signals at the
sending end of the circuit. On high-grade circuits where the distortion
is generally less than about 5 per cent, distortion in excess of a few
per cent in the test signals is very undesirable.

Undistorted Test Signals

Substantially perfect test signals are usually supplied from motor-
driven commutators. One type supplies telegraph reversals. In this
case an accurately governed motor drives two brush arms, each of
which is associated with two rings of segments so that four sources
of signals are provided by each machine. These reversals or dot
signals are used in a number of ways, their principal advantage being
that since the average of the marking and spacing intervals is zero, a
simple integrating meter circuit may be used for measuring bias.

When it is desired to employ miscellaneous or recurring teletype-
writer characters machines known as transmitter-distributors are used.
Such a device, arranged to send a standard test sentence, is illustrated
in Fig. 16. This consists of a motor-driven commutator with a con-
tinuously rotating brush arm and a direct-coupled cam transmitter
(on the left) which changes the connections to the segments of the
commutator in accordance with the code which is cut on the cams.
In another form of this device a tape transmitter ^ is used; the tape is
usually of parchment although metal tapes and wheels drilled with the
code combinations have been used.

When a number of sources of undistorted signals is required in a
repeater station a device called a "multiple-sender" is used. This
employs the distributor of Fig. 16 to operate a number of relays.
The transmitting contacts of these relays are connected to jacks at
convenient locations in the telegraph test board. The standard test
sentence supplied by this device contains desirable signal combinations
for testing transmission over lines and also for testing the operation
of teletypewriters.

The signals from the commutator face traverse two groups of relay
windings, a marking group and a spacing group, the circuit being as
indicated in Fig. 17. This circuit effectively provides polar operation
of the relays, the transmitter closing the circuit through one group of
windings to operate the relays to their marking contacts and through

MEASUREMENT OF TELEGRAPH TRANSMISSION 167

jj^fft

Fig. 16 — Test-sentence transmitter-distributor.

TO JACKS AT TELEGRAPH BOARD

RELAY
NO 1

DISTRIBUTOR

ADDITIONAL
RELAY
UNITS

•' VvVi

±

Fig. 17 — Schematic circuit of automatic multiple sender.

168

BELL SYSTEM TECHNICAL JOURNAL

the other group of windings to operate the relays to their spacing
contacts. The series-parallel arrangement of the relay windings shown
in the figure has the advantages that with the same number of relays
in series and in parallel the combined inductance is only that of a
single relay, and that any relay may be removed for inspection without
materially affecting the operation of the others. Only one transmitting
battery is used in this circuit and thus errors due to battery inequalities
are avoided. As indicated in the figure, a spark-reducing circuit is
associated with each output for the purpose of minimizing arcing and
to neutralize the effect of travel-time of the relay armature which
would otherwise cause the transmitted signals to be biased to spacing
when opening and closing the circuit under test.

Each group contains 6 relays in parallel and any number of groups
up to 8 may be used in series to provide a maximum of 48 outputs
to meet the requirements for offices of various sizes.

The above-mentioned sources of signals as maintained in the field
are usually accurate to within a few per cent distortion. For special
uses it is possible to reduce this inaccuracy somewhat by additional
maintenance.

Distorted Test Signals '

A repeating device has been provided, primarily for transmission
maintenance, by means of which the distortion of telegraph signals may
be increased by predetermined amounts. The set is generally used
with a source of undistorted signals to provide test signals having
known amounts of distortion.

BIAS-SWITCHING

RELAY f60 OPERATIONS

PER MINUTE)

Fig. 18 — Bias-producing circuit.

The schematic circuit of the signal-distorting device is shown by
Fig. 18. The signals to be distorted are connected to the input and
are repeated by the receiving relay (Rec) of the device into a biasing

MEASUREMENT OF TELEGRAPH TRANSMISSION

169

relay (Bias) through a network which modifies the wave-shape of the
signals and permits them to be biased easily by changing the current
through the auxiliary windings A and B of the Bias relay.

The manner in which bias is produced will be understood more
fully by reference to Fig. 19 which shows graphs of the currents in the

J

(I)

Fig. 19 — Currents in bias-producing circuit.

bias-producing circuit. The current in the receiving relay input
circuit is indicated by 1. These are undistorted substantially square-
topped reversals. The currents flowing through the operating wind-
ings of the Bias relay in response to the marks and spaces of the re-
versals are shown by 2 and 3. In the case shown by 2, it is seen that at
the beginnings of the marking pulses the wave fronts are steep and that
the current gradually decays to zero at the beginnings of the spacing

170 BELL SYSTEM TECHNICAL JOURNAL

pulses. In 3 this condition is reversed so that the net operating current
for the Bias relay, being the difference between the currents of 2 and 3,
has a rounded wave shape for both the beginnings of marks and the
beginnings of spaces as is indicated at 4. This is a symmetrical wave
about the zero axis and if there is no bias effect in the Bias relay the
signals will be repeated unbiased. However, if current is passed
through one of the auxiliary windings of the Bias relay the operating
point of this relay will be shifted as indicated by the dotted line and
the repeated signals will be biased, as shown by 5. In this case the
bias is 25 per cent spacing so that the repeated unit marks are 75
per cent of their original length.

One of the auxiliary windings of the Bias relay is used for introducing
marking bias and the other for spacing bias, and the sign of the bias
may be changed by switching from one winding to the other. Then
the bias effect reverses according to the dotted line of 6, and the
signal is affected as is indicated by 7. By reversing the bias periodi-
cally under the control of a commutator arrangement an effect known
as "switched bias" is produced. The reversing operation occurs 60
times per minute and is not synchronized with the signals and accord-
ingly produces a fortuitous effect on some of the signals.

The signals obtained from this device are commonly used in testing
the operating margins of subscriber teletypewriters. In this case
perfect teletypewriter signals are applied to the input of the device
and are distorted by a predetermined amount in passing through it.
These signals are then applied to the circuit extending to the sub-
scriber station. If the receiving teletypewriter at the station responds
faithfully when set at its optimum orientation point it is considered
to be satisfactory for service.

'Distorted signals obtained from this device are also used to de-
termine the extent of the distorting effects in line circuits. For this
purpose the set may be connected at either the sending or the receiving
end of the line and a distortion-measuring set at the receiving end to
give an indication of the increase in distortion caused by predistorting
the signals. With the set used at the sending end, the results of the
test indicate how much distortion may be applied as from preceding
telegraph sections. With distortion added at the receiving end, the
test may be used to show the margin in the receiving apparatus
before failure.

A front view of a panel-mounted telegraph signal-biasing set of the
relay type is shown in Fig. 20.

MEASUREMENT OF TELEGRAPH TRANSMISSION 171

nSAlSIASStT

.* < '

% ■ % } »

**^:«i^ikkNi

oocoocoo

. ::!DsClC^OOO

J I * Of Vie/ ----—

Fig. 20 — Telegraph signal-biasing set.

F. Measuring with Teletypewriters

As is well known, the start-stop teletypewriter, when properly
adjusted for this purpose, may be used as a transmission-measuring
device. The usual procedure in field testing is to compare the range
over which the orientation range finder may be shifted with sub-
stantially perfect signals to that obtained with signals from the line
under test. The orientation range finder is shifted above and below
the usual setting until perfect copy is no longer obtained, these limiting
positions determining the margins.

At the time of the previous paper, ^ the orientation range test was
the only test available to the field forces in the Bell System which
utilized the start-stop principle. At that time the teletypewriter was
not convenient to use and generally the results were not as accurate
as desired. However, the machines have been much improved and
better methods of use have been developed so that now orientation
margin tests furnish a better indication of the grade of transmission.
At the same time, the more convenient measuring sets described
above have become available and this has, of course, reduced the field
of use of the teletypewriter as a measuring device.

One of the improvements in the machines from the standpoint of

172

BELL SYSTEM TECHNICAL JOURNAL

ORIENTATION IN PER CENT

- o

1

5.0

' — 1 1 1 1

b

WITH 10 PER CE
MARKING BIA

r

/
/

1

1

/

1

/

/

/

/

/

/

/

/

/

/

r

r

^2

d

SKEW DUE TO MORE

FORTUITOUS DISTORT

ON M-S THAN ON S-

TRANSITIONS

/

^

/

/

1

/

/

/

/

/

/

/

/

/

/

/

/

./

/

1

./

/

/

/■

Z

o

a

GOOC
CONDIT

/

/

/

/

/

/

/

/

1
1

/

/
•

1

X

/

z

ii

/ 1

1

/

/

/

A

/

/

/

/

/

1/

ORIENTATION IN PER CENT

MEASUREMENT OF TELEGRAPH TRANSMISSION 173

transmission testing consists in the addition of a small crank which
extends through the cover and which is coupled to the range finder.
The crank has a detent which assists in making settings to the nearest
per cent, the scale being arranged to indicate directly the distortion
in percentage of a unit selecting pulse. This crank and scale arrange-
ment increases the convenience of measurement considerably.

It is of considerable importance to remove as far as practicable the
internal distortion ^ of teletypewriters used for measuring purposes.
These internal distortions can be identified as bias, characteristic and
fortuitous effects. These effects reduce the margin from the theoretical
limit of ±50 per cent to about ±40 per cent for the usual machines
operating at 60 words per minute.

The presence of internal distortion can be readily determined by
using signals biased by various amounts and noting the effect on the
orientation range. With a machine satisfactory for measuring pur-
poses, the results obtained would be as indicated on Fig. 21a. Here the
range is from 10 to 90 per cent for reception of perfect signals. Mark-
ing bias reduces the upper range in direct proportion and spacing bias
likewise reduces the lower range in direct proportion ; thus the machine
would be satisfactory for measuring purposes.

If the machine had internal marking bias, the orientation parallelo-
gram would be as shown in Fig. 2\h. Here the range with perfect
signals is from 10 to 80 and marking bias reduces the range in propor-
tion to the bias but spacing bias first increases the range until the
internal bias is compensated and then decreases the range as the
impressed bias is further increased. With internal spacing bias the
parallelogram would be shifted to the other side of the zero line by the
amount of the bias. It is obvious therefore that biased machines do
not give accurate results in measuring.

Characteristic and fortuitous effects may also be present in tele-
typewriters to such an extent as to make the machines unsatisfactory
for testing purposes. It will be appreciated that internal characteristic
distortion changes from signal to signal and when receiving miscel-
laneous teletypewriter characters, it has much the same effect as
fortuitous distortion and the upper and the lower margin limits would
be reduced about equally as shown in Fig. 21c. If the machine
distortions do not have the same effect on mark-to-space and space-
to-mark transitions, a skewing effect is produced in the orientation
parallelograms. Fig, 2\d shows skew due to the fortuitous effect
of the mark-to-space transitions, being greater than the fortuitous
effect of the space-to-mark transitions. Teletypewriters showing
such skew effects do not give margin reductions proportional to the

174 BELL SYSTEM TECHNICAL JOURNAL

impressed distortion and are, therefore, not suitable for measuring
purposes.

It is apparent from the above discussion that it is necessary to
adjust teletypewriters for minimum internal distortion before they
can be used for measuring purposes. Where it is desired to use
teletypewriters in testing, procedures have been established in the
Bell System to insure that they will be in proper condition and fairly
good results are obtained with them.

Although the effect of distortion on the orientation margins has
been discussed previously^- ^' '' it may be of value to state here how
distortion affects the margins at the lower and upper orientation
limits in connection with the use of teletypewriters for testing pur-
poses. In general, the maximum reduction corresponds numeri-
cally to the total distortion as indicated by the start-stop type of
measuring set described above. Distortions other than bias usually
affect both orientation limits equally so that the amount of bias can
be estimated by subtracting the smaller reduction of the two from the
larger. In addition it is possible to obtain an idea of the characteristic
distortion by the indications obtained during the orientation test.
If the orientation limits are fairly definite, that is, if the copy changes
from good to bad when the range finder is moved only a small distance,
it is likely that the distortion is due to bias. If there is a definite
range over which certain characters are found to be consistently in
error this is due to characteristic distortion. If the limits are not
definite, that is, if there is a range over which errors occur but not con-
sistently on certain characters this is probably due to fortuitous
distortion. Although a qualitative analysis of the distortion may be
made in the manner discussed above, this indirect method is somewhat
laborious and may give misleading results. Moreover, it is impossible
to get a measurement of isolated distortions of high value.

G. Telegraph Service Monitoring Set
An automatic telegraph service monitoring set has been designed
for the purpose of giving an alarm at repeater stations whenever the
distortion on circuits becomes abnormally high or whenever an
excessive number of large distortions or "hits" is experienced. This
set is still under development; however, a description of it will be
given because it is thought to be of general interest to those concerned
with telegraph transmission measuring.

In the interest of economy and simplicity this set contains a so-
called shortest-pulse type of measuring circuit rather than a start-stop
type. Measurement on this basis will of course result in a loss in

MEASUREMENT OF TELEGRAPH TRANSMISSION

175

accuracy for some signal combinations because of the fact, as men-
tioned earlier, the distortion of the stop pulse is not added to the
distortion of other pulses. However for the purpose for which it is
used, namely to detect trouble conditions on working circuits, the
accuracy is believed to be adequate.

In this set two measuring circuits are provided, one for measuring
marks and the other spaces. These are condenser-charging circuits
in which the charge on the condenser is an indication of the duration
of the pulse. These condenser voltages are compared to a reference
voltage and only those less than the reference voltage are permitted
to influence the distortion indicator. Therefore, only the shortest
pulses are measured and this permits observation on working tele-
typewriter circuits without involving a start-stop arrangement. By
adjustment of the time constant of the condenser-charging circuits,
as for instance by means of continuously variable resistances, the
percentage distortion for which an alarm is given may be varied at will.

PEAK-DISTORTION
INDICATOR

GAS TUBE

C2

Fig. 22— Distortion-measuring circuit of telegraph service-monitoring set.

The distortion-measuring portion of the circuit used in the measure-
ment of marks is indicated by Fig. 22. Condenser C is charged during
marking intervals through high resistance R by voltage E; thus a
voltage is produced on the condenser which depends upon the duration
of the marking interval as is indicated by Fig. 23. At the time of the
transition from mark to space the condenser voltage is momentarily
compared to that of a reference source by way of the armature and
marking contact of relay 2 of Fig. 22. Immediately afterwards the
condenser charge is dissipated by the armature of relay 2 moving to

176

BELL SYSTEM TECHNICAL JOURNAL

its spacing contact. The small delay required in the operation of
relay 2 with respect to relay 1 is obtained by connection of condenser
C2 around the windings of relay 2.

SIGNAL

VOLTAGE OF
CONDENSER C.

REFC.E

Fig. 23 — Variation of charge on measuring condenser in
telegraph service-monitoring set.

If at the time of the momentary comparison between the condenser
and reference voltages these two voltages are equal, no current will
flow in the peak distortion indicator. This condition can be obtained
for marks of unit duration (for instance the duration of a selecting
pulse of the teletypewriter code) by suitably adjusting the reference
voltage REFC. E. For marks of longer duration however the con-
denser voltage will exceed the reference voltage but, by properly
poling the rectifier in series with the peak-distortion indicator, current
is effectively prevented from flowing at the time of the momentary
comparison. With this poling of the rectifier the current flowing due
to the marks being shorter than unit duration will affect the peak-
distortion indicator and if suitably adjusted will cause a gas-filled
tube to operate and thereby give an indication of distortion.

It will be apparent that the measurements of spaces may be accom-
plished by providing for that purpose another circuit of the same type
as that of Fig. 22. For the measurement of both marks and spaces
four relays are required, but only one peak-distortion indicator is
necessary.

Associated with the measuring circuit is a counting circuit which
counts the number of excessive distortions experienced in a given
time. This circuit is indicated schematically by Fig. 24. In this
circuit the charge of the condenser C is mixed with that of a larger
condenser C2 at each operation of the gas-filled tube of the distortion
measuring circuit. Thus the charge on the larger condenser becomes
an indication of the number of excessive distortions. By arranging a
timer to discharge this condenser through an indicating circuit suitably

MEASUREMENT OF TELEGRAPH TRANSMISSION

177

designed an alarm may be obtained whenever the number of exces-
sive distortions exceeds any predetermined number up to about 7
within a given time. For this purpose another gas-filled tube is

/T~g\i GAS TUBE
' ^ ^ PLATE

FIG. 22

Fig. 24 — Counting and alarm circuit of telegraph service-monitoring set.

employed having a potentiometer associated with it for the purpose of
adjusting the grid-biasing potential so that the tube will fire only for
voltages exceeding definite amounts corresponding to definite numbers
of excessive distortions. It is apparent that this type of counting
circuit could be replaced by a counting-relay circuit or by a selector-
switch circuit such as is used in automatic telephony.

A front view of the monitoring set, arranged for mounting on a
relay rack in a central office, is shown by Fig. 25.

In the present arrangement these sets have jacks at a number of
places along the telegraph board in the central office, for the purpose
of permitting attendants to use the set conveniently. Alarm lamps
and signals are provided at the board to attract the attention of the
attendant. As the use of these sets is developed, it may be found
desirable to employ them in conjunction with a patrol arrangement by
means of which a given set may be connected in turn to each of a
number of circuits for a short interval. An arrangerrient of this sort
was described by W. Schallerer.^

Other Developments

Other types of measuring apparatus have been used experimentally
in the Bell System and have been found of value in laboratory work

178

BELL SYSTEM TECHNICAL JOURNAL

Fig. 25 — Telegraph service-monitoring set, test design.

and special investigations. Among these devices are start-stop and
synchronous distortion indicators employing flashes of Hght to indicate
the position of the transitions of teletypewriter signals and a photo-
graphic recorder of teletypewriter signal transition points. A syn-
chronous flashing indicator in combination with a distributor arranged
to supply teletypewriter signals with adjustable bias is in use in shop
tests of teletypewriters and in the laboratory.

Acknowledgment

In the development of the practical telegraph transmission meas-
uring devices, which have been described, many members of the Bell
System have contributed valuable ideas and eff"ort. The authors
wish to express their appreciation of the cooperation they have
received.

APPENDIX

General

This appendix considers characteristic distortion of telegraph signals
from the standpoint of the development of simple and convenient
testing technique for application primarily to circuits transmitting
start-stop teletypewriter signals.

MEASUREMENT OF TELEGRAPH TRANSMISSION 179

A previous paper ^ developed methods of determining the correct
transfer admittance for distortionless transmission under certain
assumed conditions. One general and simplifying assumption was
that the time interval between transitions in the telegraph signals would
be an integral number of time units. If telegraph circuits were to be
designed for the transmission of telegraph signals of this nature, dis-
tortionless transmission would be expected when the overall transfer
admittance of the circuit was one of the many possible admittances
discussed in the previous paper. Although a knowledge of the admit-
tance requirements is a helpful guide in the design of circuits and per-
mits the establishment of certain boundaries, the exact adjustment of
transfer admittance to the proper value for satisfactory transmission
on the basis of admittance measurements presents many practical
difficulties and up to the present has not been generally used.

Another approach to the problem is the actual transmission of
miscellaneous signals of the type required and the adjustment of the
transfer admittance on a cut-and-try basis until the overall results are
satisfactory. For relatively simple circuits satisfactory results can be
obtained in this manner. However, for circuits which are electrically
long and contain complex networks, a more orderly approach is
desirable.

The problem may also be approached from the standpoint of ad-
justing the transfer admittance of the circuit so as to minimize the
transient associated with each transition at the times at which succeed-
ing transitions may occur. This may, of course, be done by means of
oscillograph observations, but this procedure has serious practical
disadvantages. An advantageous method, however, is to measure the
characteristic distortion of simple signal combinations while making
the adjustments. For this purpose, signals, each composed of two
transitions, repeated at intervals long compared to the duration of the
appreciable transient, are used. If the circuit is adjusted so as to
transmit without distortion signals having respectively separations of
one, two, three, etc. signal elements, between transitions, the require-
ments for distortionless transmission of miscellaneous signals of the
nature under consideration are met, as will be shown below.

Repeated two-transition signals with varying integral time-unit
intervals between transitions may be considered as telegraph re-
versals having a frequency determined by the period of repetition
and bias determined by the interval between transitions. There-
fore, telegraph reversals of varying bias may be used as a source of
test signals, with a simple bias-measuring set at the receiving end and
the input bias-output bias characteristic of a circuit determined for

180

BELL SYSTEM TECHNICAL JOURNAL

1

2

3

4

5

6

7

8

9

10

5-0^^^

-

1 .rr-

*

5

""-'"■

checking the characteristic distortion. The possible use and mean-
ing of such measurements are discussed in the following :

Bias In-Bias Out
For the purpose of discussion consider the particular code indicated
by Fig. 26.

+ E

-E

Fig. 26 — Special telegraph signal. Each character consists of ten time units.
Each time unit is one-fiftieth second and ma>' be -\-E or —E depending on the
character transmitted.

Each character to be transmitted is composed of ten time units,
each unit being 1/50 second, so that it takes 1/5 second to transmit any
of the 1024 possible characters. Although the nominal speed of signal-
ing is 25 dots per second, the fundamental frequency of any character
sent repeatedly is 5 cycles per second considered in the Fourier sense.
Among the many possible signal combinations are the following
which are equivalent to 5-cycle reversals with the amounts of bias
indicated below.

Time Units Time Bias

A, u c = 100^^,

Marie Space M +6

10 0 -f-100%

9 1 +80%

8 2 +60%

7 3 +40%

6 4 +20%

5 5 0%

4 6 -20%

3 7 -40%

2 8 -60%

1 9 -80%

0 10 -100%

It is obvious for a symmetrical circuit that if signals with any amount
of positive bias are transmitted accurately signals with the corre-
sponding amount of negative bias will be transmitted since this corre-
sponds to a reversal of the sending polarities.

The transfer admittance for distortionless transmission of these
signals will now be derived for the case in which the band width is a
minimum. It has been shown in a previous paper ^ that the minimum
band width required is equal numerically to the speed of signaling.

MEASUREMENT OF TELEGRAPH TRANSMISSION 181

Therefore a band width of 25 cycles will be necessary and sufficient
for the signals listed above; this band will also meet the requirements
for transmitting the remaining characters of the possible 1024.
The Fourier series for the biased reversal is

hE £ ■" 1

Eit) = E —- — I X! - [sin «(co/ — h) — sin nwt\

where E and b are defined in Fig. 27, which shows the impressed voltage

E —

Ojt= 0 cot = fa Cjt=ZiT

lo=Tr Cl-B)

Fig. 27 — Voltage wave for biased reversal.

wave at the transmitting end of the circuit, and B is percentage bias
divided by 100.

Let the transfer admittance be F„ at frequency corresponding to
wco. Then, the requirement for perfect transmission of the reversal,
assuming the receiving device to operate when the current passes
through EYo/l, is that

/(/) = EYo/l at o)/ = 0 and at co/ = b,

where /(/) denotes received current.

/ bF \ F "^ V

At CO/ = 0 or b,f{t) = £ - — Fo + - E — sin (- nb).

Hence, assuming for simplicity that Yd = 1

f =£-|^ + -i:-^"sin(-^6).

Substituting the value of b and transforming

Bit - F„ . ,
^r- = 2- — sm nb.
2 n=i n

In accordance with the assumption that band width is a minimum,

182

BELL SYSTEM TECHNICAL JOURNAL

F„ = 0 for n > S. Therefore, the values of F„ may be determined
from the following equations wherein the values of nb are in degrees.

Solving these simultaneous equations it is found that Yi = .967,
Fo = .865, Fs = .685, F4 = .408.

The computed admittance is the same as that which may be com-
puted from the information given in Appendix III of a previous
paper ^ which is :

F = transfer admittance at frequency /,
fs = dotting speed.

Since the bias of the signals at the circuit output must equal the bias
of the signals at the circuit input for the magnitudes of bias entering

+ 100
+80

H

0 +60

(0

+20

Y

/

/

/

/

0

-20

1-

/

/

0 -40

y

CD

/

-80

/I

-100 -80 -60 -40 -20 0 +20 +40 +60 +80 +100

Fig. 28 — Bias in-bias out characteristic for transmission of telegraph signals
formed in accordance with Fig. 26 over a system having a band width equal to the
dotting speed.

into the determination of the admittance, and since the transmission of
additional harmonics of the fundamental frequency would be required
to make the input bias equal to the output bias at additional magni-

MEASUREMENT OF TELEGRAPH TRANSMISSION 183

tudes of bias, the Bias In-Bias Out characteristic for a circuit having
an admittance as computed above would have the general character-
istics indicated in Fig. 28.

Considered in terms of the transient behavior, if the circuit had the
transfer admittance defined by the above equation, or any of the infinite
number of other prescribed admittances using higher frequencies, the
transient resulting from a single transition would be such as to have
zero value at each of all possible future transition points. Also if
the circuit were adjusted so that the four simple characters were trans-
mitted with negligible distortion, the transients would fulfill the condi-
tions for the satisfactory transmission of the other 1020 possible
characters.

From Fig. 28, it is obvious that a circuit which had a perfect transfer
admittance and a frequency band width large compared to the char-
acter repetition frequency, would have a Bias In-Bias Out character-
istic which crossed the 45 -degree line at many points and approached
it as a limit. It is interesting to note the relation between the devia-
tions of the Bias In-Bias Out characteristic from the 45-degree line
and the frequency band width. In the example under discussion there
are five waves in the characteristic which correspond to the frequency
band width divided by the number of characters per second. The
band width required is numerically equal to the product of the number
of waves in the Bias In-Bias Out characteristic and the number of
characters transmitted per second.

Start-Stop Teletypewriter Signal
Start-stop teletypewriter systems may employ varying speeds and
signal arrangements. The 60-word-per-minute (60-speed) system is
the one most generally used in the Bell System and is taken as an ex-
ample in this appendix. Similar methods of analyses and tests could
be applied to other systems.

The 60-speed teletypewriter signal consists of a starting unit which
is always spacing, five selecting units, and a stop signal which is 1.42
units in length and is always marking. The duration of a unit signal
pulse is 22 milliseconds and the total length of each character is,
therefore, 1 -f 5 + 1.42 = 7.42 times units or 163 milliseconds. With
no pause between succeeding characters there are 368 operations per
minute or

368 1 . , ^ ,. ,

-ryr- — -7-^ =6.13 opcratious per second.
60 .163

The problem of transmitting these signals without distortion is

184

BELL SYSTEM TECHNICAL JOURNAL

similar to the problem just discussed except instead of uniform spacing
between possible transitions of 1/50 second, the transitions may be
spaced at intervals of either. 022 second, .031 second, or combinations
of these intervals, and the frequency of repetition is 6.13 instead of
5 per second.

As indicated in Fig. 1, there are six teletypewriter characters (Blank,
T, 0, M, V, and Letters) which correspond to 6.13 cycle reversals
biased by certain amounts. It will now be shown that if these six
characters can be transmitted without distortion, the other 26 charac-
ters will also be transmitted without distortion. The method is the
same as that used in the preceding problem.

START
•^0

^1

^2

^3

U

I'S

^6

Fig. 29 — 7.42-Unit code start-stop teletypewriter signal.

Figure 29 indicates any teletypewriter signal where io = 0, and
i'e = 1. t\, i-i, H, i\, ib, may have values of 0 or 1 depending on the
particular character. The Fourier series for the received current over
a circuit with a transfer admittance Y having unit value at zero
frequency, is

m =

ii + ij + iz + ij + ib + 1-42
7.42

+ - X — ~ \ii[_s\n n(o)t — a) — sin w(co/ — 2a)]

+ z'zCsin n(o3t — 2a) — sin n(ut — 3a)^
+ 7'3[sin w(oo/ — 3a) — sin n(o:t — 4a)]
+ ?"4[sin n{oot — 4a) — sin n(wt — 5a)]
+ ibl^sin n{wt — 5a) — sin w(co/ — 6a)]
+ 1 [sin n{wt — 6a) — sin n co/]}.

Suppose that the transmitted frequency band is limited to 6 times the
fundamental, i.e. « = 1 to 6, and F„ adjusted so that the characters
"Letters" V, M, 0, T and "Blank" are transmitted perfectly.

The transfer admittance will now be determined for this case. The
expression for /(/) may be written for the characters just mentioned,
and would have the value 1/2 at ojt = a, for "letters," at cot = 2a for
V, at co/ = 3a for M, etc. Accordingly there result six equations which
may be simplified as follows :

MEASUREMENT OF TELEGRAPH TR.ANSMISSION

185

'Letters"

6 Y

> — Sin na =
1 n

2.7l7r

" 7.42 '

T'

fi Yn

y" — - sin 2wa
1 w

1.7l7r

- 7.42 '

,1/

6 J'^

V — - sin 3wG
T n

.7l7r
- 7.42'

0

V — '- sin 4wa
T «

- .297r
- 7.42 '

T

6 Yn

V — sin Sna
1 "

- 1.297r

7.42

"Blank"

Y — sin 6na

- 2.297r

7.42

The values of F„ computed by solving these equations were plotted
on Fig. 30 and a curve was drawn through them. It will be under-
stood, that, on the scale of abscissae, F is the fundamental frequency
of the character and the coefficients of F are values of n.

2F

5F

6F

7F

Fig.

3F 4F

FREQUENCY

30 — Transfer admittance characteristic for undistorted transmission using
frequencies up to seven times the fundamental frequency of the character.

By the methods employed in the previous paper ^ it can be shown
that, for signals employing the same permissible intervals between
transitions, the solutions of equations similar to the above approach
the smooth curve as a limit as the period of repetition is lengthened.

These equations may be used to prove that when the six simple
characters are perfectly transmitted, all other teletypewriter signals
may be transmitted on a repeated basis. For distortionless transmis-
sion f(t) should equal 1/2 at each transition point, assuming that the

186 BELL SYSTEM TECHNICAL JOURNAL

relay operates at this value of current. If the expression for /(/) is

written for each of the conditions which may occur, and is found to

equal 1/2 at the transition points, the proof is complete. For this

purpose the summation signs may be eliminated by substituting from

any of the six simultaneous equations numerical values in place of

summations of terms, in the equation for /(/), with the following

results :

Conditions

a,/ = 0 io = 0 U=\ /(/)= ;^[ii+i2 + 23 + i4 + i5 + 1.42 + z:i(-l)

+Z5(-l) + l(2.29)] = i,
co/ = a *o = 0 H=\ /W- y^[l+^2+i3+^'4+i5+1.42 + l(2.71)

+ ^2(-l)+i3(-l)+n(-l)

+^-,(-l) + l(1.29-2.71)] = L
co/ = 2a ii = 0 ^2=1 /{7)=^[0+l+?3 + /4+i'5 + 1.42 + 0(2.71)

/ .4z

or
ii=\ ^2 = 0

+ l(2.71) + /3(-l)+i4(-l)
+^5(-l) + l(.29-1.71)] = i.

co/ = 3a ^2 = 0 ^3=1 /(/)=y^[ii + 0+l+/-4 + ^5+1.42 + z-i(-l)

or
ii =1 ^3 = 0

+ 0(2.71) + l(2.71)+i4(-l)
+Z5(-l) + l(-.71-.71)] = oi,

co/ = 4a «3 = 0 u=\ /(/)= ^(ti + /:2 + 0 + l+i5 + 1.42+i,(-l)

or
iz =1 ^4 = 0

+«2(-l)+0(2.71) + l(2.71)
+i5(-l) + l(-1.71 + .29)] = i

a>/ = 5a i4 = 0 k=\ /(/)-y^[n + /2 + /3 + 0+l + 1.42 + /i(-l)

or

ii =1 i5 = 0

+Z2(-l)+i3(-l)+0(2.71)

+ l(2.71) + l(-2.71 + 1.29)] = i

co/ = 6a ^5 = 0 /6-1 /(/)= ^[ii+i2+i3+i4 + 0 + 1.42 + /i(-l)

+ i'2(-l)+^'3(-l)+i'4(-l)

+ 0(2.71) + l(2.29)] = i

Hence it is concluded that if an admittance can be found such that
"Blank" T, O, M, V and "Letters" are transmitted without distor-
tion any other teletypewriter signal may be transmitted on a repeated
basis, since the correct current value (1/2) will be obtained at any
transition regardless of what other signal combination is used for the
remainder of the character.

MEASUREMENT OF TELEGRAPH TRANSMISSION

187

Computations have also been made for the case of a repeated signal
combination consisting of any two teletypewriter characters. The
results indicate that this may also be transmitted without distortion
if the requirements have been met for the six simple characters sent
repeatedly.

When distortion is present, there is deviation of the received current
from the desired value at the time it should be 1/2 and the deviation to
be expected at any transition for any character may be computed from
equations similar to those given above. This, of course, differs from
the amount of distortion which would be measured in per cent. It is
of interest that the characteristic distortion on the more complicated
characters may be materially greater than that measured on the simple
two-transition characters.

The transient behavior of a circuit having the transfer admittance
specified by the smooth curve of Fig. 30 may be determined by methods
utilizing the Fourier integral. However, certain characteristics of this
transient, namely, the points at which it must be zero, are known in
advance from the conditions entering into the determination of the
admittances. Although these conditions do not directly prescribe
the magnitude of the transient at other points, additional information
may|beJobtained|from an inspection of Fig. 31.

1.0-
.5
0-

DISTRIBUTION OF —
I FUTURE TRANSITION
(POINTS

Fig. 31 — Received current for "letters" character assuming the
transfer admittance of Fig. 30.

This figure shows the computed received current over a telegraph
circuit having the admittance shown in Fig. 30 when a repeated tele-
typewriter "Letters" signal is transmitted. It may be noted that the
transient decays to inappreciable amplitudes at times greater than the
shortest time unit of .022 second. This is significant, since it means
that a particular arrangement of transitions is not of practical im-
portance as long as transitions do not come at intervals closer than
.022 second. With this admittance, therefore, no difficulty would be

188 BELL SYSTEM TECHNICAL JOURNAL

expected from keyboard sending, the signals from which differ from the
signals previously discussed, in that the lengths of the stop signals
occur on a random basis, and are never shorter than .031 second,
depending on the typist.

However, if signals containing bias or other distortion such as indi-
cated on Fig. 31 as distortion of future transition points were trans-
mitted over the circuit, thus decreasing the minimum interval between
transitions, the transient from one transition, for example, might
affect following transitions. A circuit having a shorter build-up time
could be made to introduce less distortion on transitions spaced at
very short intervals. The rate of build-up is a function of the area
under the transfer-admittance curve and from a design standpoint it
is necessary to provide a suitable frequency band-width to make the
slope of the received signals sufficient so that characteristic distortion
will not be excessive when closely spaced transitions are transmitted,
and also so that certain types of interference will not cause excessive
fortuitous effects.

Where the available band width is limited the area under the admit-
tance curve could be increased by transmitting the permissible har-
monic frequencies at a greater amplitude. The transient of such a
circuit would continue at appreciable magnitudes for a greater length
of time and the minimum distortion would be increased but the general
circuit stability might be improved.

The foregoing discussion of telegraph signal transmission has shown
that when a circuit is adjusted to transmit without distortion certain
selected repeated characters, the circuit can transmit on a repeated
basis any of the characters possible with signals of the nature repre-
sented by the selected characters. This is true not only for the signals
in which transitions are spaced at integral units of time but for signals
in which transitions are spaced at predetermined non-integral units of
time, such as start-stop teletypewriter signals. Incidental to the
development of the proof of the later statement, the prescribed ad-
mittance for transmission without distortion was evaluated. The
prescribed admittance for signals employing integral units between
transitions was also similarly determined and found to be the same as
that which had been determined from a somewhat different approach
in a previous paper. ^

The admittances considered have been idealized somewhat, inas-
much as no physical circuit will cut off completely at the higher fre-
quencies and, in addition, the effective transfer admittance is not only
a complex, and frequently nonlinear quantity, but is determined in
part by the characteristics of transmitting and receiving relays and

MEASUREMENT OF TELEGRAPH TRANSMISSION 189

other terminal equipment. In the present state of the art, it is
difficult to make practical use of transfer admittances in predicting
the performance of a telegraph circuit.

The significant point is that the satisfactory transmission of the
selected characters is an indication of the ability to transmit the de-
sired telegraph signals satisfactorily. Also, the measurement of the
distortion on the selected characters is particularly useful when it is
desired to equalize individual circuits of varying length and makeup
to secure a minimum of distortion.

The testing procedures suggested by the considerations of the fore-
going have been incorporated into the testing instrumentalities dis-
cussed in the main paper. These methods have been used for several
years in the adjustment and maintenance of telegraph circuits and
found to be of considerable utility.

Referenxes

A. References Cited:

1. "Measurement of Telegraph Transmission," Nyquist, Shanck and Corv, Trans.

y4./.£.£., 1927, Vol. 46, p. 367.

2. "Certain Topics in Telegraph Transmission Theory," H. Nyquist, Trans.

^./.£.£., 1928, Vol. 47, p. 617.

3. a. "Telephone Typewriters and Auxiliary Arrangements," R. D. Parker, Bell

Telephone Quarterly, July, 1929, p. 181.
b. "Modern Practices in Private Wire Telegraph Service," R. E. Pierce, Trans.
A.I.E.E., Jan. 1931, Vol. 50, p. 45.

4. "Fundamentals of Teletypewriters Used in the Bell System," E. F. Watson,

Bell System Technical Journal, Oct., 1938, p. 620.

5. "A Transmission Svstem for Teletypewriter Exchange Service," Pierce and

Bemis, Bell Sys. Tech. Journal, Oct., 1936, p. 529; Elec. Engg., Sept., 1936,
p. 961.

6. " Metallic Polar-duplex Telegraph System for Cables," Bell, Shanck and Branson,

Trans. A.I.E.E., 1925, Vol. 44, p. 316.

7. a. "Der Spielraum des Siemens-Springschreibers," M. J. deVries, Telegraphen

und Fernsprech Technik, Jan., 1934, p. 7.
b. "Der Spielraum des Springschrieber," M. J. deVries, T. F. T., Sept., 1937,
p. 213.

B. Additional References :

8. "Ein Neues Mess- und Uberwachungsgerat fiir Springschreiberverbindungen,"

W. Schallerer, T. F. T., Feb., 1935, p. 40.

9. "Versuche uber eine giinstige Verteilung der Tragerwellen in der Wechsel-

stromtelegraphie," H. Stahl, T. F. T., Nov., 1930, p. 340.

10. " Verzerrungsmesser fiir Telegraphie," A. Jipp and O. Romer, T. F. T., May,

1932, p. 121.

11. "Telegraph Transmission Testing Machine," F. B. Bramhall, Trans. A.I.E.E.,

June, 1931, p. 404.

12. "A Telegraph Distortion Measuring Set," V. J. Terry and C. H. W. Brookes-

Smith, Elec. Comm., July, 1933, p. 15.

13. "The Measurement of Telegraph Distortion," V. J. Terry, Elec. Comm., April

1933, p. 197.

14. "Determining the Transmission Efficiency of Telegraph Circuits," E. H. Jolley,

P.O.E.E. Jl., April, 1933, p. 1.

Contemporary Advances in Physics, XXXII
Particles of the Cosmic Rays

By KARL K. D ARROW

Even after fifteen years of intensive research following on two
decades of more desultory study, the cosmic rays are still a store
of new and remarkable data. The question of their ultimate origin,
though by no means extinct, has been set aside by many physicists
in favor of a fuller inquiry into their qualities. The distinctive
mark of the cosmic-ray particles is the immensity of their energies;
for, great by all previous standards as are the energy-values which
physicists now can impart in their laboratories, those manifest in
the cosmic rays are greater by factors not of thousands merely,
but often of millions. To this remote and exalted energy-range
belong the penetrating particles capable of cleaving through a metre
of lead, and the wonderful and beautiful phenomenon of cosmic-ray
showers. It is not to be wondered at that with energies so high,
particles so familiar as electrons and photons should be invested
with unfamiliar powers. So evidently they are; but some of the
charged corpuscles of the cosmic rays have properties such that
their strangeness cannot be ascribed to high energy alone, but
apparently must be based upon some fundamental difference
(perhaps a difference of mass) from all the particles thus far
identified.

^XT'HEN a new member is admitted to a small and jealously-
^ ' restricted club supposedly already filled for all time, the event
has a dramatic aspect. When a concept is formed in a nebulous way
and rapidly gains precision with the passage of the years, the story is
of philosophic interest. When physicists extend their knowledge into
ranges of energy heretofore unsuspected, and find them inhabited by
particles classifiable as electrons but in possession of powers ordinarily
unknown, and also by particles which must be put in a class by
themselves — when such things are available for telling, the tale has
scientific value. When evidence comes in the form of pictures so
striking as those which can here be shown, the science of lifeless matter
has an aesthetic splendor such as rarely embellishes it. All of these
features appear in the recent advances of the study of cosmic rays.

The small and exclusive club consists of the subatomic particles,
long supposed to comprise only the negative electron and the proton
and other positive atom-nuclei. Into it the positive electron had
been forced in 1932, and the neutron in 1933; a vacant chair was

190

CONTEMPORARY ADVANCES IN PHYSICS 191

being reserved for the negative proton, which as yet has not turned up
to claim it; few if any expected the actual applicant. The concept
now hardening into the definite form of this applicant is that of the
"mesotron." This is a particle presumed to be equal in charge to the
electron, but in mass a couple of hundreds of times as great. In so
naming it I follow (C. D.) Anderson's recent proposal, though other
titles such as "barytron" and "heavy electron" are already more or
less firmly rooted in the literature. The quality which marks it out,
when it appears with enormous energy among the cosmic rays, is an
extreme and almost incredible power of penetration. This means
that the so-called mesotrons are able to traverse decimetres, nay even
metres of lead (or of dense matter generally). Like electrons, meso-
trons may be of either sign of charge. As for the cosmic-ray par-
ticles still classified as electrons, they are marked out by their power
of producing one of the most magnificent phenomena of Nature, the
"shower of cosmic rays," or "shower" for short. Shower-production
by the supposed electrons, penetration by the supposed mesotrons,
ionization along the course of either corpuscle through air: these are
the three phenomena which will furnish most of the illustrations,
much of the text of this article. The story of their incorporation
into the structure of physical theory will furnish the remainder.

(But negative electrons and protons, not to speak of other atom-
nuclei, have been identified through having their charge-to-mass ratios
measured with the aid of electric and magnetic deflecting fields in
elementary classical ways. Why then do I not cut this introduction
short by giving the results of such a measurement upon the mesotron?
The reason is, that no such measurement has yet been made. Prob-
ably one will be made ere long. Should it give something near to
the result expected, the delay will not have been regrettable; for the
end of the delay will mark the beginning of the time, when the story
to be related in these pages will be regarded as being "of historical
interest" only — which is to say, that it will then be liable to be for-
gotten.)

So that the reader may see at once the three phenomena which are
to bulk so largely in this story, I draw his attention at once to some
of the pictures which decorate this article.^ Nearly all of them were
made (of course) with the aid of the cloud-chamber or expansion-
chamber of C. T. R. Wilson, that device so precious in physics and
precious in so many ways.

^ They decorate it with particular clarity, thanks to the kindness of Messrs.
Anderson, Auger, Erode, Corson, Fowler, Fussell, Neddermeyer, Stevenson and
Street in supplying me with prints of their splendid photographs.

192

BELL SYSTEM TECHNICAL JOURNAL

1= >

5=°

0.-0
X c

eg.

O o;
u u

^ -^

a "3

H

CONTEMPORARY ADVANCES IN PHYSICS

193

At the beginning I place, as Fig. 1, a picture of the track of a cosmic-
ray particle believed to be an electron. Anyone who has ever studied
the pictures of cloud-chamber tracks will at once be impressed by
seeing how distinctly the droplets stand apart. This separation was
achieved by letting half a second elapse from the instant when the
electron shot through, to the instant when by expansion the gas of
the chamber grew suddenly cool and the water-vapor suspended in the
gas condensed itself as dewdrops on the ions. These ions, formed by
the passage of the electron, had been diffusing through the gas during
the half-second intervening, and the diffusion-process had served in
the main to carry them apart (though there must also have been cases
of ions approaching and possibly even combining with each other).
The counting of these droplets is germane to the question as to whether
the traversing particle was or was not an electron. This question,
however, we leave till later, and turn to photographs in which the
droplets of the tracks lie close together and are uncountable, because
the expansion took place before there had been time for much diffusion.
Tracks so formed have the advantage of sharpness over what they
lose in detail.

Fig. 2 — ^Track of a particle, presumably a mesotron, traversing a metal plate without
sensible deflection. (Auger; Universite de Paris)

Figure 2 presents the track of a particle which traversed a plate of
lead as it shot across the chamber. In passing through the lead, it
underwent no sensible deflection; no other particle sprang from the
lead; and there is nothing in the aspect of the track which differs on
the two sides of the metal. It would be more impressive yet to present
a similar picture for a particle traversing ten or fifty centimetres of
lead, but here the practical limitations on the size of a Wilson chamber
defeat the physicist, or at any rate no one has overcome them yet.
Ehrenfest has lately circumvented them by the laborious scheme of
setting up two Wilson chambers, one above the other, with as much as
9 cm. of lead or gold between them. However, the passage of single

194 BELL SYSTEM TECHNICAL JOURNAL

charged particles through thicknesses as great or even much greater
is amply attested by the scheme of apparatus sketched in Fig. 3, even
without the cloud-chamber there indicated by "Ch."

OC2

Pb

Ch

OC3

Fig. 3 — Scheme of apparatus for observing very penetrative particles with counters

and cloud-chamber.

In this sketch of Fig. 3, the objects Ci and C2 and Cz are Geiger-
Miiller counters: that is to say, gas-filled discharge-tubes of a very
special design, the two electrodes of each being an axial wire and a
coaxial cylinder, and the electrode-size, voltage, and gas-content
being very carefully adjusted. These long large cylinders, usually
called simply "counters" without the prefixed names, are familiar
sights in almost every laboratory where cosmic rays are studied.
If a charged flying corpuscle penetrates such a tube, a momentary
discharge takes place in the gas. If such discharges spring up simul-
taneously in all the three tubes of such a system as Fig. 3 exhibits,
the event is recorded by a mechanism. ("Simultaneously" is of
course a word which requires detailed exegesis; it meant at first that
in all tubes discharges began within 0.01 second of each other, but
this interval has been pushed down to .0001 second and lower.)

These events, the "threefold coincidences," do actually occur.
Of course, since in each of the tubes a discharge occurs now and then
by itself, some of the coincidences must be the result of chance; but
the probable number of these meaningless ones can easily be estimated
from the frequency and the duration of the individual discharges, and
in the best experiments they are a small minority. For the great
majority, the simplest of explanations is to attribute each of them to
a single vertically-flying particle cutting through all of the counters
in succession. Yet there are other thinkable causes, and confirmation

CONTEMPORARY ADVANCES IN PHYSICS

195

of this simplest idea is needed. It was supplied when the cloud-
chamber, "Ch" in the figure, was inserted. The chamber was com-
pelled by mechanism to expand, always when and only when a three-
fold coincidence happened ; and at the great majority of its expansions
it showed a vertical track. Figure 3 exhibits the arrangement of
Street, Woodward and Stevenson at Harvard, who found the track
of the traversing particle at 202 expansions out of 219. Auger and
Ehrenfest at Paris had already set up four counters and a cloud-
chamber and a block of lead in a vertical line, and found the track of
the single traversing particle at fifty-five expansions out of sixty-nine.
Another test is made by displacing one of the counters out of line
with the others, whereupon it is found that the coincidences fall off
in number sharply. And now to come to the point which most con-
cerns us: there were 45 cm of lead between the counters in the experi-
ment of Fig. 3, and 50 cm in the experiment by Auger and Ehrenfest,
and no fewer than 101 cm in an early experiment of Rossi's with
counters though without the chamber! Such is the power of pene-
tration of some of the charged corpuscles of the cosmic rays.

Fig. 4 — Three showers, two evoked by charged particles and one presumably by a
photon. (Street and Stevenson, Harvard University)

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BELL SYSTEM TECHNICAL JOURNAL

The reader has now been introduced to charged particles which
bore through quantities of lead, apparently without doing or suffering
anything. Next he is to be introduced to particles which begin to do
something startling, when they have scarcely more than entered into
a thin metal plate. This is vividly shown to him in Fig. 4, in which —
after he can detach his eyes from the pretty sight beneath the trans-
verse leaden plate — he will see that two of the "showers" beneath
spring from the places where the metal was entered by two charged
particles coming from above. These are accordingly called "shower-
producing particles."

Fig- 5 — Shower begun by a charged particle impinging on a 6.3-mm lead plate,
and multiplied as it passes through a second such plate; in the third plate, 0.7 mm
thick, only deflections occur. (Fussell, Harvard University)

Figures 5 and 6 and 7 show examples of showers even more gorgeous
— regular cloudbursts, to continue with the metaphor (and indeed
the term "burst" is often used as a synonym for "very large shower").
Of these, the special value of Fig. 6 is that the tracks that start in the
gas itself bear witness to corpuscles of light — photons — included in
the shower; for these are the tracks of electrons ejected by photons

CONTEMPORARY ADVANCES IN PHYSICS

197

Fig. 6 — Shower comprising photons attested by the (curled) tracks of slow
electrons released in the gas. (Anderson and Neddermeyer, California Institute of
Technology)

Fig. 7 — Another example of a shower undergoing multiplication as it passes through

metal plates. (Fussell)

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BELL SYSTEM TECHNICAL JOURNAL

from atoms of the gas. (The agent which bends them into curlicues is,
of course, a magnetic field applied to the whole of the Wilson chamber.)
Showers, then, comprise photons as well as charged particles. The

450

2 250

<] P

• "single" particles
o shower particles
'^ shower-producing particles

0 50 100 150 200 250 300 350 400 450 500

E| IN MEV

Fig. 8 — Energy-losses per unit length of path (in Mev/cm) suffered by 94 cosmic-ray
particles in traveling through platinum. (Anderson and Neddermeyer)

special value of Figs. 5 and 7 is, that they show the progressive
aggrandizement of showers as these pass onward through dense matter.
This is called "the multiplication of showers." Shower particles are
themselves capable of being shower -producing particles. One could not
tell from these figures whether the multiplication is due to the charged
particles or the photons, to either singly or to both. Here again the

CONTEMPORARY ADVANCES IN PHYSICS 199

reader may consult Fig. 4, in order to notice that one of the three
showers there depicted sprang from a place in the plate to which no
charged particle came. This suggests that a photon may cause a
shower, and that the multiplication of a shower already begun is due
to the action of its charged particles and of its photons both.

Two classes of charged particles begin to take shape : the penetrating
ones on the one hand, the shower particles and the shower-producing
particles classified together on the other. To bring out another
aspect of the distinction, I now turn to the data underlying Fig. 8.

These data are derived from cloud-chamber photographs such as
Fig. 9 exemplifies. If the track of a charged particle is sensibly curved
in such a magnetic field as it is possible to apply to a Wilson chamber,
it may be possible to infer the momentum and the energy of the
particle.^ I digress to give the formulae, so as to make it clear just
what can be deduced from what amount of knowledge. The ele-
mentary procedure consists in pointing out that the charged body
describes a circle in the plane perpendicular to the magnetic field,
and that consequently the force exerted on it by the field is to be
equated to the product of its mass by its centrifugal acceleration.
Putting ne for the charge (in electrostatic units) of the corpuscle,
m for its mass, v for its speed and p for the magnitude of its momentum
in the plane normal to the field, p for the radius of the circle and H for
the field-strength, and writing down the two members of the equation,
one finds:

Hnev/c = mv^jp, (1)

p = ine/c)Hp. (2)

These equations remain valid when (as usually is the case with cosmic-
ray electrons) the speed is so great that relativistic mechanics must be
used instead of ordinary. At such high speeds equation (2) retains
its aspect. Equation (1) may also be left unaltered, but one must be
sure to remember that m is a certain function of v:

m

= WoV/1 - vyc\ (3)

Wo being known as the "rest-mass" of the body.

* Curvatures of tracks being so very important in this field of research, it is
necessary to examine with the greatest of care into all of the causes (apart from
magnetic field) which may produce or afTect them. Notable among these are
currents in the gas, which are especially obnoxious if there is a metal plate in the
chamber. Indeed it seems strange that the currents should not be more hampering
than they are, considering the expansions which occur. Sometimes people observe
that in the absence of magnetic field, there is a slight curvature of the tracks; then
in the presence of magnetic field, they deduct this amount from the curvatures
observed. The papers of Anderson and Blackett abound in information on these
delicate questions.

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Equation (2) does not involve the mass at all. In the usual loose
phrasing, Hp gives the momentum of the particle provided that its charge
is known. The like cannot be said for the energy, which is given by
Hp only if both the charge and the rest-mass are known. For particles
of the cosmic rays it is best to disregard the ordinary expression for
kinetic energy {^mv"^) and adopt for good the relativistic expression
mc^, to wit, moc'^l^l — v^/c^. Of this the portion wqC^ is not kinetic
energy: it is the "rest-energy" associated with the "rest-mass" Wo,
inseparable from the particle so long as this exists; it amounts to about
half-a-million electron-volts or 0.5 Mev for the electron, to about
1000 Mev for the proton. The remainder may be called kinetic
energy. For nearly all of the electrons and most of the other cosmic-
ray particles, this remainder is by far the greater part. The de-
pendence of the kinetic energy upon Hp is exhibited, for electrons
and for protons, by Fig. 13 (page 213). One sees that for different

Fig. 9 — Track exhibiting measurable and unequal curvatures on the two sides of
a metal plate, thus indicating changes of energy and momentum suffered in the
traversal. (Anderson)

masses a given //p-value leads to dififerent energy-values, but also
that the error due to an incorrect estimate of rest^mass becomes
proportionately smaller as the iJp-value increases. Yet the possi-
bility of the error is always there, if the mass of the particle is not
certainly known; and it affects many published "energy-values"

CONTEMPORARY ADVANCES IN PHYSICS 201

based on the presumption — often admitted in the context to be more
than doubtful — that the particles to which they refer are electrons.
The danger might be mitigated by describing these as "quasi-energy-
values" expressed in "quasi-Mev." — For actual electrons with mo-
menta as great as those figuring in the cosmic rays, the energy-value
in electron-volts is practically equal to 300 times the 7/p-value ex-
pressed in gauss-centimetres.

Many a cosmic-ray particle suffers no deflection that can be detected
in its entire course across a Wilson chamber (diameter, 15 cm. or
even more) in a magnetic field as strong as can be applied over so
great a volume (field-strength, 20,000 gauss or thereabouts). One
might well be tempted to think such a particle chargeless, for if this
were the case, the field would have no grasp at all upon it; but if it
were chargeless it could not ionize the molecules of the gas and therefore
could not form the chain of ions on which the droplets are founded.
In some of the finest of the experiments (those in Pasadena and those
in Paris) a detectable curvature of the track would be shown if this
were made by an electron of energy so enormous as 2 • 10^" electron-
volts (20,000 Mev!). The uncurved tracks accordingly speak of
electrons of energies greater than 20,000 Mev, if these particles are
electrons; and the inference is not much less drastic, if they are more
massive than an electron.

We, however, are more interested, for the present, in the tracks
which are sensibly curved ; and most of all, in the tracks which are inter-
sected by a metal plate and which show a curvature on one side of the
plate and a larger curvature on the other (Figure 9). From the two
p-values one can deduce the momentum-loss Ap and the energy-loss
A£ sufifered by the particle in passing through the plate. (Yet I
emphasize again that A/» is computable only if the charge is correctly
guessed, and A£ only if the rest-mass is correctly guessed in addition
to the charge.) With this ambition Anderson inserted such plates
for the first time into a Wilson chamber, in 1931. The idea had a
wonderful and unforeseen result, some years ago recounted in these
pages. Notice that above I spoke of the momentum-Zo55 and the
energy-loss sufifered by a particle in going through a plate. In so
doing I was making the assumption that it is a loss and not a gain
which happens. If this highly plausible assumption is correct, then
the sense in which the particle is traveling its path is knowable; it is
from the side of the plate on which the curvature is less, to the side
on which the curvature is greater. If the sense of the motion is
knowable, so also the sign of the charge of the particle is knowable,
being positive or negative according as the track is bent with its

202 BELL SYSTEM TECHNICAL JOURNAL

concavity toward the left or toward the right of an observer looking
into the chamber from the north-seeking pole of his magnet. Without
the plate, neither sense nor sign would be knowable except in the
rarest of cases.' Anderson in August 1932 found on one of his photo-
graphs the track of a particle which by this criterion was positive,
and which by the density of droplets along its track (we take up this
topic later) he identified as an electron. He thus became the discoverer
of the positive electron.

Concentrating on the measuring of A£ after the excitement of the
positive electron had subsided, Anderson presently found that its
values are very fluctuating. Thus in 1934 he published the details
of nine traversals, made by particles assumed to be electrons, through
thicknesses of lead from 7 to 15 mm. (Even with a single metal plate
the effective thickness varies, since corpuscles traverse the plate with
varying degrees of obliqueness.) These were by no means identical
in initial energy, this ranging from 38 to 240 Mev; nevertheless one
might have expected the energy-loss per unit length of path in lead to
be about the same for all, and yet the nine values thereof were scattered
all the way from 18 to 120 Mev/cm! Such fluctuations suggest that
the energy is lost in great amounts at a few events, and not in driblets
at many. They did not deter Anderson and Neddermeyer from
making such measurements on hundreds of later particles, classifying
the particles into groups according to their energy-values, and
averaging the energy-losses within each group. What then was
found has a bearing upon the problem; but we pass over it for the
time being, and consider in Fig. 8 the record of ninety-four particles
which, during a later experiment, passed through a plate of platinum
one centimetre thick.'^

Plotted horizontally are the energy-values of the particles while
above the plate, vertically the energy-changes divided by the lengths
of path in the platinum. The axis of abscissae is the locus of energy -
losses imperceptibly small; the line slanting at 45° is the locus of
energy-losses which are total, the particles shown on this line having
been stopped by the plate. The fact that some of the representative
points lie below the horizontal axis means only that for every particle
the observers subtracted its energy below the plate from its energy
above, irrespective of its direction of motion. Suppose that these

^ One might be misled by the adjective "cosmic" into believing that all cosmic-
ray particles come from above, their sense of motion making an angle of less than
90° with the downward-pointing vertical. Many, however, including Anderson's
first positive electron, have been found by this criterion to be moving upward (i.e. at
more than 90° to the downward-pointing vertical). The showers of Figs. 6 and 7
show that this is not a forced interpretation.

1 1 am indebted to Dr. Anderson for a plate exhibiting data thus far unpublished.

CONTEMPORARY ADVANCES IN PHYSICS 203

subjacent points correspond to upward-going corpuscles, and transfer
them across the horizontal axis. Then, the sprinkhng of points
extends all the way from axis to slanting line; and this is the sign of
fluctuations such as Anderson from the start had observed. Notice
however that the representative points are of four aspects: solid dots
and hollow circles, with or without downward-pointing barbs. The
dots refer to tracks which were seen in the chamber singly; the circles,
to particles which "entered the chamber accompanied by other par-
ticles." The lonely particles are prevailingly able to pass through
matter without suffering energy-losses nearly so great as those which
the others incur! Thus by itself and without any theory. Fig. 8
establishes a distinction between the singly-appearing corpuscles on
the one hand, and those which appear in company on the other.
Moreover the barbs are often attached to the hollow circles, bearing
out the inference from Figs. 5 and 7 that shower particles are likely
to be shower-producing particles; but rarely are they attached to
solid dots, never to those which lie far off from the slanting line.

(This seems the best place for mention of the similar work now
being done in England by Blackett and (J. G.) Wilson, in France by
Ehrenfest. The Englishmen have set plates of gold, lead, copper and
aluminium, of various thicknesses from 3.?) mm to 2 cm, into the
middle of an expansion-chamber in Anderson's fashion; Ehrenfest,
using a pair of cloud-chambers one over the other, was able to put
between them a block of gold no less than 9 cm thick! Their way of
reducing their data for plotting is not the same as that employed at
Pasadena, and their diagrams therefore look very different ^ from
Fig. 8. Their energy-range runs much further upward, as far as
5000 Mev, and the great majority of the particles which they plot
lie beyond the limit of Fig. 8. Many of Ehrenfest's particles got
through the great thickness of gold without losing anywhere nearly
the whole of their energy, and are therefore to be classed as much
more penetrating than electrons should be. So did nearly all of the
particles of energy greater than 250 Mev observed in England, but
there were a few of these which lost most of their energy in 0.33 cm
of lead, and of these few about half seemed to belong to showers.

^ For the benefit of those who may consult the original papers, I give the differ-
ence. Let £1 and £2 stand for the (quasi) energy-values of a particle before and
after passing through a thickness d of metal; A£ for (£1 — £2); x for \iE\ + £2).
What is plotted by Anderson and Neddermeyer (Figure 8) is a£/^ as ordinate and
£1 as abscissa. Blackett (in all his papers but the earliest), Wilson and Ehrenfest
begin by subtracting from a£ a quantity sd which is supposed to be the amount of
energy spent by the particle in detaching electrons from atoms while traversing the
metal (Blackett assigns the value 15 Mev/cm to 5 in lead, Ehrenfest takes 28 for gold) ;
they then plot (A£ — sd)jxd as ordinate and x as abscissa. Their ordinate (denoted
by them as R) is then more nearly ready for comparison with theory.

204 BELL SYSTEM TECHNICAL JOURNAL

At energy-values below 200 Mev Blackett finds almost no penetrating
particles, a singular contrast with the Pasadena observations; he
suspects that the penetrating particles become ordinary electrons when
they are slowed down into this energy-range. I mention also the meas-
urements made on some twenty penetrating corpuscles by Leprince-
Ringuet and Crussard, leading to the exceptional conclusion that
positives suffer smaller energy-losses than negatives.)

But granting that there are two sorts of particle with a right to
different names: has either a right to the name "electron"? To
settle this question, and for several other reasons, it is time to call
upon theory.

It is now some thirty years since there entered into physics a German
word, Bremsstrahlung, which can be translated literally into English
as "braking radiation," and would no doubt be so translated if
"braking" did not sound like another English word of entirely dif-
ferent meaning. This is chiefly observed emerging from X-ray tubes,
being emitted from their metallic targets when these are struck by
the stream of bombarding electrons. It consists of photons or
corpuscles of light, each containing at least a part of the kinetic energy
of one of the incident electrons. The distribution-in-energy of the
photons makes it clear that the electrons frequently lose large fractions
of their initial energy en bloc, throwing it off in individual parcels which
are these photons (indeed it sometimes happens that the entire kinetic
energy of an incident electron is shed in the form of a single corpuscle
of light). This radiation forms the so-called "continuous X-ray
spectrum" or "X-ray continuum" emerging from targets of X-ray
tubes. With the spectrum-lines which are sometimes seen superposed
on this continuum we have nothing here to do. *,

By the classical theory of thirty years ago this continuous spectrum
is attributed to the slowing-down of the electrons as they penetrate
into the metal, whence the name Bremsstrahlung. By the quantal
theory of today it is still ascribed to the slowing-down, which must
now be conceived as taking place in instantaneous jerks, occurring
probably in the close vicinity of atom nuclei. At each of the jerks,
the electron-speed is suddenly reduced and the kinetic energy goes
forth in the form of light. The later theory in its quantitative form
gives a competent account of the continuous X-ray spectrum as it
springs from the tubes of the laboratory, with their bombarding
electron-streams energized by voltages of a few tens or hundreds of
thousands. For a long time nobody seemingly troubled to extend it
to voltages of the order of thousands of millions; a futile extension
indeed this would have been, so far as X-ray tubes are concerned.

CONTEMPORARY ADVANCES IN PHYSICS 205

When finally the extension was made by people interested in the
cosmic rays, it turned out that according to the quantal theory the
liability of electrons to these "radiative energy-losses" goes up so
greatly with increasing speed, that electrons of even the cosmic-ray
energies should not be able to bore their way through as much as five
centimetres of lead !

After the meaning of this inference sank in, there ensued a period
lasting for months (in 1935 and 1936) in which several eminent theorists
were willing to concede that Nature must have set a limit to the
scope of quantal theory. It was beginning to be believed that some-
where between the energy-range attainable in the laboratory and the
energy-range manifest in the cosmic rays, there is a critical energy-
value beyond which the electron escapes from the sway of the quantal
laws, and is exempted from losing its energy by the process of Brems-
strahlung. This belief was an artifice for permitting the penetrative
particles of the cosmic rays to be called by the name of electron.
It might have remained a credible artifice, if the penetrative particles
had been the only ones — if, that is to say, there had never been any
evidence for the existence of particles among the cosmic rays having
the properties required of electrons by the quantal theory. Such a
situation may have seemed to exist at the time when the belief was
dominant. It exists no longer, as the description of Fig. 8 has just
suggested; but before considering further the data, I must introduce
something more of what the theory has to say.

Since 1934 it has been known that a photon of energy greater than
about one million electron-volts is capable, when in the vicinity of an
atom-nucleus, of converting itself into a pair of electrons of opposite
sign. About one million electron-volts — 1.02 Mev, to be somewhat
more precise — becomes "rest-energy" of the twin electrons, being
incorporated with their rest-masses; the remainder (hv — 1.02, if by
hp we denote the photon-energy in Mev) becomes kinetic energy of
the electrons. The process may be produced at command and
exhibited to the eye, by projecting the photons known as gamma-rays
against metal targets contained in expansion-chambers. The gamma-
rays originally used for this purpose proceeded from natural radio-
active substances; mostly they were those emitted by a certain sub-
stance (thorium C") with a photon-energy of 2.62 Mev. Nowadays
gamma-rays of energy several times as great can be produced by
effecting certain transmutations, in the course of which (or afterward)
they emerge from the new-born nuclei. Figure 10 shows an admirable
example of an electron-pair formed out of such a photon. Moreover,
the converse process is well-known: positive electrons falling against

206

BELL SYSTEM TECHNICAL JOURNAL

Fig. 10 — An electron-pair born from a photon. (VV. A. Fowler, California Institute

of Technology)

a plate of dense matter bring about the emission of photons of energy
0.51 Mev, and these are just what are to be expected if the positive
electrons (after being slowed down) unite with some of the innumerable
negative electrons already in the plate and produce, at every such
union, a pair of equal photons.* Much too abundant to be here
described is the evidence for the ability of electron-pairs to pass into
light and light to pass into electron-pairs, making it permissible to
imagine a continual alternation of energy between these two so sharply
contrasted forms.

Formation of the photons of Bremsstrahlung by electrons of enormous
energy, and formation of electron-pairs out of such photons: these
reciprocal processes engaged the attention of several theorists (Bethe,
Heitler, Sauter, Weiszaecker, Oppenheimer) in the years 1933 and
1934. The problem was, to evaluate by quantal theory the chance
that electron or photon would spend its energy in producing photon
or electron-pair, while traversing given thickness of given element.

* Evidently this is not quite the converse of the process previously described,
which if reversed would consist in the merger of a positive and a negative electron
with the formation of a single photon bearing away all of their energy. Some
evidence exists for the occurrence of this process. There is no sign of the fourth
conceivable process (the meeting and merger of two photons to form two electrons)
which must obviously be very rare in practice owing to the feeble concentration of
photons in actual beams of gamma-rays. Nevertheless this last is the process first
predicted by the theorist Dirac.

CONTEMPORARY ADVANCES IN PHYSICS 207

Approximations had to be made in the calculation, as nearly always
in quantal problems; but they are supposed not to affect the rightness
of the main result. To quote Oppenheimer's description of this
result: "a beam of high-energy electrons should have a good part of
its energy converted into photons in a centimetre of lead; in an equal
distance these photons will be largely reconverted into pairs."

Such was the result from which, in 1935, it was inferred that quantal
theory must be wrong because it was predicting something which
could not be found in Nature; and from which, in 1936 and thereafter,
it was concluded that quantal theory not only was correct but had
made a splendid triumph, in explaining the phenomena of showers!
It is not altogether clear why the later conclusion was not drawn at
the start; perhaps the reason is, that as lately as the summer of 1936
fine photographs of showers were still rather rare, while such pictures
as Figs. 5 and 7 with their examples of self-augmenting showers
had not as yet been made. On the other hand it would be premature
to say and misleading to imply that the process which the theory
describes is in exact and quantitative accord with the observations
on showers. There are at any rate good grounds for hoping that as
the mathematics of the theory is more fully worked out and the art
of the experiments refined, the agreement will grow better and better.
The most that seems safe to say is, that now we have a general scheme
for the interpretation of showers of a certain type, and a very hopeful
prospect that this general scheme will be converted into a detailed
and quantitative explanation as the mathematics of the theory on
the one hand, the aptness and precision of the observations on the
other hand are gradually improved.

By inserting the words "of a certain type" in the foregoing sentence,
I leave open the possibility that showers may be classified into more
than one type, and all of these but one be ascribed to other processes.
This is no mere possibility but already almost a certainty. Certain
showers which include "heavy tracks" due to protons or still more
massive particles are ascribed to nuclear explosions provoked by cosmic
rays. If a shower fails to undergo the "multiplication" illustrated
in Figs. 5 and 7, it is taken as belonging to this other type. Exception
made for such cases, it is strongly plausible to say that shower par-
ticles and shower-producing particles are electrons; that accordingly
high-energy electrons exist among the cosmic rays, behaving as the
quantal theory says that they should ; and that consequently the other
particles, setting themselves apart from electrons by their penetrative
power and their failure to make showers, are of another sort.

208 BELL SYSTEM TECHNICAL JOURNAL

Ability to penetrate matter, inability^ to make showers: these are
the complementary aspects of the property which distinguishes this
other type of particle, the mesotron. If one wishes to contrive a
particle having this property and differing otherwise as little as possible
from the electron, how must it be done? The electron has the qualities
of charge and mass; also those of spin and magnetic moment, but
these are considered (perhaps wrongly) to be little or not at all con-
cerned with shower-production. If we imagine the mass to be
increased while the charge remains the same, the liability to Brems-
strahlung will diminish; for Bremsstrahlung occurs when sudden sharp
deflections or decelerations occur, and these are less sharp and sudden
the more massive the particle is. Now Bremsstrahlung is the prelude
to the entire manifold process of the forming of a shower, and hence a
mere increase in the mass of the hypothetical particle leads in the
desired direction. The theory indicates that a particle with the
electronic charge and a few dozen times the electronic mass will be
penetrating enough. We do not need, however, to be contented with
such vague intimations, for there is yet another phenomenon in
respect of which the mesotron differs from the electron, and from this
the mass can be deduced more sharply.

So far, we have been considering the passages of particles through
solids. There, the paths are concealed, the adventures of the particles
can only be inferred — from the difference between energy before and
energy after traversal, or from the photons and the secondary electrons
which are driven out of the solid. Now we are to consider the passages
of charged particles through the gas of the Wilson chamber, which,
unlike the scriptural way of the eagle through the air, are preserved
for our inspection by the droplets. Figure 1 has shown to us a track
in which the number of droplets in unit length of path can rather
readily be counted. What does this number signify? And is it truly
an indication of the mass oT the traveling particle, as I hinted on an
early page?

The latter question might perhaps be sufficiently answered without
reference to the former; but for completeness, and for the sake of its
own interest, the former ought to be treated more fully than it was in
that brief earlier mention. In the voyage recorded in Fig. 1, nothing
so drastic happened to the traversing particle as would have been the
losing of a large part of its energy in the form of a photon of Brems-
strahlung. It lost its energy in driblets, spent in detaching electrons
from molecules and giving them a small extra bonus of kinetic energy

^ It is better to say "relative inability" since occasional showers are attributed to
mesotrons, which perhaps operate by making a violent impact on an electron and so
giving it the energy needful for starting the process.

CONTEMPORARY ADVANCES IN PHYSICS 209

with which to go wandering around in the gas. They had not speed
enough to wander far, even in the half-a-second afiForded them before
the condensation. Probably they had already adhered to molecules
before the condensing water immobilized them. One speaks of the
droplets as being condensed partly on negative, partly on positive
ions; the last-named are the molecules from which the electrons were
reft. (If, during the half-a-second, an electric field of suitable strength
is applied, the ions of the two signs drift in opposite ways, and when
the water-vapor comes down there are seen two parallel trails of
droplets with an empty space between.)

The simplest idea is that the traversing particle tears off one electron
from each of many molecules through or near which it passes, and
that half of the droplets are formed on these electrons and the other
half upon the molecules bereft. This is too simple to be true. It is
likely that sometimes the particle removes two electrons or more from
a single molecule, so that there well may be more negative ions than
positive. Much more serious is the certain fact that often when an
electron is thus released by the direct action of the traversing particle,
it shoots away with speed and energy enough to enable it to release
one or several more from neighboring molecules. Now and then one
comes on a cloud-chamber photograph in which there appears a track
with branches (Fig. 11) ; each of these is the trail of an electron which

Fig. 11 — Tracks of a charged particle bristling with short branching tracks, made by
electrons ejected from atoms with energy sufficient to ionize. (Auger)

has received a truly abnormal and extraordinary amount of energy.
Much commoner, in fact universal, is the "beaded" appearance of
such trails as appear in most of the pictures of this article: it is pre-
sumed that each of the beads is an unresolved cluster of droplets
formed on a cluster of ions, all but one pair of them made in the
indicated way. Occasionally one sees a picture in which the interval
allowed for diffusion has been so happily chosen that the droplets in
the clusters are far enough apart for counting, and yet consecutive
clusters do not overlap. In making Fig. 1 the interval allowed was a
little too long, and yet perhaps it is possible to think that the ions
are denser in some parts of the trail than in others, as though they had
been formed in clusters which have broadened almost but not quite
to the point of losing their identity.

210 BELL SYSTEM TECHNICAL JOURNAL

It is therefore necessary to distinguish, in mind if not in fact,
between the "primary ionization" consisting of the electrons and the
molecules torn apart from each other by the direct immediate action
of the traversing particle,^ and the "entire ionization" (sometimes
called "probable ionization") consisting of these together with all the
ions formed by the directly-ejected electrons. Under ideal conditions
it is presumed that the measure of the former would be the total
number of droplet-clusters,^ the measure of the latter would be the
total number of droplets, in unit length of path. Not many physicists
have tried to evaluate both of these numbers. Of those who have,
the data have been scanty, but the consensus of opinion is that the
latter is about or not quite twice as great as the former. It is, however
likely that the value of the ratio of the two is not important when
one wants only to distinguish between electron and mesotron, as we
shall presently see.

The problem of the primary ionization is one of the major tasks of
theoretical physics. Classical and quantal theorists alike have spent
great labor on the question : given a charged particle of specified charge
and mass and speed traversing air (or any other gas), how many
electrons will it set free from the molecules in unit length of path?
At this point I will give only one of the results — or rather, something
which is not a result at all, but a part of the assumptions. It is
assumed that as the traversing charged particle flies along through or
close to a molecule, it operates upon the electrons thereof by virtue of
the ordinary electric forces between its charge and the charges of the
electrons. It follows, then, that whatever expression finally may he
derived for the primary ionization must depend only upon the charge and
the speed of the traversing particle, and not upon its mass. (Mass and
momentum of the particle must indeed be great enough to hold it on
a sensibly straight course as it plows onward through the gas, despite
its losses of energy as it detaches electrons; but this condition is
always realized, with the corpuscles of the cosmic rays.)

I seem to have said that the primary ionization gives no power of
distinguishing between an electron on the one hand, a particle of equal
charge and different mass on the other. However, it does confer on
us this power, for the reason that the curvature of a particle-track in
a known magnetic field is a measure not of particle-speed but of

^ Unluckily called "secondary ionization" by some of the German theorists.

^ Best to observe the droplet clusters as individual entities, one would wish the
expansion to occur before the ions have any time at all to diffuse. To attain this,
Williams and Pickup caused the chamber to expand at moments taken at random,
and trusted to luck for the appearance of cosmic-ray tracks formed at just the right
instants. Luck served them with no fewer than four tracks betokening particles of
a distinctive mass.

CONTEMPORARY ADVANCES IN PHYSICS 211

particle-momentum (equation 2). If by luck an experimenter should
happen upon two tracks having the same curvature but made by
particles having masses ^ standing to one another in the ratio (say)
100 : 1, the speeds would stand to one another in the ratio 1 : 100,
and this might well entail a perceptible difference in the primary
ionization. It would come to the same thing, if someone should take
the data for a large number of tracks, and plot primary ionization as
function of curvature: if there are really two kinds of particle differing
in mass, there should be two sets of points lying along two curves,
and from the ordinates of these curves at any abscissa the ratio of
the masses would be derivable.

Perhaps the last sentence suggests that someone already has made
this correlation, and has found that the points for all of the single or
penetrating particles lie upon one curve, and all the points for shower-
particles and shower-producing particles lie on another. This has
not been done. The reason is, that many of the penetrating particles
exhibit no perceptible curvature of track at all, and most of the others
a very small curvature. The former are moving so fast that their
momentum cannot even be estimated, except as being beyond a certain
critical value. As for the latter, the speeds of even these are so great
as to approach the speed of light; for a given momentum-value the
speed varies only a little with the mass, and the primary ionization
varies too little to serve as an index of mass. To make a profitable
correlation, one must use only the particles of which the tracks are
notably curved. Nearly all of these are shower-particles, which
already are presumed to be electrons. To find a penetrating particle
with a highly-curved track, one must find it when it is near to the end
of its course and its energy wellnigh gone. Such is the principle
which directed some of the recent successful searches for particles
proclaiming themselves by their ionization to be more massive than
electrons.

Before looking at the track of one of these particles, we ought to
notice a couple of questions concerning ionization. One of them is:
is the distinction between primary and entire ionization — or rather,
our lack of perfect ability to make it in practice — likely to lead to
trouble? Many observers are far from clear in reporting whether
what they observe is more like the one or more like the other; but it
seems probable that the second like the first is dependent only upon
the speed and the charge of the traversing particle, not on the mass
thereof; and this diminishes the dangers from confusing the two.
The question is implicated with the second: to what extent do experi-

* Allowance being made for the relativistic dependence of mass on speed.

212 BELL SYSTEM TECHNICAL JOURNAL

ment and theory aid us in identifying the shower-particles with the
electrons? As to experiment, there exist the records of a few studies
made by the Wilson chamber upon particles acknowledged to be
electrons, of energy-values ranging from about 2 Mev downward to
some 25000 electron-volts. In respect of the trend with energy, they
agree fairly well with the assertions of the quantal theory; but when
one inquires whether the absolute value for the number of clusters of
ions in unit length agrees with the absolute value of the quantal
expression for the primary ionization at any particular energy, one is
confronted with the fact that the quantal expression contains a
multiplying factor which depends on intimate details of the structure
of the molecule, and is not exactly known. The quantal theory,
however, predicts a minimum in the curve of primary ionization vs.
energy, at an energy of about 2 Mev. Such a minimum (Fig. 12) was

I 70 -

Fig. 12 — lonization-density (entire) along the tracks of cosmic-ray particles,
plotted as function of Hp. The continuous curve is that of a theoretical function
containing a multiplying factor which has been adjusted to get the best fit to the
data. (Corson and Erode)

actually found by Corson and Erode in their study of some fifty
particles of the \:osmic rays, and probably is to be ranked as evidence
for the electronic nature of these particles quite as forcible, as would
be an absolute agreement between the observed ionization and the
predictions of a reliable theory.

Street and Stevenson, with a row of counters and an interposed
cloud-chamber such as appeared in Fig. 3, adjusted their counters
in such a way that the chamber expanded only when the counters
above the chamber had simultaneous discharges and the counter
below did not. A thousand photographs yielded to them the track

CONTEMPORARY ADVANCES IN PHYSICS

213

of one particle having a notable curvature and displaying an ionization
six times as great as that attributable to an electron; they inferred a
"mass 130," i.e. a rest-mass one hundred and thirty times as great as
that of an electron. Neddermeyer and Anderson transposed the
bottommost counter into the very centre of the cloud-chamber itself,

2 1800

/

/
/
/

/

/

/
/
/

/

/
/

/

/

/
/

/

/

/

/
/
/

ELECTRONS
+ OR-

/

/
/

/

/

y

/
/

•

/

/

/
/
/

/

/
/
/

f

PROTONS

/

/

/

f

/

/

/

/

/

/

/
/

/

}

4
/
/

A

/

f

/

y

23456789
Hp IN GAUSS-CENTIMETERS

10 II 12 13

XI06

Fig. 13 — Relation between energy and i7p-value for electrons (of either sign)
and protons. (Anderson)

and there it appears in Fig. 14, neatly intersected by the course of a
particle which above it made a track lightly curved and thinly studded
with droplets, and beneath it made a track sharply curved and densely
congested. Comparing ionization with curvature along the track
above and the track below, they found 240 to be a satisfactory ratio

214

BELL SYSTEM TECHNICAL JOURNAL

of the mass of the traversing particle to the electron-mass. Williams
and Pickup, to whose technique I have already alluded (footnote 7
on page 210), observed four tracks of which three were compatible
with a rest-mass of about 200, the remaining one requiring a mass-
value between 430 and 800. A few more such tracks have appeared
in the literature, but instead of describing them I turn for the climax
to another and an exacter way in which Fig. 14 furnishes the desired
value of mass.

Fig. 14 — Track of a mesotron slowed down by an obstacle in a Wilson chamber
and finally brought to a stop in the gas of the chamber itself. (Neddermeyer and
Anderson)

In Fig. 14, the track beneath the counter comes to a sudden end.
One could take a sheet of coordinate-paper, and plot along the hori-
zontal axis the curvature of the path as it emerges from the counter,
and along the vertical axis the length of the path from that point of
emergence onward to its end. This would give a single point of what
is known as a " range-vs. -curvature relation" or a " range- vs.-momen-
tum" relation. A second point can be found by measuring the
thickness of the glass counter-wall twice traversed by the particle,
converting it into an equivalent thickness of gas, adding this to the
length of the path beneath the counter, and correlating the sum with
the curvature of the path at the point where the particle enters the
counter. Now, range-vs. -curvature relations are among the best-
studied of the features of the charged particles already known —

CONTEMPORARY ADVANCES IN PHYSICS 215

electrons, protons, alpha-particles. These two points pertaining to
the particle of Fig. 14 lie far from the curves appropriate to any of
the three. An electron departing from the counter in a path of such
a curvature as there is shown would have traveled 2000 times as far
before reaching the end of its course! a proton, on the other hand,
only one seventy-fifth as far! This at the moment is deemed the
sharpest and most clear-cut evidence for the existence of a particle
intermediate in mass between proton and electron, to which Anderson
now assigns a mass of 220 (± 35) times the electron-mass.^

It is fitting to end this article by mention of several other kinds of
evidence which have bearing on the question of the mesotron; mainly
they are relatively indirect, and would require much space to describe
and assess. Inferences have been drawn from the number of electrons
ejected with high energy from metal plates by penetrating particles
traversing these: J. G. Wilson derives a mass- value greater than 100.
A curious inference has been drawn from the deflections suffered by
these particles in traversing metals: the magnitude of these should by
theory be independent of the mass of the particle — since it does appear
to be the same for penetrating particles as for electrons, it is deduced
that the mesotron and the electron can differ only in mass. Inferences
have been drawn from the trend of cosmic-ray intensity with elevation
in the atmosphere, and from the trend of cosmic-ray intensity beneath
metal screens as function of the material and thickness of these last
(it was thus that Auger as early as 1934 was led to suspect the existence
of two kinds of charged particle among the rays).

Inferences have also been drawn from nuclear theory. To enter
adequately into this difficult field is impossible here: it must suffice
to say that Yukawa conceived, as a constituent of nuclear structure,
of a particle possessing the charge of an electron and a mass of about
the magnitude which the mesotron appears to have, and possessing in
addition the quantity of instability. The "Yukawa particle," that
is to say, has the qualities demanded of the mesotron, and in addition
is liable to emit an electron; what is left behind is then a neutral
particle which could elude observation. The emission is expected to
follow the law familiar in radioactivity, the durations of individual
Yukawa particles being distributed according to the law of chance
about a mean value. Is there evidence that the mesotron behaves in
this way?

^ Values diverging from this by more than the estimated uncertainties have been
published by other observers of other particles, and may betoken an underestimate
of the uncertainty or the existence of particles of several masses. A "nomograph"
for facilitating the evaluation of mass from curvature of path combined with ioniza-
tion-density or range is given by Corson and Erode.

216 BELL SYSTEM TECHNICAL JOURNAL

For this there is some evidence, of the following kinds. First let
us compare (in imagination) the number (per unit time per unit area)
of penetrating particles flying vertically downward and the number
flying obliquely downward. The comparison can be readily made
with such an apparatus as that sketched in Fig. 3, the cloud-chamber
being superfluous and the lead absorber reduced to the least thickness
sufficient to stop electrons; the axis is oriented first at 90° and then
at various lesser angles d to the horizontal plane. Even the whole of
the atmosphere is insufficient to stop such mesotrons as the cloud-
chamber discloses; and yet the observations show a marked decline of
the number thereof as d decreases. But the particles which travel
obliquely traverse a greater distance from the top of the atmosphere
than those which come vertically down, and take a longer time in
■doing so; the decline of number with decrease of 0 may therefore be
ascribed to the perishing of the mesotrons en route to the apparatus
as the route grows longer and longer. Second: Let us compare the
effect of the obliquely-traversed atmosphere with that of a sheet of
lead in cutting down the number of particles arriving at the apparatus.
One must make a guess as to the thickness of lead which would be
required to produce a falling-off^ of the number of particles equivalent
to that observed in the atmosphere, if the falling off were due to
actual stopping of mesotrons in air and lead respectively, and the
impermanence of the mesotron did not enter in at all. It is commonly
conjectured that the equivalent thicknesses of lead and air would
stand to one another inversely as the densities of these materials.
When, however, the effects of such "equivalent" thicknesses are com-
pared, it is found that the falling-off beyond the lead is decidedly less
than that beyond the air. Now the mesotrons take very much less
time for traversing the sheet of lead than the wide expanses of the
atmosphere; and the "anomaly," as it has been called, is tentatively
explained by assuming that few of them perish in the lead, many in
the long journey through the atmosphere.

Estimates of the mean life of the mesotron thus made yield values
of the order of a millionth of a second. It is supposed by many that
the mesotrons are born in the upper layers of the atmosphere. Such
conjectures, however, lead beyond the scope of this article, which must
be confined to these few recent fruits of the seemingly exhaustless
cornucopia of the cosmic rays.

Selections From The Literature

Energy-losses of particles traversing metals: Anderson and Neddermeyer,
London Conference on Nuclear Physics (1934); Phys. Rev. 50, 263 (1936); Nedder-
meyer and Anderson, Phys. Rev. 51, 884 (1937); Blackett and Wilson, Proc. Roy. Sac.

CONTEMPORARY ADVANCES IN PHYSICS 217

160, 304 (1937) ; Blackett, ibid. 165, 1 1 (1938) ; Wilson, iUd. 166. 482 (1938) ; Leprlnce-
Rine;uet and Crussard, Comptes Rendus 204, 112, 240 (1937); Ehrenfest, Comptes
Rendns 207, 573 (1938).

Penetrating particles detected with counters, with or without cloud-
chambers: Street, Woodward and Stevenson, Phys. Rev. 47, 891 (1935); Street and
Stevenson, Phys. Rev. 51, 1005 (1937); Auger and Ehrenfest, Comptes Rendus 199,
1609 (1934).

Tracks of particles with characteristic ionization densities: Electrons:
Corson and Erode, Phys. Rev. 53, 773 (1938). Mesotrons: Street and Stevenson,
Phvs. Rev. 52, 1003 (1937); Ehrenfest, Comptes Rendus, 206, 428 (1938); (E. J.)
Williams and Pickup, Nature 141, 684 (1938); Maier-Leibnitz, Naturwiss. 26, 677
(1938); Neddermeyer and Anderson, Phys. Rev. 54, 88 (1938), and literature there
cited.

Theory of showers: Oppenheimer, Phvs. Rev. 50, 389 (1936); Carlson and
Oppenheimer, ibid. 51, 220 (1937); Bhabha'and Heitler, Nature 138, 401 (1936),
Proc. Roy. Soc. 159, 432 (1937) ; Bhabha, Proc. Roy. Soc. 164, 257 (1938) ; Montgomery
and Montgomery, Phys. Rev. 53, 955 (1938).

Deflections of particles: Blackett and Wilson, Proc. Roy. Soc. 165, 209 (1938).

Electron's recoiling from imp.\cts of mesotrons: Wilson, Nature 142, 73
(1938).

Instability of mesotron: Blackett, Nature 142, 992 (1938); Rossi, ibid. 993;
(T. H.) Johnson and Pomerantz, Phys. Rev. 55, 104 (1939).

General reviews: Euler and Heisenberg, Ergebnisse d. exakten Naturwiss. 17, 1
(1938); Froman and Stearns, Rev. Mod. Phys. 10, 133 (1938).

Hurricane and Flood — ^September 1938

By W. H. HARRISON

Editor's tiote: The following was presented by Mr. Harrison as
the closing address of a symposium on the effects of the hurricane
and floods of September 21, 1938 on transportation, power and com-
munication utilities. The symposium was held in New York at
the Winter Convention of the American Institute of Electrical
Engineers, Thursday, January 26, 1939. After the close of the
meeting a motion picture on the hurricane prepared by the Bell
System for the information of its own employees was shown.

THE experiences of the telephone companies are naturally much the
same as those already described. The aftermath tally showed
that more than one-half million telephones were put out of service^in
the New England States about thirty per cent of the telephones in that
area. Through the destruction of toll lines, the storm temporarily cut
off telephone communication with the outside from over two hundred
towns. The total damage to telephone plant was in the neighborhood
of ten million dollars.

The story of restoration — the immediate provision of emergency
services — the handling of emergency supplies in unprecedented quanti-
ties— the augmenting of forces locally to supplement the normal forces
— and the mobilization of forces from other areas — all are replete with
engineering interest and are very intriguing, but it would not be ap-
propriate to take the time to tell the story here. A few facts will give
you a sketchy idea of the situation.

As to materials:

3,500,000 feet of lead covered cable
54,000,000 feet of paired wire
7,000,000 feet of steel strand for guys
and supporting cables

As to mobilization of forces:

Local construction forces were expanded from 3,000 to 5,000. In
addition, 2400 highly skilled linemen, cable splicers and installers and
over 600 fully equipped construction trucks and other special motor

218

HURRICANE AND FLOOD— SEPTEMBER 1938 219

vehicles were brought from fourteen other telephone companies as far
south as Virginia and as far west as Nebraska and Arkansas.

Of striking significance in the prompt restoration of service was the
traditional Bell System background of standardization of materials and
methods. This standardization greatly facilitated the collection of
large quantities of suitable supplies and made possible maximum efifec-
tiveness of the men who came from many parts of the country. The
striking effectiveness of these measures is a great tribute to the engi-
neers who long ago by their recognition of the value of standardization
laid the broad foundation for this efifective work.

In every disaster much is learned with regard to formulating plans
and caring for specific situations. Of interest in this specific situation,
there had been serious floods in much of this territory in 1936. The
experience at that time pointed to certain precautionary measures and
we know of no case where these did not prove effective in the present
situation. For example, while the water rose five feet above the
ground floor level of the main telephone building in Hartford, it was
successfully kept out of the building by bulk-heads about the doors
and windows, provided since the 1936 flood. Also, at various places
where lines had been carried away due to the failure of bridges or other
forms of river crossings the restored lines did not fail.

Over and above all of these more or less specific points, which I might
say are somewhat routine, lies a broad engineering fundamental vividly
illustrated by this whole experience.

Engineers by their work have made a pattern of life which has come
to make individuals and communities dependent to a large extent in
their day-to-day activities and mode of living, on the proper function-
ing of the services of power, transportation and communication.

Having done this, they have seen their works fall before the fury
of nature — have seen the utter disruption of the organized scheme of
life, with all the anguish that goes with such disruption.

It is in the light of this experience that an engineering fundamental
of first magnitude presents itself, and one which offers a long range
problem that is going to call for nicely balanced judgment, both on the
part of the engineer and the management. This fundamental stands
out clearly — dependability of service, and specifically the degree to
which dependability can soundly and wisely be built into the physical
plant.

It is trite to say that dependability is fundamental to good service, that
it is of prime consideration in the design, construction and operation of
all communication, power and transportation facilities. On the other

220 BELL SYSTEM TECHNICAL JOURNAL

hand, it would be foolhardy to assume that any man-made structure
could completely withstand the fury of the elements, as typified by this
storm.

Consider the circumstances. For four days rain was progressively
heavier. It totaled between five and ten inches at many New England
points. At some places more than six inches of rain fell in one day.
As a result large rivers were brought to flood stage and small brooks and
streams became raging destructive torrents. And then came the hurri-
cane— then the seas. Wind velocities as high as from 120 to 180 miles
per hour have been reported. Raging flood and tidal waters inundated
important sections of many communities. Our services extended over
the entire band of the storm and we can definitely trace the relationship
of high wind velocities and resultant damage.

Another important circumstance, and bearing particularly on engi-
neering consideration, is that nothing like this had happened in this
area since the year 1815.

Obviously, to build plant to be unyielding to the sea and to be
hurricane tight against such occurrences at century intervals would be
as unsound as to ignore them altogether. Thus a challenge is presented
to the engineer, taxing his best judgment. On the one hand, not failing
to take every reasonable precaution in the future design of the plant,
such as the avoidance of known exposures, the provision of alternate
routes, the use of emergency restoration facilities of every conceivable
character, adequate emergency operating routines; and on the other
hand, not to be led by the tragedy of the storm to recommend extreme
construction and operating procedures such as wholesale substitution of
underground for aerial plant, which would obviously not be in the
public interest.

This, it seems to me, is the broad lesson that we draw from this ex-
perience and the challenge presented to the engineer.

It was my good fortune to have been in the midst of the restoration
work. It was comforting and inspiring to see how the men and women of
all service agencies responded to the call, each presented with a trying
problem of his own but ever ready to lend helpful and efTective co-
operation to those in other utilities, and all motivated with the com-
mon objective of maximum service to the community in this period of
great distress. I know we in the telephone end could not have done
our job had we not had the help of others, including the highway and
other public agencies.

The final measure of any man's work is, has it been for mankind?
A grateful public has put the mark of approval on the work of the men

HURRICANE AND FLOOD— SEPTEMBER 1938 221

and women of the utilities and transportation groups in the stricken
area. My admiration for them knows no bounds. Frequently when
we fail of expression we turn to the pens of immortals.

Two lines in one of Kipling's poems — "Sons of Martha " — beautifully
express the work of these men and women :

" Not as a ladder from earth to Heaven, not as a
witness to any creed,
But simple service simply given to his own kind
in their common need."

A Terrain Clearance Indicator *

By LLOYD ESPENSCfflED and R. C. NEWHOUSE

There is described a radio altimeter that gives continuously on
the plane a measurement of the separation between the plane
and the earth's surface or projections therefrom. There is pro-
jected from the plane and reflected from the earth back to it a
very short radio wave, the frequency of which is continuously
swung back and forth. The returned wave is thereby made to
differ from the outgoing wave in frequency by an amount that is
proportional to the echo path; and the difference or "beat" fre-
quency is indicated on a frequency meter calibrated in feet of
separation. The paper outlines some of the early efforts in this
field, some of the technical problems involved, the theory of the
system and the practical experimental results that have been
obtained.

Introduction

'T^HE problem of an altimeter for aviation has engaged the attention
-■- of many inventors and experimenters for twenty years or more.
As a result, about every conceivable fundamental method of attacking
the problem, by the utilization of acoustic or electric phenomena, is
disclosed in the art, including the many U. S. patents on the subject.

The familiar aneroid altimeter has reached a high degree of perfec-
tion and enables the pilot to maintain level flight at any desired alti-
tude but it gives no clue as to the variation of the elevation of the
terrain beneath. The pilot has to know his position at all times and
perform a mental calculation, in order to know his height above the
ground at any given moment. A number of airplanes have drifted
ofif their normal courses and have crashed on higher ground.

An altimeter based upon the use of a sound echo is subject to two
fundamental limitations. The first of these limitations is the ex-
tremely high noise level produced by the airplane's motors and pro-
pellers, which tends to submerge the relatively weak echo at heights
of more than a few hundred feet. The second is that the speed of
sound is not enough greater than the speed of airplanes. At a height
of one thousand feet approximately two seconds are required for a
sound to travel to the ground and return. In this time interval a
modern airplane would travel six hundred feet and the clearance may
have changed materially.

* Read before the Institute of Aeronautical Sciences at the Chicago meeting,
November 19, 1938, and to be printed in the Journal of the Institute.

222

A TERRAIN CLEARANCE INDICATOR 223

There is in radio the corresponding phenomenon of an echo, an
electric-wave reflection. The velocity of a radio signal is so great
that an echo from the earth's surface is almost instantaneous; in fact,
the time interval is so small as to give rise to a problem in measuring
it. For instance, for heights less than a thousand feet the time to be
measured is less than two millionths of one second.

The method used in the present instrument is extremely simple in
theory. A radio transmitter is provided on the airplane which sends
toward the earth a signal, the frequency of which changes at a definite
rate with respect to time. The signal is reflected by the earth and
returns as an echo after a time delay equal to twice the height, divided
by the velocity of propagation. During this interval the frequency
of the transmitter has changed and now differs from that of the echo
by an amount equal to the product of the rate of change of frequency
and the time of transit. The reflected wave is combined in the plane
receiver with some of the outgoing wave energy and the difference or
"beat" frequency is measured by a frequency meter. Since the read-
ing of the meter is that of the "beat" frequency, it is proportional to
the time delay of the echo and, hence, to height and thus can be
calibrated directly in feet.

Early Efforts

The evolution of this method is interesting because it illustrates
how one art is built upon another, and also the familiar story of separate
inventors arriving at the same answer almost simultaneously, actually
somewhat in advance of the existence of instrumentalities having the
characteristics required to make the invention practically serviceable.

Many systems employing electromagnetic waves for the purpose of
indicating altitudes of an aircraft have been proposed.^ Among early
workers in this field who independently of each other were concerned
with methods involving frequency modulated waves were J. O.
Bentley ^ of the General Electric Company; Professor W. L. Everitt ^
of Ohio State University and certain students in his department of
Electrical Engineering including the junior author* and M. W.
Hively; and the senior author.

Under the direction of Professor Everitt, some experimental work
on the frequency modulation method, using wire lines, was undertaken
in the school year 1928-29. On the basis of this work a grant was
made by the Guggenheim Fund for the promotion of aeronautics and
an investigation was continued with experimental tests, during the
following school year under the auspices of the Ohio State Engineering
Experiment Station. The experiments were reported upon in the

224 BELL SYSTEM TECHNICAL JOURNAL

bulletins of the Station, and in a graduate thesis ^ of the junior author
and J. D. Corley.

As early as 1920, the senior author proposed the use of electric wave
reflection in railway safety systems ^ and entertained the idea of
frequency-modulated transmission with beat-tone detection for
measuring distance along a track. Radio wave reflection for aircraft
altitude determination was considered at times from 1926 to 1930
when a patent application was filed '' for an arrangement similar to that
which has been worked out, including the use of a frequency meter to
give continuously a visual indication of the altitude.

At that time, however, a really practical terrain clearance indicator
could not be built due in large part to the lack of suitable radio in-
strumentalities. Vacuum tubes capable of operating on frequencies
approximately fifty times higher than those generally available were
indicated as necessary before a satisfactory system could be built.

A long-range program, however, of vacuum tube development for
high frequencies was under way in Bell Telephone Laboratories. This
resulted in the production of suitable tubes, and they were described
by A. L. Samuel ^ to the Institute of Radio Engineers in October,
1937. One of these was capable of providing a stable output of be-
tween five and ten watts at a frequency of approximately 500 mega-
cycles, so it became feasible to undertake the development of a practical
terrain clearance meter.

The Japanese have been experimenting recently with apparatus

operating upon the same basic theory and a paper ^ was published in

Japanese in 1936. A later paper i" was published in English in 1938

by the same author, which describes the apparatus and the results of

tests made on the ground over short distances with the equipment at

rest.

Technical Problems

At the time this development was undertaken a number of questions
presented themselves as to what the earth's surface would do to the
incident wave in reflecting it. It seemed possible that the signal
might be so scattered and broken in reflection by small irregularities
that the echo would be more like static than a useful signal.

Even if the reflected signal proved satisfactory over the smoother
surfaces, it was hard to predict what would happen when flying over
timber land or over very irregular mountainous terrain. There was
also the question of what would happen when the surface happened
to be that of a city where an airplane flying at 250 to 300 feet per second
passes over several buildings and streets with abrupt altitude changes
of possibly hundreds of feet several times in the course of one second.

A TERRAIN CLEARANCE INDICATOR 225

Even with the most directive systems that can be devised, the beam
radiated from the airplane is so spread that echoes can be expected to
arrive simultaneously from several surfaces, for instance from both the
leaves on the trees and the ground between the trees, or from the top
of a building and from the adjacent street.

Several problems were anticipated in the apparatus itself. The
theory is based upon a frequency-modulated signal free from any ampli-
tude modulation, and it was questioned whether a transmitter could
be built to operate on ultra-high frequencies which would be suffi-
ciently free from amplitude modulation, when subjected to the vibra-
tion of the airplane, to be satisfactory. Since the receiver utilizes
both the direct and reflected signals in making the altitude measure-
ment, it is necessary that some signal be picked up directly from the
transmitting antenna but not enough to overload the receiver and
thus prevent reception of the echo. It was expected that difficulty
would be encountered in sufficiently reducing the direct signal.

After considering all these problems, it was decided that the cheapest
and easiest way of determining the answers was to build the apparatus
and try it out to see if correct operation could be obtained, first, under
the more or less ideal conditions of flying over smooth water and, then,
over less favorable surfaces.

Most of the measuring equipment available for radio frequency test
work is useless at ultra-high frequencies. Hence, it was necessary to
get the system functioning as a whole before any means were available
for determining the best adjustment of the radio-frequency parts of the
system. Because of the difficulty of providing, while on the ground,
an adequate reflector at distances of from a few feet to thousands of
feet from the apparatus, it was necessary to install the equipment in an
airplane very early in the development and make most of the tests
during flights. Nearly a hundred airplane flights were made in one
of the Bell Telephone Laboratories' airplanes during the development
period of seven months which preceded the public demonstrations
made in the United Air Lines Flight Research Airplane.

Operation and Theory
The fundamental parts of the altimeter in relation to their applica-
tion are shown in Fig. L An ultra-high frequency oscillator is pro-
vided, whose frequency is varied up and down by a modulator which
consists of a small rotating variable condenser driven by a motor.
The oscillator is connected through a coaxial transmission line to a
transmitting antenna which is located on one of the lower surfaces of
the airplane. The signal is radiated downward by this antenna. A

226

BELL SYSTEM TECHNICAL JOURNAL

radio receiver is connected through a similar coaxial line to a second
antenna similarly located but arranged in such a way that a minimum
of direct signal is received from the transmitting antenna and as much
echo as possible from the ground. The direct and reflected signals are

TRANSMITTER

FREQUENCY (
MODULATOR I

OSCILLATOR f

(ultra-high FR£Q.)l

FREQUENCY- I

MODULATED J

SIGNAL 1

RECEIVER

(?

METER

^

1 FREQ. METER
J CIRCUIT

t

] AMPLIFIER

^

] DETECTOR

Fig. 1 — Overall system.

applied to a detector circuit in the receiver. The output of this de-
tector is a signal of a frequency equal to the instantaneous difference
existing between the direct and the reflected signals and is proportional
to the height of the plane above the terrain. This signal is ampHfied
by the receiver and applied to a frequency meter or counter circuit
which is so designed that a current proportional to the frequency and,
hence, to the height flows through a meter calibrated in feet and
located on the airplane's instrument panel. A number of types of

A TERRAIN CLEARANCE INDICATOR

227

indicating frequency meter circuits " of the condenser charge and dis-
charge variety have been described in the technical Hterature.

The operation of the system can be understood more easily by
reference to Fig. 2. The variation of the transmitter frequency with

signals:
direct reflected

'MAX

RADIO
FREQ,

LOW

FREQ.

0

^^

1.

2Fm

— KEY —
H = HEIGHT OF AIRPLANE
C = VELOCITY OF PROPAGATION OF
RADIO WAVES

^=TIME DIFFERENCE

FrT1=N0. OF CYCLES OF FREQ.-

MODULATION PER SECOND

2AFFm= RATE OF CHANGE OF
TRANSMITTER FREQ.

Fd =FREQ. DIFFERENCE IN DETECTOR

OUTPUT = 2H (2 AF F^) = 4AFFmH
C ^ ^ C

±

:v:

v:

T TIME

Fig. 2 — Operating theory.

time is indicated by the soUd sawtooth Hne.* The value of the ordi-
nate of this curve at any point is the transmitter frequency for the
corresponding time. The frequency is varied from Fmin. up to Fmax.
and back Fm times per second, so the rate of change of frequency is
2AF Fm when AF is substituted for T^max. — -^min. The linear fre-
quency variation shown, while ideal, is not essential for the successful
functioning of the apparatus. The dashed sawtooth line represents
the variation with time of the frequency of the echo signal from the
earth's surface. This curve is displaced to the right by a time equal
to twice the height divided by the velocity of propagation, or, in other
words, the time it took the radio signal to go down to the earth and

* A simple harmonic wave that changes in frequency from instant to instant is no
longer a single frequency but a series of discrete frequency components. In the
present instance, the number of cycles of frequency modulation per second is small
compared to the transmitter frequency swing, so the spectrum occupied by the signal
is substantially that of the swing itself.

228 BELL SYSTEM TECHNICAL JOURNAL

return. This results in a frequency difference between the direct and
reflected signals which is equal to the product of the time delay IHjC
and the rate of change of frequency, and is given by the equation,

Fd = 4Ai^ FmH/C cycles per second.

The difference is plotted again at the bottom of the diagram and
appears as a series of trapezoids of height Fd. The time delay,
IH/C, has been greatly exaggerated in comparison with l/Fm, the
time interval corresponding to one cycle of frequency modulation,
in order to make the difference, Fd, large enough to show on the dia-
gram. Fd is actually only a few cycles in hundreds of millions. It
will be noted that Fd drops momentarily to zero twice for each com-
plete sawtooth variation of the transmitter frequency. This is due
to the necessity of varying the transmitter frequency first up and then
down, instead of forever in one direction. Hence the theory must be
considered from the standpoint that one altitude measurement is
made for each upward and another for each downward sweep, AF, of
transmitter frequency so that a total of 2Fm measurements are made
per second. The number of cycles of frequency Fd, occurring during
one frequency sweep, is

Fs = FdX^= 2AFHIC,

since TTv;- is the time of one sweep, AF. F^ is directly proportional to

both the height and to the amount of transmitter frequency change,
AF.

The fact that 2Fm separate measurements are made per second is
important only when considering small altitudes. The height which
gives a value of unity for F^ corresponding to a frequency meter signal
of IFm cycles per second is the minimum height which can be indicated
since lower altitudes give the same reading. Lower altitudes cause
only a fraction of a cycle of frequency, Fd, to be generated per sweep,
but since this fraction is repeated 2Fm times per second, it constitutes
a signal of the same frequency 2Fm and is so counted by the frequency
meter. In order to make this minimum altitude small, it is necessary
that AF be large, since they are inversely proportional to each other.
A frequency sweep of approximately 25 megacycles is required to
provide measurements down to the present minimum of about twenty
feet. If a high antenna efficiency is to be obtained over a band 25
megacycles wide, it is necessary that the percentage variation from the
average frequency during the modulation cycle be small. This

A TERRAIN CLEARANCE INDICATOR

229

be

230

BELL SYSTEM TECHNICAL JOURNAL

percentage variation is made small by the use of an average frequency
of approximately 450 megacycles. The use of this ultra-high fre-
quency has the additional advantage that the antennas can be both
small and efficient and cause little drag upon the airplane.

Apparatus

Figure 3 is a photograph of all the units of the altimeter, with the
exception of the transmission lines used to connect the antennas to
their respective units. The units are as follows: left to right, receiver,
power unit, and transmitter, with a junction box in the upper right.
In the foreground are the two dipole antennas and the indicating meter
with its range-shift switch. The meter and one of these antennas are
shown in larger scale in Fig, 4. The meter has two scales, the upper

^t^^-j ,£iK-

Fig. 4 — Antenna, meter, and range switch.

extending from 0 to 5000 feet and the lower 0 to 1000 feet. The
position of the range switch determines the scale to be used in reading
the meter.

Figure 5 shows an assembly of the various units located approxi-
mately as they would be installed in an air transport. The trans-
mitter, power unit, receiver and a junction box are installed in the
baggage compartment just aft of the cockpit with cable connections

A TERRAIN CLEARANCE INDICATOR

231

o

H CD £D

5 Z LU

^ O Z

5

If) cr. > X

Z W Q] a.

< :S <j »-,

q: O tu !iJ < D

h- Q. EC 5 CC --1

ij) u

< m o Q LU u. U)

b

232 BELL SYSTEM TECHNICAL JOURNAL

to the airplane battery and to the meter and range switch on the
instrument panel. The transmitting antenna is shown below the
wing to the left of the engine nacelle and the receiving antenna to the
right of the other engine nacelle. Coaxial transmission lines connect-
ing the antennas to the transmitter and receiver, respectively, are
indicated by the lines extending through the wings from the antennas.
It was necessary to exaggerate the size of some of the units in order to
make them large enough to see in the diagram.

The installation with apparatus as pictured in Fig. 3 weighs com-
plete with all cables and connections about seventy pounds. Since
the equipment shown in the pictures represents a working model built
with the idea of attaining performance rather than minimum weight,
undoubtedly some reduction in weight will be obtained in future
models.

The antenna installation shown utilizing half-wave dipole type
antennas approximately a quarter wave-length below the reflecting
surface of the wing is not particularly directional. The signal is
radiated over approximately the whole hemisphere below the wing
centered on the transmitting antenna. The strength of the signal
is greatest in the downward direction but does not fall off rapidly in
other directions. The advantage of this antenna arrangement is that
the distance to the nearest reflecting surface is measured regardless of
whether it is directly beneath, or to the front or side. As a result very
little change in reading occurs when the airplane banks steeply. Some
advance indication also is given when the airplane in level flight
approaches higher terrain.

Performance

The terrain clearance indicator in its present experimental form
indicates altitudes between approximately twenty and five thousand
feet. When over smooth water or land, it is subject to errors as
indicated by a consideration of the fundamental equation upon which
the altimeter is based,

F, = AAFFmH/C.

Since Fd is directly proportional to both AF and Fm, any variation of a
given percentage in either will result in a corresponding percentage
error in the reading of the meter. It is believed from the data available
that the errors due to variation of either AF or Fm do not exceed ±1
per cent.

Additional errors can also occur in the frequency meter circuit.
These errors are believed to be less than ±7 per cent, so that a total
error of ±9 per cent might occur if all the errors were simultaneously

A TERRAIN CLEARANCE INDICATOR 233

in the same direction. Fortunately, all these are of a percentage nature,
so that the error in feet becomes smaller as the ground is approached.
An absolute error in the indication is still possible because of the limita-
tions of the milliammeter used on the instrument panel. The Weston
aircraft meter used is guaranteed to be correct to within one per cent
of its full scale reading at any point on its scale, which permits maxi-
mum errors of ten feet on the 1000-foot scale and fifty feet on the
5000-foot scale.

When flying over rough water, wooded terrain or cities, reflected
signal is received from surfaces at different distances simultaneously,
resulting in addition and subtraction interference effects, thus some-
times momentarily reducing the echo signal below the minimum re-
quired for accurate indication. In such a case, the meter hand may
swing down momentarily as much as 10 per cent. For the present
limited transmitter power and receiver sensitivity, at altitudes above
2500 feet, these momentary signal reduction effects become progres-
sively more serious when flying over irregular surfaces so that for a
substantial part of the total time the echo signal may be below the
minimum required for correct meter reading. This is indicated by a
reading fluctuating between 3000 and 5000 feet when flying at 5000
feet over a surface dotted by buildings, timber, etc. The meter swings
up to the correct reading every time the airplane passes over a smooth
field or body of water of any size. Up to 2500 feet the echo signal has
proved to be sufficient for steady operation over all kinds of terrain.

Tests have been made over New York, Raritan, Newark and San
Francisco Bays, Great Salt Lake, Lakes Erie and Michigan, the tim-
bered mountains of Washington and Oregon, the deserts and mountains
of the southwest and the cultivated areas of the midwest during the
period of the recent demonstration flights made with the equipment
installed in the United Air Lines Flight Research Airplane.

An indication of the character of the surface over which the air-
plane is flying is given by the variations in the meter reading. A
city usually causes rapid fluctuations of the order of fifty feet, depend-
ing, of course, upon the height and the spacing of the buildings.
Cultivated farmland causes fluctuations of lower frequency and
amplitude. An isolated high object such as a skyscraper or a chimney
is indicated only by a slight meter kick as the airplane passes over it,
which may not be noticed by the observer. If the airplane passes
over only a few feet above the object and the top is large enough to
contribute momentarily most of the echo signal received by the air-
plane, the indication is unmistakable and the correct distance to the
object is indicated by the meter. For instance, the gas storage tank

234 BELL SYSTEM TECHNICAL JOURNAL

near the Chicago airport is an excellent object upon which to demon-
strate the altimeter performance. The instrument is useful as a
position indicator when approaching an airport on a course which
crosses an obstruction of appreciable height and size since the mo-
ment of passage over the obstruction is clearly indicated. In fact,
use as a position indicator may be one of the altimeter's most valuable
applications.

A study of the circumstances in connection with a number of
crashes in the west during recent years has revealed that in most of the
cases the airplanes crashed after having been within a few feet of the
ground without the pilot knowing it for several minutes before they
struck. In such a situation the terrain clearance indicator should be
capable of warning the pilot in ample time to avert a crash.

The writers wish to express their appreciation of the contributions
of a number of other members of the technical staff of the Bell Tele-
phone Laboratories to the success of this project.

References

1. H. Loewy, U. S. Patent 1,492,300.
H. Loewy, U. S. Patent 1,585,591.

C. F. Jenkins, U. S. Patent 1,756,462.

E. F. W. Alexanderson, U. S. Patent 1,969,537.

F. H. Drake, U. S. Patent 1,987,587.

2. U. S. Patent 2,011,392 issued August, 1935 to J. O. Bentley.

3. Page 29 of "Solving the Problem of Fog Flying," a publication of the Daniel

Guggenheim Fund for the Promotion of Aeronautics, 1929.

4. "Altitude Measurements by Reflected Electro-Magnetic Waves" by Murray

Hively and R. C. Newhouse, Ohio State University Library, 1929.

5. "An Electro-Magnetic Altimeter" by R. C. Newhouse and J. D. Corley, Ohio

State University Library, 1930.

6. U. S. Patent 1,517,549 issued December, 1924 to Lloyd Espenschied.

7. U. S. Patents 2,045,071 and 2,045,072 issued June, 1936 to Lloyd Espenschied.

8. "A Negative Grid Triode Oscillator and Amplifier for Ultra-High Frequencies,"

A. L. Samuel, Proceedings of Institute of Radio Engineers, 25, Oct. 1937 (1243).

9. "A Research of Direct Reading Altimeter for Aeronautical Use by Radio Re-

flection Method," Sadahiro Matsuo, Journal I. E. E. Japan, No. 571, Febru-
ary, 1936.

10. "A Direct-Reading Radio-Wave-Reflection Type Absolute Altimeter for Aero-

nautics," Sadahiro Matsuo, Proceedings of Institute of Radio Engineers, Vol. 26,
1938 (848).

11. Trans. A. I. E. E. 49, 1930 (1331).
Proc. I. R. E. 19, 1931 (659).

Review of Scientific Instruments 6, 2, January, 1935.
Journal of Scientific Instruments 14, 1937 (136).

Transcontinental Telephone Lines *

By J. J. PILLIOD

Late in 1937 a large construction project was completed which
added 16 telephone circuits to the transcontinental layout, and
the work was so planned that 48 additional circuits can be obtained
by the addition of equipment but without stringing additional wire.
A brief description of some features of this project and the general
development of the transcontinental telephone routes since the
first one was opened for service in 1915 is given in this article.
Although most of the discussion relates to transcontinental lines,
the methods described are generally applicable to other similar
situations.

T ESS than twenty-five years ago, it was impossible to talk by tele-
-■— ' phone from coast to coast across the United States. Further-
more, it was impossible to talk between points separated by any such
distance anywhere in the world. By 1915, technological advancement
had reached a point such that telephone service could be established
across the country, and three telephone circuits had been built which
connected San Francisco and the Pacific Coast with points in the East.
Four telegraph circuits were also provided by the new wires. An
improved loading system and especially the successful development of
the vacuum-tube telephone repeater were outstanding factors which
made telephone connections of such length possible for the first time in
history.

Open-wire lines played the major role in the early transcontinental
telephone circuits. The transmission losses caused by cable were so
great that it was avoided whereever possible. The steady improve-
ment of telephone repeaters, types of loading for use on cable circuits,
and carrier telephone systems for use on open-wire lines made it
possible to provide rapidly and economically more telephone circuits
across the continent as use of the service grew. In the cross section

* This paper has been prepared from an address given before the Communications
Group of the A. I. E. E., New York Section, March 22, 1938, and published in Elec-
trical Engineering for October, 1938. Since the paper was written, three type J
12-channel carrier systems have been placed in service on the new line. Two of
these systems operate between Oklahoma City and Whitewater, 1200 miles, and
the third between Oklahoma City and Albuquerque, N. M. Twelve additional
intermediate repeater stations have been constructed. Three of these are located
at such remote distances from primary power that experiments are being made in
generating by means of wind-mill power plants part of the power required. One
such station is shown in Fig. 8. Editor.

235

236 BELL SYSTEM TECHNICAL JOURNAL

just west of Denver there are today one hundred and forty through
telephone circuits and about the same number of telegraph circuits
carried by four open-wire routes, the last of which was completed
during 1937. While open wire was used almost exclusively as a matter
of necessity in the first transcontinental telephone lines, cable is now
used for about half of the circuit mileage. This is a striking illustra-
tion of the large-scale changes which have taken place in the interest
of more reliable toll telephone service.

Continued Importance of Open-Wire Lines

The open-wire line seems destined to continue to play an important
part in long-distance telephone communication, particularly where
distances are great and circuit requirements on any one route are
relatively small. Improvements in the usage to which the wires may
be put have made this increasingly so. The three circuits on the
first transcontinental line were operated at voice frequencies and were
obtained from two pairs of line conductors, the third circuit being
derived by means of phantom circuit arrangement of these two pairs.
The development of carrier telephone systems made it possible to ob-
obtain three additional circuits on some pairs of wires, using frequencies
above those required for existing voice-frequency circuits. Carrier
telephone systems were first installed on a transcontinental route in
1926 and were quickly followed by others, so that today ninety-six of
the one hundred and forty circuits mentioned earlier are obtained by
means of these three-channel carrier telephone systems. Develop-
ment work, however, has been continued, and it is now expected that
it will be possible, by means of carrier telephone systems using still
higher frequencies, to obtain as many as twelve more telephone circuits
on some pairs of wires. It has been with a view toward using such
systems and obtaining a total of sixteen telephone circuits on a pair of
wires that the latest of the four transcontinental routes has been
designed.

Construction of New Transcontinental Line

Early in 1937, it became clear from a study of loads carried on
existing transcontinental routes that additional circuits would be
required in the near future. Circuits in cable were available as far
west as Omaha, Kansas City, Oklahoma City, and Dallas. After
consideration of all the factors, it was decided to construct the new
facilities west from Oklahoma City to Los Angeles on the route shown
in Fig. 1. It was also decided to carry out the work in such a way
that the route could be utilized for the future addition of a relatively

TRANSCONTINENTAL TELEPHONE LINES

237

Z^'J -In

tczz I t-

UJ O O t "- '''

o o o o o z

238

BELL SYSTEM TECHNICAL JOURNAL

S S S S I I 5 S 5

lJ

.-. = n

6 5 0 0

V v y_

_S_S OS I I S 5

_S i_l

I J

Fig. 2 — Cross-arm arrangements. Left — 50-wire phantomed line, capacity 77
telephone circuits. Right — 32-wire non-phantomed line, capacity 256 telephone
circuits.

TRANSCONTINENTAL TELEPHONE LINES 239

large number of circuits through the application of the twelve-channel
carrier-current telephone system then under development. Among the
conditions favoring this particular route is freedom from winter storm
hazards throughout most of the distance, which, looking ahead, is
particularly important to the future application of twelve-channel
carrier telephone systems. The work done in 1937 consisted of build-
ing a length of nearly three hundred miles of new pole line and stringing
four pairs of wires throughout most of the section from Oklahoma
City to Whitewater, California, a distance of 1,200 miles. Initially
the voice channel and three-channel carrier telephone systems have
been developed on these four pairs, providing a total of sixteen tele-
phone circuits.

Wire Spacing and Transpositions

Open-wire telephone lines designed to carry frequencies up to 140
kilocycles per second, as used in the operation of the twelve-channel
carrier telephone systems, have structural requirements substantially
more stringent than those designed to carry only three-channel sys-
tems, which use frequencies up to 28 kilocycles. The usual type
of open-wire toll telephone line has ten wires on each crossarm,
spaced at about one-foot intervals, five on each side of the pole
and with the crossarm spaced twenty-four inches apart. In the case
of the line designed to conduct high carrier telephone frequencies, this
configuration has been changed and is illustrated by Fig. 2. Eight
wires are strung on each arm, grouped as four pairs, two on each side of
the pole. The wires of the pair are spaced eight inches apart, and
the nearest wires of the two pairs on each side of the pole are spaced
twenty-six inches, while the spacing at the pole is thirty inches. Cross-
arms are spaced thirty-six inches apart.

These new wire spacings reduce the coupling between pairs on the
same line or between pairs on this line and pairs on other lines which
may parallel it. New transposition systems are used further to reduce
this coupling. Transpositions are closer together and a transposition
bracket of the type shown in Fig. 3 is used to turn the wires completely
over at as nearly a given point as possible. Transpositions in one or
more pairs are installed on every pole with an occasional exception,
and certain pairs are transposed at every other pole. The wires of a
pair must be adjusted to the same sag within close limits. These sag
variations are held to a fraction of an inch, and a check of the completed
work indicated that fifty per cent of the spans had been adjusted to
within one-quarter inch. Telescopes are used to help obtain these
close sag adjustments, and a final check is made by oscillating the
wires in a span and observing the periods at which they oscillate.

Fig. 3 — Transposition bracket shown as installed. Tie wires are not used with this

type bracket.

Fig. 4 — Flat tie wire shown as installed.

1.4

" 1.2

0.4

_^

Z'

X

y

ICE 5^"dIAM.
ON WIRES y

/

/

y\

/^

/

/

y

^x

WET
WEATHER

.

- —

•.

=^^

DRY
WEATHER

1

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140

FREQUENCY IN KILOCYCLES PER SECOND

Fig. 5 — Attenuation of open-wire pairs, 165-miI copper, 8-inch spacing, CS insulators.

z 12

^

^

7

^

/

1

0.19 DECIBELS
PER MILE

^

/^

/^

X

y

/

y

/

/

f

20

40 50 60 70 80 90 100 110
FREQUENCY IN KILOCYCLES PER SECOND

120 130 140 150

Fig. 6 — Attenuation of 165-mil copper, 8-inch spaced pair of wires measured on a
105-mJle section of the Amarillo-Albuquerque line in clear weather.

242

BELL SYSTEM TECHNICAL JOURNAL

Pole Spacing and Insulators

Poles must be spaced uniformly in order that the transpositions may
be most effective, and an occasional deviation of only thirty-five feet
is the maximum permitted. Where it is impossible to locate poles
within this limit, such as is the case at long-span crossings, special
fixtures are suspended from steel cables at the proper points to permit
making the transpositions.

New types of insulators on steel pins, each pair of which is elec-
trically bonded, are used to improve the stability of the transmission
characteristics.

40 50 60 70 80 90 100 110
FREQUENCY IN KILOCYCLES PER SECOND

120 130 140 150

Fig. 7 — Far-end crosstalk between wires 7-8 and 9-10 of Amarillo-Albuquerque line,
measured from pole 1 to pole 4236, a distance of 105 miles.

40 50 60 70 80 90 100 110
FREQUENCY IN KILOCYCLES PER SECOND

120 130 140 150

Fig. 8 — Impedance of 165-niil copper, 8-inch spaced, CS insulated pair of wires on
Amarillo-Albuquerque line, measured from pole 1 to pole 4236.

TRANSCONTINENTAL TELEPHONE LINES

243

6 rt

X3 <S
."3 ui

•SH

^ ex

■(->

244

BELL SYSTEM TECHNICAL JOURNAL

y^

bo ■
s -o
•n o
u o
O q=

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= H

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^ in

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TRANSCONTINENTAL TELEPHONE LINES 245

Wire 165 mils in diameter was used on this construction west of
Oklahoma City because of its strength and resultant relative freedom
from interruptions. Transmission losses were also a factor in this
case. Rolled sleeve joints were used in splicing the wire because of
their strength and good electrical characteristics. Flat tie wires,
shown in Fig. 4, were used to reduce chafing of the line wire when
the wires vibrate. Tie wires are not used at transposition points, as
may be seen in Fig. 3.

Repeater Stations

The computed losses on open-wire pairs of this type at high-carrier
frequencies and under different weather conditions are shown by Fig. 5.
Field tests confirm these data. To off"set the line losses it will be
necessary to locate repeater stations at intervals of from fifty to one
hundred miles, depending upon the weather conditions which may
be expected. Between Oklahoma City and Whitewater, California,
in order to operate the twelve-channel carrier telephone systems, it will
be necessary to equip sixteen intermediate repeater stations. Most of
these will be unattended and maintained from other offices.

It is not practicable, of course, to bring the open-wire pairs directly
into all repeater stations and in some cases entrance cables several
miles long must be used. Although ordinary non-loaded cable pairs
may be used for this purpose, their usage involves transmission diffi-
culties, and except where other factors dictate the use of this type of
facility, it is planned to use low-loss cable conductors of a new design.
These cable pairs have more favorable impedance characteristics as
well as lower losses.

With the building and the further equipping of this latest open-wire
line across the western states, open-wire facilities have played one
more important part in the development of long-distance telephony.
Although cable is being found more and more useful, there still remain
many important links in the nation-wide telephone communication
network where, for the present at least, the open-wire line can serve
best and the development of it toward maximum usefulness is still being
carried on.

Abstracts of Technical Articles from Bell System Sources

Paper as a Medium for Analytical Reactions} B. L. Clarke and
H. W. Hermance. Absorbent paper has long been used in chemical
laboratories for filtering suspensions. Paper has also found a special
use as a container or holder for certain testing reagents; litmus paper
is a common example. In this article and a preceding one {Indus. &
Engg. Chem., Anal. Ed., June 15, 1937), are reported exploratory
investigations on the extension of the use of absorbent papers in
chemical analysis.

Rapid identification "spot tests" have been described by Feigl in
which, by successively placing drops of unknown and reagent solutions
on filter paper, characteristic color changes are produced. Methods
and apparatus are described in the present articles whereby some of
the variables in such tests are controlled. Chief among these innova-
tions is the use of semi-soluble instead of soluble reagents, and the
precipitation of these compounds directly on the paper fibres to form
a more or less permanent test paper. By these changes in technique
the sensitivity — the smallest amount of a given metal detectable —
is decreased from ten to one-hundredfold. For example, 0.002
microgram of copper can be detected by the new method, as compared
with 0.2 by the old.

In another application a very dilute solution of some metal ion is
slowly siphoned through a small circular piece of reagent paper
suitably mounted. The metal is entrapped on the paper in an in-
soluble form strongly adsorbed by the paper. Theoretical analysis
indicates that copper, for example, may be removed from a solution
in this way so completely that only 8 X 10~^^ microgram will be left
in a liter.

Neutral Particles in Physics.^ Karl K. Darrow. During the
early days of science, the elementary particles which scientists and
philosophers alike saw fit to postulate were always imagined as
chargeless. With the remarkable growth of the understanding of
electricity during the nineteenth century, and with the invention of
instruments for detecting small charged particles during the twentieth,
it became the custom to suppose that the fundamental particles of

1 Indus. & Engg. Chem., Anal. Ed., October 15, 1938.
^Amer. Phil. Soc. Proc, September 30, 1938.

246

ABSTRACTS OF TECHNICAL ARTICLES 247

matter all bear charges and that the forces exhibited in Nature are
all electrical (exception being made for gravitation). A noted and
serious objection to this view was temporarily met by the adoption
of quantum mechanics. Since 1930 a reversal of trend has set in,
heralded by the discovery of the neutron as a subatomic chargeless
particle capable of independent existence; and at present there is a
strong tendency to develop the view that neutral as well as charged
particles of subatomic size, and non-electrical as well as electrical
forces, exist together in Nature.

Electrical Networks for Sound Recording.^ F. L. Hopper. Electrical
networks are employed in sound recording for modifying and limiting
the frequency-response characteristic. The necessity for their use,
application, and design is described. Particular emphasis is placed
upon the constant-resistance type of structure.

Sound Pictures in Auditory Perspective.^ Franklin L. Hunt.
Soon after sound reproduction in auditory perspective was demon-
strated over telephone circuits between Philadelphia and Washington
in 1933, experimental sound pictures in auditory perspective were
made at. the Bell Telephone Laboratories' sound picture laboratory.
Listening tests showed that they distinctly enhanced the illusion
that the sound originated at its apparent source on the screen and they
strikingly improved the feeling of spaciousness and reality. The
auditory perspective effect is not primarily dependent upon perfect
synchronism of the two sound-tracks required, nor on frequencies
above the present commercial range. Existing equipment can be
converted to project sound pictures in auditory perspective without
great difficulty.

Composition and Colloidal Properties of Balata Latex} A. R. Kemp.
This paper reports the composition and colloidal properties of two types
of balata latex from Dutch Guiana. The white variety is shown to be
superior to the red, owing to its higher content of hydrocarbon.

It is shown that balata latex is very stable owing to the presence
of a highly protective water-soluble substance in its serum. It cannot
be coagulated by acids or salts, but is readily coagulated by alcohol
or acetone.

The balata latex particles are spherical and vary in diameter from
about 0.1 to 2.5 microns with an average diameter of about 0.5 micron.

The balata latex particles are shown to enclose the resins, which

» Jour. S. M. P. E., November 1938.

« Jour. S. M. P. E., October 1938.

^ India Rubber World, December 1, 1938.

248 BELL SYSTEM TECHNICAL JOURNAL

appear to be present in a dispersed state in the hydrocarbon. The
particles are shown to contain about 18% of water, determined as
water of retention in pressed coagulum.

The "resins" have been separated from both types of balata latex
as water-white viscous liquids which deposit crystals of j3-amyrin
acetate on standing. The red balata latex resin is shown to be more
viscous than the white and to differ from it as regards its iodine value,
refractive index, and solubility in cold 95% ethyl alcohol.

The serum constituents have been separated into four main frac-
tions: protein, carbohydrate, gummy substance, and ash. Minor
constituents such as tannin and amino-acid have also been noted.

A complete analysis of balata ash has been made and compared
with the analysis of ash from Hevea latex by Bruce. Balata ash was
found to contain higher contents of CaO, Na20, and MgO and lower
contents of K2O and P2O5 than Hevea latex ash.

New data are presented on the density, refractive index, dielectric
constant, and heat of combustion of balata hydrocarbon which are
believed to be more reliable than similar data previously available in
the literature. Data on the effect of temperature on the refractive
index of balata and gutta percha hydrocarbon are presented, showing
the crystallization of the gutta hydrocarbon on cooling, which starts
at about 37° C. resulting in an abrupt increase in refractive index
occurring between 37° and 35° C.

A Short-Wave Single- Sideband Radio Telephone System.^ A. A.
Oswald. There is described briefly a short-wave single-sideband
system which has been developed for transoceanic radio telephone
service. The system involves the transmission of a reduced carrier or
pilot frequency and is designed to include the testing of twin-channel
operation wherein a second channel is obtained by utilizing the other
sideband.

The paper indicates the reasons which led to the selection of this
particular system and discusses at some length those matters which
require agreement between the transmitting and receiving stations
when single-sideband transmission is employed.

The Oxide-coated Filament. The Relation between Thermionic Emis-
sion and the Content of Free Alkaline- earth Metal.'' C. H. Prescott,
Jr. and James Morrison. The oxide-coated filament had its begin-
ning in the sealing-wax era of vacuum technique. The obscure acci-
dent of its origin is not recorded, but all of our older physicists knew

6 Proc. I. R. E., December 1938.

' Jour. Amer. Chem. Soc, December 1938.

ABSTRACTS OF TECHNICAL ARTICLES 249

that an enhanced emission of electrons could be obtained by smearing
sealing-wax on a platinum ribbon and burning it off in air. The first
authentic study is recorded by Wehnelt, who investigated the voltage-
drop in a gas discharge tube with cathodes coated with various metallic
oxides. Its further evolution and development to the status of a
cathode in Western Electric vacuum tubes has been described by H. D.
Arnold. A comprehensive treatment of its history, the various
modifications in current use, and divergent theories of its preparation
and behavior has been given by Saul Dushman in a treatise on "Ther-
mionic Emission." A later review is given by J. H. deBoer.

The present work is devoted to a quantitative determination of the
relation between thermionic emission and the content of free alkaline
earth metal. To this end we have employed a filament which is a
platinum rhodium core coated with barium, strontium, and nickel
carbonates. On heating in a reducing atmosphere this coating becomes
a grossly homogeneous colloidal mixture of barium oxide, strontium
oxide, and free nickel. After a thorough preliminary clean-up of the
experimental tube, the requisite amounts of free alkaline-earth metal
are generated by reaction with methane. The electrical measure-
ments are summarized by the use of the Richardson equation for
thermionic emission. Free alkaline earth metal has been determined
by oxidation with carbon dioxide and analysis of the gaseous reaction
products.

Using a filament coated with a colloidal mixture of barium oxide,
strontium oxide, finely divided nickel, and free alkaline earth metal,
we have investigated the quantitative relation between thermionic
emission and the content of active metal. A high level of activity
was found from 15 ;ug./sq.cm. to 60 /xg./sq.cm. of equivalent Ba, with
a slight apparent maximum at 30 /ig./sq.cm. where the thermionic
current at 1050° K. is 600 m. a./sq.cm. The electron work function
is 1.37 V.

The radiant emissive power at 0.66 m is approximately 64%, in-
dependent of the content of active metal.

The free alkaline earth metal was determined by oxidation with
carbon dioxide and analysis of the gaseous reaction products.

A Single- Sideband Receiver for Short-Wave Telephone Serviced
A. A. RoETKEN. A new radio telephone receiver has been developed
for the reception of reduced-carrier single-sideband signals in the
frequency range from 4 to 22 megacycles. This receiver employs
triple detection in which the first beating oscillator is continuously

^Proc. I. R. E., December 1938.

250 BELL SYSTEM TECHNICAL JOURNAL

variable and the second is fixed in frequency. The first oscillator is a
very stable tuned-circuit type, the proper adjustment of which is
maintained through the use of an improved type of synchronizing
automatic-tuning-control system. The second oscillator is crystal
controlled. Separation of the carrier and sideband is accomplished in
the receiver by means of band-pass crystal filters which provide
extremely high selectivity. Unusually high stability and selectivity
characterize the performance of the receiver.

Dielectric Constant and Dielectric Loss of Plastics as Related to their
Composition.^ W. A. Yager. Data are presented for the frequency
variation of the dielectric constant and dielectric loss factor of various
plastics over a broad frequency band extending from 1 kc. to 35 mc.
The extremely low loss of polystyrene compared to that of polar plastics
confirms the theory that a hydrocarbon is inherently more satisfactory
from a dielectric point of view. Of the several possible mechanisms of
dielectric loss which might account for the high-frequency dielectric
absorption observed in polar plastics, the rotation of polar units in
the chain and of polar side groups appears most probable. The fact
that the loss factor maxima of phenol fibers, phenol fabrics, and phenol
or urea formaldehyde molding compounds containing cellulosic fillers
occur at essentially the same frequency is viewed as evidence that this
dielectric absorption is an intrinsic property of cellulose. Substitution
of mineral fillers for cellulose reduces the high-frequency loss to that
residing in the polar resin binder. Furthermore, the dielectric loss of
mineral-filled molding compounds is less moisture-sensitive. The
large increase in dielectric loss at low frequency always found in ma-
terials of relatively high free-ion conductivity manifests itself in
Duprene, and the humidified phenolic plastics containing cellulose
fillers or laminations.

^Electrochemical Society Preprint No. 74-24, October 12-15, 1938.

Contributors to this Issue

H. A. Affel, S.B. in Electrical Engineering, Massachusetts Institute
of Technology, 1914; Research Assistant in Electrical Engineering,
1914-16. American Telephone and Telegraph Company, Engineering
Department and the Department of Development and Research,
1916-34; Bell Telephone Laboratories, 1934-. As Assistant Director
of Transmission Development, Mr. AfTel is concerned with toll trans-
mission problems, including the development of carrier telephone
systems.

J. W. Beyer, B.S., State College of Washington, 1915; Westing-
house Electric and Manufacturing Company, 1915-16. Instructor in
Electrical Engineering, State College of Washington, 1916-19,
Western Electric Company, Engineering Department, 1919-24. Bell
Telephone Laboratories, 1924-. Mr. Beyer is concerned with the
development of carrier telephone terminals and pilot channels for
open-wire circuits.

E. C. Blessing, B.S. in Electrical Engineering, Purdue University,
1922, Western Electric Company, Engineering Department, 1922-25 ;
Bell Telephone Laboratories, 1925-, Mr. Blessing has been engaged
in the development of carrier systems.

S, I. Cory, B.E.E., Ohio State University, 1916. American Tele-
phone and Telegraph Company, Engineering Department and Depart-
ment of Development and Research, 1916-1934; Bell Telephone
Laboratories, 1934-. During this entire time Mr. Cory has been
engaged in transmission development work, chiefly on telegraph
systems and transmission-measuring methods.

Frank A. Cowan, B.S. in Electrical Engineering, Georgia School of
Technology, 1919. American Telephone and Telegraph Company at
Atlanta, Ga., 1920; Long Lines Engineering Department, Special
Service Group, New York, 1922; appointed Division Transmission
Engineer, Division No. 1, New York, 1926; appointed to present
position. Engineer of Transmission, Long Lines Department, 1928.

Karl K. Darrow, B.S., University of Chicago, 1911; University of
Paris, 1911-12; University of Berlin, 1912; Ph.D., University of

251

252 BELL SYSTEM TECHNICAL JOURNAL

Chicago, 1917. Western Electric Company, 1917-25; Bell Telephone
Laboratories, 1925-. Dr. Darrow has been engaged largely in writing
on various fields of physics and the allied sciences.

Lloyd Espenschied, Pratt Institute, 1909, has taken an important
part in much of the Bell System's invention and development in the
field of radio and carrier currents; also in technical contacts and inter-
national conferences abroad. Previously, in the Department of
Development and Research of the American Telephone and Telegraph
Company; now, as Research Consultant of the Bell Telephone
Laboratories, participates in a broad front of electric-communications
development.

Frank Gray, B.S., Purdue, 1911; Ph.D., University of Wisconsin,
1916. Western Electric Company, Engineering Department, 1919-25.
Bell Telephone Laboratories, 1925-. Dr. Gray has been engaged in
work on electro-optical systems.

William H. Harrison, Vice President and Chief Engineer, American
Telephone and Telegraph Company. Pratt Institute, graduate in
Industrial Electrical Engineering, 1915. New York Telephone Com-
pany, repairman, apparatus inspector, 1909-14. Western Electric
Company, engineer, 1914-18. American Telephone and Telegraph
Company, 1918-33, Department of Operation and Engineering,
engineer; Equipment and Building Engineer; Plant Engineer. Bell
Telephone Company of Pennsylvania, Diamond State Telephone
Company, Vice President in charge of Operations, 1933-37. Amer-
ican Telephone and Telegraph Company, Department of Operation
and Engineering, Assistant Vice President, 1937-38; Vice President
and Chief Engineer, 1938-.

L. W. HussEY, A.B., Dartmouth, 1923; M.A., Harvard, 1924; B.S.
in E.E., Union College, 1930; Mathematics Department, Union
College, 192^29. Bell Telephone Laboratories, 1930-. Mr. Hussey
has been engaged principally in work on the stability of regenerative
systems and on modulation in non-linear resistances.

B. W. Kendall, S.B., Massachusetts Institute of Technology, 1906;
Instructor in Physics at Massachusetts Institute of Technology,
Barnard College, and Columbia University, 1906-13. Engineering
Department of the Western Electric Company, 1913; Bell Telephone
Laboratories, 1925-. As Toll Development Director Mr. Kendall has
charge of the development of carrier, voice frequency, and telegraph

CONTRIBUTORS TO THIS ISSUE 253

circuits. His early work was on repeaters in connection with the
transcontinental line; he has also been connected with carrier-current
development since its inception.

R. C. Newhouse, B.E.E., Ohio State University, 1929; Guggenheim
Fellow, Ohio State University, 1929-30; M.Sc, Ohio State University,
1930. Bell Telephone Laboratories, 1930-. During most of this
period Mr. Newhouse has been engaged in the design and development
of aircraft radio transmitters. In recent months his efforts have been
confined to the development of the terrain clearance indicator, for
which he has been given the 1938 Lawrence Sperry Award by the
Institute of the Aeronautical Sciences.

J. T. O'Leary, B.S. in Electrical Engineering, Villanova College,
1918. American Telephone and Telegraph Company, Department of
Development and Research, 1919-34. Bell Telephone Laboratories,
1934-. Mr. O'Leary has been concerned with the transmission aspects
of carrier systems.

E. Peterson, Cornell University, 1911-14; Brooklyn Polytechnic,
E.E. 1917; Columbia University, A.M. 1923; Ph.D. 1926. Electrical
Testing Laboratories, 1915-17; Signal Corps, U. S. Army, 1917-19.
Western Electric Company, Engineering Department, 1919-25; Bell
Telephone Laboratories, 1925-. Lecturer in Electrical Engineering,
Columbia, 1934-. As circuit research engineer. Dr. Peterson's work
has been largely in theoretical studies of non-linear circuits and circuit
elements.

J. J. PiLLiOD, E.E., Ohio Northern University, 1908. American
Telephone and Telegraph Company, Long Lines Department, 1908-
11; General Engineering Department, 1912-13; Long Lines De-
partment, Division Plant Engineer, 1914-17; Engineer of Trans-
mission, 1918-19; Engineer, 1920-. Mr. Pilliod is the head of the
Long Lines Engineering Department.

J. N. Reynolds, B.S. in Electrical Engineering, Purdue University,
1904; E.E. 1907. Western Electric Company, Engineering Depart-
ment, 1904-25. Bell Telephone Laboratories, 1925-. Mr. Reynolds
has been continuously associated with the development of machine
switching apparatus. As Special Studies Engineer, he is now engaged
in the development of improved forms of crossbar switch and allied
apparatus.

254 BELL SYSTEM TECHNICAL JOURNAL

Frederick J. Scudder, New York Telephone Company, 1905-10;
Western Electric Company, Engineering Department, 1910-25; Bell
Telephone Laboratories, 1925-. Mr. Scudder has been engaged in
the development of machine switching systems since 1910, and in his
present capacity as Systems Development Engineer is in charge of
fundamental studies and circuit development of panel and crossbar
systems.

R. B. Shanck, B.E.E., Ohio State University, 1915. Railroad
telegraph service, 1909-10. American Telephone and Telegraph Com-
pany, Plant Department, 1910-11 and summers 1912-14; Engineering
Department and Department of Development and Research, 1919-34;
Bell Telephone Laboratories, 1934r-. As Telegraph Transmission
Engineer, Mr. Shanck is engaged in development work on the trans-
mission features of telegraph systems and the measurement of telegraph
transmission.

VOLUME XVra APRIL, 1939 NUMBER 2

THE BELL SYSTEM

TECHMC AL JOURNAL

DEVOTED TO THE SCIENTinC AND ENGINEERING ASPECTS
OF ELECTRICAL COMMUNICATION

Some Ceramic Manufacturing Developments of the Western
Electric Company — A. G. Johnson and L, I, Shaw . . . 255

The Production of Ultra-High-Frequency Oscillations by
Means of Diodes — F. B, Llewellyn and A. E. Bowen . . 280

A Representation of the Sunspot Cycle — C. N, Anderson . . 292

The Number of Impedances of an n Terminal Network

— John Riordan 300

Copper Oxide Modulators in Carrier Telephone Systems

—R. S. Caruthers 315

Some Applications of the Type "J" Carrier System

— L. C. Starbird and J. D. Mathis 338

Line Problems in the Development of the Twelve-Channel
Open-Wire Carrier System

— L. Af. Ilgenfritz, R, N, Hunter and A, L. Whitman 363

Abstracts of Technical Papers 388

Contributors to this Issue . 391

AMERICAN TELEPHONE AND TELEGRAPH COMPANY

NEW YORK

50c per Copy $1.50 per Year

THE BELL SYSTEM TECHNICAL JOURNAL

Published quarterly by the

American Telephone and Telegraph Company

195 Broadway, New York, N. Y.

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A. F. Dixon
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EDITORIAL BOARD

H. P. Charlesworth

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American Telephone and Telegraph Company

PRINTED IN U. S. A.

The Bell System Technical Journal

Vol XVIII April, 1939 No. 2

Some Ceramic Manufacturing Developments
of the Western Electric Company

By A. G. JOHNSON and L, I. SHAW

A general picture is given of the development work involved in
the introduction of manufacturing processes for vitreous enameled
resistances, vitreous enameled iron and copper base number plates,
pressed glass lenses, extruded and pressed porcelain parts, and
close tolerance ceramic insulators for use in telephone apparatus.
The reasons for undertaking the manufacture of these products,
some of the major problems encountered in developing suitable
processes, and the work done in overcoming these difhculties includ-
ing several major contributions to commercial methods of manu-
facturing similar parts are described.

ORIGINALLY, the ceramic parts used in the telephone and
associated equipment were not manufactured by the Western
Electric Company because the technical requirements and volume of
consumption of such parts did not warrant the development or estab-
lishment of processes or the facilities for manufacture. The later
development of such manufacturing processes for some of the ceramic
parts has been necessitated largely by inability to secure an adequate
supply of parts meeting the close limits required for satisfactory
functioning of the apparatus, although there have usually been other
influencing factors. Such developments have, in most instances,
been advantageous from an economic standpoint. The experimental
work has been confined to that required for the above ends and
only a very limited amount of research work has been done. Some
of the major projects for which it was necessary to develop new methods
of processing to obtain the desired quality at a satisfactory cost are
outlined.

Switchboard Lamp Cap Lenses
The first major project undertaken was the development for manu-
facture of switchboard lamp cap lenses of the types shown in Fig. L
One factor necessitating this undertaking was the difficulty experienced

255

256 BELL SYSTEM TECHNICAL JOURNAL

m m ^ ^ 9

3 ^ ^

9

^ ® ^ ®

2D _ 01

3 «• ^

(3 « ® »

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a

J -

a

SOME CERAMIC MANUFACTURING DEVELOPMENTS 257

in obtaining a suitable supply since manufacture of parts of this general
class was largely a side line incident to the production of artificial
gems. Development of a technique for molding these lenses was
therefore undertaken. The method adopted consists of forming the
lenses from glass rod softened by heating in gas flames. The forming
is performed by using steel dies in a small punch press on the front of
which are mounted the gas fixtures.

Since the colored glass rod used in lens manufacture was obtainable
at that time only from European sources, with the advent of the World
War it was decided to undertake manufacture of the rod. This
development required a careful consideration of the characteristics
desired in lenses for use in switchboard lamp caps. These lenses
must have sufficient light dispersion characteristics to make the lens
visible at any angle from which it may be viewed in service. The
degree of opacity must also be such as to make either weak light
signals visible or to prevent glare with strong light signals. In view
of the cost relation between lamp cap lenses and switchboard lamps,
variations in the light diffusion and light transmission of lenses must
be kept at a minimum since the degree of such variations frequently
determines the useful life of the lamps. In addition the lenses must
be able to withstand repeated impact shocks from plug tips and the
relatively rapid heating in the operation of forming the lenses by
punching.

In view of the characteristics desired, glasses having approximately
twenty to thirty per cent lead oxide were investigated. Small gas-
fired crucible furnaces were used in the preliminary work for batch
melting and an impact machine was devised to simulate blows received
in service in order that theoretical life tests could be made on the glasses
developed. Comparative tests were also made on the light trans-
mission qualities of the various glasses developed.

Originally, light dispersion in lamp cap lenses was obtained with
sandblasted lenses of clear glasses. The first work therefore consisted
of the development of suitable clear glasses of the desired colors.
Silica, sodium oxide, and lead oxide combinations were investigated
and approximate limits for these constituents were established to
cover glasses of suitable viscosity, durability, and clarity. Final
compositions were then evolved by progressive small changes in the
amounts of the various constituents used. Since the color and working
characteristics of the glasses were influenced by the rates and amounts
of heating, the furnace conditions, and other variations encountered
in melting and working the glasses, these progressive changes involved
considerable time to evaluate properly the results of'any composition

258 BELL SYSTEM TECHNICAL JOURNAL

change. The resultant compositions are illustrated by the following

batch which was developed and used for clear amber glass; and the

functions of the various raw materials in this composition are given

below :

Glass Sand 45

Red Lead 30

Sodium Nitrate 10

Sodium Carbonate 10

Manganese Dioxide 3

Ferric Oxide 2

100
Scrap Glass — 50 parts approximately.

As is common practice, glass sand was used as the most economical
means of obtaining the desired silica content. The sodium content was
introduced by the use of sodium nitrate and sodium carbonate. The
oxidizing action of the nitrate and manganese dioxide assisted in (1)
the prevention of lead reduction; (2) the oxidation of any organic
materials present; and (3) the maintenance of the iron in ferric form.
The liberation of gas during the decomposition of the sodium nitrate
and carbonate tended to stir the glass during melting and in addition
the escape of large gas bubbles during this decomposition assisted in
the removal of small bubbles of occluded gas. Some of the sodium
was introduced as sodium carbonate because it was cheaper than the
nitrate. Red lead was used as an economical means of obtaining
the desired lead oxide content and to lessen the possibility of any
difficulties from unoxidized lead particles. A percentage of glass
scrap from the punching and drawing operations was used in each
batch as a means of reclaiming the scrap, facilitating melting and
improving the working characteristics of the glass when drawn into
rods. The amber color obtained in this glass was of course dependent
on the predominance of the brown color of ferric iron. If sufficiently
oxidizing conditions were not maintained during melting and working,
the iron would be reduced to the ferrous state resulting in a greenish
color. The color intensity obtained was very sensitive to changes in
the amount of heating and to atmospheric conditions in the furnace.
This complicated the problem of maintaining the glass within close
limits for color and translucency.

After satisfactory glasses with twice the impact strength of the
previously imported glasses were developed, open pot manufacture
of clear glasses was started on a limited basis.^ It was then found
desirable in order to obtain better signaling characteristics to obtain

i-H. T. Bellamy Patent 1,271,652, "Method of Making Colored Glass," July 9,
1918. •

SOME CERAMIC MANUFACTURING DEVELOPMENTS 259

the required light dispersion in certain colors of lenses without the
use of sandblasted surfaces. Several methods of dispersing the light
were tried including the application of a translucent layer of glass
on the back of a clear lens, but as it was difficult to control economically
the amount of light dispersion by these methods, it was decided to
use opalescent glasses. Calcium phosphate and cryolite were found
suitable as opacifiers and satisfactory compositions were developed by
means of further progressive changes to suit the particular working
conditions in the shop.

Several serious objections were found to the open pot method of
manufacture, the most important of which were the long heating
period required for new pots and their relatively short life. The
manufacture of opalescent glasses increased these difficulties because
of the more corrosive nature of these glasses as a result of which the
maximum life of the pots was approximately twelve days. In view
of this, a small 500-pound capacity gas fired melting furnace known
as a day tank was designed and constructed. This tank consisted of
a rectangular box shaped furnace lined with refractory blocks about
twelve inches thick. With this equipment, a complete batch was
melted each night and the resultant glass formed into rods during the
next day. Under continuous operation, furnace life of about three
months was obtained which was considered very satisfactory in view
of the corrosive nature of these glasses.

Satisfactory compositions and methods of manufacture were finally
developed for the production of glasses in the required colors. This
development resulted in the elimination of an unsatisfactory supply
situation, reduced the cost of lenses appreciably, and greatly improved
the quality of lenses.

Spirally Grooved Resistance Cores

At the same time that development work on glasses was being
carried on, a preliminary survey was made of the advantages of manu-
facturing instead of purchasing the ceramic cores used in filament
resistances. As the preliminary survey indicated that definite ad-
vantage would be realized, development for manufacture was under-
taken. The part, shown in Fig. 2, consists of a thick-walled tube with
a spiral groove on the outer surface in which a resistance filament is
placed. Tests first were made on pressing blanks from sodium silicate
and powdered slate mixtures. These parts adhered to the die, were
difficult to dry, and were very weak in the fired state. Further work
was done with talc and sodium silicate mixtures which were stronger
but still had the objectionable feature of adhering to the dies. Addi-

260 BELL SYSTEM TECHNICAL JOURNAL

tional compositions were then made of talc and clay with and without
sodium silicate and feldspar. It was found that most satisfactory
results were obtained with a ball clay, kaolin, and talc body in the
proportions of forty per cent, ten per cent and fifty per cent, and this
body was therefore adopted.

Originally, attempts were made to cut the groove in the fired core
with a diamond tool but this resulted in excessive chipping of the

^f»i^t*f^0*Hiii'^^H^^'^

iHJjnsj'mmjMMiif;

^9HH@^

Fig. 2 — Ceramic core and completed filament resistance.

groove. A chaser with alternate teeth was then tried out, with the
thought that the gradual cutting action would prevent chipping.
This also proved unsuccessful. The use of a circular saw, emery
wheel, and a phosphor bronze disc charged with diamond dust were
also considered. These methods were not completely satisfactory
although better results were obtained. Rolling the thread in the core
while in the leather hard state after extrusion was then tried with
good results and a suitable machine was developed for performing
this operation. -

With this machine, an extruded blank of slightly oversize diameter
was placed on a revolving mandrel. An arm was provided to hold a
shaving tool ahead of a disc which formed the thread. This arm was
attached to a segment of a nut and the movement of the arm when
the nut segment was engaged with a thread integral with the mandrel,
shaved the core to exact diameter and carried the disc longitudinally
across the core forming the spiral groove. An auxiliary arm carrying
two knives was then engaged which cut the core to exact length and

2 H. T. Bellamy Patent 1,384,587, "Manufacture of Composition Cores," July 12,
1921.

SOME CERAMIC MANUFACTURING DEVELOPMENTS 261

chamfered the ends. The finished core was then removed from the
mandrel, dried and fired. This method of manufacture produced
cores of superior quaHty at a greatly reduced cost.

Porcelain Protector Blocks

The next major development was that of the manufacture of pro-
tector blocks. These small porcelain blocks, used in open space cut
outs and shown in Fig. 3, are illustrative of parts where it was necessary

Fig. 3 — Porcelain protector blocks.

to undertake manufacture for quality considerations and where such
manufacture resulted in cost reduction. They were originally pur-
chased from domestic sources which were unable to meet consistently,
required limits as close as +. 020-inch and —.015-inch on a .390-inch
dimension. The dimensional deviations encountered necessitated
sorting to insure proper functioning in the field, and it was necessary
to scrap a large percentage of the purchased parts. Difficulties were
also experienced in the assembly of the blocks because of manufacturing
defects such as small fins and low strength.

Common commercial practice on most porcelain parts of this
type at that time was to form the parts on a hand screw press, re-
move fins by hand, and fire the blocks in refractory containers in
intermittent furnaces. The amount of hand labor involved was
large and early studies of the economics of manufacture showed
it would be necessary to develop new methods of manufacture before

262 BELL SYSTEM TECHNICAL JOURNAL

the development and plant expenditures associated with the installa-
tion of manufacturing facilities would be warranted. A survey of
commercial practices indicated that mechanization of the forming
operation and simplification of the finning, firing, and material prepara-
tion procedures were possible.

The two general methods of processing first considered were: (1)
extrusion of a plastic column having the end cross section of the block,
cutting this column to block lengths and forming complete in the
plastic state; and (2) automatic pressing of damp granules. The first
method offered some advantages in forming because of the thin walls
of the protector blocks, but the greater shrinkage from raw to fired
states which would result from the use of plastic material would
involve greater dimensional variations. Because of this factor it was
decided to confine the development effort to a study of the possibilities
of automatic pressing of damp granules.

The uses of the porcelain protector blocks required a body as highly
vitrified as was consistent with dimensional requirements, to minimize
moisture absorption in service and to prevent the adherence of car-
borundum particles during lapping operations in assembly. High
vitrification was also required to insure sufficient mechanical strength
to withstand handling during assembly and service. Accurate dimen-
sions were essential for satisfactory functioning in service.

Two general types of bodies were considered, talc-clay combinations
and feldspar-clay-silica combinations. An investigation of talc-clay
mixtures indicated that the eutectic proportion of the two minerals
was approximately sixty-five per cent talc and thirty-five per cent
clay with small variations dependent upon various clay compositions.
The fusion temperature of this eutectic was approximately cone 12 or
2390° F. This combination, however, was not satisfactory since it
softened over an extremely small temperature range and formed a
very fluid glass in the melted state. A longer temperature range for
softening and greater melted viscosity was obtained by the addition
of feldspar. A eutectic composition of twelve and one-half per cent
talc and eighty-seven and one-half per cent spar was found which
fused at cone 6 or 2174° F. Using ten per cent to twenty per cent of
this flux, a well vitrified body was obtained at cone 8 or 2237° F
The firing range of this body was still much narrower than desired
and any excess firing resulted in blistering. Although it was evident
that commercial use of this body would require extremely close regu-
lation of temperature, it was decided to investigate its pressing char-
acteristics in view of the small amount of abrasive material it contained
and the importance of abrasion on dies and equipment with automatic
molding.

SOME CERAMIC MANUFACTURING DEVELOPMENTS 263

A study of the pressing behavior of the body under automatic
molding speeds and conditions indicated that development work would
be necessary to prevent the molded parts adhering to die surfaces.
An investigation of this factor indicated that the sticking to dies was
caused primarily not by adhesion between the metal and the molded
clay surface but rather by the vacuum effect of a dense air-tight layer
of material against the metal. This was shown by the facts that the
tendency for sticking decreased with (1) a decrease in the plastic
content of the body or a decrease in moisture content; (2) a decrease
in the viscosity of the die lubricant which thereby tended to clog the
pores of the molded surface to a less extent; and (3) an increase in the
volatility of the die lubricant. Two methods of overcoming the
sticking difficulties with molding compositions were therefore sug-
gested: (1) opening up the structure of the molded part by the use of
coarser material to provide capillaries for the escape of entrapped
air, and (2) the use of an improved lubricating compound. Since
it was not feasible to improve the lubricant sufficiently, an attempt
was made to obtain much coarser talc. The talc normally avail-
able at that time was such that on sieve tests approximately five
per cent to ten per cent remained on the 300-mesh screen. The
availability of coarser talc was investigated and it was found that
material coarser than eighteen per cent on 300-mesh was not available
at an economical price. In view of the fact that the talc was very fine
grained and non-plastic, it gave a very dense molded structure without
contributing materially to the strength required to hold the molded
part together. It therefore seemed advisable to use a clay, feldspar,
and silica body and to minimize abrasion by the selection of suitable
tool steels and the proper design of equipment.

In arriving at a suitable body composition of the feldspar type it
was decided to use a composition which would mature at about cone
12 or 2390° F. Sufficient feldspar was used to obtain a low porosity
when fired over a reasonably wide temperature range. The amount
of clay used was governed by the raw strength required. Enough
silica was used to obtain sharp definite outlines and to avoid warpage.
The following composition was arrived at:

Flint 22.5

Feldspar 37.5

Ball Clay 20.0

Kaolin 15.0

China Clay 5.0

100.0

264 BELL SYSTEM TECHNICAL JOURNAL

Further development work was then confined to methods of process-
ing this body to obtain satisfactory results on an automatic machine.
A survey of available commercial pressing equipment indicated that
machines of the type used in the manufacture of various pharma-
ceutical tablets or pellets offered the most promise for adaptation to
molding protector blocks. The development of suitable equipment
was complicated by the extremely thin walls of the parts and the
necessity for rapidity of operation. In the hand molding method
commonly used in the industry, a slow application of the molding
force was possible at the end of the stroke and likewise a gradual
withdrawal of the top die was possible after completion of the forming
operation.

After some preliminary work with various types of tableting ma-
chines, we concentrated our efforts on single-plunger-type machines
with double dies. One of the major problems was a satisfactory
method of die lubrication since with the machine operating at twenty-
eight strokes a minute, the die surfaces were exposed for oiling only
an instant during each cycle. The use of an atomizer-type device with
a mixture of lard oil and kerosene was finally adopted with the amount
of lubricant closely controlled by oil sight cups. Exact timing of the
application of the spray to dies was obtained by automatically operat-
ing air check valves. This method proved more satisfactory than
wiping with saturated felt or incorporating a lubricant in the body
particles before molding.

The various stages of the molding cycle are shown in Fig. 4. The
cycle of operation at twenty-eight strokes per minute was as follows:
as the bottom die reached the lowest position, a feed hopper was
vibrated over the cavity. The withdrawal of this hopper removed
excess material, after which the top punch descended forming the
part. The bottom and top punches then moved upward until the
bottom of the part was flush with the top of the die. A projection
on the hopper then pushed the part free. Before the hopper reached
a position over the cavity, any particles of clay adhering to the dies
were blown off and the lubricant was sprayed over each die. The
lower and upper dies were then returned to the original positions.

A large amount of work was also necessary to adjust the size and
moisture characteristics of the pressing material not only to secure
well formed parts and prevent sticking but also to secure fired parts
meeting the desired requirements. A mixture of colored and un-
colored particles was used in the study of these characteristics in
order that the flow movements in the die during compression could
be studied. As a result of this work, it was found that most satis-

SOME CERAMIC MANUFACTURING DEVELOPMENTS 265

Fig. 4 — Block forming press.

266 BELL SYSTEM TECHNICAL JOURNAL

factory results could be obtained with 10-24-mesh material and a
12.75 per cent ± .75 per cent moisture content. This moisture content
was sufficient to give a compact part and body mix still could be fed
satisfactorily to the dies. Methods ofjprocessing the body mix were
then worked out to hold it within these limits.

The use of material within these close size limitations involved
considerable effort to establish economical methods of production.
Common practice consisted of slaking the clay in water, adding the
other body ingredients, mixing thoroughly with water, filter pressing,
complete drying, addition of water to obtain the desired moisture
content, aging and screening. The effect of aging was investigated
and found negligible with the moisture content to be used and it was
therefore decided to dry the material after filter pressing to the
required approximate twelve per cent moisture content before the
disintegrating and sizing operations. Methods of handling were
evolved to obtain a maximum percentage of material between 10 and
24-mesh and to regranulate the fines without again mixing them with
excess water.

Various methods of economically removing fins after forming were
investigated and initially the fired parts were tumbled with small
porcelain balls. This method removed fins and produced smooth
surfaces. Another advantage of the method was the automatic
elimination of any weak or flawed parts by breakage during the
tumbling. Later, further developments in methods of firing described
hereafter made it more economical to remove the fins in the raw state
by vacuum brushing the parts in multiple after they were arranged on
trays at the pressing machines.

Initially the parts were fired using the practice then commonly
followed in the industry. With this method, the parts were placed
in saggers and fired in an intermittent kiln. This method involved
costly handling, heat losses due to heating and cooling the furnace at
each firing, and considerable expense from sagger replacements. A
small continuous kiln was therefore installed in which the parts were
carried in layers on top of cars through successive preheating, firing,
and cooling zones which were continuously maintained at definite
temperatures, the heat from the cooling fired ware being used to heat
the incoming ware.

Summarizing, the method of manufacture finally developed for
porcelain blocks consisted in mixing feldspar, clay and flint with water
to get an intimate mixture, filter pressing, drying to proper moisture
content, sizing, automatically molding the parts, removing fins in
multiple, and firing in a continuous kiln. This method resulted in a

SOME CERAMIC MANUFACTURING DEVELOPMENTS 267

marked improvement in quality and reduced the cost of parts. The
method of automatic pressing developed constituted a major con-
tribution to existing commercial methods of manufacturing small
porcelain parts.

Vitreous Enameled Copper Base Number Plates

Manufacture of parts similar to the vitreous enameled number
plates used on calling dials and shown in Fig. 5 was limited to producers

DEF

GHI ^
4

ABC
2

1

JKL
5

MNO
6

PRS

(

3PERA1

^ TUV
8

WXY
9

0

Fig. 5 — Copper base number plate.

of enameled parts of the watch dial type. Because of our unusual
requirements for dimensions and character location together with the
need for a collar and locating pins, only one source of supply could be
developed. With rapidly increasing schedules for calling dials and
because of the possibility of conditions deyond the control of the
supplier interfering with the continuity of supply, this situation was
unsatisfactory and made it advisable to undertake manufacture to
remove possibilities of any embarrassment from a supply standpoint.
As sources of supply for copper enamels were also limited, various
enamel compositions were investigated. It was found that the fol-
lowing composition would give an enamel satisfactory for color,
texture, gloss, fusibility, and durability when fired on copper blanks:

268 BELL SYSTEM TECHNICAL JOURNAL

Red Lead 40

Pearl Ash 6

Sodium Nitrate 9

White Arsenic Oxide 6

Flint 31

Borax 8

100

In practice constituents of this enamel were first thoroughly melted
to a homogeneous glass, giving on cooling a glass magma having high
opalescence. The dead white opacity of this enamel could only be
developed by slow cooling through the range necessary to precipitate
the arsenic compounds. Manufacturing considerations, such as the
necessity of an enclosed room for commercial smelting to avoid con-
tamination as well as to avoid the possible health hazards involved in
the smelting of arsenic-lead combinations, led us to purchase the
required enamel. The fact that a suitable composition had been
developed and was available for manufacture if necessary was an
advantage from a supply standpoint.

Various enameling procedures were considered. In order to cover
the vertical surface of the collar satisfactorily, it was essential that
this surface be coated either by dipping or by spraying. It was equally
important to apply the enamel coating to the flat surface of the plate
by dusting on a thick coat of dry powdered enamel. This dust coat
was necessary because of the thickness of enamel required on the flat
portion to strengthen the number plate and also to obtain the desired
quality of finish on the surface bearing the numerals and characters.
From an economic standpoint, it was also imperative that only one
enamel fire be used. Initially, efforts were made to dust enamel on a
blank already completely coated with a thin coat of enamel slip con-
sisting of finely divided enamel frit suspended in water by means of
clay or bentonite. It was found on firing that the added refractoriness
of the enamel slip containing the clay or bentonite resulted in a
roughened fired surface over the dusted area. This was caused by the
formation of gases in the decomposition of the clay or bentonite while
the enamel was in a viscous state. It was therefore necessary to
protect the flat portion of the plates by templates during spraying.
As this was costly, a study was made of other means of floating the
enamel frit for collar application.

In order to overcome these process difficulties, it was desirable to
find a material which would (1) satisfactorily hold the heavy lead
enamel particles in suspension and prevent packing, (2) not attack the
enamel or impair its durability, (3) decompose before the enamel
started to fuse, and (4) be inexpensive. Soluble alginates appeared to

SOME CERAMIC MANUFACTURING DEVELOPMENTS 269

possess these properties and excellent results were obtained from their
use.^ These substances were made from kelp. Their most interesting
property as a suspending medium was the ability of the alginates when
added to water even in small percentages to make solutions of high
viscosity. For example, water solutions of ten per cent ammonium
alginate would stand stiff. Some of the advantages in our use of
alginates for suspending number plate enamel were: (1) uniformity of
composition resulting from the alginates being a manufactured product
rather than a natural mineral ; (2) the fact that dried sprayed coats of
alginate suspended enamel were less subject to damage from handling;
(3) a low decomposition temperature which resulted in the material
being driven off before fusion of enamel, thus avoiding bubbles in the
enamel ; and (4) increased resistance of the finished enamel surfaces to
chemical attack and their ability to withstand greater mechanical shock
and distortion without damage, since any refractory materials present
when the enamel was fired would not be completely fused or incor-
porated into the glass, leaving points more readily attacked chemically
as well as lines of mechanical weakness.

Using alginate suspended enamels, suitable manufacturing processes
were developed for the application and firing of enamel and the appli-
cation of characters to the fired plates. A machine was devised for
the application of the sifted coating, and rotary continuous furnaces
were installed for the firing operations.

Originally the decalcomania method was used for character applica-
tion. In this process, the enameled parts were first coated with a thin
coat of sizing and, after partial drying, they were placed in a locating
fixture mounted on a small arbor press and pressure was applied to a
properly located transfer by means of a soft rubber pad. The paper
backing of the transfer was then removed by soaking in water and, to
insure contact, the characters were repressed with a silk covered pad.
The sizing was then baked off before firing to remove organic materials
and eliminate shadows around the characters. This method was
costly and even well trained, careful operators did not produce satis-
factory plates.

To eliminate these defects, an offset printing and dusting method
was developed in which an electrotype printing plate was covered with
printer's ink and an impression was transferred to the number plate
by means of a rubber transfer pad. Powdered vitrifiable colors were
then dusted over the entire surface of the plate and the unprinted
areas of the part brushed clean with a camel's hair brush. In printing
two color plates, the black letters were printed and dusted first, after

3L. I. Shaw Patent 1,806,183, "Suspension," May 19, 1931.

270 BELL SYSTEM TECHNICAL JOURNAL

which the red numerals were printed and dusted. By using a special
black powder which would give an intense black in combination with
a thin film of red powder, one firing for both colors was possible. This
method required close control of temperature and humidity of the air
in the room which was therefore air conditioned.

Even under good conditions considerable difficulty was experienced
at times with the adherence of the powder to unprinted areas. In
addition, the application of the powder and the brushing operation
required the installation of a special well exhausted unit and involved
some problems in the recovery of the ceramic dust which were quite
expensive. Efforts were therefore made to incorporate the glass
powder directly in the printing vehicle. The development of a

pj

^

jklT

5 /

1

MNo\
^6li

1

▼prs\

\7^

K-Ti

r^-i

^Ptjaro/?

\xk

nTxrJ

^^

Fig. 6 — Iron base number plate.

ceramic printing ink covered tests on various printing vehicles to deter-
mine what vehicle or mixture of vehicles would be most suitable.
Difficulty was encountered in incorporating a sufficient amount of
inert, finely pulverized, intensely colored glasses into a vehicle and
still retaining the properties essential for offset printing by transferring
an impression from an electrotype plate to a vitreous enamel. This
problem was finally solved by the use of a relatively large percentage
of uncalcined ceramic material in combination with light and heavy

SOME CERAMIC MANUFACTURING DEVELOPMENTS 271

ink varnishes.* Motor driven presses using this ink were also devel-
oped to faciHtate the printing operations.^

The manufacture of these parts was undertaken primarily to
ehminate an undesirable supply situation but Western Electric manu-
facture resulted in improvements in quality of enameling, quality of
printing, and in mechanical strength. This latter characteristic was
important since it reduced assembly losses from cracked plates.

While vitreous enameled copper base number plates have been
replaced by other types, the developments outlined were the basis of
subsequent enameling developments.

Vitreous Enameled Iron Base Number Plates
The low level of illumination at some pay stations led to the design
by the Bell Telephone Laboratories of a large iron base number plate,
shown in Fig. 6, to be mounted flush with the finger wheel of the dial.
Since the demand for these plates was relatively small, they were
originally made by the usual process followed in the industry in enamel-
ing similar articles. This process consisted of applying and firing one
ground coat for adherence and then applying and firing two sprayed
cover coats to obtain the whiteness and opacity desired; all being
felspar enamels. The whiteness was not as good as that obtained on
the copper base plates with lead enamels and in addition considerable
difficulty was experienced in the field due to the fading of the characters
as a result of chemical action on plates exposed to corrosive gases such
as sulphurous fumes in certain locations. The process was also costly.
Since maximum whiteness and opacity was obtainable in the lead-
arsenic type of enamels previously described when applied by dusting
on dry, it was desirable that the coating be applied in this manner.
In order to avoid several enamel applications and firings, it was also
desirable that other portions of the plate be protected by some corrosion
resistant coating other than vitreous enamel which would necessarily
have to retain such corrosion resisting properties after exposure to a
temperature of 1500° F. for six minutes and also be capable of being
enameled with satisfactory results. Numerous coatings were tried and
it was found that a Western Electric black oxide finish on iron would
satisfactorily meet all requirements.^ Using this finish, it was possible
to fuse the enamel directly on the upper surface of plates, to retain
corrosion resistant qualities on all other exposed surfaces, and to reduce
the number of process operations. A number plate of greatly improved
appearance and durability also resulted. In addition, the curved

^L. McLaughlin Patent 2,030,999, "Ink," February 18, 1936.

5 L. McLaughlin Patent 1,951,430, "Printing Apparatus," March 20, 1934.

« W. J. Scott Patent 1,962,751, "Ceramic Coated Articles," June 12, 1934.

272 BELL SYSTEM TECHNICAL JOURNAL

surface obtained in dusting a base plate having a groove around the
edge prevented the entrapment of air between the plate and the
printing pad during the printing operation, thereby resulting in a
simplification of that processJ

As a result of our development of enameling over the black oxide
finish it would have been possible to replace the previously described
copper-base number plate by one employing a sifted coat of enamel
over such finish on a steel blank. However, the application of the
black oxide finish on enameling iron was so costly that manufacture of
number plates by this process was not competitive. We therefore
continued our developments and found that it was possible to enamel
directly over an electroplated copper-nickel finish consisting of a
minimum of 25 m.s.i. each of copper and nickel on a mild steel blank
and get a smooth enamel coat having very good adherence.^ As this
finish had the necessary rust resistance and the blank was relatively
flat, the enamel could be applied in a single sifted coat on the face only
to produce a satisfactory number plate. Also with the steel base it
was not necessary to have a thick coating of enamel for strength as was
the case with the copper base number plate. In fact, due to the good
adherence of the enamel coat, if the thickness of enamel after firing
was less than 0.010 inch the plate could be flexed considerably without
chipping the finish. On the other hand, it was necessary to have a
minimum of 0.007 inch of enamel to hide sufficiently the gray color of
the nickel surface. Additional refinements of the enameling process
were eff^ected by improvements in the uniformity of enamel distribution
and in the printing of characters; and the process was generally autom-
atized. These developments produced a number plate of superior
quality and appearance at a reduced cost. As all final details for
commercial manufacture have not been completed further details of
this process will not be given here.

Vitreous Enameled Resistances
With the increased use of panel-type machine switching, the de-
mand for vitreous enameled resistances for controlling the current for
operating relays and switches increased materially and manufacture
of these parts was undertaken. These resistances were required to
dissipate a considerable amount of heat in service and to reach a high
operating temperature without being damaged. The units therefore
consisted of a suitable resistance wire wound on a ceramic core and
covered with a vitreous enamel. Some of the types now being manu-
factured at Hawthorne are shown in Fig. 7.

^ W. J. Scott Patent 2,020,476, "Ceramic Articles," November 12, 1935.
«S. R. Mason and W. J. Scott Patent 2,020,477, "Ceramic Article," November
12, 1935.

SOAIE CERAMIC MANUFACTURING DEVELOPMENTS 273

♦■"Hfcn * c^

ir

€¥

m

Fig. 7 — Ceramic cores and vitreous enameled resistances.

274 BELL SYSTEM TECHNICAL JOURNAL

Since the application of vitreous enamel to the resistances involved
plunging the porcelain cores into a hot furnace and their removal into
cold air without cracking, and since in use they were also subject to
considerable heat shock, it was necessary to develop a body with
thermal shock resistance characteristics that would still have the
necessary fired strength. It was also required that this body be
suitable for the extrusion of lound cores and for the molding of more
complicated shapes from a granular body. A somewhat porous fired
structure was also desirable to facilitate the application of the enamel.

These desired characteristics indicated that a clay-talc combination
would be suitable. Mixtures containing a greater percentage of clay
than the eutectic mixture of the two minerals were investigated to
avoid vitrified parts at the temperatures then used in the tunnel kiln
for other products. Tests were made of extrusion and molding proper-
ties, fired, breaking and impact strengths, and resistance to thermal
shocks. On the basis of these tests a talc-clay body composition was
selected. Dies were then constructed based on the fired shrinkage of
this body of about fifteen per cent in extruded and twelve per cent in
molded forms.

Using these cores, suitable sizes -of wire were selected considering
the dimensions of the core, the resistance value desired, heat to be dis-
sipated at certain wattages, and the maximum operating temperature
permissible, and satisfactory winding methods were established.
These methods were based on the use of motor driven machines in
which the wire was spaced on the revolving cores by the transverse
movement of a guide controlled by lead screws of various pitches. To
facilitate any necessary minor resistance adjustments, methods were
provided for checking the resistance of the units before connecting the
wire to the second terminal. Since the heating received by the wire
during the enamel firing increased its resistance value, tests were made
to establish resistance value factors for winding use.

Difficulty was experienced with the resistance becoming open in the
firing operation and it was shown that this condition was caused by
the formation of a film of glass between the resistance wire and the
terminal during the firing operation. Various methods of attaching
the resistance wire to terminals were tried and it was found that the
use of lead as solder would prevent the formation of a film of glass
between the wire and the terminal even though the fusion temperature
of the lead was considerably below the enameling temperature.
Ordinary soft solder could not be used due to the tin content embrit-
tling the standard copper lead wires during the enamel firing. While
silver solder could be used it was costly both for material and in
application.

SOME CERAMIC MANUFACTURING DEVELOPMENTS 275

In developing an enamel to be used for resistances, it was desirable
that the melting temperature be as low as possible consistent with good
durability in order to maintain at a minimum the thermal shocks re-
ceived by the porcelain cores and any changes in the resistance of the
wire during firing. A very high viscosity during fusion was also de-
sirable in order to avoid running of the enamel during firing, an unde-
sirable feature which would result in exposed wires and unsightly lumps
unless the enamel was applied in numerous thin coats. Conversely to
these requirements, it was necessary that the enamel coating be glassy
in appearance, smooth, free from blisters and pin holes, and capable of
being fired in a relatively short time.

These factors indicated the desirability of investigating lead-boron-
silica mixtures and the elimination of any raw clay or similar refractory
substance in the enamel slip. The enamel finally developed was as
follows:

Red Lead 48.0

Boric Acid 24.0

Flint 10.0

Soda Ash 3.7

Cryolite 6.0

Tin Oxide 1.6

Manganese Dioxide 0.5

Cobalt Oxide 0.6

Iron Oxide 4.0

Zinc Oxide 1.6

100.0

White Lead 10.0

Light Calcined Magnesia 1.3

All of the materials other than the white lead and light calcined
magnesia of the above composition were fritted or melted to a glass
and then quenched in water. The fritting of these materials was done
to insure complete formation of stable compounds and to permit more
rapid firing of the enamel coating on resistances to a smooth homo-
genous glass. The proportions of sodium, lead, boron and silica were
selected to obtain a stable coating with the desired viscosity character-
istics at as low temperature as possible. Sufficient opacity of the
coating was obtained through the use of cryolite and tin oxide. The
cryolite also functioned as a flux. A pleasing dark color was obtained
economically with the iron, cobalt and manganese contents. The zinc
oxide functioned as an additional flux and also aided considerably in
the formation of a smooth coating. Slight variations in the sodium
content of this enamel affected its viscosity markedly and also affected
its expansion characteristics.

276

BELL SYSTEM TECHNICAL JOURNAL

After fritting, the resultant glass was sized and suspended in a water
suspension of white lead and light calcined magnesia in a tank provided
with mechanical agitation. This method of suspension aided in in-
creasing the fired viscosity without the formation of blisters and pin
holes. Smooth glassy resistances were obtained with this enamel in a
ten minute firing at 1150° F. without appreciable bubbling or flowing
of the coating. This eliminated the necessity of three or four thin
fired coats and resultant greater variations in resistance values after
firing.

Close Tolerance Ceramic Barriers and Insulators

In the design of the handset type of telephone transmitter, it was
found desirable to use a thin washer type insulator, shown in the lower
portion of Fig. 8, as a barrier to control the path of the current between

/

Fig. 8 — Close tolerance insulators.

electrodes. This necessitated very close dimensional tolerances, un-
usual freedom from surface and edge defects, and reasonable strength
to withstand the clamping force used in assembly.

Various materials such as fiber, lava and metal coated with vitreous
enamel, were tried and lava gave the most promising results. In view
of the cost of lava parts, experiments were made using the usual process
of dry pressing a porcelain body in which the clay content furnished the
raw strength. The difficulties inherent with this process were the
fragility of the raw part and the variable dimensions resulting from
uneven drying and firing shrinkages. Because of the fragility of the
parts, it was necessary to mold them 0.050 inch thick and then lap the

SOME CERAMIC MANUFACTURING DEVELOPMENTS 277

fired parts to the desired thickness of 0.030 inch. This operation was
costly and losses from breakage were high. The narrow dimensional
limits of ±.002 inch on thickness were also hard to maintain because
of the difficulty of keeping the lapping surfaces parallel. In view of
this, it was decided to machine the parts from natural talc rod or lava.

The mineral talc or lava, being soft, was easy to machine and the
firing shrinkage was only one per cent as compared to about ten per
cent with dry pressed porcelain. While less difficulty with warpage
and dimensional variations was experienced, the machined surfaces,
while reasonably smooth and accurate, were not equal in quality to
surfaces obtainable with molded parts. The chief difficulty with the
process was in obtaining a satisfactory raw material free from flaws
and fissures. The first work was done with domestic lava which was
somewhat granular in structure but large rejections resulted from pitted
surfaces and chipped edges. A survey of domestic lavas showed that
only a small percentage was sufficiently dense. Chinese white lava
was found to be homogeneous and fine grained but of uneven shrinkage.
Best results were obtained with Italian green lava and this material
was used in commercial production. Due to breakage because of
fissures, the number of good insulators per foot of rod was very low and
the manufacturing cost was therefore excessive.

In view of this, various domestic manufacturers of glass, porcelain,
lava and other types of ceramic parts were canvassed but no source
of supply that could meet the required quality limits could be located.
It was therefore decided to make a thorough investigation of new
molding compositions for the job. As a first step in this study, it
was necessary to do away with drying shrinkage which required
a binder which would give sufficient strength in the raw state to
withstand the various finning and handling operations prior to firing.
It was also desirable that such a binder should not affect the fired
structure of the parts. "V^arious organic substances such as pitches,
phenolic resins, asphalts, paraffins, and waxes were tried in both
hot and cold molded bodies. It was found that a large percentage
of these binders could be incorporated into a body without defor-
mation during firing.^ As a mixture of paraffin and carnauba wax
was found satisfactory for cold molding and in addition possessed
sufficient hardness to furnish the necessary molded strength, this
combination of materials was chosen for the binder.^"

8 W. J. Scott Patent 1,847,102, "Ceramic Material," March 1, 1932. W. J. Scott
Patent 1,977,698, "Ceramic Material and Method of Making the Same," October 23,
1934.

1" L. I. Shaw and W. J. Scott Patent 1,847,197, "Ceramic Material and Method of
Making the Same," March 1, 1932.

278 BELL SYSTEM TECHNICAL JOURNAL

Another major factor in the development of a suitable molding
compound was the abrasive effect of the molding body on the die
parts. Because of the close tolerances required, this factor was
important in order to avoid excessive tool expense. Talc was therefore
chosen as the chief body constitutent to obtain a long die life. The
balance of the body was made up of twenty-five per cent clay which
gave the desired density in both molded and fired states. With the
talc-wax compound, a long die life was obtained even with the close
tolerances required. As a result of the use of a combination of waxes
as a binder this composition had a low uniform shrinkage of approxi-
mately four per cent as compared to about ten per cent with most
dry pressed porcelains. In addition, variable shrinkage and warpage
resulting from drying strains were eliminated.

In molding this body, the lubrication of die surfaces was found to
be critical because of the extreme thinness of the part. It was im-
practicable to apply a sufficiently exact amount of a liquid lubricant
to prevent the parts from either adhering to the dies or being weakened
from the absorption of the liquid. This problem was overcome by
tumbling the granulated molding material with a fraction of a per cent
of zinc stearate.^^ The stearate coated grains of material were then
molded without any additional die lubricant.

Using the above composition, the process developed was as follows:
The talc and clay were thoroughly milled in a carbon tetrachloride
solution of the waxes. After drying, this mixture was disintegrated
and sized, after which the particles of compound were coated with
zinc stearate. The parts were then molded four at a time in a com-
mercial self-contained hydraulic press within an accuracy of ± 3
per cent of the total thickness and ± 1 per cent of the inside diameter.
After molding, any fins were removed and the parts trimmed within
±1.5 per cent of the total thickness in a finning machine which was
an adaptation of a commercial automatic indexing head drill press.
In this machine, the parts were fed to a rotating end cutter by a
revolving indexing head and were held under this cutter by a vacuum
applied to the underside of the parts. Tungsten carbide cutters
were used to obtain long tool life. After finning, the parts were fired
in small trays in a continuous kiln. The parts were then individually
gauged for thickness, roundness and inside diameter and individually
inspected for cracks, flaws, and burrs. They were then examined
under a 10 to 1 glass for smoothness and regularity of inner edge
before being used in the assembly of the transmitter.

"JW. J. Scott Patent 1,847,196, "Ceramic Article and Method of Making the
Same," March 1, 1932.

SOME CERAMIC MANUFACTURING DEVELOPMENTS 279

This development permitted the manufacture of ceramic insulators
within limits not feasible with other methods of manufacture at that
time except by machining from mineral talc and to closer dimensional
tolerances than ever before attained in molded ceramic parts. The
cost of the parts was reduced to a fraction of that of machined parts
and their quality was greatly improved. Since that time the process
has been used in the manufacture of other close tolerance ceramic
parts for telephone use such as the insulator shown in the upper part
of Fig. 8.

Although the outline of miscellaneous manufacturing developments
given herein does not include all of the engineering development
effort on glass, porcelain and vitreous enamel problems it gives a
general picture of the type and scope of past engineering work in the
production of ceramic articles for telephone apparatus. The miscel-
laneous ceramic parts used in telephone apparatus were described in
an earlier publication.^^

12 A. G. Johnson and L. I. Shaw, "Ceramics in the Telephone," Industrial and
Engineering Chemistry, Vol. 27, pp. 1326-1332, November, 1935.

The Production of Ultra-High-Frequency Oscillations by

Means of Diodes

By F. B. LLEWELLYN and A. E. BOWEN

The general problem of obtaining oscillations by the use of
diodes with critical electron transit time is outlined. Some of the
properties of a 10 cm. oscillator tested experimentally are included.
Extraneous losses were reduced when the oscillator was enclosed
within a wave guide.

THE theory of the production of negative impedance by means of
an electron discharge between two parallel planes has been
known for some years. ^ The negative resistance appears whenever the
electron transit time is approximately 134. 23^^, 334, etc. cycles of a
given high-frequency current. Using this property, Miiller was able
to construct tubes giving 100 cm. oscillations.^ The operating
efficiencies were quite low, and in the frequency range covered by
these tubes it seems fairly conclusive that other methods of producing
oscillations are more effective than the critical transit time diode.
However, there is promise in the application of diode operation to
much higher frequencies than those of Miiller.

In a diode where the electron discharge occurs between two parallel
planes where one performs the function of electron emitting cathode
and the other constitutes an anode biased at a positive potential, the
effective impedance presented to an external source is inherently low
in magnitude. This is because of the capacitance between the two
planes which causes the decrease in impedance at high frequencies.
For the production of oscillations, the capacitance must be combined
with a resonant structure having the proper inductance to resonate at
the desired frequency and having a resistance which effectively is less
in magnitude than that of the electron stream. Because of the low
losses thus required of the coupling or tuning circuit the properties
of concentric lines and of tuned cavities offer a favorable method of
attack. These structures also have the property that the impedance
presented to the diode proper may be made low to match its capacitive
reactance at the high frequencies desired.

The two most important sources of circuit resistance are ordinary
ohmic loss modified in the usual way by skin effect in the conducting

^ For numbered references see end of paper.

280

ULTRA-HIGH-FREQUENCY OSCILLATIONS 281

material forming the resonant system and secondly the losses caused
by radiation of energy. These latter are extremely important where
the negative resistance is only a few ohms as in the present instance
and necessitate the use of nearly closed structures. This again directs
attention to the properties of cavities and concentric lines tuned by
internal capacitive resonance, the low capacitance being formed by
the electrodes between which the electron discharge flows. It was on
the basis of these principles that the actual diode models were con-
structed.

The general aspect of these tubes is shown in Fig. 1 which presents
a section through the axis of revolution. The cylinders of radii r\ and
^2 respectively constitute the outer and inner conductors of a con-
centric line. At one end of the inner conductor a flange partly closes
the system thus confining most of the energy within the cavity. At
the other end of the inner conductor the flat surface of the inner
conductor constitutes an emitting cathode while the opposing surface
of the outer conductor constitutes the positively biased anode which
also completely closes the end of the cylinder. The system is tuned
by the capacitance between cathode and anode and the effective
inductance of the coaxial line of length h. The emitter was coated in
the experiments with an oxide of the uncombined type and was heated
by a filament located within the inner cylinder. The spacers for
separating the inner cylinder from the main body of the outer con-
ductor were composed of fused quartz in order to obtain low losses and
good mechanical rigidity. A water jacket was supplied to assist in
cooling the anode.

In reference to Fig. 1, the tuning relation between the cathode-
anode capacitance and the inductance of the resonant circuit connected
to it requires the following relation to be satisfied,

1 2Trh X ...

7rr2^ lOge —

Here X stands for the free space wave-length. The other quantities
in the formula are illustrated in Fig. 1 and all dimensions are in cen-
timeters. The radii ri and r^ refer respectively to the inner surface
of the outer cylinder and the outer surface of the inner cylinder.
Improved formulas for the resonant frequencies of cavities of this type
have recently been published by Hansen.^

The formula (1) is based on the approximation that the presence of
electrons between cathode and anode does not affect the dielectric

282

BELL SYSTEM TECHNICAL JOURNAL

constant of the resulting capacitance. This approximation is a good
one when the electron transit time is greater than a cycle, as is the
case here.

The next design formula required is the resistance of the electron

(r^ ^r^

Fig. 1 — Ten-centimeter diode used in tests.

Diode

ri

ri X

h

No. 24

1.270

0.635 0.203

1.870

No. 37

1.220

0.635 0.105
Centimeters

1.870

ULTRA-HIGH-FREQUENCY OSCILLATIONS 283

stream. Reckoned per square centimeter of area this may be written,**

rp = • ^Q, ° [2(1 - cos d) - d sin 0] ohms for cm.^, (2)

where /o is the direct current density in amperes per square centimeter
flowing to the anode and 6 is the electron transit angle, given by

Ax
d= — p^ radians, (3)

xVFo

Here Vo is the constant potential difference in volts between the
cathode and anode and A is a numerical factor which depends upon
the amount of space charge within the electron discharge, being equal
to 6300 for negligible space charge and to 9500 for complete space
charge with intermediate values for intermediate space charge. As an
alternative the resistance (2) may be written

12 ro

rp = -

[2(1 - cos d) - d sin 0] ohms for cm.^, (4)

where ro is the low-frequency series resistance of the device. With
space charge, ro is the slope of the static characteristic derived from
Child's equation

, 2.33 Vo'" , 2 ,,.

""Toe" — 5— amperes/cm.'^. (5)

More generally ro is given by the expression

1 48 re*
To = -TTT^ /oyi^^ ohms for cm.^, (6)

where A is the same as was defined under (3).

Figure 2 shows a graph of the electron stream resistance as a function
of transit angle and is repeated from previous papers.^ However, it
may not have been emphasized in the literature that the graph as well
as equations (2) and (4) apply not only with complete space charge
but with intermediate values when interpreted correctly, namely in
terms of the d-c. current density /o rather than in terms of the applied
potentials.

TT

Whenever the transit angle is equal to 2Trn + - where w is 1, 2, 3,

* Equation 41 in this reference applies where the initial velocities are very small.
With complete space charge q = J and Oo = 0 whereas without space charge g = 0.
Either condition gives the same series resistance in terms of Iq.

284

BELL SYSTEM TECHNICAL JOURNAL

etc. then the electron stream exhibits a negative resistance. From
this it may be inferred that oscillations are possible not only for values
of n equal to unity but also for larger values, thus yielding the possi-
bility of higher order oscillations when the circuit coupled to the
electron stream is properly proportioned. If we start with a given
cathode temperature with space charge and attempt to obtain the
longer transit times by a decrease in applied potential, the smaller
currents obtained will decrease the negative resistance. Hence, with
space charge it is advisable to employ the smallest value of n possible
in actual circuit design.

For computation work the general formula (2) may be greatly
simplified because we need to know only the maximum values which

0.03
0.02
0.01

/

"N

/

^

-^

v.-

/

-0.03

0 2 4 6 6 10 12 14 16 18 20 22

e

Fig. 2 — Relation between transit angle d and diode resistance.

the negative resistance attains. These occur in the neighborhood of
transit angles given by

^ = 27rw+-, « = 1, 2, 3, ••.
and under these conditions the effective negative resistance is

Rn =

1.4X4/o/4w + 1

area 10^ irr-^

ohms.

(7)

(8)

The detailed steps in circuit design are these: First the allowable
value of current density /o must be determined. This depends upon
the ability of the cathode to emit electrons and as a practical limit
something in the neighborhood of 300 mils per square centimeter
cannot be exceeded. When this current has been decided upon then
the value x of the separation between cathode and anode may be
found from (3) and (7) with the lowest value of n which will give
practical figures. The space charge condition (4) also gives the lowest
allowable potential for which the required current can flow and hence

I

ULTRA-HIGH-FREQUENCY OSCILLATIONS 285

the best efficiency in the simple diode of Fig. 1. From these values
the negative resistance may be computed from (8).

As a next step the remainder of the circuit must be proportioned.
The tuning relation (1) yields the values of height h for a given diam-
eter. The next consideration is to insure that the sum of all positive
resistances is less than the negative resistance of the diode. For a
circuit with dimensions small compared with the wave-length, approxi-
mate formulas for the resistances associated with the losses in the
circuit conductors can be readily derived from classical circuit analysis.

A most important resistance, not so readily computed, is caused by
radiation of energy through the gap between the insulating flanges
which separate cathode and anode. In most uses of the device, this
radiated energy constitutes the useful load on the oscillator but care
must be taken that the load is not so heavy as to stop the oscillations
altogether. An important distinction must be made as to whether
the tube is to radiate into free space or into some enclosure such as a
hollow wave guide, for example. In the latter case the radiation may
be regulated to a large extent by the geometry of the enclosure. For
values of radiation resistance when energy is directed into free space
an article by S. A. Schelkunoff ^ may be referred to.

For oscillation, as pointed out, thesumof all these positive resistances
must be less than the negative resistance of the electron discharge and
for high efficiency the radiation resistance should be much greater than
the sum of all of the other positive resistances. This is usually found
to be the case, and in fact the radiation resistance is likely to be so
great as to stop oscillations unless the gap is made sufficiently small.

In designing a hollow wave guide mounting for diodes of the sort
pictured in Fig. 1 it was recognized that since the high-frequency wave
energy issues from the coaxial resonator as a wave guided along the
heater leads, the natural and probably most effective thing to do was
to dispose these leads so that the field associated with them would
conform as nearly as possible to one of the wave types which can be
supported in a hollow wave guide. Of these wave types, the so-called
/fi type® is readily generated by high-frequency current in a wire
extending across a diameter of the guide, and the wave guide mounting
shown in cross section on Fig. 3 is such as to give rise to this type of
wave. For mechanical reasons a brass pipe of circular cross sections
was chosen for the guide, and its diameter (3J^^ inches) was chosen
large enough so that it would freely transmit an IIi wave of the ex-
pected frequency. In the mounting, the high frequency circuit is
completed from the anode to the wall of the guide through a stopping
condenser.

286

BELL SYSTEM TECHNICAL JOURNAL

Preliminary experiments with diode no. 24 had shown that when
wave power issuing from the tube was allowed to radiate into free
space, a space current of 500 milliamperes with anode voltage of about
300 volts was required to maintain oscillations. An interesting and
instructive experiment is then to determine by how much this current

^^ZZ^^^^ZZZ

Fig. 3 — Hollow wave guide mounting for diodes.

is reduced when radiation is held to as low a value as possible. For
this purpose an assemblage as in Fig. 4 was used. Here a wave guide
mounting of form comparable to Fig. 3 is clamped into sections of wave
guide closed at the two ends by closely fitting but longitudinally ad-

UL TRA -HIGH-FREQ UENC Y OSCILLA TIONS

287

justable reflecting pistons. By thus completely enclosing the tube,
escape of energy into free space is avoided, and the losses external to the
tube are reduced to the ohmic losses (including dielectric losses) incident
to the existence of the wave within the guide. The presence of wave
power within the guide is indicated by a crystal detector-microammeter
combination connected to an antenna extending a short distance within
the guide, as shown in Fig. 4. Adjustment of the pistons closing the

EZZ

r/''/^////y>^/////.

^

1

!/'/'/>.

V////////^?^///^^^///J//,

lUL

ZZZZZZ2ZZZZZZZZZZ2

////////\

^\\\\\\i

Y/y/////////^////^^/^)'y//////x

Fig. 4 — Apparatus arrangement for "No Load" test of diode.

ends of the wave guide system allowed the attainment, for each value of
anode current and voltage, of the most favorable impedance conditions
for abstraction of energy from the diode.

The results of this experiment are shown on Fig. 5, which gives the
boundaries of the domain of oscillation of the two tubes whose dimen-
sions are given on Fig. 1. The large gain in extent of the oscillation
region of tube no. 24 is immediately apparent; the free space oscillation
limit of Ep = 300 volts, /p = 500 ma. has been lowered to £p = 210
volts, /p = 110 ma. For tube no. 37 oscillations occur at much lower
voltages, as is to be expected from the smaller anode-cathode distance,
and the minimum plate current required to maintain oscillations is
also somewhat smaller.

In the arrangement of Fig. 4 no useful power is extracted from the
diode. To examine the oscillation domain of the diodes when deliver-
ing useful power, the arrangement of Fig. 6 was used. Here in a
section of wave guide closed at both ends by tightly fitting but longi-
tudinally adjustable pistons there are placed the diode mounting shown
on Fig. 3 and a power absorbing and measuring element. The
assemblage constitutes in effect a wave guide transformer, for by

288

BELL SYSTEM TECHNICAL JOURNAL

suitably adjusting the positions of the pistons with respect to the
source and the power absorber, and by a proper choice of the distance
between the source and the power absorber, the impedance of the
latter can be matched to that of the source, so as to ensure the maximum
delivery of power.

500

2 300

£ 250

u

<■ 200

150

LIMIT OF AVAILABLE^aV
POWER SOURCE f;X

^

/■ ' ■ ' ■

\

/•■ •'■.'•

•N

/.' . .■ /

. -.x

r----"

/•

/•'••.•■

• /

MAXIMUM SAFE

'.••.

/■ '. •'•'.■

.' •'/

HEATER CURRENT — ~.^^.

/"• ■ • ■ • '

■•'/

/:

'••

/•.••■. •.-.

./

/••;•:

•;

/; .■ •.■ • •■ •

/

/■■'■:■

:■/

•• ■ •■■ ■/

/■;;•:•■•

.7

/•••.•.•:••

/

f ■:■:■. ■

/

#. '

• • ' '/

/••■•■••••.■••:

/:■.:'::■

/

■ '■■'■ ■'..'

/•

/•

.'•••: ••.''/

1 \

■ • ' ■•/

/•.;:

f

v^

f

// DK

3DE

fy NO. 24

DIODE

NO. 37

50

0 50 100 150 200 250 300 350 400 450

PLATE VOLTAGE

Fig. 5 — "No Load" oscillation domain of diodes no. 24 and no. 37.

The power absorbing and measuring element shown on Fig. 6 repre-
sents a new and useful way of measuring power at the very high fre-
quencies involved in this investigation. It makes use of the high
negative temperature coefificient of resistance of boron. In the middle

ULTRA-HIGH-FREQ UENC Y OSCILLA TIONS

289

of a wire extending across a diameter of the wave guide, parallel to the
Hnes of electric force in an Hi wave, there is placed a small crystal of
boron. Connection to the crystal is made by fine platinum wires,
melted into two small globules on opposite sides of the crystal.* By
virtue of its small size and the fine leads connected to it, small amounts
of power dissipated in the resistance of the crystal will raise its tem-
perature materially, with a consequent large change in its resistance.
With a stopping condenser, an ohmmeter connected as shown in Fig. 6
serves to indicate the resistance of the crystal when absorbing high-
frequency power, and calibration curves showing resistance as a func-
tion of power absorption can be obtained with direct current.

JUL

W?^^/^/////^^////^/////////2/j/^/^^^^j//////^^?^^j^r^,

^^//^JJ^^/JJ^^/^/77

&

^^^^

"^?////n

Fig. 6 — Apparatus arrangement for "Loaded" test of diode no. 24.

Power output and efficiency data obtained during these measure-
ments are shown on Fig. 7. Power outputs of a few tenths of a watt
at efficiencies ranging from one to two tenths of a per cent are
obtainable.

In consideration of the wave-length of the oscillations generated by
these two diodes, it will be recalled that they were designed nominally
for a wave-length of about 10 centimeters. For diode No. 24 the
wave-length was close to 10.6 cm. (2830 mc.) and for diode no. 37 it
was somewhat higher, about 11.55 cm. (2600 mc). This difference is
of the order to be expected from the difference in the dimensions of
the two tubes.

While the wave-length should be fixed largely by the dimensions of
the coaxial resonant circuit built into the diode, it is to be expected
that it will be affected to a small extent by the applied voltage and by

* These were developed by Mr. G. L. Pearson of the Bell Telephone Laboratories.

290

BELL SYSTEM TECHNICAL JOURNAL

the position of the piston closing one or both of the ends of the wave
guide. In the case of diode No. 37 the wave-length was found to vary
over a range between 11.50 and 11.65 cm. with plate voltage and over
a range between 11.52 and 11.56 cm. with piston position.

0.30
0.E8
0.26

0.24

If)

H 0.22

!5
5

2 0.20

3 0.18

(-

0 0.16
a:

UJ

1 0.14
Q.

0.12
0.10

HEATER CURRENT
IN AMPERES

•^

4.90

^''^^

y

y^

^

.^

/

-^

4.80

K

^

^

y

;/

/

'~~--

4.70

4.70

/

^

/

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PLATE VOLTAGE

Fig. 7 — Power output and plate efficiency for diode no. 24.

In conclusion, the writers wish to mention the work done by Mr.
C. A. Bieling of the Bell Telephone Laboratories in working out suitable
mechanical design features and in the actual assembly and processing
of tubes which were built and tested.

ULTRA-HIGH-FREQUENCY OSCILLATIONS 291

References

1. W. E. Benhani, "Theory of the Internal Action of Thermionic Systems at Moder-

ately High Frequencies," Phil. Mag., March 1928 and Phil. Mag. Supplement,
Vol. 11, February 1931.

2. Miiller, "Experimentelle Untersuchungen uber Elektronen-Schwingungen," Iloch.

u. Elek., Vol. 43, No. 6, June 1934.

3. W. W. Hansen, "On the Resonant Frequency of Closed Concentric Lines," Jour.

App. Phys., Vol. 10, No. 1, January 1939.

4. F. B. Llewellyn, "Operation of Ultra-High-Frequency Vacuum Tubes," Bell

System Technical Journal, Vol. 14, No. 4, October 1935.

5. S. A. Schelkunoff, "Some Equivalence Theorems of Electromagnetics and Their

Application to Radiation Problems," Bell System Technical Journal, Vol. 15,
No. 1, January 1936.

6. G. C. Southworth, "Hyper-Frequency Wave Guides — General Considerations and

Experimental Results," Bell System Technical Journal, Vol. 15, No. 2, April
1936.

A Representation of the Sunspot Cycle *

By C. N. ANDERSON

ALTHOUGH sunspots had been observed occasionally back to
ancient times, their study may be said to date from their redis-
covery by Galileo in the spring of 1610 with the then newly invented
telescope. Since then much has been written about their nature, their
periodicities and possible influence on human affairs.

The purpose of the study reported on in this paper was to analyze
the components of the sunspot data and thereby to reconstruct a
curve which would not only represent the variation in sunspot numbers
from 1749 to date but would also be consistent with times of maxima
and minima from 1610 to 1749. A number of attempts along this
line have been made in the past,^' *• ^- ^- ^' " all of which have neg-
lected the data previous to 1749 and all have used a slightly different
method of analysis. It is believed that the agreement in the present
study is somewhat better than in those of the past; nevertheless, no
claim is made for any great accuracy in predicting future sunspot
activity. Harmonic analysis based on a fraction of a period is always
a source of danger and, furthermore, we have no assurance that all
the components of the sunspot curve are periodic functions.^ In fact,
some papers have appeared in which each cycle was treated as a more
or less independent outburst.^- ^'^•^^' ^^ Nevertheless, because of the
long base line over which agreement is obtained in this present study,
it is hoped that the results may not be too much in error for at least
a few cycles.

The data used are the series of relative sunspot numbers begun by
Rudolph Wolf,^ Professor of Astronomy at Zurich and continued by
his successors Wolfer and Brunner. Wolf began his systematic
observations of sunspot numbers in 1849. He endeavored to make
some allowance for the area of the spots and to avoid having a small
spot of short duration count as much as a large group. With this in
mind, he applied the following formula to his observation:

Relative sunspot number = k^lOg +/),

where g and / are the group and total spot numbers respectively,

* Presented before the Astronomy Section of A.A.A.S. at Richmond, Va., De-
cember 28, 1938.

292

A REPRESENTATION OF THE SUNSPOT CYCLE 293

and ^ is a constant depending on the type of telescope and other
factors affecting the observation. The figure 10 is an arbitrary one
arrived at by Wolf from investigation of a number of individual cases
and which seemed to give him the proper relationship.

A careful study was then made by Wolf of all existing records of
prior data. Hofrat Schwabe of Dessau supplied data for the period
1826 to 1855 to which a correction was applied determined from a
study of the overlapping data and from the percentage of spotless days.
Johann Casper Staudacher of Niirnberg had made a total of 1131
observations (from one to ten every month) by means of a helioscope
during the period 1749 to 1799. He often gave detailed descriptions
and included many sketches. Imagine a man making observations for
fifty years without any attempt at analysis and then have the data
resurrected fifty years after his death to form an important con-
tribution to the record. Flaugergues (1794-1830), Tevel (1816-
1836), Adams (1819-1823) and Arago (1822-1830) supplied most of
the data for the intervening period between the observations of
Staudacher and Schwabe. Wolf lists about a hundred references
(225 up to 1866) to sunspots prior to 1850. In most cases, the obser-
vations were incidental to other solar observations such as culmina-
tions, solar diameter, eclipses, transits, or on the nature of sunspots
rather than their number. Each record was carefully studied, and
from them all Wolf obtained a representation of sunspot numbers
for as far back as 1749 and established the times of maxima and minima
with an accuracy of ± 2 years or better back as far as 1610 A.D.
Although the data prior to 1849 include a certain element of un-
reliability and all the data represent relative numbers which have been
obtained from the observations by applying a weighting factor, it is,
however, not only the best record but the only one for such a long
period of time. In the aggregate it is probably a good indication of
the variation of solar activity.

The method employed in the present analysis is briefly as follows :

(a) The yearly averages of sunspot numbers from 1749 to the end
of 1937 were first plotted in the conventional way as shown in Fig. 1 ;
it was noted that in certain sections of the curve, notably after 1840,
the maximum amplitudes of alternate eleven-year periods were
higher than the intervening ones.

ih) The data were redrawn with alternate eleven-year periods above
and below the time axis; this not only smoothed out the envelope
of the maxima but also simplified the analysis by eliminating a com-
puted mean value base line which has been employed in previous
analyses; the maximum-amplitude component becomes approximately

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SUNSPOT NUMBERS

A REPRESENTATION OF THE SUNSPOT CYCLE 295

twenty-two years instead of eleven years and the physical justification
is the similarity in the polarity of the leading spots in alternate eleven-
year periods.

(c) Quarterly values were obtained from the curve in order to
obtain a smaller unit and to approximate better such periods as
22.25 years, 17.33 years and other periods not an integral number of
years; the values were assigned + or — signs in accordance with
whether they were above or below the time axis.

(d) A periodogram was computed and the component of maximum
amplitude appeared to be 22.75 years; this component was eliminated,
a new periodogram computed and so on; after many trials it was
finally decided that no solution could be found which would reduce
the residue satisfactorily with 22.75 years as the main component.

(e) Inspection of the analysis indicated an improvement would be
obtained by a decrease in the period and accordingly a change was
made to 22.5 years and the computations repeated; a solution was
finally obtained which fit the 1749-1937 curve of sunspots fairly well
but, when extrapolated back to 1600 A.D., did not fit particularly
well the observed times of maxima and minima for the period 1610
to 1749; a still further reduction in the chief component was necessary.

(/) The computations were repeated with 22.25 years as the chief
component; after the computation of the series was completed, it was
discovered that the components were either harmonics or nearly
integral harmonics of 312 years; many of these components had been
in use since the original periodogram.

(g) A search was made for the 312-year period, since it should be
possible to check in the cases of two minima and two maxima, with
the following results :

Minima

1610.8 ± 0.4

1923.1

Diff. 312.3 ± 0.4

Maxima

1615.5 ± 1.5

1928.6

313.1 ± 1.5

Minima

1619 ± 2

1933.6

314.6 ± 2

Maxima

1626 ± 0.5

1937.7

311.7 ± 0.5

giving a weighted average of 312.5 years or an average of 312.0 years
using the two most reliable values.

(h) Computations were again repeated using harmonic components
of 312 years. This gave a very good representation of the data from
1749 to date and also agreed with the times of maxima and minima
for the period 1610 to 1749. The resultant curve is shown in Figs.
2 and 3.

The components of the reconstructed curve are shown in Fig. 4.
It is of interest to note that the 22.25-year component which is largely

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298

BELL SYSTEM TECHNICAL JOURNAL

AMPLITUDE -RELATIVE SUNSPOT NUMBERS

A REPRESENTATION OF THE SUNSPOT CYCLE 299

responsible for the eleven-year periodicity of sunspots has an ampHtude
of only about 2/5 of the greatest amplitudes of the resultant maxima.
Next in importance are the two adjacent periods at 17.3 and 18.4
years, respectively.

In conclusion, the study has resulted in a representation of yearly
sunspot averages which agrees as well as could be desired with the
data and which is also consistent with the reported times of maxima
and minima back as far as 1610 a.d. The chief component has been
treated as a 22-year (22.25 years) component instead of eleven years.
In the course of computation the components appeared to be har-
monics, or nearly so, of a 312-year period. A substantiation of this
312-year cycle' was found in a check of the overlapping data (maxima
and minima from 1923 to date).

It had been hoped that the resultant distribution of amplitudes
versus frequency of the components might be capable of simple inter-
pretation and that a rather simple explanation of the phenomena of
sunspot periodicity might result, such as one or two forces acting
upon a nonlinear system with a given fundamental period. Further
studies may still indicate this to be the case.

The author wishes to express his appreciation of the assistance of
Miss Helen Grant with the rather tedious computations.

References

1. " Mitteilungen iiber die Sonnenflecken," Rudolph Wolf, Naturforschende Gesell-

schaft in Zurich Vierteljahrsschrift, 1856-1865.

2. "iJber Eine Neue Theorie zur Erkliirung der Periodicitat der Solaren Erscheln-

ungen," J. Halm, Astronomisches Nachrichten, Vol. 156, 44, 1901.

3. "On the Periodicities of Sunspots," A. Schuster, Phil. Trans. Royal Soc, London,

Vol. 85, 1911.

4. "Determination of Periodicities by Harmonic Analyzer with Application of the

Sunspot Cycle," A. A. Michelson, Astrophysical Journal, Vol. 38, 1913.

5. "On the Harmonic Analysis of Sunspot Relative Numbers," Hisashi Kimura,

Monthly Notices of R.A.S., Vol. 73, 1913.

6. "On the Harmonic Analysis of Wolf's Sunspot Numbers," H. H. Turner, Monthly

Notices R.A.S., Vol. 73, 549, 1913.

7. "On the Expression of Sunspot Periodicity as a Fourier Sequence," H. H.

Turner, Mofithly Notices R.A. S.,Yol 73, 714, 1913.

8. "On a Method of Investigating Periodicities in Disturbed Series with Special

Reference to Wolfer's Sunspot Numbers," G. Udny Yule, Phil. Trans. Royal
Soc, London, Ser. A226, 1926-27.

9. "A New Analysis of the Sunspot Numbers," Dinsmore Alter, Monthly Weather

Review, October 1928.

10. " Untersuchungen iiber die Haufigkeitskurve der Sonnenflecke," H. Ludendorff,

Zeitschrift fiir Astrophysik, Vol. 2, May 1931.

11. "IJber Perioden der Sonnenflecken," S. Oppenheim, Astronomisches Nachrichten,

Vol. 232, 369, 1932.

12. "Forecasting Sunspots and Radio Transmission Conditions," A. L. Durkee,

Bell Laboratories Record, Vol. XVI, December 1937.

13. "The Mathematical Characteristics of Sunspot Variations," John Q. Stewart

and H. A. A. Panofsky, Astrophysical Journal, Vol. 88, November 1938.

The Number of Impedances of an n Terminal Network

By JOHN RIORDAN

This paper gives the enumeration of impedances measurable at
the n terminals of a linear passive network. The enumeration
supplies background for the study of network representations and
the numerical results which are given up to ten terminals are
perhaps surprising in the rapidity of the rise of the number of
impedances with the number of terminals; almost 126,000,000
impedances, e.g., are measurable for ten terminals.

A LINEAR passive network having n accessible terminals may be
completely represented by an equivalent direct impedance net-
work,^ consisting of branches, devoid of mutual impedance, connecting
the terminals in pairs. The number of elements (branches) in this
representation is equal to the number of combinations of n things
taken two at a time, i.e., |«(w — 1). Each of the elements is defined
by an impedance measured by energizing between one of the terminals
it connects and the remaining terminals connected together and taking
the ratio of the driving voltage to the current into the other terminal
it connects. The network then is represented by a particular set,
of ^n{n — 1) members, of impedances measurable at its terminals;
as will appear later, the set is of short-circuit transfer impedances.

The direct impedance network is one among many network repre-
sentations; it is taken as illustrative of two aspects, (i) the necessity
of a certain number of elements ^n{n — 1) and (ii) the expression of
these elements in terms of measurable impedances. It is well known
that any linearly independent set, of |w(» — 1) members, of the
measurable impedances of an w-terminal network will serve as a
network representation; hence the enumeration of representations may
be taken in two steps, the first of which, the enumeration of measurable
impedances, is dealt with in the present paper.

The number of measurable impedances for two to ten terminal

linear passive networks is given in Table I, which lists the driving-point

impedances, Dn, transfer impedances (open or short circuit), r„,

certain additional transfer impedances to be described later, Un, and

the total Nn- As mentioned below, this total counts once only

1 Item (b) in the list of equivalent networks given by G. A. Campbell "Cisoidal
Oscillations," Trans. A.I.E.E. 30, pp. 873-909 (1911), p. 889; or p. 81, "Collected
Papers of George Ashley Campbell," Amer. Tel. & Tel. Co., New York, 1937.

300

NUMBER OF IMPEDANCES OF AN n TERMINAL NETWORK 301

impedances which are equal by the reciprocity theorem; the doubling
of Tn in forming the total is due to the equality in number of open-
circuit and short-circuit transfer impedances. The numbers increase
rapidly with n, reaching almost 126,000,000 for ten terminals. The
number of representations, which is the number of combinations of
the measurable impedances |w(« — 1) at a time less the number of
non-independent sets, at a guess increases even more rapidly, indicating
a variety of equivalents, few of which seem to have been investigated.

TABLE I

Measurable Impedances of an m-Terminal Network

n

D„

Tn

Un

Nn=Dn-\-2Tn + Un

2

1

0

0

1

3

6

3

0

12

4

31

33

60

157

5

160

270

1,050

1,750

6

856

2,025

12,540

17,446

7

4,802

14,868

129,570

164,108

8

28,337

109,851

1,257,060

1,505,099

9

175,896

827,508

11,889,990

13,720,902

10

1,146,931

6,397,665

111,840,180

125,782,441

Because the field of the work is somewhat unusual, considerable
space is given to details in the formulation of the problem before
proceeding to the enumeration proper. The enumerating expressions
obtained are found susceptible of some mathematical development
which, though subsidiary to the main object of the paper, seems of
sufficient interest to justify the relatively brief exposition given. The
arrangement is such that readers not interested in this mathematical
half may obtain the substance of the paper without it.

Formulation of the Problem

The enumerating problem is essentially one of combinations, as
indicated schematically in Fig. 1, which shows the n terminals of a
linear passive network together with the apparatus required for
impedance measurement, that is, a source, a voltmeter and an ammeter,
each supplied with two terminals (shown solid to distinguish them
from the network terminals). Each of these latter may be connected
across any pair of the n terminals except that the ammeter, which
constitutes a short circuit, may not be connected to terminals to which
either the source or voltmeter is connected; in the former case no
current will be supplied to the network and in the latter the voltmeter
will read zero. The ammeter may be connected in series with the
source to read the source current, of course.

302

BELL SYSTEM TECHNICAL JOURNAL

Although but one source, voltmeter, and ammeter are shown, as
many of each as will produce distinct impedances should of course be
included. Multiple sources are not required because if the source
voltages are in defined proportions, as is necessary to determine
impedances independent of source voltage, the corresponding measur-
able admittances are linear combinations of single-source admittances,
by the principle of superposition; a similar requirement on source
currents produces impedances which are linear combinations of single-
source impedances. A single voltmeter is sufficient because it has no
effect on network currents or voltages and it is immaterial whether

'■W

/

^v^'

n-TERMINAL

LINEAR PASSIVE

NETWORK

O 0

IMPEDANCE-MEASURING EQUIPMENT SHORT-CIRCUIT LINKS

Fig. 1. — Elements involved in impedance enumeration.

impedances are supposed measured by successive positions of a single
voltmeter or by many voltmeters. The connection of an ammeter is
equivalent to a short circuit (except of course when in series with a
source) across the terminals the ammeter connects; this alters network
voltages and currents and the impedances measured without the
ammeter differ from those with it. Hence a plurality of ammeters or
its equivalent is required; for convenience, all ammeters except that
one determining a specific impedance under consideration are supposed
replaced by the short-circuiting links on the right of Fig. 1, thus
focussing attention on the single items of the enumeration.

NUMBER OF IMPEDANCES OF AN w TERMINAL NETWORK 303

The classification under which the enumeration is conducted is
illustrated by Fig. 2, which shows typical positions of source, voltmeter
and ammeter for measuring impedances of three classes. In the first
of these, the ammeter reads the source current, the voltmeter source
voltage (across some pair of the network terminals) and the class is
that of driving-point impedances, D„. In the second class, that of
transfer impedances Tn, there are two types of connection: in the
first the ammeter reads the source current, the voltmeter a non-source
voltage, the voltage-current ratios being open-circuit transfer im-
pedances; in the second the voltmeter reads the source voltage and

DRIVING POINT
IMPEDANCES (Dn)

'-<I>-1

OPEN CIRCUIT SHORT CIRCUIT

TRANSFER IMPEDANCES (in)

UA

GENERALIZED TRANFER IMPEDANCES (Un)

Fig. 2 — Arrangemeftt of apparatus for measuring impedances of three classes.

the ammeter a non-source current, the voltage-current ratios being
short-circuit transfer impedances. It will be noted that the two
connections differ only in that the ammeter and voltmeter are inter-
changed. The third class is that of generalized transfer impedances
Un, in which both voltmeter and ammeter are across non-source
terminals.

The last class, of course, might be supposed to include the two
preceding ones but the separation proves convenient not only for
numerical work, as will appear, but also for keeping distinct both
well-recognized and formally different classes.

304 BELL SYSTEM TECHNICAL JOURNAL

The most important of these differences in classes is that arising
from the reciprocity theorem. Of the three classes, only the T
(open-circuit and short-circuit transfer impedances) includes members
which are equal by the reciprocity theorem; this follows because the
reciprocity theorem requires interchange of voltmeter (or ammeter)
and source with associated ammeter (or voltmeter) and the T class
alone permits this. It is a matter of taste whether such duplicates
should be counted separately or as one ; in the interest of keeping large
figures as low as possible they are here counted as one, since the
classification is such that the other alternative may be taken merely
by doubling the r„.

Another reason for keeping the T class distinct is that total open-
circuit and short-circuit transfer impedances for a given number of
terminals are equal in number. This is proved immediately by
observing that the two connections shown in Fig. 2 for this class are
in one-one correspondence: each may be obtained from the other by
interchanging voltmeter and ammeter. Moreover, if T°x, n and T\, n
are the numbers of open-circuit and short-circuit transfer impedances
measurable when short circuits have been placed across the n terminals
in all possible ways so as to realize x terminals, each merged group of
terminals counting as a single terminal, the correspondence leads to
the relation

since the interchange of voltmeter and ammeter in the measuring
arrangement for open-circuit transfer impedances results in one less
available terminal, two terminals being merged by the ammeter short
circuit. Note that T^i, „ = T\, „ = 0, since with just two terminals,
no non-source voltages and with n terminals no non-source currents
are measurable.

Equation (I) is important in determining enumerating expressions
in the section following.

Enumerating Expressions

The laws of enumeration appear most simply exposed by examining
the simplest cases first.

For two terminals, there is but one measurable impedance, the
driving-point impedance between the terminals.

For three terminals, with the terminals distinct, there are three
driving-point and three open-circuit transfer impedances, for there are
three ways of selecting driving pairs of the three terminals and for
each selection two ways of selecting pairs for open-circuit voltage

NUMBER OF IMPEDANCES OF AN n TERMINAL NETWORK 305

measurement, the total of six transfer impedances being halved to
eliminate reciprocity theorem duplicates. With two of the terminals
connected by an ammeter, there are again three driving-point and
three transfer impedances, the latter being short-circuit transfer
impedances, for there are three ways of connecting pairs of terminals
and one driving-point and two transfer impedances for each, the
total of transfer impedances again being halved to eliminate duplicates.

There are no generalized transfer impedances because with an
ammeter connected, there is only one measurable voltage, the driving-
circuit voltage.

With terminals designated by /i, t^ and /a, the conditions arising
from connection of terminals may be exhibited as follows:

Terminals distinct ti\ti\ tz
Pairs connected txt^ I tz

tMh

t\\t%tz

the lines of separation dividing the terminals into groups such that

the terminals in any group are merged into a single terminal. Paying

attention only to the number of terminals in each group, the groups

illustrated may be designated by the partition notation (111) or (P)

and (21), the numbers in the designation being partitions^ of the

number 3.

The enumeration for three terminals may then be exhibited as

follows :

Measurable Impedances

Group

Driving Point

Open-Circuit Transfer

Short-Circuit Transfer

Total

(21)

3
3

3
0

0
3

6
6

6

3

3

12

It will be noted that the open-circuit and short-circuit transfer
impedances satisfy equation (1), that is, T°z, 3 = T\, 3.

This table and its correspondents for larger values of n show that
the impedances may be expressed as sums with respect to x, where x
is the number of terminals defined as in equation (1), from 2 to w;
thus e.g., Z)„ = Y^Dx, n where Dx, „ is the number of driving-point
impedances measurable for all conditions of merging of n terminals
such that the resulting number of terminals is x. Moreover, con-

^ A partition of a number n is any collection of positive integers whose sum is
equal to n. It may be noted that the number of parts of a partition is the number
X of equation (1) ; the partition (1^) has three parts corresponding to the three distinct
terminals; (21) has two parts corresponding to two terminals, each merged pair of
terminals counting singly.

306 BELL SYSTEM TECHNICAL JOURNAL

sidering for the moment only the driving-point and open-circuit
transfer impedances, the numbers Di, „ and r°x, n are the products of
two factors: (i) the number of such impedances measurable for x
terminals, which is independent of n and (ii) the number of ways the
n terminals may be merged so as to result in x terminals, which is
independent of the impedance classes. By equation (1) this result
applies also to T\, „ and, as Ux, n is related to T\, „ by a factor
independent of n, as will be shown, it applies generally.
This leads to the following equation :

\TA^Y.\t.\ S., n. (2)

L Un J ^=2 [ «x J

The small letters are the several factors of the first kind and Sj,, „ is
the common second factor.

The small letters are determined as follows: A driving point im-
pedance may be measured between every pair of terminals; hence dx
is the number of combinations of x things taken two at a time, that is:

dx =

(^l) = hx{x- 1) = i(x)2. (3)

where (x),- is the factorial symbol x{x — 1) • • • (x — i -\- \).

For a given pair of driving terminals, there are ( j — 1

measurable open-circuit transfer impedances since a voltmeter can be
connected to every pair of the x terminals except the driving pair;
hence, multiplying by the number of driving terminals and by the
factor one-half to eliminate reciprocity theorem duplicates:

t - h""

2»-^

(4)

= |[4Cr)3 + (x)4].

The second, factorial, form is given for convenience of later develop-
ment.

By equation (1) this serves for enumeration of both open-circuit
and short-circuit transfer impedances; the direct enumeration of the
latter appears more difficult.

Considering, for the generalized transfer impedances, a fixed source
and an ammeter in a fixed (non-source) position, the voltmeter may

be connected across ( . 1 pairs of terminals when x terminals are

NUMBER OF IMPEDANCES OF AN n TERMINAL NETWORK 307

available; one of these pairs is the source pair measuring a short-
circuit transfer impedance which must be excluded; hence, remember-
ing that reciprocity theorem duplicates are eliminated in the latter:

L' X, n — •^

= 2

- 1

- 1

■>■ X, n

-t ° x-\-\, n ^^ 2

1

^x+l-Ji+l, n-

Degrading x by unity to obtain the form of equations (2), the third of
the lower case factors is reached as follows:

'-a)[a)-][Cr'-'

= i[20(x)4 -f 10(x)5 + We].

(5)

The common factor 5^, n remains for determination.

Returning to the connection conditions illustrated for three terminals,
this number is the number of ways separators may be placed between
letters of the collection /i, k- • -tn symbolizing the terminals so as to
produce x compartments, symbolizing merged terminals. The ter-
minal symbols ti- • -tn may be thought of as the prime distinct factors
(excluding unity) of some number and the number Sx, n is then
identically the number of ways a number having n distinct prime
factors may be expressed as a product of x factors. The enumeration
for this latter problem is given by Netto,^ who gives the recurrence
relation

•Ji, n+l ^^ X^x, n \ »Jx— 1, n

with

Sn.

1, 5i, n = 0, X > n, 5o. n = 0, « 4^ 0.

This is the recurrence relation for the Stirling numbers of the second
kind,^ the notation for which has been adopted in anticipation of the
result. These numbers are perhaps better known as the "divided
differences of nothing," that is, as defined by the equation:

5x. n = lim-,A^2» = -jA^O^
z=o x! x!

where A^ denotes x iterations of the difference operator with unit

3 "Lehrbuch der Combinatorik," Leipzig, 1901, pp. 169-170; Whitworth, "Choice
and Chance," Cambridge, 1901, Prop. XXIII, p. 88, gives a generating function for
the solution of this problem which, it is not difficult to show, leads to the same answer.

* Ch. Jordan, "Statistique Mathematique," Paris, 1927, p. 14.

308 BELL SYSTEM TECHNICAL JOURNAL

interval, that is, of the operator defined by

A/(2) =fiz+\) -}{z).
For convenience of reference, a short table of the numbers follows:

0 1

1 0

2 0

3 0

4 0

5 0

1

3 1

7 6 1

15 25 10

The table may be verified and extended readily by the recurrence
relation.

With this table (extended to w = 10) and corresponding tables of
dx, tx and Ux running to x = 10, the values given in Table I may be
calculated by equations (2) and in this sense this paper is completed
at this point. The sections below contain an algebraic and arith-
metical examination of the numbers.

Generating Identities
The generating identity for the function

n
«=0

exp [a(g' - 1)] = E -, L a-Sx, n.

„=0 ^ • 1=0

This leads, by differentiating 5 times with respect to a and setting a
equal to unity, to the generating identity:

°° fn "

(e' - 1)^ exp (e' - 1) = E -, L {x).Sx, „.

n=0 '* • «=0

This relation may be rendered more summarily by introducing the
notation of the symbolic or umbral calculus « of Blissard ; the expression
on the right is written exp tb where 6 is an umbral symbol standing
for the sequence (6o, 5i, • • -Sn- ■ •) in this case infinite, through the
relation 5" = 5„ and:

*E. T. Bell, "Exponential Polynomials," Annals of Math. 35, 2 (April, 1934) p.
265- or J. Riordan, "Moment Recurrence Relations . . . ," Annals of Math. Statistics
8, 2', pp. 103-111 (June, 1937), eq. 3.4.

6 Cf. Bell, I.e. p. 260 where further references are given.

NUMBER OF IMPEDANCES OF AN n TERMINAL NETWORK 309

n

1=0

All algebraic operations on umbral symbols are carried out as in ordi-
nary algebra except that the degrading of subscripts must not be
performed until operations are completed. It must be noted that
5" = 5o, hence is unity only when 5o = 1, as in the present case and
not always as in ordinary algebra.

The umbrae for the impedance numbers are written D, T and U,
and by use of the generating identity above have the following gener-
ating identities:

exp tD = i(e' - 1)2 exp (e' - 1),

exp tT = i[4(e' - 1)^ + (e' - 1)*] exp (e' - 1), (6)

exp tU = |[20(e' - 1)^ + 10(e' - 1)^ + (e« - 1)«] exp (e' - 1).

These follow immediately from the base generating identity and
the factorial expressions for dx, t^ and Ux-

Expanding these expressions in powers of e' gives alternate ex-
pressions as follows:

exp tD = Ke^' - 2e' + 1) exp (e' - 1),

exp tT = i(6*' - 6e2' -j- Se' - 3) exp (g« - 1), (6.1)

exp tU = i(e«' + 4^5' - ISe^" + SSe^' - 36e' + 11) exp (e' - 1).

To recapitulate, these expressions mean that Z>„, Tn and Un are
the coefficients of /"/w! in the expansions of the right-hand sides;
taking Dn, for example, the first equation of (6) is equivalent to the
equation :

Dn^Um—Bie^ - 1)2 exp (e' - 1)],
<=o ^^

which may be shown to be equivalent to the first of equations (2).

The generating identities lead immediately to recurrence relations,
as will now appear.

Recurrence Relations

Recurrence relations to be derived are all obtained by differentiation
with respect to /. Under this operation umbrae behave like ordinary
variables; thus

-r exp tD = D exp tD

= Di + D2t + D^^^+ ••• ^n+i^^+ •••,

as may be verified readily.

310

BELL SYSTEM TECHNICAL JOURNAL

In the first type of recurrence only successive values of the numbers
themselves appear. The derivation is illustrated for the Dn, the
simplest case. Differentiating the first of equations (6) leads to the
relation :

D exp tD = \{e^' - e') exp {e' - 1),
or

(e' - \)D exp tD = e'{e' + \)W - ^f exp (e' - 1)
= (e2' + e') exp tD.

Equating coefficients of /"/n! in this relation gives the umbral re-
currence :

D{D + 1)" - Z?„+i = {D + 2)« + (^ + 1)",

which in ordinary form is:

{n - 2)Dn = L

(';)(2'+»-(,;0]-"-

The process is common to the three classes of numbers and pro-
duces similar results which may be put in general form as follows:

a„An = E

n\ , n

A n—it

(7)

where A „, a„, 6, and c, are defined for the three cases by the following
table:

An

an

D„

n-2

Tn

An-\2

Un-Z

480

"(:)-

L \ ^ /

hi

C-i

2'+l
3' + 6-2«+5

1

2^ + 2

7^+10-6'-(-5-5^-60-4'

6^+4 -5' -15 -4^

+ 35-3^+34-2^-25

+ 35-2^-36

Somewhat more convenient recurrences may be obtained by allowing
the presence of numbers other than those for which the recurrence is
sought. For this purpose it is expedient to introduce the exponential
numbers €„ of E. T. Bell.

These are defined by the generating identity:

exp /e = exp (e' — 1)

or by the equivalent formula:

(/"
e„ = lim^exp (e' - 1) = Z ^x, n,

NUMBER OF IMPEDANCES OF AN n TERMINAL NETWORK 311

which shows their close relation with the impedance numbers. They
have the recurrence relation :

€n+l = (e + 1)"

and

60 = ei = 1.

Now, returning to the first of equations (6) and again differentiating:

D exp tD = \[2{e' - l)e' + (e' - l)^^'] exp (g' - 1),
= (e' — l)e' exp (e* — 1) + e' exp tD,
= 2 exp tD + (e' - 1) exp (g' - 1) + exp t{D + 1),
= 2 exp tD + exp /(e + 1) - exp te + exp t{D + 1),

from which, passing to the coefficient relation, comes the umbral
recurrence :

J9„+i = 2D,, + (Z) + 1)» + e„+i - en.

Similar recurrences for the T and U numbers are derived in the
same way; writing Ae„ = Cn+i — Cn, the results may be summarized
as follows:

Dr^+X = 2Dn+ (D + 1)" + Ae„,

Tn+i =4r„+ (r+l)" + 3Z)„, (8)

Un+i = 6Un + (t/ + 1)" + 46r„ - 4r„+i

+ 30Z)„ - 6Dn+i + 6Aen.

The expressions in parentheses, it will be remembered, are short-
hand binomial expansions; thus:

p+i)»=e(:)zp..

Relations with the Exponential Integers

The generating identities in equations 6.1 furnish immediate rela-
tions with the exponential integers, e^. Writing exp (g' — 1) as exp le,
as above, and passing from generating relations to coefficient relations,
these results are as follows:

D. = |[(6 + 2)" - 2(e + 1)" + 6„],

r„ = |[(e + 4)" - 6(6 + 2)« + 8(6 + 1)» - 36,.], (9)

t/n = i[(e + 6)" + 4(6 + 5)" - 15(6 + 4)"

+ 35(6 + 2)« - 36(6 + 1)« + ll6„].

Expanding internal parentheses by the binomial theorem, the general
result is as follows:

312 BELL SYSTEM TECHNICAL JOURNAL

n ,• \

where the coefficients «{ for the three cases are as follows;

An

Dr.

2»-i - 1

(2^-1 - l)(2»'-2 - 1)

i[6^ + 4-5^ - 15-4^ + 35-2' - 36]

Note that in the first case (Z)„)q:i = 0, in the second (Tn)ai = a^ — 0,
in the third (f/n)«i = 0:2 = as = 0. Thus a given table of values of
e„ up to w = ^ determines Z)„ up to ^ + 2, Tn up to ^ + 3, and Un
up to ^ + 4.

Somewhat simpler relations may be derived as follows. Repeated
differentiation of the generating identity of the e„ with respect to /,
and passage from the generating relations to coefficient relations leads
to the following:

6n+l = (e + 1)",

€n+2 = (6+ 1)"+ (e + 2)",

e„+3 = (6 + 1)" + 3(e + 2)" + (€ + 3)",

or, in general:

m
1=1

This formula may be inverted by the reciprocal relations for the
Stirling numbers of the first and second kinds ^ which run as follows:
If

m

then

m
x=l

where Sx, m is the Stirling number of the first kind defined by the
recurrence relation

Sx, m+\ ^^ •^i— 1, TO Woj, rn

and the boundary conditions Sm.m = '^, s^.m = 0 x > m, So. m = 0,
m > 0.

^ Nielsen; "Handbuch der Gamma Funktion," Leipzig, 1906, p. 69.

NUMBER OF IMPEDANCES OF AN n TERMINAL NETWORK 313
The inverted formula * is :

m
1=1

A short table of the Stirling numbers of the first kind follows:

0

1

2

3

4

5

6

0

1

1

0

1

2

0

-1

1

3

0

2

-3

1

4

0

-6

11

-6

1

5

0

24

-50

35

-10

1

6

0

-120

274

-225

85

-15

1

The three equations resulting from applying this transformation to
equations (9) are as follows:

Tn = i[fn+4 — 6e„4.3 + 5e„+2 + 8e„+i — 3e„], (10)

Un = lE^n+e ~ llCn+b + 30e„4-4 + 5en+3

— 56€„+2 — 5€„+l + lle„].

For computing purposes, values of e„ and Ae„ up to w = 10 are
given in Table II.

TABLE II
Exponential Numbers

0

1

0

1

1

1

2

2

3

3

5

10

4

15

37

5

52

151

6

203

674

7

877

3,263

8

4,140

17,007

9

21,147

94,828

[0

115,975

562,595

^ Noting that S a'^Sx, m = {a)m, where (a)m is the factorial symbol used through-

out, the inverse relation may also be written:

(e + m)"- = e"(«)m.

In this notation, the inverses to equations (2) for the impedance numbers have the
following simple forms which are worth noting:

{D)n = dn
iT)n = tn
{U)n = Un

314 BELL SYSTEM TECHNICAL JOURNAL

Congruences

For numerical checks, it is convenient to note the simplest con-
gruences ^ for the three numbers. These follow from the Touchard
congruence for the e numbers ^^ which runs as follows:

ep+„ = e„^.i + €„ mod p,

where /> is a rational prime greater than 2.

Since by equations (10) each of the impedance numbers is a linear
function of the e numbers, each has a similar congruence as follows:

Dp+„ = D„+i + Dn mod p,

Tp+n = Tn+i + Tn mod p, (11)

Up+n = Un+\ + Un mod p.

Special values for the first few congruences are as follows:

Remainder, mod p

n

Z)p+„

Tp^n

Up^n

0

0

0

0

1

1

0

0

2

7

3

0

3

37

36

60

These are sufficient for checking every value in Table I at least
once and the values for w = 5, 6, 7, 8 are checked twice.

Acknowledgment

This paper arose as a result of a suggestion made by R. M. Foster
on a former paper '^ and thanks are also due him for continuous
counsel and critical scrutiny which have enlarged the boundary and
sharpened the outline of the problem.

* The congruence Dn = r mod p is equivalent to the equation Dn = mp + '',
where m is an integer; that is, r is the remainder after division by p (or the remainder
plus some multiple of p).

"See E. T. Bell, "Iterated Exponential Integers, "Annals of Math., 39, 3 (July,
1938), eq. 1.101, p. 541.

11 "A Ladder Network Theorem," Bell System Technical Journal 16, pp. 303-318
(July, 1937); see especially footnote 3; I take this opportunity to draw attention to
an error in that footnote: for four terminals (see Table I) there are 157, not 64,
measurable impedances; hence the upper bound to the number of representations is
18,883,356,492, not 74,974,368.

Copper Oxide Modulators in Carrier Telephone Systems *

By R. S. CARUTHERS

Copper oxide modulators are widely used in telephone systems
for translating either single speech channels or groups of speech
channels to carrier frequency locations on the lines. A number of
simple circuit arrangements have been developed that enable sup-
pression of certain undesired frequencies to a degree that is im-
practical in tube modulators. These modulators transmit equally
well in either direction and the modulating elements are more non-
linear than in tube modulators. As a result numerous effects are
found that ordinarily are not important in the tube arrangements.
Analytical studies have been considerably simplified by the use of a
small signal, and a large carrier controlling the impedance variation
of the copper oxide. It is found in this case that the superposition
and reciprocity theorems hold for all the circuits that it has been
possible to analyze even though the modulator is made up of non-
linear elements. Open and short-circuit impedance measurements
can be made use of as in four-terminal linear networks, and a
generalized reflection theory developed. Performance data are
given for an idealized modulator under a variety of operating
conditions.

Introduction

AT least as early as 1927, copper oxide rectifiers were being tried as
modulators for the speech channels of carrier telephone systems
in this country. At this time only a rather large type of rectifier was
available, better adapted for power use rather than in modulating the
few milliwatts of a speech signal. Largely because of instabilities these
early units were found to be unsatisfactory for modulator use. Further
developments in copper oxide rectifiers made in various laboratories
extended the variety and improved the quality of the product available,
so that by about 1931 they began to be promising as serious com-
petitors for vacuum tubes in modulators. Since 1931 continued im-
provements in copper oxide rectifiers have rapidly increased their
field of application until now they are employed in practically all
modulators of the latest types of carrier telephone systems.

In the new systems a copper oxide modulator is used instead of the
previous push-pull arrangement of two vacuum tubes. In cable/

* Presented at Winter Convention of A.I.E.E., New York, N. Y., January 23-27,
1939.

' The general features of carrier telephone terminals have been described in a
paper "Cable Carrier Telephone Terminals" by R. W. Chesnut, L. M. Ilgenfritz
and A. Kenner, Electrical Engineering, January 1938.

315

316 BELL SYSTEM TECHNICAL JOURNAL

open wire and coaxial carrier systems, from twenty-six to twenty-
eight of these modulators are needed in each direction for translating
each twelve-channel group of speech bands from voice to carrier and
back again. These copper oxide modulators have no power costs,
tube replacements or possibilities of power failures. In Fig. 1 the
four 3/16 inch diameter copper oxide discs generally used in a carrier
telephone modulator are shown individually, assembled with con-
nections, and potted in a can.

The carrier terminals have tended to become increasingly complex
as it became their function to place more and more channels on a
single pair of wires. The extreme simplicity and reliability of copper
oxide modulators have been of great value in helping to overcome this
tendency. Copper oxide modulators have been used from zero fre-

Fig. 1 — Four disc copper oxide modulator.

quency to nearly four million cycles. Certain modulators for coaxial
carrier systems have been designed to modulate simultaneously as
many as sixty speech channels spaced over a 240,000-cycle band of
frequencies.

Copper oxide modulators probably differ most from tube modulators
because the simplicity of the rectifier elements allows a much greater
variety of circuit arrangements to be used. Although the underlying
principles of operation are not new, it has become necessary to investi-
gate numerous transmission effects that could be neglected in tube
modulators. This has resulted not only from the newer circuit arrange-
ments with their smaller losses, but also from higher transmission
standards for the overall system along with the greatly increased
numbers of modulators in long circuits. Copper oxide modulators,
unlike tube modulators, transmit signals equally well in either direc-
tion. While this is a simplification in allowing a modulator also to

COPPER OXIDE MODULATORS IN CARRIER SYSTEMS 317

be used as a demodulator, the modulator becomes complicated by
the effects of reflections back and forth into the signal bands of
numerous frequency bands of modulation products.

Circuit Arrangement

The circuit arrangements used in copper oxide modulators generally
are concerned either with carrier suppression, with carrier transmission
along with the signal, or with balancing action to suppress certain un-
wanted bands of signal frequencies. In most carrier telephone systems
economy of frequency space and amplifier load capacity demands the
use of single-sideband, carrier-suppressed transmission.

In Figs. 2(a), 2(b), and 2(c) three types of copper oxide modulators
are shown, each arranged to suppress the carrier in both the signal input
and the signal output circuits. In Figs. 2(d) and 2(e) the carrier is
balanced out in only one signal branch. In the usual arrangements
a signal band selective filter must be used in each signal branch to
restrict transmission to that of the wanted frequency band. Largely
in this way interferences are guarded against, not only into other
channels or systems to which the modulator output circuit is connected
on the line or at the distant end, but also back into the complex array
of facilities to which the input circuit may be connected.

In any of the circuits shown, modulation results from either the
reduction or reversal of the current flow between the input and output
signal circuits at periodic intervals as the carrier varies the copper
oxide resistance back and forth between high and low values. In
Fig. 2(a) where the connections of the input and output signal circuits
are periodically short-circuited by the carrier-actuated copper oxide,
transmission of the modulated signal into the input circuit or the
unmodulated signal into the output circuit is prevented by filters, each
of high impedance at the frequency of the other signal. In Fig. 2(b) the
connections between the signal and modulated signal circuits are open-
circuited periodically by the carrier. In this case each filter should
have a low impedance at the other signal frequency. In Figs. 2(c), 2(d)
and 2(e) the copper oxide rectifiers are made to become alternately low
and high resistance in pairs as the polarity of the carrier is either in
the same direction as the arrows or in the opposite direction. As a
result, current flow from the input signal circuit into the output is
periodically reversed by provision of a periodically reversing low im-
pedance path. In effect each signal is balanced from the other's
circuit.

Although an indefinite number of other circuit configurations can
be used, no novel transmission feature would be found which was not

318

BELL SYSTEM TECHNICAL JOURNAL

SIGNAL
INPUT

noCtnoV
neC+noV

neCinoV

SIGNAL
OUTPUT

CARRIER SUPPLY

(a)

nnCtnoV SIGNAL

neCtnoV output

, V. - ^ ,

I I

CARRIER SUPPLY

DeCtneV

noCtneV
I I

CARRIER SUPPLY

(C)

SIGNAL
INPUT

OoC+neV
neC±noV

CARRIER SUPPLY

noCtnoV
HeCineV

SIGNAL
OUTPUT

(d)

SIGNAL
INPUT

neC+noV
DeC+neV

noCtnoV
noCtneV

SIGNAL
OUTPUT

(e)

CARRIER SUPPLY

Fig. 2 — Types of copper oxide modulator circuits.

COPPER OXIDE MODULATORS IN CARRIER SYSTEMS 319

present in the five circuits already shown. Third order modulators in
which the copper oxide is arranged to give equal interruptions to the
signal in both positive and negative half cycles of the carrier are excep-
tions not considered here. In addition, circuits like Hartley's, in
which phase discriminations have been obtained in the sideband out-
puts from two modulators by altering both the carrier and signal input
phase of one, can be viewed as composed of two modulators of any of
the types illustrated.

In these copper oxide modulators all modulation product frequencies
can be grouped into four classes:

UqC ± TIqV,
floC ± UeV,
fleC ± nov,

UeC ± rieV,

in which c and v are the carrier and input signal frequencies and wo is
any odd number 1, 3, 5 etc., while fie is any even number 0, 2, 4, 6, etc.
If c and V contain more than one frequency each, Wo and Ue are respec-
tively the odd and even combinations of all multiples of the c and v
frequencies. All frequencies of one of these four types appear together
in a specific branch of the modulator circuit; and they will not appear
in another branch unless from a dissymmetry among the copper oxide
units or unless inherent in the circuit configuration. The branches in
which the modulation products appear are shown in the circuits
illustrated. It is apparent that only in the case of the double-balanced
circuit of Fig. 2c, are all of these types of products completely separated
in different parts of the circuit. In the other circuits shown the
classes of products appear together in combinations of two types.
In any balanced circuit that can be drawn the above relationships
will be found to hold.

Modulation products will be of a type to which the circuit offers
some degree of balance, of a type that can be made to vary in im-
portance relative to the signal by adjustment of either the carrier or
signal voltage, or of a type to which neither balance nor level adjust-
ment is of any benefit. Satisfactory operation of such modulators
requires large carrier voltages relative to those of the signal, so that
products like c ± z^, 2c ± z;, 3c db v, etc. tend to be of large magnitude
while products like c ± 2z;, c ± ?>v, etc. tend to be small. Further-
more, the former types can be made to predominate even more over
the latter types either by increasing the carrier amplitude or by de-
creasing the signal levels. A 6 db reduction in signal results in 12 db
reduction oi c ±. 2v and 18 db reduction in c ± 2>v. In any circuit

320

BELL SYSTEM TECHNICAL JOURNAL

application interferences of this type lend themselves to reduction
in so far as carrier power is available for high signal level operation, or
in so far as noise does not limit for low signal levels. Laboratory
measurements of some of these modulation products made during the
development of a group modulator for a twelve-channel open-wire
carrier system are shown in Fig. 3 for a double-balanced modulator

INPUT

FREQUENCY

IN KC

INTER-
FERENCE
PRODUCT

C

V

300

185

2V

300

233

C + 3V

300

70

C + 2V

300

79

V

145

80

2C+V

-40 -35 -30 -25 -20 -15 -'0 -5

output of lower sideband (c-v) in decibels
(below 0.006 watt)

0 -10 -5 0 5 10

CARRIER LEVEL IN DECIBELS'
(FROM 0.75 volt)

Fig.

3 — Intensity of modulation products in a representative double-balanced
copper oxide modulator.

like that of Fig. 2(c). Single 3/16 inch diameter discs as shown in Fig. 1
were used in each bridge arm. About 20 to 30 db reduction in inter-
ference by balance alone is quite readily obtained in the normal run
of manufactured copper oxide rectifier elements, for those products
to which the circuit arrangement offers a balance. Any further
improvement must be obtained either by closer control of manufacture

COPPER OXIDE MODULATORS IN CARRIER SYSTEMS 321

or disc selection, by artificial balancing with some means such as
condenser-resistance potentiometers, or by statistical averaging
through use of numbers of discs in each bridge arm.

In single-channel modulators interferences caused by the signal into
its own signal band will occur only in the presence of the signal. In
such cases they need be only 20 to 30 db below the signal, except in
special cases, as for example, modulators for broad-band program
channels. In multi-channel systems interferences may be produced in
the silent channels by the active channels. This kind of interference
or crosstalk is ordinarily made to be 70 db or more below the wanted
signals for commercial telephone service. In such cases overlapping
bands of frequencies not improved by level adjustment are avoided
by judicious choice of the carrier frequencies.

Circuit Impedance and Loss

In all modulators the carrier serves merely as a means for obtaining
a simple periodic variation of the impedance presented to the signals.
It is not only immaterial to the signals how this variation is obtained,
but the signals also are totally unaware of whether electrical, mechan-
ical or other means are used, just so long as the signals themselves are
unable to affect the time variation of this impedance. In a copper
oxide modulator, only by making the carrier amplitude large com-
pared to the signal amplitudes across the rectifier elements, can the
impedance of the rectifiers be made to vary at carrier rather than signal
rates. Too large a signal amplitude not only results in the production
of undesired frequencies, but also the impedance and loss character-
istics of the modulator vary with the signal amplitude. With small
signals the carrier energy is used up in maintaining the copper oxide at
prescribed impedance values at each instant of time, and none of the
modulation products involving the signal receive more than a negligible
amount of energy from the carrier. As a result the output signal
energy will always be less than that of the input signal, partly because
of iV losses within the copper oxide, and partly from the diversion of
the input signal energy into the energies of the many modulation
product frequencies.

The signal impedance of a copper oxide modulator is a combination
of a characteristic impedance of the rectifier elements and the im-
pedance of the connected circuits at all the modulation product fre-
quencies. The characteristic impedance of the rectifier can be viewed
crudely as an average of the impedance encountered by a small signal
over a cycle of the carrier, treating each instantaneous value of the
carrier voltage as a d-c. bias. If the impedance for small super-

322

BELL SYSTEM TECHNICAL JOURNAL

imposed a-c. voltages is measured on a single copper oxide disc at
various d-c. bias voltages, this impedance generally changes with
both bias and frequency. Measurements to 200 kilocycles made on a
3/16 inch diameter disc are shown in Fig. 4. At all negative bias

0.3
0.2

0.1

0.05

0.02

^ 0.01

s

\,

\

1. REVERSE

\

\

S^

\

FORWARD

\

Voo \

>

200 \

\

■■*=.I"=J=.

"■""■"" — ";

r~~c"

^_

10

V

\ \

200

"~

^N

\

\

-"~

-\

y

\''

^

\

\\

\

\

\

\\

I

\

\\

\
\

\

100

300 400 500 600 800 1000

CAPACITY IN MICROMICROFARADS

2000

500 1000 5000 10,000

RESISTANCE IN OHMS

100,000

Fig. 4 — Impedance of a copper oxide disc at various forward and reverse d-c. voltages
for small superposed a-c. voltage.

COPPER OXIDE MODULATORS IN CARRIER SYSTEMS 323

voltages the impedance is a resistance in parallel with a condenser.
This resistance decreases rapidly with increasing frequency while the
shunt capacity decreases only a moderate amount. At moderate
positive voltages (about 1/2 volt) the impedance becomes resistive and
does not change appreciably with frequency. Experimentally it is
found that the signal impedances in resistance terminated modulators
can be made largely free of reactance at high frequencies by using
either large carrier amplitudes, inductive tuning of the copper oxide
capacities, or lower impedance connected signal circuits to accentuate
the importance of the low-resistance part of the copper oxide character-
istic. Very much lower circuit impedances must be used at the
higher frequencies. Where 600 to 1000 ohms is a satisfactory im-
pedance at speech frequencies, less than 50 ohms may be the best
impedance to use, at three megacycles.

Impedance measurements on a double-balanced modulator designed
to translate a twelve-channel group of frequencies for cable carrier
systems from a band at 60 to 108 kilocycles to a 12- to 60-kilocycle
band are shown in Fig. 5 for several resistance terminations. Absence
of any impedance irregularities with frequency is apparent. Also, the
tendency is shown for the modulator impedance to become less
reactive with lower resistance terminations.

Inasmuch as copper oxide discs are available in sizes from 1/16 inch
to more than an inch in diameter, a wide range of circuit impedances
are possible varying from only a few ohms to thousands of ohms.
Large area discs roughly are equivalent to small area discs in parallel.
Thus by usiftg a disc of n times the area of a small one or n of the
small ones in parallel, the best circuit impedance becomes 1/wth at
the same carrier voltage. Either discs in series or ones of smaller
diameter enable the impedance to be raised in a corresponding manner.
The lower impedance and greater energy dissipations of larger discs, or
paralleled smaller ones at the same carrier voltage, obviously allow
greater input signal energies before the signal impedance and loss begin
to vary with the signal, and overload distortion appears. Similarly
series stacks of discs, or series-parallel combinations, offer wide choice
in both the signal levels that can be satisfactorily modulated and in the
impedance levels. Usually r.m.s. carrier voltages across individual
discs in the conducting direction will best be made somewhere between
3/10 and 3/4 volts.

The impedances of the connected circuits at the modulation product
frequencies react back on the signal impedances in a way similar to
the way that the two terminating impedances of a four-terminal linear
network react on each other. In the case of the copper oxide modu-

324

BELL SYSTEM TECHNICAL JOURNAL

lator a reaction from some modulation product back into the signal
impedance is less and less as the product becomes of higher order, or as
the circuit loss to it becomes greater. Where the impedances of the
connected circuits have bothersome interactions with the copper
oxide impedance either at the signal frequencies or the lower loss
modulation products, resistance pad separation is usually the simplest
solution if the increased loss can be tolerated.

400

350

300

250

200

150

50

-50

uj-lOO
O

-200

-250

OUTPUT RESISTANCE

TERMINATION IN

OHMS =

^

800

425

230

■ ■

230

425

^

^...^

800

'

60

65 70 75 80 85 90 95

INPUT FREQUENCY IN KILOCYCLES PER SECOND

100

105

Fig. 5 — Impedance of a representative double-balanced modulator.

Energy losses in copper oxide modulators between signal input and
single sideband signal output have been found to be no greater than
8 or 9 db even at frequencies of 3 or 4 megacycles. At lower fre-
quencies 5 or 6 db losses are normal, but losses as low as 2 db have been

COPPER OXIDE MODULATORS IN CARRIER SYSTEMS 325

obtained under less practical operating conditions. Experimental loss
measurements are shown in Fig. 6 for a double-balanced modulator
using single 3/16 inch diameter discs in each bridge arm. This
modulator was designed to simultaneously modulate sixty speech
channels occupying a 240,000-cycle band width. The modulator loss,
like the impedance, depends on the impedance terminations of the
modulator at all the modulation product frequencies as well as on
the internal losses of the modulator. Short circuit,. open circuit, or
reactive terminations at the unwanted frequencies, permit energy
losses only through reflections at the signal circuit junctions to the
modulator or within the modulator. With proper terminations and
loss-free copper oxide, 100 per cent efficiency frequency translations
are theoretically possible. In a practical case, a larger carrier ampli-
tude results in a smaller percentage of the time in which the rectifier

9

CARRIER 3000 KC

• —

-^

-^

—

■—

^.

fi

■■■^~

24

40

2480

2520

2560

2600

2640

2680 2720

7
6

-

CARRIER

1 ^

1300 KC

'

.^^

740 780 820 860 900 940 980 1020

FREQUENCY OF LOWER SIDEBAND OUTPUT IN KILOCYCLES PER SECOND

Fig. 6 — Loss in a double-balanced group modulator for coaxial systems.

elements have impedances that are comparable to the connected
circuits and that are neither blocking nor conducting. Signal energies
are lost in this time interval, so a higher efficiency modulator results.
The time spent on the intermediate resistance parts of the rectifier
characteristic can be further reduced by introducing harmonics into
the carrier wave, so that a square type of wave results. The resistance
of the rectifier is abruptly switched back and forth between blocking
and conducting values in this manner. When the connected circuit
impedances at the unwanted frequencies are very high or low, best
efficiencies result when transmission between the signal circuits is
blocked most of the time. Thus in a circuit like that of Fig, 2.(a) when
the filters are high impedance at the unwanted products, highest
efficiency results when the copper oxide is a low resistance short circuit
for the major portion of the carrier cycle. In Fig. 2(b) an open circuit
is desirable most of the time.

326 BELL SYSTEM TECHNICAL JOURNAL

Linear Modulator Theory

The analytical studies that have been of most benefit in the develop-
ment of copper oxide modulators have made use of a variable resistance
characteristic controlled by the carrier. This assumption has made it
possible to investigate modulator performance ^ for a wide variety of
characteristics under a great many operating conditions. Copper
oxide modulator performance in particular cases as well as the effects
of the circuit elements on this performance can readily be inferred
from the data at hand about these idealized modulators.

In limited space it is not possible to discuss the varieties of re-
sistance modulators that have been analyzed. However, certain view-
points will be discussed that have been very useful not only for obtain-
ing solutions for some of the hypothetical cases, but also in supple-
menting laboratory experiments on actual modulators.

All of these analytical studies have assumed a signal sufficiently
small compared to the carrier, that it can be varied in magnitude
without noticeable changes in the signal impedance or in the linearity
between input and output signal amplitudes. This is in agreement
with design procedure, as the circuit impedances and losses are deter-
mined on such a linear basis.

Superposition Principle

All of the modulator circuits with which we have been dealing,
though composed of non-linear elements, have been resolved into the
equivalent of linear systems by virtue of using a large carrier and small
signal amplitude. We may simultaneously apply any number of
signal frequencies, but all have negligible efTect on the periodic changing
of the non-linear element resistance by the carrier. These frequencies
may be modulation product voltages, some applied at the output
terminals and some at the input terminals, but in all cases, even though
frequencies may coincide, it can be shown that the principle of super-
position will hold without interaction between the applied forces and
the responses. This permits a great simplification in the mathe-
matical approach to modulator analysis, because the modulation
product or signal voltages can be applied one at a time and the current
responses summed. The voltage-current ratios at each frequency can
then be replaced by equivalent impedances.

Any non-linear resistance like copper oxide will have a current-
voltage characteristic that can be expressed as accurately as de-

^ A physical picture of modulator performance in terms of linear networks is
developed in a paper published in the January 1939 Bell System Technical Journal,
"Equivalent Modulator Circuits" by E. Peterson and L. W. Hussey.

COPPER OXIDE MODULATORS IN CARRIER SYSTEMS 327

sired by

i = aie + a^e^ + • • • + «„«". (1)

If a carrier and signal voltage are applied to this non-linear element,
each term beyond the first will independently produce currents of
new frequencies composed of the intermodulation products of these
two voltages. If in turn the external impedances at these new fre-
quencies are not zero, new voltages will appear across the non-linear
element to produce still more new frequencies. In this case the
simplest consideration is to minimize the number of voltages by
presenting zero impedance to the modulation products. If the carrier
voltage is C cos ct and the input signal voltage 5 cos st, the current
flow in the wth term is

i = a„{C cos ct -\- S cos st)". (2)

In the binomial expansion of this expression it is obvious that
linear response to the signal and freedom from distortion result when
the ratio of carrier to signal is made sufficiently large so that only
the first two terms are important.

i « a„[(C cos c/)" + n{C cos ct)"-^-S cos 5/]. (3)

The first term in equation (3) is the current flow at d-c. and har-
monics of the carrier; it has no effect on the input signal and output
signal except in so far as impedance termination presented across the
non-linear element at the carrier harmonic frequencies may alter the
carrier voltage harmonic content. The signal input current and
the signal output current, as well as the unwanted modulation products
of the signal, result from the second term. The even values of n
produce the even order sidebands, second order being the output
signal, while the odd values of n produce the input signal current and
the odd order sidebands. These currents can be evaluated from

2 , ^-- 2

COS" ^ = -:r;r + L -^r;:iT ^^^ ^^>
in which iiC"_^ is equal to the combination of n things taken — - — at

2

r n — m . , ,. , r^ — ^ 'j. 1

a time for — - — mtegral and is equal to zero tor — r — non-integral.

328 BELL SYSTEM TECHNICAL JOURNAL

The signal input current is

is = —2^ ^"~'^ cos St, ' (4)

while the second order output signal sideband is

ic±s = ^„_t' C"-'S cos {c ± 5)/. (5)

Similarly, if the output signal voltage at second order sideband
frequency (c ± s) had been applied along with the carrier in place of
the input signal, and of an equal amplitude, then the following currents
of the output and input signal frequencies would result:

ic±s = 2„_/ C"-'S cos {c ± s)t, (6)

n-l

GnflK

n—2
2

i. = ^^^C--'S COS St. (7)

If both signal input and output frequency voltages are applied simul-
taneously, equation (3) then becomes

i « an[(C cos c/)" + n{C cos ct)''~^-S cos st

+ n(C cos c/)"-i-5 cos (c ± 5)/]. (8)

The current responses obviously are the sum of the separate responses
from independent application of the two frequencies. Even if a
complex array of terminating impedances are supplied so that voltages
appear across the non-linear element at all the modulation product
frequencies, each new voltage will individually produce its own current
response, quite independently of the responses that are being produced
by the other voltages. It can readily be seen then that superposition
does not depend on any assumptions about what the terminating
impedances may be.

Reciprocal Theorem

Equations (5) and (7) show that the sideband response to an input
signal voltage is exactly equal in magnitude to the input signal re-
sponse to the same amplitude sideband voltage. It can readily be seen
that any two modulation products also bear such a reciprocal relation-

COPPER OXIDE MODULATORS IN CARRIER SYSTEMS 329

ship between their voltages and currents, as a result of using the same
amplitude and frequency of carrier harmonic multiplier of their
respective voltages to modulate between the two frequency positions.
Although reciprocity has been proved valid here only for short-circuit
terminations at the modulation product frequencies, it can also be
proved under numerous other conditions of circuit operation. It
seems that, regardless of modulator complexity of impedance termina-
tions or frequency loss effects, the reciprocal theorem is a necessary
attribute of such a linear and bilateral system in which there are no internal
energy sources. Two-way systems in which an aniplifier for example,
is included as an internal energy source in one or both directions will,
of course, violate the reciprocal theorem if the gains in the two direc-
tions are different. This arrangement is, however, both bilateral and
linear.

Complete Performance Criteria

The laws for transmission between a signal input frequency and a
•signal output frequency can be completely specified from open and
short circuit impedance measurements at the signal input and output
frequencies, regardless of the complexity of the modulator. (From
such measurements optimum impedance terminations can even be
determined for linear-bilateral systems with internal energy sources.)

The four-terminal network of Fig. 7 is assumed to represent a modu-

Rp

2
— ^>-

Q

Fig. 7 — Four terminal network equivalent of a linear modulator.

lator with a large carrier amplitude and having small signal voltage P
of frequency p applied at the input terminals 1-2 at the left. Current
of the output signal frequency q flows out of the terminals 3-4 into
the impedance Rq. The generator P is assumed to have zero internal
impedance at its own frequency. Impedance terminations at the 1-2
and 3-4 terminals at all other modulation product frequencies are
perfectly general; whatever they are in a particular case, it is assumed
that they are undisturbed as the terminations of the input and output
at the signal frequencies are varied between open circuit and short
circuit. The following symbols are used for the impedances looking
into the modulator at the input terminals at input signal frequency p
and at the output terminals at signal output frequency q.

330 BELL SYSTEM TECHNICAL JOURNAL

Zpo = impedance at p for open circuit at q\
50 — q p\

Zp> = " " p " short " " g;

Zq, = " " q " " " " p;

Rq = impedance termination at frequency q;
Rp = impedance of modulator at frequency p with i?g at 3-4 terminals

for frequency q;
Ka = transfer admittance between voltage at frequency p applied

at the 1-2 terminals and short-circuit current at frequency q

flowing from 3-4 terminals;
Kb = transfer admittance between voltage applied at 3-4 terminals

at frequency q and short-circuit current at frequency p

flowing from 1-2 terminals.
For Rq first short-circuited

U^ = PKa, (9)

ip, = /- • (10;

^ JDS

If the short circuit on Rg is removed, the following two additional
currents will flow due to superposition of a new voltage — iqR,

and

in =

— iqRq
Zj qs

ip2 = -

- iqRgKb,

iq =

-- Ui + i

PKa
Q2 D »

1+^
^ qa

ip

= ip.

+ *'P2 =

P PKaKbR q
^-' OS

(11)

(12)
(13)

(14)

The efficiency of the frequency translation, measured by the ratio
of the power delivered to i?, to the power into terminals 1-2, is

i^r-

i -R . . .

"^ ipP ~ J_ _ KaKbR, ' ^ ^

P' 1 _1_ "^

7

^ as

COPPER OXIDE MODULATORS IN CARRIER SYSTEMS 331
which is maximum for

Rq= ■ ^'' (16)

"V/l — KaKhZpsZqs

The maximum efficiency is then

K "^7 7

-t»-a ^-^ ps^^ qa

''7max. —

(1 + Vl - KaKj^paZ^sf

When equation (16) is substituted in (14) it is found that

(17)

R,=?-= ^"^ =. (18)

tp Vl — KaKbZpsZ qs

In order to evaluate KaKb, open circuit impedance measurements
must also be made. By superposition methods like those used in
obtaining equations (11) and (12) it can readily be shown that

(19)
(20)

(21)
(22)

^ qa

and KaKb can be determined from any three of the open-short measure-
ments by using (21) and (22). It follows that

Z

KaKbZpsZ qa = 1 — -^— • (23)

Upon substitution in (16) and (18) it is found that

1

Zpo

1

Zps

— KaKbZqa,

1

Z qO

1

^ qa

— KaKbZ ps.

From these two

equations,

it follows that

Z, pa

Zp^

Z qa

Z qO '

1 1

KaKb =

^ ps Z pO

Rq = <Zq^q, . (24)

and

Rp = ^ZpoZpa (25)

when 3-4 is terminated in i?g for maximum efficiency.

Open and short-circuit measurements enable us to compute the
optimum efficiency from equation (17) only if the transfer admittance

332

BELL SYSTEM TECHNICAL JOURNAL

Ka is known. If the reciprocal theorem holds, Ka = Kb and Ka can
be determined from (23). The optimum efficiency is then

1

'Jmax.

1 +

(26)

If the input signal generator has an internal impedance, most efficient
energy delivery to the modulator will, of course, result if this im-
pedance is made equal to Rp.

Equivalent T, -k and bridge networks can obviously be drawn from
the open and short-circuit measurements as in four-terminal linear
networks.

It appears that even in a plate or grid circuit modulator the formulae
of equations (24), (25) and (26) can be applied to the plate or grid circuit,
respectively, where the signals are small compared to the carrier,
inasmuch as the modulating parts of these circuits are linear and
bilateral with no internal energy sources.

Double-Balanced or Reversing-Switch Modulator ^

A number of interesting conclusions can be reached about copper
oxide modulators by assuming that the copper oxide acts like a switch
having a low-resistance value when the positive half-cycle of the
carrier voltage is across the disc and a high-resistance value during the
negative half-cycle. The circuits of Fig. 2(c), 2(d) or 2(e) can then be
represented by the equivalent circuit of Fig. 8.

AA^-

O

(^

Vo

POSITIVE
HALF CYCLE

NEGATIVE
HALF CYCLE

-wv

Fig. 8 — Equivalent circuit of a double balanced modulator.
2 Referred to in the German literature as the "ring modulator."

COPPER OXIDE MODULATORS IN CARRIER SYSTEMS 333

The input signal generator Fo is applied out of an input circuit
impedance Za, and the output signal is delivered to the output circuit
impedance Zh. Both Za and Zb in general will be functions of fre-
quency.

\i Za = Zb = R at all frequencies it can easily be shown that the
circuit will operate most efficiently for

R = <RrRf. (27)

The signal input current will then be the only frequency in ia'.

From the properties of lattice networks it follows that

1
+ 1

''^^'^^ -^^^^' ^^^^

\Rr

\Rs

where

Letting

and

m =

+ 1 for positive half-cycle of carrier
— 1 " negative '

(I K

4 / 1 1

/(/) = — I cos ct — - cos 2>ct + 7 cos Set-

TV \ 6 J

k = ^ , (30)

S+1

V,k 4

cos ct — - COS 3/ + Y cos 5c/-

The magnitude of the single-sideband output current is

and the efficiency

(31)

H^ = ^.-=-'J^ (32)

V=-,k\ {^i)

In addition currents flow in the output circuit at both sidebands
of all odd harmonics of the carrier frequency. These can be repre-

334

BELL SYSTEM TECHNICAL JOURNAL

sented by ^3+, iz-, 4+, etc. No currents flow at the sideband fre-
quencies of the even harmonics of the carrier, «2+. ^2-, • • ■ •

If Fo should be replaced by an equal amplitude generator at any of
the sideband frequencies, Fi+, F2_, etc., then the input current would
in any case be

Y}± T =i^
2R ' '" 2R '

Ii+ =

etc.

The correspondence between the magnitudes of these entering currents
and the magnitudes of the output currents at the modulation product
frequencies are shown in Table I. Reciprocal relations between the

TABLE I

Correspondence between Currents Entering and Leaving a
Reversing-Switch Modulator

Corresponding Components on Other Side of the Modulator

Component on

One Side of

Modulator

2k*

2k

2k

2k

IT

3x

Sir

77r

h

/._ I1+

Iz- I3+

h- h+

h-

h+ ■

h-

/o h-

I2+ I4-

Ii+ /e-

h +

Is- ■

/i+

/o I2+

h- I4+

U- h+

h-

h+ ■

h-

h- h-

/.+ h-

h+ Il-

h +

h- ■

h+

I\+ I3+

h- h+

ls- I7+

h-

/9+ •

h-

/2- /4-

h h-

h+ h-

h^

/.o- •

h^

h+ U^

lo 1^+

I2- Is+

U-

/10+

U-

h- h-

L- Ii-

/.+ I9-

h+

/..- •

/4 +

I3+ 1^+

/.+ h^

h- h+

h-

/n+ •

/6-

h- h-

h- h-

lo Iio-

h+

lu- ■

/5+

h+ 1^+

I2+ Is+

lo I\o+

I2-

I12+

h-

h- I7-

h- h-

h- In-

/.+

In- ■

/6+

Ib+ Ii+

h+ h+

I\+ Iu+

/l-

/l3+ •

h-

h- Is-

li- Iio-

I2- I\2-

/o

/.4_ •

I1 +

Ii+ Is+

Ii+ I10+

I2+ I12 +

lo

/l4+

Is-

h- h-

Is- lu-

I3- Iiz-

/l-

/16- •

Note : A current of the frequency indicated in the first column will be modulated
to produce the components written on the same line, the magnitudes of which are
the magnitude of the generating current multipled by the factors at the top of the
columns.

_W

1

*k = -5-4=4

V

+ 1

driving voltage at one frequency and the output current at another
frequency are obvious.

COPPER OXIDE MODULATORS IN CARRIER SYSTEMS 335

TABLE II

Performance of Double-Balanced Modulator (Ideal Reversing Switch) for
Various Input and Output Terminations

Modulator Terminations

Modulator Impedance

Modulator L
Efficienc

OSS or
y

t Circuit

Output Circuit

Input
Signal

Output
Signal

Inpi

Voltage Ratio

Signal

Others

Signal

Others

db

R

R

R

R

R

R

2

IT

3.9

R

any value

R

R

R

2
w

3.9

R

R

R

0

2R

7r2 - 2

R

2

jr

3.9

R

R

R

=o

(tt^ - 2)R
2

R

2

3.9

R

(7r2 - 2)R
2

(tt^- - 2)R
2

0

R

TT^rTT^ - 2)R

6r - 16

TT

-)

V2(7r-' - 2)

R

2R

TT^ - 2

2R

IT- - 2

00

R

(67r= - 16)/?
tt'-'Itt^ - 2)

^

7

V2(7r2 _ 2)

R

0

R

0

0

0

00

R

CC

R

00

00

00

CO

R

0

R

00

4

v^-

47r
4 + Tr^

.85

R

QO

R

0

Xr

p

47r

4 + TT^

.85

R

0

Tr-

00

R

>

1

0

R

oc

T'^

0

R

?^

1

0

R.

Rs'

Rr

Rr'

Zi*

z *

■Co

n*

'Zi

Zo =

7r2(/?r + i?/) - 4(/?r - /?r') '

w^R/(R, + /?/) + 4r/?.. - /?./)/?/
ttHRs + Rr') - 4(R, - /?./)

47rf/?/ + R/)^JRJ<r

7r-(/?, + /?/j(/?. + /?.,') - 4(/?. - Rr'){Rs - R/)

336

BELL SYSTEM TECHNICAL JOURNAL

Generalized Reflection Theory

Superposition permits us to apply simultaneously driving forces of
the frequencies tabulated above in any relative phases and ampli-
tudes that we care to choose on either side of the modulator. If
simultaneously /o is applied on one side of the modulator and
Z^^- R

is applied to the other set of modulator terminals,

2k

v Zi+ + K

then the total current at the output terminals at the sideband fre-
quency (1+) will be

(/h-)

2k

1 -

R

Zi+-\-R

(34)

This is equivalent to saying that a resistance R at the sideband
frequency (1 + ) has been connected to the output terminals of the
modulator and in this resistance is an internal zero impedance generator
of voltage

2k Zi+ - R

2R(h+)

Zx+ + R

(35)

This resistance R at sideband frequency (1 +) must be infinite at
all other frequencies, if in parallel we assume another resistance of R
at all frequencies except (1 +) at which it is infinite.

The equivalent impedance at frequency (1 +) at the modulator
terminals connected to the (1 +) resistance with its internal gen-
erator, is the ratio of (1 +) voltage to (1 +) current.

IT TT

A+-

^1+

- R'

+ R

R

2k

1 -

Zi+ - /? 1

Zl+ + i? J

which reduces to

Z = Zi

(36)

(37)

Zi+ may be real or complex as it involves only the amplitude and
phase of the superimposed voltage of upper sideband frequency. It
can readily be seen then that the solution for current flow at this
frequency of equation (34) is identical with the case of linear networks
in which the current is expressed as that flowing in a matched circuit
modified by a reflection factor. Reflection from any modulation
product frequency can be similarly treated.

COPPER OXIDE MODULATORS IN CARRIER SYSTEMS 337

A number of cases have been worked out of efficiencies and im-
pedances in such modulators for transmission betw een an input signal
and a single-sideband output signal. The modulating element has
been assumed perfect (^ = 1) and the terminations pure resistances.
The results are shown in Table II.

Acknowledgments

The writer wishes to acknowledge his appreciation of the assistance
of numerous associates in the Bell Telephone Laboratories in arriving
at the views on copper oxide modulator performance recorded in this
paper. In particular, acknowledgment is due to Mr. R. W. Chesnut,
Dr. E. Peterson and Dr. G. R. Stibitz.

Some Applications of the Type "J'^ Carrier System*

By L. C. STARBIRD and J. D. MATfflS

Previous papers before the American Institute of Electrical
Engineers describe the development of a twelve-channel type J
Carrier System. This paper discusses some of the practical
problems encountered in extending the circuit capacity of existing
open-wire lines by the use of this carrier system.

The first systems of this type were placed in commercial opera-
tion late in 1938. One of these systems is discussed in detail from
the standpoint of obtaining satisfactory operation with the most
economical arrangement of new and existing facilities.

A TWELVE-CHANNEL carrier telephone system for open-wire
-*- ^ lines was described before the American Institute of Electrical
Engineers early this year/ and a discussion of the requirements of hne
facilities for its operation is being presented.^ Since the first three
systems to be placed in commercial operation are located in Texas, it
seems appropriate to present to the Southwest District Convention the
major problems arising from the practical application of this type
system on existing open-wire plant.

In 1935 it became apparent that existing open-wire facilities on some
of the major toll lines in Texas would soon be exhausted. In the case
of the Dallas-Houston, Dallas-San Antonio, and Dallas-Longview lines,
current growth and requirements for the future indicated that while a
toll cable would probably have to be provided ultimately, the develop-
ment of the open-wire twelve-channel J carrier system makes available
an arrangement for obtaining a large number of additional circuits
over the existing lines to provide for the immediate requirements and
also permit postponement of more costly relief measures for a number
of years.

The type J system operates in a frequency range above that of the
three-channel type C carrier system and can be superposed on the same
conductors with the type C, thereby providing a total of sixteen
circuits from one pair of conductors. However, conductors suitable

* Presented April 18. 1939 before the A.I.E.E. in Hcuston. Texas.

^ "A Twelv^e-Channel Carrier Telephone Svstem for Open Wire Lines," by B. W.
Kendall and H. A. Affel, Winter Convention, A.I.E.E., 1939. Bell System Technical
Journal, Januarv 1939.

2 "Line Problems in the Development of the Twelve-Channel Open-Wire Carrier
System," by L. M. Ilgenfritz, R. N. Hunter, and A. L. Whitman, District Convention,
A.I.E.E., Houston, 1939. This issue of the Bell System Technical Journal.

338

SOME APPLICATIONS OF TYPE "J" CARRIER SYSTEM 339

for type C carrier operation are not necessarily satisfactory for the
operation of the new system.

The three Hnes under consideration were practically of the same
construction, being twelve-inch phantomed lines originally built for
voice frequency circuits only and later modified for the application of
type C carrier systems. Over lines of this type, it is practicable to
operate a single type J system without any material change in the line
wire because no crosstalk considerations are involved, although it is
necessary to select by transmission measurement pairs which are free
from absorption effects. Where more than one system is required a
transposition arrangement has been designed for use with line con-
ductors of a non-phantomed pair spaced six inches apart and thirty
inches between conductors of horizontally adjacent pairs. This design
can be used either for new wire or for existing wire retransposed, and
can be applied without regard to the existing phantomed transposition
design, thereby permitting respacing and retransposing any portion of
the existing wire, a phantom group at a time if desired.

Advance Engineering

With these operating limitations a review of the circuit requirements
established a plan to place a J carrier system on one of the phantom
groups of the Dallas-Longview line during 1938. This system would
not only provide sufficient circuits to meet the additional requirements
but would furnish sufficient spare circuits to release one phantom
group of twelve-inch wire for respacing and retransposing. This plan
was not applicable to the Dallas-Houston and Dallas-San Antonio
lines since circuit relief was required for the 1937 business, and the J
carrier system would not be available until 1938. These lines each
consisted of five crossarms of 104 mil wire over the greater portion of
their length. An inspection showed that, although the poles were of
sufficient strength to support additional crossarms, it would be
difficult to maintain the necessary wire clearance with an additional
crossarm below the existing wire and also that new wire so placed
would be susceptible to interference from possible breaks in the wire
above.

The solution of this problem was the addition of a crossarm two feet
above the others on a simple extension fixture. This fixture shown in
Fig. 1 consists of a four-inch steel "H" beam fastened to the pole by
the through bolts which also support the two upper crossarms. By
placing four pairs of six-inch spaced conductors on the new crossarm
and by using four type C carrier systems, sixteen additional circuits
were obtained to furnish the circuit relief for 1937 and, in addition to

340

BELL SYSTEM TECHNICAL JOURNAL

4,

_ n..

a

d

a

a

%

1
t

-»

9

Fig. 1 — Typicarpole with extension fixture.

SOME APPLICATIONS OF TYPE "J" CARRIER SYSTEM 341

the immediate relief, four suitable J carrier paths were provided of
which one on each line was needed in 1938. Figure 2 is a typical pole
head and shows how the ultimate circuit capacity of this open-wire
plant has been expanded from 69 to 133 circuits by the addition of one
crossarm and eight conductors. The use of 128-mil wire instead of
104-mil wire provides greater strength and, considering the particular
location, reduces the probability of interrupting sixteen circuits by a
single wire break or other physical interference.

12 J
3 c

12 J

3 C

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aa

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/—~ I PX — ^ r~

"Hi sB' "^a'l sQ' ^a

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? ;;-

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^a- -alia- -QJ Ja;

/ 1 PX \

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Bisa aisB

, 1 PX ,

I -Q!id-%lg£

.

LEGEND

_^ P = PHYSICAL CIRCUIT

^^ PX= PHANTOM CIRCUIT

S ' SIDE CIRCUIT

C = "C"CARRIER CIRCUIT

0 = "D"CARRIER CIRCUIT

J = "j"CARRIER CIRCUIT

Fig. 2 — Pole head diagram showing circuit capacity of the Dallas-Houston and

Dallas-San Antonio lines.

The program of placing three type J carrier systems in service in
Texas during 1938 was established. Figure 3 is a map of a portion of
the state showing the routes of the lines and the principal cities along
the routes. Since the length and attenuation of each of these lines are
such that the carrier systems can not operate without intermediate
amplification, it was necessary that the number and locations of
repeater stations be determined.

Typical System

The layout of a particular system is largely controlled by available
repeater gain, existing entrance cables, line attenuation under normal

342

BELL SYSTEM TECHNICAL JOURNAL

LEGEND

@ =TERMINAL STATION
(J) --REPEATER STATION

Fig. 3 — Routes of toll lines on which the J carrier systems are applied.

SOME APPLICATIONS OF TYPE "J" CARRIER SYSTEM 343

and adverse weather conditions, location and availability of existing
telephone buildings, and availability of commercial power for new
buildings. Line attenuation is increased greatly by deposits of ice on
the wire during sleet conditions. Although data are available regarding
the frequency of large deposits of ice, there is very little information as
to the amounts or frequency of occurrence of small deposits. Under
normal wet weather conditions the maximum attenuation of six-inch
spaced 128-mil facilities at 140 kilocycles is 0.35 db per mile.

On the Dallas-San Antonio line the facilities available consisted of
286 miles of six-inch spaced 128-mil copper wire and 42,000 feet of
16-gauge non-loaded paper insulated cable. Using repeaters having a
maximum amplification of 45 db in each direction of transmission, the
provision of two intermediate repeaters would provide sufficient gain
to take care of the wet weather conditions with no extra margin ; three
repeaters would provide 45 db margin and four would provide 90 db
margin for the overall system. Considering the location of this line
and the small probability of obtaining large deposits of ice in ac-
cordance with past experience, it was decided to select tentatively three
intermediate repeater stations which would provide sufficient gain to
take care of attenuation up to about 0.5 db per mile as compared to the
wet weather value of 0.35 db per mile.

For type C operation over this line, only one type C carrier repeater
point is required, and it is at Austin. Considering the availability of
power equipment and operating personnel and the possibility of future
J carrier terminals being located at Austin, it is desirable that this be
one of the repeater points on the J system. A division of the attenu-
ation of the facilities north of Austin indicated that the other stations
should be in the vicinity of Temple and Milford.

At these repeater stations amplification is needed only on the type J
system and the other circuits on the line pass through these stations
without amplification. Under these conditions energy may be
transferred from the output of one type J repeater to the input of the
same repeater or to the input of a repeater on another J system via
crosstalk paths involving the wires which are not used for type J
systems. The effect of this transfer of energy is accentuated by the
fact that there is a large difference in transmission level between the
output of one type J repeater and the input of the same or another
repeater. In order to minimize these effects it is necessary that all
wires on the line be given special treatment, including a gap in the toll
line, longitudinal choke coils in all wires at terminal poles and crosstalk
suppression filters in the non-J pairs in the repeater station itself. In
selecting locations for repeater stations, consideration must also be

344 BELL SYSTEM TECHNICAL JOURNAL

given to the possible coupling between type J systems by interaction
paths involving other conductors adjacent to the toll line.

Before definite selection of repeater station locations may be made,
it is necessary that each repeater section be checked in detail and in
this check the entrance cable arrangement may be controlling. The
newly developed spacer insulated spiral-four cable, either loaded or
non-loaded, or non-loaded pairs of the conventional paper insulated
cable may be used between the open wire and equipment. Generally
the existing voice and C carrier circuits use loaded entrance cable pairs
and in most cases a change to non-loaded facilities would require
extensive rearrangements in these circuits. In order to use non-loaded
pairs for the J carrier and leave the C carrier and voice on loaded
facilities, filters are placed at the terminal pole to separate the J
carrier frequencies from the C and voice frequencies at that point. A
limitation on the use of existing cable is that suitable pairs must be
selected by crosstalk measurements and balanced at 140 kilocycles to
meet the requirements of the system. The paper insulated conductors
have the largest attenuation of any of these facilities, and the loaded
spiral-four the least. The various entrance arrangements from the
open wire to the office equipment are described in more detail else-
where.^ The choice of the facility used in any particular case will
depend upon the resultant overall economy.

The large number of non-loaded pairs in the existing 1 .6 mile entrance
cable at San Antonio indicated that sufficient pairs could be selected
which would be satisfactory from the crosstalk standpoint for J carrier
operation. Six pairs were subsequently selected and balanced.

At Austin a single toll entrance cable, one mile in length, with two
complements, terminates the line from the two directions. Although
the two complements are separated by a layer shield, this cable is not
suitable from a crosstalk standpoint for operation of the J carrier in
and out of the office; therefore, at least one additional cable is required
from the central office to the toll line. For this purpose a new non-
loaded spiral-four entrance cable was indicated for the type J system
with the type C and voice circuits continuing to use the existing cable.
The separation of the type J circuits from the non-J circuits on the
same pairs is accomplished by filters which are located in a small
building at the junction of the toll line and the entrance cables. The
use of a single entrance cable for the non-J wire in both directions on
the telephone line indicated that it might be necessary in the future to
use crosstalk suppression filters at this point. Accordingly, the filter
hut was made large enough to include future crosstalk suppression

^ Loc. cit.

SOME APPLICATIONS OF TYPE "J" CARRIER SYSTEM 345

filters if required as well as the line filters which separate the type J
from the non-J circuits.

A repeater station at Temple could have been located in the existing
central ofiice or could be located in a separate building in or near the
city. In either case a new power plant was needed since the existing
plant could not be economically modified to serve the J carrier repeaters.
The telephone line is continuous through the city, only those w^res
used for Temple circuits being terminated in the ofiice through one
entrance cable 0.6 mile in length. This cable is not suitable for J
operation in both directions, which would require one additional cable
if the repeaters were located in the central office. Numerous signal
and supply lines in proximity with the telephone line within the city
off'ered interaction crosstalk complications. A separate repeater
station near the toll line in or near the city avoids the placing of a long
entrance cable, reduces the overall system attenuation, and eliminates
the problem of interaction crosstalk from paralleling lines. Other
factors including cost showed very little difference between a separate
station and placing the repeaters in the central office. An unattended
station near the toll line was indicated.

A common entrance cable at Dallas terminates the wire on both the
Houston and San Antonio lines, the terminal of the Houston line being
2.9 miles from the central office, and of the San Antonio line one mile
further. This cable previously had been placed in three different
sections, each section having a different make-up, and there was
considerable doubt as to the number of suitable pairs for J operation
that could be obtained. The use of either a loaded or non-loaded
spiral-four cable would not improve attenuation sufficiently to change
the number or materially alter the locations of the repeater stations
from those tentatively selected, but would provide some additional
margin for sleet conditions. The expense of loading the spiral-four
cable, if placed, could not be justified by the improvement in overall
attenuation. Using either non-loaded spiral-four or existing non-
loaded paper insulated conductors requires filters at the open-wire
terminus. With these considerations, it was decided that suitable
pairs would be used in the existing cable until exhausted. Subsequent
crosstalk selection tests have indicated that twelve pairs, six for each
line, are available.

Since there was no suitable central office building at Milford, the
repeater station in that vicinity must of necessity be in a new building
preferably near the toll line. Commercial power is available only near
the town, forcing a tentative location to be selected at the edge of the
city.

3-16

BELL SYSTEM TECHNICAL JOURNAL

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SOME APPLICATIONS OF TYPE "J" CARRIER SYSTEM 347

With these selections of entrance cable facilities and tentative
repeater station locations, the distribution of gain and line loss by
repeater sections is shown in Table I. A satisfactory distribution of
line loss has been obtained and an analysis of these data shows that
further improvement is impracticable. Therefore, the tentative
repeater station locations were adopted.

Figure 4 is a diagram of the major line and equipment parts of the
Dallas-San Antonio lead. The J carrier path is shown by heavy solid
lines, the C and voice on the same wire with the J by light solid lines,
and all other circuits, classed as non-J, by dotted lines. Figures 5 to 8,
inclusive, show in more detail the arrangements at the huts and
repeater stations. The figures for the Dallas Hut and Temple Re-
peater Station are typical, and huts and unattended repeater stations
not shown differ from these only in minor details. It will be noted that
all wire on the toll line is brought through the repeater stations while
only that wire on which J carrier is superposed is routed through the
huts except at Austin where all wire to the north is brought through
the hut to allow the future application of crosstalk suppression filters if
required. For both huts and unattended repeater stations, short
lengths of loaded spiral-four conductors are used from the six-inch
spaced wire at the terminal poles to the equipment in the buildings. A
single continuously adjustable load unit is used for each pair and is
located with the equipment. Paper insulated pairs under the same
cable sheath as the spiral-four conductors are used for the non-J wire.

As previously mentioned, the conditions at Austin were complicated
by a single cable for existing circuits and a new cable for J carrier in
both directions. Figure 9 is a diagram of the existing and new cables
to the filter hut and terminal poles, and Fig. 10 shows the inter-
connection of circuits and equipment used at the filter hut, terminal
poles, and central office.

Terminal and repeater equipment in existing offices is located in
space adjacent to other equipment terminating toll circuits, and makes
use of the common office equipment and power plant. The relation of
the J carrier terminals to the other equipment in the Dallas Toll Office
is shown in Fig. 11.

The new repeater stations and the filter huts are arranged for
unattended operation. The equipment in the filter huts is such that no
adjustment or attention is required other than periodic inspections.
In the unattended repeater stations the power supply equipment is
automatic in its operation. Although periodic maintenance attention
is necessary, it is desirable that any abnormal condition be recognized
as soon as practicable and a system of alarms has been provided from
each unattended station to an adjacent main repeater or terminal

348

BELL SYSTEM TECHNICAL JOURNAL

C CARRIER a V.F
FROM NON-J WIRE

EXISTING TOLL
ENTRANCE CABLE

TERMINAL POLE

OPEN WIRE SECTION

CROSSTALK
SUPPRESSION FILTER

NON-J WIRE

C CARRIER a VF.

J TERMINAL

12 CHANNEL UNIT

NEW BRANCH CABLE
TO FILTER HUT

ILTER TO SEPARATE
C a J PATHS

EXISTING TOLL
ENTRANCE CABLE

C CARRIER a V.F.
FROM NON-J WIRE

AUSTIN
CENTRAL OFFICE

J TERMINAL
12 CHANNEL UNIT
C- CARRIER a VF
ON 6" WIRE

SAN ANTONIO
TOLL OFFICE

Fig. 4 — Arrangement of facilities for a typical J carrier system.

SOME APPLICATIONS OF TYPE "J'.' CARRIER SYSTEM 349

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BELL SYSTEM TECHNICAL JOURNAL

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SOME APPLICATIONS OF TYPE "J" CARRIER SYSTEM 351

352

BELL SYSTEM TECHNICAL JOURNAL

■///

Fig. 8— iongitudinal choke coils and protectors on terminal pole at unattended

repeater station.

SOME APPLICATIONS OF TYPE "J" CARRIER SYSTEM 353

office. This alarm has been arranged to operate by direct current over
one conductor between offices without interfering with existing tele-
phone circuits but at the expense of one DC telegraph path. For fuse
failure, rectifier failure, power off, power restored, high-low voltage,
high-low temperature, fire, burglary, pilot channel failure, and end of
pilot channel control, alarms are sent and identified. A questionable
alarm may be rechecked from the attended office.

P\ CABLE TO
OFFICE

SP. 4 CABLE

TO OFFICE

NORTH -

TERMINAL

POLE

legend:
sr 4 'spiral four

P.I. « FttPER INSULATED

Fig. 9 — Cable arrangement at Austin.

Special Problems

Some of the problems encouRtered in connection with the other two
systems may be of interest. At Corsicana, a repeater point on the
Dallas-Houston system, a filter hut was used on only one side of the
repeater station. The situation which led to this arrangement is that
an intermediate cable in the Dallas-Houston line extends 0.2 mile
north and 0.5 mile south from the local central office. As it is
necessary that the J system operate through this entrance cable and
since space was available in the local central office building, repeater
equipment similar to that installed in unattended buildings was placed
in one room in the office.

The section of cable north of the central office terminates on a corner
in a business district with all adjacent property occupied by buildings,
making it more economical to use loaded spiral-four cable to this
location than to extend the existing cable to an available site and
provide the necessary filter hut and equipment. For the longer cable,
it was more economical to provide the filter equipment in a hut in
order to use existing facilities. Although this cable terminates in a
fully developed residential area, a site for a filter hut was obtained
adjacent to an alley in the rear of one of the residences facing the
street on which the terminal pole is located.

354

BELL SYSTEM TECHNICAL JOURNAL

The use of non-loaded paper insulated pairs in existing entrance
cables has been mentioned. However, it is in general not practicable
for crosstalk reasons to use all the non-loaded pairs which are available
in one cable, and the selection of pairs suitable for type J operation is
illustrated by a discussion of the methods used on the Dallas cable.

FILTER HUT

LEGEND

P I = PAPER INSULATED
SP 4 = SPIRAL FOUR
TERM= CABLE TERMINAL
t )' CABLE

EXISTING .,.

SHIELDED— <=ttt=
CABLE

Fig. 10- — Circuit connections through Austin.

The Dallas cable is composed of three sections of different make-up.
The section nearest the central ofhce, 1.3 miles long, and the inter-
mediate section, 1.6 miles long, each contained 22 idle non-loaded pairs,
and the third section, one mile long, had only six. The Houston line

SOME APPLICATIONS OF TYPE "J" CARRIER SYSTEM 355

-a

d
3
o

•T3

C

356 BELL SYSTEM TECHNICAL JOURNAL

terminates at the end of the second section, the third section extending
the cable to the San Antonio line.

Since the number of cable pairs to the San Antonio line was limited
to a maximum of six and since the rate of circuit growth over the two
lines was expected to be approximately the same, requiring cable relief
over the entire distance when the branch to the San Antonio line was
exhausted, an objective of six pairs to each line was set up.

Measurements of crosstalk coupling at 140 kilocycles in terms of
inductance and capacitance unbalance were made between each pair
and all other pairs in each section and the pairs rated in their order of
desirability. It is of interest that this required a total of 854 measure-
ments. Those pair combinations whose coupling of the mutual
inductance type was high were rated as the least desirable. This was
done because capacitance balancing was to be used to obtain crosstalk
reduction. The more desirable pairs in the first two sections were
connected through to the six pairs in the last section by cut and try
method until the overall condition was such that all six pairs were
acceptable. By a similar procedure, using the remaining pairs in the
first two sections, six pairs to the Houston line were made acceptable.
No record is available as to the number of tests made in the cut and try
process.

A cable terminal on which balancing condensers were mounted was
installed in the central office building and connected to the selected
pairs. This terminal contained sixty-six sm.all adjustable wire wound
condensers which were connected between each pair and every other
pair. The condensers were adjusted to reduce to a minimum the
capacitance component of the crosstalk coupling.

Buildings

For the three J carrier systems, four new repeater stations and eight
filter huts were needed. The same type of construction was used for
all : Concrete foundation with floor slab above grade, double four-inch
brick walls with rock wool insulation between but with solid brick at
corners and openings, pitched roof with wood framing, fire resistant
wall board ceiling, fire resistant composition shingles, and heat insu-
lation above ceiling and below floor slab.

All of the racks for equipment in the unattended repeater stations are
arranged in three rows with power, repeater, and line equipment in
separate rows within a floor space of 17 feet by 16 feet which will allow
the ultimate installation of six repeaters in each building. The
entrance cables from the terminal poles enter from iron conduit through
the floor and are racked and spliced on the side wall adjacent to the

SOME APPLICATIONS OF TYPE "J" CARRIER SYSTEM 357

line bays. The stubs from the cable terminals at the top of the line
bays are carried overhead to splices on the wall. A ceiling height of
13 feet is maintained above the equipment but reduced along the pitch
of the roof to 11 feet 8 inches at the side walls.

For all huts except that at Austin, three adjacent bays of racks are
needed. With these along one side wall of the hut, the opposite side is
available for splicing the entrance cable. At Austin an ultimate of

Fig. 12 — Unattended repeater station.

nine racks, for filters in both directions of transmission, led to the use of
racks along opposite sides of the hut with a splicing pit under the floor
made accessible by trap doors in the floor between the lines of racks.
In this case, the cable terminals are installed at the bottom of the racks
with their stubs dropped directly through the floor slab into the
splicing pit. The racks in the hut are seven feet high and a ceiling
height of eight feet is used. Figures 12, 13, 14, and 15 are pictures of a
typical repeater station, typical filter hut, and the special hut at
Austin.

358

BELL SYSTEM TECHNICAL JOURNAL

For correct operation of the equipment, temperature limits of 32 to
110 degrees Fahrenheit are desirable. Also, it is necessary that there
be no precipitation of moisture on wiring or equipment. To maintain
the desired conditions, each of the huts is equipped with a 2 kw. blower
type electric heater arranged to operate at low temperature or high
relative humidity, but with operation blocked when the temperature

Fig. 13 — Equipment in unattended repeater station.

reaches 95 degrees. Each new unattended repeater station is equipped
with a 4 kw. heater similarly controlled, and, on account of the heat
dissipation of power plant and vacuum tubes, also has forced ventila-
tion which is operative under conditions of high temperature. The
system of forced ventilation consists of spun glass intake filter, exhaust
fan, electric solenoid controlled shutters at intake and exhaust, and
thermostat, and is interconnected with the office alarms to prevent fan
operation in case of fire.

SOME APPLICATIONS OF TYPE "7" CARRIER SYSTEM 359

a

T3

C

T

360

BELL SYSTEM TECHNICAL JOURNAL

SOME APPLICATIONS OF TYPE "J" CARRIER SYSTEM 361

Conclusion

Upon completion of the buildings, equipment installation, and line
facility rearrangements, adjustments in the equipment were made to
match the lines used. Networks associated with the terminal and
intermediate amplifiers were adjusted so that the amplification for any
particular frequency would be equal to the attenuation at that fre-
quency in the preceding repeater section; the automatic pilot channel
equipment^ compensates for attenuation changes. In repeater sections
containing long toll entrance cables, it was necessary to sacrifice range
of automatic pilot channel control to obtain the best equalization.
However, satisfactory equalization and range of pilot channel control
were obtained in every case.

As mentioned previously, the Dallas-Longview system operates on
twelve-inch spaced phantomed wire. In Fig. 16 the attenuation

36
34

A

32

A

30

4

28

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J

24
22

20

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2
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30 40 50 60 70 80 90 100 110 120 130 140 150

FREQUENCY- KILOCYCLES PER SECOND

Fig. 16 — Attenuation of two twelve-inch spaced phantomed pairs of the Edgewood-
Longview repeater section.

1 Loc. cit.

362

BELL SYSTEM TECHNICAL JOURNAL

characteristics of two possible pairs are shown. The absorption peaks
of pair "A" at 92 and 127 kilocycles are within the frequency range of
channels the fourth and twelfth of the J system and would impair the
quality of those channels if pair "A" were used. Therefore, pair
"B" is used as the regular path for the system. The quality of the
channels obtained from these systems is shown by Fig. 17. Curve

5.0

25

0

-2.5

-5.0

5.0

2.5

0

-2.5

-5.0

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600 1200 1800 2400 3000

FREQUENCY-CYCLES PER SECOND

3600

Fig. 17 — Quality of derived circuits, "A" for typical channel of systems on six-
i ich spaced wire, " B " and " C " for the best and poorest channels of system on twelve-
inch spaced wire.

"A" is representative of that obtained from a system operating over
six-inch spaced wires; "B" and "C" are the best and poorest obtained
from the Dallas-Longview system.

The Dallas-San Antonio, Dallas-Longview, and Dallas-Houston
systems were placed in commercial service in September, October, and
November, 1938, respectively. Experience with these systems is that
the circuits obtained compare favorably with those obtained from any
other facilities in quality and continuity of service, and that a definite
need has been fulfilled in providing an economical method of increasing
the capacity of the existing plant.

Line Problems in the Development of the Twelve-Channel
Open-Wire Carrier System *

By L. M. ILGENFRITZ, R. N. HUNTER, and A. L. WHITMAN

The development of the type J twelve-channel carrier telephone
system for open-wire lines required an increase of nearly 5 to 1 in the
transmission frequency range of the lines. In the provision of
suitable line facilities a number of new problems were encountered
with respect to attenuation, noise and crosstalk. Methods for
meeting these problems and the results obtained are described.

Introduction

ANEW carrier telephone system for open-wire telephone lines
has been described recently.^ This system increases the number
of two-way telephone circuits which can be obtained on a single pair of
wires from the previous maximum of 4 to a total of 16. This has been
achieved by extending the frequency range from a maximum of about
30 kilocycles to more than 140 kilocycles. The exploitation of this new
range of frequencies on open wire has involved the solution of a number
of interesting problems, among which are these :

(1) Not only does the attenuation of an open-wire line under ordi-
nary weather conditions rise substantially with frequency but ex-
tremely large increases in attenuation occur at the higher frequencies
when ice forms on the wires.^ • ^ In spite of these effects a high degree of
stability of transmission has been secured on all channels by the
provision of automatic control of repeater gain and equalization.

(2) New crosstalk problems created by the extension of the fre-
quency range have been solved by the development of transposition
designs with numbers of transpositions not greatly in excess of those
employed for the lower frequency systems. Problems have also
arisen in controlling the crosstalk around the repeaters and in reducing
the effect of impedance departures between the line circuits and the
equipment.

Frequency Allocations

The type J system operates on circuits on which type C carrier
systems were already operating in the frequency range up to about 30
kilocycles. To provide enough frequency separation between the two

* Presented April 18, 1939 before the A. I. E. E., in Houston, Texas.
1 Reference numbers refer to the list of references appearing at the end of the
article.

363

364

BELL SYSTEM TECHNICAL JOURNAL

1
1

— T

^ J
1-

J
J

J
J J

bo

?f

TWELVE-CHANNEL OPEN-WIRE CARRIER SYSTEM 365

systems the lower frequency limit of the J system was set at 36
kilocycles; the necessary frequency space for 12 channels in each
direction set the upper limit at about 140 kilocycles. This range is
split into two parts, one used for transmission in one direction and the
other for the opposite direction. Figure 1 illustrates the relation of the
frequency bands occupied by the type J and type C systems and the
voice-frequency channel. Different "staggered" locations of the
frequency bands are to be employed in order to simplify crosstalk
problems.

Filters are used for separation of the type J from the type C and
lower frequency facilities on the same pair of wjres. This separation is
done by means of a combination of high and low pass filters which
split apart the frequency ranges above and below the band between 30
and 36 kilocycles. To simplify the design of these filters, the low
frequency group of the type J system is transmitted in the same
direction as the high frequency group of the type C system. This
arrangement of transmitting certain frequencies in a particular direc-
tion is generally used throughout the telephone plant in order to avoid
serious crosstalk difficulties. Accordingly, with few exceptions, west to
east transmission or south to north transmission takes place in the
same frequency bands throughout the country and similarly, east to
west or north to south transmission employs the same frequency bands.
These are indicated in Fig. 1.

Line Attenuation

An open-wire pair affords the lowest loss transmission medium of any
conductor employed in the telephone plant. It is, however, peculiarly
subject to the effect of weather, which may cause large and often rapid
changes in the attenuation. In consequence, some form of gain
regulation is required.

Even for carrier systems operating up to 30 kilocycles, manual
regulation is inadequate for the longer systems and automatic devices
have been provided for most systems over 500 miles in length. The
attenuation changes caused by changes in resistance of the wire with
temperature or by changes in the shunt losses when insulators become
wet are much larger at the higher frequencies of the J system, and
therefore, an automatic regulating scheme is required. Tests were
made on open-wire circuits to determine more precisely the charac-
teristics needed for such a regulator. During sleet storms, when wires
are covered with ice, the increases in attenuation are far beyond any
caused by rain. Figure 2 shows increases which may be caused by ice
as compared with the normal dry and wet weather values.

366

BELL SYSTEM TECHNICAL JOURNAL

/

/

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165 ^
6

IL CO
NCH

PPER
SPACI

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MG

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f1

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WEATHER

40 60 80

FREQUENCY- KILOCYCLES

Fig. 2 — Attenuation variation with weather.

The deposits on the wire may be actual ice, or in some cases wet
snow or frost adhering to the wire. Figure 3 shows an example of such
deposits. Theory shows that the increase in attenuation is caused by
energy losses in the ice itself and that leakage across the insulators is
usually a negligible factor.

An extensive survey of the effects of ice has been carried on at
various points throughout the country during the past four years and a

TWELVE-CHANNEL OPEN-WIRE CARRIER SYSTEM

367

large amount of information has been accumulated. These tests have
shown that the shape of the attenuation-frequency characteristic differs
considerably for different ice formations and even if the ice deposit
remains the same for a time, the attenuation-frequency characteristic
may vary with temperature as in Fig. 2. The two upper curves of the
figure were measured at different times during the same storm. There

1

Fig. 3 — Ice on wires and insulators near Amarillo, Texas.

was no apparent change in deposit between the two measurements.
This change in shape of the characteristic, of course, makes the
regulation problem more difficult. In spite of the extreme severity of
ice effects in certain regions, it is expected that satisfactory reliability
will be obtained on type J systems by placing the repeaters sufficiently
close together.

Regulation Problem

In the first type J systems the regulator, actuated by a single pilot
frequency in each direction, compensates for the attenuation changes
caused by temperature and wet weather.

The required varieties of attenuation slopes with ice on the wires
could not be provided by a simple regulator. Hence provision is to
be made in later designs for a regulator with variable slope controlled
by two pilot frequencies which is expected to be satisfactory in areas
subjected to sleet conditions. The regulating range will also be
increased so that a completely automatic control of gain up to about
75 db will be available.

It was found that during periods when ice coated the wires the

368 BELL SYSTEM TECHNICAL JOURNAL

circuit noise measured at the end of a repeater section usually decreased
as the attenuation increased. This is important because otherwise the
extra increase in the repeater gain to take care of the higher attenuation
at such times would make the noise excessive. The study of ice
conditions throughout the country which has been carried on and is
still continuing will be useful in laying out repeater stations along some
of the routes which eventually will be candidates for the application of
type J systems.

Open-Wire Crosstalk ^

The crosstalk problem on open-wire lines is one of the most im-
portant. Crosstalk is controlled by transpositions which are intro-
duced into the various pairs in accordance with a predetermined design.
The creation of the necessary designs requires consideration both of the
complex theory of transpositions and measurements on lines con-
structed by practical methods.

However, the design of transposition systems is considerably
simplified by the use of different frequencies for the two directions of
transmission. The only crosstalk between systems which is directly
important is that known as far-end crosstalk, which is that between a
talker at one end of one circuit and a listener at the opposite or far end
of another. Near-end crosstalk, which is that between a talker and a
listener at the same or near ends of two circuits, becomes a source of
interference between circuits only when portions of it appear as far-end
crosstalk because of reflections at points of impedance irregularity in
the circuits.

Because of the high cost of a transposition design to keep both near-
end and far-end crosstalk down to small values, only small reflections
are permitted where open-wire and cable meet, or where circuits are
terminated in equipment. A number of the difficulties which had to be
overcome to attain small reflections are discussed later in the paper.
With this control the transposition designer can concentrate most of his
attention on far-end crosstalk, the near-end crosstalk requirements are
relaxed, and a cheaper transposition arrangement can be used.

What can happen when reflection occurs may be seen by comparison
of the near-end and far-end crosstalk curves in Fig. 4. The similarity
in the shapes of the two curves, and particularly the fact that the peaks
occur at the same frequencies, show that what appears to be far-end
crosstalk is in this case mostly reflected near-end crosstalk. It is for
pair combinations such as this one, where the near-end crosstalk is
much larger than the far-end, that the closest control of reflection
effects is required. With the values of reflection realized in the J
system, reflected crosstalk will ordinarily be unimportant.

TWELVE-CHANNEL OPEN-WIRE CARRIER SYSTEM

369

To obtain satisfactory crosstalk conditions at the higher frequencies
some changes in line construction are necessary. To use type J
carrier systems on existing open-wire routes, methods were devised for
modifying the line construction in as economical a manner as possible.

PAIRS 3/4.-9/10
J-3 TRANSPOSITION SYSTEM

60 70 80 90 100 110 120

FREQUENCY-KILOCYCLES PER SECOND

Fig. 4 — Near-end and far-end crosstalk — J-3 transposition system.

For new lines, such as the new part of the Fourth Transcontinental
line,® advantage was taken of the greater degree of freedom in struc-
tural design which was possible.

Figure 5 shows three types of open-wire pole head configuration

370

BELL SYSTEM TECHNICAL JOURNAL

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TWELVE-CHANNEL OPEN-WIRE CARRIER SYSTEM 371

suitable for J system operation. The left-hand diagram shows a
method of reconstructing part of one of the older types of open-wire
lines built with 12-inch spacing between wires of the pairs and with the
"Alternate Arm" transposition system which was developed for the
use of type C systems on the side circuits of the horizontal phantom
groups on alternate arms. This method is a flexible one in that one or
more phantom groups may be converted at a time, as on the second
crossarm shown. For such an application not only was removal of the
phantoms and retransposition necessary, but the spacing of the two
wires of each pair was reduced to 6 inches. This general method of
construction was used for the Dallas-Houston and Dallas-San Antonio
lines,® except that the 6-inch pairs were constructed with new wire on
a new crossarm rather than by respacing 12-inch pairs.

Another common type of open-wire pole head configuration, the
middle diagram of Fig. 5, is that made up of 8-inch spaced non-
phantomed pairs transposed in accordance with the K-8 transposition
system on an eight-span base. Through design studies supplemented
with field experiments it was found that such a line could be converted
for J systems much more cheaply than an Alternate Arm line. If J
systems are restricted to the pairs on the outer ends of the crossarms,
with two inner pairs, about one or two transposition changes in each
pair per mile are enough. This scheme was followed in reconstructing
the line between Charlotte, North Carolina, and West Palm Beach,
Florida.

For new lines yet to be built, a greater degree of latitude in structural
design is naturally possible. The right-hand diagram of Fig. 5
shows an open-wire pole head configuration designed to allow J
systems to be operated on all of the pairs. The unique feature of this
configuration is that, while 8-inch spacing is preserved between the
wires of the various pairs, the adjacent non-pole pairs on a crossarm are
separated by twenty-six inches and the crossarms by thirty-six inches.
The reduction in coupling made possible by this increased spacing
keeps the crosstalk for any combination of pairs down to a suitable
value with transposition arrangements not necessarily more compli-
cated than those employed for the other configurations. This type of
construction was used for the new parts of the Fourth Transcontinental
line.

Fig. 6 shows a comparison of the number of transpositions
used in a typical section of open-wire line for various types of circuits
from voice frequency phantomed circuits to non-phantomed circuits
intended for J system operation. From the original arrangement
where there was one transposition point in every ten spans, about

372

BELL SYSTEM TECHNICAL JOURNAL

}/i mile, the number of transpositions for J carrier operation has been
increased so that for the J-3 design, which was used for the new wires
on the Fourth Transcontinental line, there are four transpositions in
each eight-span interval and every pole is a potential transposition
point.

VOICE FREQUENCY PHANTOMED CIRCUITS
OAiD (E SECTION)

1-2
3-4

)C

1-2
3-4

C CARRIER PHANTOMED CIRCUITS
(ALTERNATE ARM SYSTEM)

X )E X

X X

)C

1-2
3-4

C CARRIER NON-PHANTOMED CIRCUITS
{K-8 SYSTEM)

X W X X i\ X —

XXX X X X )[ X X X XXX

I -2
7-8*

J CARRIER NON-PHANTOMED CIRCUITS
{K-8-2 system)

X k X )f X )£ X —

XXXXXXX3tXAX)[XXX

I -2
3-4

(j-3 system)

-X-Hf-^<-

X )t X

X )[ X

XXX x;ix X X xux x x x)tx x x x

32 POLE SPANS OR 0.8 Ml.

X

X = SIDE OR PHYSICAL CIRCUIT TRANSPOSITION
= PHANTOM TRANSPOSITION

• PAIR 7-8 IS SHOWN SINCE PAIR 3-4 IS NOT
INTENDED FOR J-SYSTEM OPERATION ON A
K-8-2 LINE.

* * FOR THE VOICE FREQUENCY AND ALTERNATE ARM
LAYOUTS THIS DISTANCE IS 40 SPANS.

Fig. 6 — Illustrative transposition arrangements.

It may be seen from Fig. 6, however, that the number of transposi-
tions required in pairs for J carrier operation is not necessarily larger
than the number employed in systems intended for C carrier operation
with a top frequency of 30 kilocycles. The superiority of the J system
transposition arrangements as compared with those designed for C
system operation results from the choice of specific arrangements which
best limit the systematic effects for frequencies in the J system range.

TWELVE-CHANNEL OPEN-WIRE CARRIER SYSTEM

373

Typical far-end crosstalk measured between 8-inch spaced pairs 11/12
and 19/20 on a new J-3 line and on a reconstructed K-8-2 line is shown
by Fig. 7. The superiority of the new line with its fewer wires, greater

1200

J-3 LINE ClOl MILES)

K-8-2 LINE (89 MILES)

1

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1000

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Fig. 7 — Far-end crosstalk between 8-inch spaced pairs 11/12 and 19/20.

pair separations, better transposition system and smaller irregularities
is evident.

Absorption Effects

The attenuation of an open-wire pair may be quite unsatisfactory if
there are what are known as absorption effects, caused by induction
into surrounding circuits such that energy is absorbed in particular
frequency bands and the attenuation of the pair increased. These
effects, which depend on the transposition arrangements in the
circuits, may cause objectionable transmission distortion at critical
frequencies unless the transpositions are planned to avoid them. The
same arrangements necessary to control crosstalk between J systems
will automatically eliminate absorption effects with one exception. If

374

BELL SYSTEM TECHNICAL JOURNAL

only part of the pairs on a line are designated and transposed for J
systems and the remaining pairs are not so transposed, absorption in a J
pair can be caused by a nearby non-J pair. Consequently, considera-
tion of the crosstalk relations at J frequencies between all of the pairs

u .4

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FREQUENCY- KtLOCYCLES PER SECOND

Curves A and B: Side 19/20 and 1/2 respectively, on Alternate Arm line, 104 mil,

12-inch, 56.7 miles, 90° F. at Mascoutah, 111.
Curve A is transposed for voice frequencies.
Curve B is transposed for carrier operation up to 30 kc.
Curve C is pair 39/40 on K-8-2 line, 104 mil, 8-inch, 68 miles, 50° F. and CS insulation

between Denmark, S. C. and Rincon, Ga. Transposed for carrier operation up

to 140 kc.

Fig. 8 — Attenuation of open-wire pairs of different types.

on the line cannot be avoided even though some of them will not be
used for J systems.

Figure 8 illustrates the effect of absorption on three different pairs.
Curves A and B show the absorption measured over the type J
frequency range on a line of the Alternate Arm type. Curve A was

TWELVE-CHANNEL OPEN-WIRE CARRIER SYSTEM 375

obtained on a side circuit transposed for operation at frequencies only
up to about 10 kilocycles. The absorption at frequencies above this
becomes very large. Curve B shows the absorption present on one of
the C carrier side circuits on the same line transposed for operation up
to 30 kilocycles. Curve C shows how absorption disappears on a non-
phantomed pair specially transposed for type J operation. If this
pair were measured at much higher frequencies, similar absorption
"bumps" would be found, perhaps at frequencies of 200-300 kilocycles
or higher.

Since absorption effects depend on the systematic addition of
crosstalk currents along a line, a continuous succession of identical
transposition sections tends toward greater absorption while a random
succession of different kinds of transposition sections of different
lengths will reduce it. The Dallas-Longview J system is operating on
an Alternate Arm side circuit, transposed for C carrier operation and
without any modifications to adapt it for the higher frequencies.
Because of the fortunately irregular succession of different transposition
sections found here, it was possible to select, after tests, a pair with no
serious absorption.

Construction Irregularities

With the new transposition designs, the systematic crosstalk
resulting from the transposition arrangements has been reduced in
nearly every case so far that the remaining crosstalk is controlled
principally by construction irregularities. An important source of
irregularity is the difference in sags of the various wires in each span of
the line, particularly sag differences between the two wires of each pair.
Another potentially important source of irregularity is the variation in
the spacings between successive transposition poles. It is relatively
easy to make this factor unimportant as compared with sag differences.

The large amount by which the crosstalk can be reduced by careful
methods of construction coupled with the highly developed systematic
transposition patterns is illustrated by the fact that between certain
pairs the crosstalk in a 75-mile repeater section is reduced to a value
which would be produced by a capacitance unbalance between them of
less than 2 mmf, which is about the same in magnitude as the capaci-
tance between wires of a foot of the open-wire pair. This large
crosstalk reduction is in spite of the fact that at 140 kilocycles the
phase change along an open-wire circuit is about 7° in a single span, the
shortest distance between any two transpositions, and about 28° for
the more common four-span interval.

376

BELL SYSTEM TECHNICAL JOURNAL

Interaction Crosstalk at Repeater Points
Another type of problem was introduced by what is known as
interaction crosstalk. This is the crosstalk which occurs from one side
to the other of a J repeater station. Figure 9 illustrates two paths

REPEATER
OPEN-WIRE LINE | STATION qPEN-WIRE
Ij REPEATER 1

LINE

TALK

\

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/ 1

/ \

PATH / 1

A 1
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8 1 lj

REPEATER '

V 1

\ 1

LISTEN

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1 1

1

S -INDICATES A SUPPRESSION DEVICE

Fig. 9 — Interaction crosstalk at a J repeater station.

which it may take. Path A shows the crosstalk from a system to itself
which may cause transmission distortion or repeater singing while
Path B is the path of crosstalk between different circuits. The
essential feature of this interaction crosstalk is that, as Fig. 9 shows,
the crosstalk path at a repeater station passes through the J repeater
and hence the crosstalk is amplified by the repeater gain.

The new problems of controlling this crosstalk were the result of
larger magnitudes of crosstalk at the higher frequencies, the larger
repeater gains and the fact that with more repeaters there were more
points on a system where it could occur. Magnitudes of interaction
crosstalk which had previously been thought of as inconsequential
assumed a new importance. For instance, with the gain of about 75 db
proposed for the repeater for use in sleet areas, an initial value of
unamplified interaction crosstalk as low as 0.25 crosstalk unit would be
magnified to 1400 units, which might considerably exceed the far-end
crosstalk existing at the same time in one repeater section.

Several new methods for reducing this interaction crosstalk were
devised. In the first place, in order to prevent direct coupling between
the wires of the open-wire line on the two sides of the station, it was
found necessary to cut a gap in the line. With the wires entirely
removed for a distance usually of about eighty feet, the line is brought
into the station from the two terminal poles by means of the lead-in
cables.

TWELVE-CHANNEL OPEN-WIRE CARRIER SYSTEM 377

It was also seen to be necessary to block the paths provided by
the wires of the telephone line itself. For this purpose, crosstalk
suppression filters were designed and built to be installed in all of the
non-J circuits on the line. These give losses of the order of 70 db at
140 kilocycles not only in the metallic transmission circuits but also in
other circuits, made up of various combinations of the line wires, which
may conduct crosstalk currents through the stations.

In addition to the crosstalk suppression filters and in order to
provide an extra margin of safety against interaction crosstalk currents
which might find their way through the repeater station by stray paths,
longitudinal choke coils have been connected at the pole heads between
the open wires and the lead-in cables. These coils do not disturb
ordinary transmission but add high impedance in the longitudinal
circuits.

These measures for controlling interaction crosstalk have been
found to be adequate so far as the telephone line is concerned. At an
occasional J repeater station, however, located on a right-of-way
occupied by several pole lines, there is found another pole line paral-
leling the telephone line with a separation sometimes as little as 2 to 5
feet between the nearest wires of the two lines. Such wires provide
other interaction crosstalk paths past the repeater station and impair
the effectiveness of suppression measures installed in the line on which
the J system is operated. The by-passing effects of such a foreign line
can be controlled by crosstalk suppression devices similar to those used
in the telephone line wires.

Figure 10 shows a comparison of the interaction crosstalk measured
at a J repeater station before any suppression measures were installed,
the other wires of the line being continuous at the station location,
with the corresponding interaction crosstalk when the line was run
through the suppression devices in the station. The values shown
would be amplified by the gain of the J repeater on the disturbed
circuit before they reached the listener. The efTect of the by-passing
foreign line is illustrated by the difference between the middle and
bottom curves, the bottom curve showing the measured crosstalk
when the by-passing line was cut to simulate the effect of suppression
measures in it.

Staggered Systems

It would not be possible with the open-wire line configurations now
in use to design transposition arrangements that would permit the
operation of identical J systems on all pairs. For this reason four
types of J systems with difTerent channel carrier frequency allocations

378

BELL SYSTEM TECHNICAL JOURNAL

will be provided in the future. The frequency assignments for these
systems are shown in Fig. 1.

The "staggering" advantage, or effective crosstalk reduction be-
tween systems, is effected because (1) the inversion or displacement of
channels in the different systems with respect to each other makes the

1.0

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/

^/

A

s

\/

^r

v

V

\f

1

\

i

\

I

\

^LINE WIRES CONNECTED THROUGH
REPEATER STATION SUPPRESSION DEVICES A

'

\

\ /

\

y

A

A^

A

A \

y\

A

^r

\A/-

V

^\ /

^LINE WIRES CONNECTED
THROUGH STATION AND WIRES

v

\i

\^

V

OF PARA

LLELING LI

ME OPEN

90 100 110 120 130 140 150

FREQUENCY- KILOCYCLES PER SECOND

Fig. 10 — Unamplified interaction crosstalk between two J circuits at an auxiliary

repeater station.

crosstalk unintelligible and (2) the reduction of the overlap between
channels results in less energy being transferred between them by
crosstalk. The net benefits of "staggering" obtained by the alloca-
tions shown in Fig. 1 range from about 6 to 16 db.

The most effective pair assignments for the four types of J systems
can best be obtained from actual crosstalk data on the particular
sections of line involved. The "staggering" advantages obtained are
sufficient so that the highest remaining crosstalk will usually occur
between the like J systems operating on non-adjacent pairs.

TWELVE-CHANNEL OPEN-WIRE CARRIER SYSTEM

379

Noise

Observed external sources of noise in J systems are atmospheric
static, dust storms, radio stations, power line carrier and power supply
systems.

Of these possible sources the more important will usually be atmos-
pheric static which will be greatest during the summer months. In
regions where dust storms occur, their effects are expected to exceed
that of atmospheric static but will be more likely to occur during the
winter and early spring.

The following table shows values of noise at 140 kilocycles, caused
by atmospheric static, found at the open-wire line terminals of one
repeater section; the values are those which it is expected will be
exceeded during one per cent of the summer season extending from
May to September. If the repeater spacings shown were used, the
total static noise in the top channel at the end of a circuit with 20
repeaters would be 20 db above reference noise at the — 9 db level.
However, other factors such as ice may require the use of shorter
spacings.

Transposition System

Wire
Spacing
(Inches)

Noise
(db)*

Repeater Spacing

in Miles —

128-Mil Wire

Alternate Arm

12
8
6

+ 10

+ 5

- 2

67

K-8-2

82

J-1

103

* Above reference noise, 10 ^ watt at 1000 cycles.

Line Impedance

As mentioned previously in the discussion of crosstalk, it is important
that the line impedances be matched closely and large irregularities be
avoided. Because of the different wire sizes and pair spacings, a wide
range of open-wire line impedances may be encountered. Novel
construction arrangements and the development of new lead-in circuits
have made it possible to secure a reflection coefficient of about five
per cent at the junction between the open-wire pair and the toll
entrance and office equipment at the highest transmitted frequency.

The transposition arrangement and wire spacing of a pair affect the
smoothness of its impedance because they affect the reactions between
circuits which cause absorption eff'ects. The marked improvement
which can be obtained by proper design is illustrated by comparison of
Curves A and B of Fig. 11. Curve A shows the impedance of a

-S80

BELL SYSTEM TECHNICAL JOURNAL

,1

1
(1

1 1
1 1

1

\

11

1 1

A

1

1

\

A

/ V

• 1
1 1

l\

— J

\

1

h

"; /

' 1

'^\ i
\ V

:

i \

L

1

\ 1

1 1
1 1
1 1

'• (
1

1'. 1

1'.;

''I

1

/

ly

--vif

»

1*

, 1
1 1

1

-c

^ — J

— %i '

1

1

\

1

A - 104 MIL, 12 INCH SPACED, SIDE 17-18 OF AN "ALTERNATE ARM" LINE
B-165 MIL, 8 INCH SPACED, PAIR 17-18 OF NEW J-3 LINE
C - 128 MIL, 6 INCH SPACED.PAIR 31-32 OF K-e-2 LINE WITH
MISCELLANEOUS LENGTHS OF TREE WIRE, ETC.

^'

^

c^\

I

/I

IL

/

"Ai

f'

1 1
1 1

ii'

'ii'

f\

'"i i

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--

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w7

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\

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/

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/

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\/

60 8Q

KILOCYCLES

Fig. 11 — Impedances of open-wire pairs of different types.

12-inch spaced side circuit on an Alternate Arm line. This par-
ticular circuit was one intended for use at frequencies not above 10
kilocycles. In striking contrast Curve B shows the comparatively
smooth impedance of an 8-inch spaced non-phantomed pair on a
new line transposed in accordance with the J-3 system.

TWELVE-CHANNEL OPEN-WIRE CARRIER SYSTEM

381

"Tree" wire, a special line wire with abrasion-resistant insulation,
has been used on open-wire lines for many years in places where the
lines were exposed to tree branches. During line tests in Florida,
another use for tree wire was found where the open-wire line, along a
causeway or bridge, is subject to fouling by fishing tackle. Curve C of
Fig. 11 shows what a half-mile or so of this tree wire, supplemented by

50 75 100

FREQUENCY- KILOCYCLES PER SECOND

Fig. 12 — Attenuation of toll entrance cable pairs.

several sections of 165-mil wire at railroad and power-line crossings,
can do to the impedance of a 128-mil pair. To reduce the irregularities
a new type of insulated line wire of smaller diameter and with thinner
insulation was developed. This wire has about the same impedance
characteristic as the line wire.

Intermediate Cable Treatment

When open-wire lines have to be placed underground to pass
through towns or to cross natural barriers such as rivers which cannot

382 BELL SYSTEM TECHNICAL JOURNAL

be spanned economically with open wire, cable is used. In the past,
the circuits in such cables were frequently loaded to reduce their
attenuation and to match the impedance of the open-wire circuits in
order to avoid reflection effects and degradation of voice-frequency
repeater balance. To load paper-insulated cable pairs for frequencies
up to 150 kilocycles would require exceedingly short loading spacing,
of the order of 200 feet, which would be expensive and in many cases
impractical with existing manhole locations. An alternative, the use
of a transformer to match the open wire and cable impedances, was
rejected as it was found impractical to design a transformer which
would be adequate over the entire frequency range.

To overcome these difficulties, a new low-capacitance type of cable
was developed which could be loaded to match the open-wire impedance
with coil spacings about the same as those previously used. Loading
coils of different sizes were developed to provide for loading to the
different impedances of the open-wire circuits.

The new cable employs 16-gauge conductors in a spiral-four arrange-
ment, supported by hard rubber disc spacers about 0.6 inch in diameter.
These are surrounded by copper and iron tapes for shielding and
strengthening purposes. The units so formed may be assembled
either in single units in a lead sheath as for lead-in purposes, or in
multiple units, up to a maximum of seven for full-sized cable, within
the same lead sheath. For duct runs or submarine cables, the multiple
assembly is usually employed, and, in the latter case, with outside
armoring and jute protection. If the submarine span is more than
about 600 feet, intermediate submarine loading is employed.

As an alternative, it sometimes happens that where a long inter-
mediate cable is involved, an auxiliary type J repeater station can be
placed conveniently at one end of this cable. In this case, the filter
hut described in the discussion of toll entrance arrangements in the next
section may be used at the end of the cable opposite the repeater
station and the cable treated as a toll entrance cable for the auxiliary
office, A further alternative is to provide filter huts at the two ends
of a non-loaded intermediate cable. However, if the cable is short, the
new disc-insulated cable with loading is to be preferred.

Previous practice at the ends of open-wire lines has been to use
paired bridle wire with weather-proof insulation and usually of smaller
gauge than the line wire to connect the open-wire pairs to cable
terminals mounted on the pole. Other pairs of bridle wire were
connected between the open wires and protectors. Because of the
much more severe reflection requirements at the higher frequencies of
the type J system, these arrangements were no longer satisfactory. The

TWELVE-CHANNEL OPEN-WIRE CARRIER SYSTEM 383

characteristic impedance of bridle wire is roughly one-fifth of that of
the open-wire circuit and it has been necessary to avoid the use of even
several feet of it between the open-wire and the cable terminal or
protectors. To accomplish this, separate terminals for each disc-
insulated unit are mounted on the crossarm near the open-wire pairs to
which they connect. Four insulated wires from each terminal go by
the shortest feasible route to the longitudinal choke coils and protectors
and thence to the open-wire pairs.

Toll Entrance Arrangements

The new disc-insulated cable used for intermediate cables was also
suited for lead-in or toll entrance cables.

When an auxiliary station is established at a point along an open-
wire line where there has not previously been an office, it is usually
located close to the line so that the lengths of lead-in cable required are
comparatively short. Lengths of this cable up to about 175 feet can be
loaded to open-wire impedances with adjustable loading units in the
repeater station. For longer lead-in cables up to 300 feet, supple-
mentary loading may be mounted directly on the pole at the cable
terminals.

When an auxiliary repeater station is not close to the open-wire line,
or at main repeater stations which are frequently in towns and sepa-
rated from the open-wire line by greater lengths of toll entrance cable,
it is still possible to use the loaded disc-insulated cable. Because of the
cost of this cable and its loading, however, it has sometimes been found
more economical to build a hut near the open-wire terminal pole and to
separate the type J from the type C and lower frequency facilities at
that point by means of filters. The connection from the open-wire
line to the hut is provided by what is usually a short length of loaded
disc-insulated cable. From that point, the type J frequencies are led
into the toll office over non-loaded paper-insulated pairs while the C
and lower frequency facilities are brought in over the existing pairs,
usually loaded. By thus limiting the frequencies transmitted over the
non-loaded cable pairs to the J range, it becomes practical to design
transformers for suitable impedance matching.

The line filter sets located in the hut are designed for a nominal
impedance of 560 ohms which is a compromise for the range of
impedances normally found with diflterent wire sizes and spacings. An
accurate match with the line is obtained with a building-out network
which is adjusted at the time of installation to fit the particular open-
wire pair involved. On the office side of this line filter set a trans-
former provides for stepping down the impedance from 560 ohms to the

384 BELL SYSTEM TECHNICAL JOURNAL

impedance of the toll entrance cable, which is usually about 125 ohms.
Adjustment of this impedance over the necessary range to match
impedances of particular cable pairs is provided by means of taps on
the transformer. At the office another transformer similarly tapped is
employed to match the toll entrance cable pair impedance to that of the
office wiring.

Fig. 12 shows the losses of the commonly used 19-, 16- and 13-gauge
paper-insulated toll entrance cable, a new 10-gauge low capacity cable,
and the new disc-insulated cable. Because of the high losses of the
smaller gauge pairs, it is sometimes economical to place new 10-gauge
cable to save repeater costs.

For the office wiring of the J system a rubber-covered shielded pair
is used to provide the desired flexibility and freedom from capacitance
variation due to humidity changes. Its impedance at 140 kilocycles
is approximately 125 ohms. The repeater and terminal high frequency
impedances are designed to match this impedance very closely.

Fig. 13 illustrates the arrangement of the toll entrance equipment
involved in matching the line impedance to that of the equipment with
a minimum of reflection. The terminal is illustrated to the left. The
high frequency line passes to the line filter set which is here shown as
located in a filter hut. There it is joined by the type C and lower
frequency circuits and passes through the lead-in cable and protective
arrangements on the terminal pole.

Proceeding toward the right in the figure, the arrangement at an
auxiliary repeater station is shown. In this case the type J frequencies
are amplified in the repeater, but the type C and lower frequencies are
by-passed through filters which suppress longitudinal and metallic
transmission above 30 kilocycles. At the right is shown a combined
type J and type C main repeater office.

Satisfactory crosstalk between pairs in entrance and intermediate
cables carrying J systems is efifected through special selection methods
and the application of balancing condensers.

Reflection Coefficients

The success of the various measures taken to insure good impedance
matching is shown by the curves of Fig. 14, which are of reflection
coefficients measured at an auxiliary repeater station. Curve A, the
solid line, gives the coefficient between the open-wire pair and the lead-
in cable at the terminal pole. The smaller variations are due partly to
irregularities of the open-wire line and, at the lower frequencies, partly
to the test terminations at the distant end. The contribution of the
cable loading and office equipment is indicated by the dash-line curve

!5M5B55M5ffiQ

lifl^

386

BELL SYSTEM TECHNICAL JOURNAL

25
24
23
22
21
20
19

O 16

^ 13

U 10

1

J REPEATER
DIRECTIONAL
/ FILTER
CUT-APART

/

30-KC LINE FILTER
CUT-APART

A

REFLECTIONS AT
TERMINAL POLE:
-A -OPEN WIRE VS
EQUIPMENT

- 8- 575 OHMS VS

EQUIPMENT

|\

V* —

\lil

iT~

II

\

f 1

1 1

,

(

\

/

1
\

\f

1

It '

1
1

Kit

;i 1

ij

/iJ

u

/

I

TV

l/ u

\

fl

1

1 1

u

n

L .

T

V

i,

■1

*

/'

»^v

/

IT

l^-

^

Wi

0 10 20 30 40 50 60 70 80 90 100 HO 120 130 140 150

FREQUENCY IN KILOCYCLES PER SECOND

Fig. 14 — Reflection coefficient at junction between open-wire and toll
entrance equipment.

TWELVE-CHANNEL OPEN-WIRE CARRIER SYSTEM 387

B, which was obtained with the open-wire Hne replaced by its nominal
impedance, a 575-ohm resistance. The reflection between the open-
wire and toll entrance and repeater equipment is well under 5 per cent
over nearly all of the transmitted range.

Conclusion

The successful transmission of frequencies up to 140 kilocycles over
open-wire pairs as compared with earlier operation up to 30 kilocycles
has involved modification of the construction of the open-wire lines,
new transposition designs, new toll entrance arrangements, including
new types of cable, the improvement of impedance matches in various
parts of the circuits, closer repeater spacings and, where ice is en-
countered, provision for much greater gain margins with more flexible
regulation.

The first system was placed in commercial service in September
1938. By the first part of this year about 60,000 channel miles were
in service over type J systems.

References

1. "A Twelve-Channel Carrier Telephone System for Open-Wire Lines," B. W.

Kendall and H. A. Affel, A. I. E. E. Winter Convention, January 1939.
Bell System Technical Journal, January 1939.

2. "Open-Wire Line Losses," L. T. Wilson, Bell Laboratories Record, Vol. XVI,

November 1937, Pages 95-98.

3. "High Frequency Attenuation on Open-Wire Lines," H. E. Curtis, Bell Labora-

tories Record, Vol. XVII, December 1938, Pages 121-124.

4. "Open-Wire Crosstalk," A. G. Chapman, Bell System Technical Journal, Vol. 13,

January and April 1934, Pages 19-58, 195-238.

5. "Transcontinental Telephone Lines," J. J. Pilliod, Electrical Engineering, Vol. 57,

October 1938, Pages 418-419 and 423. Bell System Technical Journal, Janu-
ary 1939.

6. "Some Applications of the Type J Carrier System," L. C. Starbird and J. D.

Mathis, A. I. E. E., Southwestern District Convention, April 1939. This
issue of the Bell System Technical Journal.

Abstracts of Technical Articles from Bell System Sources

Exploration of Pressure Field Around the Human Head During
Speech} H. K. Dunn and D. W. Farnsworth. A sin,8:le speaker in
a seated position repeated a fifteen-second sample of connected speech,
while r.m.s. pressure measurements were made in thirteen frequency
bands, and at seventy-six positions, in different directions and dis-
tances. The results are applicable to intelligibility and microphone
placement problems. They show, in general, the greater variation
with direction at higher frequencies. Directivity due to the size of
the mouth opening appeared to enter above 5600 cycles per second,
the a.xis at these frequencies being about 45° below the horizontal,
in front.

Frequencies below 1000 cycles per second were found strongest
directly downward from the lips, or nearly so. The power radiated in
different directions has been calculated, and a summation gives a
spectrum of the total speech power emitted by the mouth. It is
proposed that similar spectra for other speakers may be obtained from
pressure measurements at a single point, using the relations discovered
for this speaker. The necessity for protecting a microphone used
close to the mouth, from the puffs of air accompanying the speech,
is demonstrated and explained.

A Tubular Directional Microphone.- W. P. Mason and R. N.
Marshall. A tubular directional microphone is described which
consists of a pressure type microphone coupled to an acoustic im-
pedance element composed of a large number of tubes whose lengths
vary by equal increments. The function of this variation in length is
two-fold. Plrst, the multiple resonances of the individual tubes occur
at intervals so close together that the net effect of the bundle is that
of an acoustic resistance over a fairly wide frequency range and so
does not impair the high quality of the attached microphone. Second,
high directivity is secured, because for sound incidence other than
normal each tube introduces a different path length with phase
cancellation resulting in a composition chamber between the micro-
phone and the ends of the tubes. The theory of operation is summar-

1 Jour. Acous. Soc. Amer., January 1939.

2 Jour. Acous. Soc. Amer., January 1939.

388

ABSTRACTS OF TECHNICAL ARTICLES 389

ized and data are presented to show the performance of the instrument
which is in fair agreement with the theory.

Peak Field Strength of Atmospherics Due to Local Thunderstorms at
150 Megacycles} J. P. Schafer and W. M. Goodall. Atmospherics
in the 150-megacycIe frequency range were investigated with a broad-
band receiver and cathode-ray-tube scanning technique. The results
are of general interest in connection with the problems of atmospheric
noise interference on various types of ultra-short-wave radio-com-
munication channels. Some of the conclusions are:

(1) The peak intensity of disturbances varies 20 decibels between
different storms at the same distance. (2) The inverse distance
relation is a good approximation for the calculation of the variation of
peak disturbance with distance, for any distance and height of re-
ceiving antenna likely to be used in a commercial system. (3) The
use of high instead of low receiving antennas increases the signal-to-
disturbance ratio almost directly with height for storms within 10
miles. (4) The durations of some of the narrower peaks in any
particular lightning discharge are at least as short as a few micro-
seconds. (5) The maximum peak field strength of disturbances for a
storm one mile distant is 85 decibels and for a storm ten miles distant
is 65 decibels above 1 microvolt per meter at a frequency of 150
megacycles with a band width of 1.5 megacycles.

The technique of observations provided a visual indication of the
noise interference which might be expected with television signals.
It appears that with signal field strengths, such as might reasonably
be expected, atmospherics due to thunderstorms will be noticeable
for ultra-short-wave television transmission at times when storms are
in progress near the point of reception.

Metal Horns as Directive Receivers of Ultra-Short Waves} G. C.
SouTHWORTH and A. P. King. The paper describes some experiments
made to determine the directive properties of metal pipes and horns
when used as receivers of electromagnetic waves. The experiments
were of two kinds. One consisted of measurements of received power,
with and without the horn in place, and the other of the determination
of the directional patterns of the horns in two perpendicular planes.
The results indicate that electromagnetic horns of this kind provide a
simple and convenient way of obtaining effective power ratios of a
hundred or more (20 decibels). The effects of varying the several
horn parameters are investigated. It is shown that there is an

^Proc. I. R. E., March 1939.
* Proc. I. R. E., February 1939.

390 BELL SYSTEM TECHNICAL JOURNAL

optimum angle of flare. The possibility of forming arrays of pipes
or horns is mentioned.

Hindered Molecular Rotation and the Dielectric Behavior of Condensed
Phases} Addison H. White. The polarizability of a liquid or a
collection of randomly oriented single crystals in which polar molecules
are unable to move except to rotate from one to the other of two
equilibrium orientations separated by an angle /i and of potential
energies whose difference is E, is

a = {fxy6kT){]. - cos^)lcosh^EI2kT,

where /x is dipole moment. This model accounts for the reduction of
a in solids and liquids from the value y?l^kT observed in gases, and
at the same time provides for anomalous dispersion in terms of dis-
continuous molecular processes.

* Jour. Chemical Physics, January 1939.

Contributors to this Issue

Clifford N. Anderson, Ph.B., University of Wisconsin, 1919;
M.S., 1920. Supervising principal of schools, Amery, Wisconsin,
1913-17. Ensign Aircraft Radio, U.S.N.R.F., 1917-18. Instructor,
Engineering Physics, University of Wisconsin, 1919-20; Standardizing
Laboratory, General Electric Company, Lynn, Massachusetts, 1920-
21; Fellow to Norway, American Scandinavian Foundation, 1921-22;
Department of Development and Research, American Telephone and
Telegraph Company, 1922-34; Bell Telephone Laboratories, Inc., 1934
to date. Mr. Anderson's work with the Bell System has been largely
in connection with radio-telephony between boats and shore stations.

A. E. BowEN, Ph.B., Yale University, 1921. Graduate School,
Yale University, 1921-24. American Telephone and Telegraph
Company, Department of Development and Research, 1924-34.
Bell Telephone Laboratories, 1934-. With the American Telephone
and Telegraph Company, Mr. Bowen's work was concerned prin-
cipally with the inductive coordination of power and communication
systems. Since 1934 he has been engaged in work in the ultra-high-
frequency field, particularly on hollow wave guides.

R. S. Caruthers, B.S., University of Maryland, 1926; E.E., 1930.
General Electric Company, 1926-28; M.S., Massachusetts Institute
of Technology, 1928. U. S. Bureau of Standards, 1928-29. Bell
Telephone Laboratories, 1929-. Mr. Caruthers has been engaged in
the development of carrier systems.

R. N. Hunter, B.S., Worcester Polytechnic Institute, 1915. Test
Department, General Electric Company, 1915-16. Research Assistant
at Massachusetts Institute of Technology, 1916-18. American Tele-
phone and Telegraph Company, Engineering Department, 1918-19;
Department of Development and Research, 1919-34. Bell Telephone
Laboratories, 1934-. Mr. Hunter's work has been largely on problems
of crosstalk reduction in open-wire and in shielded conductor circuits.

L. M. Ilgenfritz, B.S. in Electrical Engineering, University of
Michigan, 1920. American Telephone and Telegraph Company, De-
partment of Development and Research, 1920-34; Bell Telephone

391

392 BELL SYSTEM TECHNICAL JOURNAL

Laboratories, 1934-. Mr. Ilgenfritz has been engaged in the develop-
ment of carrier systems.

A. G. Johnson, B.S. in Ceramic Engineering, Iowa State College,
1924. Western Electric Company, Development Engineering Branch,
1924-. Prior to October 1935, Mr. Johnson was engaged in develop-
ment work on ceramic, rubber, phenol fibre, and plastic molding
manufacture. At the present time, he is Engineer of Raw Materials
at the Hawthorne Plant, Chicago, Illinois.

Frederick B. Llewellyn, M.E., Stevens Institute of Technology,
1922; Ph.D., Columbia University, 1928. Western Electric Com-
pany, 1923-25; Bell Telephone Laboratories, 1925-. Dr. Llewellyn
has been engaged in the investigation of special problems connected
with high-frequency circuits and vacuum tubes. In his present
capacity as Circuit Research Engineer he directs a group in the study
of amplifying problems.

J. D. Mathis, B.A., University of Texas, 1924; M.A., University
of Texas, 1925; Tutor in Physics at University of Texas, 1924-25.
Telephone equipment maintenance, 1920-24. Southwestern Bell
Telephone Company, equipment engineering, 1925-. Since 1932
Mr. Mathis has been engaged principally in the engineering of central
office equipment for telephone repeaters and carrier systems in Texas.

John Riordan, B.S., Sheffield Scientific School, Yale University,
1923. American Telephone and Telegraph Company, Department of
Development and Research, 1926-34; Bell Telephone Laboratories,
1934-. Mr. Riordan 's work has been mainly on problems associated
with inductive effects of electrified railways.

L. I. Shaw, B.S. in Ceramics, Alfred University, 1907; M.S.,
Syracuse University, 1908; Ph.D., University of Wisconsin, 1911;
Instructor, Northwestern University, 1911-17; Assistant Chief Chem-
ist, U. S. Bureau of Mines, 1919-24. Western Electric Company,
Hawthorne Plant, Chicago, Illinois, 1924-. As Development Engi-
neer, Dr. Shaw's work has been largely in the fields of ceramics,
chemistry, hazards, and raw materials.

L. C. Starbird, B.E.E., University of Arkansas, 1921; Instructor,
University of Arkansas, 1921-25. Southwestern Bell Telephone
Company, 1925-; Equipment Engineer, 1926-32, Transmission and
Protection Engineer, Texas Area, 1932-. Mr. Starbird's work has
been largely in the application of carrier and repeater equipment.

CONTRIBUTORS TO THIS ISSUE 393

A. L. Whitman, Harvard University, A.B., 1918; B.S. in Electrical
Engineering, 1920. Harvard University Sheldon Fellowship for
traveling study in Europe, 1920-21. American Telephone and
Telegraph Company, Department of Development and Research,
Inductive Interference and Noise Prevention Group, 1921-34. Mem-
ber of Technical Staff, Transmission Development Department of Bell
Telephone Laboratories, 1934-. Mr. Whitman is now engaged in
field studies of noise and crosstalk as related to carrier-telephone
transmission systems utilizing a broad band of frequencies.

VOLUME XVm JULY, 1939 haJMBERS

THE BELL SYSTEM

TECHNICAL JOURNAL

DEVOTED TO THE SCIENTinC AND ENGINEERING ASPECTS
OF ELECTRICAL COMMUNICATION

Frequency-Modulation: Theory of the Feedback Receiving

Circuit — John R. Carson 395

The Application of Negative Feedback to Frequency-Modula-
tion Systems — J. G. Chaffee 404

Survey of Magnetic Materials and Applications in the Tele-
phone System — V. E. Legg 438

Impedance Properties of Electron Streams — Liss C. Peterson 465

Plastic Materials in Telephone Use

— J. R. Townsend and W, J. Clarke 482

The Dielectric Properties of Insulating Materials

—E, J. Murphy and S. O. Morgan 502

Abstracts of Technical Papers 538

Contributors to this Issue 544

AMERICAN TELEPHONE AND TELEGRAPH COMPANY

NEW YORK

50c per Copy $1.50 per Year

THE BELL SYSTEM TECHNICAL JOURNAL

Published quarterly by the

American Telephone and Telegraph Company

195 Broadway, New York, N. Y.

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F. B. Jewett
A. F. DuEon
S. Bracken

R. W. King, Editor

EDITORIAL BOARD

H. P. Charlesworth

O. E. Buckley

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Copyright, 1939
American Telephone and Telegraph Company

PRINTED IN U. S. A.

The Bell System Technical Journal

Vol XVIII July, 1939 No. 3

Frequency-Modulation : Theory of the Feedback
Receiving Circuit

By JOHN R. CARSON

THIS paper may be regarded both as a continuation of a prior one
by the writer and Thornton C. Fry ' and as a companion of that
by J. G. Chaffee - the inventor of the circuit under consideration. For
an understanding of the present, an acquaintance with the prior paper '
is absolutely necessary, since the fundamental analysis and the formu-
las there developed are too lengthy to be repeated here. References
to that paper will be designated by (Ref.).

As the name implies, in the feedback circuit part of the incoming
signal, after passing through a band-pass filter, a frequency detector ^
and a demodulator, is fed back through a variable frequency oscillator.
The output of the variable frequency oscillator is connected to one
branch of a modulator on the other branch of which the incoming high-
frequency wave is impressed. While this method of feedback differs
in some respects from that of the well known feedback amplifier, it is a
fair inference that some if not all of the very important advantages of
the feedback amplifier may also be present in the circuit under discus-
sion. This inference is verified by the mathematical analysis of this
paper.

After a brief development of the elementary theory and formulas of
the feedback circuit as a receiver of frequency-modulated waves, the
greater part of the paper is devoted to deriving formulas for the signal-
to-noise power ratio — a criterion of fundamental importance in estimat-
ing the merits of the system. These are then compared with the corre-

1 "Variable Frequency Electric Circuit Theory," this Journal, October 1937.

^"The Application of Negative Feedback to Frequency-Modulation Systems,"
/. R. E. Proceedings, May 1939; this issue of the Bell Sys. Tech. Journal.

^ The function of the "frequency detector" is to detect or render explicit the
variation of the "instantaneous frequency" of the frequency-modulated wave. A
more precise term, therefore, would be "frequency variation detector," but for
brevity the term used in the text is preferable.

395

396

BELL SYSTEM TECHNICAL JOURNAL

spending ratios formulated in (Ref.) for straight reception and also
reception with amplitude limitation. In this way, as regards reduc-
tion of noise and "fading," the feedback circuit is found to have ad-
vantages comparable with those attainable by amplitude limitation."*

I

The receiving system operates as follows (see sketch) :

INCOMING
HIGH-FREQ.

MODU-
LATOR

BAND- PASS

FILTER

/'MID-FREQ.= \

2

KH

FREQUENCY
DETECTOR

DEMODU-
LATOR

VARIABLE-
FREQUENCY
OSCILLATOR

LOW-PASS

FILTER
/CUT-OFF'i

LOW-FREQ.
OUTPUT

Feedback receiving circuit.
The incoming frequency-modulated wave at terminals I , I is taken as

E exp ( iwct -\- i\ \ s dt\ , (1)

where E is the wave amplitude, wc the carrier frequency, X the modu-
lation index and 5 = s{t) is the low-frequency signal which it is desired
to recover.

This wave is impressed at terminals 1, 1 on one pair of terminals of a
"product" modulator; on the other pair of terminals of the modulator
there is impressed the output of a local variable-frequency oscillator:

M exp ( iwMt + iix

j\dt)

(2)

Here cojv/ is the "carrier" frequency of the oscillator, /z (a positive real
quantity) is the index of modulation of the oscillator and a = a{t) is
the low-frequency current fed back to the oscillator.
The output wave of the modulator is then equal to

Ci£Af exp ( i{wc — i^M)t + i I (X5 — tJi(j)dt \

4- CiEM exp ( i{oic + w.v)/ -f i I (X^ + ixa)dt J . (3)
* Armstrong, Proc. I. R. E., May 1936, also see (Ref.).

FREQ UENC Y-MOD ULA TION 397

The second term of (3) is suppressed by the band-pass filter.^
Then writing wc — co.v = coc, it follows that the effective output
wave is

CiEM exp ( iwct + i I {\s — ix(7)dt j

(4)

oic isthe intermediate carrier frequency and is always < ojc, the trans-
mitted carrier frequency. The constant Ci is a parameter depending
on the characteristics of the modulator.

The wave (4) is transmitted through the band-pass filter, and the
wave arriving at terminals 2, 2 is then

C1C2EM exp f iojcf + i I (X5 — ijLa)dt j . (5)

The parameter C2 (taken as a constant) depends on the transmission
characteristics from the modulator to terminals 2,2.

Assuming an ideal frequency detector (see Ref.) the output to the
terminals of the rectifier (or demodulator) is

CiC-iCsEM ( 1 + ^'^ ) exp ( io)J + i I (ks - fxa)dt j

(6)

Here the parameters C3 and coi depend on the characteristics of the
frequency detector.
Finally assuming that

>^i^^ < 1 (7)

the low-frequency output of the rectifier ^ is

c.ccscEM (^\ + ^^ "/'')• (8)

If the constant term of (8) is suppressed and a fraction tj of the rectified
output is fed back to the oscillator we have, finally,

m \s ' . .

a = — - — ■ , (9)

fx I -\- m

^ Indeed the principal function of the band-pass filter is to suppress frequencies in
the neighborhood of wc + ^m-

" More generally a demodulator. In the present paper a straight-line rectifier is
postulated for mathematical simplicity but the theory applies equally well to other
forms of detection or demodulation.

398 BELL SYSTEM TECHNICAL JOURNAL

where

m = C1C2C3C4 J

The low-frequency current deUvered to the receiver through the low-
frequency output circuit proper differs from a as given by (9) by a
constant factor only.

From the foregoing we note that

\s - fxa = -T-— — (11)

and that the "instantaneous frequency" of the intermediate high-
frequency wave (4) is

'•^o + r^- (12)

Hereinafter, without any loss of generality, we suppose that
— 1 = s{t) ^ 1. Consequently the intermediate frequency-modulated
wave has a frequency variation lying between ± X/(l -|- m), whereas
in the incoming frequency-modulated wave, the frequency variation
lies between ± X.

We note also from (9) that if the parameter ni is large compared
with unity, the low-frequency received wave is approximately given by

o- = -5. (13)

n

The recovered signal is thus (for large values of m) seen to be inde-
pendent of the amplitude, E, of the incoming high-frequency wave;
therefore, the system is insensitive to "fading."

II

We now take up the problem of calculating the relative low-frequency
noise and signal powers, the ratio of which is of fundamental importance
in appraising the merits of the receiving circuit. In this we shall
closely follow the methods developed in Section IV (Ref.).

We suppose that at terminals 1, 1 there enters, in addition to the
signal, a typical noise element

a„ exp (i(coc + oin)t + idn). (14)

FREQ UENC Y-MOD ULA TION 399

We write for convenience in the subsequent analysis

a„ = AnE. (15)

^„ is then the relative amplitude of the noise element, referred to the
amplitude E of the high-frequency signal. We shall suppose through-
out that ^n is small compared with unity; that is, the noise is small
compared with the signal.

We further suppose that at terminals 2, 2 between the band-pass filter
and the frequency detector there is introduced a second typical noise
element

bn exp (i(aj, + co„)/ -f i/3„), (16)

which is entirely independent of the noise element (14). This may be
regarded as caused by tube-noise in amplifiers (not shown in sketch).
We write

hn = B,,E (17)

so that Bn is the relative amplitude of the noise element, referred to
the amplitude E of the incoming signal wave. It also is assumed small
compared with unity.

The total input to the frequency detector, neglecting the random
phase angles, is then

CiCiEM

whf

exp ( / I 0 J/ j +^„exp ( i I (S2 -f i]„«)^/ j

expT/ r (0 + ^n'')dt\\ , (18)

_>_ Bn

ciCiM

^ = (j^c -\- \s — yL(X

^n" = COn - \S (19)

0„* — cOn — \s -{- yLcr.

The output of the frequency detector is then (see Ref.'
CidCzEMexp lit U dt

X\ 1 -^~{\s - txa)

L wi

+ ^ „ M + — (co„ - M0-) exp ( * I Un^i

400

BELL SYSTEM TECHNICAL JOURNAL

After the output as given by (20) is rectified, the constant term sup-
pressed, and only first powers in An and Bn retained, we get finally

m/fjL
\ -\- m

X5 + yl„ I COl + w„ —

1 + w

X5 I COS

+

Bn

CiCsM

(cOi + C0„) COS

r fin' dt 1 .

dt

Now the right-hand side of (21) corresponds precisely with formula
(64) (Ref.) on which the calculation of the relative low-frequency noise
and signal powers is based. Consequently following the methods
developed in Ref. and assuming An and Bn small we get

mjij.
\ -\- m

1 X%2

3 (1 + my

i^aNa

-f (^ COa^ + C0i2 + {\S - IXaf \ C^aN.'IcWAP

(22)

The relative low-frequency noise and signal powers are then (omitting

/ til I a
the common factor

Pn = ^ C^a'Na'

Ps = X'^?.

1 + m
1 +3

+ 3^^^^

1 O^a'Nb^

3 ciWM'-

(1 -f m)2

1 +3

^ ^ ^ (X5 - f.ar

(23)

In these formulas NJ is proportional to the noise power level in the
neighborhood of the carrier frequency uc', it enters at the input ter-
minals 1, 1 (see Ref. Appendix 2). Nb^ is proportional to the noise
power level in the neighborhood of the intermediate carrier frequency
cocl it enters at terminals 2,2. oja is the highest essential frequency in the
low-frequency signal s(t); it is the cut-off frequency of the low-pass
filter.

Formula (22) is solvable (see Appendix) but a simple approximate
solution, valid when the noise is small compared with the signal, is
made possible by observing that under this restriction

\S — IJLCX =

\ -\- m

(11)

■ FREQUENCY-MODULATION 401

to a good approximation. Introducing this approximation into Pn
as given by (23) and writing

m = 7V,2 + N,^lc^WM\ (24)

we have

i'. = ^..^=(.+3(^)%3^(^?), (25)

Ps = \^s\
Now from the inequality, necessary for rectification,

X

COi >

\ -\- m

it is seen that as the parameter m is increased, coi may be reduced by
the factor 1/(1 -\- m). In accordance with this, we replace coi by

coi/(l + m) in (25) and get

Ps = XV.

i+z,-f^i(^r+(„^y^)]. (26)

(1 + m)- \\ COa

The noise power Pat can be still further reduced by eliminating oji
from (26) by a circuit arrangement explained in Ref. Section III; if
this is done we get, instead of (26),

P^=LjN^(l^3j^^^I^J^
3 _ \ (1 + my ,

Ps = X252.

We have now to compare the relative noise and signal powers of the
feedback with (1) straight reception without feedback and (2) reception
with amplitude limitation.

For straight reception (without feedback) we have (see equation (68),
Ref.), corresponding to (26),

P;.=^c.„W^(l+3('^V+3^^

Ps = X252,
and corresponding to (27)

1

(28)

..v==3..3^^(l+3(Ay
Ps = X'sK

(29)

402 BELL SYSTEM TECHNICAL JOURNAL

When noise reduction is effected by amplitude limitation the corre-
sponding relative noise and signal powers (see equation (78), Ref.) are

PM=\o,a'N\ (30)

Ps = X252.

If we assume as above that — 1 < 5 — 1 and s- is of the order of
magnitude of 1/2, then in practical applications X/co„ ;» 1 and wi > X.
On this basis comparison of (26) with (28) and (27) with (29) shows
that, when m^ \, the noise power with feedback is very much smaller
than without feedback, the ratio of the noise powers in the two cases
being approximately 1/(1 + w)^. (This assumes, of course, that iV^
is approximately equal in the two cases.)

Comparing, however, the noise power with feedback to that obtain-
able by amplitude limitation, it will be seen that in order to reduce the
former to the order of magnitude of the latter it is necessary that

^^/""^ <1. (31)

(1 + w)

From the preceding it is seen that the performance of the feedback
circuit and the reduction in noise-power ratio obtainable depend in a
fundamental manner on the parameter m, defined above by the formula

m = C1C2C3C4 (32)

If the characteristics of the modulator rectifier and variable-
frequency oscillator are stipulated, it is possible to calculate m in terms
of these characteristics and the constants and connections of the network.
It is experimentally determinable (among other ways) as follows:

Let the feedback circuit be opened between the low-pass filter and
the variable-frequency oscillator, and let the filter be closed by an
impedance equal to that of the oscillator as seen from the filter. Then
m = 0 (since there is no low-frequency feedback to the oscillator) but
m/iJL is finite.

Denoting the value of a under these circumstances by cri, it follows
from (9) that

(Ti = — X5. (33)

M
Consequently dividing ai by a, as given by (9), we have

\ -\- m = (Ti/a,

m^^-^^^- (34)

FREQ UENC Y-MOD ULA TION 403

Stated in words, 1 + w is the reciprocal of the ratio of the values of
0- without and with the low-frequency feedback into the oscillator. It
should be noted that this requires that the band-pass filter transmit the
frequency band 2X centered on coc.

Appendix

In formula (22), the expression {\s — /jLay has been replaced by
W/(l + m)^ its value when the noise is absent. When noise is
present, but small compared with the signal, this should still give a
good approximation for o--. We now propose to derive an exact solution
of (22) ; to this end we write

X5

\s — ixa ^ - — ^ nit) (la)

1 + /«

which is always possible.

Now inspection of (la) shows that n{t) is the value of /jlct when 5 = 0;
consequently w^ = /jL^ao^ where ao^ is given by (34). Furthermore,
since 5 and n are entirely independent, sn = 0, and

X252"

(\s - ix(xY = + mVo^ . (2a)

(1 -|- m)"

Substitution of (2a) in (22) gives for Pn, instead of (23),

3 \ \a;2/ (1 -f m)-

+ o>aP.WN^^Ic{WM\ (3a)

The second term is a second order quantity in the noise power and
may therefore be neglected when the noise is small, as is assumed
throughout this paper.

The Application of Negative Feedback to
Frequency-Modulation Systems *

By J. G. CHAFFEE

Negative feedback can be applied to a frequency-modulation
receiver of superheterodyne type by causing a portion of the output
voltage to frequency-modulate the local oscillator in such phase
as to reduce the output signal. As a consequence of this arrange-
ment the effective frequency modulation of the intermediate wave
is diminished by the feedback factor. This reduction is accom-
panied by a decrease in noise and distortion. Restoration of the
original signal level by increasing the degree of modulation at the
transmitter brings about a corresponding increase in signal-to-noise
ratio provided the disturbance is not too great, while distortion
ratios are improved to about the same extent. These effects are
treated analytically for the case where the disturbance level is suffi-
ciently low to permit simplifying assumptions to be made. The
results are in general agreement with observations made on an
experimental laboratory system.

Comparing the feedback system with a frequency-modulation
system using amplitude limitation, the ratio of signal level to noise
level in the absence of modulation is identical in two systems.
During modulation the noise level increases in the feedback system
by an amount depending upon the ratio of the effective frequency
shift of the intermediate-frequency wave to the signal band width.
By keeping this ratio small, the increase in noise during modulation
can be made relatively unimportant.

In cases where the disturbance level is high, phenomena have
been observed which are very similar to those encountered when
amplitude limitation is used.

Introduction

' I ''HIS paper describes a method for improving the performance of
-■■ receivers designed to receive frequency-modulated waves. In
its broader aspects this method can be described as the application of
the principle of negative feedback to a superheterodyne frequency-
modulation receiver. In its details the application of the feedback
principle necessitates the use of a rather unusual circuit arrangement.
This circuit differs from that of the simple feedback system in that
the voltages fed back are not of the same frequency as those applied

* Presented before New York Section of I. R. E., May 3, 1939. Published in
Proceedings, I. R. E., May 1939.

404

NEGATIVE FEEDBACK 405

to the input of the receiver, and are caused to influence the response of
the system by modifying the performance of the modulator.

In the ordinary feedback ampHfier a part of the output voltage is
carried back to the input and there combined with the applied voltage.
The result is to modify the output and if the gain of the system is
thereby reduced the feedback is said to be negative. The many ad-
vantages which result from negative feedback have been described by
Black ^ and are coming to be more generally appreciated. The present
paper deals with a method for adapting this principle to a frequency-
modulation receiver and will show an example of its application to an
experimental system in the laboratory.

General Discussion
Method of Applying Feedback

Consider a frequency-modulation receiver in which the incoming
wave is combined with the output of a local oscillator in a modulator to
produce a wave of intermediate frequency. This is then amplified,
converted into an amplitude-modulated wave, and finally detected.
The frequency of the intermediate wave is equal to the instantaneous
difference in the frequencies of the incoming carrier and the local
oscillator. So long as the frequency of this oscillator remains fixed the
intermediate wave will be frequency-modulated in exact correspond-
ence with the incoming wave. Suppose now that the local oscillator
is frequency-modulated from a source of the same frequency and phase
as that applied to the transmitter. As the index of modulation at the
local oscillator is increased from zero the extent to which the inter-
mediate wave is modulated will diminish since its instantaneous fre-
quency is equal to the difference in the frequencies of the two sources.
It then follows that if these two devices are modulated to the same
extent the difference frequency will become constant and the output
of the system will be zero. Finally a further increase in modulation of
the local oscillator will cause the intermediate wave to be modulated
with a 180-degree phase reversal.

This process can be readily analyzed as follows: Assume the oscilla-
tor at the transmitter to have been frequency-modulated by the
signal wave

e = El cos pt. (1)

The voltage delivered to the modulator by the incoming wave will be

A cos (coit + Xi sin pt + </)i) (2)

^ H. S. Black, "Stabilized Feedback Amplifiers," Elec. Engg., vol. 53, pp. 114-120,
January 1934.

406

BELL SYSTEM TECHNICAL JOURNAL

where Xi = Awi -^ p = pEi -^ p, and Acoi is Itt times the maximum
frequency shift. The local oscillation impresses the wave

where

B cos {wit + X2 sin pt + ^2)

X2 = Aw2 -^ p-

(3)

Application of these waves to a square-law modulator will yield a
difference frequency wave proportional to

AB cos [(coi — C02)/ + (xi — X2) sin pt + 4)1 — 02] (4)

for the case where coi > 0)2, or when the reverse is true

AB'cosJ_{w2 — ooi)i — (xi — Xi) sln'pt + 02 — <^i]. (5)

In either case the resultant modulation index of the intermediate wave
is the numerical difference of the original indexes, the difference in sign

MODULATOR

INTERMEDIATE FREQUENCY
AMPLIFIER

FREQUENCY
DETECTOR

FREQUENCY
MODULATED
OSCILLATOR

VvWVW"
-www-

Fig. 1 — Basic feedback circuit.

in the two cases signifying that the detected outputs will be of opposite
phase. If Xi = X2 the modulation is reduced to zero, and if X2 > xi
modulation reappears with a phase reversal. It might be noted that
if X2 were originally made negative, thus causing the two oscillators to
be frequency-modulated in opposite phase, the apparent modulation
of the incoming wave could be increased indefinitely.

Suppose, now, that instead of frequency-modulating the local oscil-
lator from an independent source, the equivalent is accomplished in a
practical way. For this purpose a voltage from the output of the
receiver is impressed upon the local oscillator as shown in Fig. 1. The
transmitted wave will then have a modulation index Xi = piEi -^ p,
while the local oscillator, being acted upon by a portion of the output
voltage £0, will have an index ^2 = kpiEo -^ p. If the frequency de-
tector 2 is assumed to be linear the amplitude of the detected output

^ The term frequency detector is used in this paper to designate the combination of
conversion circuit and amplitude detector. A more extended discussion of modula-
tion and detection is given in Appendix A.

NEGATIVE FEEDBACK 407

will be proportional to the product of the amplitudes A and B of the
incoming and local oscillator waves, the resultant index of the inter-
mediate wave, and the slope factor ai. Thus we can write the output
voltage amplitude

Eo = aaiAB{xi — X2)p = aaiAB(piEi — kpiEo). (6)

Therefore

„ attiABpiEi

1 + akaiABpi

(7)

Setting aaiAB = p. and kp2 = — iS we obtain the familiar form encoun-
tered in the analysis of feedback amplifiers

p.(piEi)

Without feedback the output of the system is merely p.{piEi). The
feedback factor 1 + aaJzABp-i is a measure of the extent to which the
over-all gain of the system has been modified by feedback. If this
factor is greater than unity the feedback is negative, while if k is made
negative by reversing the feedback connections the effect is regenera-
tive, and instability is encountered when the factor becomes zero.
It will be noted that when aaikABpi^ 1, (7) becomes

£. = ^- (9)

Thus for large amounts of feedback, the output signal becomes inde-
pendent of such factors as fading of the incoming wave, variations in
the local oscillator voltage, or changes in detector efficiency. Hence
automatic gain control is secured. This feature is equivalent to that
found in ordinary feedback amplifiers in that for large amounts of
feedback the over-all gain becomes independent of variations in the
performance of the amplifier proper.

Reduction of Noise

The application of negative feedback in the manner described
brings about a reduction in signal level by decreasing the effective
modulation of the received wave. It then becomes possible to increase
the modulation level at the transmitter to a corresponding degree and
thus to restore the output signal to its former value. This process is
made possible through the use of frequency rather than amplitude
modulation since the permissible degree of modulation is then deter-

408 BELL SYSTEM TECHNICAL JOURNAL

mined by the receiver characteristics. It will be shown that feedback
also reduces the noise level at the output of the receiver, provided that
the disturbance is not too great. Thus when the modulation level is
raised to offset the effect of feedback an improvement in signal-to-noise
ratio is realized.

The mechanism by which noise is reduced can be described qualita-
tively as follows : Noise at the output terminals of the receiver is caused
to frequency-modulate the intermediate wave in such fashion as to
produce, upon detection, a component which tends to cancel that
which would exist in the absence of feedback. An analysis of this
process for the case where the carrier is large compared with the dis-
turbance responsible for the noise is developed ^ in Appendix B, It is
assumed that the disturbance can be represented by a continuous
spectrum of sinusoidal voltages of equal amplitude but phased at
random. Impressed along with the disturbance is the signaling wave
(2). Then if N"^ is the mean disturbing power per unit of band width
in the vicinity of the carrier frequency, and ri is the resistance of the
input circuit, it is shown that the output noise power is "*

27VVi

F2

2 , ai^Acj^ ^ ai^qa-

^0 + 27?? +

qa (10)

where ao and ai are, respectively, the gain and slope factor of the inter-
mediate amplifier and conversion system as defined by (47), and qa
represents the upper limit of frequency response of the output circuit,
or the upper limit of audibility as the case may be. F is the feedback
factor (1 — fJL0). The corresponding signal power is

A^afAc^ (11)

The reduction in signal level occasioned by feedback can be offset by
increasing the frequency shift of the transmitted wave. If it is in-
creased so as to have the value Ai2 = FAco then the shift of the inter-

3 An analysis of the effect of feedback upon noise in this system was first developed
by J. R. Carson by methods similar to those used in "Variable Frequency Electric
Circuit Theory with Application to the Theory of Frequency Modulation," Carson
and Fry, Bell Sys. Tech. Jour., vol. 16, pp. 513-540, October 1937. This has been
embodied in a paper by Mr. Carson entitled, "Frequency Modulation: Theory of
the Feedback Receiving Circuit," published in this issue of the Bell Sys. Tech. Jour.
Carson's treatment is more general in that an arbitrary signal wave is postulated
whereas the analysis given in Appendix B is restricted to a sinusoidal signal wave.
The methods used here are more elementary and may therefore appeal to a somewhat
wider audience.

^ The expressions for signal and noise power used in this section are relative.
Factors determining their absolute magnitude are given in the Appendix. In all
cases the symbol Aco^ is to be taken as signifying (Aco)^.

NEGATIVE FEEDBACK

409

mediate-frequency wave will be restored to its original value Aco and
the signal level will remain unchanged. Then the noise power becomes

Pn =

27VVi

ao2 +

~2W

which can be written

2iVVi

ao' +

ai^Ac

+

(12)

(12a)

The noise-to-signal power ratio is improved by the factor F~, since

Ps "

1 4A^Vi

- f2 ^2

ai^Aco^ ' 2 ' 3Aw2

qa.

(13)

Of the factors in (12) the first is the result of modifications of the
amplitude of the incoming wave by the disturbance. Although sub-
ject to reduction by feedback it can be balanced out completely by the
use of differentially connected frequency detectors having slope
factors fli and — ai. The second term is dependent upon the degree
of modulation of the intermediate wave. It is usually of less conse-
quence in its effect upon the listener. The remaining term is the result
of phase modulation of the signal wave by the disturbance. Under
the condition that the output signal is held constant by increasing the
transmitted band, all terms which contribute to the noise level in a
given case are reduced alike by feedback.

If differential frequency-detection is employed (12a) becomes

Pn =

2Nhiar

f2

Aco

Qa'

2^3

(14)

During non-signaling periods the first term becomes zero. Hence
during periods of modulation the background noise power is increased
by the factor

1 +

3 Ai22

2 F'qa'

^ 2 2.2

(15)

If conditions are such that the maximum shift experienced by the
intermediate-frequency wave is numerically equal to q^ then the noise
level will be increased by 4 decibels during periods of full modulation.
In the experimental system to be described the ratio of Aw to qa was
allowed to attain a value of 1.75, resulting in a maximum increase of
7.5 decibels.

410

BELL SYSTEM TECHNICAL JOURNAL

In order to secure large noise reduction it is necessary to produce a
frequency shift in the transmitted wave much greater than the signal
band width. Thus, in common with frequency-modulation systems
employing amplitude limiters,^ this advantage is secured at the expense
of band width. In this connection it is of interest to compare ampli-
tude limitation and feedback systems on the basis of equal width of
transmitted band. Hence it will be assumed that in each case the
transmitted wave is modulated to the extent of ± Afi = ± FAco. In
Fig. 2 are shown idealized characteristics of conversion systems which
might be used in the two systems. The adjustment shown in Fig.
2(a) is suitable for use with the limiter system. With the feedback
system that shown in Fig. 2(b) would be necessary to secure the same
percentage of amplitude modulation after conversion. This represents

(b)

FREQUENCY

|-«j(i;-*l

FREQUENCY

Fig. 2 — Idealized conversion-system characteristics for (a) limiter system,
(b) feedback system.

the minimum band width which could be provided in the conversion
system with feedback, though several considerations make it desirable
to use an adjustment lying somewhere between the two shown. The
manner of tuning or the slope factors assumed in each case are im-
material to the present comparison provided that, in either system, the
linear portion of the characteristic is of sufficient extent to effect proper
conversion of the intermediate-frequency wave.

The noise-to-signal power ratio obtainable with the feedback system
will be that given by (13) with the first term omitted since it is balanced
out by the push-pull arrangement. Thus

Pn
P.

4iVV

2[2

qa'

3Ac

qa.

(16)

* E. H. Armstrong, "A Method of Reducing Disturbances in Radio Signaling by
a System of Frequency Modulation," Proc. I. R. E., vol. 24, pp. 689-740, May 1936.

NEGATIVE FEEDBACK 411

In the system corresponding to Fig. 2(a), the signal power will be

— T~' ^^'^

Equation (10) can be used to determine the noise power level for a
frequency-modulation system without amplitude limitation by setting
F = \. If balanced detection is used the term in a^ becomes zero.
It has been shown by Carson and Fry ^ that the addition of an ideal
limiter removes all terms but the third, with either single or balanced
detectors. Hence for the limiter system the noise ratio becomes

Since Afi = T^Aco this can be put in a form similar to (16)

Ps F^A^ \ 3Aw2

Comparing (16) and (19) it is seen that the noise ratio in the feedback
system is greater than that for the limiter system by the factor (15).
This is a consequence of the increase in noise level which occurs during
modulation in the former system. The ratio of noise level during non-
signaling periods to signal level is identical in the two systems.

While the noise increment which appears during modulation is
usually not of great consequence from a practical standpoint, it can be
reduced by increasing the feedback factor beyond the point dictated
by the signal band which it is permissible to transmit. In previous
discussions it has been assumed that the application of a given amount
of negative feedback is to be accompanied by a corresponding increase
in modulation level at the transmitter. In this way the modulation of
the intermediate frequency wave is kept constant so as to maintain a
fixed signal level as the band width of the transmitted wave is in-
creased. Having arrived at a limiting value of band spread the feed-
back factor can be increased further. Suppose that modulation of
the transmitter is to be limited to a value of A12 = /^lAco, but that the
feedback applied to the receiver is made to exceed Fi by a factor
which we shall call F2. Then the actual feedback factor will be ^^1^2
and we have

P^ = .IT (20)

p 27VVi

-T Ar — ^ ^ ^ „

Qa (21)

412 BELL SYSTEM TECHNICAL JOURNAL

giving

Pn 4A^V

:ir_l_ + _^l. (92)

Ps A^F

Thus the additional feedback represented by the factor F2 is directly
effective against the noise increment accompanying modulation. Re-
duction of this increment brings about a still closer correspondence
between the limiter and feedback systems as is seen by setting F = Fi
in (19) and comparing with (22).

The above discussion and the analysis given in Appendix B are based
upon the assumption that the carrier amplitude is large compared
with that of the disturbance. A rigorous analysis, applicable to the
case where this ratio is unrestricted, becomes exceedingly involved.
However, a rough indication of what is to be expected in the presence
of a high level of disturbance can be obtained quite simply from (52)
developed in Appendix B. Assuming that modulation is not present
this can be put in the simple form

1 Q'(ao + OlCOn)

1 + J7 f p j cos UiJ.

When Q' <^ A' the wave form of the output noise produced by a single
element of disturbance is very closely a sinusoid. However, when Q'
and A' become comparable in magnitude the output wave becomes
badly peaked when wj = nir. While the above expression is only a
very rough approximation under these conditions, a plot of the wave
form so obtained exhibits all of the essential characteristics of the curves
given by Crosby in a recent paper ^ dealing with noise in frequency-
modulation systems using amplitude limitation. These curves show a
similar peaking of the output-noise wave form when the ratio of carrier
to disturbance amplitude is in the vicinity of unity. The description
given by Crosby of the manifestations of this phenomenon observed
in an experimental system applies rather closely to what has been found
in the feedback system. A more detailed account will be found in a
later section.

Examination of (52a) shows that the output wave can assume very
large and even infinite peak values when Q' and A' are approximately
equal. The existence of high peak values of noise implies both a large
instantaneous deviation in the frequency of the intermediate wave, and
a conversion-circuit characteristic of unlimited extent. The finite

* MurrayG. Crosby, "Frequency Modulation Noise Characteristics," Proc. /. R.E.,
vol. 25, pp. 472-514, April 1937. The curves referred to are given in Fig. 4 of the
above paper.

NEGATIVE FEEDBACK 413

limits of the characteristic of the over-all intermediate-frequency
system have the effect of holding the maximum peaks of noise to a
value equal to the highest signal peaks obtainable in the absence of the
disturbance. Furthermore, the existence of high noise peaks in the
presence of modulation can result in the momentary assumption by the
instantaneous intermediate frequency of values outside of the region
to which the system is normally responsive. Thus the output signal
will appear to be chopped by the higher noise peaks, and as a conse-
quence its energy content will be considerably reduced.

The above effects are, of course, present in systems using limiters and
have already been discussed in greater detail by Crosby.®

Distortion Reduction

One of the chief benefits which can be realized through the use of
negative feedback is the reduction of non-linear distortion products
generated in the forward branch of the system. While the distortion
in properly designed amplifiers is sufficiently low for many purposes,
cases frequently arise in which the requirements are much more severe.
In an amplifier which is to handle several channels in a high grade
multiplex system, the distortion products should be of the order of 60
decibels below the fundamental of the output. This degree of excel-
lence is most readily obtained by using negative feedback.

In radio systems designed for multiplex service it is of equal impor-
tance that the distortion level be kept at a correspondingly low level if
crosstalk is to be avoided. It is therefore of interest to inquire into
the manner in which distortion is modified in the present feedback
system.

An analysis of the effect of feedback upon distortion is given in Ap-
pendix A. If the transmitter is modulated with a signal wave 5 = S{t)
so that its instantaneous frequency becomes

o) + piS (23)

then, in the presence of non-linearity in the receiver, the output of the
system can be written as a power series in the variable frequency term
piS. Thus for the first three orders we shall have

a = aAB[b,p,S + hi{p,Sf + 63(pi5)«]. (24)

If feedback is applied without altering the modulation level at the
transmitter it is shown that the above series becomes

<T,= aAB[ ^pi5 + ||(pi5)2

+ 1

2bl

)j(pi5)^). (25)

414 BELL SYSTEM TECHNICAL JOURNAL

When the feedback factor F is large this can be written

c p

= a^5 ( ^Pi5 + || {p,SY + 1 [ Z,3 - ^' j {pySf ) . (26)

Upon increasing the modulation by the factor F so as to restore the
original level of the fundamental, the output becomes

a/ = aAB(h,p,S + ~ b,{p,Sy + (bz -^\ {p,Sf

(27)

Second order distortion products are reduced with respect to the
fundamental level by the feedback factor. Third (and higher) order
products are modified to an extent depending upon the relative values
of the distortion coefficients and the amount of feedback. If, as can
readily be the case when a balanced detecting system is used,

63 »^' (28)

third order products are reduced in the same manner as those of second
order. In any case, by applying sufficient feedback a point will be
reached where a given increment in feedback will produce a corre-
sponding reduction in all distortion products.

Equation (25) shows that the greatest improvement in distortion is
obtained if the modulation level is not increased when feedback is
applied. The large reductions result partly from feedback and in part
from the fact that the system is operating at reduced percentage of
modulation. Under this condition there is no improvement in back-
ground noise ratio, though the noise increment which takes place during
modulation is diminished; see (10) and (11). Depression of both
noise and distortion, but with greater emphasis upon the reduction of
the latter, can be effected by raising the modulation level by an amount
somewhat less than the feedback factor. This procedure has already
been discussed in connection with (22) which gives the resulting noise-
to-signal power ratio. Under similar conditions we have, from (25),

a/' = aAB [^PiS + ir\ ^, {piSf

^1 L ^2^

1

+ ^4 Us - ^ (puS)

(29)

when the feedback factor is large.

Equations (22) and (29) are most readily interpreted by means of
Fig. 3, which illustrates the manner in which the receiver output is
modified as the feedback is increased.

NEGATIVE FEEDBACK

415

It is assumed that a constant signal level is maintained by an in-
crease in modulation level up to a point corresponding to the factor Fi.
Beyond this point the modulation remains fixed while the feedback

FEEDBACK IN DECIBELS

Fig. 3 — Theoretical manner in which components of receiver output are modified
by feedback. Modulation level at transmitter is assumed to be increased by the
feedback factor up to point P, and subsequently to remain fixed.

factor is increased to FiF^. Since signal and noise levels have been
expressed in terms of power, distortion levels are similarly expressed.

416 BELL SYSTEM TECHNICAL JOURNAL

These levels, to an arbitrary decibel scale, have been plotted against
decibels of feedback, given by the expression

10 log F^ = 20 log F.

Balanced detection and the fulfillment of condition (28) have been
assumed.

Over the region in which a constant signal output is maintained by
increasing the modulation level, noise and distortion levels decrease in
accordance with the feedback. The noise level during modulation
continues to exceed the background noise by 4 decibels, assuming an
initial frequency shift equal to the highest signal frequency to which
the system is responsive.

Beyond the point at which the feedback factor has reached the value
Fi, the modulation level at the transmitter is held constant. A further
increase in feedback brings about a corresponding decrease in the
effective percentage of modulation for the system, causing the signal
level to fall in similar fashion. Distortion products now fall off still
more rapidly with respect to the signal, so that an increase in feedback
amounting to 1 decibel improves the second and third order distortion
ratios by 2 and 3 decibels, respectively.

The ratio of signal to background or non-signaling noise remains
fixed in this region in spite of the reduction in effective modulation.
This ratio is that which would be obtained in a limiter system in which
the same high-frequency band is transmitted. The noise increment,
however, is diminished by the additional feedback and is made to ap-
proach zero.

By suitable choice of the variables Fi and F^ it is possible to propor-
tion the benefits of feedback in the most advantageous manner. Thus
if noise is of more consequence than distortion, modulation would be
increased to the full extent of the feedback; if distortion is of primary
concern, as it might well be in a multiplex system, operation as indi-
cated in Fig. 3 would be preferable.

Experimental Results

Description of Equipment
Experimental confirmation of the principles which have been out-
lined has been obtained with the aid of a laboratory system shown
schematically in Fig. 4. This arrangement provided a transmitter,
receiver, and source of disturbance all under local control. The trans-
mitter operated at a carried frequency of 20 megacycles. This was
frequency-modulated by means of a circuit basically similar to that

NEGATIVE FEEDBACK

417

described by Travis/ Tube noise voltage appearing at the output of
a high gain radio frequency ampHfier supplied the high-frequency
disturbance.

At the receiver an oscillator similar to that at the transmitter served
to beat down the incoming wave to an intermediate frequency of 438
kilocycles. This was applied to a three-stage amplifier having sub-
stantially uniform gain over a band of 50 kilocycles, and thence de-
livered to a balanced frequency detector. In addition to signal voltage,
automatic-frequency-control potentials were derived from the detec-
tors. Both were carried back to the local oscillator, but in order to
permit independent control of the amount of feedback their respective
paths were kept separate. In this way full frequency control could be
had even with signal feedback reduced to zero.

TRANSMITTER RECEIVER

SIGNAL
INPUT

4KC

o-i LP

1 "^'L

FREQ
MOD

osc.

^^

NOISE

ATTEN

GEN.

SIGNAL FEEDBACK PATH

Fig. 4 — ^Schematic of experimental feedback system.

Details of the frequency detector and feedback connections are
shown in Fig. 5. The conversion system derives its characteristics
from anti-resonant circuits LiC\ and L2C2, double-winding coils being
used to isolate the rectifier anodes from the plate battery. One circuit
is tuned to a frequency 15.4 kilocycles above the intermediate carrier
frequency and the other to a corresponding point below, their character-
istics intersecting at a point where the gain is approximately one half
of the peak value. Detection takes place in linear rectifiers Di and -02-
By means of the arrangement shown, signal potentials are impressed
upon the grids of amplifiers Ax and A2, while frequency-control voltage
appears across condensers Cz, C4. This voltage becomes zero when
the receiver is correctly tuned and appears with proper polarity to

'Charles Travis, "Automatic Frequency Control," Proc. I. R. E., vol. 23, pp.
1125-1141, October 1935.

418

BELL SYSTEM TECHNICAL JOURNAL

produce correction of the frequency of the local oscillator in case of slow
drifts in the frequency of either oscillator.

The use of a conversion system having peaks separated by an
amount considerably exceeding the greatest frequency deviation is the
result of a compromise between the readily adjustable and high
impedance anti-resonant type of load circuit and others which, though
more linear in their characteristics, lead to much lower gain in the
conversion stage. While a peak separation of 14 kilocycles would
have sufficed in view of the limitations of the transmitter, a consider-
ably greater peak separation without corresponding increase in modu-
lation was used. As a result that portion of the circuit characteristic
actually embraced by the modulated intermediate-frequency wave

BEATING
OSCILLATOR
(FREQ MOD.)

-X-

CORRECTI
NETWOR

EH

ATTENUATOR

L.P.
fILTER

Fig. 5 — Details of balanced frequency detector and feedback connections.

presented a much better approximation of a straight line than would
have been possible with minimum peak separation. The penalty for
adjusting the circuits in this manner is merely a loss in detecting effi-
ciency and not an impairment of the signal-to-noise ratio. This can
readily be overcome by additional audio-frequency amplification.

The signal-frequency feedback path includes an attenuator for ad-
justing the feedback and a corrective network for preventing singing
around the feedback loop. Frequency control and feedback paths are
finally combined at the modulation terminals of the local oscillator.

The necessity for the inclusion of a corrective network to modify the
transmission characteristics of the feedback path is evident from Fig. 6.
This shows the measured gain and phase characteristics of the receiver

NEGATIVE FEEDBACK

419

I

alone, viewed as a voice-frequency network between points A and B
in Fig. 4. This was obtained by applying signal frequencies to the
modulation terminals of the beating oscillator and making observations
at point B with switch 5 open, proper termination being provided at
both sides of the break. The unmodulated transmitter served, in
effect, as the beating oscillator during this measurement. At the
lower signal frequencies the phase is practically 180 degrees as indicated
by (4) with Xi = 0. As the signal frequency is increased the phase

210

180

150

120

90

60

a 30

a.

o

z

- - 30

u

to

< - 60

I

Q.

- 90
-120
-150
- 180

, ^

PH A '^f^

'

--^..^

^

s

N

S

^

^

„

C

A

Ih

g

i

\

N

c

-

K

\^

^

\

\

\

\

\

\

V

\

\

\

\

\

30

25

in
20 -I

UJ

in
1 5 '->

Q
10 Z

O
0

- 5

500 1000 5000 10000

FREQUENCY IN CYCLES PER SECOND

Fig. 6 — Phase and gain characteristics of receiver measured between points A and B
of Fig. 4 with switch 5 open. Transmitter in operation but not modulated.

is progressively shifted from this value. Except for that produced by
the output transformer, the shift takes place within the intermediate-
frequency amplifier and conversion circuits. Its magnitude'is a meas-
ure of the slope of the phase-frequency characteristic of the inter-
mediate frequency system.

The existence of positive gain at a point of zero phase shows that
singing would occur if feedback connections were made directly to the
beating oscillator. It was therefore necessary to reduce the gain below

420

BELL SYSTEM TECHNICAL JOURNAL

unity at the point of zero phase. This was accomplished by including
in the feedback path a network designed by R. L, Dietzold. The
gain-frequency characteristic of this network is shown in Fig, 7. The
modified loop characteristics as measured between points A and C
with switch S open, and with the attenuator set for an 8-decibel loss,
are given in Fig. 8. Full feedback is applied only over a band extend-
ing to 4 kilocycles, so that the range of frequencies applied to the trans-
mitter and delivered to the listener must be restricted to this figure.

20

'>

1 0

/

/

/

^

^

\

1

/

0

-1 0

^

\

/

- 20

\

\

^

^

/

-30

500 1000 5000 10000

FREQUENCY IN CYCLES PER SECOND

50000 100000

Fig. 7- — Gain-frequency characteristic of corrective network inserted in
signal feedback path.

The limit of stable feedback which can be realized is indicated by the
difference between the loop gain within the useful band and that at the
frequency corresponding to zero phase.

Distortion Measurements

The manner in which distortion levels at the output of the receiver

were observed to vary with feedback is depicted in Figs. 9 to 12. In

each case the modulation level for zero feedback was such as to shift

the frequency of the transmitter ± 7 kilocycles at the rate of 1000

NEGATIVE FEEDBACK

421

cycles per second. Figure 9 shows the effect of increasing the modula-
tion in proportion to the feedback so as to maintain a constant output
level for the fundamental. Both second and third harmonics tend to
be reduced in proportion to the feedback, the improvement in third-
harmonic level being 23.5 decibels for 25-decibel feedback. Failure to
realize full reduction of the second harmonic is the result of distortion
beginning to manifest itself in one or the other of the modulated
oscillators. At the point of 25-decibel feedback the transmitter and

270
240
210
180

- 30

- 60

V

x

«v

^

^

^

'*«

N

s,

PHASE

V

\

I

\

GAIN

1

'• '

-O

t

r-1

»-,

r^''

" ^

^

\

\

26

db

<

\

\

\

\

\

s^

—

—

~

~~

--..^

---*

X

100

500 1000 5000 10000

FREQUENCY IN CYCLES PER SECOND

25

15 M

40000

Fig. 8 — Gain and phase characteristics of complete feedback loop including corrective
network. Measured between points A and C of Fig. 4 with switch S open.

beating oscillator were being modulated to the extent of ± 124.5 and
± 117.5 kilocycles, respectively.

The curves of Fig. 10 were obtained by maintaining a constant funda-
mental level up to the point of 15-decibel feedback and then allowing
the modulation level at the transmitter to remain constant thereafter.
The results correspond rather closely with the theoretical curves of
Fig. 3 and show the very rapid decrease in distortion which takes place
when the modulation level remains unaltered; see (25). A more ex-
treme example of this method of operation is shown in Fig. 1 1 where

422

BELL SYSTEM TECHNICAL JOURNAL

modulation was left at its initial value. Harmonic levels soon reached
a point beyond which they could not be measured accurately.

In a practical system the loss in signal level resulting from operation
in this manner could easily be overcome by the addition of a low-
distortion audio-frequency amplifier at the output of the receiver.
This amplifier might well embody negative feedback of the more usual
type.

Oc

c

— 0 0 0 c

FUNDAMENTAL

— o-(

>— O— (

)— 0 —

- 5
-10

- 15
-20
-25
-30
-35

-40
-45

^'^^

*^^

■^

^!I^

^^>^

^"^

^::?

k^^THIRD HARMONIC

-50

^o

h^-

SECOND HARMONIC '

*^^

-55
-60

s

^

=^

s^

r^

i 10 12 14 16 18
FEEDBACK IN DECIBELS

20 22 24 26

Fig. 9 — Effect of feedback upon receiver distortion. Fundamental level kept
constant by increasing transmitter modulation in proportion to the feedback.
Modulation with no feedback = zt 7 kilocycles at 1000 cycles per second.

A composite of these distortion measurements is given in Fig. 12.
Harmonic levels are plotted in decibels below the fundamental and are
indicative of the improvements brought about by feedback. If it is
assumed that any loss in signal is compensated by additional audio-
frequency amplification, the fundamental level would be represented
in all cases by the axis of abscissae.

Noise Measurements
In Fig. 13 are given the results of a series of observations of receiver
output noise versus amount of feedback for a number of high-frequency

NEGATIVE FEEDBACK

423

disturbance levels. Measurements were made in the absence of modu-
lation and hence are indicative of the manner in which background
noise is modified by feedback. The signal level indicated is that
which could be maintained at low noise levels by increasing the modu-
lation in proportion to the feedback, and is not significant for observa-
tions falling within or close to the shaded area, as will be explained
subsequently.

f

- 5

- 10

- 15
-20
-25
-30
-35
-40
-4 5
-50
-55
-60
-65
-70
-75
-80
_ a tk

C

) 0 0

FUNDAMENTAL

""^

^

^^

^,

-^^

^\^

^

^^

/THIRD HARMONIC

N

^^

^-

SECOND HARMONIC^'^^

\,

\

^

k

\

V

\

^

L

\^

8 10 12 14 16

FEEDBACK IN DECIBELS

20 22 24

Fig. 10 — Effect of feedback upon receiver distortion. Conditions same as indicated
for Fig. 9 up to 15-decibel feedback; modulation held constant thereafter.

The lowest noise level shown is that generated within the receiver
while the higher levels were produced by disturbances introduced from
the noise generator. The relative magnitude of the effective carrier
and disturbing voltages at the grids of the amplitude detector is indi-

424

BELL SYSTEM TECHNICAL JOURNAL

cated on each curve. This was obtained in the following manner:
With the transmitter turned off the noise attenuator was adjusted until
the introduced disturbance produced the same value of rectified current
as that observed when the carrier alone was applied. This determined
the input level from the noise generator which produced equal root-

0

- 5
-10

- 15

-20

-25

^ -30

_i

ui

g-35

u {

Q '

Z -40

_l

u] -45

u

_i

-50
>

^-55

_i

UJ

a.

-60

-65

-70

-75

-80

-85

^

■^«-

N

"^

^

FUNDAMENTAL

^^

K

^io^

^^^

^

<^

'^

-^

k

\

^.

\

\

\

\

|\^— SECOND HARMONIC

\

^.

\^

\,

THIRD HARMONIC-A^

N.

\

\

\,

s

k

\

6 8 10 12 14 16

FEEDBACN IN DECIBELS

18 20 22 24

Fig. 11 — Effect of feedback upon receiver distortion. Modulation held to a constant

value of ± 7 kilocycles.

mean-square values of intermediate-frequency carrier and disturbance.
Since at very low inputs from the noise generator the net intermediate-
frequency disturbance was determined partly by tube noise generated
within the receiver, a curve of output noise without feedback versus

NEGATIVE FEEDBACK

425

input from the noise generator was obtained. In the region where the
effect of receiver tube noise was evident the assumption of a linear rela-
tionship between disturbance level and output noise permitted correc-
tion of the curve so that equivalent disturbance levels could be related
to any setting of the noise attenuator, or to the receiver output noise
level without feedback.

The signal-to-noise ratios at the output of the receiver without feed-
back are considerably higher than the corresponding ratios of carrier
and disturbance levels existing at the amplitude detectors. This is the

70

Z 60

"D 50

O

LJ

O 40

30

/

y

//

f

o

J\

y

rw

/^

.i/\

^

1/

r

^

/

/ ^

^

/

/
-^^

^

'(pS'

~~ ^

(c)

A

'^

^

^

X

/

/"

*<~^>

^

i:^

^

/

/

5$

[^

>'"

^

==^^

^v\\^

8 10 12 14 16 18
FEEDBACK IN DECIBELS

20 22 24 26

Fig. 12 — Composite of data from Figs. 9 to 11 expressing ratios of harmonic levels to
fundamental level. Curves (a) from Fig. 9, (6) from Fig. 10, and (c) from Fig. 1 1 .

result of two factors. The intermediate-frequency wave is modulated
to the extent of i 7 kilocycles while the range of frequencies appearing
at the output terminals of the receiver is limited to 4 kilocycles.
Hence at the output of the balanced detector the noise level in the
absence of modulation is 9.6 decibels below that which would be ob-
served at the output of an amplitude-modulation system. Further-
more the admittance characteristic of the complete intermediate-fre-
quency system is such that the effective disturbing voltage delivered to

426

BELL SYSTEM TECHNICAL JOURNAL

the amplitude detectors is 11 decibels greater than that admitted by
an amplitude modulation system having the minimum intermediate-
frequency band width of 8 kilocycles.

Aural observation of the character of the output noise showed that,
excluding the shaded area in Fig. 13, the normal characteristics of
fluctuation noise are preserved as feedback is applied. Upon crossing

10 12 14 16
FEEDBACK IN DB

Fig. 13 — Effect of feedback upon receiver output noise level for various amounts
of high-frequency disturbance. Ratio of root-mean-square values of carrier and
disturbance is shown on each curve. Shaded area indicates region of "crackling"
in the absence of modulation.

the boundary of the shaded area the noise becomes punctuated with
intermittent clicks which increase in rapidity and violence as the feed-
back factor is raised, giving rise to what can be described as "crack-
ling." After passing through a region of maximum turbulence the
noise gradually assumes the nature of a much higher level of fluctuation
noise,

NEGATIVE FEEDBACK

A21

\

The region embracing the appearance of the above phenomenon is
also characterized by a marked reduction in signal level. At high
modulation levels "cracking" begins at a somewhat lower disturbance
level than is necessary to initiate it in the absence of modulation. The
initial effect is to impart a roughness to tone modulation. Further
increase in disturbance level produces a rapid depression of the signal,
so that it soon becomes submerged in noise. The manner in which this
depression takes place is shown in Fig. 14. The signal, produced by
1000-cycle modulation was measured by means of a highly selective

O t5

Jr^-^

Y

^

f\

J

\

/

/

X X NO FEEDBACK

C^^3 25 DB FEEDBACK

/

I

f

/

/

I

f

5 10 15 20 25

R. M.S. CARRIER-DISTURBANCE RATIO IN DB

Fig. 14 — Depression of output signal by the disturbance. Modulation: ± 7
kilocycles for no feedback, ± 78.5 kilocycles for 21 -decibel feedback, and ± 124.5
kilocycles for 25-decibel feedback. Points P and Q denote incidence of crackling in
the absence of modulation, for 21- and 25-decibel feedback, respectively.

analyzer so that observations could be carried well below the general
noise level.

The point at which depression of the signal begins coincides with the
appearance of roughness in the output tone resulting from the momen-
tary suppression of the signal by the higher noise peaks. A further
increase in disturbance level increases the number of peaks per second
which rise above the critical value, and the energy content of the signal
is rapidly diminished. The point at which faint crackling could first
be detected in the absence of modulation is indicated on each curve.

The signal-to-noise ratios obtained with zero and with 25 decibels of

428

BELL SYSTEM TECHNICAL JOURNAL

feedback are shown in Fig. 15. These are plotted against the ratio of
root-mean-square carrier and disturbance levels at the end of the
intermediate-frequency channel. Signal levels were measured in the
presence of the disturbance so as to take into account the depression of
the signal, while noise levels were observed in the absence of modulation.

70

60

50

<

z
o

m 30
<ri

a.

20

10

X

/

■y

^

'7

^

J

Y

25 DB

/

/

t

/

f

A

/

9.6 DB

(

J

/

/

f

/

/
f

/

/

*

ml /

/
/

/.

/ 1 '
A*

THEORETICAL

0-^25DB FEEDBACK

4

/

*

/
/
t

0 10 20 30

R.M S. CARRIER-DISTURBANCE RATIO IN DB

Fig. 15 — Output signal-to-noise ratio vs. carrier-disturbance ratio witii and
without feedback. Modulation ± 124.5 kilocycles for 25-decibel feedback and
± 7 kilocycles for no feedback.

The improvement resulting from the application of feedback is given
by the difference between the two curves and approaches the theoret-
ical improvement at the low noise levels. The curve obtained with
feedback exhibits a rather sharp break when the ratio of carrier to
effective disturbance is in the vicinity of 10 decibels. Experimental

r

NEGATIVE FEEDBACK 429

data ^ published by Crosby indicates that in the case of fluctuation
noise the ratio of the maximum peak ampHtude to the root-mean-
square value is about 13 decibels. The corresponding figure in the
case of a sine wave is 3 decibels. Hence equality of carrier peak ampli-
tude and the highest peaks of the disturbance obtains when the ratio
of their root-mean-square values is 10 decibels. With feedback this
condition appears to define a fairly critical disturbance level above
which the output signal-to-noise ratio is very rapidly diminished.
Crosby has shown ^ that with systems employing amplitude limiters a
similar condition marks the point beyond which the noise improvement
realized at the lower disturbance levels is soon lost. This point he
has termed the "threshold of noise improvement."

A less sharply defined break also occurs in the curve expressing noise
conditions in the absence of feedback. This is the result of a progres-
sive destruction, at the higher disturbance levels, of the balancing out
of amplitude efifects in the push-pull detector which is realized when
the noise is low.

While direct comparison of the feedback system with an actual
amplitude modulation system was not possible with the equipment
used, it is thought that a comparison based upon theoretical considera-
tions may be of interest. The procedure is as follows: The noise ratios
shown in Fig. 15 for the system without feedback are, for disturbances
below the threshold value, 9.6 decibels in excess of those which would
be realized in a fully modulated amplitude system. A dotted line,
displaced from the linear portion of the measured curve by this amount,
is shown. The abscissae of the dotted curve do not represent the true
carrier-disturbance ratio which would obtain in the amplitude system
for the reason that, ideally, the intermediate-frequency amplifying
system would have a band width of but 8 kilocycles. In such a system
the signal-to-noise ratio would be equal to the carrier-disturbance ratio
except at the very high noise levels. Hence the intercept of the dotted
line with the axis of abscissas marks the point of equal carrier and
disturbance levels in this system. The difference of 11 decibels be-
tween this point and the zero point on the scale as drawn measures the
amount by which the disturbance at the rectifiers in the experimental
system exceeds that which would be found in the ideal amplitude
system.^ Consequently, if it is desired to relate the data of Fig. 15
to the disturbance ratio which would exist at the input to the detector
in the amplitude system, and hence to the signal-to-noise ratio in that

^ Comparison of the areas under idealized curves representing the square of the
transmission through the intermediate-frequency systems in the two cases indicates
a difference of 10.1 decibels.

430

BELL SYSTEM TECHNICAL JOURNAL

system, it is merely necessary to displace the experimental curves to
the right by 11 decibels.

Figure 16 shows such a comparison between the feedback system ad-
justed to give 25 decibels of feedback, and an ideal amplitude modula-

60

5^°

z

30

20

/

A- AMP. MOD. SYSTEM

B-FEED BACK SYSTEM

C- IDEAL LIMITER SYSTEM

C

y/

/

<

/

^1

/

'/

^Y

1

\

A

/

f

/

/

/

/

/

/

X

/

\

/

1

/

/

0 10 20 30 40 50

AMP. MOD. SYSTEM R.M S. SIG.-NOISE RATIO IN DB

Fig. 16 — Theoretical comparison of signal-to-noise ratios obtained at 25-decibel
feedback (curve B) with amplitude-modulated system (curve A) and ideal limiter
system with deviation ratio = 31.1 (curve C). Point X = threshold of noise im-
provement for limiter system. Point Y — point jvhere "crackling" first became
evident in the presence of ± 124.5-kilocycle modulation.

tion system. There is also included a curve showing the theoretical
performance which would be approached by a frequency-modulation
system using amplitude limitation. Transmitted band width and
audio-frequency response equal to that used in the experimental feed-

\

NEGATIVE FEEDBACK 431

back system have been assumed. This corresponds to a deviation ratio
of 124.5 kilocycles -^ 4 kilocycles = 31.1, resulting in a theoretical
noise deduction of 34.6 decibels at low disturbance levels. The thres-
hold of noise improvement, indicated at the point x, is located at a
point where the peak signal-to-noise ratio in the amplitude system is
equal to the square root of the deviation ratio.® This factor takes ac-
count of the higher disturbance level in the intermediate-frequency
channel of the wide-band system. Assuming a factor of 10 decibels
between maximum peak and root-mean-square values of fluctuation
noise this corresponds to a root-mean-square signal-to-noise ratio of
24.9 decibels in the amplitude system.^ In the feedback system the
point at which crackling was first observed in the presence of modula-
tion is shown at Y. This coincides very closely with the theoretical
threshold of noise improvement in the limiter system.

Conclusions

It has been shown that the application of negative feedback to a
frequency-modulation system affords a means for effecting large reduc-
tions in both noise and receiver distortion. The theoretical analyses of
these effects, while they have been simplified to an extent which makes
them inadequate to cover all conditions which can be encountered in
practice, are adequately substantiated by the observed performance
of the experimental system within the limitations of the theory.

Substantial benefits are realized only when the amount of feedback
is large, and when the disturbance level is not too great. In common
with frequency-modulation systems employing amplitude limitation a
large reduction in noise must be paid for by increasing the band width
of the transmitted wave. While the principles involved in the two
systems are quite different, their performance as regards noise modifi-
cation, both at high and at low levels of disturbance, exhibits striking
similarities. The ability to reduce distortion is, on the other hand, a
feature found only in the feedback system.

Acknowledgment

The writer wishes to acknowledge his indebtedness to the following
of his colleagues: To Dr. H. W. Bode for his investigations of the
problem of stability in feedback systems, and to Mr. R. L. Dietzold for
the design of the stabilizing network which was used; to Mr. W. R.
Bennett whose unpublished work on basic frequency-modulation prob-

^ In the absence of more exact information regarding the performance of a system
using this large a deviation ratio the portion of this curve below the threshold has
been omitted.

432 BELL SYSTEM TECHNICAL JOURNAL

lems has been of great value; and to Messrs. E. A. Krauth and O. E.
DeLange for assistance in the experimental work. Reference has al-
ready been made to the theoretical work of Dr. J. R. Carson.

APPENDIX A

Analysis of Distortion Reduction

Assume that the transmitter is frequency-modulated with a signal
wave which we shall represent by the symbol 5 = S{t). Then the
instantaneous frequency of the transmitter will be

coi + p,S. (30)

The instantaneous phase of the transmitted wave is the integral of this
expression and the voltage delivered to the input of receiver can be
written •

A cos ( coi/ + pi r Sdt + <^i ) . (31)

Designating the low-frequency voltage delivered at the output of the
receiver as a = (j{t) the result of feeding back a portion of ka of the
output so as to frequency-modulate the local oscillator is the wave

B cos I Wit -j- p2 I k<^dt + </>2 I . (32)

Application of these two waves to the modulator produces the inter-
mediate-frequency product '"

aAB cos coo/ + p\ I Sdt — Pi I kadt + <^o i^^)

where

Wo = coi — a>2

00 = 01 — 02.

Terms in the above which involve the integral sign represent phase
angles which vary with time. Hence we shall rewrite {2)2>) more
compactly

aAB cos [coo/ + ^(0 + 0o]. (34)

It has been shown by Carson and Fry ^ that the process of detecting
a frequency-modulated wave is, in effect, its differentiation. Since the
high-frequency wave itself exhibits the integral of the signal wave, see

"* This expression constitutes a more general form of (4).

NEGATIVE FEEDBACK 433

(30), it can be reasoned that a differentiation process is necessary for
the recovery of the signal itself.

Differentiation of the argument of the cosine term in (31) yields the
instantaneous frequency (rate of change of phase with respect to time)
of the received wave given by (30). Now it can be shown that with a
strictly linear frequency detector, the low-frequency output is propor-
tional to the response of the conversion system at the instantaneous
frequency. The recovered signal is, therefore, proportional to the
variable part of the instantaneous frequency and hence to the time
derivative of the variable phase term in the original wave.

In the case of non-linearity in the characteristic of the frequency
detector the output can be expressed, to a sufficiently close degree of
approximation, as a power series in the derivative of the phase term
d{t). Hence the output of the receiver can be written in the form

<j{t) = aAB Z hn

[IM^

(35)

= aAB E hnlpiS - kp2(x'y (36)

n

where the coefficients hn are based upon the transfer admittance
characteristic of the receiver.

What is now desired is the relationship between a and 6". This can
be expressed in the general form

a = aAB L c„[pi5]". (37)

n

Equations (36) and (37) can now be equated. Replacing a in the
right-hand side of (36) by the series (37) we shall have

cipiS + CiipiSy + csipiSy + • • •

= b£piS - kaABp2(c^prS + c,(pisy + Mpisy +•■•)]

+ b^LpiS - kaABp,{c,p,S + C2{piSy + cipiSy +•••)? (38)

-f bsipiS - kaABp2(c,p,s + C2(pisy -f- czipisy +•••)?

After expanding, coefficients of like powers of piS can be equated.
Then solving for the first three orders of Cn we find

^ ^1 ^ bi , .

^' 1 -f abikABp2 1 - fx^ ^ ^

- = (T^ <■'''

_ hz _ laABkp-jhi^ ,.. .

'' (1 - fji^r (1 - M^)^ ^^'^

434
where

BELL SYSTEM TECHNICAL JOURNAL

H = aABbi and

= — kpi

Inserting these values in (37) and writing (1 — ^j8) = F, the receiver
output becomes, with feedback,

(42)

(Tp = aAB

;^p.s+|i(p,s)^+(|i-^v^)(p.s)3;

When F » 1 this can be written

ap = aAB

"^P,5 + ||(p,5)= + l(6,-^')(p,5/

Without fee

idbacl

t we have

(43)

cr = aAB[b,p,S + h^ipiSy + &3(pi5)3]. (44)

APPENDIX B

Analysis of Noise Reduction

In the following analysis it is assumed that the amplitude of the
disturbance producing the noise is sufficiently small compared with
that of the incoming signal wave so that the principle of superposition
will apply. Hence the manner in which the effect of a single disturbing
component is modified by feedback will first be developed. Then the
effect of a disturbance consisting of a continuous spectrum is derived
by direct summation.

Consider first the case where there are impressed upon the grid of
the modulator the incoming wave and the local oscillator voltage ^^
as defined by (31) and (32), plus a single disturbing component

Q cos [(coi + co„)/ + 0„]. (45)

Then the intermediate-frequency product will be

aAB cos coq/ + p\ I Sdt — Pi I kadt

+ aBQ cos (wo + con)/ - p2 I k(Tdl + 0„ . (46)

For simplicity assume that the intermediate-frequency amplifier and
conversion circuit have the ideal transfer admittance characteristic

F(co) — a^ -\- ai(w — Wo).

(47)

" Arbitrary phase constants will be omitted from these expressions since they do
not affect the final result.

NEGATIVE FEEDBACK

435

Then all derivatives of Y with respect to co above the first are zero, and
the steady-state response is equal to its response at the instantaneous
frequency of the applied wave. Hence after conversion we shall have

aAB[ao + ax{piS — p2^o")] cos coo^ + | {piS — p2k(r)dt

-f aBQl^ao + ai(wn — p2^o-)] cos (wo + a)„)/ — I p2k(Tdt + 0„

(48)

Application of (48) to a linear amplitude detector will yield a low-fre-
quency output proportional to its amplitude. The amplitude factor is
readily calculated for the case where AB ^ BQ. For if

then

X cos X -\- Y cos y = Z cos z
Z = VX2 + 72 -f 2XFCOS (x - y)

and when X '^ Y

Z = X -\- Y cos (x — y) .
Hence the output of the linear detector will be

7 ( aAB\^aQ -f ai{piS — p2^o-)] + aBQ\^aQ -f ai(w„ — P2^cr)]

X cos ccj — pi I 5'(f/ + 0n

(49)

(50)

The term ajABao represents direct current. Assuming that this is not
fed back to the local oscillator we can then write

where

0- = A'\^ai(piS — P2^(t)] + Q'[,ao + ai(co„ — P2^o-)] cos ^ (51)

A' = ayAB
Q' = ayBQ

Solving for a-
1

^ = (wj — I plSdt -f (j)n \

1 + ai^'^p2

aiQ'kpi cos ^ "1 -'
^ 1 + a,A'kp2\

■ X [^'aipi5 + Q'{a, -f Oicon) cos ^]. (52)

436 BELL SYSTEM TECHNICAL JOURNAL

^ =^ ^ [ 1 - '''^'^'^''''^^ j lA'a^p.S + Q'{a, + aico„) cos ^] (53)

where F = \ -{- aiA'kpz = 1 — /x/3 as before. Finally, neglecting
terms in Q'"^, we have

a = i [^'aipi5 + (2' (ao + aico„ - ^^^ll^P^^ cos ^ ] . (54)

The first term is the recovered signal while the remaining terms repre-
sent noise. Both signal and noise are modified by feedback. If we let

PiS = Aco cos pt (55)

then the noise becomes

— (ao + aiojn) - -p {A'ai^kp2^oi cos pt)

X cos {iOnt — X sin pt + 4>n). (56)
By means of the Jacobi expansions this can be put in the form
Q' ^ \ r , N A'ai^kpifnpl J. . ,

% L («0 + fllWn) -p Jm{x)

X cos [(aj„ - mp)t + </)„] (57)

where Jm{x) is the Bessel coefficient of the first kind.

Now let it be assumed that the disturbance consists of a very large
number of sinusoidal components of like amplitude Q, random phase,
and uniformly distributed along the frequency scale. The summation
of this series of voltages can be represented by the very general
expression

/(/) cos [a,/ + </>(/)]. (58)

So long asf(t), the equivalent amplitude of the high-frequency disturb-
ance, is small compared with the carrier amplitude A, the approxima-
tion (49) will be valid and the total output noise can be obtained by
summing up the effects of the individual elements which constitute the
disturbance.

The effect of a single disturbing element is given by (57). Any term
of this expression can be made to have the frequency qii m and aj„ are
so chosen that

co„ = mp ± q. (59)

Then for each value of m in (57) there will be available values of co„

NEGATIVE FEEDBACK

437

to satisfy both of the conditions expressed by (59). The total effect
is obtained by summing the output power resulting from each con-
tribution since the original elements have random phases. If ^2 is the
resistance of the output circuit the total power of frequency q becomes

Q'

2r2F^

ao + ai(mp + q) —

A'ai^kp2mp

+ z

a-0 + ai{mp — q) —

F

A'ai^kpimp
F

JJ{x)

JmKx)

(60)

This is readily evaluated with the aid of tables appended to an earlier
paper. '^ The result is

r2F''

ao' +

+

aiV ]

(61)

The amplitude factor Q remains to be~defined. If N^ is the mean
disturbing power per unit band width in the vicinity of the carrier
frequency and ri the resistance of the input circuit, the peak amplitude
of any element is defined by the relation

N^do

2ri

(62)

Thus the power associated with each element becomes differentially
small, and if the value so obtained is entered into (61) there is obtained
the output noise power contained in a band extending from qto q -\- dq.
Then we shall have

dW

INhijayBY

ao'-\-

a i^Aw'
~2F^

+ aiV

dq.

(63)

The total noise power in a band extending to a limiting frequency qa is

The corresponding signal power is

_(aT^^)^

(65)

12 J. G. Chaffee, "The Detection of Frequency Modulated Waves," Proc. I. R. E.,
vol. 23, pp. 517-540, May 1935.

Survey of Magnetic Materials and Applications
in the Telephone System

By V. E. LEGG

The great diversity of magnetic characteristics demanded by
telephone apparatus, and the large number of available magnetic
materials propose intricate problems in the choice of materials and
design of apparatus to attain greatest efficiency and economy.
The present paper undertakes to evaluate magnetic materials in
relation to apparatus needs. After a review of the earlier develop-
ments, the materials now available are listed, together with data
on technical characteristics and raw materials costs. The advan-
tages of various materials for specific applications are described.
The scope of possible further improvements in magnetic materials
is surveyed.

Historical

'TpVVENTY years ago, the telephone system used primarily iron, to-
-*■ gether with a small amount of silicon iron, for applications requir-
ing soft magnetic materials, and carbon, tungsten or chromium steel for
permanent magnet applications. The permalloys ^ were already fairly
thoroughly developed by 1920 in what is now the Bell Telephone
Laboratories, and 78.5 permalloy ^ shortly attained commercial recog-
nition for its utility as a continuous loading material for submarine
telegraph cables.' This and other nickel-iron alloys were soon serving
in many types. of telephone relays, and in various coils where the
designs could be profitably modified to adapt them to the new ma-
terials. Upon the development of commercial means for embrittling
and pulverizing permalloy, this material was soon in extensive use
because it offered improved characteristics over the compressed pow-
dered iron core material previously in use. Redesigns of filter and
loading coils have introduced such economies that practically all these
coils made by the Western Electric Company have until recently
employed compressed powdered permalloy cores.^

A desire to reduce the losses in a-c. apparatus arising from eddy cur-
rents in magnetic parts led to the development of permalloys of higher

1 H. D. Arnold & G. W. Elmen, Jour. Frank. Inst. 195, 621 (1923).

2 The approximate chemical compositions of the various materials herein discussed
are given in Tables I and II.

3 0. E. Buckley, Jour. A. I.E. E. 44, 821 (1925).

* W. J. Shackelton & I. G. Barber, Trans. A. I. E. E. 47, 429 (1928).

438

MAGNETIC MATERIALS IN TELEPHONE SYSTEM 439

resistivity, containing several per cent chromium or molybdenum.^
The problems of embrittlement and pulverization of molybdenum
permalloy were also successfully solved. This material has been
recently adopted for manufacture of filter and loading coil cores,^ in
which material of higher resistivity is especially advantageous.

Attempts to decrease the losses due to hysteresis led to the discovery
of the nickel-iron-cobalt alloys — the perminvars. A molybdenum-
perminvar was perfected for use in the continuous loading of submarine
telephone cable.''

The large economic advantages promised by improvements in soft
magnetic materials confined much of the earlier work to this field.
However, within the last 20 years new permanent magnet materials
have been discovered here and abroad which offered radical improve-
ments in this direction. Such materials have been introduced in
telephone apparatus wherever found advantageous.

Characteristics of Available Materials

The number of different magnetic materials in use is quite large
on account of the various combinations of properties required for
special applications and on account of a multiplicity of trade names.
For the present purpose, an abbreviated listing is given of typical
materials covering the whole range of magnetic properties, particu-
larly those of interest to the telephone system. A compilation of
representative data is given in Tables I and II.

The fundamental property which distinguishes a ferromagnetic ma-
terial is that when it is subjected to a magnetic field it develops
magnetic flux considerably larger than similarly attained in air. The
magnetizing forces of interest in telephone apparatus range from less
than 10~^ to upwards of 10^ oersteds, and the flux densities from less
than 1 to 30,000 gausses or more. The relation of flux density B to
magnetizing force H for important materials as first magnetized is
given on a logarithmic scale in Fig. 1. The ratio of 5 to ^ is the
permeability, which can be read on the diagonal scale ^ in the figure.
It is evident that the initial permeability mo and the maximum permea-
bility Mm vary over a wide range from the hard magnet steels to the
softest magnetic alloys. For commercial materials, 4-79 Mo-perm-
alloy gives the largest initial permeability — around 22,000, and 78.5
permalloy gives the largest maximum permeability — ^about 105,000.

5G. W. Elmen, Jour. Frank. Inst. 207, 583 (1929).
"O. E. Buckley, Jojir. Applied Phvs. 8, 40 (1937).
' G. W. Elmen, Elec. Engg. 54, 1292 (1935).
8 Scale due to Aiken; Jour. Applied Phys. 8, 470 (1937).

440

BELL SYSTEM TECHNICAL JOURNAL

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442

BELL SYSTEM TECHNICAL JOURNAL

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tivity

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Soft Magnetic Materials

Magnetic Iron

4 Per Cent Silicon Iron

45 Permalloy (Ni, Fe)

78.5 Permalloy (Ni, Fe)

4-79 Mo-Permalloy (Mo, Ni, Fe)

2 V Permendur (V, Co, Fe)

45-25 Perminvar (Co, Ni, Fe)

Magnet Steels

3 Per Cent Chrome
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MAGNETIC MATERIALS IN TELEPHONE SYSTEM

44J

FUUX DENSITY IN GAUSSES (B)

444 BELL SYSTEM TECHNICAL JOURNAL

The saturation flux density for the soft magnetic materials can be read
from these curves, and it is Hsted in the adjacent Table III in the
column headed 47r/oo. The pre-eminence of 2 \^-permendur is note-
worthy.

Further important magnetic properties are obtained from the
hysteresis loop. This gives the B, II relationship for a material which
has already been magnetized up to a peak value //,„. The flux density
remaining after the removal of a very large magnetizing force is the
residual By, and the reverse magnetizing force necessary to bring the
flux to zero is the coercive force He. The area of the B, H loop
when the peak magnetizing force is very large gives the maximum
energy W^ dissipated by hysteresis in the material when it is carried
from positive magnetic saturation to negative, and back again. Table
III gives values of W^, Br and //«. The low values of these properties
for 4—79 Mo-permalloy are noteworthy. Among soft magnetic ma-
terials, iron and 2 V-permendur have high residual and coercive force,
properties which are occasionally useful.

Permanent magnet materials should have large values of Br and He,
although a sacrifice of residual can be more or less compensated by an
increase in coercive force. A more fundamental criterion of perma-
nent magnet quality is the peak energy product (5-//)max. obtained
from the demagnetizing section of the hysteresis loop." Values of
this product are given for several magnet steels in Table III. Mishima
steel is seen to be foremost in this regard, with remalloy nearly as good.

The last column in Table III gives the resistivity p of each material.
A high resistivity such as obtained with molybdenum additions to
permalloy and perminvar is desirable in suppressing eddy current losses
for alternating current applications. Eddy current losses can also be
suppressed by proper subdivision of the material, but this method
becomes costly with fine subdivision.

For apparatus depending upon the tractive force of a magnet, the
high flux density properties of materials are most important. Since
these do not show up clearly in Fig. 1, an accompanying Fig. 2 has
been prepared in which the {B — H) scale is quadratic, and thus pro-
portional to tractive force. The relative merits of various materials
for such applications are seen by inspection of these curves. 2 V-
permendur is outstanding at high flux densities, iron and 45 permalloy
at intermediate, and 4-79 Mo-permalloy at low flux densities.

The use of a purifying hydrogen anneal has been shown by Cioffi '- to

increase the ease of saturating iron and most magnetic alloys. The

"S. Evershed, /. /. E. E., London, 58, 780 (1920); 63, 725 (1925).
12 P. P. Cioffi, Phys. Rev. 39, 363 (1932).

MAGNETIC MATERIALS IN TELEPHONE SYSTEM

445

RELATIVE TRACTIVE FORCE

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INTRINSIC FLUX DENSITY (B-H) IN GAUSSES

446 BELL SYSTEM TECHNICAL JOURNAL

improvements for iron and 2 V-permendur are shown in Fig. 2. Im-
provements in 4—79 Mo-permalloy and in 45 permalloy are similarly
possible/ A hydrogen purified alloy having very nearly the composi-
tion of the latter material is produced commercially under the name
of Hipernik.^^ A material similar to hydrogen purified 4r-79 Mo-
permalloy has been produced under the trade name "1040" Alloy. ^'^

Adaptations for A-C. Uses

For a-c. applications, eddy current, hysteresis and residual losses
are generally important, in addition to the permeability. The ma-
terials for these applications have to be laminated or used in powdered
form to limit eddy current losses. Such modifications generally affect
the magnetic qualities, often adversely, through the introduction of
impurities or stresses, or through the concentration of magnetic flux
in parts of the material adjacent to air-gaps.

Many a-c. applications involve flux densities so low that the per-
meability does not rise to more than perhaps 10 per cent above mo-
Similarly, many applications involve operation at frequencies low
enough to insure that the a-c. permeability is approximately equal
to the permeability obtained by d-c. methods. (At higher frequencies,
eddy current shielding reduces the a-c. permeability below the d-c.
value, as discussed in Sec. 4b.) In these ordinary cases, the a-c.
losses in a material working at a flux density Bm and frequency /, are
conveniently described in terms of the increased resistance R per unit
inductance L of the winding encircling the material. ^^ These resist-
ance increments are:

1. Hysteresis, i?fe/L = a^m/x/. where a is the hysteresis loop constant.
At these low flux densities, the permeability coefficient

X = (m — fJ,o)ffJioBm-

It is related to the hysteresis coefficient to a good approximation by the
equation X = Sa/x/S.

2. Residual, Rr/L = c/j./, where c is the residual loss constant.

3. Eddy current, Re/L = ep.p, where e is the eddy current loss con-
stant. It is proportional to the square of the laminar thickness, or
particle diameter, and inversely proportional to the resistivity of the
material.

Table IV gives easily attainable values of the constants of im-
portance in a-c. applications for several typical materials. Data on

13 T. D. Yensen, Jour. Frank. Inst. 199, iii (1925).

" H. Neumann, Arch. f. tech. Messen 4, 42T, 168 (1934).

15 V. E. Legg, B. S. T. J. 15, 39 (1936).

MAGNETIC MATERIALS IN TELEPHONE SYSTEM

447

Other materials are also listed in Table I. Manufacturing tolerance
limits are frequently somewhat less favorable than here indicated.
In the section on laminated cores in Table IV, the eddy current coeffi-
cient e has been computed for several common sheet thicknesses.
Values for other thicknesses can be calculated as proportional to the
square of the thickness ratios.

TABLE IV
Alternating Current Loss Data on Sheet and Powdered Materials

Material

Size

Perme-
ability

Resis-
tivity

pXlOs

Hys-
teresis
Coeff.
aXlOs

Re-
sidual
Coeff.
cXlQs

Eddy

Current

Coeff.

eXlO'

Laminated Cores

45 Permalloy . .
45 Permalloy . .
78.5 Permalloy .

4-79 Mo-Permalloy . . .
3.8-78.5 Cr-Permalloy
45-25 Perminvar

7.5^5-25 Mo-Perminvar.

2 V-Permendur

4% Silicon Iron

Magnetic Iron

14 mil sheet
3 mil sheet
6 mil sheet

6 mil sheet
6 mil sheet
6 mil sheet

6 mil sheet
14 mil sheet
14 mil sheet
14 mil sheet

2,700

45

0.4

8

2,700

45

0.4

14

9,000

16

0.2

0

22,000

55

0.05

0

10,000

65

0.3

0

365

19

0.01

0

550

80

0.1

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800

26

1.0

—

400

60

120

75

250

10

50

—

1,160

53

600

173
146
505

120
2,000

870
5,200

Loading Coil Cores

Isoperm '^

Grade B Iron Powder.
Grade C Iron Powder.

81 Permalloy Powder

2-81 Mo-Permalloy Powder

Sendust ^^

Ferrocart '*

1.7 mil sheet

80 mesh powder

200 mesh powder

120 mesh powder
120 mesh powder
120 mesh powder
5 micron powder

85

45

2.3

20

35

10

50

110

26

10

80

140

75

16

5

37

125

40

1.6

30

65

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100

13

10

5

60

15
88
31

51

17
4.0
0.8

Mechanical Sensitivity
Stresses beyond the elastic limit in soft magnetic materials should
be avoided if possible, since they lower the permeability, and in general
increase the hysteresis loss. A partial exception to this statement is
found with the " Isoperms " (essentially 50 per cent Ni, 50 per cent Fe).
These alloys, after excessively hard rolling, annealing, and final moder-
ately hard rolling, develop low permeabilities and low hysteresis losses

i«0. Dahl & J. Pfaffenberger, Zeit.f. tech. Phys. 15, 99 (1934).

" H. Masumoto, Tohoku Sci. Rep. Honda Anniv. Vol., p. 388 (1936).

i« M. Kersten, Elektrotech. Zeit. 50, 1335 (1937).

448

BELL SYSTEM TECHNICAL JOURNAL

in the direction of rolling ^^ (see Table IV). Such materials have
been used to some extent abroad for loading coil cores. Aside from
the difficulty of attaining as low hysteresis loss, high permeability, and
high stability as obtainable with permalloy powder cores, such ma-
terials appear to be at an economic disadvantage because of the high
cost of rolling sheet thin enough for eddy current loss reduction.

Stresses well within the elastic limit increase or decrease the permea-
bility of materials, depending on the composition. -° Furthermore,
tension and compression generally have opposite effects. The changes
in permeability due to such weak stresses are not permanent, but
practically disappear when the stress is removed.

Cost of Magnetic Materials

Many materials having very desirable technical qualifications can-
not be used extensively because of their high costs. Thus, nickel at
2>Sil\h., cobalt at $1.35/lb., tungsten at $1.80/lb., and vanadium at

COMPOSITION MATERIAL

IN PER CENT
IRON NICKEL OTHER

95 3C 2SL
99.94

99.3 0.5 SI

96 451

54.4 45 0.6 Mn
20.9 78.5 0.6 Mn
16.4 79 4 MO 0.6 Mn
16.4 79 4Cr 0.6 Mn
17 81 2 MO

50 50 Co

49 49C02V

29.4 45 25CO 0.6 Mn

21.9 45 25C0 7 5M00.6Mn 75-45-25 PERM INVAR

85 9.5 SI 5.5 Al SENDUST

COST

IN CENTS PER POUND
20 40 60

58
71
55

CAST IRON

MAGNETIC IRON

Si IRON, FIELD

Si IRON, TRANSFORMER

45 PERMALLOY
78.5 PERMALLOY
4-79 MO PERMALLOY
4-79 Cr PERMALLOY
2-81 MO PERMALLOY

PERMENDUR
V-PERMENDUR
45-25 PERMINVAR

98 I Cr 0.6C 0.4 Mn 1 % Cr STEEL

95.6 3Cri.0C0.4Mn 3°/oCrSTEEL

1 c 3 5Cr 7W \

52 36Coa5Mn/ HONDA KS STEEL

44.6 18 27Co 6.7TL 3.7A1 HONDA, NEW

29

13 A1

I7M0 12CO
I6CO 290

MISHIMA STEEL

REMALLOY

OXIDE

Fig. 3 — Raw materials cost of various magnetic alloys.

"O. V. Auwers, Wiss. Ver. a.d. Siemens-Werk. 15, 112 (1936).
200. E. Buckley & L. W. McKeehan, Phys. Rev. 26, 261 (1925).

MAGNETIC MATERIALS IN TELEPHONE SYSTEM 449

$2.80/lb. increase the cost of an alloy very considerably in comparison
with iron or steel at less than 7(z5/lb. High priced magnetic alloys can
only be justified in general when their extraordinary characteristics
permit ofifsetting apparatus performance or economies. Of course,
they may be absolutely necessary for certain types of apparatus.

The cost data for Tables I and II have been calculated from recent
prices ^^ for raw materials of quality suitable for magnetic alloys.
The cost of raw materials is given in Fig. 3 for selected alloys. The
low raw materials costs of iron, silicon-iron, and chromium steel are
notable, as well as that of the powder core material "Sendust."
45 permalloy is the cheapest of the high permeability materials, while
Mishima steel is the cheapest of the high quality permanent magnet
materials.

Comparisons based on raw materials costs are not entirely satis-
factory. The cost of alloying and reducing to finished form may
overshadow the cost of raw materials, particularly when high purity,
exact tolerances, and small rates of production are involved.

Applications

Almost all magnetic properties are utilized in some type of telephone
apparatus. They are generally linked inseparably with electrical and
mechanical properties. The proper design of any apparatus strikes
a compromise between the various technical features and cost. The
technical features of materials used in present day apparatus are
listed below. Acceptable common properties, such as mechanical
soundness and workability, are assumed for all materials unless spe-
cifically mentioned. Listing is made on the basis of the magnetic
effect utilized.

1. Simple Tractive Force {Relays)

The force of attraction between two neighboring surfaces of area A,
between which the flux density Is B, is

F = kABK

The primary telephone application of this effect is to relays and
switches. For greatest tractive force, materials capable of attaining
high flux densities are desirable. However, the air gap in the magnetic
circuit absorbs such a large proportion of the available magnetomotive
force that higher or lower permeabilities in the core material are
frequently less important than efficiency of design. A typical relay
structure is shown in Fig. 4.

2' Steel, Oct. 3, 1938.

450

BELL SYSTEM TECHNICAL JOURNAL

Reference to Figs. 1 and 2 points to 2 V-permendur as outstanding
in the flux density range above 15,000 gausses. This material is
excluded for many applications because of its high cost. High tem-
perature hydrogen annealing improves the high flux density behavior
of most magnetic materials, as noted above in connection with Fig. 2.
Using ordinary methods of annealing, the next best material for high
flux operation is the standard magnetic iron, while 45 permalloy is
preferable at flux densities below 12,000. For the low magnetizing
forces available in sensitive relays, 4-79 Mo-permalloy gives the largest
tractive forces.

There are frequently other requirements in addition to tractive
force in relay construction. The operation and release characteristics

Fig. 4 — U-type relay, showing the magnetic circuit

are determined by the resistivity and coercive force of the material.
Sensitive, quick release relays require materials like permalloy, while
slow release types may utilize the larger coercive force and residual
of magnetic iron or cold rolled steel.^^- 23

Relays for a-c. applications may have objectionable eddy current
losses in their cores. Such losses can be reduced by use of high
resistivity material. Thus, 45 permalloy has one-fourth the loss of
iron for the same core thickness and flux density.

2. Polarized Tractive Force {Receivers, Ringers, Relays)
If permanent polarizing flux density Bp exists between two neighbor-
ing surfaces, and a small additional flux $ is applied by means of a

22 H. N. Wagar, Bell Labs. Record 16, 300 (1938).

23 F. A. Zupa, Bell Labs. Record 16, 310 (1938).

MAGNETIC MATERIALS IN TELEPHONE SYSTEM 451

magnetomotive force M, the additional tractive force will be approxi-
mately

Rail + njHr)

where i?„ in the latter part of the above equation is the reluctance of
the air-gap, n is ratio of the reluctance of the ferromagnetic circuit
with iron removed to the reluctance of the air-gap, and iir is the
reversible permeability, i.e. the permeability measured with very small
a-c. magnetizing forces in the presence of the polarizing flux density.
It thus appears that materials for such applications should have
high saturation values. The apparatus should be designed to obtain
a low value of w, and to operate at a flux density to make the above
force a maximum.

Figure 5 gives values of ^r as a function of polarizing or superposed
flux density Bp. It should be remarked that the reversible permea-
bility is practically single valued ^"^ when plotted against polarizing
flux, in contrast with the "butterfly" loop obtained by plotting against
polarizing field strength. The superiority of permendur in Fig. 5 is
obvious. Values of the force factor for n = 100 and n = 1000 have
been computed for these materials for an arbitrary value of air-gap
reluctance and magnetomotive force. It is evident that the full
advantage of permendur is not realized unless the apparatus design
is such as to attain a low value of the air reluctance ratio n.

Permanent magnet materials are frequently employed to supply
polarizing flux. When they form a part of the circuit for the alter-
nating flux, their reversible permeability becomes important. Refer-
ence to Table II shows that 5 per cent W steel has the highest permea-
bility of the common permanent magnet materials. However, its
energy product {B'H)max. is so low that other materials are preferred
for applications where space is limited, despite their low reversible
permeabilities.

The earliest application of polaiized structures in the telephone
plant was to the receiver. The receiver of the present day is con-
structed with remalloy permanent magnets, 45 permalloy pole-pieces,
and a permendur diaphragm.-^ The magnetic circuit is shown in
Fig. 6.

The second application of polarized structures is to the telephone
bell or ringer. Here a permanent magnet is used, to supply polarizing
flux to the two cores for the coils through the shoe at one end and the

^* R. Cans, Phys. Zeit. 12, 1053 (1911).
25 W. C. Jones, B. S. T. J. 17, 338 (1938).

452

BELL SYSTEM TECHNICAL JOURNAL

armature at the other.-'' Non-magnetic stop pins are required on the
armature to prevent sticking. This compHcated magnetic circuit has
been developed to meet the numerous requirements placed on ringers.
Polarization is necessary for an a-c. ringer which is to operate without

20,000

5000
4000

3000
'in
> 2000

O 1000
If)

>■

_l

OQ 500
uj 400

£ 300
a.

-I 200

n=AIR RELUCTANCE RATIO

" HlJ

"V.

4-79 Mo
PERMALLOY

^\

\

\

\

\

\

4
PERM

5
"VLLOY

\

h

X

\,

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\

1

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2V PERMENDUR 1

" — V

..^

N

"V

V

N,

\

S

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45 \

PERMALLOY '

r —

\

s

MAGNETIC IRON

li/

"Ti=ioo """*•*

1

V ^s

T
PERMENDUR
1

\

\ ^.

\

S,

\\

\

■n=ioo

--'"

V

^ \

= 1000

\

^^

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- \

7\_ri

\

r<^fl = IOOo\|

, '

\ Y

^>»

\

MO PERMALLOY

\

MA

GNETIC
RON

n = ioo(

3
k

\

6 8 10 12 14 16 18

POLARIZING FLUX DENSITY IN GAUSSES

20

100

24

XIO-

Fig. 5 — Reversible permeability and relative polarized tractive force
for various magnetic alloys.

interrupter contacts, and it is employed in selective ringing on party
lines. A high coil inductance is required to limit the transmission

''^ K. B. Miller, "Manual Switching and Substation Equipment" (McGraw-Hill,
1933 ed.), p. 67.

MAGNETIC MATERIALS IN TELEPHONE SYSTEM

453

losses due to the shunting effect of ringers across the Hne, especially
in the case of party lines.

The third application of polarized structures is in certain relays for
composite ringing, duplex telegraph, and special selecting circuits.
Various materials are used in such relays, depending upon the sensi-

DIAPHRAGM

AIR GAPS-

POLE PIECES-

-POLARIZING-
MAGNETS

Fig. 6 — Magnetic circuit of the new telephone receiver.

tivity required, so that no general statement can be made as to needs
in this field. The problems encountered are essentially similar to
those met in the receiver and ringer, for which numerous materials are
available.

454 BELL SYSTEM TECHNICAL JOURNAL

3. Force on Current {Moving Coil Receivers, Light Valves, Motors)
A straight wire of length / carrying a current i in a perpendicular

magnetic field of flux density B is pushed at right angles to the field

and the length with a force

F = Bil = txHil,

where m is the permeability and H is the magnetizing force in the
nearby material from which the flux is derived. Again, the prime
requirement for a useful material is high flux capacity, and high
permeability, so that the magnetizing force need not be large. The
magnetizing force has been supplied generall^^in the past by means
of direct current in windings built into th^' apparatus. With the
normally available voltages and currents, sufficient magnetizing forces
could be obtained only with coils having a large number of turns, and
low resistance. This generally involved such large structures that
cost considerations compelled the use,6^f'iron cores with perhaps pole-
pieces made of permendur. Lately rnany structures are being designed
to replace costly electromagnets with' permanent magnets made from
Mishima type steel.

Moving coil receivers and loud speakers " are the most important
representatives of this type of apparatus. Others are the string
oscillograph,'-* the light valve,-^ phonograph record recorder, ^"^ and
various types of power machinery. ^^ Several of these are now con-
structed with permendur pole-pieces, and cast Mishima steel magnets,
or remalloy magnets where hot rolling will assist in producing small,
accurately sized parts.

4. Induced Electromotive Force ^

The electromotive force between the terminals of a coil of N turns
linking flux ip is

^T d(p

-^ = ^i-

The arrangement of coils and interlinking flux difl'ers considerably in

the various types of apparatus employing this effect.

The flux variation is provided by means of mechanical motion of

the coil in instruments such as the electromagnetic microphone. It is

varied by means of fluctuations in magnetizing current in inductance

" E. C. Wente & A. L. Thuras, B. S. T. J. 10, 565 (1931).

28 A. M. Curtis, B. S. T. J. 12, 76 (1933).

" G. E. Perreault, Bell Labs. Record 10, 412 (1932).

30 H. A. Frederick, B. S. T. J. 8, 159 (1929).

" R. D. deKay, Bell Labs. Record 16, 236 (1938).

MAGNETIC MATERIALS IN TELEPHONE SYSTEM 455

coils and transformers. In the moving coil microphone, the cylindrical

coil moves axially in a slot between an inner magnetized cylinder and

an outer magnetic cylinder which receives the radial flux threading the

coil. For such a cylindrical coil in a uniform radial field, the e.m.f. is

dx
— e = IB jr , where / is the total length of wire composing the coil,

and X is its displacement perpendicular to the radial field. For a

stationary coil linking a varying flux as in a transformer, — e — AN -j-

= A Nil -^- , where A and /x are the area and permeability of the core
at

within which the magnetizing force is H. It is evident from these

equations that high flux density or permeability are desirable, in order

to yield the largest e.m.f. with least material.

4a. Microphones, Magnetic Tape Recorders, Magnetos

An application involving a moving coil is the public address micro-
phone,^^ where the flux is established by means of a cobalt steel magnet,
and is concentrated upon the moving coil by means of permendur
pole-pieces.

An inverse application in which the coil is stationary and the magnet
moves is the magnetic tape recorder. ^^ In this, a steel tape which has
been magnetized by speech currents is drawn between permalloy pole-
pieces in pick-up coils. High coercive force, high signal-to-noise ratio,
mechanical soundness, durability, and cheapness of the tape material
are desirable.

The telephone magneto employs the e.m.f. generated by rotating a
coil in a magnetic field. It has been constructed with iron armature
and pole-pieces, and chrome steel field magnets. Recent designs
using modern magnetic materials have indicated the possibility of
large economies in volume.*^ The magnetic properties of available
materials have now reduced the volume required by magnetic parts to
a point where the major problem in magneto design is to compress
the gears and shafts into correspondingly small space and yet main-
tain sufficient mechanical strength, durability, and convenience of
operation.

4b. Inductance Coils

A very important application of induced e.m.f. focuses attention on
the inductance of a coil of N turns surrounding a (closed) core of area A ,

32 R. N. Marshall & F. F. Romanow, B. S. T. J. 15, 405 (1936).

33 C. N. Hickman, B. S. T. J. 16, 165 (1937).'

34 Ericsson Bulletin No. 12, 46 (1938).

456 BELL SYSTEM TECHNICAL JOURNAL

magnetic path length /, and permeabiHty //. The inductance is in-
creased through the presence of the core by an amount

L = 47riVV^//.

As noted earlier, when eddy current shielding is negligible such an
inductance is accompanied at frequency/ by hysteresis, residual, and
eddy current resistances to give a total as follows:

RIL = ixJ{aB,n + f + e/).

At frequencies high enough to introduce eddy current shielding,
the effective inductance due to a core of laminar thickness / and
resistivity p is reduced below the ordinary inductance Lo by the ratio

TIT — ^ ^'"^ ^ "I" ^^" ^
' "^ ~ "d cosh e + cos 0 '

where 6 = iTrt^nof/p. Figure 7 shows this ratio and the ratio Re/wLo
as functions of 6. As a practical example, the permeability of 6 mil
(0.015 cm.) 4-79 Mo-permalloy is reduced to about 75 per cent of its
initial value (22,000) at 1 kilocycle, and to about 17 per cent at
10 kc.

The telephone loading coil adds inductance to the telephone line,
but it must not add excessive resistance. Furthermore, its inductance
must be extremely stable with the lapse of time, and under severe
operating conditions, such as occasional current surges induced from
lightning discharges. Iron wire cores for loading coils were supplanted
over twenty years ago by compressed iron powder cores, and these in
turn gave way to permalloy powder cores. The latest improvement
is the introduction of 2-81 Mo-permalloy powder cores.'' The reduc-
tion in size of cores with these improvements is shown in Fig. 8.

Another method of loading a line is by sheathing the conductor with
a continuous layer of magnetic material. This method was used
with notable success on submarine telegraph cables by wrapping
permalloy tape upon the conductor, and annealing before applying
insulation.^ The location of the loading material is shown in Fig. 9.
The continuous loading of long submarine telephone cables has been
shown to be feasible using thin 7.5-45 Mo-perminvar tape.^

Retardation and choke coils have a great variety of applications,
running from a tiny coil weighing 3^ ounces ^* to a 4600 lb. generator
ripple suppressor.^*^ The contrast is evident in Fig. 10. Retardation

35 D. W. Grant, Bell Labs. Record 11, 173 (1933).
3« R. A. Shetzline, Bell. Labs. Record 17, 34 (1938).

MAGNETIC MATERIALS IN TELEPHONE SYSTEM

457

coils, used as network elements, are generally equipped with com-
pressed powder cores, and the same improvements are indicated as
for loading coils noted above. Laminated permalloy cores are often
used for low-frequency applications (ringing, telegraph), where high
inductance is desired, and a-c. losses are naturally low.

1.0
0.9
0.8

0.6

0.35

0.30
0.28
0.26
0.24
0.22
0.20
0.18
0.16

0.14

~^

— •

--^

^

\

\

Mo Lo

\

\

\
\
\

\

\
\
\
\

/

/'

N

.

/

/

/

\\

/

/

\

\

/Re

\\

/

(jOLq

/

\

/

\

s.

/

\

y

1

/

\

s.

e2

1

\

e

0.8

1.0 1.2 1.4 1.6 2.0 2.5 3

e

7 8 9 10

Fig. 7 — Effect of eddy current shielding on apparent permeability and on eddy
current resistance/reactance ratio of sheet core material.

Coils designed for direct currents must have cores with high a-c.
permeability in the presence of superposed field, i.e. they must be
made of high permeability magnetic materials having high saturation
values. Reference to Fig. 5 shows permendur outstanding in this
regard. In practice, the low costs of silicon iron or magnetic iron are

458

BELL SYSTEM TECHNICAL JOURNAL

frequently decisive in the selection of these materials instead of the
technically superior materials noted above. Air-gaps are often found
necessary to reduce the superposed field strength in the magnetic core.

Fig. 8 — Relative sizes of compressed powder cores for loading coils;
A. Iron, B. 80-permalloy, C. 2-81 Mo-permalloy.

=csszssz

wmm^^W^mm^^

PERMALLOY
LOADING- MATERIAL-

Fig. 9 — Permalloy loaded telegraph cable; A. Armored deep sea type, B. Gutta
percha insulated core, C. Enlarged cross sectional view.

This serves to retain a fairly large reversible permeability in the core,
and, if the air gaps are not too large, it yields a larger net effective
permeability than could be obtained without air-gaps.

MAGNETIC MATERIALS IN TELEPHONE SYSTEM

459

A further type of inductance is the impulse coil used in harmonic
generators.^'' The cores of these coils should be saturated over most
of the magnetizing cycle, and reverse very quickly and completely
just as the magnetizing force passes through zero. This implies use
of material having a high permeability, and a high resistivity, such as
4-79 Mo-permalloy.

Fig. 10 — Large and small coils used in the telephone system.

4c. Transformers

With transformers, the inductance and losses of the individual coils
can be analyzed as simple inductances, for which the considerations of

" E. Peterson, J. M. Manley & L. R. Wrathall, Elec. Engg. 56, 995 (1937).

460 BELL SYSTEM TECHNICAL JOURNAL

4b apply. In addition, however, the coupUng factor between coils on
the same core becomes of especial importance. In the usual design
the flux linkage common to the primary and secondary is largely con-
tained in the magnetic material, while the leakage flux is controlled by
the reluctance of the air path. It is thus evident that a large value
of core permeability is required to obtain a high coupling factor.
Of course, advantages indicated by high permeability may be lost
through improper design.

The earliest transformer employed in the telephone plant was the
induction coil. This originally consisted of two windings on a core
composed of a bundle of iron wires. ^^ Later, silicon iron sheet cores
were introduced.

Input and output transformers have varied applications for which
special types of cores are required. Where superposed current is not
involved, space and weight can be economized by use of high perme-
ability materials such as chrome or molybdenum permalloy. ^^ Eddy
current shielding at higher frequencies will offset much of the perme-
ability advantage indicated for these materials unless they are lami-
nated sufficiently. However, thin laminations are costly to prepare
and stack, and difficult to insulate and handle without mechanical
injury and corresponding reduction of permeability. An intermediate
thickness of permalloy sheet is generally chosen, which secures a
considerable advantage in permeability over iron, without prohibitive
cost.

Where a winding must carry direct current, conditions are similar
to those applying to choke coils, and materials with high reversible
permeability at high magnetizing forces are required. Frequently,
for large magnetizing forces, it is desirable to include air-gaps in the
magnetic circuit. Silicon iron is the ordinary material for such
application, as it is for power transformers.

4d. Magnetic Shielding

A further application of induction effects is in magnetic shielding
of apparatus. A magnetic shield consists of a high permeability shell
(4-79 Mo-permalloy, or 78.5 permalloy) which shunts flux around the
enclosed apparatus. For a-c. shielding, alternate layers of copper and
permalloy sheet are very effective in magnetic shunting and eddy
current screening of the enclosed space.""^ High initial permeability,

^* Cf . p. 43 of Reference 26.

39 A. G. Ganz & A. G. Laird, Elec. Engg. 54, 1367 (1935).

« W. G. Gustafson, B. S. T. J. 17, 416 (1938).

MAGNETIC MATERIALS IN TELEPHONE SYSTEM 461

mechanical workability, and low cost are desirable for such appli-
cations.

5. Magnetostriction

The relative change in length of a magnetic bar upon magnetization,
bljl, ranges from negative to positive values, depending on alloy com-
position, and is roughly proportional to B". If a polarizing field is
applied, small additional alternations of field will give accompanying
and nearly proportional alternations of length of a bar. These alterna-
tions evidence themselves in the electrical constants of a coil enclosing
the bar.

This efifect can be utilized in oscillators and filters for frequencies
which involve the use of mechanically resonating bars of convenient
size. Among the high permeability materials, 45 permalloy appears
to give the largest magnetostrictional effect.'*^ In order to limit eddy
current losses, the material must be laminated more or less finely,
depending on the frequency.

The inverse magnetostriction effect by which e.m.f. is generated in
a coil when the core is vibrated, becomes objectionable as a source of
circuit noise in the transformers of high gain amplifiers.'^ An alloy
with minimum magnetostriction such as 81 permalloy or 4r-79 Mo-
permalloy is preferred for such cases.

Other efTects of magnetostriction are the generation of sound by
the cores of coils subject to alternating magnetization, and the appear-
ance of undesired resonance effects in the electrical circuit at fre-
quencies at which the core resonates mechanically.

6. Thermal Variation of Permeability

The initial permeability of ordinary magnetic materials increases
more or less slowly with increasing temperature, until a maximum
value is reached, above which temperature the permeability declines
very rapidly to the non-magnetic, or Curie point. The Curie point of
an alloy can be moved down the temperature scale by adding non-
magnetic materials, such as Mo, Cr, Cu, etc., to the alloy. ^^

The positive temperature coefficient of inductance of powder core
coils due to thermal change of permeability becomes objectionable in
crystal filters, where only very small variations in the resonant fre-
quencies can be tolerated.*' It is made slightly negative to counteract
the small positive coefficient of mica condensers by the admixture with

« A. Schulze, Zeit. f. Phys. 50, 448 (1928).

«2 G. W. Elmen, Bell Labs. Record 10, 2 (1931).

« C. E. Lane, B. S. T. J. 17, 125 (1938).

462 BELL SYSTEM TECHNICAL JOURNAL

the regular 2-81 Mo-permalloy powder of a small amount of permalloy
powder containing about 12.5 per cent of molybdenum. The latter
material has a Curie point just above room temperature.

Conclusion: Desirable and Possible Improvements

It appears from the above inspection of the magnetic elements of
apparatus that there is a general desire for all properties which con-
tribute to magnetic effects to be increased, and for those which cause
apparatus energy losses to be decreased. A considerable success has
already been achieved in these directions. The obstacles to further
improvement are in part difficulties in commercial application of
laboratory techniques, and in part ultimate limitations to the properties
of materials.

The chart in Fig. 11 shows the recent trend toward the realization
of the best possible magnetic properties in new materials or by im-
proved processes. Values are given for the year 1920 (i.e. before com-
mercial application of the permalloys), for 1939 as commercially and
as experimentally realized, and for what may be considered as the
attainable limit. It is evident that most of the properties which could
be improved have been improved in commercial materials by a factor
of ten or so within the last twenty years. A further improvement of
several properties by a factor as large as ten has been observed by
experimental procedures. These improvements have not been utilized
in all cases, either because they may not be of great practical value,
or because they involve processes which are commercially impracti-
cable, or materials which are very expensive. Thus, the highest
value of n,n has been attained on a single crystal of H2 purified iron ^*
cut so as to make a hollow parallelogram with sides parallel to the
(100) crystal axes, and annealed in H2 below the 01-7 transformation
point. The highest permanent magnet quality has been attained with
a platinum cobalt alloy "^^ costing some $400 per pound.

One of the main objectives of commercial magnetics research has
been the attainment of higher permeabilities — initial, maximum,
reversible, and at high flux densities. The reversible permeability is
closely linked with the initial permeability and saturation flux density.
The permeability at high flux densities *^ appears to be susceptible to
considerable increases by proper treatment of materials. The initial
permeability can be increased by proper technique, but such gains
are frequently sacrificed in practice because of unavoidable mechanical

« P. P. Cioffi & O. L. Boothbv, Phys. Rev. 55, 673 (1939).
« W. Jellinghaus, Zeit. Tech. Phys. 17, ii (1936).
«For example, at 5 = 10,000, or 5 = 20,000.

MAGNETIC MATERIALS IN TELEPHONE SYSTEM

463

1920

1939

COMMERCIAL

EXPERIMENTAL

=_"ZERO"

THEORETICAL
LIMIT

Fig. 11 — Improvements in the properties of magnetic materials since 1920,
in relation to theoretically possible properties.

464 BELL SYSTEM TECHNICAL JOURNAL

stresses, or because of large eddy current shielding. Higher maximum
permeabilities than now attainable do not promise great utility.
However, the low values of coercive force and hysteresis loss found
with materials having high maximum permeability may be sufficiently
desirable, regardless of permeability needs.

Another important objective of magnetics research has been to
reduce energy losses. Hysteresis loss at low flux densities, as indicated
by the loop area coefficient a, should be decreased to cut down har-
monic generation and modulation in magnetic core coils. Perminvar
has shown desirably reduced losses, but it is sensitive to magnetic and
mechanical conditions. Eddy currents are controlled by resistivity
and degree of subdivision of the magnetic core. The resistivity of
magnetic alloys can be increased to around 100 microhm-cms. by
alloying with large enough quantities of chromium, molybdenum, etc.,
but at a serious sacrifice of magnetic quality for resistivities above
about 60. Eddy current suppression by laminating or pulverizing
the magnetic material thus offers a greater range of control than re-
sistivity adjustment.

Permanent magnetic materials have also reached a very successful
stage, from the magnetic point of view. The greatest handicap of
the better materials is extreme hardness, which hampers fabricating
processes.

Impedance Properties of Electron Streams

By LISS C. PETERSON

The input impedance of an idealized space charge grid tube is
investigated under general conditions of space charge between the
accelerating grid and the negatively biased control grid. It is
shown that under certain space charge conditions the input
capacitance and conductance both may be negative. These im-
pedance properties persist up to frequencies for which the transit
angle is quite large. Possibilities of designing electronic negative
capacitances are thus opened up. Experimental results are also
given; these give a broad confirmation of the theoretical deductions.

PART I
Theory

IN the early stages of vacuum tube history the theoretical work on
d-c. space charge treated mainly potential distributions associated
with fairly small initial velocities of the electrons. With the advent
of multi-electrode tubes this situation changed for it then became
necessary to consider also potential distributions occurring when elec-
trons are injected with large initial velocities. Idealizations were
introduced to the extent that consideration was given only to space
charge conditions which can exist between two parallel planes at
known potentials when electrons with normal velocities corresponding
to these potentials are injected into the region through one or both
planes.^

Some time ago it was discovered experimentally that space charge
may under certain conditions produce a negative capacitance. The
negative capacitances were found during a series of low-frequency
measurements of the control-grid-to-ground capacitance of an experi-
mental space-charge-grid tube. In the course of these measurements
it was found that with all the electrodes carefully by-passed to ground
for a-c. except the negatively polarized control grid, the input
capacitance as well as the input conductance was negative in certain
domains which depended upon the d-c. operating voltages.

In order to arrive at an understanding of this fact, a-c. phenomena
must be considered under the general d-c. space charge conditions

1 Plato, Kleen, Rothe, Zeitschrift f. Phys., 101, July 1936. C. E. Fay, A. L.
Samuel, W. Shockley, Bell Sys. Tech. Jour., January 1938. B. Salzberg, A. V.
Haeff, R.C.A. Review, January 1938.

465

466 BELL SYSTEM TECHNICAL JOURNAL

referred to. The investigation comprises the calculation of the im-
pedance between two parallel planes in vacuum, at known d-c. poten-
tials, when an electron stream with normal d-c. velocities corresponding
to these potentials is injected at right angles to the planes. As a
further step, the effect of a negatively polarized grid interposed be-
tween the two planes will be considered. This latter arrangement
may be taken to correspond to an idealized space charge grid tube.

Before these calculations are presented it is well to set forth as
concisely as possible those results of the d-c. space charge analysis ^
which will be of most immediate interest. For this purpose we start
with a qualitative review of the work of Fay, Samuel and Shockley.

V02

Vom

Fig. 1 — Potential distributions between two planes of positive potential.

Consider two planes a and b, Fig. 1, of fixed d-c. potentials Foi and
T^o2 {Vq2 — Vqi) respectively, separated by a distance d. Let a uni-
directional and uniform electron stream of /q amp./cm.^ be injected
into the space from the left at right angles to the planes. When the
injected current is extremely small the potential distribution does not
differ very much from the free space one, represented by curve 1 on
Fig. 1. As the injected current is increased slightly, the potential
curve starts to sag, curve 2, and a further small increase causes a
potential minimum to develop at the electrode of lower potential,
curve 3. Still more increase in injected current makes the potential

^ Loc. cit.

IMPEDANCE PROPERTIES OF ELECTRON STREAMS 467

minimum T'om sink and move towards the electrode of higher potential,
curve 4. This state of affairs, with a continuously decreasing potential
minimum, continues until a critical value of injected current is reached.
The potential distribution may now be represented by curve 5. The
slightest further increase in injected current causes the potential
minimum to sink abruptly to zero: a virtual cathode is formed. This
abrupt change will be referred to as a Kipp.

With this qualitativ^e discussion of the various potential distributions
in mind a more detailed classification may be made. If both planes
are assumed to be at positive potentials we may classify the different
potential distributions as follows:

1. Type B

2. Type C

3. Type D

Type B corresponds to virtual cathode operation. This mode of
operation will be of no interest in this paper. Type C corresponds to
the case when a potential minimum at positive potential is present
between the planes and type D to the case when no such potential
minimum is present. For the purpose of analysis it is convenient to
distinguish between two types of D solution, i.e., Di and D2. This
comes about because the equations for potential distribution between
the planes may exhibit a minimum outside the planes. The Di
solutions correspond to the case when no such minimum exists and the
D2 solutions to the case when such a minimum does exist.

Let us consider Type C distributions in some more detail. For this

purpose attention is directed to Fig. 2. Here the ratio -jy^ is shown
as a function of the injected current /o with the ratio ^^^ as parameter.

1^01

The dotted curve represents a boundary line; for currents smaller
than that given by this boundary no potential minimum can exist
between the planes. Consider the curve 0:187. At the point a. the
potential minimum sets in and as more current is injected the potential
at the minimum decreases continuously until the point |S is reached.
Any further increase in current causes the potential minimurn to sink
abruptly to zero; thus ^ corresponds to the Kipp point. Now it is
seen that within a section of the curve a/? there are two possible
solutions, namely those corresponding to the section 1871 of the upper
branch and those corresponding to the lower branch 187. Let us
designate by Ci space charge conditions corresponding to the upper
branch a/S and by C2 those corresponding to the lower branch 187.

468

BELL SYSTEM TECHNICAL JOURNAL

After this survey of the several possible d-c. space charge conditions
we may proceed to the a-c. phenomena involved. At the present
time the impedance between the two planes of Fig. 1 can be found only
if the electrons move in one direction, i.e. if no virtual cathode is
present between the planes, and therefore this assumption is made.
It will be further assumed that electrode "a" where the injection takes
place is at a-c. ground potential. This insures constant conduction
current and electron speed at the plane of injection. The impedance

Fig. 2 — Variations of the magnitude of the potential minimum as
function of injected current.

may then be found by proper application of the general theory de-
veloped by MiiUer and Llewellyn. ^ The result is that the impedance
may be represented by a series combination of a resistance r and a
capacitance C having the values

r = J,

T^ 2 - 2 cos 0 - 0 sin

c = a

1

(1)

0"

1 - /o

2 sin g - g - g COS

2 J. Miiller, Hochfrequenztechnik u. Electroakustik, May 1933; F. B. Llewellyn,
Bell Sys. Tech. Jour., October 1935.

IMPEDANCE PROPERTIES OF ELECTRON STREAMS 469

where

Jn — T — -^0
kme

e = coT ■

Co = -J is the cold capacitance

T is transit time, seconds

e is electronic charge, coulombs

m is electronic mass, grams

— = 1.77 X 10^ coulomb/gm.

e is permittivity of vacuum = 8.85 X 10~^^ Farads/cm.^
k = 10-7.

Present interest lies mainly in the range where the transit angle d is
small. Expanding (1) and assuming 6 small, we have:

r =

1 (2)

C ^ Co ^3 •

6d

These formulas are also found in Miiller's paper.^

With regard to the resistance r it is immediately seen that it is
always positive and has the same equation as for complete space
charge with current /o and transit time T.

From the capacitance equation it is immediately evident that an
increase is caused by the presence of electrons. The dielectric constant
of space charge under the stipulated conditions is seen to be dependent
upon the d-c. conduction current Iq. As the injected current is
increased the capacitance increases initially at a fairly slow rate, but

as Jo -7-j becomes comparable with unity the capacitance rises rapidly.

It becomes infinite for

and if the left member of (3) were to become greater than unity the
capacitance would be negative. The possibility of such a condition
deserves careful consideration.

2 Loc. cit.

470 BELL SYSTEM TECHNICAL JOURNAL

From the discussion of the d-c. space charge it follows that the
d-c. current has an upper limit; i.e., the Kipp current with the value

_ 4 \2e (VFoi + VFoa)^

To determine the relation between the Kipp current (4) and the
current (3) required for infinite capacitance, consider the d-c. equations:

Uh = Ua -f- aai + T TT

kme 2 . .

2 kme 6

where Ub and Ua are electron speeds in cm./sec. at planes h and a re-
spectively and aa is the acceleration in cm./sec.^ at plane a. Elimi-
nating aa and introducing the values of iih and Ua in terms of Vqi and
Foi we find

\ ek 1q la

(6)

When the transit time T is eliminated between (3) and (6) the result is

But this is precisely the Kipp current as given by (4). Equation (3),
therefore, expresses the Kipp relation between current and transit
time. It has thus been found that the series capacitance at the Kipp
point becomes infinite, w^hereas the impedance between the two planes
is a pure resistance.

Consider next the possibility of Jq ^ attaining values larger than

unity when the d-c. current /o is limited to values smaller than the
Kipp value (4). The only manner in which this could happen would
be for (6) to have one root T^ such that T^ > Tk where Tk is the
transit time at Kipp. To determine this (6) is transformed by intro-
ducing /ok and Tk as parameters. Thus,

^)'-/^-3^ + 2 = 0. (8)

1 K / J-QK J- K

The discriminant D of (8) is

Ikq \ ^ / 1 -^A'O

^ = 'x ^-17' (')

IMPEDANCE PROPERTIES OF ELECTRON STREAMS

An

and as /o — /a'o it is clear that

Z) < 0.

(10)

Hence, since the discriminant in general is negative (8) has three
real roots. Two of these are positive and one negative. A double
root occurs for /q = /a'o, and the value of this root is clearly T = Tr'
For currents smaller than the Kipp current there are two positive
roots Ti and T^ such that Ti < Tr and T^ > Tk-

Thus it becomes evident that space charge conditions corresponding
to the roots T^ result in a negative capacitance. Interpreted in terms

CATHODE

O O

O S!

o o

Fig. 3 — Schematic of a space charge grid tube.

of Fig. 2, the roots Ti correspond to the upper branch a^ and the
roots 7^2 to the lower branch y^. Hence, it is evident that space
charge corresponding to the lower branch has a negative dielectric
constant.

Consider next the system pictured schematically in Fig. 3. It
differs basically from that in Fig. 1 in that a negatively polarized
grid has been interposed between the planes a and h of Fig. 1. The
arrangement shown in Fig. 3 may be considered to be equivalent to
a space charge grid tube with the accelerating grid Gi and control
grid Gi. The grid Gi is assumed to be by-passed to the cathode for
a-c. The planes indicated by 2 and 3 are imaginary planes located

472

BELL SYSTEM TECHNICAL JOURNAL

on opposite sides of the control grid wires and are assumed to be
sufficiently far away from the grid to insure that the potential distribu-
tion at these planes is essentially that of a grid-free space. Moreover,
if the grid is fine-meshed these planes may be located quite close
together so that the distance between them is negligible in comparison
with the distances between Gi and plane 2, and between plane 3 and
the plate. This insures that the potentials of the two planes are
practically equal. Since the grid d draws only displacement current,
the conduction currents at the planes 2 and 3 are equal. Since the
potentials of the two planes are equal, the electron speeds are also
equal. The boundary conditions in the plane of Gi are the same as
those used in deriving (1), i.e., constant conduction current and
electron-speed. Then, following the method employed by Llewellyn ^
in his treatment of the negative triode, the input impedance may be
found. Since the details are uninteresting the result is merely quoted.
On the assumption that the plate is short-circuited to the cathode by
a large condenser the input impedance between grid and cathode
may be written as:

Z ^ Z,-\-

AxA,

eiA^ + A^ + G.B-i + D.Ci)'

(11)

where Zg is the impedance (capacitive) between the planes 2 or 3 and
Gi and where Ai, A^, Gu B^, Di and d have the values:

A, =
A2 =

Gy =

B,=

C2 =

In (12):

1

(ic

1

{io})Hi + -^ (2 - 2e-'»i - idi - id,e-'^0
kme

(iooydi + ^ (2 - 2e-'«2 - i92 - id2e-'^')
kme

1

(1 _ g-iBi _ ie^e~^^i)

1

(*w) 2

3 la^SG^e-^^^ + g-^«2 - 1) -f Mo2iw(g-''«2 - 1)

1 - e-'^i - T

ao2

(1 -e-

iBi

hneiioiY

t(j^U02

idie'

-"o]

(12)

M02 is the d-c. speed at planes 2 or 3.

ao2 and aos are the d-c. accelerations at the planes 2 and 3
respectively.

2 Loc. cit.

IMPEDANCE PROPERTIES OF ELECTRON STREAMS

473

When the transit angles di and 6^ are very small and when the effect
of the space between control grid and anode may be ignored, evaluation
of (11) yields the result:

1 -

Z = Z, + ry

where

4 2wo2

1 - Ji

TV
6di

1 - Jc

2Uni.

1 - /r

2un

Cn =

d\

tOi

1 - J,

2Uo2

(13)

(14)

Co is the capacitance in the absence of electrons.

The input impedance is thus seen to be a series circuit composed of
a resistance and a capacitance, i.e.

where

Z = p +

1

icoC

J.

1 - Jc

7?

2Uq2

4 2mo2 ddi

1 -

TV

2Uo2

1_ 1 1 ^ ~-^'6d[

1 - /o

2Mo2

(15)

(16)

(17)

In studying the capacitance and resistance as functions of space
charge it is evident from (16) and (17) that space charge enters

.3

In what follows

7* T^ ^ T T^ '

essentially through the functions -^ — - and °

2u(

6di

474

BELL SYSTEM TECHNICAL JOURNAL

the capacitance Cg is assumed to be so large that the first term in
(17) may be ignored. The ratio between "hot" and "cold" capaci-
tance may then be written :

y^ 1 — Jq ;s

Co

Write the conductance 1/p as

1 - /(

TV
6di

p ri

(18)

(19)

and note that the first factor of the right member is always positive.
F may be termed the relative input conductance.

Before the theoretical curves are discussed a few words about the

J T i 2"" 3

functions -^ and Jo -rr- are in order. Thev will be expressed in

2z<o2 oai

terms of two parameters, i.e., ^ and ^ where

Fo2

ip =

Vol

(20)

and ^ is a constant of integration which assumes different values
depending upon the type of space charge present.^ In terms of these
parameters one may show that :

Jo^ =

Jo

J

[V^l/2 ^ 1 _ V(g^)l/2 + 1]3

6di (|i/2 _ 2)VFMn;

- {{^<py" - 2)V(i^F^TT

Tr- _ \:<e'' + 1 - <(^<py^' + 1]-

2«o2 {^fY'-

Type
0 < t < «,,

(21)

[_\e" - 1 - V(^«^)^/' - 1?

/o

Ti^ [V^

1/2

- ((^^)i/2 + 2)V(^^)i/2 - 1 [

1 - V(i^F^"^T]2

2uc

U^pY"

1

Type
< ^ < ^,

(22)

2 The parameters I /a and 1//3 used by Fay, Samuel and Schockley are related
to ^ as follows:

i = a Type Di

I = - Type D2.

IMPEDANCE PROPERTIES OF ELECTRON STREAMS

475

T 3

^0 T^-r

/o

[Va/2 _ 1 4. V(^^)l/2 - 1]3

ddi (^1/2 _|_ 2)V?^'" - 1

2n<

ikfY"

Type

(23)

"P \ ^if ^

The parameter ^ is without physical significance for the D solutions
but serves merely as a convenient constant of integration. For the
solutions of C type, however, ^ is of direct physical significance. For

here ^ represents the ratio -^7— . In the language used in the previous

Va

1 .

qualitative discussion of space charge it is clear that ^ = — is the point

where a potential minimum sets in and ^ = ( 1 H — p I is the Kipp

point. Calculations for C2 solutions are not included.

The result of the calculations of capacitance and conductance are
shown on Figs. 4 to 8. Figure 8 is an enlargement of Fig. 7 for small

-^

1

^^

V

\

TYPE C,

N

V

\

\

\

1

^ '^KIPP.

\

'

1.3 1.4 1.5 1.6 1.7 1.8 1.9

INTEGRATION CONSTANT /^

2.0 2.1

2.2

Fig. 4 — Relative input capacitance of an idealized space charge grid tube for different
space charge conditions (voltage ratio tp = 1.0).

values of F. Three values of the parameter <p were selected, i.e., 0.04,
0.25 and 1. The curves demonstrate regions of negative capacitance
as well as of negative conductance. Note that as the parameter (p is
made smaller both the capacitance and conductance pass through

476

BELL SYSTEM TECHNICAL JOURNAL

/■

.

1

\
I

\

1

1

I

\
I

L' 1

02

1
1

i

"'0 123456789 10

INTEGRATION CONSTANT /F

Fig 5 — Relative input capacitance of an idealized space charge grid tube for different
space charge conditions (voltage ratio <p = 0.25).

z -12

■20

/

^-'

■

/

Di

D2

1 V

""0 2 4 6 8 10 12 14 16 18 20

INTEGRATION CONSTANT 'JT

Fig. 6 — Relative input capacitance of an idealized space charge grid tube for different
space charge conditions (voltage ratio <p = 0.04).

IMPEDANCE PROPERTIES OF ELECTRON STREAMS

477

zero for smaller values of ^. Consider for instance the case for which
(f = 0.04. The capacitance is here negative even in regions of small
space charge and it is seen that over a wide range of the parameter ^
the capacitance is nearly constant. Both capacitance and conductance

-5.0,

— ^

1

KIPP I

6 8 10 12 14

INTEGRATION CONSTANT ^i"

20

Fig. 7 — Relative input conductance of an idealized space charge grid tube for different

space charge conditions.

2.5 5.0

7 5 10.0 125 1570 17.5 20.0 22.0 25.0

INTEGRATION CONSTANT \/|"

Fig. 8 — Relative input conductance of an idealized space charge grid tube for different

space charge conditions.

pass through zero for the same value of ^ and one sees that in case of
<P = 0.04 no critical adjustment seems necessary. The conclusion is
thus arrived at that the idealized space charge grid tube may be
made to operate without input capacitance or loading up to moderately

478 BELL SYSTEM TECHNICAL JOURNAL

high frequencies. In addition, the possibility of designing an electronic
negative capacitance is opened up and this is a highly desirable ob-
jective.

However, it must be kept in mind that in the discussion, effects
such as velocity distributions, electron deflections and dispersion forces
have been neglected. Furthermore, in an actual tube the capacitance
Cg must also be considered. At the Kipp the capacitance C is equal
to — oc ; therefore, as the Kipp point is approached a positive capaci-
tance is expected.

The capacitance and conductance both pass through zero when

Jo^=l, (24)

or when

J" 2

«02 = /o -y- • (25)

But in general

Wo2 = uoi + aoiTi + Jo-j- > (26)

where Woi and aoi are the d-c. speed and acceleration in the plane of
grid Gi, Fig. 3.

The relation between initial speed and acceleration for zero capaci-
tance and conductance is, therefore:

woi + aoiTi = 0 (27)

and since both 7/01 and Ti are inherently positive, the initial acceleration
must be negative. For the capacitance to be negative the requirement
is obviously

«oi + aoiTi < 0. (28)

Necessary requirements for a negative capacitance are thus a finite
electron speed and a retarding field at the plane of injection.

PART II
Experimental

In this section some experimental results will be discussed. The
measurements all refer to the capacitance between control grid and
ground of some experimental tubes. The tubes were cylindrical in
structure and contained two positive grids close to the cathode followed
by a negative control grid. The first positive grid has the essential
function of controlling the magnitude of the current whereas the

IMPEDANCE PROPERTIES OF ELECTRON STREAMS

479

second determines the initial speed with which the electrons enter the
space adjacent to the control grid.

In Fig. 9 the measured input capacitance and plate current are
shown as functions of the voltage Vgi of the first grid. It is seen that
as the plate current increases the capacitance gradually decreases,
passes through zero somewhat before the plate current has reached its
maximum and then becomes negative; it passes through a minimum
and then gradually assumes a positive value equal to about twice the
cold capacitance. This behavior of the capacitance is typical of the
formation of a virtual cathode, which in the present instance appears

Vp

= 160 V.

r— '

Vg3= -6V.
If =0.36 a.

,;

~^

/

r

N

U

/

w

8 10 12 14 16 18 20
VOLTAGE ON FIRST GRID

22 24 26

Fig. 9 — Measured input capacitance of experimental vacuum tube no. 55
(grid signal — 0.18 volts r.m.s. at 50 kc).

to be gradual. The negative capacitance is present in a small interval
of the voltage Vgi immediately before and perhaps also during a part
of the virtual cathode formation.

Figure 10 shows the measured input capacitance as a function of
the control grid bias Vgz for several values of the voltage Vgi. For
comparison purposes the corresponding plate currents are also shown.
In the region of low plate current where a virtual cathode is present
the capacitance is positive and larger than the cold capacitance.
Where the plate current curve starts to bend over, that is, where the

480

BELL SYSTEM TECHNICAL JOURNAL

virtual cathode starts to release, the capacitance decreases. It is
negative in a small domain and turns ultimately positive. The plate
current curve corresponding to Vgi = 30 volts indicates that the

10

£ 0

Z -5

-10

-15

-20

-25

i 1. »——

1

■^^

\

^^. 30
25 \^

S^

VG| in volts =20

\

y

/

Vp = teov

Vg2 = 30V.
If=0.36A.

\

}

r'

\

/

\

\

'

\

I

1

\

■10 -8 -6 -4

CONTROL GRID VOLTAGE

Fig. 10 — Measured input capacitance of experimental vacuum tube no. 55
(grid signal = 0.18 volts r.m.s. at 50 kc).

virtual cathode is present throughout the range of negative bias and
the corresponding capacitance curve is positive everywhere.

Figure 11 refers to capacitance measurements on a tube in which a

IMPEDANCE PROPERTIES OF ELECTRON STREAMS

481

Kipp occurred. Again the capacitance behaves essentially the same
except that it suddenly jumps from a large negative value to the
positive value corresponding to virtual cathode operation.

In comparing the theoretical and experimental results, it is seen
that the theory gives predictions which are broadly in accord with
experiments.

-35

10

Vp

= 175V

-,4tS^

Vg4 = 150V.
Vg3=-2V.
Vg2=75V.
If = 0.64A.

y

r*!

^KIPP.

^y

y

1
\

^

^

V

,

^

>

k

0 c

i

\

5 (

} 1

0 1

2 1'

\ 1

6 1

6 2

0 2'c

Fig. U-

VOLTAGE ON FIRST GRID

-Measured input capacitance of experimental vacuum tube no. 59
(grid signal = 0.05 volts r.m.s. at 50 kc).

Acknowledgment

I am indebted to Mr. E. J,. Buckley for assistance in the experi-
mental work, to Miss M. Packer for the numerical calculations, to
Mr. C. A. Bieling for the mechanical tube design, and last but not
least to Dr. F. B. Llewellyn for stimulating discussions.

Plastic Materials in Telephone Use*

By J. R. TOWNSEND and W. J. CLARKE

ORGANIC plastics are used extensively in the manufacture of
telephone apparatus and equipment. They belong to the class
of materials known as insulators but are very often employed not
only for their electrical properties but for their unique manufacturing
and structural possibilities. Good insulating materials are very im-
portant in the telephone field although the voltage and current used
are much smaller than in the power field. Progressive improvement
in transmission, especially for long distance telephone service, has re-
quired that the telephone industry as a whole provide sensitive instru-
ments and that there be a minimum loss of the electrical impulse due
to leakage through insulating materials.

Rubber became at one time the most universally used insulating
material in telephone apparatus. Where superior insulating proper-
ties are required, rubber has been employed not only in the soft
vulcanized form as a covering for wire but as hard rubber. Its use
was considerably curtailed as a molding material during the period of
the world war due to the high price of rubber. This stimulated the
substitution of phenol plastics which were found to produce more
permanent parts. Although rubber must be classed as an organic
plastic, it will not be dealt with here except in passing since it com-
prises a large field in its own right and quite distinct from that of the
synthetic plastics. In recent years rubber has been greatly improved
in life, stability, light sensitivity and resistance to cold flow so that its
technical uses in the telephone plant are again increasing.

Shellac and asphalt plastics, both natural materials, were among the
early important plastics employed in the telephone art. A shellac
compound is still the best material for a panel system commutator
where there are many long and delicate contact segments and where
the principal problem is to obtain accurate location between the insula-
tion and the brass segments together with uniform wear. The low
molding temperatures and pressures for the shellac mica compound
contribute to the success of the manufacture of this part. (See Fig. 1.)

Other early plastics that have found some limited uses are cellulose

* Presented before the Organic Plastics Section of the Paint and Varnish Division
of the American Chemical Society, Baltimore, Md., April 3-7, 1939.

482

PLASTIC MATERIALS IN TELEPHONE USE

483

nitrate and casein. However, the cellulose nitrate plastics were only
sparingly employed for telephone construction because of the serious
fire hazard. Casein has long been used for key buttons and similar
minor applications.

The great expansion of the use of molded plastics in the telephone
plant really began with the development of organic materials which
had superior manufacturing and structural characteristics over other
materials. The newer plastics are of value, therefore, as much from
the economies of manufacture as from their superiority over the pre-
viously used materials.

Plastics are conventionally divided into two groups: (1) the thermo-
plastics and (2) the thermosetting plastics. The first, considered as

Fig. 1 — Panel system commutator (flash type mold).

organic materials, are permanently soluble and fusible as well as fairly
rigid at normal or working temperatures and may be deformed under
heat and pressure. The second are initially thermoplastic and become
insoluble and infusible after a period of time upon application of heat
and pressure. These important properties are due to the chemical
nature and molecular structure of the materials. All synthetic
plastics are polymeric substances, that is, they are the result of a
polymerization or condensation from simple organic molecules by
linkage of the molecules in fairly definite ways. By a polymerization
reaction is meant a reaction in which a more or less considerable
number of molecules unite to form larger complexes of the same chemi-
cal composition. A condensation reaction on the other hand is one

484 BELL SYSTEM TECHNICAL JOURNAL

in which molecules join together to give a larger complex but during the
reaction there is a separation of a small amount of water, alcohol or
some other substance, so that the final chemical composition is not
quite the same as at the start.

Those materials which are thermoplastic and readily soluble owe
these characteristics to the fact that the molecules are linked essentially
in chain-like fashion. The forces holding the chains together are of a
secondary valence character, that is, the chains are free to move apart
when heat is applied or a solvent is present. Vinyl, acryl and styryl
resins are typical thermoplastics and incidentally each is formed from
a monomeric material containing the characteristic ethylene grouping
CH2 = C<. The properties of synthetic materials of the thermo-
plastic type vary with the average chain length and distribution, and
with the nature of any side groups which may be attached to the main
hydrocarbon chains. The materials do not have sharp melting points
as do more simple organic substances but soften gradually when they
are warmed. Usually on further heating decomposition occurs to
the monomeric form before any rapid flow point is reached.

The molecules of thermosetting plastics are initially in chain-like
form also, although the chains are generally much shorter in length
than those of the thermoplastics. On heating, the material fuses and
the chains become cross-linked sufhciently to give a permanent and
rigid three-dimensional structure. In the case of a phenol-for-
maldehyde resin the linkage between chains is directly through CH2
groups (or according to some investigators through — O — CH2 or
— CH2 — O — CH2-groups) and the force necessary to separate the
chains is therefore high and of an order equal to that needed to break
up any complex organic molecule. Infusibility and inability to go
into solution are consequently the prominent characteristics of a
phenolic resin in the heat-hardened form. In other materials belong-
ing in this class the cross-linkage may be brought about through oxygen
or sulphur atoms though the hardening action sometimes occurs
more slowly. Certain oxygen convertible alkyd resins for example are
particularly useful as organic finishes because they may be greatly
hardened and in this case very much toughened by a baking process,
the necessary oxygen for cross-linkage of the polymeric resin being
absorbed from the surrounding air.

The properties of the more modern materials including the phenol
plastics, the cellulose derivatives and the ethenoid (vinyl, acryl and
styryl) type plastics, have yet to be fully evaluated but certain elec-
trical and mechanical characteristics of these materials have already
resulted in their adoption to a|'greater or lesser extent in the telephone

PLASTIC MATERIALS IN TELEPHONE USE 485

plant. Phenol plastics have been employed in the molding of the
regular telephone hand set, recent production being in excess of
1,000,000 units per year. Cellulose acetate is widely used in foil form.
Plastics in the form of synthetic organic finishes are used for protection,
decoration and insulating purposes on apparatus and equipment.
For the purpose of discussion, plastics in the telephone plant may be
grouped as follows:

1. Molding plastics.

2. Sheet materials (phenol fiber, acetate foil, etc.).

3. Synthetic organic finishes, adhesives and miscellaneous special items.

Objectives of Ideal Telephone Plastics

Telephone apparatus and equipment are not sold as consumption
goods but the service rendered by it is sold to the subscriber. Good
service means a minimum of breakdown due to replacement of mal-
functioning parts, repairs and maintenance. High maintenance costs
are inconsistent with the best service at the lowest cost. Uniformly
high quality of materials throughout the economic life of the telephone
plant is therefore essential.

The molding plastics and sheet materials account for the bulk of the
plastics used in the telephone plant and the objectives of these materials
are similar enough to permit them to be listed together. There are
given below the general and specific properties that must be considered
in such materials when they are to be used in the telephone industry.
The level of quality demanded in specific properties will obviously
depend on the application.

1. General requirements.

a. Strength, hardness, toughness.

b. Low density (to decrease mechanical inertia, aid manual use).

c. Chemical inertness in air, or in contact with other materials.

d. Resistance to humidity (minimum of swelling and shrinkage

with variations of moisture content of the air).

e. Ability to withstand temperature, heat and cold without too

great impairment of strength and shape.

/. Ability to reproduce die surface accurately and give good ap-
pearance to finished part.

g. Light stability.

h. Relative non-inflammability.

i. No odor, no harm to the skin.

j. Resistance to insect attack.

486 BELL SYSTEM TECHNICAL JOURNAL

2. Specific mechanical properties.

a. Transverse strength.

b. Impact strength.

c. Cold flow.

d. Shrinkage.

e. Wear resistance.
/. Machinability.

3. Specific electrical properties.

a. Insulation resistance

1. as afl^ected by humidity.

2. as afifected by light.

b. Dielectric constant.

c. Power factor.

d. Dielectric strength.

4. Moldability.

a. Free flow at moderate temperature and pressure.

b. Favorable setting characteristics.

c. Short molding cycle.

d. No tendency to stick to die.

e. No abrasion of die surface.

/. Minimum shrinkage in mold.
g. Low bulk factor.

5. Economic considerations.

a. Low density materials preferred.

b. Cost.

c. Die life.

d. Utilization of scrap. ^

e. Molding cycle time.

/. Trimming and finishing characteristics.
g. Refinishing or maintenance.

The objectives of an ideal plastic in the telephone industry depend
upon the use to which the material will be put in the telephone plant.
The material may be a structural member, an insulator, or both, and
may be in the hands of the public or in a telephone exchange. All of
the above requirements need not be met but excellence in a majority
of these properties is generally desirable.

The Molding of Telephone Parts

Molding involves consideration of (1) the molding compound (2)
the die (3) the press (4) the heating and cooling system (5) method of
ejecting part from mold (6) finning and trimming methods. Regard-
less of the type of plastic, these operations are necessary.

PLASTIC MATERIALS IN TELEPHONE USE 487

As to the molding compounds, the Bell System obtains from the
suppliers whatever materials are needed and this is generally true for
the industry. These range from the plain wood flour-filled phenolics
to the various thermoplastics depending on the application. Exact
compositions are seldom specified in order that the manufacturer be
given all possible opportunity to exercise his ingenuity to produce
satisfactory quality material.

The die or mold is such an important item in the molding of a
material that several points should be emphasized about it. The
dies are always expensive. Every part is an individual design problem,
involving flow of material in the cavity, use of inserts, opening and
closing, the clamping of die parts under high pressures, and alignment.
Everything possible must be done to reduce the complication of the die;
eliminate inserts if possible, provide generous fillets, ample taper for
removal of parts, and facilitate flow of the compound. The Bell
System has found it advantageous to make most of its own dies. The
conventional boring, milling and hobbing processes are used. Very
little success has been had with other methods, such as casting with
hard alloys.

In spite of the expensive and time-consuming effort that must be
encountered in designing and building a molding die, the finished die
when properly used represents one of the most indestructible tools of
modern manufacture. The parts are finished, require little or no
surface treatment, the dimensions are accurate and sub-assembly
operations may already be completed as the part emerges from the
die.

The dies used are of the three general types: the open or flash die,
the closed or positive die, and the injection die. The open type con-
sists of two parts which come together at a cutting edge or ridge that
surrounds both halves of the die. Since this ridge or cutting edge
must withstand the full pressure of the press it is usually about one-
eighth of an inch wide. Flash dies are all relatively simple, readily
loaded, and the charge need not be measured accurately, any excess
being forced out as the two halves close until the cutting edges come
into contact. Such molds may be used for any molding compound not
requiring high pressure and which does not have high die shrinkage.
Shellac-mica commutators (Fig. 1) are manufactured by means of a
flash die.

The positive type die consists of a plunger and a cavity shaped to
produce the finished part. The plunger may aid in shaping the part.
Only enough material is placed in the die to make the part. The ma-
terial may be weighed in separate charges or preformed by a separate

488

BELL SYSTEM TECHNICAL JOURNAL

operation. The cavity is loaded and the plunger forced down, forming
the part. Multiple cavity molds cannot be loaded exactly alike and
hence some provision must be made for the escape of excess material,
forming a flash that must be subsequently removed. Such dies must
be carefully designed so that the fin is located for easy trimming and to
provide the best appearance. These multicavity molds are frequently
called semi-positive molds to differentiate them from a truly positive
mold where there is little flash. A typical telephone part made in a
semi-positive mold is the handset handle shown in Fig. 2.

Fig. 2 — Mold for handset handle.

The recently developed process of injection molding which consists
in forcing plastic material through a nozzle into a completely closed die
from an external compression chamber is also being used and promises
to alter many of the present operations. Since the opening and the
closing of the die are not related to the application of pressure, greater
freedom of design is possible. Furthermore, since full pressure is not
applied by this method until the die cavity is completely filled with
material, the material already in the die tends to support inserts and

PLASTIC MATERIALS IN TELEPHONE USE

489

hold them in their true position. Hence more delicate inserts are
possible by this method of manufacture. Since the material is en-
closed in an auxiliary pressure chamber and is not exposed to the
atmosphere, greater freedom from room dust is possible, rendering
this method ideal for colored plastics. A terminal block used to
terminate the subscribers telephone cord is made from thermoplastic
molded cellulose acetate compounds as shown in Fig. 3.

Finishing and trimming methods are largely determined by the
design and the class of service required of a molded part. In the case
of the injected cellulose acetate terminal block mentioned above the
gates are trimmed off by a simple trimming punch and the scrap is

Fig. 3 — Terminal block.

reused. This part is covered in service and the appearance of the
block is therefore not a major factor.

The telephone handset, since it is in the hands of the public, must
be carefully finned for two reasons: (t) to avoid surface roughness
and (2) to provide good appearance. The handset handle was orig-
inally ground along the fin left by the semi-positive mold and then
buffed. The operation was not only expensive but tended to grind
off a large portion of the surface of the handle. This removed the
resin-rich surface and tended to expose the filler of the phenol plastic
molding compound, thus reducing the appearance life of the handle.
The more recent product of the Bell System is being grooved along
the die parting line. This removes the fin, a minimum of the resin-

490 BELL SYSTEM TECHNICAL JOURNAL

rich surface and does not detract from the appearance of the handset.
Automatic grooving machines were developed for this purpose. Figure
4 shows a grooved handset handle.

It has been found necessary to pay close attention to the design in
order that die parting lines, ejector pin marks, gate marks and the like
will appear at points where they may be readily eliminated by simple
trimming and grooving operations, or where they may be left without
objection to appearance or function of the part.

Fig. 4 — Grooved handset handle.

General Test Methods and Requirements

The most satisfactory test is one that can be applied to the finished
part to measure the ability of that part to perform its function satis-
factorily in service. This ideal is seldom realized, not only because of
the difiiculty of defining the service requirements but of finding tests
that are wholly representative of service conditions. It is customary,
therefore, to apply a series of tests whose sum total will approach the
ideal as nearly as practicable. Molded organic plastic parts are
different from parts made from most other materials in that the
molding process may modify them and render them quite different
from the raw material. In the case of thermosetting compounds
this is particularly true.

Tests are in the main applied, therefore, to a molded part of repre-
sentative specimen of the fabricated material. In the telephone plant
the items that are of most importance are strength, both transverse
and impact, permanence of form, appearance, effect of moisture and
drying on swelling and shrinkage, insulation resistance, electrical
breakdown potential, and reaction on adjacent materials. Methods

PLASTIC MATERIALS IN TELEPHONE USE

491

of making all of these tests have been worked out and are supplemented
by apparatus tests made on the manufactured product.

There is no known test that will measure completely the quality
of a phenol plastic part and it is necessary to resort to the expedient
of testing standard bars molded under specified conditions. Five bars
are molded in a positive type die as shown in Fig. 5. The step arrange-

Fig. 5 — Specimen mold and bars.

ment provides for flow within the die similar in many respects to the
molding of actual parts. The test bars provide transverse or flexural
strength, impact insulation and cold flow test specimens. The methods
used, whenever possible, are those of the American Society for Testing
Materials.

492

BELL SYSTEM TECHNICAL JOURNAL

The cold flow test is specially designed to note the distortion of
materials which in service are under pressure, such as spring pileups,
inserts and apparatus in the form of banks and terminal blocks. The
specimen which is 3/^ X 3^ X 3^" in size is first conditioned at 150° F.

Fig. 6 — Impact machine.

for 4 hours and then to 90 per cent R.H. and 85° F. for 68 hours to
permit absorption of moisture. It is then held under 4000 lbs. per
square inch for 24 hours at 120° F. i 1° and the percentage change in
thickness determined.

PLASTIC MATERIALS IN TELEPHONE USE 493

Typical Applications of Thermosetting Plastics
Phenol Plastics

A typical phenol plastic telephone part is the handle for the handset.
This part is molded in a multiple semi-positive die of the kind de-
scribed above.

In addition to the laboratory tests on the raw material, samples of
the molded handles must withstand a dropping test. After being
conditioned, handles representative of a given lot are equipped with
transmitters and receivers and dropped down a nearly vertical chute
to strike on a steel block. The test is made by dropping first at 36
inches and then increasing the drop in increments of 2" until the handle
breaks.^ Normal product handles will withstand a drop of 55 inches
on a steel block without failure.

The electrical properties of phenol plastic compounds are adequate
for most uses in the telephone plant. Two grades are recognized,
however, the mechanical and the electrical. Fully 90 per cent of the
uses involve the mechanical grades. For certain high-frequency in-
sulation purposes special mica-filled phenol plastics are used in place
of the regular wood and cotton filled varieties.

One of the outstanding disadvantages of a phenol plastic is the
ease with which it carbonizes on exposure to electrical arcing. For
this reason phenol plastic compounds have only a limited use for com-
mutators and similar applications. However, in addition to handsets
they have proved of value for mouthpieces, receiver cases, subset
housings, non-magnetic coil forms, coil cases, jack mounting blanks
and terminal blocks.

Phenol Fiber

Phenol fiber for telephone apparatus is made of alpha cellulose
paper, Kraft paper and rag paper by the usual impregnation with a
suitable phenol resin varnish and lamination of a number of sheets
under heat and pressure. The most important requirement for the
paper is that it shall be pure, clean and free from electrolytes. The
paper is carefully tested for chlorides, conductivity of water extract
and for alcohol soluble materials. Several grades of phenol fiber are
necessary to meet the requirements, some of which are largely me-
chanical and others electrical.

The principal tests for phenol fiber are cold flow and shrinkage,
insulation resistance, corrosion tendency, arc resistance, transverse
strength and impact. Arc resistance applies to the case where wiping

' "The Impact Testing of Plastics," Robert Burns and Walter W. Werring, Proc.
A.S.J.M., 19, Vol. 38, 1938.

494

BELL SYSTEM TECHNICAL JOURNAL

contacts cause an arc to flash across the surface of the phenol fiber.
This is a condition peculiar to telephone apparatus and a special test
has been designed which simulates service conditions. An insulator
cam (see Figs. 7 and 8) is prepared as the test specimen. The cams
are rotated at a speed of 10.5 to 11.5 revolutions per minute. Two
metal cams are attached concentrically with each surface of the phenol
fiber cam. Attached to a brush that wipes over the cam tensioned to

BLANK OUT BLACK PORTIONS

COPPER SHEET
(0.0201" thick)

ARCING CAM
Fig. 7 — Arc resistance test cam.

a pressure of 60 grams is a circuit containing S}/2 counting relays which
supplies a severe inductive load. This is representative of a severe
service condition. Failure is indicated when tracking of carbonaceous
material shorts a cam segment the distance of 15° or when the 1/32"
thick material is punctured, and the test is then stopped automatically.
A good grade of fiber will resist over 1,800 revolutions whereas a poor
grade will fail in 4 to 100 revolutions.

PLASTIC MATERIALS IN TELEPHONE USE

495

Phenol Fabric

Phenol fabric is similar to phenol fiber except that it is made with

fabric instead of paper. It is generally used for its mechanical strength

since its electrical properties are inferior to fiber. Phenol fabric is

used in tools where high strength and resistance to impact and bending

— NOTES —
ARCING BRUSH AND ADJUSTABLE
SIGNAL BRUSH ARE SHOWN IN
PROPER POSITION FOR START OF A
TEST WITH ARCING BRUSH JUST
BREAKING AND SIGNAL BRUSH
JUST MAKING

IN THIS POSITION THE POINTER
SHOULD BE AT 90 DEGREES ON THE
PROTRACTOR SCALE
WHEN THESE ADJUSTMENTS HAVE
BEEN MADE ADVANCE PROTRACTOR
IN A CLOCKWISE DIRECTION 15
DEGREES FROM ORIGINAL SETTING
AND START THE TEST

BANK OF 208-TYPE
RELAYS
208Bq 208Gr)

B p Go

PIGTAIL
CONNECTION

HIGH-SENSITIVITY
RELAY

+i

APPROXIMATELY
no VOLTS DC

Fig. 8 — Circuit for arc resistance test.

are necessary, in terminal plates, cable terminals, gears and in general
where phenol fiber does not have suitable structural properties.

Urea- Formaldehyde Plastics
Condensation products made from urea and formaldehyde have
attractive possibilities as thermosetting plastics. Relatively light-

496 BELL SYSTEM TECHNICAL JOURNAL

fast colored parts with porcelain-like surface luster are possible with
these materials. The molding cycle is slightly shorter than for phenol
plastics and the material at first is somewhat more fluid. Tight molds
are therefore necessary in order to get sufficient pressure.

The principal difficulty with urea-formaldehyde plastics has been
that on exposure to heating and cooling or humidification and drying
cycles, there is a tendency toward cracking, particularly at changes in
section and around inserts. Molded into uniform thin sections with-
out inserts they are reasonably satisfactory plastics.

At present there are practically no urea-formaldehyde plastics em-
ployed in telephone apparatus because the wide continental climatic
conditions and exacting requirements will not permit their use. Re-
cently there have been improvements made from a stability stand-
point and it is believed future application may be found for these
plastics, particularly in view of their color permanence.

Applications of Thermoplastic Materials
Cellulose Acetate

The principal use of cellulose acetate is for interleaving in coils.
Various relay coils are made of layers of cellulose acetate over which a
layer of enamel coated copper wire is wound. Layer upon layer of
wire and acetate sheet form a coil. These are then assembled on a
core and spoolheads attached. One of the phenol fiber spoolheads
has a surface coating of cellulose acetate and the winding is pressed
against this spoolhead and dipped in acetone. This dissolves or
softens the exposed edges of acetate and the whole coil is firmly secured
to the spoolhead.

Cellulose acetate is used for this purpose since it is practically inert
as regards corrosion of the fine copper wire in contact with it and in
this respect it is superior to any known material. It is permanent,
reasonably fireproof and has high insulation resistance. Two grades
of cellulose acetate sheet are used in telephone practice. These are
the window grade used as a window or covering over designations and
an electrical grade for coil use. The principal tests for the electrical
grade are insulation resistance, shrinkage, and resistance to burning.

The principal use of molding grade of cellulose acetate is for the
terminal block (Fig. 3) mentioned above. Here the application is
mainly structural since it has more than adequate electrical insulation.
Another application for cellulose acetate is a test strip where a surface
layer of acetate over phenol plastic avoids carbonization of the latter.

PLASTIC MATERIALS IN TELEPHONE USE 497

A crylate Resins

The clear water-white plastics derived from the polymerization of
the esters of acrylic and methacrylic acid are at present being used
only for windows, viewing lenses on designation strips and other optical
uses in telephone apparatus. This is a new plastic and applications
will no doubt develop in time, taking advantage not only of color but
of the mechanical and electrical properties and insensitivity to moisture.

Vinyl Resins

Vinyl acetate and vinyl chloride polymers and co-polymer products
form interesting thermoplastic resins. Their use in communication
work has been limited so far to phonograph records, where the resist-
ance of the co-polymer to warping due to humidity and the superior
wear resistance of the plastic have been the important factors. The
advantage of non-inflammability imparted by chlorine is more than
offset by the acidic nature of the fumes given off from vinyl chloride
polymers when heated or burned and this has discouraged use of these
materials in the telephone plant.

Polystyrene

There have been no important commercial applications for poly-
styrene as yet in Bell System telephone communication although much
experimentation is being carried on with polystyrene plastic. The low
electrical losses of this material make it of special interest in high-
frequency work but its mechanical properties have not been satis-
factory. In Germany and Italy it is reported that polystyrene has
been employed as an insulating plastic in various cable structures for
experimental and commercial use. However, in this country the
spacing insulators for the coaxial cable from New York to Philadelphia
have been made of a special grade of hard rubber which has proved to
be a tougher material for the purpose.^

Synthetic Coatings

An important application of synthetic organic materials in the tele-
phone plant is in the finishes that are put on Bell System apparatus.
There are three major reasons why such finishes are needed — (1) for
the improvement in appearance of certain fabricated parts, especially
the exposed portions of subscriber station apparatus, both in private
homes and public places, (2) for the mechanical and chemical protec-

^ "Systems for Wide-Band Transmission over Coaxial Lines," L. Espenschied and
M. E. Strieby, Bell Sys. Tech. Jour., October 1934; and Elec. Engg., Vol. 56, 1937.

498 BELL SYSTEM TECHNICAL JOURNAL

tion of the underlying structural material which is usually a metal,
and not infrequently, (3) for electrical insulation purposes. Other
minor reasons for finishes exist on special apparatus. Many parts are
fashioned from such metals as steel, brass, aluminum and zinc alloys.
After such practices as punching and die casting the surfaces of these
parts are left in an unsightly condition, and furthermore unless pro-
tected, they may soon begin to corrode. In certain cases electroplated
finishes may be employed to advantage, but organic finishes, because
of their low cost and ease of application, find wide use. A good organic
finish for telephone apparatus must not only have a lasting decorative
value but must also protect the parts against the great variety of
conditions to which the apparatus is exposed.

For example, the common black finish which is applied to various
parts of subscriber station apparatus, such as the zinc alloy handset
mounting, coin collector boxes and metal bell boxes must be suffi-
ciently tough and adherent to withstand perspiration, impact and
severe abrasion. Rigorous tests have been applied to find the most
durable finishes for such parts. They must maintain their appearance
so as to harmonize with the smooth molded black phenol plastic parts.
Advantage has been taken of the recent improvements in synthetic
resin finishes and a modified alkyd resin vehicle has been employed
in the present black enamel. A thorough baking is given to the enamel
which results in a more durable finish for telephone apparatus than the
former black japan.

There are a number of applications for synthetic finishes where
corrosion protection is important from the standpoint of the proper
functioning of the apparatus. The aluminum diaphragms in marine
and aviation loud speakers and in sound power instruments are pro-
tected by a baked finish containing a heat-hardening phenolic resin
vehicle into which is incorporated a chemically inhibitive pigment.

The familiar olive-green finish applied to the metal lining of tele-
phone booths is also a synthetic finish. This coating is often subjected
to unusual service conditions which only a modern type of finish can
withstand. Advantage is also taken of the high initial reflectivity
and the retention of light reflection of certain alkyd resins and these are
used in the white booth head-lining enamel. Synthetic finishes are
generally specified for' the finishing of Bell System trucks, etc.

Other applications of finishes include lacquers and wrinkled enamels.
A recent interesting development has been the use of ethyl cellulose
dipping lacquers to form a continuous, fairly thick, envelope around
small telephone parts such as resistances, condensers and the like.

PLASTIC MATERIALS IN TELEPHONE USE 499

This frequently eliminates a potting operation and provides an ex-
cellent mechanical protection for the parts.

The employment of organic coatings for insulation purposes is
another important application deserving mention. In general the
conditions in the telephone plant are not such as to demand resistance
to very high voltages. Millions of feet of copper wire receive a baked
clear enamel coating applied in multiple thin coats to assure maximum
flexibility and uniformity. Carefully chosen pigmented alkyd baking
enamels are used in exchanges as insulating finishes for various hooks,
bars and other small parts of the metal framework upon which the ex-
change wiring is tightly and compactly fastened and from which elec-
trical insulation is needed.

An appreciable amount of clear cellulose acetate lacquer is at present
used on switchboard wire. This is applied as a thin coating of a
specially plasticized lacquer over a layer of textile insulation, the latter
being colored in various ways for ready identification. The require-
ments of a good lacquer coating material for switchboard wire are
chiefly (1) low cost, (2) reasonably good insulation, even under pro-
longed high humidity conditions such as occur during the summer
months in many parts of the country and (3) good transparency so as
not to alter the identification colors on the textile serving. Smooth-
ness, flexibility, inflammability and corrosion hazard are other important
factors that receive consideration.

A synthetic plastic which has recently found a small but important
place in the telephone plant is polybutene. When coated on fabric
this plastic has given an excellent membrane material for a new type
of handset transmitter. It is dust and moisture-proof, light in weight,
flexible and alkali resistant, not impairing in any way the acoustical
properties of the instrument.

Synthetic Resins as Adhesives

A growing use for synthetic resins in the telephone plant is in the
form of adhesives. The amount of material consumed in this way is
not large but the applications are frequently important from the stand-
point of the functioning of the apparatus as well as from the economies
involved. The older kinds of adhesives such as casein and animal
glue are still employed for joining together various large parts (es-
pecially wood, as in cabinet work, etc.) but they are brittle and gener-
ally unsatisfactory in the assembly of small light parts (metal, phenol
fiber, ceramic, etc.) such as go into special communication apparatus.

500 BELL SYSTEM TECHNICAL JOURNAL

The trend in the design of most apparatus has been toward smaller
lighter parts and at the same time toward more rapid assembly.
Synthetic resin adhesives are aiding this trend by avoiding in various
places the dependence upon bolts, screws and similar mechanical
locking devices. Proprietary resin-cellulosic lacquer adhesives and
vinyl and acrylate polymers are proving of value because they give
strong tough joints that are affected but little by moisture and are not
apt to give trouble from corrosion or growth of mildew. The use of
these materials for assembling parts in a thermoplastic manner looks
particularly encouraging. When the surfaces which are to be joined
are carefully cleaned, then primed with an air-dried coat of a suitable
thermoplastic resinous adhesive and finally molded together under
heat and pressure, tensile strengths of several tons per square inch
are possible between the joined parts. Synthetic resin cements and
adhesives are employed in the construction of the handset transmitter,
moving coil microphones, loud speakers, switchboard lamps, vacuum
tubes and the wood veneer of telephone booths.

Conclusion

Many important applications of plastics have been made in the
telephone field. These have sprung from the economies of design,
methods of fabrication, as well as from the excellent serviceability of
the molded plastic products. It might be well to emphasize again the
chief limitations of present day plastics which have prevented wider
use. When exposed to outdoor conditions which involve the effect of
temperature and sunlight, many plastics, particularly the newer
thermoplastic materials, are revealed to be insufficiently permanent
for telephone use with respect to the physical and chemical character-
istics associated with color, distortion at elevated temperatures,
surface deterioration due to action of sunlight and brittleness at
moderately low temperatures.

Modern trends in stylized designs make it necessary to take ad-
vantage of the molding art in order to achieve good ornamentation.
This will probably result in the use of plastics on surfaces exposed to
light. The effect of light is not confined to direct sunlight for it has
been found that daylight filtered by ordinary window glass for long
periods will cause reduction in surface electrical resistance of plastics.
In fact, the effect of light seems to be over a rather broad range of the
spectrum, becoming intensified as the ultra-violet range is approached.

PLASTIC MATERIALS IN TELEPHONE USE 501

A few of the new thermoplastics are quite inflammable, a charac-
teristic that will be a serious handicap to their extended use in ex-
changes and other locations where a fire might disrupt the service of a
whole community.

There are still certain weaknesses of organic finishes with respect to
impact abrasion, perspiration and moisture penetration, although there
have been great advances made in this field in recent years.

The Dielectric Properties of Insulating Materials, III
Alternating and Direct Current Conductivity

By E. J. MURPHY and S. O. MORGAN

This paper deals with the variation of a-c conductivity with
frequency and with that of apparent d-c conductivity with charg-
ing time for dielectrics exhibiting anomalous dispersion (i.e.,
having dielectric constants which decrease with increasing fre-
quency). The a-c conductivity of a dielectric exhibiting simple
anomalous dispersion approaches a constant limiting value 7oo as
the frequency increases. The discussion shows that y^ possesses
properties similar to those of the conductivity due to free ions,
although in most cases it depends upon the motions of polar mole-
cules or bound ions. It is also shown that the apparent conduc-
tivity for constant (d-c) potential approaches an initial value as
the charging time is diminished. This initial conductivity 70 is
demonstrated to be equal to the limiting value of the a-c conduc-
tivity attained at high frequencies (700), a relationship which
simplifies the description of the behavior of dielectrics exhibiting
simple anomalous dispersion. Dielectrics possessing the property
of anomalous dispersion then have two conductivities: one is due
to local motions of polar molecules or bound ions; the other is due
to the migration of free ions to the electrodes.

Both 7o and 700 refer to methods of measurement. It is to be
noted that in many non-homogeneous dielectrics, especially those in
which one part is of much higher resistivity than the remainder,
both 7o and 700 may be a measure of a free ion conductivity. As
the equality of 70 and 7«, is independent of the nature of the
polarization responsible for them, experimental agreement between
a-c and d-c measurements cannot be used to distinguish whether
the dielectric loss in a material is due to polar molecules, to bound
ions, or to free ions present in a non-homogeneous dielectric. How-
ever, in homogeneous dielectrics 70 (or 700) is a conductivity due to
polar molecules or bound ions.

Introduction

' I ''HE preceding paper ^ dealt with the dielectric constant, showing
-■- mainly how it varies with the frequency of the applied alternating
voltage for those dielectrics which behave in the simplest manner, and
indicating the general character of the structural features responsible
for this behavior. The discussion is extended here to the conductivity,
1 Murphy and Morgan, B. S. T. J., 17, 640 (1938).

502

DIELECTRIC PROPERTIES OF INSULATING MATERIALS 503

which is not less important than the dielectric constant as a property
of an insulating material. Though general aspects of the conductivity
will be described for the sake of completeness, we wish mainly to show
that materials which possess the property of anomalous dispersion
may be considered to have two quite definite conductivities: one of
these is the ordinary d-c conductivity due to free ions or electrons;
the other is a special value of the a-c conductivity which will be dis-
cussed in this paper. We believe that the recognition of the existence
in many materials of two conductivities instead of one is of considerable
advantage, particularly in interpreting the behavior encountered in
direct-current conductivity measurements on insulating materials, a
subject upon which there has existed a considerable divergence of
opinion.

The measurement of the direct-current conductivity of an insulating
material is usually complicated by the fact that the current which
flows when a constant potential is applied does not remain constant
but decreases with time. The meaning of this variation of the current
is open to more than one interpretation. Some investigators consider
that its final value, approached asymptotically, and perhaps not closely
approximated until a constant potential has been applied for an hour
or more, is the proper basis for the calculation of the true conductivity
of the material. Other investigators, notably Joffe, consider that the
current/time curve should be extrapolated toward the instant of
applying the voltage in order to obtain the proper value of the current
to use in calculating the true conductivity. On this account the terms
initial conductivity, final conductivity and true conductivity frequently
appear in papers on the conductivity of insulating materials. While
it has been usual to take either the initial or the final conductivity as
the true conductivity, rejecting the other, it is shown here that with
certain exceptions both conductivities are true conductivities in the
sense that they are independent properties of the material having a
different, though related, physical significance.

The relationships which will be brought out here depend in an
essential way on the nature of the variation of a-c conductivity with
frequency for materials which possess the property of anomalous dis-
persion. The a-c conductivity of a dielectric exhibiting simple anoma-
lous dispersion increases as the frequency increases until the frequency
is high as compared with the reciprocal of the relaxation-time; it then
approaches asymptotically a constant limiting value. It is shown
here that this limiting value of the conductivity, which will be referred
to as the infinite-frequency conductivity, is a true conductivity of the
material, analogous to the ordinary d-c conductivity, and that it is

504 BELL SYSTEM TECHNICAL JOURNAL

equal to the initial conductivity obtained by extrapolating the ap-
parent d-c conductivity towards the instant of applying the measuring
voltage. We believe that this relationship considerably simplifies the
description of the meaning of certain types of measurements upon
dielectrics.

In spite of the fact that several terms are already used to distinguish
different conductivities, there remains some ambiguity in the meaning
of these terms. For example, the physical meaning of the term d-c
conductivity when applied to a dielectric is vague. Moreover, it will
be evident in the later discussion that the initial conductivity will
depend upon free ions for some materials and upon polar molecules for
other materials. To avoid this confusion we have found it convenient
to use two terms which refer to the nature of the conduction processes
rather than to the method of measurement : these are free ion conduc-
tivity and polarization conductivity. The first is the ordinary conduc-
tivity due to the drift of free electrons or ions to the electrodes; the
second is a conductivity determined by the energy dissipated as heat
by the polarization currents in the dielectric. The latter bears the
same relation to the neutral polarizable aggregates in the material,
which carry the polarization currents, as does the free ion conductivity
to the free ions in the dielectric. The terms free ion conductivity and
polarization conductivity, or some other terms having approximately
the same meaning, are essential to the discussion as they refer unam-
biguously to two distinct properties of the material, while the terms
initial, final, true, infinite-frequency, a-c and d-c conductivity all refer
to different methods of measuring these two properties of the material.

The current flowing in a dielectric to which a constant potential is
applied often decreases with time for periods of the order of a few
minutes or longer measured from the time of applying the potential.
This decreasing current is variously referred to as a residual charging
current, an absorption current, an anomalous conduction current or an
irreversible absorption current, depending upon the interpretation given
to the phenomenon. We have already indicated that these residual
currents complicate the measuring technique in the determination of
the d-c conductivity of insulating materials. The most definite kinds
of residual currents are those which are simply a manifestation of the
structural characteristics which give rise to anomalous dispersion of the
dielectric constant. These residual currents and the residual charges
associated with them will be referred to here as the direct-current
counterparts of anomalous dispersion to indicate that they are not
independent properties of the material, but necessary requirements of
the existence of anomalous dispersion occurring at sufficiently low

DIELECTRIC PROPERTIES OF INSULATING MATERIALS 505

frequencies. The information obtainable from the study of such
residual currents is the same in kind as that obtainable from the study
of dielectric constant and conductivity by means of alternating cur-
rents; the residual phenomena, however, provide data regarding
polarizations having relaxation-times which are too long for convenient
investigation by alternating current methods. Residual currents of
this kind have no significance in principle which is different from that
of low-frequency a-c measurements.

Conductivity and Dielectric Loss

The conductivity of a material is usually thought of as a property
which depends upon the ease with which electric charge can be trans-
ferred through the material by the application of an electric field,
though it is recognized that a dissipation of electrical energy as heat
occurs in the material through which the current is passing. In these
terms we think of the conductivity as a quantity proportional to the
current per unit voltage gradient, which in turn is proportional to the
number of charge carriers, their mobility, and the magnitude of the
charge borne by each carrier. For conductors it does not matter
whether we define the conductivity, 7, as the factor by which the
voltage gradient, E, must be multiplied to give the current density, /,

I = yE (1)

or as the factor by which the square of the voltage gradient must be
multiplied to give the heat, W, developed per second in a unit cube of
the material,^

W = IE = yE\ (2)

for the heat developed by a given voltage is proportional to the current,

no matter of what material the conductor is composed. This is due to

the fact that the energy obtained by the moving charges from the

applied electric field is dissipated continuously to the surrounding

molecules or lattice structure as heat, and the electrons or ions then

drift with constant average velocity in the direction of the applied

field, developing heat at a rate proportional to the current.

However, the proportionality between current and heat developed

which is characteristic of conductors does not obtain in dielectrics.

When an alternating current flows in a dielectric it dissipates some

electrical energy as heat; however, the amount is generally much

smaller than would be dissipated by an equal current flowing in a

^ Cf. for example, Mason and Weaver, "The Electromagnetic Field," Chicago
(1929), p. 233.

506 BELL SYSTEM TECHNICAL JOURNAL

conductor and, unlike conductors, the ratio of heat developed to current
flowing varies with the material. This is due to the fact that most of
the current flowing in a dielectric under ordinary conditions is a
polarization current, or rather a sum of several polarization currents of
different types, and in general a polarization current dissipates less
energy as heat than an equal current flowing in a conductor. In fact
a part of the current flowing in a dielectric — the optical polarization
current — passes through the dielectric material without developing
any heat in it at the ordinary frequencies of electrical transmission.
Electrical energy can be transmitted through a good dielectric in a
suitable range of frequencies with very little loss; in other words, the
dielectric is transparent to currents which have a suitable frequency of
alternation. In these circumstances the conductivity of the material
as measured on a bridge would be very small though the current density
per unit voltage gradient might be quite large. Evidently, then, the
view of conductivity as simply a measure of the ease of transfer of
electric charge through a material is not in general suitable for ap-
plication to dielectrics.

The fact is that the complex conductivity represents the ease of dis-
placement of electric charge in a dielectric while its real part (i.e., the
a-c conductivity as measured on a bridge or equivalent measuring
device) is the quantity to which the rate of heat development in the
material is proportional. Therefore, in dealing with alternating cur-
rents flowing in dielectrics it is usually more convenient to regard the
a-c conductivity as the factor which determines the rate of dissipation
of electrical energy as heat in the material, rather than as a quantity
w^hich is proportional to the current density per unit voltage gradient
or to the ease of displacement of electric charge in the material. In a
later part of the discussion, however, it will be shown that the limiting
high-frequency value of the a-c conductivity may be thought of as
representing ease of displacement of electric charge, too, as in a
conductor.

The heat developed in a dielectric by polarization currents is called
dielectric loss and is analogous to the Joule heat developed by free
electrons or ions in a conductor; however, it is a property of neutral
aggregates of particles, such as polar molecules, rather than of free ions.
In the case of a polarization due to polar molecules, for example, the
equilibrium distribution of the orientations of the molecules is slightly
changed by the application of an electric field. The dielectric constant
depends upon the difference between the distribution of orientations
with and without the applied field, while the dielectric loss represents
the part of the energy of the applied field which is dissipated as heat

DIELECTRIC PROPERTIES OF INSULATING MATERIALS 507

because of the "friction" (i.e., the molecular equivalent of macroscopic
friction) which the molecules experience as they change from the one
equilibrium distribution of orientations to the other. Evidently, the
dielectric loss may be quite as characteristic of the structure of the
material as is the dielectric constant.

In an ideal insulating material there would be no free ion conduction,
but in actual materials there are some free ions or electrons and these
produce Joule heat as they drift towards the electrodes in the applied
field. The total heat developed is the sum of the dielectric loss and
the Joule heat; and, as the latter is proportional to the d-c or free ion
conductivity, the dielectric loss is proportional to the total a-c conduc-
tivity (as measured on a bridge for example) less the d-c conductivity.

To give the discussion a more concrete basis, let us consider a di-
electric which has a dielectric constant e' and a loss-factor e" (or in
other words which has a complex dielectric constant e' — ie"). Let it
be contained in a parallel-plate condenser having a plate separation
of d centimeters, and area A cm^ for one surface of one of the plates.
If a potential difference V is maintained between the plates of this
condenser, a charge q per unit area will appear on either plate and a
polarization P will be created in the dielectric. The current flowing
in the leads to this condenser is Adq/dt, if we assume for the present
that the conductivity due to free ions may be neglected. The conduc-
tivity is then given by

where E = Vjd. The charge g can be calculated from the dielectric
constant of the material by means of relations which are provided by
the general theory of electricity, namely

eE = D, (4)

D = E + AtP, (5)

D = 4:wq (for a parallel-plate condenser). (6)

So (3) becomes

yE=^ = -—=~^— (7)

^ dt 4r dt 4:Td dt' ^^

where all of the electrical quantities are expressed in electrostatic
units. When the applied potential is alternating, V may be expressed
as the real part of F = Foe'"', where Fo is the amplitude. The di-
electric constant may then be written as the complex quantity t' — ie" ,

508 • BELL SYSTEM TECHNICAL JOURNAL

as shown in the preceding paper. The current density in the dielectric
is then

^+.^)£o.- (8a)

= (7' + iy")E,e''-'\ (86)

where 7' = e'co/Air and y" = e'w/Aw. It is evident that 7' + iy" (=7)
is the complex conductivity.

The dielectric constant and conductivity for alternating currents
are determined by measurements, made with bridges or by other
means, which give the admittance or impedance of the condenser con-
taining the dielectric at the particular frequency at which the measure-
ment is made. This admittance ^ may be expressed in terms of the
equivalent parallel capacitance (Cp) and conductance (Gp) and an
alternative expression for (8) is then

dq 0.9 X 1012 .^ , .^ . ,, ^, .„.

• J = -^ (Gp + tCp<^) Foe"-', (9)

where Gp is expressed in mhos (or reciprocal ohms) and Cp in farads
and 0.9 X 10^^ is the ratio of the farad to the electrostatic unit of
capacitance and also of the mho to the e.s.u. of conductance.

By comparing (9) with (8), (8a) and (8&) we obtain expressions for
7', e" and e' in terms of the quantities Cp and Gp as directly measured
on a bridge or similar arrangement. However, the expressions ob-
tained are briefer if we make use of the fact that, when expressed in
farads, the capacity Co of the empty condenser is

^' " Ayrd X 0.9 X W ' ^^^^

Then it is evident that

e' = CpICo, (11)

e" = Gp/Coc^, (12)

y' = Gp/AwCo (13)

= €"a;/47r = e"//2. (13a)

^ Measurements on a series bridge give directly the equivalent series resistance
Rs and capacitance C. These data can be converted into equivalent parallel con-
ductance and capacitance by the general relationships

DIELECTRIC PROPERTIES OF INSULATING MATERIALS 509

In equations (11) to (13a) e', e" and 7' are expressed in e.s.u., while
Cp and Co are expressed in farads and Gp in mhos. The substitution
of the frequency, /, for oj in (13a) depends upon the fact that/ = 27rw.
While it is usual to express e' and e" in e.s.u., it is more convenient
for most purposes to have 7' in the units ordinarily used for specific
conductance: thus when expressed in ohm"^-cm~^

7-. '^ = ''f , (14)

^ 47r X 0.9 X 1012 1.8 X 10^2 ^^^;

8.85 X 10-2 ^

= — r ^p = -J ^P' (14^)

v-o mmf -^

where Co mmf is the capacitance in micromicrofarads.

By expressing equation (8) in the equivalent polar form certain
quantities appear which are closely related to 7', e' and e" and which
are commonly used in describing the characteristics of dielectrics.
The polar form is

7 = 7oe'^

where 70 = (7' + y"^y'^, a quantity which is a measure of the
amplitude of the complex current in the dielectric for unit voltage
gradient, while 6 — tan^^ t'Vt' is its phase angle. It is customary

to use the loss angle which is defined as I — — ^ J =8, rather than the

phase angle in the description of dielectric properties. It is evident
that 8 = tan -^ 777" = tan-^ e'Ve' and that

tan 8 = Gp/Cpoo. (15)

Similarly, the power factor is given by

cos e = 77(7" + 7"')i/2

= e"l{e" + e"'y'' = Gp/{Gp' + CpWy^. (16)

When the current given by (8) is multiplied by the voltage, Eq cos oot,
we obtain the instantaneous power, and from this the mean power W
can be obtained by integration over a whole number of half periods.
We then obtain

trperseco„d = y (1)^ = ^(1)' (16«)

and

F per cycle = '-^ (^J . (166)

510 BELL SYSTEM TECHNICAL JOURNAL

This demonstrates the statements made earlier that 7' is proportional
to the heat developed per second and e" to that developed per cycle in
the dielectric. In the above equations W is in ergs per second or per
cycle when Eq, 7', and e" are in e.s.u.

It can be seen from equation (8) that the total current flowing in the
dielectric has a dissipative and a non-dissipative part: e' is proportional
to the non-dissipative part, and e" to the dissipative part. The loss-
angle, €" je' , may be interpreted as the ratio of the dissipative to the
non-dissipative current and the power factor as the ratio of the dissi-
pative current to the total current.

The Frequency-Dependence of Conductivity

When the dielectric with which we are dealing possesses the property
of anomalous dispersion, the expression for the loss factor e" as a
function of frequency is

1 -f co2r2

(17)

as was shown in the preceding paper. Substituting this expression
for t" in (14) we obtain:

, _ e^ ^ J_ (ep - eoo)coV , .

'^ 47r 47r ■ 1 + co^r^ ^^^

1 (eo-eJcoV ^^g^^

47r X 0.9 X 10^2 1 -f- coV^

where 7' is expressed in e.s.u. in (18) and in ohm"^-cm~^ in (18a), and
Co is the static dielectric constant, e^ the infinite-frequency dielectric
constant and t is the relaxation-time.

Differentiation of (18) with respect to frequency shows that 7' has
no maximum when plotted against frequency; the conductivity of any
dielectric to which {18) applies should always increase with frequency,
where it changes at all. On the other hand, dififerentiation of (17) with
respect to w shows that the dielectric loss-factor has a maximum which
occurs when wr = 1. The dielectric constant e' is given by

e' = 6. + ^^^^, (19)

1 + w r

and it will be seen that it shares with the conductivity the property of
having no maximum when plotted against frequency. In Fig. 1
schematic curves are drawn which show the diff^erences in the frequency
dependence of 7', e" and e' for a material having an absorptive polariza-

DIELECTRIC PROPERTIES OF INSULATING MATERIALS 511

tion of relaxation-time t. The conductivity goes up as the dielectric
constant goes down, as if the one were being transformed into the other.
The most interesting feature of (18) is that as the frequency in-
creases 7' approaches a limiting value, and that this limiting value,

o ♦

ORIENTATIONAL
OR BOUND ION
POLARIZATION

OPTICAL
POLARIZATIONS

I03T

FREQUENCY, -^

Fig. 1 — Schematic diagram comparing the frequency dependence of dielectric
constant (e'), loss factor (e") and conductivity (7')- This applies to a polarization
having a single relaxation-time (r). The frequency in cycles per second is wllw.

which will be designated as 700, has the value

Too =

eo — Ca

Co — €»

(20)
(20a)

47r X 0.9 X lO^V '
where (20) gives 7«, in e.s.u. and (20a) in ohm"^-cm~\ The con-

512

BELL SYSTEM TECHNICAL JOURNAL

ductivity of ice provides a good example of this behavior, and Fig. 2
has been plotted to illustrate it, using data obtained by the writers
on the conductivity of ice at different temperatures. The leveling-off
of the conductivity curve at high frequencies is not observed in all
materials. For many materials the conductivity continues to increase
as the frequency becomes higher, though the rate of increase is often

4.4

XIO"^

TEMPERATURE
IN DEGREES C
= -0.8

4.0
3.6

/

-2.6

/

-3.8

2.8

1/

/

2.4

V

-7.4

2.0
1.6

y^

^

=^

-11.8

1.2

\

-20.5

0.8
0.4

-45,8

°

0

'•

T

0 10 20 30 40 50 60 70 80 90 100

FREQUENCY IN KILOCYCLES PER,SECOND

Fig. 2 — The dependence of 7' upon frequency for ice at several different tem-
peratures.* The quantity 7' is the a-c conductivity less the d-c conductivity. The
curves show that the limiting value 7cd approached by 7' as the frequency increases is
lower the lower the temperature.

* The curves of Figs. 2, 4 and 5 are drawn through experimentally determined
points. The experimental points are shown only where the curves should theo-
retically be linear or nearly linear. The fact that the points deviate by only com-
paratively small amounts from the theoretical curves in their linear sections is a
sufficient indication for the present purpose of the agreement between the theoretical
curves and the experimental data for ice.

DIELECTRIC PROPERTIES OF INSULATING MATERIALS 513

not great. It is to be expected that many complex materials would
not have a conductivity which varies with frequency in accurate
agreement with (18), because the assumptions from which (18) was
derived are perhaps the simplest which could be made regarding the
structure of a dielectric.

Discussion of y^ in Terms of a Model

A convenient way of demonstrating the physical meaning of 700 and
at the same time of showing the general character of the physical
mechanism which is responsible for 7' becoming larger as the frequency
increases is to consider the operation of the model * used in the pre-
ceding paper to develop the formulae for dispersion. This model
depends upon the dielectric containing bound ions about which the
only things specified were the following:

(1) That the displacement of a bound ion from its equilibrium
position in the dielectric by the applied electric field is opposed by a
restoring force proportional to the displacement; if the displacement
is designated as 5 the restoring force is/5.

(2) That these ions experience in their motion a frictional force
proportional to their velocity in the direction of the applied field; this
frictional force is given by rs, where s is the velocity and r is a constant.

(3) That the moving ions have a charge e and a negligible mass.
These are the essential features of the model and they can be repre-
sented concretely by imagining an ion held in a certain small region,
electrically neutral as a whole, in for example a glassy dielectric, by
forces characteristic of the structure of the solid. We may suppose
that this ion makes small excursions within this region around the
point (0 in Fig. 3) toward which it is attracted by a force proportional
to the displacement, and that its interaction with the molecules which
surround it in the dielectric is such that it experiences in effect a
frictional force proportional to its velocity in the applied field. The
ion of this model is, therefore, subjected to the same sort of frictional
resistance as are ions in solution in a liquid.

From the relationship between polarization and displacement which
was discussed in the preceding paper, it is evident that the polarization
may be considered to be proportional to the displacement of the bound
ion of this model. (If P is the polarization per unit volume due to a
large number (w) of bound ions, each of charge e, the polarization is
evidently proportional to the average displacement s per ion, where
s = Pjne, but for the present purpose it will be sufficient to consider
the displacement 5 of a single bound ion.) We may, therefore, discuss

^ For further details, see page 652 of the preceding paper, B. S. T. J., 17 (1938).

514

BELL SYSTEM TECHNICAL JOURNAL

the dependence of conductivity on frequency in terms of the displace-
ment and velocity of a single bound ion. As we are not concerned
here with very high frequencies, we may employ the abbreviated
equation of motion given in equation (17) of the preceding paper to

AMPLITUDE OF DISPLACEMENT, S , OF ION
IN AN IMPRESSED FIELD, F = Fq COS U)t

A- LOW FREQUENCY ((jj«T-')

e'=eo y'=o

DISPLACEMENT OF ION FROM EQUILIBRIUM POSITION 0

Fig. 3 — The mechanism of anomalous dispersion illustrated by a simple model.

The model consists of a single bound ion. The potential energy of this ion in-
creases when it is displaced from its equilibrium position 0. The ion also experiences
a frictional force proportional to its velocity, as if it were an ion in solution. The
upper part of the diagram shows the way in which the amplitude (5) of displacement
of the ion by a given applied field varies with the frequency. It has its maximum
amplitude at low frequencies {A in the diagram) and a comparatively negligible
amplitude at high frequencies (C in the diagram). In this model the amplitude is a
measure of the dielectric constant. The limiting value Tcd of the conductivity
prevails under the conditions C where the amplitude is comparatively negligible.

discuss the motion of the bound ion of this model ; this equation is

rv -\- js = eF,
where v — ds/dt.

When a d-c voltage Vi is applied to this model, it establishes a field
Fi which displaces the bound ion to a new equilibrium position Si if the
field is allowed to act upon the ion for a sufficient time. The new

DIELECTRIC PROPERTIES OF INSULATING MATERIALS 515

equilibrium position Si of the ion corresponds to the static value Pi of
the polarization of the model. When the voltage is varying with the
time according to V = Vo cos cot, the greatest amplitude which the
displacement can have is 5i, and in general the amplitude will fall short
of this value by an amount which increases with increasing frequency.
The value Si is then closely approached only when the frequency is
low as compared with the reciprocal of the relaxation-time, because at
high frequencies the applied field reverses its direction before the ion
has had time to reach Si. At sufficiently low frequencies, namely
where w is negligible by comparison with 1/r, the frictional dissipation
of energy by the moving ion is so small that there is practically no
difference between the instantaneous position of the ion when the
voltage has any given value and the position it would finally attain
upon reaching equilibrium for that voltage. The ion then moves
through a succession of near-equilibrium positions, as in a reversible
process in thermodynamics. The dielectric constant has its static
value and the conductivity is zero unless there is a d-c conduction
component in the total conductivity.

At the high-frequency extremity of a dispersion region we see that
the situation is simply reversed : the alternations in the direction of the
applied field are so rapid that the bound ion does not have time to
move an appreciable distance from its equilibrium position before the
direction of the applied field is reversed (C, Fig. 3). The amplitude
of the displacement of the ion by the applied field is then small as
compared with Si and the dielectric constant of the material receives
practically no contribution from the bound ion of this model in these
circumstances. However, though the amplitude of motion of the ion
shrinks to a small fraction of Si, its velocity is comparatively high and
independent of frequency. The conductivity jx is proportional to the
average velocity of the bound ion of the model under these conditions.

As the restoring force is proportional to the displacement, its effect
upon the motion of the ion is negligible by comparison with that of the
applied force when the displacement 5 is small as compared with Si.
On this basis, the fact that the conductivity is an increasing function
of frequency may be attributed to the decrease in the influence of the
restoring forces as the frequency increases. In fact, when the ampli-
tude of displacement is very small as compared with Si, the ion moves
as if the only force opposing the applied force were the frictional force;
that is, its average velocity is the same as that of a free ion subjected
to the same applied field and the same friction.

For many of the purposes of this discussion we could use a model of
the dielectric consisting of an air capacity Cs in series with'a resistance

516 BELL SYSTEM TECHNICAL JOURNAL

Rs both being shunted by a second air condenser C«. In this equiva-
lent circuit, Cs and Rs refer to the polarizations responsible for anoma-
lous dispersion, and C«. to the optical polarizations. The frequency-
dependence of the equivalent parallel capacitance and conductance
of this network is

Cp = Coo I i 4- o}^T^

and

(Co — Cx)orT
1 + oi'T^ '

(22)

where Co = Cs + C^, and T = CsR,. In the above expressions
(Co — Co,) and T are analogous respectively to eo — e^ and t in equa-
tions (17) and (19).

The physical basis for the infinite frequency conductivity in this
model depends upon the fact that at high frequencies the impedance
of Cs is so low that nearly the whole drop in voltage is over the re-
sistance Rs. This simple network is capable of representing the
frequency-dependence of materials exhibiting anomalous dispersion
due to a polarization having a single relaxation-time. In fact, when
the frequency is sufficiently high that it is in the range where the con-
ductivity is independent of frequency, the required network becomes
even more simple, for it then reduces to Cx shunted by Rs, where the
magnitude of C«, corresponds to e^ and that of Rs to I/tx-

Polarization Conductivity

The operation of the models which have been discussed above pro-
vides a basis for interpreting the physical nature of 7x. The essential
characteristics brought out by these models are listed below. They
show the justification for considering y^ to be a conductivity in the
same sense as the ordinary d-c conductivity.

(1) To obtain y' in an actual measurement on a dielectric, we sub-
tract the d-c conductivity 7/ from the total a-c conductivity. There
is then no contribution from free ion conduction in y' and consequently
none in 700, its limiting value at high frequencies. Polar molecules or
other polarizable aggregates in the dielectric must then be the origin
of 7x.

(2) In the second place 700 is independent of frequency, a property
which puts it on the same footing as the d-c or free-ion conductivity
in at least one respect.

(3) Earlier in this paper it was mentioned that the heat developed
in a conductor for a given voltage is proportional to the total current,

DIELECTRIC PROPERTIES OF INSULATING MATERIALS 517

but that in dielectrics this proportionaHty does not in general prevail.
The current in a dielectric is complex and heat is developed only by its
dissipative component. If the expressions for e' and e" given in (17)
and (19) are substituted in (8) we see that when w becomes large by
comparison with 1/t, i.e., when 7' becomes 7a,, the imaginary compo-
nent of the current reduces to eooco/47r; this is the optical polarization
current. If it is subtracted from the total current given by (8), the
remaining current contains no imaginary component. This current
then develops as much heat in the dielectric as would a current of the
same magnitude flowing in a conductor.

(4) In connection with the foregoing we see that unlike lower values
of 7' the infinite-frequency conductivity 700 is a measure of the ease
with which electrical charge can be displaced in the material by a unit
applied field. This characteristic of 7=0 agrees with our usual concep-
tion of the physical basis of the conductivity of an electrolyte or a
metal. (We assume in this connection that the optical polarization
current e^oijAiir may be neglected in comparison with the current
responsible for 7«,. Where this is not the case, appropriate modifica-
tions in the above statements are required.)

(5) It is characteristic of a dielectric that when the charged particles
which form part of its structure are displaced by a force of external
origin, there is a restoring force tending to return them to their initial
positions. On the other hand, in an ideal conductor there are, by
definition, no restoring forces of this kind. The above discussion of
the model shows that in a dielectric possessing the property of anoma-
lous dispersion it is possible to make the influence of the restoring
forces on the motion of a bound ion negligible in comparison with that
of the applied force by sufficiently increasing the frequency above the
value corresponding to the reciprocal of the relaxation-time. This is
the condition which prevails when 7' equals 700- Thus at low fre-
quencies (oj <3C T^O the part of the dielectric structure which is re-
sponsible for anomalous dispersion behaves as a dielectric; whereas at
high frequencies (w y^ t"^ it behaves as a conductor. A result of this
is that a dielectric exhibiting anomalous dispersion of the simple kind
conforming to equation (39) of the preceding paper will behave in an
electric circuit like a pure capacity shunted by a pure resistance over
the whole of that range of frequencies where e' and 7' are both prac-
tically independent of frequency and equal respectively to €00 and 700.
Pure ice, for example, behaves in this manner over a considerable range
of frequencies. (See Figs. 2 and 4.)

(6) The average velocity of the bound ion of our model becomes
independent of frequency when co is large as compared with l/r. This

518

BELL SYSTEM TECHNICAL JOURNAL

constant velocity is equal to that which a free ion would have under
the same voltage gradient if it were moving in a medium subjecting it
to the same frictional resistance as is experienced by the bound ion of
our model.

(7) In ordinary electrolytic conduction the conductivity is usually
represented as the product of three factors: the number of ions per
unit volume; their valence or charge per ion; and the average mobility
of each ion, i.e., the average distance which an ion drifts per second in

100

20 30 40 50 60 70 80

FREQUENCY IN KILOCYCLES PER SECOND

Fig. 4- — Dependence of e', e", 7' and €"/(«' — «co) upon frequency for ice at — 2.6° C.

the direction of the applied field. The above statement refers to one
species of ion; when two or more species are present in the solution,
the total current or conductivity is the sum of the currents or conduc-
tivities contributed by each type. The infinite-frequency conductivity
7oo may also be represented as the product of three factors similar in
physical meaning to those just mentioned as applying to conduction
by ions in solution. Thus reference to Table I, Item 2, will show that

DIELECTRIC PROPERTIES OF INSULATING MATERIALS 519
for the model we have employed to illustrate this discussion,

The factors in this expression may be seen to have the following general
significance: the quantity e is the charge on each bound ion; n is the
number of bound ions per unit volume; and ej^irr is a measure of the
mobility per ion. This mobility does not refer to the motion of an
ion which is free to move through the dielectric from one electrode to
the other but to the mobility of a bound ion in small, local translational
motions or the rotational mobility of a polar molecule. The remaining

(I 9 \ 2
-^^— r — I is not of direct significance in the present connection.^

We see then that y^ is also analogous to ordinary electrolytic conduc-
tion in that its physical mechanism may be represented as depending
upon a mobility, a concentration and a factor such as dipole moment
or charge per bound ion. The latter factor has a function in this
mechanism which is similar to that of the valence or charge per ion in
electrolytic conduction.

These considerations indicate that although 700 is a property of
polarizable units such as polar molecules it has the usual attributes of
a conductivity due to free ions or free electrons. A dielectric which
exhibits simple anomalous dispersion conforming to equations (17)
and (19) then has two conductivities. One of these is the conductivity
due to free ions; this will be called the free ion conductivity and desig-
nated throughout this paper by 7/. The other is a conductivity which
is a characteristic of the polarizable complexes responsible for anoma-

5 When 600 = 1, equation (23) reduces to

-^—zi — I would be absent if the material possessed

no optical polarizations. Evidently 70, depends upon the optical refractive index
Vfx, as well as upon the characteristics of the absorptive polarization. In mixtures
it may be possible to vary these two factors independently. Since optical polarization
currents make no direct contribution to the energy dissipation in the dielectric, even
up to the highest radio frequencies, it is interesting to observe that they make an
indirect contribution according to equation (23). Their indirect action takes place
by virtue of their effect on the actual internal field which acts upon each polarizable
aggregate in the dielectric. The effect of the interaction of the optical polarization
with the absorptive polarizations is to increase the apparent mobility of the polar-
izable complexes responsible for anomalous dispersion.

520 BELL SYSTEM TECHNICAL JOURNAL

lous dispersion ; this will be called the polarization conductivity '^ and
designated by 7poi in this paper.

The magnitude of the polarization conductivity of a material is
proportional to the number of polarizable units of structure such as
polar molecules or bound ions per unit volume which contribute to
anomalous dispersion. It also depends upon the mobility which these
polarizable units have in the local translational or rotational motions
in which they engage in consequence of thermal agitation. It finally
depends upon the permanent dipole moment of the polar molecules or
upon the charges upon the bound ions.

The concentration of ions able to contribute to conduction in di-
electrics is generally low because in many cases the free ion conductivity
depends mainly upon a small percentage of impurity in the material.
On the other hand, the concentration of polarizable units which are
able to contribute to the polarization conductivity may be much larger
and in fact even equal to the total number of molecules per unit volume.
Consequently, the polarization conductivity Tpoi may often be more
reproducible in measurements upon different specimens of the same
dielectric than is the free ion conductivity.^ It may well be that in
many materials diffusion coefficients, thermal conductivity, mechanical
dissipation and other similar properties which might be expected on
theoretical grounds to be related to electrical conductivity will bear a
simpler or more easily demonstrated relationship to polarization
conductivity than to free ion conductivity.

An example of the advantage of using the infinite-frequency conduc-
tivity instead of the d-c conductivity appears in measurements of the
conductivity of ice. In Fig. 5 the infinite-frequency conductivity (or
polarization conductivity) of ice is plotted against the reciprocal of
the absolute temperature, using unpublished data of the writers. The
data for 700 are reproducible and the curve shows a relation similar to
that usually observed for the d-c conductivity of solids. Direct-
current measurements on the same specimens on the other hand
yielded very erratic results. It may be seen from Fig. 5 that the
polarization conductivity is much higher than the d-c conductivity.

^ We suggest for this conductivity the name polarization conductivity because it
is a property of polarizable units of structure. In cases where the polarization is due
to the change of orientation of polar molecules, we might instead refer to it as an
orientational conductivity or a polar molecule conductivity, contrasting it thereby with
the translational aspect of ordinary conduction by free ions. As ions which are
loosely bound to some stationary or moving unit of the dielectric structure are often
capable of producing anomalous dispersion, at least two types of polarization con-
ductivity are possible; these may be described as the orientational conductivity and
the bound ion conductivity.

'' Joffe has obtained evidence that the initial conductivity, which we show here
to be in some cases a polarization conductivity, is often superior in reproducibility to
the final conductivity. (Cf. Reference 15.)

DIELECTRIC PROPERTIES OF INSULATING MATERIALS 521

I

/

/

/

O SPECIMEN 1
• SPECIMEN 2

/

/

t

/

/

f

i

y

/

A

/

/

•

,, y

/

/

/

i

/

/

/

/

/

/

<^

/

/

FREE-ION OR D-C
CONDUCTIVITY, y^

1 1 nx

6.2 6.0 5.8 5.6 5.4 5.2 5.0 4.8 4.6 4.4 4.2
RECIPROCAL OF ABSOLUTE TEMPERATURE , -p-j^

3.8 3.6
X I0"3

Fig. 5 — An illustration of polarization conductivity. The temperature-depend-
ence of the polarization conductivity of pure ice in the range — 0.8° C to — 190° C.
The free-ion (or d-c) conductivity is also shown for a single temperature. .

Types of Infinite-Frequency Conductivity

In Table I of the preceding paper there were Hsted several types of
polarization capable of yielding anomalous dispersion curves dis-
tinguishable from each other only by the values of the constants.
Corresponding to each is a different expression for the polarization
conductivity and these expressions are listed in Table I of this paper.

522 BELL SYSTEM TECHNICAL JOURNAL

This list shows that there are at least three main types of infinite-
frequency conductivity. The first of these is the type which depends
upon the change of the orientation of polar molecules according to the
Debye theory. This type of polarization conductivity is of more
theoretical interest than any of the others and perhaps also of more
practical importance; as already mentioned, it may be described as an
orientational conductivity to emphasize that no translational mobility
is necessary for it to occur.

TABLE I

Expressions for the Constant Value 7«j Approached by the A-C
Conductivity as the Frequency Increases

Type of Polarization

1. The Orientational Polarization due to Polar Mole-

2. A Distortional Polarization having a Relaxation-

Time given by r = r// Too = ;j^ • ( ^^3 — )

3. Polarizations due to Spatial Variations of Conduc-
tivity and Dielectric Constant

(o) A two-layer dielectric, layers 1 and 2 having re-
spectively static dielectric constants 61 and ti and

free-ion conductivities 71 and 72 Too = 7 ; rv;; j r

(ei + f^%r\y\ + T2)
(i) Special case of (3fl) where ti is much larger

than T2 Too = { i )

(c) Special case of (3&) where ti = 62 Too = Ti/4

{d) Special case of (3a) consisting of a high resistance

transition layer at the dielectric/electrode

interface, where ti is the conductivity of the

dielectric Too = Ti

(e) Conducting spheres dispersed in an insulating

medium of the same dielectric constant Too = />7i

Note: The infinite-frequency conductivity Too is given here in e.s.u. (See equation
20.) In Table I of the preceding paper {B. S. T. J., 17, 640 (1938)) the values of
(eo — «oo) and t are given for the polarizations listed above; the expressions given
there for t should be divided by 47r in the case of Items ia, c, d and e, as should also
the expressions for eo — 600 in the case of Item 2. The quantities which appear in
the above Table are defined in an appendix to the preceding paper. ti and T2 are
expressed in e.s.u. in this table.

The remaining members of the list of Table I originate in the

properties of ions rather than those of molecules. These ions must be

more or less bound in order to have an infinite-frequency conductivity

differing from the zero-frequency conductivity.^ The nature and

* It will be recalled that the terms infinite-frequency and zero-frequency are not
used here in their general meaning but merely as a convenient way to indicate opposite
directions of extrapolation of dispersion curves. They refer respectively to the high-
frequency extremity of a dispersion curve where 7' becomes practically independent
of frequency and to the low-frequency extremity where the dielectric constant
becomes practically independent of frequency.

71

DIELECTRIC PROPERTIES OF INSULATING MATERIALS 523

strength of the binding forces may vary widely amongst the types of
polarization which have an infinite-frequency conductivity. An ion
will be regarded as bound if its potential energy increases when it is
displaced from an equilibrium position by an applied field. ^

Included among the infinite-frequency conductivities which depend
upon the presence of ions in the dielectric is a type for which macro-
scopic inhomogeneities in the dielectric are responsible; for example,
a two-layer or multiple layer laminated dielectric, or a dielectric in
which space-charges ^° form because of spatial variations in its re-
sistivity or because of a transition layer of high resistance at the contact
between dielectric and electrode. Examples of the infinite-frequency
conductivity due to this type of mechanism are given in Items dia, b,
c and d of Table I.

This type of infinite-frequency conductivity is of little interest in
principle, but in practice there may be many instances in which the
measurement of the infinite-frequency conductivity provides a con-
venient means of determining the conductivities of the constituents of
these non-homogeneous systems. For example, when one layer of a
two-layer dielectric has a much higher conductivity than the other, 700
assumes a value which is related simply to the free ion conductivity
of the layer which has the higher conductivity (see Item 3b, Table I).
If the dielectric constants of the two layers are equal, 700 is equal to
one-quarter of the conductivity of the high-conductivity layer. The
conductivities 71 and 72 of the two layers are considered in the present
connection to be free ion conductivities. A more complicated situation
is possible where 71 and 72 are in part polarization conductivities due
to polar molecules or bound ions.

The special case of a space-charge caused by a thin layer of high
resistance at one or both of the electrodes is of interest in connection
with the methods recommended by Joffe for the measurement of the
true conductivity of crystals. This will be discussed in more detail
later but for the present it may be noted that the infinite-frequency

^ It is necessary to confine the application of the last statement to direct voltages
or to frequencies lower than those for which 7' is equal to 7co. When the frequency is
high enough for the latter condition to prevail the amplitude of displacement of the
ion becomes so small that the applied field produces no appreciable increase in the
average potential energy of the ion; this is illustrated in Fig. 3 at C.

'" The external effects of a space-charge occurring in a dielectric because of spatial
variations in its resistivity' may be reproduced by a uniformly distributed polarization
of suitably adjusted magnitude and relaxation-time. Several different polarizations
of different magnitudes and relaxation-times would in some instances be required.
In referring to such a space-charge as a polarization we may think of the term as
applying to the uniform distribution of polarization which could replace the space-
charge in its external effects.

524 BELL SYSTEM TECHNICAL JOURNAL

conductivity for this system has the simple value

Too = l/47rCoi? = Ti

as shown in Item 3<f, Table I. Here 71 is the free ion conductivity of
the main part of the dielectric, R is its resistance and 47rCo(= Ajd) is
the ratio of thickness to length of specimen. (In Table I of the pre-
ceding paper the symbol C«> is used in place of Cn.) The infinite-
frequency conductivity in a non-homogeneous system of this type is a free-
ion conductivity.

Bound ions may also be distributed with macroscopic uniformity in a
dielectric. An example of this type of bound ion conductivity ^^ is
one due to conducting particles dispersed uniformly in a relatively
non-conducting medium. This is the case referred to in Item 3e of
Table I. Macroscopic uniformity is obtained in this case by the
random distribution of a large number of particles. However, there
are some general experimental indications that the distribution of
bound ions may in some materials depend upon the basic internal
structure of the dielectric and involve some regular geometrical
configuration repeated throughout the material.

In certain dielectrics which absorb an appreciable amount of water
when in a humid atmosphere, conduction takes place in aqueous
conduction paths permeating the solid. Examples of these materials
are cotton, paper, silk and wool. This property is probably shared by
many other polymeric substances. The water in these materials is
distributed in minute capillaries, the dimensions and other character-
istics of which probably determine the form and distribution of the
conduction paths. ^^ There exists in these materials a condition capable
of producing a bound ion conductivity inasmuch as there are indica-
tions that the conducting paths are not of uniform cross-sectional area.
Evidence for the existence of a bound ion conductivity in the kind of
material to which we have just referred is provided, for example, by
conductivity measurements on cotton. ^^ Raw cotton contains salts
which can be removed by extraction leaving the material otherwise
practically unchanged. These salts are likely to be distributed in the
material with macroscopic uniformity as they form part of its natural
structure. The fact that the removal of these salts decreases the

" As already mentioned we shall call any infinite-frequency conductivity which is
caused by a macroscopically uniform distribution of bound ions a bound ion conduc-
tivity. In some places this term will be applied to any conductivity due to bound ions
irrespective of whether or not that conductivity is the limiting high-frequency value.

1^ One of the basic structural units of cellulose and other similar materials is the
micelle. This usually contains a large number of molecules and the capillaries we
refer to may correspond to the intermicellar spaces.

1^ Murphy, Journal of Physical Chemistry, 33, 200 (1929).

DIELECTRIC PROPERTIES OF INSULATING MATERIALS 525

dielectric loss indicates that the material possessed a bound ion
conductivity before the salts were removed.

Some of the materials belonging to the class of dielectrics which we
have just discussed are closely related in chemical and in physical
structure to compounds which are important biologically and in the
study of plant and seed structure. Many are also of commercial
importance as insulating materials.

It is not necessary that the conduction paths be composed of aqueous
solutions: in some materials plasticizers or products of pyrolysis are
sufficiently conducting for this purpose. The dielectric behavior of
certain plastics may be interpreted as evidence for the existence of such
non-aqueous conduction paths in the material, producing a free ion
conductivity, a bound ion conductivity and a contribution to the
dielectric constant. Imperfections of structure occurring in crystals
are able to produce a bound ion conductivity and there is experimental
evidence that these imperfections do occur. ^^ The regular lattice ions
in an ionic crystal have too high a binding energy, and dissipate too
little energy in their motions in a radio frequency electric field to
produce a bound ion conductivity.

The polarization which is responsible for the bound ion conductivity
is of the interfacial, or Maxwell-Wagner, type. This type of polariza-
tion may be of importance in materials with a cellular structure
and in materials which may be described as interstitially conducting
dielectrics.

In the above discussion we have outlined the character of three
widely different types of infinite-frequency conductivity :

(a) An orientational conductivity depending upon the small changes
which an applied field produces in the average orientation of polar
molecules.

(b) A bound ion conductivity depending upon the displacement of
uniformly distributed bound ions.

(c) An infinite-frequency conductivity which is proportional to the
free ion conductivity of one of the constituents of a dielectric consisting
of two or more layers of widely difi^erent conductivities.

The Relaxation-Time

The relaxation-time is closely related to the infinite-frequency
conductivity. This may be seen by reference to equation (20), which
shows that the relaxation-time is given by

4tToo

"See, for example, A. Smekal, Zeits.f. techn. Physik, 8, 561 (1927).

526 BELL SYSTEM TECHNICAL JOURNAL

This equation shows that specifying the values of r and (eo — €«,)
gives as much information as specifying 7^ and (eo — €00). In some
applications there are advantages in using r but in other applications
greater simplicity of description is gained by using 700.

There are several convenient ways of calculating the relaxation-
time. The more familiar ones depend upon the position of maxima
which occur in certain dielectric properties when they are plotted
against the frequency: there are maxima in the loss factor vs. frequency
curve, in the tangent of the loss angle vs. frequency curve and in
the power factor vs. frequency curve. As these maxima occur at
different frequencies, the corresponding expressions for the relaxation-
time are also different. They are listed in Table II. It will be ob-

TABLE II
List of Formulae for Calculating the Relaxation-Time (t)

1. The frequency at which the maximum in loss factor (e" or

«' tan 6) occurs is Wmax(l) T = l/'«Jmax(l)

2. The frequency at which the maximum in loss angle (e"/e' or

..\ • /*«> 1 •
tan 5) occurs is Wmax(2) '^ — \

\ eo C0max(2)

3. The frequency at which the maximum in power factor

e"/(e'' + t"'yl^ occurs is a,n,ax(3) T = V2 J^ -^—

' to Wmax(3)

4. The quantity «"/(«' "■ «<») is a linear function of co ''' ~ Jf ('"/(*' ~«oo))

5. The relaxation-time is proportional to the ratio of the
absorptive part («o — ««>) of the static dielectric constant to

the infinite-frequency conductivity (700) r = (eo — eQo)/47r7oo

Note: An example of the application of these formulae is provided by the curves of
Fig. 4. The value of t for ice at — 2.6°C is 25.8 microseconds as calculated from the
position of the maximum in e", 24.6 microseconds as calculated from (eo — e«i)/^T'"Y<x),
where 7t» is in e.s.u., and 23.1 microseconds as calculated from the slope of e"/(e' — eoo).

served that the simplest of these formulae for the relaxation-time is the
one involving the maximum in the loss factor.

The function e"/{e' — e^) is a linear function of co with slope equal
to T. This property provides an alternative method of calculating the
relaxation-time. An example of its application to an actual material
is provided by the data for ice plotted in Fig. 4.

It is interesting that e"/{e — e^) has no maximum while e"Je' has a
maximum. The physical basis of this is that in subtracting e„ from e'
we remove the contribution to e' made by optical polarizations. What
is left represents only the dielectric constant due to the polarization
responsible for anomalous dispersion. Consequently the tangent of
the loss angle of the polarization current responsible for anomalous

DIELECTRIC PROPERTIES OF INSULATING MATERIALS 527

dispersion has no maximum when plotted against the frequency and
its behavior is, therefore, in contrast with the tangent of the loss angle
of the total polarization current, i.e., the sum of the optical polarization
current and the absorptive polarization current.

From the above discussion it will also be evident that the physical
basis for the maximum in tan 5 is different from that of the maximum
in e". As we have just shown, the maximum in e"le (= tan 6) de-
pends upon the inclusion of optical polarizations in t' . On the other
hand, there would be a maximum in e" even if the part of the dielectric
constant which is due to optical polarizations (e^,) were neglected or
considered to be zero. This will be evident by differentiation of
equation (17).

The maximum in e" is an intrinsic property of the absorptive polari-
zation. The general nature of the mechanism by which it occurs is as
follows: e" is proportional to y'loi] as the frequency increases y'jc^ at
first increases, but when y' reaches the constant value y^, further in-
crease in frequency causes y'/co to decrease.

The quantity r which we have discussed here is a property of the
dielectric as a whole as we indicated in the preceding paper. This
quantity is connected with the relaxation-time t' of the individual
polarizable units by the relation

when the material is of cubic or isotropic structure. This relation-
ship is a consequence of the fact that the actual force acting upon a
particle within a dielectric depends not only upon the applied field
of external origin but also upon a force exerted by the polarization
induced in the dielectric.

The Relationship between Dielectric Constant and
Dielectric Loss

If e'max is the value of the dielectric constant at the frequency where
the loss factor e" is at a maximum when plotted against frequency,
we have

/ _ I ^0 ~ ^00 _ €o -|- 6^0 ,-,.

e max — ^« ~r 1 I , 9 ^2 ~ 9 ' \^^)

i ~r U' max" •^

// (fO ~ foojWmaxT' ^0 ~ ^<x,

By addition and subtraction of (26) and (27) we obtain the following

528 BELL SYSTEM TECHNICAL JOURNAL

relationships:

Co = C niax "I t max) (28)

too t max C maX) \^^/

€0 — Coo = 2c"n,ax- (30)

The comparison of the last equation with equation (20) brings out
an interesting contrast between the maximum dielectriQ loss per cycle
(«"niax) and the maximum dielectric loss per second (tx)- The maxi-
mum dielectric loss per cycle is completely determined by the difference
between the static dielectric constant and the optical dielectric constant. On
the other hand, the dielectric loss per second depends as well upon the
relaxation-time. The relaxation-time usually varies rapidly with
temperature, whereas (eo — €«,) changes comparatively slowly with
temperature. The temperature-dependence of the maximum dielec-
tric loss per cycle is related to the polarizability of the material, whereas
the temperature variation of the maximum dielectric loss per second is
primarily a measure of the change of internal friction with temperature.

In the foregoing we have discussed the conductivity, dielectric loss
and relaxation-time of dielectrics which have simple properties with
respect to the frequency-dependence of these quantities. However,
for many dielectrics, particularly solids, the experimental data are not
in agreement with the dispersion formulae for a single relaxation-time
which has been discussed here. The explanation usually adopted for
this discrepancy is that the polarizations induced in the dielectric
possess a distribution of relaxation-times.

The D-C Counterparts of Anomalous Dispersion

A dielectric so constructed that it exhibits anomalous dispersion
under an alternating voltage should show some equally characteristic
behavior when a direct voltage is substituted for the alternating one.
These characteristics may be described as the d-c counterparts of
anomalous dispersion. They include certain definite types of variation
of current with time under constant applied potential.

In the appendix the d-c counterparts of anomalous dispersion are
derived by employing the model used throughout this paper. This
enables us to demonstrate an especially simple relationship between
the a-c and d-c conductivity.

Equation (16) of the appendix gives the apparent conductivity as a
function of charging time. As it has been assumed that e^CoR <$C t,
the first term of equation (16) will quickly become negligible. Then
for charging times, measured from the instant of applying the voltage,

DIELECTRIC PROPERTIES OF INSULATING MATERIALS 529

such that t::>> tc^ eooCoR, the apparent conductivity yciQ has the
value

^0 ~ Coo ,,.<

To = -^ = Too- (31)

47rT

The special value of ydt,) which we have designated as 70 in (31) will
be called the initial conductivity.

Equation (31) states that the infinite-frequency conductivity (700),
obtained by a-c measurements, is equal to the initial d-c conductivity (70)
which would be obtained by extrapolating current-time curves toward the
instant of applying the voltage. This relationship, which has not been
demonstrated previously to our knowledge, is of interest in connection
with the interpretation of conductivity measurements.

The model described in Appendix I and indicated schematically in
Fig. 3 illustrates the physical nature of the initial conductivity in a
simple manner. When a constant voltage Vi is applied to a dielectric
having the properties of this model an effective impressed field Fi is
established in the dielectric. This displaces the bound ion assumed
to be responsible for the polarization in this model. The magnitude
of the displacement 5 of this bound ion depends upon the length of time
that 7^1 is applied. If it is applied for a time which is much longer
than the relaxation-time, 5 approaches a constant value Si correspond-
ing to complete polarization of the dielectric. On the other hand,
during that stage of the charging process when the charging time tc is
negligible in comparison with the relaxation time t and at the same
time large as compared with the time constant e^C^R, the displacement
5 is negligible in comparison with Si. The resultant force tending to
displace the ion is then approximately equal to the impressed force;
eFi - fsi ^ eFi.

Near the beginning of the charging process there is a brief interval
of time (e^Coi? <<C/c <^ t), when the motion of the bound ion of our
model in the applied field is essentially the same as that of a free ion.
During this interval the prevailing conductivity is the initial conduc-
tivity defined by equation (31). Although the bound ion of the model
is actually subjected to a force tending to restore it to its initial posi-
tion, this restoring force has not had time during the initial stage of the
charging process to build up to a magnitude appreciable in comparison
with the applied force. The initial conductivity corresponds to a
condition in the dielectric where bound ions act for a brief time as if
they were free as far as conduction processes are concerned. The
infinite-frequency conductivity corresponds also to this condition.
The variation of apparent conductivity with the time of charging is

530

BELL SYSTEM TECHNICAL JOURNAL

indicated schematically in Fig. 6. As is there shown, there must be an
initial stage, always too brief to be detected experimentally, during
which the inductance of the circuit and the inertia of the charges
cannot be neglected.

The Types of Initial Conductivity

The polarization conductivity 7poi may then be measured in two
ways: either as the infinite-frequency conductivity 7cc obtained by
a-c measurements, or as the initial conductvity 70 obtained by d-c
measurements :

7pol = 7oo = 7o-

The quantity 7poi refers to a property of the material, whereas 70 and y^,
refer to the methods of measuring this property.

INFINITE-FREQUENCYy^ ^^■"^

CONDUCTIVITY, y-Qp/ y/^

/ ^eo-eooN X

^^^s. INITIAL CONDUCTIVITY ,yQ/

\ (^ - £o-eoo\

\ \f0 4TTr )

FINAL OR \.
FREE- ION \^
CONDUCTIVITY, YV^. ^^^^.^...^

<z

FREQUENCY

' 2-rT

CHARGING TIME, ic

Fig. 6 — A-C and d-c methods of measuring conductivity. A schematic diagram
comparing the dependence of a-c conductivity (7') on frequency with the dependence
of apparent d-c conductivity 7c(/c) on charging time (/<;). For homogeneous dielec-
trics 70 = Too = 7poi, where Tpoi is a conductivity due to polar molecules or to bound
ions. For some non-homogeneous dielectrics 70 = 700 = 7/, where 7/ is a conductivity
due to free ions.

Reference to Table I will show that there are several types of polari-
zation which may be responsible for 700. Consequently this will be
true also of the initial conductivity. The equality of 70 and 700
applies to all of these types of polarization and, therefore, can not
be used to distinguish between them. For this reason experimental
agreement between a-c and d-c measurements of conductivity does
not enable us to distinguish whether we are dealing with polar mole-
cules, bound ions, or free ions in a macroscopically inhomogeneous
dielectric. Thus it is clear that when we are dealing with a polariza-
tion due to polar molecules, the initial condtictivity is a true polarization
conductivity or a specific dielectric loss. If the polarization is of the
bound ion type discussed earlier in this paper, the initial conductivity

DIELECTRIC PROPERTIES OF INSULATING MATERIALS 531

is also a polarization conductivity. However, if we are dealing with a
macroscopically non-homogeneous dielectric such as a two-layer dielec-
tric or a material which has a high resistance blocking layer at one of
the electrodes 70 is a free ion conductivity. This is evident from the
previous discussion of the significance of 700.

These relationships are of interest in connection with the difficulties
encountered in the interpretation of d-c conductivity data which
were mentioned in the introduction. They apply especially to the
methods recommended by Joffe ^^ and by Richardson. ^^

When a constant potential difference is maintained between the
plates of a condenser containing a solid dielectric the current observed
does not in general remain constant but usually decreases with time.
This decrease may continue for several minutes or hours. The study
of these residual currents is of importance in connection with the
interpretation of conductivity data on dielectrics. The question
arises as to how much of the observed behavior of the residual currents
which flow in dielectrics under constant potential may be explained as
the d-c counterparts of anomalous dispersion. Many materials of
practical importance as insulators exhibit a more complicated type of
variation with frequency than is indicated by equations (17) and (19)
which refer only to the simplest observed type of dispersion. The more
complicated types of behavior observed are usually attributed to the
presence of polarizations possessing a wide distribution of relaxation-
times. However, other processes may also contribute to the deviation
of the experimental curves from the theoretical. One of these is
electrolysis which produces changes in the composition, and conse-
quently in the conductivity of the material. Another effect which
may contribute is a possible lack of constancy of the relaxation-time.
It is evident, therefore, that the d-c counterparts of anomalous dis-
persion due to a polarization of a single relaxation-time should not be
expected to explain all of the observed residual phenomena, particularly
in solid dielectrics. However, the quantitative relations derived as
the d-c counterparts of anomalous dispersion are applicable to some
materials, and for those to which they are not quantitatively applicable,
may serve as a useful guide in the interpretation of the residual cur-
rents. As another section of this paper is planned in which the in-
fluence of residual currents upon conductivity measurements will be
discussed further, we have included in the appendix some relationships
which are useful in the interpretation of the behavior of these currents.

i^A. Joffe, Ann. d. Physik, 72, 481 (1923); "Phvsics of Crystals," New York
{\92S);Zeits.f. Physik, 62, 730 (1930). See also Sinjelnikoff and Walther, Zeits. f.
Physik, 40, 786 (1927).

"S. W. Richardson, Proc. Roy. Soc, 107 A, 102 (1925).

532 BELL SYSTEM TECHNICAL JOURNAL

APPENDIX

The D-C Counterparts of Anomalous Dispersion

Having developed the a-c characteristics of the model, the properties
of which were specified in the preceding paper, ^^ we now turn to the
direct-current characteristics of this model. This involves investigat-
ing the characteristics of the currents produced when a constant or
direct voltage Vi is applied to a condenser containing a dielectric hav-
ing properties which correspond in all respects essential to the discus-
sion to those of the model just described. Let the resistance of the
leads to the condenser be R and let the source of the electromotive
force Vi have a negligible internal resistance. These conditions re-
quire the following five equations to be satisfied simultaneously: ^^

dP
r"^ -]- fP - ne'-F = 0, (1)

F = E + APt, (2)

Pt = kiF + P, (3)

D = E + Pt, (4)

£ = E.-Ci?f. (5)

(Rational e.s.u. are used in these equations for convenience but the
final relations are converted into electrostatic units. ^^) Pt denotes the
total polarization; it is the sum of the optical polarizations, given by
kiF, and the polarization P which forms comparatively slowly and
causes anomalous dispersion. The total displacement D, is given by
(4) . Co is the air capacitance of the condenser. V is the potential drop
over the condenser. The separation of the plates of the condenser is d.
When the whole drop in potential is concentrated over the condenser
the applied field strength £i is given by £i = Vi/d. Equation (5)
is obtained by equating the total drop in potential over the leads and
the condenser to the applied potential Vi.

Equations (1) to (5) may be combined to give the following:

d'^D dD

(1 + 2Po)t'CR^ + {(1 - po)r' + CR{1 + 2po + 2Pr)]^

+ (1 - Po- pi)D - (1 + 2po + 2pi)Ei = 0. (6)

1^ These properties are also outlined on page 513 of this paper.

'^ Cf . P. Debye, " Polar Molecules," pp. 86-88, where an analogous case is discussed.

1' For conversion factors see, for example. Mason and Weaver, Reference 2, page
370. The rational electrostatic unit of conductivity is smaller than the e.s.u.; the
ratio is 4ir. The dielectric constant is unaffected by changing from rational e.s.u.
to e.s.u.

DIELECTRIC PROPERTIES OF INSULATING MATERIALS 533

In this equation the following abbreviations are used: r' = rjf,
Aki = po, Ak = pi. The last two abbreviations are introduced to
facilitate comparison with an analogous derivation given in "Polar
Molecules," p. 86. D — DoC"'^ is a solution of the homogeneous differ-
ential equation obtained by letting Ei = 0, provided that the following
equation is satisfied :

, , r / 1 - ^0 \ 1 I (1 + 2^0 + 2p{) 1 ]

As we are interested here only in the special case where CR <3C r', the
1/t' term in the coefficient of a can be neglected in comparison with the
l/CR term, and the roots are

I - po - pi\ i / 1 - po\ 1

' or a = — ' '

^ - po / r \\ + 2po) CR

to a degree of approximation which improves the larger the ratio
TJCR. The general solution of the non-homogeneous equation (6) is

r> = z),r(So)^ + z),e-(^w)^'+ /A-+^^^±i^\£, = 0. (8)

\ 1 — po — pi I

For the special case of a random or cubic distribution of molecules
(in which case A = 1/3), Eq. (8) can be simplified by means of the
following relationships:

(1 + 2p,)Kl - Po) = 6., (9)

(1 + 2p, + 2pi)/{l - Po- pi) = 60, (9')

(e. + 2)/(6o + 2) = (1 - />o - ^i)/(l - ^o), (10)

Equation (8) then becomes

D = Djg-'/'xCfi + D^e-^'^ + €o£i (11)

and introducing the initial conditions, / = 0, D = 0; / = 0, —r

» at

= Ei/CR, we obtain,

D = €o£i - 6.£ig~'/^-^« - (eo - 6^)£le-'/^ (12)

534 BELL SYSTEM TECHNICAL JOURNAL

Let gc be the charge per unit area on either of the condenser plates
at any stage of the charging process, that is, at any time tc after the
instant at which the voltage was applied. On converting (12) into
e.s.u., we have for the charge at any time during the charging process:

D,^e^_ e ^^^_^,,^^c.u _ (fiZLi^ £^,-,./.. (13)

47r 47r 47r 47r

Therefore the ballistic or d-c dielectric constant at any time of charg-
ing tc, is

e(/.) = ^ = 60 - e«oe-'^'^-^"« - (eo - e^)e-'^''. (14)

The d-c dielectric "constant" appears in this equation as a function
of the charging time. Its dependence on charging time is analogous
to the dependence of the a-c dielectric " constant " on frequency. The
static dielectric constant eo is obtained when charging has been con-
tinued until tc ^ r, that is, when te is infinite the dielectric constant
has its static value {tc = «= , €(/c) = eo) and when tc is zero the dielectric
constant is zero {tc = 0, e{tc) = 0).

The charging current is obtained by differentiation of (13) and is

The charging current per unit voltage gradient, or the apparent con-
ductivity 7t(^<), is

7c(/o) = 1^ = -y^e-'c/^xCofi + ^,g-'c/r, (16)

where ^r = (47rCoi?)~^ and 7oo = (eo — e«,)/4Tr. (It will be noticed
that if we define a quantity Gn = 1/R, it follows that (4xCo-R)~^
= GjfdIA = jr since 47rCo = A/d. The quantity jr is the specific
conductance which a fictitious material must possess if it were put in a
condenser of geometric capacitance Co and required to conduct the
same current as Co when in series with an external resistance R.)

At any stage of the charging process such that tc is large as compared
with e^CoR, but at the same time small as compared with r the ap-
parent conductivity given by (16) reduces to

yc{tc) = Too.

This value of jc{tc), where e^CoR « tc « t, will be designated by 70
and called the initial conductivity. Using this terminology we see that

DIELECTRIC PROPERTIES OF INSULATING MATERIALS 535

the initial conductivity 70 as determined hy d-c measurements equals the
infinite- frequency conductivity y^ as determined by a-c measurements.

If td represents the time measured from the instant that the voltage
is abruptly reduced to zero, and qd, Dd, Qd represent respectively the
charge, displacement, and discharge current at time td, we have for
discharging after complete charging

qdtd) =^' = ^ ,-^./e»Coie + (j^^jA E.e-^'iir (17)

or

e{td) = e^e-'<"'->('^^^ + (€0 - e^)e-'<"\ (17a)

At the end of the charging process (cf. (13)) or the beginning of the
discharge process (cf. (17)) the charge per unit area per unit applied
field strength is €o/47r.

The discharge current for complete charge is obtained by differen-
tiating (17) with respect to the time:

^^ = '^= - T^h '-'"'-'"' - ^'" ^ '^^^^ e-^<"r (18)

47r 4:irCoR 4x7 ^ ^

or

yaOd) - -T-^r = jue-''"'^'^'^ + 7^e-'-"\ (18a)

Comparison of (18) and (15), or (18a) and (16), shows that for com-
plete charging (that is, tc effectively infinite or 4 » t» eoCoR) the
charging current vs. time curve is identical, except for direction, with
the discharge current vs. time curve. This is true only of the curves for
complete charging and is not true if the polarized condition in the dielectric
is not fully formed and the polarization currefits are not zero.

The discharge-current time curve for incomplete polarization of the
dielectric is not as simple as for complete polarization. When the
charging process is broken off before completion, the initial conditions
for the discharge are not the same as when charging is complete. The
charge at time td during a discharge following a charging process
which is broken off at tc is

47r 47r 47r

+ IM-^:^ E,e-^^i^ - ^^""^^-^ E,e-^^c+uyr\ , (19)

This is an example of the superposition principle for residual charges.

536 BELL SYSTEM TECHNICAL JOURNAL

The discharge current for incomplete charge is given by

— I)^ F, F,

^^ 47r AttCoR AttCoR

Or if

+ i^^)^^'""" - (\^) '-'"""'"' (20)

- i)

= - Qd = I.

+ y^Eie-''"^ - 7x£ie-^'^+'''^/^ (20a)

Equation (20) or (20a) is an example of the superposition principle
for the residual currents in a dielectric having a single absorptive
polarization with a relaxation-time t. It is evident that in the early
stages of the charging process the electronic or instantaneous polariza-
tions responsible for €„ have the same external effect as an absorptive
polarization because of the fact that the current by which they are
formed must flow through the lead resistance R. Thus the condenser
acts as though it contained a polarization yielding a dielectric constant
with a relaxation-time e^CoR.

As the time-constant e^^CoR is generally small, the first two terms on
the right of (20a) may usually be neglected and we have

Id = -y^E^e-'^i' - 7«£ie-('^+''^)^ (21)

The first term on the right of (21) is the discharge current correspond-
ing to the discharge of the condenser after the residual polarizations
have been fully formed. The second term gives the value which the
charging current would have if the charging process were continued
for the interval of time tc + td instead of being discontinued after tc
seconds. When the charging time is large as compared with r the
second term may be neglected and the magnitude of the discharge
current is the same function of the discharge time as is the charging
current of the charging time; the charging curve and discharge curve
can then be superimposed on one another if we disregard the direction
of the current. There is only one complete charging current curve and
only one discharging current curve corresponding to complete polarization
of the dielectric at any given applied potential. There is, however, an
infinite number of discharge curves corresponding to incomplete polariza-
tion of the dielectric, that is, to any time of charging which is shorter
than that necessary for complete polarization.

f

DIELECTRIC PROPERTIES OF INSULATING MATERIALS 537

The superposition principle states that any of these discharge
curves may be derived from the discharge curve for complete polariza-
tion by subtracting from its ordinates the values which the charging
current would have if it had continued during the discharge. From
the method of deriving equation (21) it is clear that the superposition
principle is a necessary consequence of an assumed exponential growth
and relaxation of the residual polarizations, as required by the theory
of simple anomalous dispersion. If these in fact do not vary exponen-
tially with the time, whatever function they do follow appears in
general to obey an empirical superposition rule. Reference to (20o)
will indicate that if there are m polarizations of different relaxation-
times which are quite far apart, each polarization will simply contribute
two terms to the expression for Id', that is,

m
3=1

+ 7fi£ie-'''/*oo(^oK _ yj^g-Uc+td)if^CoR^ (22)

Thus, the existence of the superposition principle for residual currents
as an empirical law suggests that the individual polarizations actually
vary exponentially with the time, though direct measurement of the
total discharge current seldom gives a single exponential curve. This
is, however, not the only possible interpretation.

Abstracts of Technical Articles from Bell System Sources

Radio Telephone System for Harbor and Coastal Services} C. N.
Anderson and H. M. Pruden. Radio telephone service with harbor
and coastal vessels is now being given through coastal stations In the
vicinities of seven large harbors on the Atlantic and Pacific coasts with
additional stations planned. The system is designed to be as simple
as possible from both the technical and operating standpoints on both
ship and shore.

Recent developments in the shore-station design eliminates all
manipulations of the controls by the technical operator. This is made
possible principally because of crystal-controlled frequencies on shore
and ship, a "vogad" which keeps the transmitting volume of the shore
subscriber constant, and a "codan" incorporated in the shore radio
receiver which will operate on signal carrier but is highly discriminatory
against noise. A signaling system permits the traffic operator to call
in an individual boat by dialing the assigned code which rings a bell
on the particular boat called. The ship calls the shore station by
turning on the transmitter. The radio signal operates the codan in
the shore receiver which in turn lights a signal lamp in the traffic
switchboard.

Gradually the system has been taking on more and more the aspects
of the wire telephone system.

Ship Equipment for Harbor and Coastal Radio Telephone Service}
R. S. Bair. The ultimate objective in the design of radio telephone
apparatus for use on ships is to provide equipment which is as con-
venient and simple to operate as the telephone at home. To a con-
siderable degree this has been accomplished in the new 15- and 50-watt
ship sets that have recently been designed for use on harbor craft and
coastwise vessels.

The requirements for sets of this type are discussed and the new
equipment is described in this paper.

Protective Coatings for Metals } R. M. Burns and A. E. Schuh.
This book is one of the American Chemical Society Series of Scientific
and Technologic Monographs. The chapter headings are: Protective

1 Proc. I. R. E., April 1939.

2 Proc. I. R. E., April 1939.

3 Published by Reinhold Publishing Corporation, New York, N. Y., 1939.

538

ABSTRACTS OF TECHNICAL ARTICLES 539

Coatings and the Mechanism of Corrosion — Surface Preparation for the
Application of Coatings — Types of Metallic Coatings and Methods of
Application — -Zinc Coating by Hot-Dipping Process — Zinc Coating by
Electroplating and Cementation — Protective Value of Zinc Coatings —
Cadmium Coatings and their Protective Value — Tin Coatings — Nickel
and Chromium Coatings — Coatings of Copper, Lead, Aluminum and
Miscellaneous Metals — Coatings of Noble and Rare Metals — Methods of
Testing Metallic Coatings — Composition of Paints and Mechanism of
Film Formation — The Durability and Evaluation of Paints — Paint
Practices — Miscellaneous Coatings.

"The active interest manifested during the past few years in in-
vestigations on the general subject of the corrosion of metals has led
to the carrying-out of long-time exposure tests which yielded much new
basic information having a direct bearing on our knowledge of the
useful life of coatings and coated metals. The authors have wisely
incorporated a great deal of this information in the discussion of the
different types of coatings. Likewise, it has been deemed desirable
to devote considerable space to the preliminary preparation of metal
surfaces before the application of the coating since the quality of any
coating is so dependent upon this factor.

"The new monograph, therefore, covers a much broader field than
did the previous one which was really a pioneer in the field of metallic
coatings. The investigator of the abstruse problems of corrosion as
well as the materials engineer seeking practical help in combating this
problem by preventing corrosion by protecting the surface will find
this volume a veritable mine of information on all phases of the
subject."

A Synthetic Speaker.^ Homer Dudley, R. R. Riesz, and S. S. A.
Watkins. This synthetic speaker is an electrical device manipulated
by keys and levers for the production of synthetic vocal sounds and
their combination into speech. The device was developed as an in-
teresting educational exhibit by the Bell System at the San Francisco
Exposition and the New York World's Fair.

From a buzzer-like tone and a hissing noise as raw material, the
operator skillfully shapes speech by manipulating the controls to give
inflection and the sound spectrum that differentiates one speech sound
from another.

This paper covers the development of the device and the training
of the operators to demonstrate it.

* Jour. Franklin Institute, June 1939.

540 BELL SYSTEM TECHNICAL JOURNAL

Remotely Controlled Receiver for Radio Telephone Systems} H. B.
Fischer. New radio receiving equipment for shore station used in
ship-to-shore telephone circuits has been developed. This equipment
is designed to operate on a remotely attended basis and may be located
a considerable distance from the telephone terminal equipment. The
radio receiver forming a part of the equipment has a codan circuit
which operates reliably under high noise conditions and does not
require adjustments to compensate for variations in the noise level.
An emergency battery power-supply system is provided which is auto-
matically connected to the receiver when the primary alternating-
current power supply fails. Power failures are indicated at the tele-
phone central office. A test oscillator which is controlled from the
telephone central office is provided which may be used to check the
operation of the receiver or to measure the frequency deviations of the
incoming signals. The various apparatus units are mounted in two
weather-proof cabinets which may be fastened to the same telephone
pole which supports the receiving antenna.

Analysis and Measurement of Distortion in Variable-Density Re-
cording} J. G. Frayne and R. R. Scoville. Several types of non-
linear distortion in variable-density recording are discussed and
methods of measurement outlined. The two-frequency inter-modula-
tion method is described. Mathematical and experimental relation-
ships between per cent inter-modulation and per cent harmonic dis-
tortion are established. The inter-modulation method is applied to
film processing for the determination of optimal negative and positive
densities and overall gamma. Variance of these parameters from those
indicated by classical sensitometry are traced to halation in the emul-
sion and to processing irregularities. The use of special anti-halation
emulsions appear to reduce residual distortion effects and tend to
bridge the gap between inter-modulation and sensitometric control
values.

Rubbed Films of Barium Stearate and Stearic Acid J L. H. Germer
and K. H. Storks. Films of barium stearate and of stearic acid have
been prepared on polished chromium and on smooth natural faces of
silicon carbide crystals. After these films have been rubbed with clean
lens paper, electron dififraction patterns are obtained from them by the
reflection method. Well rubbed films give patterns characteristic of a
single layer of molecules standing with their axes approximately normal

5 Proc. I. R. E., April 1939.

6 Jour. S. M. P. £., June 1939.
"^ Phys. Rev., April 1, 1939.

ABSTRACTS OF TECHNICAL ARTICLES 541

to the surface; the hydrocarbon chains of barium stearate are found to
be more precisely oriented than those of stearic acid; exactly the same
difference exists between unrubbed single layers of molecules of barium
stearate and of stearic acid deposited by the Langmuir-Blodgett
method. Thickness of rubbed films on chromium has been found, by
the Blodgett optical method, to be the same as that of unrubbed
single layers of molecules. Lightly rubbed films may be thicker than a
single layer of molecules. The arrangement of barium stearate in such
thicker films has been found to have been somewhat altered by the
rubbing. The axes of the hydrocarbon chains still stand normal to the
surface, but lateral arrangement is less regular than it is in unrubbed
films of equal thickness. In the case of stearic acid, molecules left on
top of the first layer after light rubbing in one direction are found to lie
inclined by about 8° to the surface and to point outward against the
rubbing direction (Fig. 7) ; they are arranged in crystals having a
structure different from that of the film before rubbing. Such "up-
set" films of stearic acid are completely removed by very light rubbing
in the direction opposite to that of the original rubbing, but they are
rather resistant to light rubbing in the same direction.

Diffraction and Refraction of a Horizontally Polarized Electromag-
netic Wave over a Spherical Earth.^ Marion C. Gray. Formulas are
derived for the electromagnetic field at a point on or above the surface
of a spherical earth due to the presence of a vertical magnetic dipole.
It is shown that the resultant field resembles that due to a vertical
electric dipole above a spherical earth of low conductivity, and that in
the magnetic case the values of the earth constants are of much less
importance than in the electric. Curves are included showing the
variation of the field with distance and with height.

Inductive Coordination with Series Sodium Highway Lighting Cir-
cuits.^ H. E. Kent and P. W. Blye. This paper describes the wave-
shape characteristics of the sodium-vapor lamp and discusses the rela-
tive inductive influence of various series circuit arrangements in which
such lamps are employed. A method is outlined by means of which
the noise to be expected in an exposed telephone line may be estimated.
Measures are described which may be applied in the telephone plant or
in the lighting circuit to assist in the inductive coordination of the
two systems. These measures need be considered only when a con-
siderable number of lamps is involved, since noise induction is negli-

8 Phil. Mag., April 1939.

' Electrical Engineering, Transactions Section, July 1939.

542 BELL SYSTEM TECHNICAL JOURNAL

gible when there are only a few lamps as, for instance, at highway
intersections.

Sound Picture Recording and Reproducing Characteristics}^ D. P.
LoYE and K. F. Morgan. In the improvement of sound motion
pictures, the trend has been to make the response of all parts of the
recording and reproducing circuits as nearly "flat" as possible. In
some cases, however, this has resulted in unnatural sound, and there-
fore certain empirical practices have been adopted in the studios and
theaters to make pictures sound best.

This paper describes the results of a study the purpose of which has
been to evaluate the factors which afi^ect the quality of speech as
recorded and reproduced, from the vocal cords of the actor on the
sound-stage to the brain of the listener in the theater. The character-
istics of the various factors have been determined and combined with
dialog, voice efifort, and other equalizers designed to produce an overall
characteristic " subjectively flat " at the brain of the theater patron.
These factors, as well as others which are now in the process of being
studied, are presented in this paper.

One of the most important characteristics studied is that of the
change in voice quality with a change in the efl^ort on the part of the
speaker. This is described in detail in this paper. The stage and set
acoustic characteristics, microphone characteristic, and dialog equal-
ization to compensate principally for the hearing characteristic of the
average theater listener, are among the factors described herein.

A Dynamic Measurement of the Elastic, Electric and Piezoelectric
Constants of Rochelle Salt}^ W. P. Mason. The elastic, electric and
piezoelectric constants of Rochelle salt have been measured at low
field strengths by measuring the resonant frequencies and impedance of
vibrating crystals. It is shown experimentally that the resonant and
anti-resonant frequencies of the crystal are both considerably below
the natural mechanical resonant frequency of the crystal in disagree-
ment with the usual derivation of the frequencies of a piezoelectric
crystal. By assuming that the piezoelectric stress is proportional to
the charge density on the electrodes rather than the potential gradient
as usually assumed, theoretical frequencies are obtained which agree
with those found experimentally. This theoretical derivation to-
gether with the measured frequencies supply values for the piezoelec-
tric constants. The elastic constants measured dynamically show
some differences from those measured statically. A large difference is

10 Jour. S. M. P. E., June 1939.

11 Phys. Rev., April 15, 1939.

ABSTRACTS OF TECHNICAL ARTICLES 543

found for the dynamically measured piezoelectric constants from
those statically measured, which may be attributed to the finite relaxa-
tion time for the piezoelectric elements.

A Vo gad for Radio Telephone Circuits. ^"^ S. B. Wright, S. Dob a,
and A. C. Dickieson. Commercial radio telephone connections must
generally be accessible to any telephone in an extensive wire system.
Speech signals delivered to the radio terminals for transmission to
distant points vary widely in amplitude due to the characteristics of
the wire circuits and individual voices. To provide the best margin
against atmospheric noise, it is usually the practice to equalize this
wide range of speech amplitudes and thus drive the radio telephone
transmitter at its full capacity.

Many devices have been proposed to adjust automatically the gain
in a circuit to equalize speech volumes. The difficulties of providing
a device which will respond properly over a wide range to the complex
qualities of a speech signal have only recently been overcome to a
satisfactory degree.

The voice-operated gain-adjusting device, or "vogad," described
in this paper is a practical design based upon more than a year's
experience with one of the most promising devices made available by
earlier development effort. A trial installation of this latest vogad is
now under way at Norfolk in connection with a new radio telephone
system for harbor and coastal service.
12 Proc. I. R. E., April 1939.

Contributors to this Issue

John R. Carson, B.S., Princeton, 1907; E.E., 1909; M.S., 1912,
D.Sc. (Honorary), 1936. American Telephone and Telegraph Com-
pany, 1914-34; Bell Telephone Laboratories, 1934-. As Transmission
Theory Engineer for the American Telephone and Telegraph Company
and later for the Laboratories, Dr. Carson has made substantial con-
tributions to electric circuit and transmission theory and has published
extensively on these subjects. The Franklin Institute of Philadelphia
recently awarded him the Elliott Cresson Medal. He is now a re-
search mathematician.

J. G. Chaffee, S.B., Massachusetts Institute of Technology, 1923.
Western Electric Company, Engineering Department, 1923-25; Bell
Telephone Laboratories, 1925-. ' Mr. Chaffee has been engaged in the
study of radio problems at ultra-high frequencies.

W. J. Clarke, B.Chem., Cornell University, 1924; M.A., Columbia
University, 1932. Research Laboratory, Devoe and Raynolds Com-
pany, 1924-30. Bell Telephone Laboratories, 1930-. Mr. Clarke was
at first engaged in studies of organic finishes for telephone equipment,
particularly on the compounding of improved finishing materials.
More recently his work has been concerned with investigations of
molding plastic materials.

Victor E. Legg, B.A., 1920, M.S., 1922, University of Michigan.
Research Department, Detroit Edison Company, 1920-21; Bell Tele-
phone Laboratories, 1922-. Mr. Legg has been engaged in the develop-
ment of magnetic materials and in their applications, particularly for
the continuous loading of cables, and for compressed dust cores.

S. O. Morgan, B.S. in Chemistry, Union College, 1922; M.A.,
Princeton University, 1925; Ph.D., 1928. Western Electric Company,
Engineering Department, 1922-24; Bell Telephone Laboratories,
1927-. As Dielectric Research Chemist, Dr. Morgan is concerned with
the relation between dielectric properties and chemical composition.

E. J. Murphy, B.S., University of Saskatchewan, Canada, 1918;
McGill University, Montreal, 1919-20; Harvard University, 1922-23.
Western Electric Company, Engineering Department, 1923-25; Bell

544

CONTRIBUTORS TO THIS ISSUE 545

Telephone Laboratories, 1925-. Mr. Murphy's work is largely con-
fined to the study of the electrical properties of dielectrics.

Liss C. Peterson. Chalmers Technical Institute, Gothenburg,
1920; Technical Universities of Charlottenburg and Dresden, 1920-23.
American Telephone and Telegraph Company, 1925-30; Bell Tele-
phone Laboratories, 1930-. Mr. Peterson is engaged in amplifier
research.

John R. Townsend, Brooklyn Polytechnic Institute. Bethlehem
Steel Company, 1915-17. Mathematics and Dynamics Branch, U. S.
Ordnance Department, 1917-19. Member of Technical Staff, Western
Electric Company, 1919-25; Bell Telephone Laboratories, 1925-.
He is now Materials Standards Engineer. He is the author of "Fa-
tigue Studies of Telephone Cable Sheath Alloys," "Physical Properties
and Methods of Test for Some Sheet Non-ferrous Metals," and also of
many other articles published in technical magazines and discussed
before engineering societies. Awarded Dudley Medal, A.S.T.M., 1930.

VOLUME XVm OCTOBER, 1939 number 4

THE BELL SYSTEM

TECHMCAL JOURNAL

DEVOTED TO THE SCIENTIFIC AND ENGINEERING ASPECTS
OF ELECTRICAL COMMUNICATION

Experience in Applying Carrier Telephone Systems to Toll
Cables— PT. B. Bedell, G. B. Ransom and W. A. Stevens 547

The Toronto-Barrie Toll Cable

— M. J, Aykroyd and D. G. Geiger 588

The Computation of the Composite Noise Resulting from Ran-
dom Variable Sources — E. Dietze and W. D. Goodale, Jr. 605

Load Rating Theory for Multi-Channel Amplifiers

—B. D. Holbrook and J. T. Dixon 624

The Quantum Physics of Solids, I. The Energies of Electrons
in Crystals — W. Shockley 645

DialClutchof the Spring Type— C.F. PTiebusc/i 724

Abstracts of Technical Papers 742

Contributors to this Issue . 747

AMERICAN TELEPHONE AND TELEGRAPH COMPANY

NEW YORK

50c per Copy $1,50 per Year

THE BELL SYSTEM TECHNICAL JOURNAL

Published quarterly by the

American Telephone and Telegraph Company

195 Broadway, New York, N. Y.

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EDITORIAL BOARD

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Copyright, 1939
American Telephone and Telegraph Company

PRINTED IN U. S. A.

The Bell System Technical Journal

Vol. XVIII October, 1939 No. 4

Experience in Applying Carrier Telephone Systems
to Toll Cables

By W. B. BEDELL, G. B. RANSOM and W. A. STEVENS

THE application of carrier telephone systems to toll cable con-
ductors, particularly those conductors in existing cables, is
expected to become an important means of providing additional long
distance telephone circuits. Eight hundred and thirty-seven route
miles have been equipped in the United States to date, and 17 twelve-
channel systems have been placed in service, providing a total of
about 58,000 circuit miles. Late in 1939, 200 additional route miles
are expected to be completed which, together with additional systems
on existing routes, will add nine systems and about 48,000 circuit
miles to the above figures.

The type of carrier system which has been installed is that described
by Messrs. C. W. Green and E. I. Green before the American Institute
of Electrical Engineers in 1938, and which is now designated as
type K.^ The problems incident to the application of this system to
toll cable conductors may be of general interest and it is the purpose
of this paper to describe some of these. This description will start
at the point where traffic needs have indicated that additional circuits
should be provided along a given route and economic and other con-
siderations have shown that they should be provided by means of
type K cable carrier telephone systems. For specific examples, refer-
ence will be made to the New York-Charlotte and Detroit-South Bend
projects, in which sections the application of the initial type K carrier
systems has been completed. Figure 1 shows the geographical loca-
tion of these installations, as well as some of those sections where
type K carrier systems will probably be installed in the future.

^ For references see end of paper.

547

548

BELL SYSTEM TECHNICAL JOURNAL

APPLYING CARRIER TELEPHONE SYSTEMS 549

Selection of Cables to be Equipped

Where more than two cables existed on a route selected for carrier
operation, a number of factors influenced the selection of cables to be
equipped initially. Among these were the ages of the cables, their
makeup, specific route, number of branch cables and open wire junc-
tions, and lengths of underground cable involved. Between Detroit
and South Bend there were but two cables on the route selected and
hence no selection was necessary. Between New York and Washing-
ton on the New York-Charlotte route all cables are underground, and
since there were from three to six cables in each repeater section, the
two cables which it was decided to employ were selected because they
were relatively new and had the smallest number of branches. From
Washington to Petersburg, Va., there were two cables, while between
Petersburg and Charlotte there was but one cable and it was necessary
to install a small second cable chiefly for carrier operation.

The Petersburg-Greensboro section of this second cable was in-
stalled one year ahead of the carrier application in order to make
use of part of its conductors which were loaded for voice frequency
operation. This cable is made up in most sections of 32 quads of
19-gauge conductors, of which 20 are loaded with H-88-50 loading
units, leaving 10 quads non-loaded for carrier use and two for main-
tenance purposes.

The second cable in the Greensboro-Charlotte section was installed
coincidentally with the installation of the initial carrier systems. This
cable contains 61 non-quadded pairs throughout, except in certain
sections where it also contains some loaded conductors for short voice
frequency circuits. Paired construction was used because it was ex-
pected to be slightly more economical and temporary voice usage of
the conductors was not planned.

One additional factor which, in special cases, influences the selection
of cables is that of carrier repeater spacing. This is brought about by
the fact that on multi-cable routes all of the cables may not follow
exactly the same route. For example, one cable may be aerial and
the other underground, and the two may be separated in some sec-
tions; or underground cables, for conduit reasons, may follow different
routes. It is desirable that the two cables used be near each other at
repeater points.^

One interesting feature in the construction of the Greensboro-
Charlotte Cable is the method by which the cable was attached to the
messenger. The cable was lashed to the messenger by means of a
galvanized steel wire continuous between poles, as shown in Fig. 2.
This method of installation is expected to reduce buckling, ring cuts,

550

BELL SYSTEM TECHNICAL JOURNAL

Fig. 2 — Method of lashing cable to messenger with galvanized steel wire shown in

progress.

and jumping, and avoids the necessity of splicing the cable under
tension.

Selection of Conductors for Carrier Use
In general, non-loaded cable pairs are not available in existing cables
and it is necessary to remove voice frequency loading from pairs

APPLYING CARRIER TELEPHONE SYSTEMS 551

intended for carrier operation. As has been described previously in a
paper in this Journal ^ the crosstalk mitigation plans in connection
with type K carrier are designed on the assumption that cable pairs
will be developed in units of 20 pairs for each direction of transmission.
Further, the design of this carrier system contemplates the use of
19-gauge pairs.

Ten quads (20 pairs) were, therefore, selected in each cable in which
carrier operation was planned. These quads were selected, for cross-
talk reasons, from a large voice complement. Two-wire facilities may
be used for carrier where a sufficiently large complement exists. This
results, however, in the loss of twice as many voice circuits as com-
pared to unloading four-wire quads. In the sections unloaded to date
it has been impracticable to unload two-wire facilities.

Where four-wire facilities were used, five quads from the groups
designed for each direction of voice frequency transmission in each
cable were selected. Over 20,000 circuit miles of four-wire facilities
have been unloaded for carrier use. Of this total, H-174-63 loading
units were removed from 2,280 circuit miles, and H-44-25 units were
removed from the remainder. The H-44-25 loading units removed
from 2,475 miles of four- wire circuits were transferred to two-wire
16-gauge quads loaded with H-174-63 units in the same cable, and
these latter units released, thus providing at small cost transmission
improvement on a total of 4,950 circuit miles.

Preparation of Cable Conductors

Coincidentally with the removal of the loading from the quads
selected for carrier operation, special splicing work was performed for
crosstalk and transmission reasons. The exact method of making
these splices depended upon the layup of the cable involved. For
example, if the cable involved concentric segregation, the five former
east bound quads were spliced at random to the five former west bound
quads and vice versa at each loading point; in cables involving split
layer segregation, the ten quads were spliced at each loading point in
a planned random manner.

The removal of the loading at the point nearest the center of each
carrier repeater section was left until last, so that a special splice,
called a poling splice, based on measurements of within-quad admit-
tance unbalances, might be made at each such point. ^ These meas-
urements could not be made until all loading coils on the carrier pairs
in the repeater section had been removed. Using these measurements
as a guide the quads in one half-section were connected to quads in

552

BELL SYSTEM TECHNICAL JOURNAL

the other half-section so that the unbalances in the two sections tended
to compensate. Table 1 shows for a typical type K repeater section

TABLE 1

Measurements of Mutual Inductance Unbalance (G) and Capacitance

Unbalance (C) Before and After Poling on Quads in the

Philadelphia-Philadelphia KN Section of the

New York-Philadelphia E Cable

Before Poling

After Poling

Pairs

G

c

G

c

Micromho

Mmf.

Micromho

Mmf.

1-2

.16

110

.12

SO

3-4

.12

40

.01

30

5-6

.12

80

.01

45

7-8

.01

40

.02

0

9-10

.07

85

.05

5

11-12

.06

0

0

0

13-14

.10

10

.04

25

15-16

.13

65

0

45

17-18

.11

30

0

20

19-20

.08

25

0

10

the unbalance measurements before poling and the final results after
the poling splice was made. These measurements were made at voice
frequencies, since as discussed in a previous paper ^ satisfactory re-
sults were obtained at these frequencies. It will be noted that poling
reduced markedly the unbalances in the quads in the section shown.
This is particularly true of the mutual inductance unbalances, indi-
cated in the table by G, the reduction of which is important in reducing
crosstalk at carrier frequencies.

After carrying out this and the balancing operations described later
for the reduction of crosstalk, it was still necessary to take other steps
to reduce the within-quad crosstalk. The recurrence of within-quad
coupling between carrier systems which may be assigned to two of the
pairs in a 20-pair carrier complement, has been reduced by means of
a splicing plan so worked out, that two given carrier systems will
operate on the same quad as infrequently as possible. This was ac-
complished by splitting the quads at the ends of each carrier repeater
section on a planned basis. The plan is shown in Table 2, Nineteen
types of splices are shown. This table is used as a guide in performing
the splice between the balancing bays and the input sealed test ter-
minal. For example, in performing splice type 8, sealed test terminal
jacks K-1 are connected to the pair designated 8 at the balancing bay
cable terminal, jacks K-2 to the pair designated 16, jacks K-3 to

APPLYING CARRIER TELEPHONE SYSTEMS
TABLE 2

553

Detailed Plan for Splitting Quads in Nineteen Consecutive Carrier

Repeater Sections for a Ten-Quad Group Arranged

FOR Type K Cable Carrier Operation

Pair Designa-

Planned Splice Type Number

tion at Sealed

Test Terminal

Jacks

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

K-1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

K-2

2

3

5

7

9

12

14

16

18

20

1

2

4

6

8

10

13

15

17

K-3

3

4

7

10

14

17

20

3

6

9

19

13

16

19

2

5

8

12

15

K-4

4

5

9

14

18

2

6

10

15

19

3

3

7

12

16

20

4

8

13

K-5

5

6

12

17

2

7

13

18

3

8

17

14

19

4

9

15

20

5

10

K-6

6

7

14

20

6

13

19

5

12

18

5

4

10

17

3

9

16

2

8

K-7

7

8

16

3

10

18

5

13

20

7

15

15

2

9

17

4

12

19

6

K-8

8

9

18

6

15

3

12

20

8

17

7

5

14

2

10

19

7

16

4

K-9

9

10

20

9

19

8

18

7

17

6

13

16

5

15

4

14

3

13

2

K-10

10

11

11

11

11

11

11

11

11

11

9

11

11

11

11

11

11

11

11

K-11

11

12

2

13

3

14

4

15

5

16

14

6

17

7

18

8

19

9

20

K-12

12

13

4

16

7

19

10

2

14

5

8

17

8

20

12

3

15

6

18

K-13

13

14

6

19

12

4

17

9

2

15

16

7

20

13

5

18

10

3

16

K-14

14

15

8

2

16

9

3

17

10

4

6

18

12

5

19

13

6

20

14

K-15

15

16

10

5

20

15

9

4

19

14

18

8

3

18

13

7

2

17

12

K-16

16

17

13

8

4

20

16

12

7

3

4

19

15

10

6

2

18

14

9

K-17

17

18

15

12

8

5

2

19

16

13

20

9

6

3

20

17

14

10

7

K-18

18

19

17

15

13

10

8

6

4

2

2

20

18

16

14

12

9

7

5

K-19

19

20

19

18

17

16

15

14

13

12

12

10

9

8

7

6

5

4

3

K-20

20

1

1

1

1

1

1

1

1

1

10

1

1

1

1

1

1

1

1

Note: Above numbers are pair number designations at balancing bay cable ter-
minals of pairs which are connected to Sealed Test terminal jacks as indicated.

pair 3, etc. Using this plan two systems are exposed to each other
on the same quad only once in 19 carrier repeater sections. Begin-
ning with the 20th section the plan is repeated so that between New
York and Charlotte two given systems operate together on the same
quad in only two repeater sections. Planned splices were made at
each end of each carrier repeater section so that after the quads had
been split in a definite way at one end of a section, a complementary
splice was made at the other end, to rearrange the pairs into a given
order as they go through each repeater office. Each carrier pair has
been made to appear in the same position at each carrier testboard
throughout the 19 types of planned splice sections. This is for con-
venience in maintaining and identifying them, because carrier systems
must be assigned to the same carrier pair in a series throughout the
19 types of planned splice sections if the quad splitting plan is to be
completely effective.

The poling splice and the planned splices were, of course, not re-

554 BELL SYSTEM TECHNICAL JOURNAL

quired in the paired cable placed for carrier operation between Greens-
boro and Charlotte.

Far-end crosstalk was still further reduced by means of balancing
coils installed at the end of each repeater section connected to the
repeater inputs.^' ^ After the splicing operations just discussed were
completed and the balancing coils were installed and connected to the
carrier pairs, the coupling between each pair and each other pair of
the carrier complement was reduced to the lowest value practicable by
adjustment of these coils. This was accomplished by sending a dis-
turbing testing tone on one pair, receiving on each other pair in turn,
and adjusting the coil which couples each combination of two pairs
until a minimum amount of the testing tone was measured on the
disturbed pair. Figure 3 shows these adjustments in progress while
Table 3 shows a summary of the final crosstalk measurements made
after the adjustments. About 19,000 balancing coils have been in-
stalled on the carrier routes equipped to date.

At two points on the New York-Charlotte route, retardation coils
which are described later were used to increase the attenuation in
potential crosstalk paths. At Petersburg, Va., and Burlington, N. C,
60 and 4 voice quads, respectively, connected direct from one carrier
cable to the other. These quads, through secondary induction, were
likely to serve as crosstalk paths at carrier frequencies between the
two cables. Retardation coils were installed in each quad to limit
crosstalk currents. Two other situations, where quads connected be-
tween the carrier cables, were eliminated by cable rearrangements.

Lateral Cables
At each carrier repeater station four lateral cables were installed
to bring the carrier pairs into the repeater building. One of these
was required for each direction of transmission for each cable; that is,
two input cables and two output cables were required. As a result
of the transposition of directions of transmission at each repeater point,
the two input cables connect to one toll cable and the two output
cables to the other. Figure 4 shows these cables installed at an aerial
cable repeater point. All lateral cables were installed for the prob-
able ultimate capacity for carrier systems of the cables being developed ;
that is, 100 systems on the Detroit-South Bend route, 100 systems
north and 60 systems south of Richmond, Va., on the New York-
Charlotte route.

The Location of Carrier Repeater Station Sites
The next important step in the development of a route for type K
carrier operation is the selection of points at which intermediate

APPLYING CARRIER TELEPHONE SYSTEMS

555

Fig. 3 — Adjustment of coils in crosstalk balancing panel.

556

BELL SYSTEM TECHNICAL JOURNAL

TABLE 3

Final Far-End Carrier Crosstalk Measurements after Balancing
Coil Adjustments

Section

New York Toward Charlotte

Ca.

Crosstalk

Units
39.85 kc

R.M.S.

Max.

Crosstalk

Units
28.15 kc

R.M.S.

MelX.

Charlotte Toward New York

Ca.

Crosstalk

Units
39.85 kc

R.M.S,

Max.

Crosstalk

Units
28.15 kc

R.M.S.

Max.

New York-N. Y. KS . . .
N. Y. KS-Prin. KN . . . .

Prin. KN-Prin

Prin.-Prin. KS

Prin. KS-Phila. KN....

Phila. KN-Phila

Phila.-Phila. KS

Phila. KS-Elk. KN

Elk. KN-Elk

Elk.-Elk. KS

Elk. KS-Balt. KN

Bait. KN-Balt

Balt.-Wash. KN

Wash. KN-Wash

Wash.-Wash. KS

Wash. KS-Fred. KN . . .

Feed. KN-Fred

Fred.-Fred. KS

Fred. KS-Rich. KN . . . .

Rich. KN-Rich

Rich.-Rich. KS

Rich. KS-McK. KN....

McK. KN-McK

McK.-McK. KS

McK. KS-Norl. KN....

Norl. KN-Norl

Norl.-Norl. KS

Norl. KS-Dur. KN

Dur. KN-Dur

Dur.-Dur. KS

Dur. KS-Gbo. KN

Gbo. KN-Gbo

Gbo.-Gbo. KS

Gbo. KS-Sal. KN

Sal. KN-Sal

Sal.-Sal. KS

Sal. KS-Chlot. KN

Chlot. KN-Chlot

42
37
38
37
35
35
45
29
45
36
38
35
44
39
43
43
54
45
47
43
39
48
36
57
36
53
34
56
42
61
42
57
39
57
34
54
34
43

283
148
130
212
148
250
243
116
161
204
126
107
241
179
184
224
179
173
167
167
179
138
130
190
145
173
110
179
190
155
195
219
145
338
161
265
141
200

36
36
36

33
32
31
44
28
45
36
39
34
42
38
43
40
50
43
46
46
40
53
34
62
35
56
38
56
38
58
42
58
37
54
35
52
32
42

122
122
114
130
164
100
226
112
145
164
129
114
179
195
148
167
163
152
164
176
127
155
100
174
145
170
134
195
190
145
118
195
141
346
155
245
155
155

29
40
35
30
29
37
45
36
42
35
45
43
34
44
47
44
49
39
39
30
37
56
38
56
41
59
39
65
38
59
37
55
40
43
35
53
33

184
95
212
132
100
114
127
138
145
217
207
224
219
100
182
141
170
219
167
200
190
265
148
152
161
198
167
142
200
114
205
118
173
224
245
126
245
167

31
27
37
36
28
29
2,?,
45
36
42
33
45
38
36
48
46
46
48
39
38
39
35
64
38
62
39
59
40
62
43
59
36
50
38
50
32
53
31

100
92
155
130
112
127
122
122
130
176
145
170
148
126
158
155
208
219
127
125
158
200
167
155
187
190
170
142
187
134
187
107
155
161
300
107
286
129

Note: These measurements were made in connection with balancing work where
relative values are important and do not necessarily represent the absolute magni-
tude of the crosstalk.

APPLYING CARRIER TELEPHONE SYSTEMS

557

Fig. 4 — The four lateral cables containing carrier pairs shown as installed at an
auxiliary repeater point on aerial cables.

558 BELL SYSTEM TECHNICAL JOURNAL

repeater stations, known as auxiliary repeater stations, will be con-
structed. The selection of these locations is necessary before the
transmission design of a carrier route can be completed. Repeaters
for voice frequency circuits are located on existing cable routes at an
average spacing of about 45 miles. These same offices are used as
cable carrier repeater points, but, because of the high losses at carrier
frequencies, two additional carrier repeater stations, on the average,
have been provided between each two voice frequency repeater offices.

The cables and routes having been tentatively decided upon, the
route records were studied and locations which were the most prac-
ticable from a transmission standpoint were selected. These selections
were influenced by the expected maximum section losses, taking into
account aerial and underground construction. In general, the dis-
tances between the existing voice repeater points were divided into
the smallest number of equal parts, the lengths of which did not
exceed the maximum permissible carrier repeater spacing, and repeater
station sites were tentatively located at the junctions of these parts.

A physical inspection of these tentative sites was then made and
where necessary an alternate site selected. Such factors as accessi-
bility of site, suitability for building, availability of primary power,
cost of real estate, and willingness of owners to sell determined whether
or not the tentative site could be used and, if not, what alternate
location might be used. Where a suitable existing telephone building
happened to be located near a proposed repeater station location, the
possibility of using such building was studied. It has been practicable,
however, in only one instance to use an existing building in installing
the 34 auxiliary stations provided to date. The sites which were con-
sidered satisfactory after the physical inspection were then examined
to check their suitability from a carrier transmission standpoint. In
cases where transmission limits had been exceeded, the sites were
reinspected and compromise locations finally agreed upon. In most
cases it has not been difficult to find sites which are suitable both from
a transmission and a construction standpoint. Of the 34 type K
carrier repeater stations which have been built, 20 were constructed
at the sites originally selected from a transmission standpoint. In
most of the other cases the final sites were within a short distance of
the originally selected locations. In a few cases, however, where ideal
sites fell in populous centers or comparatively inaccessible wilds, it
was necessary to take unusual steps.

In one case the site which had been selected from a transmission
standpoint fell at a location where the two cables which had been
selected followed different conduit runs and were separated by more

APPLYING CARRIER TELEPHONE SYSTEMS

559

than 2| miles. Two lateral cables, each of that length, would have
been required in order to make use of this site. Moving the location
back to the point where the cables came together would have resulted
in an excessively long carrier repeater section and would have located
the station within the business section of Wilmington, Del. The
problem was to find a compromise site between these two points where
the lengths of lateral cables would not be excessive and the repeater
section could be kept within desirable limits. A tide water stream
between these two points complicated the problem.

Nine sites were inspected and four of them studied in detail. Flood
and fire hazards, as well as high prices of real estate, were added to
the other factors governing the choice. None of the locations was
entirely desirable, but a compromise choice was finally made of a
location which resulted in the longest repeater spacing in the New York-
Charlotte project, but the lengths of the lateral cables were reduced
to between eleven and twelve hundred feet.

Table 4 shows the theoretical spacings which, considering the fixed

TABLE 4

Comparison of the Originally Specified Carrier Repeater Spacings and

AcTU.\L Spacings on the New York-Charlotte and

Detroit-South Bend Cable Routes

Project

No. of

Re-
peater
Sections

Theoretically Best Spacings

Actual Spacings Used

Min.

Ave.

Max.

Min.

Ave.

Max.

New York-Charlotte. . .
Detroit-South Bend . . .

38
13

13.5
14.9

16.5
16.1

18.8
17.6

13.2
13.6

16.5
16.1

20.2
18.4

location of existing repeater points, were selected as best from a trans-
mission standpoint, and the actual spacings which it was found neces-
sary to use. The theoretically best spacings for the two routes differed
because of the difference in spacings of the existing voice frequency
repeater points of which use has been made as carrier repeater points-
Figure 5 shows the repeater office locations as they are distributed
on the New York-Charlotte project. The various types of repeater
offices shown are discussed later in this paper.

Direction of Transmission
The circuits used for the two directions of transmission of type K
carrier systems operate in separate cables on the projects so far com-
pleted and, for crosstalk reasons, these two directions of transmission
have been transposed between the two cables at each carrier repeater
point.2 The location of branch cables and taps to open wire have an

560

BELL SYSTEM TECHNICAL JOURNAL

Fig. 5 — Route of New York-Charlotte cable carrier development.

important bearing on the selection of the direction of transmission,
since it is desirable to assign directions of transmission which will
result in a minimum number of taps to open wire and branch cables
occurring near carrier repeater inputs. Where the lengths of under-

APPLYING CARRIER TELEPHONE SYSTEMS 561

ground construction adjacent to a repeater station differ on the two
cables, it is preferable to have pairs in the cable having the longer
section of underground connected to repeater inputs. With these and
other factors in mind, tentative directions of transmission were assigned
to the cable conductors and computations of expected noise currents
made and checked with computations which assumed the directions
reversed. The total overall noise currents computed to be 1.25 db
better when assuming the directions of transmission finally selected
for the New York-Charlotte project than when assuming these direc-
tions reversed. This was largely due to the fact that south of Peters-
burg, where but one cable had existed, a small cable was added to
permit carrier operation. Pairs in this cable, because of its small size,
are more susceptible to static induction directly into the cable than
pairs in larger cables. The effect, therefore, of the greater contribu-
tion to overall noise currents, which this small cable tends to cause,
was reduced by selecting the directions of transmission so as to take
advantage of the increased shielding resulting from underground con-
struction adjacent to repeaters. Tables 5 and 6 show the final noise
level computations for the 1000-cycle point of channel 12 (57 kc on
the line) of a New York-Charlotte system. It will be noted that the
longer repeater sections contribute a great deal of noise as compared
to average or shorter sections. Noise measurements which have been
made indicate that noise conditions compare favorably with those
which it was calculated might be expected.

Non-Regulating Repeater Points

Examination of the carrier repeater sections on the New York-
Charlotte route showed seven to be unusually short and involving all
underground cable construction. The usual plan would have been to
provide flat gain regulation at each carrier repeater point, but since
these seven sections averaged but 14.8 miles in length and the theoreti-
cal transmission variation might be but ± 1.42 db, it was obvious
that the regulators having a normal range of ± 7.15 db would be
required to operate only over a small part of their range. However,
the real limitation is not the regulating mechanism but the lower levels
to which the line currents without regulated gain would drop during
periods of high cable temperature with corresponding impairments in
noise levels. In this layout, omission of regulation at one station
increases the noise level about the same as lengthening the following
repeater section about ^ of a mile. Omission of two successive regu-
lators is approximately equivalent to increasing the second repeater
section about % of a mile and the third about 1| miles. Repeater

562

BELL SYSTEM TECHNICAL JOURNAL

TABLE 5
New York-Charlotte Type K Carrier Noise Computations

Estimated
57 kc

Section Cable i-pss Noise

Level 2
at Rept.
Output

Miles

57 kc

Cable

Loss
Max.

U.G.

Aerial

Total

Temp.i

E

15.45

—

15.45

58.09

F

14.45

—

14.45

54.33

E

16.59

—

16.59

62.38

G

13.22

—

13.22

49.71

E

13.92

—

13.92

52.34

G

14.79

—

14.79

55.61

D

15.14

—

15.14

56.93

F

13.49

—

13.49

50.72

D

19.70

—

19.70

74.07

F

17.28

. — .

17.28

64.97

D

16.89

16.89

63.51

F

16.91

_

16.91

63.58

D

18.61

18.61

69.97

E

18.95

—

18.95

71.25

A

7.31

11.28

18.59

71.93

B

^

18.45

18.45

72.69

A

.10

16.54

16.64

65.55

B

.11

18.23

18.34

72.24

A

—

18.26

18.26

71.94

B

7.64

10.99

18.63

72.03

A

9.82

7.09

16.91

64.85

B

10.13

5.85

15.98

61.14

A

.08

15.43

15.51

61.09

B

.11

16.87

16.98

66.88

A

—

15.23

15.23

60.01

B

.06

14.28

14.34

56.49

A

—

16.36

16.36

64.46

B

—

16.68

16.68

65.72

A

.12

17.62

17.74

69.87

B

.05

18.05

18.10

71.31

A

—

17.79

17.79

70.09

B

2.38

16.25

18.63

72.98

A

5.64

12.18

17.82

69.20

B

—

16.41

16.41

64.66

A

1.85

14.84

16.69

65.43

B

1.82

11.92

13.74

53.80

A

—

14.47

14.47

57.01

B

3.78

9.96

13.74
627.42

53.45

New York- New York KS

New York KS- Princeton KN

Princeton KN-Princeton

Princeton-Princeton KS

Princeton KS-Philadelphia KN

Philadelphia KN-Philadelphia

Philadelphia-Philadelphia KS

Philadelphia KS-Elkton KN

Elkton KN-Elkton

Elkton-Elkton KS

Elkton KS-Baltimore KN

Baltimore KN-Baltiniore

Baltimore- Washington KN

Washington KN-Washington

Washington-Washington KS

Washington KS-Fredericksburg KN
Fredericksburg KN-Fredericksburg .
Fredericksburg-Fredericksburg KS .
Fredericksburg KS-Richmond KN .

Richmond KN-Richmond

Richmond-Richmond KS

Richmond KS-McKenney KN

McKenney KN-McKenney

McKenney-McKenney KS

McKenney KS-Norlina KN

Norlina KN-Norlina

Norlina-Norlina KS

Norlina KS-Durham KN

Durham KN-Durham

Durham-Durham KS

Durham KS-Greensboro KN

Greensboro KN-Greensboro

Greensboro-Greensboro KS

Greensboro KS-Salisbury KN

Salisbury KN-Salisbury

Salisbury-Salisbury KS

Salisbury KS-Charlotte KN

Charlotte KN-Charlotte

New York-Charlotte Totals

- 8.91

- 9.71
+ 1.10
-13.29
-10.75

- 2.19
-10.07

- 9.38
-f 8.57

- 2.03

- 3.49

- 3.42
+ 2.97
-f 4.25

5.93
6.69
2.95
6.24
5.94
5.03
1.15
8.54

- 1.51
+ 14.08

- 2.59
+ 3.89
-I- 3.66
+ 13.12
+ 3.87
+ 18.51
+ 4.09
+ 12.18
+ 3.20
+ 12.06

- 2.53
+ 1.2

- 4.09

- 8.35

+ 23.273

1 Attenuation figures used: 3.76 for U.G. at 73° and 3.94 for Aerial at 110°.
^ For top channel, referred to — 9 db switchboard level.
3 Computed on a root-sum-square basis.

sections adjacent to New York and Philadelphia are short and it was
decided, therefore, to omit regulation from the two auxiliary stations
between New York and Princeton, N. J., two between Princeton and
Philadelphia, andfone between Philadelphia and Wilmington, Del.

APPLYING CARRIER TELEPHONE SYSTEMS

563

TABLE 6
Charlotte-New York Type K Carrier Noise Computations

Section

Miles

57 kc

Cable

Loss
Max.
Temp.i

U.G.

Aerial

Total

A

3.78

9.96

13.74

53.45

B

—

14.47

14.47

57.01

A

1.82

11.92

13.74

53.80

B

1.85

14.84

16.69

65.43

A

—

16.41

16.41

64.66

B

5.64

12.18

17.82

69.20

A

1.66

16.97

18.63

73.10

B

—

17.79

17.79

70.09

A

.05

18.05

18.10

71.31

B

.12

17.62

17.74

69.87

A

—

16.68

16.68

65.72

B

—

16.36

16.36

64.46

A

.06

14.28

14.34

56.49

B

— -

15.23

15.23

60.01

A

.11

16.87

16.98

66.88

B

.08

15.43

15.51

61.09

A

6.18

9.81

15.99

61.89

B

16.84

.07

16.91

63.60

A

7.52

11.08

18.60

71.94

B

—

18.26

18.26

71.94

A

.10

18.23

18.33

72.21

B

.10

16.54

16.64

65.55

A

—

18.45

18.45

72.69

B

8.69

9.91

18.60

71.72

D

18.90

—

18.90

71.06

E

18.64

—

18.64

70.09

D

16.89

—

16.89

63.51

F

16.86

• —

16.86

63.39

D

17.33

—

17.33

65.16

F

20.21

—

20.21

75.99

D

13.51

—

13.51

50.80

F

16.00

—

16.00

60.16

E

13.36

—

13.36

50.23

G

13.93

—

13.93

52.38

E

13.49

—

13.49

50.72

F

16.69

—

16.69

62.75

E

14.50

—

14.50

54.52

F

15.38

15.38
627.70

57.88

Estimated
57 kc
Noise
Level 2
at Rept.
Output

Charlotte-Charlotte KN

Charlotte KN-Salisbury KS

Salisbury KS-Salisbury

Salisbury-Salisbury KN

Salisbury KN-Greensboro KS

Greensboro KS-Greensboro

Greensboro-Greensboro KN

Greensboro KN-Durham KS

Durham KS-Durham

Durham-Durham KN

Durham KN-Norlina KS

Norlina KS-Nor!ina

Norlina-Norlina KN

Norlina KN-McKenney KS

McKenney KS-McKenney

McKenney-McKenney KN

McKenney KN-Richmond KS

Richmond KS-Richmond

Richmond-Richmond KN

Richmond KN-Fredericksburg KS. .
Fredericksburg KS-Fredericksburg .
Fredericksburg-Fredericksburg KN .
Fredericksburg KN-Washington KS

Washington KS-Washington

Washington-Washington KN

Washington KN-Baltimore

Baltimore-Baltimore KN

Baltimore KN-Elkton KS

Elkton KS-Elkton

Elkton-Elkton KN

Elkton KN-Philadelphia KS

Philadelphia KS-Philadelphia

Philadelphia-Philadelphia KN

Philadelphia KN-Princeton KS. . . .

Princeton KS- Princeton

Princeton-Princeton KN

Princeton KN-New York KS

New York KS-New York

Charlotte-New York Totals

- 9.15
+ 5.91

- 7.60
+ 14.13
-f 2.06
+ 4.70
+ 7.10
-f 17.29
+ 5.31
+ 17.07
+ 3.12
+ 11.86

- 6.11
8.91

.78
8.49
.71
.60
5.94
5.94
6.11
2.95
6.69
4.72
4.06
3.09
3.49
3.61
1.84
8.99
-12.20

- 1.34
-12.77

- 9.34

- 9.67

- 2.75

- 5.38

- .69

+ 23.463

+
+
+

+
+
+
+
+
+
+
+
+

+

' Attenuation figures used: 3.76 for U.G. at 73° and 3.94 for Aerial at -110'
^ For top channel, referred to — 9 db switchboard level.
3 Computed on a root-sum-square basis.

Figure 6 shows a comparison of the computed levels for maximum
cable temperature conditions in the New York-Philadelphia Cable
under conditions of both regulation and non-regulation. Omitting the
regulation from a carrier repeater office where noise conditions and

564

BELL SYSTEM TECHNICAL JOURNAL

gain requirements are favorable has the advantage of economy in
saving the cost of the regulating apparatus and in an expected saving
in maintenance.

NEW YORK NEW YORK PRINCETON PRINCETON PRINCETON PHILA,DELPHIA PHILADELPHIA
I KS KN . KS KN

U— 15.45 »+• — 14.45 — »+• — 16.59 >U — 13.22 »-»■« — 13.92 »+•— 14.79-

J f^lL-ES J J J MILES

—^. >. ►^ R ►^ > 1>-

10

5

0

-5

-10

-15

-20

-25

-30

-35

-40

-45

\

\

\

i

i

\

\

\\
\\

\\

\

\

\\
\\

\

\

\

\

\

\\

\\

\

\

\\

\

\
\\

k

\

\

\

A

\

\\

\\

\

\\

\\
\\

\

\\
\\

\

V

w

\\

\

V

\\

\

\

I
\

\

^

\

\

\

\\
\\
\\

\

V

V

— - FULLY
REGULATED

\

\\

Y

NON REGULATEDV
AT TWO POINTS ^

1 1 1

Fig. 6 — Level diagram of New York-Philadelphia section, showing theoretical
maximum effect on 28 kc levels of omitting regulation at the auxiliary repeater
stations.

Noise Suppression Devices

Two types of noise suppression devices were used on voice frequency
circuits to limit noise currents which might enter the cables used for
carrier.^ The first of these is a retardation coil designed to suppress
longitudinal currents but to have a negligible effect on the metallic
currents on the side and phantom circuits. These were installed at
voice frequency repeater points, in all voice quads in cables which
contained carrier pairs connected to carrier repeater inputs. These
coils attenuate longitudinal noise currents at carrier frequencies gen-
erated in the voice repeater office which might enter the cable over
the pairs used for voice circuits and be induced into the carrier pairs.
A total of 3,000 retardation coils was installed along the New York-
Charlotte route for this purpose. The coils are connected into the
cable conductors on the office side of the point at which the carrier
lateral cable is connected to the main cable. These coils were installed
in the office cable vault or manhole. Figure 7-A shows a number of

APPLYING CARRIER TELEPHONE SYSTEMS

565

CQ

03. 0

en •&

566 BELL SYSTEM TECHNICAL JOURNAL

apparatus cases containing these retardation coils installed in the cable
vault at West Unity, Ohio.

In addition to this usage, retardation coils were installed in certain
instances in the conductors of branch cables and open wire taps. In
other branch cables and open wire taps w^here a higher degree of noise
current suppression was required the second noise suppression device
was used.^ This second device is a filter which provides a considerably
greater degree of suppression than the retardation coil. The purpose
of these is to attenuate longitudinal noise currents which might enter
the main cable over the conductors in the branch cable or open wire
tap. A typical installation of filters on aerial cable is shown by
Fig. 7-B. The question as to whether a retardation coil or a filter
was required in each particular case was determined by computations
of expected noise which might be contributed by the conductors
entering the main cable. This was done by considering the makeup
and length of the branch or tap, use to which it was put, and its
location with respect to the nearest carrier repeater input in the cable
to which it was connected. These computations, however, were made
coincidentally with those described earlier in determining the most
desirable directions of transmission.

Five hundred fifty-one retardation coils and 132 filters were installed
in the 26 branch cables and open wire taps along the New York-
Charlotte route, 11 of which connect directly to open wire. On the
Detroit-South Bend project, 12 branch cables and open wire taps were
equipped with 44 retardation coils and 124 filters. Nine of the 12 are
taps connected directly to open wire.

As a further step toward prevention of noise currents in the carrier
pairs, the shielding furnished by the lead sheaths of the cables has been
kept effective by maintaining continuous the electrical path through
these sheaths by means of shunts consisting of large condensers placed
across each insulating joint.'*

Auxiliary Repeater Station Buildings

Small buildings to house the auxiliary repeaters have been erected
at the sites determined to be acceptable from transmission and con-
struction standpoints. These structures are of fire resistive construc-
tion with concrete foundations, brick walls, and slate roofs. Since
these buildings house equipment which is expected to operate for long
periods of time without attention, no openings have been provided in
the walls except for an entrance door and ventilating units. Thermal
insulation has been provided over the ceiling. Two sizes of buildings
have been used. The larger one which is 24 ft. X 24 ft., inside dimen-

APPLYING CARRIER TELEPHONE SYSTEMS 567

sions, is used on routes where an ultimate of 100 systems is expected,
while the smaller one, 21 ft. X 24 ft., is used on a route to be developed
for a maximum of 60 systems. The ceiling height in these buildings is
sufficient to care for 11 '-6" relay racks. Eleven of the small buildings
and 22 of the larger ones have been built on the carrier projects so far
completed.

The architectural treatment of the exterior of these buildings varies
somewhat, depending upon the location of the site selected and the
character of the buildings in the immediate neighborhood. The pres-
ent designs may be classified as three types; i.e., plain brick with no
trim, plain brick with limestone trim, and plain brick with limestone
trim and artificial windows. In the latter type the window arrange-
ments are obtained by the use of a wooden frame and sash with rough
wire glass, backed by the interior brick wall. The brick portion behind
the window is painted buff on the upper half facing the window, and
black on the lower half, to simulate a true window with the shade half
drawn. Typical examples of these types may be seen in Fig. 8. The
type of building selected for each station depended upon the locality.

Arrangements have been provided in these buildings for auto-
matically controlling the heating and ventilation by the use of thermo-
statically controlled electric heater and fan units. Although experience
was generally lacking on the heating and ventilating problem for these
stations, tentative requirements were set up. A minimum tempera-
ture of 40° F. has been considered satisfactory for the operation of the
equipment in these stations and the thermostat has been set to turn
on the heater unit if the inside temperature drops below that point.

Ventilating equipment consisting of intake and exhaust ventilators,
exhaust fan and control equipment has been provided so that advantage
may be taken of the effect of cooler outside air when the temperature
inside the buildings rises to about 90° F. Consideration was given to
the direction of the prevailing winds in locating these units in the
building walls. The room side of the intake ventilator unit is equipped
with a spun glass filter. These ventilators are equipped with rigid
and movable louvers. The movable louvers are actuated by solenoids
which are connected to the exhaust fan control which functions by
means of a thermostat and a differential temperature control. The
latter includes outside and inside temperature compensating elements.
The thermostat is set at 90° which, with the differential feature of the
control, will cause the louvers to open and the exhaust fan to start
only when the inside temperature is more than 10° above that prevail-
ing outside the building. When the inside temperature has been re-
duced to within 10° of that outside, the control circuit is opened to shut
off the fan and close the louvers.

568

BELL SYSTEM TECHNICAL JOURNAL

Fig. 8 — Auxiliary repeater station buildings: A, without trim; B, with limestone
trim; C, with limestone trim and artificial windows.

APPLYING CARRIER TELEPHONE SYSTEMS 569

Terminal Office Equipment

The various major items of equipment which are provided at a
terminal office are shown schematically by Fig. 9. Two bays of
sealed test terminals — one input and one output — are associated with
the pair of cables which bring the carrier pairs into the office and are
equipped initially to terminate 40 pairs. The input high-frequency
jacks are mounted in high-frequency patching bays adjacent to the in-
put sealed test terminal bays and the output jacks in bays adjacent to
the output sealed test terminal bays. At points where more than 50
terminals are expected to be required at some future date plans have
been made for one input and two output high-frequency patching bays.
The input and output high-frequency patching and sealed test terminal
bays for two cable routes, together with a high-frequency transmission
measuring bay, are grouped so as to form a desirable arrangement for
testing and maintenance purposes. This group of bays serves some-
what the same purpose as a primary testboard on voice frequency
facilities. The arrangement of these bays as installed at New York is
shown in Figs. 10- A and 10-B.

A portable transmission measuring set has been provided and may be
placed on a writing shelf mounted in the high-frequency transmission
measuring bay. This set may be connected to the various circuits by
means of patching cords.

Line and twist amplifiers with associated flat and twist gain master
controller equipment and crosstalk balancing bays also are installed at
each terminal office. The arrangement of the amplifier equipment and
controllers as installed at New York is shown in Fig. 11.

The terminal equipment for one system consists of six channel modem
(modulator plus demodulator) panels, each of which mounts the send-
ing and receiving apparatus for two channels.' Channel modem
equipment for three systems is mounted in two adjacent bays with the
first two systems occupying separate bays. One bay of carrier supply
equipment for each ten systems provides both regular and emergency
units for generating carrier frequencies for the operation of the channel
and group modem units and pilot channel equipment. The group
modem units, one of which is required for each system, are mounted
nine in one bay. Figures 12 and 13, respectively, show the method in
which these bays are installed at New York.

The d-c power supply for the carrier equipment at terminal and main
repeater offices is obtained from the existing 24-volt and 130-volt office
power plants. Two sets of main distributing leads have been provided
for each filament and plate power supply. Odd numbered circuits are

570

BELL SYSTEM TECHNICAL JOURNAL

CHANNEL MODEM EQUIPMENT

GROUP MODEM

BRACKETS J k
1 TO 5 IN < .-- ,
FIG. 14 AS C
REQUIRED l."

ODD EVEN

HYBRID
COILS
AND NET-
WORKS

120-KC
BUS BAR

REGULAR

CARRIER

GENERATOR

AUTO.
TRANS.
CIRCUIT

EMER-
GENCY

SPARE

CARRIER

GENERATOR

120-KC

AMPLIFIERS

AND FILTERS

Fig. 9 — Schematic showing the order of equipment at a terminal office.

connected to one set of leads for each type of power, and even circuits
to another set.

The voice frequency sides of the channel modem units have been
terminated in jacks which are located in a four-wire jack field mounted
in a voice frequency patching bay. From this point the four-wire
jack circuits are connected to the distributing frame for interconnection
on a four-wire basis with other channel equipment, voice frequency
repeater equipment, or terminating apparatus, as shown schematically
in Fig. 14. Voice frequency patching bays shown in Fig. 10-B may be
considered the equivalent of a secondary testboard.

Voice frequency transmission measuring apparatus has been
mounted with the voice frequency patching bays.

Main Repeater Office Eq)uipment
There are two types of installations at main repeater offices: {a)
flat gain regulation only, and {h) both flat and twist gain regulation

APPLYING CARRIER TELEPHONE SYSTEMS

571

OUTPUT SEALED TEST-
TERMINAL BAYS

TO
PROTECTORS

X X

LINE
JACKS
iX X

BY- PASS
SETS

-(iffl:

•\ TO TOLL
.(CABLE A

CARRIER
CIRCUITS VOICE-
FREQUENCY
CIRCUITS

^^

CONTROLLERS

FLAT GAIN

1 HIGH- I r
I FREQ. I
I JACKS I

AMPLIFIER EQUIPMENT

I

I I

AMPLI-
FIER

AMPLI-
_FIER_j

USED ONLY FOR
PILOT WIRES

BY- PASS
SETS

' X X

LINE
JACKS

X X

BAL-
ANCING
COILS

CARRIER
CIRCUITS

AMPLIFIER CABLE
DEVIATION DEVIATION '

EQUALIZERS

INPUT SEALED TEST-
TERMINAL BAYS

I

VOICE-
FREQUENCY
CIRCUITS

FROM'

TOLL

CABLE B

TO
PROTECTORS

Fig. 9 — -Continued from page 570.

In general, these offices are attended regularly by maintenance forces.
They serve in some cases as control or supervisory points for the
auxiliary repeater stations. Since the installations at main stations
have been made in existing voice frequency repeater offices, the avail-
able power plant is used to furnish filament and plate current for the
amplifier equipment.

The input and output sealed test terminal bays with a high-fre-
quency transmission measuring bay have been installed adjacent to
each other to form a five-bay unit for testing and patching purposes.

Line amplifiers for each direction of transmission have been grouped
together in adjacent relay rack bays. Each bay has a capacity of 20
amplifiers, except the first, in which is mounted the test amplifier as-
sociated with the high-frequency measuring system and 19 line ampli-
fiers. Associated with the line amplifiers are the flat gain master
controllers and power supply and cable balancing equipment. A
schematic arrangement of circuits in a flat gain repeater office is
shown in Fig. 15.

Repeater offices giving both flat and twist gain regulation have been

572

BELL SYSTEM TECHNICAL JOURNAL

fe

^

APPLYING CARRIER TELEPHONE SYSTEMS

573

Fig. 11 — Line and twist amplifier and controller equipment bays as installed at

New York.

574

BELL SYSTEM TECHNICAL JOURNAL

Fig. 12 — Arrangement of carrier supply and channel modem equipment at New

York, N. Y.

provided at intervals of about 100 miles. They differ from the flat
gain regulating repeater office chiefly in that they include twist cor-
rection regulation ^ and its associated amplifiers. Provision was made
at each twist gain regulating office for the installation of amplifier and
cable deviation equalizers. The equalizers were actually connected to
the circuits, however, only at such points as were indicated by lineup
tests. To permit lineup without delay, spare equalizers were available
at points where computations had indicated they might be needed.
Amplifier deviation equalizers were required at South Bend, Toledo,
Philadelphia, Richmond, and Greensboro on completed projects. It
was not found necessary to install cable deviation equalizers at any
point. Equalizer, flat gain, and twist gain amplifiers were installed in
three-bay groups with the equalizer equipment occupying the center
bay, and controller equipment in the fourth bay, similar to the ar-

APPLYING CARRIER TELEPHONE SYSTEMS

•1

575

Fig. 13 — Bay arrangement for group modem equipment as installed at New York.

576

BELL SYSTEM TECHNICAL JOURNAL

4-WIRE VOICE-
FREQUENCY
PATCH BAY
I

xl

PADS FOR
BUILT-UP -
CONNECTIONS

4-WIRE

TERMINATING

CIRCUIT

TO TOLL
SWITCH-
BOARD

TOLL

LINE
RELAY
CIRCUIT

SWITCH-
ING PAD

TO 2-WIRE LINE OR
TOLL SWITCHBOARD

PRIMARY
TEST BOARD

4-WIRE
LINE

D-C COM-
POSITE
SET

RE-
PEATING
COILS

RE-
PEATER

(2-WIRE

TERMINATION)

TYPE C

CARRIER

TELEPHONE

CHANNELS

CARRIER
TERMI-
NATING
CIRCUIT

4-WIRE

TERMINATING

CIRCUIT

-X ^

■*>

C4-WIRE
TERMINATION)

h-X— X-

r-x-

VOICE-
FREQUENCY
CARRIER
TELEGRAPH
TERMINAL

RE-
PEATER

1 PAD \-

1 PAD |-

■^ K-

TYPE J OR K
CARRIER CHANNEL
^ ^

■| pad[-><
-| pad|-k

-K — H-

H

)C X

X X

fT

X X

X X

X X

-X — X-

n

Fig. 14 — Schematic showing the various circuit arrangements on the office side voice

frequency patching bay.

APPLYING CARRIER TELEPHONE SYSTEMS

577

578 BELL SYSTEM TECHNICAL JOURNAL

rangement shown in Fig. 11. Each group of three bays mounts equip-
ment for one direction of transmission for 17 systems. A schematic
arrangement of equipment in a twist and flat gain regulating repeater
office is shown in Fig. 16.

Auxiliary Repeater Station Equipment

Each auxiliary repeater station houses crosstalk balancing equip-
ment, sealed test terminals, line amplifiers, pilot wire regulators, and
a power plant. A typical floor plan arrangement of the equipment re-
quired in one of these stations for a maximum of 100 systems is shown
in Fig. 17. The equipment arrangement for a 60-system route is
practically the same, except that provision has been made for a smaller
number of amplifiers and crosstalk balancing bays. A schematic ar-
rangement of equipment circuits is shown in Fig. 15.

Four bays of sealed test terminals have been installed, one input and
one output for each direction of transmission. Initially each unit
contains carrier line and equipment jacks for testing or patching pur-
poses for 40 carrier and eight miscellaneous circuits. In addition, mis-
cellaneous auxiliary equipment is mounted in these bays.

Twenty-one amplifier panels for one direction of transmission may be
mounted in a bay. Two bays are required for the flat gain master
controllers and the associated controller power supply equipment.
Figure 18-B shows amplifier, controller, and testing bays.

High-frequency testing apparatus consisting of a variable test oscil-
lator and a portable transmission measuring set mounted in a mobile
relay rack bay has been provided at each auxiliary station. This unit
may be connected to the jacks in the sealed test terminals as required
by means of patch cords.

Since auxiliary stations are designed to operate for considerable
periods of time without attention, the power plant is of the automatic
type.^ It consists of a 70-cell, 152-volt storage battery which is con-
tinuously floated across regulated tube rectifiers fed from a commercial
power supply. Figure 18-A shows a typical installation. Two recti-
fiers are provided initially, one which floats the battery, and the other
which is connected automatically into the charging circuit in case of
failure of the first unit or to increase the charging rate after a prolonged
failure of the outside power. Arrangements are available in the power
service cabinet to terminate leads from a portable emergency engine
driven alternator set which may be set up outside the building. It
is expected that the battery installed initially will be of sufficient size
to provide a minimum of 24 hours reserve throughout its life, taking

APPLYING CARRIER TELEPHONE SYSTEMS

579

,.

£

Q. UJ

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- — — X 111

580

BELL SYSTEM TECHNICAL JOURNAL

\ ^ VENTILATION LOUVER

POWER SERVICE (NEAR FLOOR)

„ CABINET

1-2
POWER BAYS ^

L-,---V!l li

Z 1

ULTIMATE BATTERY

(24-HOUR RESERVE FOR

100 REPEATERS)

.WRITING SHELF

EAST-WEST EQUIPMENT

I (OUT)

2(lN)

\\\

8

DC

DC

3'-2"

fzi] /°

EAST-WEST FLAT-GAIN FUSE 1-21 22-42 43-63 BYPASS 64-64 ...L ,

CON- PANELS ^ ' AMPLI- cVcoc

AMPLIFIERS FIER '^'^^^

'^ "^ 85-101
WEST-EAST 3 4 5 6 7 8 9 i

--.I II II 1 V

_j| It Ji J 4

TROLLERS
3
C

1-21 22-42 43-63 BY PASS 64-84

V ' AMPLI-

AMPLIFIERS FIER

1 I'

EXHAUST FAN
NEAR CEILING

Fig. 17 — Floor plan arrangement of equipment for 100 systems at an auxiliary

repeater station.

into account the estimated growth of carrier ampHfier equipment re-
quirements for that period.

The entire voltage of the battery is used to furnish plate supply for
the amplifier tubes. The 70-cell battery is arranged in seven groups
of 10 cells each and taps are taken from each group to supply current
for the heaters of the tubes of each amplifier. To prevent an uneven
drain, amplifiers are connected across the battery in multiples of seven.
In case the number of amplifiers installed is not an even multiple of
seven, dummy load resistances are connected as required, in lieu of
amplifiers to fill out the unequipped multiple.

The controller power supply bay contains apparatus for the 140-volt
d-c pilot wire bridge supply and 55-volt, 60-cycle a-c supply. An
emergency rotary converter, which automatically provides 110-volt,
60-cycle a-c supply during outside power failure, and operates inter-
mittently from the battery, also is mounted in this bay.

APPLYING CARRIER TELEPHONE SYSTEMS

581

c
a

a" 2
o ^

s'i

c
o

582 BELL SYSTEM TECHNICAL JOURNAL

Cabling Problems and Floor Plan Layouts

The floor plan arrangements for type K carrier equipment have been
controlled to a considerable extent by transmission requirements, with
consideration also being given to satisfactory operating and mainten-
ance layouts both for the initial installation and for the future. The
first consideration of any space which is to be used for carrier equip-
ment is that the various units of equipment can be so located, with
respect to each other, that the established maximum wiring lengths,
as determined by transmission, operating, and economic requirements,
will not be exceeded. For example, the length of shielded pair cable
between the jacks in the input sealed test terminal bay and the input
side of the line amplifier has been limited to about 50 feet and the
potentiometer lead between the voice frequency patching bay and the
channel modem units has been kept short in order not to limit the ad-
justment range of the potentiometer and a limit of 150 feet has been
set. These limits were set in the design of the type K systems. Two
types of cabling were installed in the transmission part of the carrier
circuit; i.e., standard lead covered cable and shielded pair cable.

In cabling the carrier equipment the input leads were not run on the
same cable racks with voice frequency cables. Due to the difference in
transmission level between cabling connected to the input sides of
carrier amplifiers and that connected to the output sides, these two
groups of cabling have been segregated by running them over separate
cable racks. The input leads were spaced not closer than two feet to
any leads carrying interrupted direct current or power supply leads
which might possibly carry high-frequency noise currents. Output
leads were run on the same cable racks with voice frequency cabling
where necessary, but were kept six or more inches away from possible
disturbing leads such as those just mentioned. Cabling from the
voice frequency side of the channel modem equipment was installed
without greater precautions than are used when installing other voice
frequency cabling. Crosstalk balancing bays were installed in any
convenient location without special limitations in the lengths of lead
covered cables between these and the input sealed test terminal bays.

All cable racks carrying the rubber covered shielded cables from the
amplifier and group modem bays to the sealed test terminal and high-
frequency patching bays were arranged so that these leads were run
loosely and without sewing. This arrangement provides a ready
means for switching cables for circuit layout purposes, particularly at
terminal offices or at junctions of carrier cables.

In existing offices the high-frequency jack and testing equipment has
been located as close as practicable to the existing toll testboard posi-

APPLYING CARRIER TELEPHONE SYSTEMS 583

tions. Separate testboard lines have been established in several offices
opening off, or convenient to, the main operating aisle in front of the
toll testboards. The voice frequency patching jack bays at carrier
terminals have been located, where practicable, near the secondary toll
testboard equipment. These arrangements have been made in order
to facilitate operating and maintenance, particularly during light load
periods when a small force is on duty.

The amplifiers and group modems have been closely associated with
the high-frequency patching bays and sealed test terminals in order to
limit cabling lengths. Channel modems and carrier supply have been
located convenient to the other equipment but within wiring limitations
to the voice frequency patching bays.

The adequacy of all floor plan layouts, in providing for ultimate re-
quirements, particularly at large terminal offices, was studied. This
problem was given special consideration where it is expected that
routes in addition to the initial one may be developed later for carrier
operation. For example; at New York it was necessary to plan for the
development of K carrier and other broad band facilities on four
separate routes requiring a considerable amount of space for the
necessary terminal equipment. The installation of carrier equipment
at this office, therefore, has been made in space separate from the exist-
ing voice equipment. A floor plan arrangement of the equipment lay-
out at New York is shown in Fig. 19.

Order Wires and Alarm Circuits

One or more auxiliary stations have been associated with an ad-
jacent main or terminal office for maintenance control. Interoffice
trunk and alarm equipment provide talking and signaling facilities
between each auxiliary and main repeater station over a loaded cable
pair. The various alarm signals are terminated in lamps which are
mounted in the sealed test terminal bay at the controlling main office.
These alarms are arranged to indicate such happenings as fire, open
door, high-low battery voltage, main discharge fuse operation, a-c
power failures, etc. When an alarm signal is received at the main
station, it is rechecked and upon its reappearance an attendant may be
dispatched at once or later to the auxiliary station involved, depending
upon whether the signal is of major or minor importance.

The auxiliary stations are not always controlled by the nearest at-
tended station. For example, in several cases it has been thought
better to have them controlled by a station located in a small town
rather than a city, because in cases of necessity an attendant should be
able to drive to the auxiliary station in less time than required to drive

584

BELL SYSTEM TECHNICAL JOURNAL

r-^^l

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APPLYING CARRIER TELEPHONE SYSTEMS 585

through a city area. In other cases certain main stations are not
manned 24 hours per day and control and alarm circuits have not been
terminated at such points. In one case a main repeater station has
terminated in it the control leads from eight auxiliary stations. Four
of these are connected through the partially attended main stations on
either side.

Completion Tests and Overall System Adjustments

The usual completion tests were made on each unit of equipment
after it was installed and on each cable pair between repeater stations
after it was unloaded, in order to insure readiness of each item to be
connected to form the overall carrier system. The gains of the re-
peaters were given a final adjustment by connecting each repeater
input to the cable pair with which it was installed to work, then
sending a predetermined amount of power at 28 kc into the cable pair
at the adjacent office and adjusting the gain of the repeater until it
delivered the desired output level. The flat gain master regulator was
adjusted with respect to its pilot wire so that it would adjust the gain
of the amplifier to maintain the desired output level at 28 kc at all
cable temperatures.

The repeater sections beginning at one end of each twist regulating
section were measured progressively at the output of each repeater.
In each case transmission was checked at ten frequencies throughout
the range from 12 to 60 kc. In this way a check was obtained to deter-
mine whether proper equalization was being provided at each line
amplifier. It was necessary in some cases to change the type of
equalizer provided because the transmission characteristics of specific
cable pairs differed from the average which had been assumed in
providing equalizers. Measurements were also made on the overall
twist regulating section and transmission checked at ten frequencies
throughout the 12 to 60 kc range, since the output of a perfectly cor-
rected twist section would be the same at all frequencies within this
band.

Overall measurements similar to these were made on the high-fre-
quency line between terminal points and Fig. 20 shows the results for
typical New York-Charlotte and New York- Washington systems.
The most desirable characteristic would be a straight line and it will
be noted that this curve differs materially from such an ideal. This
difference is due to inadequate compensation by means of equalizers
for small deviations from linearity in the individual line amplifiers.
This lack of linearity in the overall high-frequency line has not ma-
terially affected the systems being operated at present but might be-

586

BELL SYSTEM TECHNICAL JOURNAL

- — ■

y

""""-^

^^

■

A

^'

_§--"'

15 20 25 30 35 40 45 50

FREQUENCY IN KILOCYCLES PER SECOND

55

Fig. 20 — Typical overall transmission frequency characteristic of high frequency line
between New York and Charlotte, N. C. (B), and New York-Washington (A).

come objectionable on future long systems and it is planned to improve
this characteristic by means of different equalizers.

The overall transmission frequency characteristic of a channel on a
New York-Charlotte type K system is shown by Fig. 21. Measure-

1

\

1

I

\

- EAST-WEST
•-WEST- EAST

\

1

/

1

/

/

\

^__

^::^

=<.

-/

— \

■^ '

0.2 0.4 0.6 0.6

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
FREQUENCY IN KILOCYCLES PER SECOND

2.8 3.0 3.2 3.4 3.6

Fig. 21 — Overall transmission frequency characteristic of a type K carrier channel
between New York and Charlotte, N. C, as measured between two-wire voice
frequency lines.

ments for this characteristic were made between the two-wire sides of
hybrid coils connected to the two directions of carrier transmission of
the channel concerned.

Use of Initial Systems

Telephone message circuits are being operated over most of the type
K channels now available for use. In most cases the channels are
used as parts of circuits which are longer than the carrier systems. For
example, most of the 60 channels between New York and Charlotte,
N. C, are used for circuits between New York and southern cities
beyond Charlotte. Some of these circuits are obtained by connecting
type K carrier channels at Charlotte to channels of type J open wire
carrier systems which operate between Charlotte and West Palm Beach,
Fla. Of the 204 channels available for use, only 21 are used as all

APPLYING CARRIER TELEPHONE SYSTEMS 587

carrier message circuits between the system terminals. This is not
necessarily typical of what the usage of type K channels will be, but is
brought about by their relatively limited application to date and
demonstrates the flexibility of the type K carrier circuit in fitting in
with the other types of circuit facilities.

Conclusions*

Although experience with type K systems in service is rather limited,
they are providing circuits of excellent quality and performance. The
band width of the individual channels slightly exceeds the original
estimates. Such instabilities of transmission as have been experienced
have, in most cases, been corrected before service was interrupted and
have been caused largely by non-recurring troubles inherent to most
installations of new equipment. In brief, the operating experience
with type K cable carrier systems confirms the view that they are
expected to become an important means of providing additional long
distance telephone circuits over cable facilities.

References

1. C. W. Green and E. I. Green, "A Carrier Telephone System for Toll Cables,"

Bell System Technical Journal, Vol. 17, No. 1, January, 1938.

2. M. A. Weaver, R. S. Tucker and P. S. Darnell, "Crosstalk and Noise Features

of Cable Carrier Telephone System," Bell System Technical Journal, Vol. 17,
No. 1, January, 1938.

3. R. W. Chesnut, L. M. Ilgenfritz and A. Kenner, "Cable Carrier Telephone Ter-

minals," Bell System Technical Journal, Vol. 17, No. 1, January, 1938.

4. A. J. Aikens, "Suppressing Noise and Crosstalk on the Type K Carrier System,"

Bell Laboratories Record, Vol. 17, No. 7, March, 1939.

5. F. W. Amberg, "Crosstalk Poling for Cable Carrier System," Bell Laboratories

Record, Vol. 17, No. 6, February, 1939.

6. P. W. Rounds, "A Longitudinal Noise Filter for the Type K Carrier System,"

Bell Laboratories Record, Vol. 17, No. 9, May, 1939.

7. H. H. Spencer, "Power Plant for Broadband Repeater Stations," Bell Labora-

tories Record, Vol. 17, No. 8, April, 1939.

8. L. Hochgraf, "Crosstalk Balancing for the Type K Carrier System," Bell Labora-

tories Record, Vol. 17, No. 6, February, 1939.

The Toronto-Barrie Toll Cable *

By M. J. AYKROYD and D. G. GEIGER

General

"TOURING 1937 a 60-mile toll cable was completed between Toronto
^-^ and Barrie which, in several respects, is unique. Among the
interesting features in the design and construction of this toll cable
were the use of non-quadded exchange cable and loading, a 60-mile
repeater spacing, planning for future carrier operation, and extended
pole spacings.

Prior to the installation of this toll cable, the territory to the north
and northwest of Toronto was served by three open-wire pole lines.
Figure 1 shows these lines and the territory served by them. The
Toronto-Owen Sound lead entering Toronto through a 7-mile entrance
cable was poorly located in towns and on highways, and was paralleled
by power lines which caused considerable noise on the longer circuits.
The Toronto-Collingwood and Toronto-Barrie lines, which were
common for some distance north of Toronto on a 6- and 5-arm lead,
entered Toronto through an 11-mile entrance cable which had been
in place about four years, and contained a number of spare conductors
due to its having been designed for two additional lines.

It was realized that, if open wire were to be continued, circuit growth
would require a new line arranged for carrier operation and a general
rebuilding, rerouting and retransposing for carrier operation of the
existing lines. In addition, carrier operation would necessitate ex-
pensive carrier loading of the entrance cables at Toronto, and the
length of these entrance cables would limit the length of the carrier
circuits for operation without intermediate repeater stations.

Studies Prior to Construction

With large expenditures foreseen for the continuance of open wire,
it was only natural that a study should be made of the possibility of
the use of a toll cable on a basic route and the use of as much as possible
of the existing lines as feeders to the cable. Cost studies on an annual
charge basis for a twenty-year period of open wire with superimposed
3-channel carrier systems, and for a 2-wire 19-gauge quadded cable

* The unusual solution of a difficult toll cable problem which is described in this
paper will be of interest because of its novelty rather than because of any expected
general application of this type of construction to toll cable routes.

588

THE TORONTO-BARRIE TOLL CABLE 589

with H88-50 loading with open wire or cable feeders, depending on the
length and numbers of feeder circuits, indicated the cable plan to be
best. In addition to the indicated money savings of the cable plan
over the period of the cost studies, other indicated advantages in the
toll cable plan were improved service continuity (the southerly section
of the territory under study is one of heavy sleet conditions) and re-
duced noise from power induction.

The quadded cable plan, however, had one disadvantage in that it
required a repeater station approximately 45 miles north of Toronto, in
a territory remote from any town or village with unfavorable living
conditions and subject to isolation during winter snow storms. The
nearest feasible location to the ideal, at Cookstown, involved such an
increase in length of cable and added expenditure that the cost ad-
vantage changed to the open-wire plan. Also, the use of B88-50 load-
ing with a repeater spacing of 50 miles appeared to offer no advantage
in that the additional cost of loading became an important factor.

These difficulties in the use of the standardized type of toll cable
led to a review of the possibility of employing some combination of
conductor and loading which would permit a 60-mile repeater spacing,
thus eliminating any need for an intermediate repeater station between
Toronto and Barrie. If such a cable were to have the same unit at-
tenuation as 19-gauge H88-50 cable, then it must have considerably
improved crosstalk and return loss characteristics. On the other hand,
if a cable could be obtained with crosstalk and return loss characteris-
tics about equal to that of 19H88-50 cable, it must have an attentua-
tion of about % that of 19H88-50 cable.

Of the standard types of cable and loading, 19-gauge non-quadded
exchange cable having a capacity of about 0.083 mf. per mile with B-135
loading appeared to have an attenuation of about the value required
to meet the second of the two requirements noted above. It was
estimated that such a cable would have the following transmission
characteristics :

1000-cycle attenuation at 68° F 0.26 db per mile

Passive singing point at repeater exceeded by 72% of

circuits 25 db

Maximum crosstalk gain 14 db

Overall active balance ^ 6.0 db

Overall circuit loss 8 db (PO-TC) with 4 db pad at PO.

These assumed limits required a 72 per cent return loss of 26 db or
better at the critical frequency which was expected to be about 2600
cycles, and a 1 per cent maximum near-end crosstalk of 74.5 db. Based

1 Computed by summation of the 72 per cent singing points at individual repeaters
with a 5 db end path.

590 BELL SYSTEM TECHNICAL JOURNAL

on these values and limits, and assuming that Toronto would be the
only gain switching center directly involved, a study was made of the
transmission possibilities for each group of circuits that was expected
to be routed through the cable. This study indicated that, provided
the return loss and crosstalk values required of the cable by the as-
sumed singing points and crosstalk gain could be met, all circuits could
be 2-wire between Toronto and Barrie with some transmission margin
and also that this type of cable could be extended at least another
20 miles to Orillia.

A cost study, assuming a 101-pair cable, of this type, indicated that
while, due to the additional loading costs of the closer loading spacings,
the cable costs were very nearly the same as for a quadded 19-gauge
H88-50 cable, the considerably reduced repeater and repeater station
costs made this plan appreciably less costly than any open wire plan.
The elimination of any intermediate repeater station removed the
repeater station difficulties of the quadded cable plans.

As no installation of such a length of this type of cable had been
made, some confirmation of the estimated values for the transmission
study, and particularly of the return loss and crosstalk, was considered
necessary. An 8-mile H-44 loaded 19-gauge exchange cable, which
had just been erected near Toronto, was chosen for study. Near-end
crosstalk measured on 286 combinations of pairs indicated 99 per cent
better than 81 db with an average of 91.7 db which, when modified
for impedance and length differences, indicated 99 per cent better than
72.5 db, and an average of 83.2 db for the proposed cable. While these
values were somewhat poorer than required, the size of the sample and
one or two other factors indicated that the proposed cable could be
erected to meet the crosstalk requirements. However, to obtain as
much crosstalk margin as possible, arrangements were made for the
manufacturer to use 6 lengths of twist, alternating 3 in each layer,
rather than the 4 twists which had previously been used for this type
of cable. It is felt that the excellent crosstalk results obtained as
outlined in more detail later are in large part due to this feature.

Singing measurements on 10 pairs averaged 19.6 db. It was evident
from impedance frequency measurements that these singing points
could be raised to the desired value of 25 db by some modification in
the networks. Accordingly an adjustable precision type network
was developed.

Also, four 1500-foot lengths of the proposed type of cable were
obtained from the manufacturer and tested for mutual capacitance of
pairs and capacitance unbalance between pairs. On statistical analy-
sis, these tests indicated a probable average near-end crosstalk of 79 db

THE TORONTO-BARRIE TOLL CABLE 591

and that for return loss 63 per cent of the circuits would be better than
27.0 db or 72 per cent would be better than 26 db at 2600 cycles,
provided the following features were incorporated :

(a) Manufacture of complete length of cable in one continuous produc-
tion with reasonably careful control of variables.

{b) Capacity equalization splicing at the mid-point of each 3000-foot
loading section.

(c) Reel lengths be assigned as to location on the basis of average reel
length capacity.

On the basis of these preliminary studies, it was decided to proceed
with the cable plan, using the B-135 standard 19-gauge exchange cable.
Figure 2 shows the plant layout finally adopted for the cable and its
feeders.

At the Toronto end it was essential to use pairs in a recently placed
19- and 16-gauge quadded toll entrance cable (mutual capacity .062
mf. per mile) about eleven miles long in order to keep the cost of the
cable to a minimum. This appeared feasible, using the same type
loading coils as in the main cable, if the loading spacings were extended
to provide the same loading section capacity as in the main non-
quadded cable, and if the cable were sufficiently well respliced to break
up the side-to-side (within-quad) adjacencies so that the crosstalk
coupling would be comparable to that obtained in the main (non-
quadded) cable.

Route

It was necessary to select the shortest practicable route passing as
close as possible to the places to be served (see Fig. 2). The route
selected is, for the most part, on a road which lies about midway be-
tween the main highways serving the territory north of Toronto. It
is expected that the location chosen will be reasonably free from
highway changes. Also, for the portion of the route south of Aurora,
an existing open wire pole line was suitable for supporting the cable on
long span construction.

At one point three miles of swamp covered with bush intervened on
the direct route, the avoidance of which meant an increase in expendi-
ture for right-of-way, as well as lengthening of the cable. It was
decided to go straight through the swamp, using swamp fixtures, as
shown in Fig. 3. An interesting sidelight on securing the route through
the swamp was the fact that an original road right-of-way was shown
on the map. On searching the records the surveyor found the original
survey notes made in 1860 and eventually confirmed the location by
finding some old pottery which, according to the records, had been

592

BELL SYSTEM TECHNICAL JOURNAL

■ . ■ ■,'-'\:\ PENETANg'

l#li^la

NOTTAWASAGA. '■}'^

^ \m\

\

'.'.',■ BAY . , ..y

< ORILLIA

SL

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'^^^"^'^^ -H> ^^ ^■''■■': LAKE ■.;;jr^-.'v.-:'^

MINESING \L r Jtl^:]/.; S 1 M C O E .•.^;;.;,;/

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OPEN WIRE

^n k .o-°^^-.-

SCALE IN MILES ^G^S^^-^^^'''^^^^:^f^^^^--'''-'-^^ ■' ' ■

^® #••■■■ LAKE

"^o«?r-.'

Fig. 1 — ■Toll lines before construction of the Toronto-Barrie cable.

THE TORONTO-BARRIE TOLL CABLE

593

SCALE IN MILES
0 5 10 15

I I I I I I ' I I I I I ' I

u^^*^^i—

Fig. 2 — Toronto-Barrie cable.

594

BELL SYSTEM TECHNICAL JOURNAL

Fig. 3 — Swamp construction.

THE TORONTO-BARRIE TOLL CABLE 595

buried at the road intersections. During the late summer and the
autumn, when the swamp had dried out, a 60-foot right-of-way was
cleared. As the soil was still moist and soft, the brush and small trees
were uprooted by a tractor, a method of clearing which proved quick
and economical. The swamp fixtures were placed before the ground
froze, and the cable during the winter.

Pole Line

The cable was erected on the existing pole line between Toronto and
Aurora. The size of the cable erected on 10 M. strand permitted the
removal of every other pole in the old line, with a resultant 185-foot
average spacing. As is shown in Fig. 4, where it was necessary to
change an existing pole, a new pole was placed and fastened to the old
pole by means of stub reinforcing bands, thus eliminating the expense
of transferring the open wire. Upon the release of the open wire by
transfer of circuits to the cable, the wire and old poles were removed.

The new section of pole line was erected on a 200-foot spacing, with
occasional spans up to 250 feet, as shown in Fig. 5. This increased
pole spacing was also expected to reduce ring cutting and bowing.

Construction Details and Tests

At a number of points open wire loops connected directly to the
cable. At these junctions there were installed open space protectors
having a lower breakdown than the cable pairs, and connected between
the open wires and the cable sheath ; also a few spans from the junction,
1000-volt protectors were connected between the open wires and driven
grounds. This arrangement was more economical than the use of
protection cable. The cable has gone through two complete lightning
seasons without any failures or even permanent protector operations
due to lightning.

In so far as manufacturing and storage facilities permitted, the
reel lengths of the cable were assigned to their locations on the basis
of obtaining as close an average loading section capacitance to the
nominal value of 0.085 mfd per mile as was feasible. All reel lengths
for the aerial sections were manufactured 1508 feet long, this length
being sufficient to permit the assignment of a reel at any point in the
line. Particular care was taken in this respect towards the ends of
the cable where departures from the average would have the greatest
effect on the return loss. To ensure proper assignment of reels, a
route map was made up to scale with the manufacturer's reel number
shown in its proper location.

596

BELL SYSTEM TECHNICAL JOURNAL

Fig. 4 — Replacement of old pole with new cu-n~n\^ d pun pole.

THE TORONTO-BARRIE TOLL CABLE

597

^

M
E

598 BELL SYSTEM TECHNICAL JOURNAL

In addition, at the mid splice of each loading section, a test spHce
was made to equaHze the capacity deviations. For these spHces
special Hnen boarding strips were used, each with 40 holes designated
by a capacity ranging from about 15 per cent below to about 15 per
cent above the expected average capacity of 1500 feet of cable. Small
inexpensive capacity meters were used, and each pair was placed in
the hole in the boarding strip corresponding to its capacity. The
pairs were then spliced high to low capacity. This method did not
require special testers, and substantially reduced splicing manhours.

Upon the completion of the splicing in each section, the section
capacity of each pair was measured and recorded, and from this was
determined the root mean square of the capacity deviations from the
average capacity. These deviations combined with the deviation of
the loading section average capacitances, loading coil spacings, and
loading coil inductances, gave an irregularity function of 2 per cent
which is almost identical with that for 19-gauge B88-50 cable. From
this irregularity ^ function a 63 per cent return loss frequency curve
was obtained, which is shown as curve M ' in Fig. 8.

When 15 miles of the cable had been completed south from Barrie, a
100-pair cross-connecting box was temporarily spliced in so that data
could be obtained as a further check on the design estimates.

For crosstalk tests each pair was terminated at the box in a 1700 ohm
resistance, and measurements were made of all pair combinations
(approximately 5000). For these measurements a 15A oscillator and
2A Noise Measuring Sets were used, thereby very materially reducing
the manhours required as compared with the labour that would have
been required had crosstalk measuring sets been used. Analysis of
these tests indicated 99 per cent of combinations better than 76.0 db,
an average of 86.6 db and 99.5 per cent meeting the required 74.5 db
of the preliminary studies.

For attenuation measurements, the pairs were looped back at the
cross-connecting box. In order to obtain a value of the attenuation
at a known temperature, a complete set of measurements was made
at about 6 o'clock in the morning after the resistance of one of the pairs
had been found to have ceased dropping due to temperature change
and the outside temperature at the Barrie office had been very nearly
constant for about one-half hour. During the time the attenuation
measurements were being taken, air temperatures were measured at
four places along the 15-mile length of cable. From these tests the
average 1000 cycle attenuation at 62° F. was found to be 0.26 db per

* See "Irregularities in Loaded Telephone Circuits," George Crisson, Bell System
Technical Journal, October 1925.

THE TORONTO-BARRIE TOLL CABLE

599

mile. In Fig. 6 is shown the mean of the attenuations of three pairs
plotted against frequency. On one pair the measurements were made
at frequencies up to 6500 cycles, from which cut-off was determined to
take place at 4000 cycles. Assuming a 60-mile circuit, the frequency
at which the attenuation is about 10 db greater than 1000 cycles, is
about 3500 cycles.

Before the return loss tests were made, impedance-frequency mea-
surements were taken on two of the balancing networks for each of the
three adjustments provided, and on a representative number of cable
pairs, to determine the optimum network adjustment. The resistance
component of the impedance for one of the networks and one cable

500 600 600 1000 1500 2000

FREQUENCY IN CYCLES PER SECOND

4000 5000

Fig. 6 — Attenuation-frequency characteristic; mean of measurements on three pairs.

pair is shown in Fig. 7 (the two networks were found to be identical).
From these tests the optimum network adjustment was determined to
be that corresponding to a cable capacitance of 0.088 mfd per mile,
which adjustment was then used for the return loss measurements.

As it was desired to obtain the singing point to be expected under
operating conditions, the return loss measurements were made with
the building-out condenser on the return loss set adjusted for optimum
return loss at 2600, 2700 and 2800 cycles. The results of these
measurements are given in Fig. 8 for comparison with the computed
curve '^' mentioned previously. The improvement at the higher
frequencies of the actual over the computed values is due almost
entirely to the method employed in making the tests, and indicates
the advantage to be derived from individual adjustment of each circuit.

600

BELL SYSTEM TECHNICAL JOURNAL

2800
2700
2600
2500
2400
2300
2200
2100
2000
1900
1800
1700

Fig. 7-

i

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1200 1600 2000 2400

FREQUENCY IN CYCLES PER SECOND

-Resistance component of impedance. 30.8 mile circuit, 19 CNB-B135.
Termination, 113 t^^pe network.

2^

DO

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800 1200 1600 2000 2400

FREQUENCY IN CYCLES PER SECOND

Fig. 8 — Return loss — -frequency characteristics. Measured on 61 circuits 30.8
miles long. Building-out condenser adjusted on each circuit for optimum return loss
in the frequency range 2600, 2700 and 2800 cycles. Curve ' A' \s the 63 per cent
return loss computed from attenuation and irregularity function measured on cable.

THE TORONTO-BARRIE TOLL CABLE

601

These return loss measurements were made on pairs looped back at the
cross-connecting box and terminated at Barrie in one of the ne'tworks.

Completion Tests

Upon completion of the cable, further overall tests were made.
Particular attention was paid to those tests made from the Toronto
end, to determine the efifects of the use of the reloaded and respliced
toll entrance cable.

Attenuation measurements at 1000-cycles were found to agree
closely but, due to the effects of the toll entrance cable at Toronto,

3000
2900
2800
2700
2600

q 2500

I

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400 800 1200 1600 2000 2400 2800 3200

FREQUENCY IN CYCLES PER SECOND

Fig. 9 — Impedance measured at Toronto. Termination at Barrie, 113 type
network. Sending-end, half section. Makeup from Toronto, 10.8 miles 16-ga.,
0.062 mf. per mile, 0.0483 mf., 32.8^ per load section; 48.7 miles 19-ga., 0.085 mf.
per mile, 0.0483 mf., 48.9'' per load section.

not to lend themselves to such rigorous analysis as those previously
made.

To show one of the effects of the Toronto toll entrance cable, Figs. 9,
10, and 11, showing the resistance and inductance components of the
impedance measured at Toronto, are included. These indicate that
the important departure from the network characteristic for these
pairs occurs in the inductance component at the lower frequencies.
This departure is probably due to the difference in the loading section

602

BELL SYSTEM TECHNICAL JOURNAL

2800
2700
2600

2500

in

2 2400

O

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lU

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1900

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800 1200 1600 2000 2400

FREQUENCY IN CYCLES PER SECOND

40

c

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0 I

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-40 :

-80 :

-120 [
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-160 «

c

-200 c

-240

Fig. 10 — Impedance measured at Toronto. Termination at Barrie, 113 type
network. Sending-end, half section. Makeup from Toronto, 9.5 miles 19-ga.,
0.062 mf. per mile, 0.0483 mf., 66.8^ per load section; 1.3 miles 16-ga., 0.062 mf. per
mile, 0.0483 mf., 32.8^^ per load section; 48.7 miles 19-ga., 0.085 mf. per mile, 0.0483
mf., 48.9^ per load section.

- 2300

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800 1200 1600 2000 2400

FREQUENCY IN CYClES PER SECOND

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O

z

-160 iS

U

Fig. 11 — Impedance measured at Toronto. Termination at Barrie, 113 type
network. Sending-end, half section. Makeup from Toronto, 9.5 miles 19-ga.,
0.062 mf. per mile, 0.0483 mf., 66.8^ per load section; 50.2 miles 19-ga., 0.085 mf.
per mile, 0.0483 mf., 48.9'^ per load section.

THE TORONTO-BARRIE TOLL CABLE

603

resistance from that of the main cable. (The geographical spacing
on the quadded 0.062 mf. cable was 4100 feet as compared to 3000 feet
on the non-quadded cable.)

Since representative return loss data had already been obtained for
circuits under working conditions (Fig. 8), the completion return loss
measurements were made for the network building-out capacity condi-
tions assumed for the theoretical return loss characteristic (curve 'A,^
Fig. 8). The results thus obtained are shown in Fig. 12 for Barrie
and Fig. 13 for Toronto. In Fig. 12, the theoretical curve is shown for

25

UjO

44
42
40

\,

\\

\

. \

A

38

\N

N

\PER cent:

36

\

^

.63

34

\

72^

N

---

32
30

S,

SJ

V

\

s.

s

<::

V

9>S

V

\

S>

28
26

\

\

X

s.

X

N

^

v^

24

22

X

^f:*^

X

^

"^

■ — -.

----

^■*«

.*_ ^

20
18

CURVE W

^

^

^■^^^

16

1200 1600 2000 2400

FREQUENCY IN CYCLES PER SECOND

2800

3200

Fig. 12 — Return loss — frequency characteristics. Measured from Barrie to
Toronto on 53 pairs; building-out condenser adjusted to theoretical value; curve 'A '
is the 63 per cent return loss computed from attenuation and irregularity function
measured on cable.

comparison, and it is to be noted that the agreement with actual results
is remarkably good. The results obtained at Toronto are better than
those at Barrie, except below 600 cycles, which is the frequency range
of the impedance departures discussed in connection with Figs. 9, 10,
and 11.

Analysis of the near-end crosstalk measurements indicated that at
Barrie 98.8 per cent, and at Toronto 96.3 per cent of the combinations
were equal to or better than the 74.5 db assumed for the preliminary

604

BELL SYSTEM TECHNICAL JOURNAL

calculations. Investigation of the combinations poorer than 74.5 db
indicated that most of the pairs involved could be assigned either to
non-repeatered short circuits or to repeatered short circuits on which
the repeater gains were considerably lower, with consequent lower
crosstalk gains, than on the full length circuits assumed for the limit
of 74.5 db crosstalk. This required the opening of one splice near
Toronto for pair rearrangement.

It was decided to place the cable under permanent gas pressure in
order to control service interruption as far as practicable. As there
was no previous experience available for cables of this size, an investiga-

40

a 38

Q

0-36
§§34

Q ~

^1-32
< D

2g30

'^^

S°28

Qo 26
za:

f

\

s.

\,

s

<:

\j

J

N

:n

/

A

/ '

\

s

^

'ER cent:

K^3

/

\

V

^

N

f/

V

N

'^

^

Y

;5s

v_

s

s

V

N

\

^

^

O ID

-IX

2"- 22

a. >■

DID

u] 20

\

X,

"^

■

^v

^

18

0 400 800 1200 1600 2000 2400 2800 3200
frequency in CYCLES PER SECOND

Fig. 13 — Return loss — frequency characteristics; measured from Toronto to Barrie
on 87 pairs; building-out condenser adjusted to theoretical value.

tion on the job was undertaken to obtain the information necessary for
successful application of the gas pressure installation. Based on the
results obtained, the installation of gas pressure was completed
satisfactorily.

Acknowledgment

The design and installation of this cable represent the coordinated
efforts of many people — members of the organizations of the Bell
Telephone Laboratories Inc., the American Telephone & Telegraph
Company, Northern Electric Company, Western Electric Company
and the Bell Telephone Company of Canada — too many for anyone
to be specifically mentioned. To all of these credit is due and is here
given.

The Computation of the Composite Noise Resulting
from Random Variable Sources

By E. DIETZE and W. D. GOODALE, Jr.

A statistical method is described for computing the meter read-
ing which would be obtained on a sound level meter when used to
measure room noise resulting from the random concurrent opera-
tion of a number of intermittent or continuous noise sources.
The application of the method in the solution of practical problems
is illustrated.

IT is generally recognized that the effects of noise upon the individual
exposed to it are, to a large extent, dependent on the loudness of
the noise. Various tests have been made of the relation between
loudness and the different effects of noise, such as interference with
hearing, reaction on the nervous system, disturbance of rest, reduction
of working efficiency,^ etc.

It has also been recognized that the ear itself, in general, is not a
convenient means for the accurate measurement of loudness, espe-
cially in absolute terms. To overcome this difficulty sound level
meters ^ have been made available for the measurement of acoustic
noises or sound in general.

This paper is concerned with the application of such sound level
meters in the study of noise problems and, in particular, with the
question of determining the contribution of individual noise sources
to the general "composite noise" including noise sources whose out-
puts are random, discontinuous variables. The paper does not con-
cern itself with the attributes of loudness or the effects of noise, but
merely with the computation of a meter reading of the total noise
from available measurements of the noise components. It is recog-
nized, of course, that not only are sound level meter readings an in-
complete description of the effect of a change in noise but that con-
siderable experience is required to appreciate properly the significance
of the decibel unit employed.

Types of Problem
The method described in this paper has been developed to meet a
very practical need experienced in the solution of a large variety of
noise problems. To illustrate, consideration may be given to reducing
1 For reference see Bibliography.

605

606 BELL SYSTEM TECHNICAL JOURNAL

the noise in a room by excluding street noise, using quieter office
equipment or sound absorbing material. Each of these measures will
involve a certain expense and will reduce room noise a certain amount.
Which of these measures will be of greatest benefit and most economi-
cal, i.e., give the greatest noise reduction per dollar expenditure?

In another assumed case, the noise from a certain noise producer,
a piece of machinery, a ventilating system, etc., is known. Will this
apparatus be objectionable in the particular location for which it is
considered?

These and similar questions can be answered by computation while
the project is still in the planning stage, whereas measurements can
be made only after the change has been made, i.e., after the money
for the project has been spent.

The computation method, as these illustrations show, is useful in
specifying apparatus and in planning working or living quarters from
the noise standpoint, in studying the comparative effectiveness of
various noise reducing means, etc. The method has been used in
many practical problems in this way, with satisfactory results. In a
number of applications covering noise from 55 to 75 db sound level
the computed and measured absolute values agreed, on the average
within 1.0 db, and in the worst case within 2.0 db. Computations of
the effect resulting from modifications of the noise sources were checked
within closer limits. A few illustrations of applications are given at
the end of this paper.

The Impulsive Character of Noises
Acoustical noise frequently is composed of sounds from a large
number of sources each of which produces a relatively small propor-
tion of the total noise. Usually these individual noise sources are
discontinuous, consisting of a series of individual impulses. Consider,
for instance, noise from a busy street. The hearers' first impression
is that of a general roar. After a period of listening, however, a
variety of individual sources may be distinguished, such as: The
movement of automobiles, squeaking of brakes, whistles, street car
wheels and bells, hammering and riveting from building operations,
footsteps and conversations of people, etc. Each of these sources has
a distinct time pattern and even those that appear most steady can
frequently be broken up into impulses. For instance, the noise from
an automobile passing down the street is composed of a series of impact
noises which depend on unevenness of the pavement, the driving gears,
number of cylinders in the engine, etc.; the hum of conversation of
people in the street is composed of individual syllabic speech sounds
from the different talkers.

COMPUTATION OF THE COMPOSITE NOISE 607

These impulses occur at a rate which usually is not uniform. Pro-
vided, however, that the general conditions do not change, the rate
approaches uniformity if the time interval considered is sufficiently
large. Some of the impulses from the different sources are super-
imposed upon each other while others fall in the intervals between the
impulses from other sources. As the amount of noise increases, two
general phenomena are observed: First, the loudness of the noise
increases due to the superposition of impulses; secondly, the noise
becomes steadier due to the more complete filling in of relatively silent
intervals (20 db or more below the average).

Definition of Terms

The solution of the problem of computing the total noise from its
component parts requires the definition of a number of terms and a
study of the characteristics of the implied measuring instrument.

Definition 1
Each individual producer of noise is referred to as a ''noise source.''
Illustrations of noise sources are: For the case of room noise — the
conversation of one person, the noise from a typewriter or from a fan
in the room. A number of sources of street noise have been men-
tioned above in illustrating the impulsive character of common noises.

Definition 2

The deflections on the measuring device {sound level meter) produced
by the impulses of a single source are called "source peaks."

A peak is obtained by passing a noise impulse into a sound level
meter. Depending on this measuring device, the characteristics of
a peak differ from those of an impulse. The characteristics of the
sound level meter, therefore, are important in connection with this
computation method. Three of these, the frequency response, the
rule of combination of the frequency components of a complex wave,
and the dynamic characteristic of the indicating meter, are here con-
sidered in detail. These are defined in the "American Tentative
Standards for Sound Level Meters" approved by the American Stand-
ards Association ^ from which the following abstracts are made :

1. The free field frequency response of a sound level meter, provided
only one response is available, shall be the 40 decibel equal
loudness contour modified by differences between random and
normal free field thresholds. Methods are given in the ASA
specification for correcting the reading when the microphone of
the sound level meter responds differently to sound waves
arriving with different angles of incidence.

60S Bell System technical journal

2. The rule of combination is specified so that the power indicated

for a complex wave shall be the sum of the powers which would
be indicated for each of the single frequency components of the
complex wave acting alone.

3. The dynamic characteristic of the indicating instrument is to be

such that the deflection of the indicating instrument for a
constant 1000-cycle sinusoidal input shall be equalled by the
maximum deflection of the indicating instrument for a pulse
of 1000-cycle power which has the same magnitude as the
constant input and a time of duration lying between 0.2 and
0.25 second.

In addition, the method of reading the sound level meter is important.
Where the noise is steady, it is fairly obvious how the meter should
be read. When, however, the noise fluctuates, a certain amount of
judgment is involved in obtaining an average. A satisfactory pro-
cedure in this event is to take a series of instantaneous readings of the
noise peaks at approximately 5-second intervals for a period of time
sufficient to include all noise sources. One or more of these series of
measurements may be made depending on the regularity of occurrence
of the noises of interest. The average and standard deviation of the
fluctuating noise may then be determined from these measurements.

Using simplifying approximations based on these specified charac-
teristics a peak may be defined as follows:

A peak is an impulse integrated by the measuring device. Its frequency
components are weighted in accordance with the loudness weighting incor-
porated in the meter and combined by direct power addition.

It will be seen from the foregoing that the duration of the source
peaks depends on the period of the indicating meter. It has been
found that 0.2 second gives satisfactory correlation between computed
values and actual sound level meter readings, and is in reasonable
agreement with the above specified characteristics. Due to the meter
characteristics, full magnitude is not indicated for impulses shorter
than 0.2 second. Several impulses in the same integration period
appear as a single peak on the meter. Impulses lasting longer may
be regarded as producing a number of consecutive peaks. A steady
noise, for instance, would be considered as consisting of a series of
consecutive peaks of equal magnitude.

On the assumption of discrete integration intervals the average
reading on a single source is the arithmetic mean of the intensities of
the source peaks. Hence for a source, j, producing on the average
mj peaks per minute of intensities, I\., h., /„,., the average reading on
the meter is given by

COMPUTATION OF THE COMPOSITE NOISE 609

On the assumption of discrete integration intervals, furthermore, a
source can produce no more than one peak every 0.2 second. The
maximum number of peaks per minute that can be obtained from a
single source, consequently, is 300.

Definition 3

The noise from all sources as measured by the indicating meter is called
composite noise.

Room noise measured at a given observing position in the room is
an illustration of composite noise. The peaks of a composite noise
are called "composite peaks." Composite peaks have similar charac-
teristics to source peaks as regards duration, frequency weighting, etc.

Statistical Method of Combining Noise Sources

In developing this computation method the principal aim of the
authors has been to provide a practical, working method which is
easy to handle yet is sufficiently reliable for engineering purposes. In
accordance with this objective, a number of simplifying assumptions
have been made. Some of these have been indicated in connection
with the discussion of the assumed characteristics of noise peaks. The
division of the time into discrete 0.2 second intervals is another ap-
proximation which has been made. The statistical treatment, in
addition, includes approximations which are usual in probability
mathematics of this type. Practical experience has shown that these
approximations do not lead to errors which affect the usefulness of the
method.

In the following an expression is derived for computing the average
intensity of the composite noise from the average intensities of the
source peaks and their number. Consideration is first given to the case
when only a single source peak may occur in each 0.2 second interval.
The consideration is then extended to cover the general case when
more than one source peak may occur in a 0.2 second interval.

When only one source peak may occur in a 0.2 second interval, the
average intensity I of the composite noise for these intervals is the
arithmetic mean of the intensities of the source peaks, weighted by
their frequency of occurrence.

610 BELL SYSTEM TECHNICAL JOURNAL

where

I\, I2, ' ' ' Tn = average intensities of the sources 1,2, • ■ • n,
mi, W2, • • • Wn = number of peaks of each source per minute,

n

N = X^ m,- = total number of source peaks per minute.

If several source peaks occur in the same 0.2 second interval, they
will appear as a single composite peak on the meter. On the assump-
tion of discrete 0.2 second intervals, these source peaks coincide.
Their intensities, consequently, add up directly. For instance, if two
source peaks occur during each integration period, the average inten-
sity of the composite noise will be twice the arithmetic mean of the
intensities. Similarly, the average intensity of the composite noise,
when the number of source peaks per 0.2 second interval averages a,
will be

Let M = the total number of composite noise peaks per minute.
The maximum value that M can have is 300, the number of integra-
tion periods per minute. Unless the composite noise is continuous,
however, there will be a certain proportion of time, to, in which no
composite peaks occur. M then can be determined from the relation :

M = (1 - to) 300. (4)

If, on the average, a source peaks per 0.2 second occur, the following

relation holds between the total number of source peaks, N, and the

number of composite peaks:

TV
ilf = - . (4a)

a

Introducing this expression in equation (3) gives

As shown by equation (4), M is a function of to, the proportion of time
in which no composite noise peaks occur. The value for to can be
found, as follows: The proportion of time when source j has a peak is
equal to the probability pj = m,/300, and the proportion of time when
source j has no peak is 5,- = 1 — />,• = 1 — (m,/300) . The proportion
of time, to, when there are no peaks from anysource then is equal to

COMPUTATION OF THE COMPOSITE NOISE 611

the product

h = eig2 • • • qj • ■ ■ Qn-

This expression can be simplified, when the number of sources is
large and none is particularly outstanding, by considering, instead of
the individual sources, an average source having m = N/n peaks.

The average probability then is

P 2An

m N

300 300«
and

N

1 -

300w
which leads to the approximation :

N

/o = g" = 1 -

300«

This expression can be further simplified when the number of sources
is large and p — N/300n is small by using the Poisson exponential
limit:

where

e = 2.718

so that for this case

M = (1 - g--'^/3oo)3oo. (4b)

Measurement of Source Distributions

The method outlined in this paper for computing the composite
noise assumes that information on the noise sources is available.
Such data, therefore, must be obtained before the method can be
applied. Representative measurements for a particular type of noise
source, however, when once obtained, can be used in any future noise
computation involving such a source.

It is necessary to consider carefully the acoustic conditions under
which the sources are measured. For greatest accuracy the ambient
noise level at the point of measurement should be 20 db or more below
the average level of the source. Errors due to reflections can be
minimized by making the measurements at a relatively short distance
from the source out of doors or in a room that contains a large amount
of absorbing material. A distance of 2 feet is a convenient value for
most cases, and will be used as a reference value throughout the rest
of this paper.

612

BELL SYSTEM TECHNICAL JOURNAL

Readings should be obtained on all the noise peaks while the source
is being operated in a normal manner. If the scale of the particular
sound level meter used is limited, it may not be possible to read the
highest as well as the lowest peaks with a single potentiometer setting.
In such cases, the distribution of peaks may be measured in two or
more groups.

Figure 1, Curve A, illustrates the measurement of source peaks in
the laboratory and represents a cumulative distribution of the peaks
from a typewriter as measured at a horizontal distance of about 2 feet
from the type bar guide. The machine was operated by an experienced
typist at an average rate.

When it is not possible to simulate actual conditions of use of a
device sufficiently well in the laboratory, measurements on the source

</i 76

.

•

o

0

•

^

^

r-~.

^^

--

^-o

"^

A

-^

B

•

"*

*

12 5 10 20 30 40 50 60 70 80 90 95 96 99

PER CENT OF PEAKS ABOVE LEVEL SHOWN BY ORDINATE

Fig. 1^ — -Distribution of noise peaks in a typing room.

will have to be taken in the field. This may involve measuring in the
presence of considerable noise from other sources. In general, it is
feasible only to measure source peaks which are above the ambient
noise level. If, however, an appreciable number of peaks is above this
noise level, the rest of the distribution can be estimated and the
average value determined. Statistical methods for doing this have
been worked out for the case of normal distribution curves.^ Experi-
ence has indicated that the distributions of noise in db frequently are
approximately normal, so that these methods are applicable.

Figure 2 is an illustration of a distribution of a group of sources
measured under adverse noise conditions. This curve shows the noise
which came from the metal trays in a cafeteria. The distribution had
to be obtained in the field because it was not feasible to estimate in

COMPUTATION OF THE COMPOSITE NOISE

613

the laboratory how the customers would handle the trays. The points
on the curve indicate the peaks that could be measured in the cafeteria
which had an average composite noise of 66.5 db. It will be seen that
the lowest peaks that could be measured satisfactorily were at 74 db
sound level. The rest of the curve was estimated using the statistical
methods referred to above.

The curves in Figs. 1 and 2 are plotted on "arithmetic probability
paper." On this paper, cumulative normal distributions appear as
straight lines.

"^ so

72

O

i^..

12 5 10 20 30 40 50 60 70 80 90 95 98 99

PER CENT OF PEAKS ABOVE LEVEL SHOWN BY ORDINATE

Fig. 2 — Distribution of noise peaks from metal trays in a cafeteria.

Effect of Room Characteristics
Generally the noise sources are at various locations so that it is
necessary to determine how much the noise from each is reduced
by its distance from the observing point assumed for the computation.
Since it is not the primary concern of this paper to discuss the dis-
tribution and decay of sounds in rooms, only a very simple approxi-
mate method of computing distance losses, based on the classical
theory of the steady-state distribution of sound in a room, is given
here. This method has been found adequate for practical purposes
in rooms having relatively simple geometric shape and large enough
dimensions so that the sound is diffused. For a more complete treat-
ment of room acoustics the reader should refer to the literature on
this subject.*

The total steady-state intensity, It, at an assumed observing posi-
tion in a room consists of two parts: Ir, the reflected sound intensity
and /d, the direct sound intensity, so that:

It = Ir -\- Id-

614 BELL SYSTEM TECHNICAL JOURNAL

Assuming the reflected sound to be uniformly distributed in the
room, it can be shown that: ^

.0038E

Ir =

aS
S — a

where E = power emitted by source, in ergs per second,
6" = total surface area of the room in square feet,
a = absorption in square feet of equivalent open window.

Introducing 7^ = aS/^S — a), the above becomes:

J. .003SE
Ir - ^^-•

Assuming the sound source to radiate hemispherically, as is frequently
the case because it is associated with a large surface acting as a baffle,
the direct sound intensity is:

where r = distance from source, in feet,

V = velocity of sound, in feet per second.

In the above expression the direct sound intensity decreases in-
versely as the square of the distance from the source. This shows
that room absorption is effective mainly in reducing the noise from
sources at a considerable distance from the observing point, but has
relatively little effect on nearby sources.

The curves in Fig. 3 give the variation in the total sound intensity, It,
with distance from the source for different values oi F = aS/{S — a),
as computed by means of the above expressions.

Computation of Composite Noise

In the following, the application of the statistical method outlined
above is discussed. Since noise measurements are usually expressed
in db sound level, it is necessary to change the form of the equations
given in the preceding sections. For this purpose equation (5) is
rewritten as follows:

h MIo MIo'^ '" M lo' ^ ^^

where Iq = reference sound intensity.

COMPUTATION OF THE COMPOSITE NOISE

615

This equation can also be written

I M m\ Ii , nil In

_ nil Ii ^2 ^2 I mn In

(5b)

Equation (5b) is somewhat more convenient in computing than (5a).
In this equation a weight factor is associated with each intensity ratio,
which is in each case the actual number of peaks divided by the
maximum possible number of peaks.

^-4
O

(0 LU

5 6

QO

\

s-a

"^

^

EQUIVALENT OPEN WINDOW AREA
S= SURFACE AREA IN SQUARE FEET

^

^

\\^

--,

^

^

>.

^

F=200 1

1

^

^

^

400

^

^

\
\

600

i

\

>;

\

\

">w

800

1000

\

\

\

\

\

\

V

20

DO

\.

«...__4000

1 1.5 2 3 4 5 6 7 8 9 10 15 20 30 40 50

DISTANCE BETWEEN OBSERVER AND NOISE SOURCE IN FEET

Fig. 3 — Loss of intensity with distance from noise source for various
amounts of room absorption.

Assuming that the intensity corresponding to the average of the
db distribution of each source may be used, the following relations
exist for the source noises in db sound level :

Ai = 101o£

/i

A-i = 10 logio-p
-to

An = lOlogio-y?

(6)

616

BELL SYSTEM TECHNICAL JOURNAL

and for the average composite noise in db sound level :

A = lOlogio-T- .
It is usually convenient to use logarithmic weight factors

ini ^1

^i-101og,0 3QQ

(7)

Wi = 10 log]

W2

300

Wn = 10 logio
W = 10 logio'

nin
300

M
300

(8)

Figures 4 and 5 permit ready computation of these logarithmic weight
factors. The chart in Fig. 5 is based on the relation between M and
N given in equation (4b). It should be recalled that the derivation
of this equation involved a number of approximations. This ex-
pression especially does not apply when one or more of the noise
sources are continuous, in which case the exact expression (eq. 4) gives
M = 300 (for to — 0). Hence w = 0 in this case.

The terms of equation (5b) then can be rewritten in logarithmic
form by using equations (6), (7) and (8), as follows:

^i + z.. = ioiog.o^^f;

A2 -\- W2 — 10 logic

nil h
300 To

^„ + ^„= 10 logio l^j^
vl+z. = 10 logio 300 j^

(9)

This gives the following formula:

(A+w) (Ai-\-W\i

10"^o~ = 10""i^

(Ai+Wii

+ 10~^^~ +

10

10

(10)

from which the average composite noise A can be found.

The application of this expression is materially simplified by the
use of the chart shown in Fig. 6. Power addition of a number of

COMPUTATION OF THE COMPOSITE NOISE

617

components may be carried out with this chart by first adding two
components, then adding the resultant to a third component and con-
tinuing until all components have been summed up. Incidentally,

200
100

\

>

\

\

s.

80

\,

>

V

60
iij

z

2 40

Oi

UJ

Q. 30

i 20

u.
O

cr

UJ
CO

\

\

\

\

\J

k

\,

\

«.e

\,

■v

6
5
4

3
2

1

\

\,

\

\

•

\

N

\

-8 -10 -12 -14 -16 -18
i = LOGARITHMIC WEIGHT FACTOR

-26

Fig. 4 — Relation between peaks per minute (w,) produced by a noise source
and its logarithmic weight factor (Wj).

the chart shows that the contribution to the composite noise from a
source whose weighted intensity {Ai -\- Wi) is 20 db or further below
that of another noise source {A% -\- w^) is negligible.

618

BELL SYSTEM TECHNICAL JOURNAL

1000

\

800

\

\

600

\

\

_ NUMBER OF SOURCE PEAKS

O O o o
o o o o

\

\

\

s.

\

\

N

s

5 80

\

N.

50

N,

N

30
20

10

\

N

\

0 -I -2 -3 -4 -5 -6 -7 -8 -9 -10 -II -12

W = LOGARITHMIC WEIGHT- FACTOR OF COMPOSITE NOISE

Fig. 5 — Relation between total number of peaks per minute (iV) and the logarithmic
weight factor of composite noise (w).

INCREASE IN HIGHER NOISE

IN DECIBELS
p — .— r\j ro 0
o w> o y b cp c

\,

\

\

\,

\

^^

6 8 10 12 14

DIFFERENCE BETWEEN NOISES IN DECIBELS

Fig. 6 — Power addition of noises.

COMPUTATION OF THE COMPOSITE NOISE 619

Applications
In the following, several applications of the theory are made to
illustrate its practical usefulness.

I. The composite noise in a typing room is computed. This com-
puted noise is compared with actual measurements. The effect of
increased room absorption is discussed.

II. The effect on the composite noise of installing additional office
equipment is computed for the two cases where this equipment pro-
duces a continuous noise and where its noise is intermittent.

III. The maximum permissible noise from added equipment is de-
termined on the basis that the composite noise level shall not be
increased by more than 0.5 db.

Problem I

For the purpose of computing the noise at a given location in the
typing room, the following information was obtained :

A distribution of the noise from a typical typewriter was measured
at a distance of 2 feet from the type bar guide while the machine
was being operated at a normal rate. This is shown by Curve A of
Fig. 1.

A location was chosen as a point of observation, and the distances
between it and the typing desks were measured.

Estimates of the time spent in typing at each desk were obtained
which, taken together with data on average typing speeds, gave infor-
mation on the number of typing peaks produced per minute at each
desk.

Computation of the absorption of the room using the usual values
of absorbing coefficients ^ gave a value of 650 units for F.

Noise due to other sources, such as conversation and street noise,
was negligible in this room.

The table shown below was then prepared.

In this table Column 2 gives the average noise A/ produced by
each of the sources at 2 feet distance. This value is the median point
of Curve A in Fig. 1. Column 3 is the average number of source peaks
per minute m, produced at each desk. Column 4 is obtained from
Column 3 by using Fig. 4. The total number of source peaks is
A'' = 750, and from Fig. 5 the composite noise weight factor w =
— 0.4 db. The distances between the observing position and each
source are given in Column 5 and the losses in db due to these distances
are given in Column 6. These values were obtained from Fig. 3 for a
value oi F — 650. Column 7 is obtained by subtracting the losses of
Columns 4 and 6 from the values of Column 2.

620

BELL SYSTEM TECHNICAL JOURNAL

Adding the values of Column 7 successively on a power basis by-
means of the curve in Fig. 6 gives A -^ w from which is obtained the
total composite noise A = 69.7 db sound level. This differs by ap-
proximately 1 db from the average of the measured composite noise
distribution shown by Curve B of Fig. 1.

The effect of sound treatment on the walls and ceiling in reducing
the typing room noise may readily be calculated by means of the
curves in Fig. 3. Supposing that the added absorption raises the
value of F from 650 to 2000 units, this figure shows that noise pro-
duced by sources 20 feet or more away from the observing point would
be reduced by approximately 5 db. At shorter distances the reduction
would be less. For the observing position here considered, a com-
putation similar to that carried out above indicates that the composite
noise level would be reduced about 3 db by the added absorption in
the room.

TABLE

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Source
No.

Aj' = Average

Source Noise

at 2 ft.

■mj = Source

Peaks per

Minute

Wj = Freq.
Weight
Factor

Distance
from
Source

Intensity
Loss vs.
2 Feet

Aj +Wj = Weighted

Source Noise at
Observing Position

db Sound Level

db

Feet

db

db Sound Level

1

71.9

105

-4.5

18

-7.4

60.0

2

71.9

90

-5.2

13

-7.2

59.5

3

71.9

90

-5.2

9

-6.7

60.0

4

71.9

120

-4.0

9

-6.7

61.2

5

71.9

120

-4.0

7

-6.0

61.9

6

71.9

40

-8.8

7

-6.0

57.1

7

71.9

65

-6.6

7

-6.0

59.3

8

71.9

120

-4.0

7

-6.0

61.9

Total Source Peaks: N = 750

w = — 0.4 db
(Fig. 5)

Power Addition A + w = 69.3 db
(Fig. 6)

A = 69.7 db sound level.

Problem II

A piece of office machinery, such as an addressing or copying
machine, which produces an average sound level of 75 db at 2 feet
distance, is to be installed in the typing room considered in Problem I,
20 feet away from the observing position. How much will the com-
posite noise level be raised?

(a) The machine produces a steady noise. The new value for the
number of composite noise peaks is then 300 and the weight factor
of this noise is zero. The distance loss of the machine noise (for
F — 650) is — 7.5 db from Fig. 3. Hence, the weighted value of

COMPUTATION OF THE COMPOSITE NOISE 621

the noise from the new machine at the observing position is:
75 - 0 - 7.5 = 67.5 db sound level.

Adding this figure to the weighted value of the existing composite
noise {A -\- w = 69.3 db) on a power basis gives the new composite
noise value of 71.5 db sound level (the new weight factor being zero).
Hence, the composite noise at the listening position is increased 1.8 db
by the machine.

(6) The machine produces noise intermittently. The increase in the
composite noise level will not be as great in this case as in the preceding
case. For example, assuming the rate to be 100 peaks per minute,
the new value of N will be 850 peaks per minute and the corresponding
weight factor from Fig. 5 will be — 0.3 db. For the noise from the new
machine, the weight factor (by Fig. 4) is — 5.0 db. The distance loss
as before will be — 7.5 db. The weighted value of the machine noise
at the observing position is then :

75 - 5.0 - 7.5 = 62.5 db sound level.

Adding this figure on a power basis to the weighted value of the exist-
ing composite noise, 69.3 db, results in a new weighted composite sound
level, A -\- w = lOA db. Since w = — 0.3 db, this gives A = 70.4 db.
Hence, the composite noise is increased 0.7 db by the intermittent
machine noise.

Problem III

What is the maximum permissible noise, measured at 2 feet, which
the machine considered in Problem H, may produce without raising
the composite noise in the typing room by more than 0.5 db?

(a) The machine produces a steady noise. In this case, the composite
noise has 300 peaks and its weight factor is zero. The existing com-
posite noise was 69.7 db sound level (see Problem I). The maximum
permissible value of the new composite noise level is consequently

A = 69.7 + 0.5 = 70.2 db sound level.

Let the unknown machine noise be A^ (its weight factor is zero), and
since for the existing composite noise A -\- w = 69.3, equation (10)
gives :

70.2 69.3 4j

10^ = 10"^ + 101°.

Entering the ordinate of Fig. 6 at the value of 70.2 — 69.3 = 0.9 db,
the chart indicates that A^ must be 6.3 db below 69.3. Hence ylg
= 63 db sound level at the observing position.

622 BELL SYSTEM TECHNICAL JOURNAL

The distance loss for 20 feet is — 7.5 db. The machine then could
produce a noise of:

63.0 + 7.5 = 70.5 db sound level

at 2 feet distance without raising the composite noise level by more
than 0.5 db at the observing position.

(b) The machine produces noise intermittently. The solution of the
problem in this case follows the same lines as in Part (a) except that
the weight factors are changed. The rate for the new machine noise,
Aq, is assumed to be 100 peaks per minute, so that Wg = — 5.0 db, as
in part (b) of Problem II. The maximum permissible value of the
new composite noise is 70.2 db sound level (as before) but its weight
factor now is — 0.3 db as in part (b) of Problem II. The weighted
value of the existing composite noise as before is 69.3 db sound level.
Equation (10) then gives:

(69.9) 69 3 U9-5.O)

10""io~ = lO"!"" + 10"^^*^.

From Fig. 6 it is found that for a value of 69.9 — 69.3 = 0.6 on the
ordinate, the abscissa is 8.3 db. Hence, ^9 — 5.0 must be 8.3 db below
69.3 or ^9 = 66.0 db sound level at the observing position. Applying
the same distance loss as before, the machine could produce a noise of
73.5 db sound level at 2 feet without increasing the composite nqise
level by more than 0.5 db at the observing position.

From the computations, then, it may be expected that adding a
steady noise will increase the general noise level more than adding an
intermittent noise having the same average value, when there are a
number of sources operating. That this is actually so can readily be
verified by sound level measurements. As has been stated, sound
level measurements under most conditions are directly related to the
effects of noise upon the individual exposed to it, and the method
described provides a convenient and reasonably reliable way of com-
puting such readings and thereby makes possible the engineering
analysis of noise problems.

Bibliography

1. "Environment and Employee EfiSciency" by Harold Berlin and others —
Office Management Series No. 81 — Copyright 1937, American Management
Association.
"City Noise" — Report of Noise Abatement Commission 1930, Dept. of Health,
New York City.

COMPUTATION OF THE COMPOSITE NOISE 623

2. "American Tentative Standards for Sound Level Meters for Measurement of

Noise and Other Sounds" — Z24.3 — Approved American Standards Associa-
tion, Feb. 17, 1936.
"Indicating Meter for Measurement and Analysis of Noise" by T. G. Castner,
E. Dietze, G. T. Stanton and R. S. Tucker — District Meeting A. I. E. E.,
April 1931, Rochester, N. Y.

3. "Determination of Normal Curve from Tail" — Table XI of "Tables for Statis-

ticians and Biometricians" by Karl Pearson — Part I — Second Edition, 1924.
"Graduation by a Truncated Normal" by Nathan Keyfitz — Annals of Mathe-
matical Statistics — Vol. 9, March 1938.

4. "Collected Papers on Acoustics" by W. C. Sabine,

"Reverberation Time in 'Dead' Rooms" by Carl F. Eyring — The Journal of the

Acoustical Society of America, Vol. I, No. 2, January 1930,
"Architectural Acoustics" by V. O. Knudsen.

5. Official Bulletin of the Acoustical Materials Association, No. 6, March 1938.

Load Rating Theory for Multi-Channel Amplifiers *

By B. D. HOLBROOK and J. T. DIXON

The amplifiers of multi-channel telephone systems must be so
designed with regard to output capacity that interchannel interfer-
ence caused by amplifier overloading will not be serious. Proba-
bility theory is applied to this problem to determine the maximum
single frequency output power which a multi-channel amplifier
should be designed to transmit as a function of N, the number of
channels in the system. The theory is developed to include the
effects of statistical variations in the number of simultaneous
talkers, in the talking volumes, and in the instantaneous voltages
from speech at constant volume.

Introduction

TN A perfect multi-channel carrier telephone system, each channel
-^ would be entirely free from interference produced by the energy
present in the other channels. Since all the channels are amplified
by the same repeaters, which as a practical matter cannot have per-
fectly linear characteristics, this is an ideal that may be approached
but not completely realized. The interchannel interference must be
kept down to a value which will be satisfactory for the grade of transmis-
sion concerned, further reduction being uneconomic. To do this the
repeaters must meet definite load capacity requirements and modula-
tion (non-linearity) requirements. The load capacity requirement is
most conveniently specified in terms of the maximum single frequency
sine wave power which a multi-channel amplifier must transmit with-
out appreciable overloading. The modulation requirement pertains
to the performance of the amplifier for impressed loads equal to or
smaller than the load capacity, and specifies the allowable power in
the modulation products resulting from such loads. Because of the
numerous factors which affect these requirements, their determination
is a rather complicated matter and the present discussion will be
restricted solely to a determination of the load capacity requirement.
The object is to determine this quantity as a function of N, the number
of channels in the system.

The criteria ordinarily used for determining the load capacity of
single-channel amplifiers are of little use here because of two funda-

* Presented at Great Lakes District Meeting of A.I.E.E., Minneapolis, Minn.,
September 27-29, 1939.

624

LOAD RATING THEORY 625

mental diflferences between single-channel and multi-channel systems.
In the first place, the modulation produced in a single-channel amplifier
depends only upon the input to that channel and occurs only when the
channel is energized. In addition, the most important frequencies
resulting from modulation fall directly back upon frequencies already
impressed and the net effect appears as a distortion of the original
input, rather than as noise. The situation is entirely different in a
multi-channel system. In this case, the modulation products falling
into one particular channel are in the main unrelated either to the
impressed frequencies or to the volume of impressed speech in that
channel. Thus it is no longer possible to think of the interference as
distortion ; the effect must rather be considered as that of a particular
kind of noise whose level depends upon the load on the other channels
of the system. For a given grade of service, the ratio of signal to
noise must be much larger than the ratio of signal to modulation prod-
ucts resulting in distortion; thus it is to be expected that the non-
linearity requirements will be more stringent for multi-channel opera-
tion than for single-channel operation.

The second fundamental difference between single-channel and
multi-channel systems arises from the character of the load which each
system must be designed to handle. A single-channel amplifier must
be capable of handling one channel at the maximum volume normally
expected. Inasmuch as the amplifier will be loaded only about one-
fourth of the time, even in the busiest hour, and as the average im-
pressed volume will be some 15 db below the maximum that must be
provided for, the ratio of maximum to average load of such an amplifier
is inherently very high. In a multi-channel system, however, the
several channels will very rarely be heavily loaded simultaneously.
There is thus a favorable diversity factor, increasing with the number
of channels, and multi-channel amplifiers may accordingly be worked
successfully at lower ratios of maximum to average load.

Occasionally, of course, there will be short periods of excessive
loading during which the interchannel interference in multi-channel
systems will rise above the value normally permitted. This sort of
thing often occurs when it is desired to make economical use of facil-
ities of any kind in common. In machine switching systems, for ex-
ample, it is common practice to associate a large number of lines with
a smaller number of switches and trunks. The number of switches and
trunks provided is sufficient to ensure a satisfactory service, with a very
small probability of requiring more facilities than are available. The
multi-channel amplifier problem presents a situation identical in prin-
ciple, though the methods of solution are necessarily very different.

626 BELL SYSTEM TECHNICAL JOURNAL

The application of probability theory is evidently indicated as the
method of attack.

Those characteristics of multi-channel amplifiers which are im-
portant to the problem will be described first. Then a description
will be given of the variables which must be taken into account in com-
puting load capacity. Finally, the combined effects of these variables
will be determined on a statistical basis to establish the required load
capacity as a function of the number of channels in the system.

Characteristics of the Multi-Channel Amplifier

At the present time, multi-channel systems of primary interest
employ single sideband transmission ; the carrier frequencies are largely
suppressed and different amplifiers are used for the two directions of
transmission. For such systems negative feedback amplifiers have
outstanding advantages, particularly with respect to stability of gain
and reduction of modulation effects, and are thus being used almost
exclusively in present day multi-channel systems. The following
discussion is related particularly to such systems, although many of
the calculations are also applicable to less common types.

At light loads the principal modulation products in a negative
feedback amplifier increase approximately as the square or the cube of
the fundamental output power. Beyond a certain critical point,
however, the modulation increases very rapidly and the total output
of the amplifier soon becomes practically worthless for communication
purposes. This critical point will be called the "overload" point.
For most tube circuits it is either the point at which grid current begins
to flow, or that at which plate current cutoff occurs. This point
obviously defines the instantaneous load capacity.

Below the overload point the higher order modulation products
are negligible in comparison with second and third order products,
and the interference may be regarded as due to the latter sources alone.
Beyond the overload point, however, the higher order products become
important very rapidly and the resultant disturbances appear in most,
if not all, of the channels. With given tubes, the interference below
the overload point may be altered by changing the amount of feedback.
The interference above the overload point, however, may be little
changed in this way because of the rapid loss of feedback as the
amplifier overloads. Accordingly, in designing an amplifier, the
necessary load capacity may be determined solely by insuring that the
output will rarely rise above the overload point, afterwards adjusting
the amount of feedback so that the inteference below the overload
point will be tolerable. There are thus two problems which may be

LOAD RATING THEORY 627

handled separately, at least for negative feedback amplifiers, it being
understood that the results are combined in the final design. As
previously stated, only the load capacity problem will be considered
in detail here but many of the methods used have been applied suc-
cessfully to the interchannel modulation problem.

The Load on a Single Channel

The total load applied to a multi-channel amplifier varies rapidly
between widely separated limits. A complete knowledge of the
variations in the load applied to a single channel is necessary first;
these variations arise from several recognizable causes which may be
discussed separately.

Number of Active Channels

First of all, a single channel at a given instant may or may not be
carrying speech; if not, it contributes nothing to the multi-channel
load. A channel will be called "active" whenever continuous speech
is being introduced into it; i.e., a channel is active during the time it is
actually carrying speech power, and also during the short pauses that
occur between words and syllables of ordinary connected speech. A
channel is said to be "busy" when it is not available to the operator
for completing a new call. Busy time is by no means all active time,
for a busy channel is inactive during much of the time the connection
is being completed, during pauses in the conversation, and finally
during the time the other party is talking. The fraction of time
during the busiest hour that a channel may be busy depends on the
size of the group of circuits of which it is a member and on the methods
of traffic operation. Measurements on circuits in large groups, made
by Mr. M. S. Burgess, indicate that the largest fraction of the busiest
hour that a channel may be active is about \. For channels in small
circuit groups, this figure may become considerably smaller but it is
unlikely that any probable increase in group size or improvement in
operating practices will increase it appreciably. This figure, which
will be represented by r, may accordingly be taken as a conservative
estimate of the limiting probability that a channel will be active in
the busiest hour.

The number of channels that are active at a given instant in an
iV-channel system may be anything from zero to N. Inasmuch as the
channels are independent, it is possible to write down at once the
probability that exactly n of them are simultaneously active. This
probability is

628 BELL SYSTEM TECHNICAL JOURNAL

Talking Volumes
A second source of variation in the load on a given channel is that
the impressed volume may have any value within rather wide limits
when a channel is active. By "volume" is meant the reading of a
volume indicator of a standard type. Its importance in the present
problem arises from the fact that the volume is an approximate mea-
sure of the average speech power being introduced into the channel.
Although some other instrument might give a better measurement of
the latter quantity, only the volume indicator has been used sufficiently
widely in the plant to give data on the distribution of average speech
power per call under commercial conditions. The average speech
power is dependent on the type of instruments, the character of the
speech, and the time interval over which the average is determined.
From an analysis of phonograph records of continuous speech it is
found that the average speech power of a reference volume talker may
be taken as 1.66 milliwatts, and the relationship between volume'
and average power may be expressed by the following equation :

^^ , , „, 10 logio Average Speech Power in Milliwatts ,^.

Volume (do) = ^ : -^— . (2}

1.66

This equation is based on the long average speech power. It will
be understood that for purposes other than load rating computations,
a different relation might be found more suitable.

The use of equation (2) to relate volume to average speech power
is applicable to speech in a single channel. It is convenient to refer
to a quantity related in the same way to the total average power con-
tributed by a number of channels as the "equivalent volume."

The single-channel volumes on commercial circuits are conveniently
measured at the transmitting toll test board, which will be taken as a
point of "zero transmission level." Henceforth it is assumed that
there is no gain or loss between this point and the output of the ampli-
fier, so that the latter is also a point of zero transmission level. While
this will seldom be the case in an actual system, the necessary change
in the load capacity is easily computed. The volumes at this point
are found to be distributed approximately according to the "normal"
law; that is, the probability that the volume will be between V and
V -\- dV \s given by

1

(V-Vo)^

p{V)dV^-^e 2.2 dV. (3)

-v27ro-

^ Subsequent to the preparation of this paper, a new volume indicator was stand-
ardized for use in the Bell System. With the new volume indicator, volume is
expressed in vu, + &vu being approximately equal to reference volume (0 db) as
used herein.

LOAD RATING THEORY

629

For calls on typical toll circuits, the best present values for the param-
eters are Vo = — 16.0 db and a = 5.8 db. These parameters de-
pend, of course, upon the character of the local plant and upon the
habits of telephone users, and changes in either will affect their values.
Curve A of Fig. 1 shows this distribution of talker volumes at a point
of zero transmission level. Curve B of Fig. 1 is the talker volume
distribution used for load rating computations when a particular
amount of peak amplitude limiting occurs in the terminal equipment.
This will be discussed later. Although the mean volume is Vo, the

1.0

lij 0.7
U

<£ 0.6
<

CD 0.3

N,

\

\,

\

\

\

\

\

V

\

\

V

\

\

s

^^

\

L

\ FOR

\ computations:
\ a — without peak
^ w limiting

1 \ B- WITH PEAK
\^tr^ LIMITING

\
\
\

\

\

\
\

N
'■k —

-25 -20 -15 -10 -5-5 0 5

TALKER VOLUME IN DECIBELS (ABOVE REFERENCE VOLUME)

Fig. 1 — Talker volume distribution.

volume corresponding to the mean power of the distribution (3) is
equal to Vo + .115a•^ as may be seen by converting the volume scale
of the distribution to power ratios, averaging, and reconverting the
average to volume in db. For the values of the parameters given
above, Vo + M5a^ = - 12.1 db.

Instantaneous Voltage Distribution
Finally, the voltage in an active channel fluctuates widely even at
constant volume. Not only the differences between successive syl-
lables and the differences between vowel sounds and consonants, but
also the fane structure of single sounds, are important in this connec-

630 BELL SYSTEM TECHNICAL JOURNAL

tion. The total voltage impressed on the amplifier is the quantity
which determines whether or not it will overload, and the phases as well
as the amplitudes of the frequency components in the several channels
must be considered in determining this. It is most convenient for
analysis to work directly with instantaneous voltages of speech, the
frequency of occurrence of the magnitudes being expressed in the form
of a distribution function.

This distribution function has been measured by Dr. H. K. Dunn,
using apparatus which measures 4 samples per second of the instantane-
ous voltage out of a commercial subset and typical loop. By operating
the apparatus until about 1000 successive samples have been measured,
usable distribution curves of instantaneous voltage are obtained; this
is readily checked by making repeated runs comprising the same
number of samples on speech recorded on high quality phonograph
records. It is, of course, known that commercial transmitters have
considerable asymmetry as regards positive and negative voltages
but the poling referred to the toll board is expected to be random. As
the measurements were considerably simplified by doing so, it ap-
peared desirable to average out this asymmetry by arranging a linear
rectifier ahead of the sampling apparatus to obtain equal samples of
positive and negative voltages.

Such measurements have been made for a number of different
talkers, different commercial subsets, and different volumes, with the
speech input held at substantially constant volume in each test.
The various subsets now in commerical use all give essentially the
same distribution curve. The resulting distributions, if they are
considered as functions of the ratio of instantaneous to rms voltage,
are also nearly independent of the speech volume at the subset.
Specifically, the only important effect of volume is that which may be
ascribed to amplitude limiting in the transmitter; i.e., to the fact that
the transmitter itself has a limited load capacity. However, this
effect does not appear until the volume is 10 db or more above the mean
of the volume distribution curve, and is only of importance for talkers
at still higher volumes. For all lower volume talkers, the instantane-
ous voltage distribution may be considered as the same for all volumes
w^hen expressed as a ratio of instantaneous to rms voltage. The
cumulative distribution curve of the quantity EjU, where E is the
rectified instantaneous voltage and U the rms voltage, is shown by the
curve w = 1 of Fig. 2.

Voltage Limiting

While this curve of Fig. 2 is accurate for the bulk of the talkers, it
changes for the high volume talkers who overload the subset trans-

LOAD RATING THEORY

631

mitters. It is also the custom to provide a certain amount of ampli-
tude limiting in each channel by suitable circuit design of the channel
terminal equipment. This limiting alters the shape of the instantane-
ous voltage distribution curve for a range of voltages below the maxi-
mum, the extent of the modification depending on the talker volume
and the characteristics of the limiting device. Its effect on the load
capacity will be considered later.

0.9
0.8

■ in 0.5

CO

<

y

\V

\\

1\

w

\

.^

^%

»,

\

\

%

p

^

\

\

%

n = 64

\

\

K

X

4^

^

^

^-^

^

\

^^

\

V

\^

^

\

^^o

\

s 4

= 1

%

v^

^^

^

64^

r:]

—

0.10

0.09

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0 0.5 1.0 1.5 2.0 2.0 2.5 3.0 3.5 4.0

RATIO OF RECTIFIED INSTANTANEOUS VOLTAGE TO RMS VOLTAGE

Fig. 2 — Instantaneous voltage distributions for n talkers.

Multi-Channel Instantaneous Voltage Distributions
The number of variables with which it is necessary to deal makes
the general load capacity problem rather a complicated one. The
analysis .will be easier to follow if the effects of the different variables
are taken up one at a time, thus building up a complete theory in
successive steps. To do this, it is advantageous to start with a case
so simplified that it rarely, if ever, occurs in ordinary practice; i.e.,
that in which the volumes in all the channels are regulated to a common
constant value, and in which the number of active channels is also kept
constant. For this condition, it is necessary to consider only the
effects of the distribution of instantaneous voltages in each channel.
This distribution curve is the same for all of the channels, since all
are at the same volume, but the voltage in any channel at a particular
instant is entirely independent of the condition of the other channels.

Overload Expectation
The total voltage Impressed on the amplifier by a number of channels
at a given instant is the sum of the instantaneous voltages in the

632 BELL SYSTEM TECHNICAL JOURNAL

separate channels. Since disturbances will be produced in many of
the channels when the applied voltage goes beyond the overload point,
it will be useful to know the fraction of the time that this may be ex-
pected to occur; this fraction will be called the overload expectation
and denoted by e. It is important to notice that this quantity e is not
necessarily the fraction of the time during which the performance of
the amplifier will be unsatisfactory. This might perhaps be the case
for a device having an instantaneous cutoff characteristic, but for an
ordinary amplifier the time constants (among other things) affect the
results of overloading. The interpretation of the overload expectation
will be discussed further later; consideration must be given first to
how it is obtained.

The n- Channel Voltage Distribution

The load in each channel is applied at voice frequency to the input
side of a modulator, the voice frequency instantaneous voltage distribu-
tion being as shown by the curve w = 1 of Fig. 2. The overloading
of the amplifier is determined, however, by the distribution of the sum
of n such voltages after each has been shifted by the modulator to the
appropriate carrier frequency, one side-band being suppressed. It
may be shown that if the phases of the various components of the voice
frequency input were random, the distribution of instantaneous voltage
at side-band frequency would be identical with that measured at voice
frequency. It is known, however, that the phases at voice frequency
are not entirely random, and there may thus be differences between
the two distributions. The results of a number of tests bearing upon
this point indicate that any error resulting from the use of the dis-
tribution measured at voice frequency will be small for systems of
few channels, and will rapidly disappear as the number of channels
is increased.

Theoretically, the resultant w-channel voltage distribution can be
derived from the single-channel distribution by straightforward
analytical methods; in the present case, however, expression of the
result in useful form is very difficult because of the form of the single-
channel curve. This difficulty might be resolved by using graphical
or numerical methods, as applied later to the volume distribution
curves; fortunately, the fact that the voice frequency voltage distribu-
tions may be used throughout permitted the resultant w-channel
distributions to be obtained much more easily. Since the addition of
voltages from the several carrier channels does not depend materially
upon the frequencies at which the channels appear in the system, the
addition of n channels at voice frequency will give the desired n-

LOAD RATING THEORY 633

channel distribution directly. Mr. M. E. Campbell effected this
addition by the use of phonograph records, the w-channel distributions
being determined by means of the instantaneous voltage sampling
apparatus previously mentioned.

As material for this process, 16 high-quality phonograph records
were made of the outputs of commercial subsets through representative
subscriber loops. Both male and female voices were used. The
speech was furnished by reading magazine stories containing consider-
able conversational material, due precautions being taken that the
volume on each record was substantially constant throughout. A
calibrating tone was cut on each record to enable it to be played at any
desired volume and most of the volumes recorded were well below the
point at which the transmitter began to act as a voltage limiter.

These individual records were then combined in groups of four,
with all records adjusted to the same volume by means of the calibrat-
ing tones, and re-recorded. Several such 4-voice records were made;
by combining them again in the same way, 16-voice records and finally
64-voice records were obtained. The instantaneous voltage distribu-
tions were measured before and after each re-recording to insure that
the recording process introduced no errors. A few minor discrepancies
were found, but all were small enough to be disregarded. Each single-
voice record appeared several times in a 64-voice record, but since the
phases of its dififerent appearances were random, this had no appreci-
able effect on the resultant voltage distribution. This was verified
by comparing the voltage distributions of the various possible 16-
voice combinations. By this process w-channel voltage distributions
were obtained for n = 1,4, 16 and 64.

These distributions, together with a normal curve, are shown in
Fig. 2 in cumulative form. To show the curves conveniently to the
same scale, it has been necessary to plot for each case not the distribu-
tion of E, the rectified instantaneous voltage, but that of E/U, where
U is the rms voltage. The rms voltage, it will be remembered, is
directly related to the equivalent volume by equation (2). The
figure shows clearly the gradual transition from the single-channel
distribution to the normal one for large n, and also indicates that for 64
active channels the curve is normal within the precision of the measur-
ing apparatus. Hence, the normal distribution may justifiably be
used for any value of w > 64.

Further significance is accorded the above data by plotting the
ratio of the voltage exceeded a fraction e of the time to the single-
channel rms voltage, as a function of the number n of active channels,
for several fixed values of e. From the data given, points on such

634

BELL SYSTEM TECHNICAL JOURNAL

curves can be obtained for w = 1, 4, 16, 64; furthermore, the fact that
the distribution for « > 64 is normal permits drawing the asymptote
for large values of n. The points read from Fig. 2 and replotted in
this way give the full lines shown in Fig. 3.

In order to make practical use of these curves, it is necessary to
know what value of e corresponds to satisfactory performance of the
amplifier. Experiments have been conducted on a number of different
multi-channel amplifiers, each loaded by various numbers of active
channels all at the same volume. It has been found that for low
enough values of e, no audible disturbance is produced but that as e is
increased by increasing the load on the amplifier, the disturbance
falling into a channel not energized increases rapidly to a large value.
Two different amplifiers having the same computed load capacity
may show noticeable differences in performance in this respect when
subject to identical fixed loads of the type being considered, thus in-
dicating the influence of circuit design on the value of e. In general,
however, the allowable values of e measured for all of the amplifiers
that have been tested lie in a relatively narrow band on either side of
the curve for « = 0.001. The broken curve of Fig. 3 represents the

-1^40
Occ 35

O'^ 20

'^l? 15

O

ceo 10

>u.

—

^"^

^

--•

'"

^

^^

oPt

K>^fi

'^^^

^^

'0x^

f-'

^^0^

^^^

^

^

.--

--

z^

O0^

^

^-^

"^

^

-'^

^^

^

^^

,-«'

^

I 5 10 50 100 500 1000

NUMBER OF ACTIVE CHANNELS fn)

Fig. 3 — ^Overload voltage for n active channels.

approximate upper limit of the observations, extrapolated parallel to
the € = 0.001 curve above n = 14. It is possible that some amplifiers
would overload even if operated in accordance with this curve, but for
the great majority of amplifiers of types thus far tested the operation
would be satisfactory, with perhaps a small margin.

Multi-Channel Peak Factor
It is useful at this point to introduce the concept of "multi-channel
peak factor," which is defined as the limiting ratio cf the overload

LOAD RATING THEORY

635

voltage to the rms voltage for a given number of active channels at
constant volume. The ratio of the overload voltage for n active
channels to the rms voltage of one active channel is given directly by
the broken curve of Fig. 3, and the rms voltage for n channels is
simply Vw times that for one channel. A simple computation then
gives the multi-channel peak factor. This is plotted in Fig. 4 as a
function of the number of active channels n. The reduction in multi-
channel peak factor as the number of active channels increases reflects
the transition from the single-channel distribution curve to the normal
curve, as depicted in Fig. 2.

MULTICHANNEL PEAK
FACTOR IN DECIBELS

^

^^

^-

.

I 5 10 50 100 500 1000

NUMBER OF ACTIVE CHANNELS (n)

Fig. 4 — Multi-channel peak factor for n active channels.

The Distribution of Equivalent Volume

The multi-channel peak factor deals only with the effects of changes
in the instantaneous voltages of the channels, all other variables
being fixed. It is next necessary to extend the treatment to include
the effects of the other load variations that occur in practice — those
in number of active channels and in channel volumes. It is im-
portant, first of all, to notice that the instantaneous-voltage variations
occur very rapidly, while changes in the other two quantities are, in
comparison, very slow. In the experiments described above, the loads
were so fixed that the equivalent volumes could be changed only by
changing the operating transmission level of the amplifier; in practical
cases the amplifier transmission level is kept fixed, but the equivalent
volume is constantly changing because of changes in number of active
channels and in channel volumes.

The amplifier is thus loaded with a constantly changing equivalent
volume but because of the great difference in the time-scales of the
two classes of variations the load may be regarded as a succession of
equivalent volumes, each constant for a small interval of time that
nevertheless is long enough to include a representative sample of the
resultant instantaneous voltage distribution. If the distribution
function for equivalent volume is computed, and then corrected by the

636 BELL SYSTEM TECHNICAL JOURNAL

multi-channel peak factor, the fraction of such intervals during which
the amplifier will be unsatisfactory from the standpoint of overloading
may be determined. For a particular amplifier, the operating trans-
mission level must be so chosen that this fraction will be small enough
to make any adverse effects on transmission unimportant. For sys-
tems of very many channels the proper value of this fraction is probably
about 1 per cent. During the busiest hour, this corresponds to 36
seconds during which audible interference may occur and as this will
be broken up into many very short intervals, the total efifect should be
slight. For systems of very few channels, the equivalent volume may
reach objectionably high values during these intervals and it might be
necessary to make this fraction smaller than 1 per cent to secure good
performance. For illustrative purposes, the 1 per cent figure will be
used in what follows without implying that it may not need alteration
in some cases. The methods used are applicable no matter what value
is chosen for the fraction of time overloading is permitted.

Controlled Volumes

As the simplest case to which the above procedure may be applied,
and one that may occasionally be of practical interest, consider a
commercial system with all the channels controlled to the same volume.
If there are N channels in the system, the probability that exactly n
channels will be active at any given time is given by equation (1),
with r = 0.25. By computing the value of p{n) for all values of n,
and taking the cumulative sum, the value of n which makes the sum
0.99 (or the next greater n) is readily determined. This determines
the number n of active channels that is exceeded 1 per cent of the
time. A plot of these values of n is given by the curve of Fig. 5, as a
function of N, the number of channels in the system. For small values
of N this curve has been drawn in a manner to smooth out the steps
introduced because n must of necessity be an integer and when the
value of n read from the curve is not an integer, the next higher in-
tegral value is to be used. It is of interest to compare this curve with
the two straight lines of the figure. The lower straight line represents
the asymptote for sufiiciently large N and the upper straight line is for
the condition where all channels are active simultaneously {n = N).

The average power for n channels is n times that of one channel, and
the equivalent volume expressed in db is 10 logio n above that in one
channel. The equivalent volume may thus be computed as a function
of n, and by means of Fig. 5, as a function of N. Curve A of Fig. 6
shows the values of equivalent volume so determined as a function of
N, the number of channels in the system; it applies specifically to the

LOAD RATING THEORY

637

1000

200

100

50
40
30

20

/

/
/
/

./

^

/

/^'

/

//

•

/
/

.^

/

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/
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/

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f

NUMBER 0

ACTIVE
CHANNELS'.

^)

/
/
/
/

.^}

^'

V

f

^
t

^y /

s

'M

< /

^^

^/

o<l'

/

A'

4

\

/

1

V

/

s^

^^'

/

EACH CHANNEL
ACTIVE 25 PER
CENT OF TIME

/

V

/

/'

/

y

/

/

/

/

ii

oz
> <

< UJ
> N

P5

I 5 10 50 100 500 1000 5C

NUMBER OF CHANNELS IN SYSTEM (n)

Fig. 5 — Number of active channels as a function of the number of channels

in the system.

30

25

20

15

10

5

0

-5

-10

-15

-20

A- VOLUME controlled'

a MMr-r^MTorM . en ^ EXCEEDED 1 PER

""vSSm'eT"''" J cent of time

C- EQUIVALENT VOLUME CORRESPONDING
TO AVERAGE POWER

^,^-

^

'^

^

-^

-^

^

•-

r^^'

B_,

■-

'-

— -" '—''*"

^^

^-

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'-

A

-

-^

--""

^^

C

-^

-•

'"■

^ — ""

5 10 20 30 50 100 200 300 500 1000

NUMBER OF CHANNELS IN SYSTEM (N)

Fig. 6 — Equivalent volume for systems of N channels.

638

BELL SYSTEM TECHNICAL JOURNAL

case where the volume of each of the active channels is controlled so
as to be 12.1 db below reference volume. The choice of this particular
volume is purely arbitrary, but it corresponds to the average power of
the single talker volume distribution.

The equivalent volumes given by curve A of Fig. 6 are a measure
of the average power of the N channels, as computed by means of
equation (2). To determine the required instantaneous load capacity
of the system, the average power must be corrected by the multi-
channel peak factor which is read directly from Fig. 4, using for the
number of active channels the values read from Fig. 5.

For design purposes, it is more convenient to use the rms power
of the single frequency test tone whose peak value represents the

5 10 50 100 500 1000

NUMBER OF CHANNELS IN SYSTEM (n)

Fig. 7 — Load capacity for systems of N channels.

instantaneous load capacity. As the ratio of the peak to rms power of
a single frequency tone is 3 db, this test power is obtained by subtract-
ing 3 db from the instantaneous load capacity. This required test-
tone capacity is plotted as a function of N in curve A of Fig. 7, which
gives the output capacity required for an iV-channel system with
volume control as specified above.

Uncontrolled Volumes

For systems in which volume control is not used, the application

of this procedure becomes more involved. To study this more general

case, it is convenient first to interchange the conditions of the preceding

section, letting the number of active channels be fixed at any value n

LOAD RATING THEORY 639

and examining how the distribution curve of equivalent volume may
be obtained for this fixed number of channels. The relation between
volume and average speech power given in equation (2) may be re-
written for this case in the form

Wi
Ft = 10 logio^T^db,
vvo

where Wo = 1.66 milliwatts, Wi is the average speech power in milli-
watts, and Ft is the volume in db for any one of the active channels,
all at a point of zero transmission level.

Likewise, the relation between equivalent volume and average
speech power for n active channels is given by the expression

HWi

V = w-channel equivalent volume = 10 logio -^ttt — db.

Wq

Since the distribution of the channel volumes Ft is known and the
volumes of the various channels are independent, the straightforward
procedure to obtain the distribution of the w-channel equivalent
volume F would involve the following steps: (1) the obtaining of the
distribution function of Wi by a transformation of that of Ft; (2) the

n

calculation of the distribution function for the quantity Yin) = II PFj;

1

(3) the transformation of the Y{n) distribution to that of F by invert-
ing the process used in step (1).

The difficulties in this process are all in the second step, where,
having given p\{W), the distribution of average powers for a single
channel, it is required to obtain pniY), the distribution for n active
channels, with Y defined in terms of W by the relation given im-
mediately above. The formal solution requires the evaluation of
integrals of the following type:

Pn{Y) = f pn-k{W)Pk(Y- W)dW.

Jo

By successive calculation of such integrals for w = 2, 4, 8 . . . .taking
k each time equal to w/2, the required distributions may be obtained
for the necessary range of values of n.

As in the case of the instantaneous voltage distributions, it has not
proved feasible to perform the integrations analytically. It was
necessary to resort to numerical evaluation of these integrals; by
combining the transformations in steps (1) and (3) with the process

640 BELL SYSTEM TECHNICAL JOURNAL

of evaluating the integral, the process was somewhat shortened. In
this way equivalent volume distributions have been obtained for
w = 2, 4, 8, 16 . . . ; needed points on the distribution curves for
intermediate values of n are obtainable by interpolation.

The accuracy of such a process depends upon the number of division
points used in the numerical integration and this as a practical matter
must be kept fairly small. When the process must be repeated many
times, the errors introduced at each step may accumulate and lead to
inaccuracies for large n. It is thus desirable to have some control over
the accuracy other than by repeating the calculation with a larger
number of division points. This is provided by calculating the
moments of pn{Y) from those of pi{W) without the use of numerical
integration.

The moments Sk of pi{W) are defined by

Su = r Wp.iW) dW,

and the moments 7"^^"^ of pniY) similarly. By the use of the semi-
invariants of Thiele,^ it may be shown that

Ti^") = nSy,

Ti^n) = nS2 + n(n - l)Si\ etc.

By comparing the moments of the distributions obtained by numerical
integration with those calculated in this way, and making occasional
minor alterations in the curves to bring the first and second moments
into agreement, assurance was obtained that all the distributions used
are reasonably accurate, with no accumulation of error as n becomes
large.

Examples of the cumulative distribution curves of equivalent volume
for 1,4, 16 and 64 active channels are given in Fig. 8. The decrease in
standard deviation which occurs as n increases is of interest for it
indicates how the fluctuations in load due to talker volume varia-
tions are reduced by combining a large number of channels in one
system.

Having now w-channel equivalent volume curves for a range of
values of n, the resultant equivalent volume curves may be calculated
when the restriction to a fixed number n of active channels is removed.
Let pn(V) denote the probability that, with n channels active, the
equivalent volume lies between V and V + <iF and let p{n) denote the
probability that just n channels will be active. Then the total proba-

'^ T. N. Thiele, "The Theory of Observations," 1903; reprinted in Annals of
Mathematical Statistics, Vol. 2, 1931. See especially Sections 22, 29.

LOAD RATING THEORY

641

bility that the equivalent volume will be between V and V -}- dV is
given, for an iV-channel system, by

p(V) = p{l)Pi(V) + p{2)p2{V) +

+ p{n)pn{v).

The pn{V) are given by equivalent volume curves such as those in
Fig. 8 and the p{n) by equation (1). Examples of curves thus com-
puted are given in Fig. 9, which shows the equivalent volume distribu-
tions at a point of zero transmission level for 3, 12 and 240 channel
systems. The equivalent volume that is exceeded 1 per cent of the
time, read from such curves, is plotted as curve B of Fig. 6.

1.0

0.9
S 0.8

Q

UJ

^ r\-r
O 0.7

X

UJ

'n 0.6

UJ

i 0.5

_j
O
> 0.4

0.3

0.2

0.1

X

"N

\

\

V

\,

\

\

6^

\

s

\,

\

\

)

y

\

\

s.

\

16

\

\

\

^

\

\

A

\

\

1

n=, ^

\

\

\

\

\

s.

\

\

\

\

N,

\

\,

\

\

^

\

V

\

^

-22 -20

-18 -16 -14 -12 -10 -8 -6 -4 -2 0
EQUIVALENT VOLUME IN DECIBELS

10

Fig. 8 — Equivalent volume distributions for n active channels.

This curve gives, for any number of channels having uncontrolled
volumes, the equivalent volume which will be exceeded just 1 per cent
of the busy hour. To obtain the necessary load capacity, this must be
corrected for the multi-channel peak factor. In the controlled
volume case, for a given number iVof channels in the system, there was
no difficulty in deciding the value of n, the number of simultaneously
active channels, for which the multi-channel peak factor should be
taken. Now, however, there is no unique relation between equivalent
volume and the number w; in addition, the multi-channel peak factors
were measured with all n channels at the same volume, which repre-
sents a condition rarely holding on a system without volume control.
It is apparent, however, that in the majority of cases in which the
equivalent volume approaches values on curve B of Fig. 6, the number

642

BELL SYSTEM TECHNICAL JOURNAL

of simultaneously active channels will be greater than the average
number Nt of active channels. Since the multi-channel peak factor
decreases as n increases, the peak factors for n = Nt active channels
may be safely used. A more detailed analysis, feasible only for very
small systems but avoiding the use of this approximation, shows that
its effect is small and tends to give load capacities slightly higher
than actually required, but the difference diminishes rapidly as the
size of the system is increased.

For the uncontrolled volume condition, therefore, the multi-channel
peak factors are read from Fig. 5 for values of « = Nt. They are
added to the equivalent volumes obtained from curve B of Fig. 6, and

0.9

Q
LlJ

Q 0.8

UJ
UJ
O

X 0.7

LJ
(0

ui 0-6

3 0.5

O

>

>- 0.4

g 0.2
0.1

-.^

\

\

N.

)

i 240

\

\

>

\

\

\

V

\

^

\

\

N

\,

V

K'

N

N = 3

k,

\

1

k

V

\

\

^

k

\

*>^

-22 -20

-18

-16 -14 -12 -10 -8 -6 -4-2 0 2
EQUIVALENT VOLUME IN DECIBELS

Fig. 9 — Equivalent volume distributions for systems of N channels.

reduced to single frequency power as previously described for the
volume controlled case. Curve B of Fig. 7 is obtained in this manner
and shows the load capacity required in an amplifier for an iV-channel
system in which the volumes of each channel are distributed in accord-
ance with curve A of Fig. 1. The load capacity which is approached
asymptotically as N increases indefinitely is represented by curve D
of Fig. 7.

The load capacities given by Fig. 7 are valid only for systems for
which the basic single-channel data apply. As these may not hold in
specific cases, and may be subject to modification in the future,
estimates of the effects of small changes in these data are useful.
These effects cannot be described simply for moderate numbers of

LOAD RATING THEORY 643

channels but for large numbers of channels the effects are readily
estimated from the change in the location of the asymptote shown on
Fig. 7. The equation of this asymptote is as follows:

L = 10 logio iVr + (Fo + .115(72) + MPF -K Po - 3 db,

where L = test tone load capacity,

MPF = asymptotic multi-channel peak factor,

Po = long average power of a reference volume talker in db
above .001 watt.

The other quantities are as defined before.

Peak Voltage Limiting

The curves referred to in the preceding discussion have so far
neglected the effects of peak voltage limiting in the transmitters and in
the channel terminal equipment. Fundamentally, the effect of such
limiting is to modify the distribution of instantaneous voltages in the
individual channels. The extent of the modification, however, de-
pends on the volume. For single-channel systems it is obvious that
the improvement in load capacity due to limiting will be substantially
equal to the reduction in the maximum peak voltage. For a large
number of channels the improvement will approach the reduction in
the rms voltage per channel. An approximate method of accounting
for these complicated reactions is to consider that peak voltage limiting
modifies the upper end of the single-channel volume distribution.
Strictly the amount of such modification is a function of the number
of channels as well as of the characteristics of the limiters. Curve B
of Fig. 1 represents a compromise between the dififerent effects which
is believed to give reasonably accurate results for both small and large
numbers of channels for the limiting characteristic of present terminals.

With the talker volume distribution modified in accordance with
curve B of Fig. 1, computations of the load capacity with voltage limit-
ing present may be made in a manner identical with that previously
described. Curve C of Fig. 7 shows the results obtained for this
amount of limiting.

All of the load capacity curves of Fig. 7 are based on the equivalent
volume which would be exceeded 1 per cent of the time, irrespective
of the number of channels in the system. Where voltage limiting
is used, it appears reasonable to consider this percentage as fixed
because the action of the limiters serves to restrict the range of
voltages above the overload point, thus reducing the severity of any
overloading effects. When there is no limiting, and particularly

644 BELL SYSTEM TECHNICAL JOURNAL

for a small number of channels, the range of overloading voltage is not
so restricted and overloading effects may become undesirably severe
during the 1 per cent of time when the overload voltage is exceeded.
If voltage limiting is not provided in some form, it may be important
to reduce the percentage of time during which overloading may occur
for small numbers of channels. This is a matter to be determined
by experience and, if necessary, would require modification of curve B
of Fig. 7 in the direction of requiring more load capacity for a small
number of channels, thus increasing the spread between curves B and C.

Operating Margins, etc.

The curves which have been given for output capacity versus
number of channels apply to a single amplifier, or to a system in which
all amplifiers are identical and work at the same output level without
appreciable impairment of overall performance. In practice, the
number of amplifiers in tandem in a long system may be very large and
problems of equalization and regulation may make it difficult to
maintain exactly the same level conditions at all amplifiers. In addi-
tion, aging of tubes, and other effects will introduce some impairment.
It is important, therefore, to allow a margin for these effects in the
design of an amplifier for a multi-channel system. The proper margin
is essentially a matter of system design and it is often economical to
build a liberal margin into the amplifiers in order to allow greater
latitude and economy in the design of equalizing and regulating
arrangements.

In addition to the speech loads, there are also impressed on the
amplifiers various signaling and pilot frequencies, carrier leaks, etc.
It is not always possible in practice to make these negligibly small and
the load capacity requirements must be corrected to allow for their
presence. Multi-channel telephone systems are also required to
transmit other types of communication circuits, such as program
channels and voice-frequency telegraph systems, superposed on one
or more telephone channels. Modifications of the methods applied
to speech loads may readily be made to determine the effect of these
on the amplifier load capacity.

Acknowledgment

Many members of the Bell Telephone Laboratories, in addition to
those mentioned in the text, have contributed to various phases of this
work. The authors take this opportunity to acknowledge their
indebtedness to these colleagues, and in particular to Dr. G. R. Stibitz,
who first developed the theoretical approach here used.

The Quantum Physics of Solids, I
The Energies of Electrons in Crystals

By W. SHOCKLEY

It is proposed to make this paper the first of a series of three
dealing with the quantum physics of solids. This one will
be concerned with the quantum states of electrons in crystals.
The discussion will commence with an introductory section devoted
to the failure of classical physics to account for phenomena of an
atomic scale. Next, the quantum theory of electrons in atoms
will be discussed, together with the resultant explanation of the
structure of the periodic table; this is designed to illustrate the
meaning of various quantum mechanical ideas which are important
in understanding solids. Furthermore, much of the detailed in-
formation about atomic quantum states of particular atoms will
be needed in the later discussion of the properties of certain solids.
As an introduction to the modification of the quantum states oc-
curring when atoms are put together to form a crystal, a short
section will be devoted to structure of diatomic molecules. The
next section will be concerned with quantum states for electrons
in crystals. Whereas in an atom there are a series of isolated
energies possible for an electron (corresponding to the various
quantum states), in a crystal there are bands of allowed energies.
This concept of energy bands is essential to the theory of crystals
in much the same way that the concept of energy levels is essential
to that of atoms. In terms of energy bands, the energy holding
crystals together can be interpreted on a common basis for a wide
variety of crystal types. This will be followed by a brief descrip-
tion of various crystal types and by a discussion of thermal proper-
ties in which the smallness of the electronic specific heat will be
shown. The last section will be devoted to a discussion of para
and ferromagnetism on the basis of the energy band picture.

In the second paper, problems connected with electric currents
and the motion of electrons through crystals will be discussed.
This leads to the concept of the Brillouin zone which is complemen-
tary to that of the energy band, the two together forming the
basis for discussing the quantum states of electrons in crystals.
The third paper of the series will contain a comparison between
theory and experiment for the alkali metals, the principal emphasis
being placed upon the physical picture of the state of affairs in
these simple metals.

Introduction

^'' I '^HE parts of all homogeneal hard Bodies which fully touch one

-■- another, stick together very strongly . . . I . . . infer from

their Cohesion, that their Particles attract one another by some Force,

which in immediate Contact is exceeding strong, at small distances

645

646 BELL SYSTEM TECHNICAL JOURNAL

performs the chymical Operations above mention 'd, and reaches not
far from the Particles with any sensible Effect. . . . There are there-
fore Agents in Nature able to make the Particles of Bodies stick to-
gether by very strong Attractions. And it is the Business of experi-
mental Philosophy to find them out." But it was not destined for
experimental philosophy to finish the business which Sir Isaac Newton
set for it in the above words i until two centuries had elapsed. Only
since the advent of quantum mechanics have scientists had laws
capable of explaining the cohesive forces of solid bodies and predicting
their numerical magnitudes. The new laws were developed first in
order to explain the behaviors of independently acting atoms but, as
we shall see, they are laws capable of extension to systems containing
large numbers of atoms and thus to solid bodies. The fact that a
solid body remains a solid body, resists being pulled apart, and exerts
the cohesive forces of which Newton wrote, is explained by showing
from theory that atoms packed together in a solid are in a state of low
energy, and to change the state requires the expenditure of work. In
this paper we shall describe how the quantum mechanical concepts
developed for isolated atoms are applied to interacting atoms and lead
to methods of calculating the energies and forces binding atoms to-
gether in crystals.

A crystal is a regular array of atoms. The regularity of this atomic
array is frequently exhibited in the macroscopic appearance of the
crystal. A crystal of potassium chloride — sylvine — is a good ex-
ample (Fig. lA). The natural growth faces of the crystal are parallel
to planes passing through the atoms, which are arranged in the micro-
scopic array pictured in Fig. IB. It is evident that the microscopic
arrangement of the atoms in the crystal is one of its most basic features.
In sylvine the atoms are arranged on the corners of cubes in an alter-
nating fashion. The arrangement of the atoms in the crystal is called
a "lattice." Sodium chloride— rock salt — has the same arrangement
as sylvine and the type lattice pictured in Fig. IB is known as a "sodium
chloride lattice." The distance between atoms in a given lattice is
specified by giving the value of the "lattice constant," which for a cubic
crystal is defined as the distance between like atoms along a line
parallel to a cube edge. Lattice constants are usually expressed in
angstroms; 1 angstrom = lA = 10~^ cm. The lattice constant of
sylvine, designated by "a" in Fig. IB, is 6.28A. Figure IC suggests
how a large number of atoms, arranged as in Fig. IB, produce the
shape of the crystal photographed for Fig. lA. Studies of the direc-
tions of the natural growth faces and cleavage faces of crystals are

1 "Opticks" 3rd ed., 1721, p. 363.

THE QUANTUM PHYSICS OF SOLIDS

647

Fig. 1 — Crystal structure.

A. Macroscopic appearance of a crystal; retouched photograph of a sylvine crystal.

B. Microscopic arrangement of atoms in crystal showing natural planes.

C. Large number of atoms arranged as in B to show formation of A.

648 BELL SYSTEM TECHNICAL JOURNAL

primarily of importance as an aid in classifying and identifying min-
erals; and although they do give some information about the arrange-
ment of the atoms in planes within the crystal, the information is
too meager to permit a determination of the microscopic structure.
The latter can be deduced by the methods of x-ray diffraction. X-rays
are light waves of very short wave-length and they are diffracted from
crystals in much the same way as light is diffracted from a ruled grating.
From studies of x-ray diffraction patterns, the arrangements of atoms
in a large number of crystals have been determined. Exceedingly
strong forces act to hold the atoms in these arrangements and, by appli-
cation of the laws of quantum mechanics, we shall try to find them out.

There is now no question that the elementary building blocks of
the material world are primarily electrical and of two sorts.^ The
negative particles, electrons, are all alike and have the same charge
— e and the same mass m\ the positive particles, atomic nuclei, are
not all alike and may differ in charge and mass from one another.
The positive charge is always some integral multiple, Z, of the funda-
mental charge e and we shall not be concerned with the mass except
to say that it varies upwards from about 2,000 times the electron mass.
An atom of a chemical element consists of one nucleus surrounded by
enough electrons to neutralize its charge ; all atoms of a given chemical
element have the same nuclear charge, Z, which is appropriately
known as the "atomic number"; atoms having the same nuclear
charge but different masses are called "isotopes"; their chemical be-
haviors are slightly different, so that it is possible by chemical processes
to separate one isotope of a chemical element from the others, but this
difference is so slight that we can neglect it here. An atom, then,
consists of a number of electrons circulating about and attracted by
the nucleus, which, by virtue of its relatively great mass, is effectively
an immobile center for their motions. A simple molecule consists of
an assemblage of a few such atomic systems and a crystal of an
immense number. The fundamental problem of atomic mechanics —
which is now solved quite satisfactorily but not yet perfectly— is to
find the laws governing the motion of these particles.

The necessity of finding such laws is made most apparent by con-
sidering the failure of the older laws of "classical mechanics," Newton's
laws. These laws were satisfactory for dealing with large bodies —
but not perfect; for, as is well known, they are approximations to the
more adequate laws of relativity — and they were successfully applied

" Since we are here concerned with problems of a chemical nature, we may disre-
gard those particles such as positrons, mesotrons, neutrons, etc., which are concerned
with cosmic rays and nuclear processes but not with ordinary atomic behavior.

THE QUANTUM PHYSICS OF SOLIDS 649

even to single atoms so long as no attempt was made to investigate
the internal structure of the atom. Considering the atom to be a
perfectly elastic miniature billiard ball having size, mass, and velocity
but no internal properties, classical mechanics was able to handle in a
statistical fashion the dynamics of large systems of atoms in a gaseous
form and to deduce a number of valid conclusions concerning the
specific heat, gas laws, viscosity, and diffusion constants of gases.
On the other hand, failure attended all endeavors to apply these laws
to the swarm of electrons surrounding a nucleus. A system of this
sort is unstable classically and can never come to thermal equilibrium.
Applying the classical laws of statistical mechanics, one finds that
some of the electrons will move very close to the nucleus, the energy
lost in this process being acquired by other electrons which move farther
out. According to classical mechanics this process will continue with-
out ever reaching equilibrium and during it the atom will be thoroughly
torn apart.

Another difficulty in the classical theory arises from the electro-
dynamics of an accelerated electron. An electron moving in the field
of a nucleus is accelerated, and classical electromagnetic theory pre-
dicts that under these circumstances electromagnetic energy will be
radiated — the atom being in effect a microscopic radio transmitting
station in which the charging currents in the antenna are represented
by the motions of the electrons. According to this theory an atomic
system would continually radiate energy, and it could be proved that
no equilibrium like that actually observed between matter and radia-
tion would ever be achieved.

Thus, classical mechanics and electromagnetics were incapable of
taking the electrons and nuclei as building blocks and constructing
solids or even atoms from them. To put it bluntly, the classical laws
were wrong; although adequate for large-scale phenomena, they were
inapplicable to phenomena of an atomic scale.

Nevertheless, modified applications of the classical theory had a great
number of successes in the atomic theory of solids. Dealing with the
atoms as elastic idealized billiard balls led to the correct value for the
specific heat of solids, at least at normal temperatures, and the electron
theory of conduction in metals was in many respects quite successful.
None of the successes of the conduction theory were completely
satisfying, however, because the assumptions needed to explain one
set of facts were incompatible with other sets of facts and the whole
field was greatly lacking in unity. According to this classical theory
a metal contained free electrons which could move under the influence
of an electric field and thus conduct a current. Their motion was

650 BELL SYSTEM TECHNICAL JOURNAL

impeded by collision with the atoms (ions, really, since they are atoms
which have given up free electrons) according to some theories, and with
the spaces between atoms according to other theories, and this im-
peding process gave rise to electrical resistance. The free electrons
were capable of conducting thermal as well " as electrical currents.
Although the theory gave reasonable values for the electrical and
thermal conductivities of metals at room temperature, the predicted
dependence upon temperature was wrong: the resistance of a pure
metal is known from experiment to be very nearly proportional to
the absolute temperature; the classical theory, unless aided by very
unnatural assumptions, predicted proportionality to the square root
of the absolute temperature. Another difficulty, the greatest in fact
which beset the old theory of free electrons in metals, was concerned
with the specific heats of metals. According to the billiard ball
theory of gases, the specific heat arose from the kinetic energy of
motion of the gas atoms; thus the specific heat at constant volume of
one gram atom of a monatomic gas was (3/2)R, where R is the gas
constant. This was in good agreement with experiment. For solids
this specific heat was just doubled, giving {6/2)R because of the
addition of potential energy to the kinetic. For a metal the free
electrons were regarded as having kinetic energy. In order to explain
the observed electrical properties of a metal, the number of electrons
was taken as approximately equal to the number of atoms. Hence,
as for a monatomic gas, a specific heat of {S/2)R was expected for the
electron gas and, therefore, a specific heat of (9/2) i? was predicted for
a metal. Measurement shows that most crystals, metals included, fit
quite well the value of (6/2)i? and that (9/2)i? is incorrect. Thus
classical theory was left with the dilemma that to explain electrical
properties one free electron per atom was needed while to explain
specific heat one free electron per atom was far too many. This di-
lemma is very neatly resolved in the new theory; in this paper we
shall show why the free electrons are not free for specific heat and in
a later paper why they are free for conduction. We shall also show
that the new theory leads to quite proper values for the conductivity
and also explains facts concerning the resistance of alloys, which the
classical theory could not do.

According to the classical theory there was one quantity that should
be the same for all metals and this was the ratio of the thermal to the
electrical conductivities. This ratio, known as the Wiedemann-Franz
ratio, was predicted to be equal to the absolute temperature times a
universal constant L called the Lorentz number. This prediction
was in reasonable agreement with experiment. The new wave me-

THE QUANTUM PHYSICS OF SOLIDS 651

chanical theory predicts the same result, but with a slightly dififerent
value for L. According to the old theory L = Ik^/e"^ = 1.44 X 10~^
volts'/degree^ where k is Boltzmann's constant, while the new gives
L = Tr^P/3e^ = 2.45 X 10~^ voltsVdegree^, and the experimental values
for several elements are Cu 2.23, Ag 2.31, Au 2.35, Mo 2.61, W 3.04,
Fe 2.47 — all times 10"^ volts'/degree^. We see that the constancy
of the Lorentz number predicted by both theories is in reasonable
agreement with experiment, but that in predicting the numerical
value of the constant the new theory is better than the old.

The fundamental problem of how the electrons and nuclei form
stable atoms and crystals was, as we have said above, inexplicable on
the older theory. The newer quantum mechanics of Bohr and later
that of Schroedinger, Heisenberg, and Dirac were needed. Bohr
postulated that out of the infinity of possible motions for the electrons
of an atom, only a certain restricted set was permitted. Each per-
mitted motion corresponded to a definite energy for the atomic system
as a whole. This concept of energy levels for the atom gave a natural
interpretation to nature of atomic spectra and explained the meaning of
the combination principle. In order to restrict the atomic motions to
certain energy levels, Bohr supposed that the laws of atomic dynamics
were such that only those modes of motion were permitted for which
certain dynamical quantities, called phase integrals, had values equal
to multiples of Planck's constant h. For the case of the hydrogen atom
these laws led to the now well-known Bohr orbits for the electron and
to energy levels which were in good agreement with experiment. For
atoms with more electrons it was very difficult to apply Bohr's laws
except in a very approximate and unsatisfactory way. However, two
very valuable concepts came from his theory which are preserved in the
newer wave mechanical theory. These were that the individual elec-
trons could be thought of as restricted to certain orbits and that these
orbits were specified by giving them certain quantum numbers. It
was found that three quantum numbers were needed to specify the
orbit. All atoms were found to have the same general scheme of
orbits. The number of electrons moving in these orbits varies from
atom to atom and for any given atom is equal to the atomic number Z.
In order to explain the facts of spectroscopy and the periodic table
of the elements, it was necessary to introduce a rule known as Pauli's
principle. This principle states simply that no more than two elec-
trons may occupy the same orbit in an atom; that is, no more than
two electrons of an atom may have the same three quantum numbers.
As we shall discuss in the next section, a complete specification of the
state of an electron in an atom requires four quantum numbers; two

652 BELL SYSTEM TECHNICAL JOURNAL

electrons in the same orbit have different values for their fourth quan-
tum number. We shall use the term "quantum state" to signify the
permitted behavior corresponding to specified values for the four
quantum numbers. In this language, Pauli's principle asserts simply
that no two electrons in a given atom can be simultaneously in the
same quantum state; that is, Pauli's principle is a quantum mechanical
analogue of the classical principle that two bodies cannot occupy the
same place at the same time. The two ideas — first that the motions
of the electrons are quantized so that only certain quantum states are
allowed, and second that in an atom only one electron can occupy a
given quantum state — form the basis of all quantum mechanical
thinking. We shall make use of them continually in the following
discussion. We shall use them, however, not in connection with the
orbits of Bohr but instead with the wave functions of Schroedinger.

The Bohr theory can be applied only with difficulty to any atom
but hydrogen. The difficulty lies in determining the motions of the
electrons in the complex interacting fields of the electrons and the
nucleus. This problem is even more difficult in the case of a solid
where there are many atoms, and it would seem hopeless to try to find
out why the electronic orbits in insulating crystals such as rock salt
or diamond do not permit electrons to move through the crystal and
carry a current, while the orbits in metals do. Indeed not only does
the Bohr theory have the foregoing disadvantage but it is probably
wrong. Fortunately there is a theory both sounder and easier to apply
embodied in the "wave equation of Schroedinger."

One feature, probably not sufficiently stressed, about Schroedinger's
equation is its relative convenience. The word "relative" must be
used here because it is usually very laborious to obtain solutions for the
equation and only in the simplest cases can we obtain exact solutions.
Compared to the classical equations and the equations of Bohr, how-
ever, it is convenient. Quite satisfactory approximate solutions can
be obtained for Schroedinger's equation even for the complex case of
solids, where it would be prohibitively difficult to obtain as good
solutions for the classical and Bohr equations.

Electrons in Atoms
According to the Schroedinger theory, a diff"erential equation can
be written down for any system consisting of electrons and atomic
nuclei. This equation contains an unknown wave function and an
unknown energy and the instructions of the theory are to solve the
equation for the unknown quantities. Furthermore, the wave func-
tion must satisfy a certain mathematical requirement which embodies

THE QUANTUM PHYSICS OF SOLIDS 653

in a generalized form the restrictions imposed by Pauli's principle.
As is too frequently the case in mathematical physics, it is much easier
to state the problem than to solve it; the solutions of Schroedinger's
equation are, in fact, so difficult to obtain that exact solutions have
been found for atomic systems only of the simplest type, namely those
consisting each of a single nucleus and a single electron. For this
case, the quantum states and their energies are all exactly known.
For other cases approximations of varying degrees of exactness must
be used. The difficulty arises from the interactions between the elec-
trons. If it were not for these interactions, one could obtain exact
solutions for atoms having many electrons. The difficulty is that the
interactions — they are merely electrostatic repulsions — prevent each
electron from being independently in a definite quantum state. The
interaction of each electron with another is in general small compared
to its interaction with the nucleus. To a first approximation, then,
the electrons are treated as not interacting and then corrections are
applied to this over-simplified picture. (In this first approximation,
the generalized mathematical statement of Pauli's principle reduces
to the one we gave in the last section — only one electron may occupy
a given quantum state.) As a result of this procedure of over-simplifi-
cation followed by corrections, our exposition will commence with a
discussion of the quantum states of an electron in an atom as if these
quantum states were private possessions of the electron and not influ-
enced or disturbed in any way by the other electrons. We shall then
correct this picture to some extent by considering how the energy of
a given electron depends upon the behavior of the other electrons.
One correction term which we shall introduce in this way is the impor-
tant "exchange energy" discussed below. Thus atomic theory repre-
sents a field of endeavor in which further progress is made largely by
improvements and refinements. It should be emphasized, however,
that the corrections and refinements are not additional assumptions,
which are added to the theory, but that they represent instead only
steps forward in improving the wave mechanical solutions.

The last paragraph mentions that an approximate treatment of
Schroedinger's equation leads to a set of possible quantum states
for an electron in the atom. We shall discuss Schroedinger's equa-
tion and the wave functions corresponding to the quantum states
in more detail later and at present be concerned only with a descrip-
tion of the results. In a neutral atom the electrons arrange them-
selves in the quantum states in such a way as to make the energy
of the atomic system a minimum. Consistent always with Pauli's

654 BELL SYSTEM TECHNICAL JOURNAL

principle, only one electron can occupy a particular quantum state.
When the atom is in the arrangement of lowest energy, we can say
that each electron has a definite energy corresponding to whichever
quantum state it occupies. This energy is most conveniently de-
fined in terms of the amount of work required to take an electron
from its state in the atom and put it in a standard state defined
as zero energy. An electron in the zero energy state is to be thought
of as at rest and so far removed from the atom that there is no energy
of interaction between them. In this way we can define the energy
of every occupied quantum state in the atom. Each of these ener-
gies must be taken as negative — since potential energy is yielded up
when the electron returns to the atom — and by definition represents
how tightly the electron is bound to the atom. One of the electrons
will be the most loosely bound (it may be that there are several with
the same energy) and the energy required to remove it is called the
"ionization energy." From our definition this is obviously the mini-
mum energy required to convert the atom to a positive ion. The
definition of the energy of a quantum state given above can be used
only when an electron is in the quantum state; we can, however,
define the energy of an unoccupied state conveniently in terms of the
energy the atom would have if the state were occupied by "exciting"
one of the electrons to this state by giving it the proper amount of
energy.^*

The Quantum States of the Atom

Using this definition of the energy of a quantum state, we find that
for all atoms the arrangement of quantum states in energy is as shown
in Fig. 2, where the ordinates represent energies and states of equal
energy appear as divisions of the horizontal lines. Figure 2 does not
indicate which states are normally occupied, nor could it unless we
knew how many electrons there were in the atom. The general scheme
of Fig. 2 is applicable, with certain changes discussed below in the
energy scales, to any neutral atom in its normal state, and the energy

'* This definition is subject to restrictions because the energy of an electron in
the state in question depends upon the arrangement of the other electrons in the
atom and this arrangement depends in turn upon which electron was excited to the
initially unoccupied state. In constructing the figures we have supposed that the
electron (or one of the electrons in case there are several) that is most easily removed
from the atom is caused to shift from its normal state to the unoccupied state in
question; this shift will change the state of the atom and since the atom was initially
supposed to be in the state of lowest energy, the change in energy cannot be negative
and will in general be positive but may in certain special cases be zero. The energy
of the unoccupied state is defined as the energy of the occupied state from which
the electron is taken plus the change of energy caused by shifting the electron. _ This
is equivalent to saying that the energy of the unoccupied state is the ionization
potential of the atom after an electron has been shifted from the highest state nor-
mally occupied to the normally unoccupied state in question.

THE QUANTUM PHYSICS OF SOLIDS

655

levels represented on Fig. 2 apply to unoccupied and occupied states
as well.

I have already mentioned that four quantum numbers are required
to specify each quantum state. These are indicated by the letters

1=3

1=2

1=1 1=0 1=0 1=1

1=2

1 = 3

4f

J— I 4d

III I.I 4p

3d ^^^

I I 1-

4f

4C| I I I I I 1 L

4p I I I I I I

^-^^ 3d
45 1 I I I |_j

3P

J l__l

2p

J I I

3P

I I I I

2P

1_J L

-2-1 0 I 2 = m

-spiN^ nns=-^

+ SPIN, ms= + 2

Fig. 2 — Quantum states for electrons in atoms.

w, /, m, and fUs- Roughly speaking, the "principal quantum number
w" fixes the "energy level" of the state; however, there is some de-
pendence upon the "angular momentum quantum number /." The
dependence of energy upon the third quantum number, "the magnetic
quantum number m," is slight and will be neglected in this paper.
We shall consider the energy to be specified by giving n and /. A
notation borrowed from spectroscopy is applied to this pair of quantum
numbers and one uses the apparently quite fortuitous choice of
letters s, p, d, f, g, h, etc., to stand for / = 0, 1, 2, 3, 4, 5, etc., and a
state with n = 3 and / = 2 is known as a "3d state" and an electron
occupying such a state is called a "3d electron." The quantum laws
permit the following values for n, I, and m:

n takes on all positive integral values. (All states with n greater
than four have been omitted from the figure; they lie between
the highest states shown and zero energy.)

656 BELL SYSTEM TECHNICAL JOURNAL

For a given n, I takes on all positive integer values from 0 to « — 1

inclusive.
For a given n and /, m takes on all integer values including zero

from — / to + / inclusive.

The difference between right and left sides of the figure corresponds
to the fourth quantum number: an electron, in addition to its electric
charge, possesses angular momentum or "spin" about its axis. The
rotating charge resulting from this angular momentum produces a
magnetic moment. The angular momentum is quantized and there
are two possible values + 1/2 and — 1/2 for the "spin quantum
number Ws," corresponding to the right and left halves of Fig. 2.
Electrons occupying states on the right half of Fig. 2 have their spins
parallel to each other and directly opposite to electrons occupying
states on the left half. As already implied, the quantum numbers /
and m also correspond to angular momentum and magnetic moments
for the electron "orbits" (really wave functions) in the atom.^

For our purpose we need two results of the theory of the spinning
electron, first that its spin introduces a duplicity of quantum stales
as indicated by the two halves of Fig. 2, and second that all the elec-
trons of one spin have their magnetic moments parallel and opposite to
those of the other spin. Later when we consider the question of mag-
netism, we shall be concerned with the direction in space of the spin
vector and the magnetic moment, but not now.

Several units of energy are employed in describing atomic processes.
The simplest of these is the electron volt; it is the energy acquired or
lost by an electron in traversing a potential difference of one volt.
For example, in a vacuum tube operating with one hundred volts
between cathode and plate, the electrons strike the plate with a kinetic
energy of one hundred electron volts, 100 ev. Another unit is the
ionization potential of hydrogen, and as hydrogen has only one elec-
tron, which normally occupies the \s state, this is also the energy of
the Is state. This energy is called the "atomic unit" of energy or the
"Rydberg." Another unit of energy useful in chemical processes is
the kilogram calorie per gram atom; this is related to the others as
follows: if the energy of each atom in one gram atom is increased by
one electron volt then the energy of the whole system is increased by
23.05 kilogram calories. The conversion factors are: 1 Ry = 13.5 ev,
1 ev per atom = 23.05 Kg.-cal./gm. atom.

' For a discussion of the quantum states of the electrons from the point of view of
angular momentum see "Spinning Atoms and Spinning Electrons" by K. K. Darrow,
Bell System Technical Journal, XVI, p. 319, or standard texts on spectroscopy.

THE QUANTUM PHYSICS OF SOLIDS

657

Variation of the Energy Levels with Atomic Number
All atoms have the same general scheme of quantum states indicated
in Fig. 2. Quantitatively the energy scale varies from atom to atom.
Thus the Is state lies at — 13.5 ev for hydrogen and at — 24 ev for
helium. This decrease (i.e., becoming more negative or moving lower
down on Fig. 2) is due to the increase in nuclear charge, Z = 1 for
hydrogen and 2 for helium, which results in greater attraction and
tighter binding for electrons in helium. This steady downward motion
of the levels continues as one goes from element to element in the
periodic table. However, the ionization potential, the energy required
to remove the most easily removed electron, does not steadily increase.
In Fig. 3 we show the ionization potentials of the first twenty elements.

ATOMIC NUMBER
Fig. 3 — Ionization potential versus atomic number.

Since we are interested in the energies of electrons rather than in
ionization per se, the ionization potentials have been plotted as nega-
tive giving in this way the energies of the states in the atom. The
main features of this figure can be explained by using Fig. 2 and the
Pauli principle.

The Pauli principle, also known as the exclusion principle, permits
only one electron to occupy each of the states of Fig. 2. The electrons
in a many-electron atom will tend to go to the states of lowest energy.

658 BELL SYSTEM TECHNICAL JOURNAL

Thus in helium, since its two electrons can have oppositely directed
spins, each fills one of the \s states; we say the " electron configuration "
of helium is Is^ (read as "one ess squared"). For lithium, Z = Z, the
third electron, which cannot go to the completely filled Is states,
goes to the next highest, 25, giving Xs^ 2s. In going from helium to
lithium, all the states move to lower energies but not so much lower
as to make 25 for lithium as low as Is for helium. For this reason
lithium can be relatively easily ionized, as is seen in Fig. 3.

Before continuing the discussion of particular atoms, we must point
out that two changes accompany each advance from one element to the
next in the periodic table. In each step the nuclear charge increases
by one plus unit and at the same time an electron is added to the
atom and the combined effects produce the results of Fig. 2. Quite
different results are obtained if one electron alone is added to the
atom. Then instead of the general falling of the levels which accom-
panies the double change, there is a general rising of all the levels.
This is due to the unbalanced negative charge on the added elec-
tron, whose presence on the atom raises the potential energy of all
the electrons and therefore raises their energy levels. For some atoms,
the raising of the energy levels produced by an unbalanced electron
may be so great that the electron is not bound at all or at least only
very slightly, and for these atoms negative ions do not form. On the
other hand, when an electron is removed from an atom all the remain-
ing electrons become more tightly bound and the energy levels are
lowered.

Exchange Energy

In Fig. 4 we show the electron configurations for the elements from
lithium to neon. The decrease in ionization potential in going from
beryllium to boron is due to the completed filling of the 25 states and
the consequent start of filling of the 2p states. The decrease in going
from nitrogen to oxygen suggests that not only do the 25 and 2p states
lie at different levels but that the 2p states themselves lie at two
different levels. This is true but in a rather special sense : the difference
in energy between the two sets of 2p states depends upon how they are
occupied. This difference is an "exchange energy." We shall discuss
the origin of the exchange effect in the next paragraph but one; how-
ever, the aspect of it needed for this paper is illustrated in Fig. 4.
We there imagine that the quantum states are represented by little
trays upon which are placed weights to represent occupancy by elec-
trons. The exchange effect corresponds to hanging the trays on
springs; in this way we see that as the electrons fill up the 2p states

THE QUANTUM PHYSICS OF SOLIDS

659

with one spin (the same effect occurs for either spin; the figure shows
+ spin), these states are depressed in respect to the 2p states with
the other spin. The springs must, however, be considered to pull the

2P

2S 2S

?P

NITROGEN
1S2 2S2 2p3

.ii

lAi

lAi iAj

BERYLLIUM

OXYGEN
1S2 2S2 2P'*

lAi lA,

^2 p<i2

IS*: 2S'= 2p

FLUORINE
1 S2 2S2 2p^

CARBON
IS2 2S2 2p2

iL Lil

NEON
ls2 2S2 2p6

Fig. 4 — Electron configurations illustrating the exchange effect.

trays up against stops with a force such that a single weight upon a
tray will produce no lowering whereas two or three weights will. This
effect seems contradictory to the simple idea that adding electrons
raises the potential energy and the energy levels; however, it must be
remembered that we are here discussing neutral atoms and that with
each added electron there is also an added plus charge on the nucleus.
These two charges produce the dominant variation in the energy levels
and upon this variation the exchange effect is superimposed.

The reader may verify that so far as the distribution of electrons
in the 2p states is concerned, the exchange effect will lead to the con-
figurations shown in Fig. 4 for the states of lowest energy for the atoms.
Let us consider carbon for example; if the electrons have opposite
spins — that is, if there is one weight on each 2p tray — there will be
no lowering due to the exchange effect; if the electrons have the same
spin, however, then each loses energy because of exchange and the
energy of the atom is less than for the case of parallel spins. The
fact that one electron is not enough and that two or more electrons
are required to produce the exchange effect is a natural consequence
of the origin of the exchange energy.

The exchange energy is due to the electrostatic repulsion between
the electrons and results directly from the application of Pauli's prin-
ciple to Schroedinger's equation. The exchange effect emerges in a
quite straightforward fashion from a consideration of wave functions,
but usually no attempt is made to explain it in non-mathematical

660 BELL SYSTEM TECHNICAL JOURNAL

terms. It seems to the writer, however, that the explanation given
below does contain the mathematical essence in physical language.^*
Pauli's principle, we have said, is the quantum mechanical analogue
for electrons of the classical law that two bodies may not occupy the
same place at the same time; it is, however, more general in the sense
that it does not apply alone to location but rather to a combination of
location and velocity and spin, and it requires that any two electrons
differ essentially in one or more of these. Now a difference in the
values for the spin quantum numbers of two electrons is a sufficiently
great difference to permit them to have the same velocity and the
same location (i.e., be very near together compared to atomic dimen-
sions). If the spin quantum numbers are the same, however, there
must be a difference in location or in velocity. Now two electrons
having the same values of n and /, as for example two 2p electrons,
move in similar orbits and have much the same velocities; hence, if
their spins are the same they must differ in location — that is, they will
satisfy Pauli's principle by keeping away from each other. If, how-
ever, their spins are different, then they need not keep away from each
other, and in their motion about the nucleus they are, on the average,
closer together than for the case of the same spin. Since the energy
of repulsion between the two electrons decreases as they move farther
apart, the average energy of the electrons is less for the case of parallel
spins, for which Pauli's principle requires most difference in location;
and this is just the effect shown in Fig. 4. Furthermore, if the elec-
trons differ in their values of n and /, then their velocities are quite
different and the restriction upon location is not so important and
their electrostatic energy of repulsion for parallel spins is nearly the
same as for opposite spins. There is, however, a small exchange effect
between electrons of different n and / values as may be appreciated
in Fig. 4 for boron, for example, by noting that one 2s level i de-
pressed compared to the other owing to the presence of the 2p electron.
We see that helium and neon correspond to electron configurations
which fill all the levels below w = 2 and w = 3 respectively. One
sometimes refers to the states with w = 1 as the K shell, and to those
with w = 2, 3, 4, etc. as L, M, N, etc., shells. The rare gases helium
and neon then correspond to electron configurations consisting of
"closed shells "^ — that is, to shells all of whose states are occupied.

3a As the aspects of exchange energy needed for the exposition are those discussed
above in connection with Fig. 4, this explanation is not essential to the later argu-
ment of this article and is given in the hope that it may invest the concept of ex-
change energy with the appearance of a little more physical reality. If it fails in
this, the reader is requested to disregard it.

THE QUANTUM PHYSICS OF SOLIDS
The Periodic Table

661

The elements from lithium to neon constitute the first short period
of the periodic table, Fig. 5. The second short period, running from
sodium to argon, is built up in a similar way by filling the 3s and 3p

I H j He ]

TlL Be|B

1-1 Ate

I s

Na Mgj Al SI

O f^Ne]

2S,2P

3S,3p

/

/

/'

K ca I sc Ti V

19 20 ] 21 22 23
I '-' -n -n

CO

<o

Cr Mn Fe Co NliCu Zn|Ga Ge As Se B

24 25 26 27 28 I 29 30 I 31 32 33 34 35

lO >fi <o >"- CO o^ "2^^ ! o fy fO ^ ^

-o -o "D -D -o-^J^I,, Q. Q. a. Q.

in <^ <r) in \ m '^ \ '" <n in <n <n
Fig. 5 — First part of the periodic table.

r1 Kr

I 36

4S,3d,4p

levels. Some of the chemical properties of the elements of these
periods are quite easily understood in terms of the electron con-
figurations of the atoms. An atom of lithium or of sodium has one
easily removed electron and thus can become a positively charged ion ;
only one electron, however, can be so easily removed, and for this
reason sodium and lithium do not have doubly charged positive ions
in chemistry and are, therefore, monovalent positive elements. Simi-
larly beryllium and magnesium have two easily removable electrons,
and are divalent; however, their electrons are harder to remove than
those of the alkali metals; hence the alkaline earth metals, beryllium and
magnesium, are not so electropositive as the alkalis.* The halogens,
fluorine and chlorine, present a contrasting picture. Instead of having
one loosely bound electron, they have one low-lying empty state.
They can therefore hold tightly an extra electron, and thus be negative
ions. The rare or noble gas elements helium, neon and argon consist
only of closed shells. They can neither gain nor lose electrons in
chemical compounds and are, therefore, generally aloof to chemical
urges.

* For brevity we shall refer to the alkali metals and alkaline earth metals simply as
alkalis and alkaline earths.

662

BELL SYSTEM TECHNICAL JOURNAL

The Transition Elements

Actually argon does not correspond to a complete system of closed
shells, since for it none of the M states in the M shell is occupied. For
the elements below copper, Z = 29, these 2>d levels lie above the 45
and below the 4/>. They are filled up progressively in the series of
elements scandium, titanium, vanadium, chromium, manganese, iron,
cobalt, and nickel, which are known as the transition elements of the
first long period of the periodic table. The first two elements after
argon are potassium (an alkali) and calcium (an alkaline earth); these
are similar to sodium and magnesium in having respectively one and
two 5 electrons. The first transition element, scandium, however, is
not like beryllium or aluminum, for with it the filling of the M states
begins. The electron configurations for several of the transition ele-
ments are shown in Fig. 6. An interesting case occurs at chromium;

1-

CALCIUM

4S2

3d

4S 4S

3d

-

SCANDIUM 3d 4S2

III'''

ill ±

CHROMIUM 3d^4S

JL.

MANGANESE 3d^4s2

-4

-8

-1?

NICKEL 3d®4s2

AiLL ±, ^

COPPER 3d'°4S

Fig. 6 — Electron configurations for transition elements.

for it the exchange effect is so great that the 3>d levels drop below the
4^ and one 45 electron is transferred. Since there is an exchange
effect between all electrons of the same spin, the remaining occupied
45 state in chromium has the same spin as the occupied M states. A
similar transfer of a 45 electron occurs at copper, which is then left
with one 45 electron and tends therefore to be monovalent (in the
divalent copper ion the 45 electron and one M electron are removed).
These transition elements are of particular interest because three of
them, iron, nickel, and cobalt, are ferromagnetic in the solid. The
atoms themselves are magnetic, as may readily be seen for chromium,
for example; in it all the electrons have their spins parallel and hence
their magnetic moments add to give a free chromium atom a magnetic

THE QUANTUM PHYSICS OF SOLIDS 663

moment six times as large as the spin magnetic moment of the electron.^
The same exchange effect which causes the Zd quantum states to fill
unevenly in the isolated atom causes, in the case of the metal, an
uneven filling of the "energy bands" which arise from these Zd states.
We shall return to this topic in the section on ferromagnetism.

Solving Schroedinge/ s Equation

The possible quantum states of an atom are obtained by solving
Schroedinger's equation for an electron moving in the potential field
of the nucleus and the other electrons. In Fig. la we have represented
the potential energy of an electron in an atom. If this potential
energy (call it U) is known as a function of the position x, y, z, of the
electron, then the Schroedinger equation is

^. + ^.+ a^ + -^(£- W = 0, (1)

where m is the mass of the electron, h is Planck's constant and £ is
an unknown energy and 4^ an unknown wave function, for which a
physical interpretation will shortly be given. It is found that this
equation possesses proper solutions only for certain values of E\ once
these values are known, the equation can be solved for the unknown
wave functions. The fact that only certain values of E are possible
will probably seem more natural after reading the discussion given
below of a mechanical system. The permitted energies and wave
functions give the system of quantum states of Fig. 2,

The wave equation of Schroedinger is similar in form to many of the
other wave equations of mathematical physics. In Fig. 1g to 1j we
represent a stretched membrane like a rectangular drumhead. If the
mass per unit area of the membrane is o- and the surface tension is T,
then the wave equation for it is

5^2 + ai2 +-7-^-0. (2)

where / is the unknown frequency of vibration and ^ is the unknown
vertical displacement. Applied to the membrane, this equation has
solutions only for certain values of/; the standing wave patterns corre-
sponding to the four lowest frequencies are shown in Figs. 7g to 7j.

^ For transition elements other than chromium, the motions of the electrons in
their wave functions produce magnetic moments that must be considered as well as
the spin; for a discussion of this point the reader is again referred to "Spinning Atoms
and Spinning Electrons" by K. K. Darrow, Bell System Technical Journal, XVI, p.
319 and to texts on atomic physics.

664

BELL SYSTEM TECHNICAL JOURNAL

The type of vibration of the system in one of these patterns is called
"a normal mode." The patterns are described by two "quantum
numbers" p and g which are equal to one plus the number of nodal
lines (indicated by arrows) running across the membrane from front
to back and from right to left respectively. In Figs. 7b and 7c we
show the wave patterns corresponding to the Is and 25 states of the
atom; the quantum numbers of the V' waves are also correlated to
nodes. In the case of the membrane the frequencies and standing

Fig. 7 — The atom and some mechanical and electrical analogues.

(a) Potential energy of an electron in the atom.

(b) The Is wave function.

(c) The 2s wave function.

(d) A mechanical analogue and

(e) its normal mode of vibration.

(f) An electrical analogue.

(g) to (j) The first four normal modes of vibration of a stretched

drum head. (From "Vibration and Sound" by P. M.
Morse, McGraw-Hill, New York, 1937. Courtesy of the
McGraw-Hill Book Co.)

THE QUANTUM PHYSICS OF SOLIDS

665

wave patterns are determined not only by the values of mass per unit
area, a, and tension, T, of the membrane but also by the "boundary
condition" that it be clamped on its rectangular edge; at this edge the
vertical displacement <p must vanish. The corresponding boundary
condition for the atom is that the wave function \l/ vanish at all points
infinitelv far from the nucleus.

Fig. 8 — The electron charge densities for four wave functions. Cross-sections
are given for the \s and 25 wave functions and perspective views for the 2p. Is rep-
resents a ball of charge; 2^, a ball surrounded by a shell; 2p m = 0, a dumbbell-like
distribution; 2p m = ± 1, a doughnut-like distribution seen edgewise. '

The quantity [t^I^ has a direct physical interpretation: its value
at any point in space gives the probability of finding the electron at
that point. If it were possible to take a photograph of the electron's
motion with a time exposure so long that a true average of its positions
would be obtained, this photograph would represent \^\-. In Fig. 8

666 BELL SYSTEM TECHNICAL JOURNAL

we show the predicted patterns as obtained by H. E. White,® who
photographed a model representing the wave functions. We see that
for the 25 wave function the electron is much farther from the nucleus
on the average than for the I5; this accounts for higher energy of the
25 state. For a hydrogen atom the 25 and 2p actually have the same
energy. For other elements the 25 lies lower as shown in Fig. 2; this
is because an electron in the 25 state penetrates the K shell and feels
the full charge of the nucleus whereas an electron in the 2p state stays
outside of the K shell and is thus shielded from the nucleus by the two
electrons of the K shell.

For purposes of illustration we have considered the rectangular
drumhead as a mechanical analogue for the wave equation. Other
analogues are represented by sound waves in rooms and in organ pipes
and by standing electromagnetic waves in wave guides, tuned cavities,
and rhumbatron oscillators. We shall use two simple analogues in our
later discussion. One is the mechanical vibrator represented in Fig. Id
which we consider to be restricted to vertical motion. It is a system
with a single frequency — like an imaginary atom with only one possible
state — and its one normal mode of vibration is a simple harmonic
motion up and down equally far above and below its equilibrium posi-
tion as indicated in Fig. 7e. The other is an electrical analogue, Fig. 7/,
consisting of a section of transmission line terminated at each end by a
high inductance. This system has a series of normal modes of vibra-
tion and a related series of allowed frequencies. The allowed fre-
quencies correspond to the energy levels of the atom.

Electrons in Molecules
We shall next consider what happens when two atoms are brought
so close together that their quantum states "interact." Two similar
atoms widely separated have each a distinct set of quantum states and
wave functions and the scheme of energy levels for the two atoms is
obtained by duplicating the energy level scheme of Fig. 2. However,
if the atoms move so near together that the wave functions for the
corresponding quantum states of the two atoms overlap, there is an
alteration in the energy levels. Figure 9 is intended to illustrate this
process. Figure 9a shows the potential energy of an electron for
points on a line passing through the centers of the two nuclei, and Figs.
9b and 9c show for points on the same line the values of the correct
wave functions in this field. These wave functions are obtained,
approximately, by using the \s wave function for the two separate

^Physical Review, 37, 1416 (1931). I am indebted to Professor White for the
photographs used for these illustrations.

THE QUANTUM PHYSICS OF SOLIDS

667

atoms; b represents the sum of the wave functions and c the difference.
The process involved in getting these molecular wave functions is
mathematically similar to that of finding the normal modes for a sys-
tem of two similar coupled oscillators. In Fig. 9d we represent two

lij a:

///////////////

(b)

(d)

\ <--^1 ^~-^y T

(e)

(f)

(9)

INDUCTIVE
COUPLING

Fig. 9 — A diatomic molecule and some mechanical and electrical analogues.

(a) The potential energy of an electron for points on a line through

the two nuclei.

(b) and (c) Values of two wave functions for points on the same line.

(d) Two coupled oscillators.

(e) and (f) Their normal modes of vibration,
(g) Two coupled circuits.

weakly coupled oscillators. The normal modes of vibration for the
coupled system are as indicated in Figs. 9e and 9/. These two modes
have different frequencies. Similarly if two electrical circuits are
placed so that there is some inductive coupling between them, we find
that each frequency is split into a pair. This inductive coupling is
similar to the overlapping of the wave functions; thus the coupling
between the circuits is large when the electromagnetic field of one
reaches over to the other. We may summarize the situation by saying
that before coupling each frequency occurred twice, once for each sys-

668

BELL SYSTEM TECHNICAL JOURNAL

tern; after coupling two frequencies are present and the corresponding
modes of vibration belong not to the individual systems but instead
to the pair of systems. For the case of atoms each quantum state
occurs twice, once for each atom, before the atoms interact; after inter-
action there are still two quantum states but now they have different
energies and are shared by both atoms.

As the atoms are brought closer together the energies separate more
and more. The behavior is indicated qualitatively in Fig. 10. The

INTERNUCLEAR DISTANCE (OR STRENGTH OF COUPLING)

Fig. 10 — Energy levels of a diatomic molecule versus internuclear distance.

L levels (25 and 2p) split at larger distances than the K levels because
their wave functions extend farther from the nucleus (see Figs. 7 and 8)
and overlap at greater distances. The details of the splitting are
somewhat complicated and only the start is shown here. For the
mechanical analogues shown in Fig. 8, the coupling raises one fre-
quency and leaves the other unaltered. On the other hand, the
quantum mechanical interaction results, at large distances, in equal
displacement up and down for the energy levels.

We can use Fig. 10 to describe the formation of a molecule of
hydrogen, H2. We start initially with the single electron of each atom

THE QUANTUM PHYSICS OF SOLIDS 669

in the Is state. When the atoms have come together the Is states
have spHt into two energies with two states for each energy — one
with each spin. In the H2 molecule, the two electrons will both
go into the lower Is states, which both have the wave function of
Fig. 8b. Bringing the atoms closer together decreases the energy
of the electrons and results in the binding together of the atoms.
This tendency of the electrons to reduce their energies by drawing
the atoms together is opposed by the electrostatic repulsion between
the nuclei. The repulsion between the nuclei is inoperative when
the atoms are sensibly separated because then each nucleus is shielded
from the nucleus of the other atom by the electron of that atom.
When the atoms are closer together, however, the electrons no longer
perform this shielding perfectly and the nuclear repulsions are impor-
tant. Hence with decreasing interatomic spacing the electronic energy
decreases and the energy of repulsion of the nuclei increases, and the
equilibrium internuclear distance is the one which makes the total
energy of the molecule a minimum.

The situation is quite different for two helium atoms. There being
two electrons in each, for them all four of the " \s molecular orbitals,"
as the states of Fig. 9 are called, are occupied. When all the molecu-
lar orbitals are occupied, there is no decrease in energy when the two
atoms are brought together: in this case the decrease of energy for the
electrons in the two lowest states is compensated by the increase for the
electrons in the upper states — more than compensated, as a matter of
fact, because the upper states rise slightly more rapidly than the lower
ones fall. This effect results in a repulsion between two helium atoms.
This repulsion is a consequence of the closed shell nature of the helium
atom and always occurs between such closed shells even if the atoms
are different, as, for example, a neon and an argon atom. We shall
refer to this closed shell repulsion, which occurs when the wave func-
tions of the two closed shells encroach upon each other, as an "en-
croachment energy." The encroachment energy, as we have said,
always corresponds to a repulsive force between the closed shells. We
shall find that it plays a very important role both in ionic crystals
and in metals.

The encroachment energy occurs not only between rare gas atoms
but also between ions of elements which as neutral atoms have partly
filled shells but in the ionic form have closed shells. Consider, for
example, an alkali halide molecule such as LiF. For this case the
2s valence electron of lithium is transferred to the vacant 2p level of
fluorine (see Fig. 4), thus leaving two ions with closed shell configura-
tions, the Li+ being He-like, the F~ being Ne-like. These two oppo-

670 BELL SYSTEM TECHNICAL JOURNAL

sitely charged ions attract each other and draw together until the
encroachment repulsion between their closed shells balances the attrac-
tion and holds them apart. Conversely if one of two atoms having
closed shells normally is converted to an ion, the closed shell arrange-
ment will be destroyed and an attraction will result.. For example,
He2"'' ions, which may be thought of as formed from an atom and an
ion, have been observed in the mass spectrograph.''' The attraction
is explained by noting that in this case there are three electrons and
the effect of two of them in the lower \s molecular orbital overbalances
the one in the upper orbital and gives rise to a net attraction.

Electrons in Crystals

We must now investigate the quantum states and their energy
levels for electrons in crystals. As in the case of the diatomic molecule
we shall study the dependence of the energies upon the distance be-
tween atoms, which in the case of a crystal is called the lattice constant.
We shall treat the lattice constant as a variable and shall refer to the
values for it found experimentally as "observed" or "experimental
lattice constants" and indicate them on the figures by the symbol ao.
We shall consider the allowed states to be occupied in accordance with
Pauli's principle and on this basis find how the energy of the crystal
as a whole depends upon the lattice constant. In this section we
shall deal with crystals at the absolute zero of temperature and leave
the complicating features of thermal effects to a later section. Accord-
ing to theory, the equilibrium state of a system at absolute zero is that
one which makes the energy least. Hence, a knowledge of the de-
pendence of energy upon lattice constant can be used to predict the
equilibrium lattice constant — that is, the one which should be found
experimentally — for according to the theory quoted above, the equi-
librium lattice constant is the one which makes the energy of the
crystal least.

In Fig. 11 we show the potential energy for an electron in a one-
dimensional crystal, the distance being measured along a line passing
through the atomic nuclei of the constituent atoms. In the interests
of simplicity we imagine that high potential walls through which the
electron cannot pass bound the crystal at both extremities. These
boundary conditions lead to a simpler set of wave functions than would
boundary conditions like those discussed for the free atom. The sim-
plification of problems by arbitrarily choosing certain boundary con-
ditions is a standard device in some branches of quantum mechanics;
it introduces an error, but if the crystal is large, the error is negligible;

7 F. L. Arnot and Marjorie B. M'Ewen, Proc. Roy. Soc, 171, 106, 1939.

THE QUANTUM PHYSICS OF SOLIDS

671

h- >■

uj q: T

(a)

LlXiXUJ

(h)

WAVE FUNCTIONS

NORMAL MODES

(b)

-rOl

_Q— 1=^— a — a-.

(L)

XT"-°--^

(j) -^

□"

--n^ ^,XT— cn^

(k)

Q.

2

<

^

v::^.

,^

V^

/^'

S v

^'

(e)

izr-v

-o-

--izr

y ^

(I)

-izr

,;^N

^

^^

^

N.^^

(f)

^^y"

.□x

-d_n-

,0.

(m)

^

^ /

"^^

,i;^.

(9)

^' ^V

0 ^

xlZk

(n)

X2(

V^

J

(o)
Fig. 11 — A one-dimensional crystal and some mechanical and electrical analogues.

(a) The potential energy of an electron for points on

a line through the nuclei.

(b) to (g) Wave functions for points on the same line,
(h) Coupled oscillators.

(i) to (n) Their normal modes of vibration,
(o) Coupled circuits.

672 BELL SYSTEM TECHNICAL JOURNAL

the situation is similar to that which arises through neglecting "edge
effects" in calculating the capacity of a parallel plate condenser.

In Fig. 11 we show also a series of coupled oscillators with boundary
conditions corresponding to those prescribed for the atoms. For
this case there are six coupled oscillators, which when uncoupled had
six independent normal modes of vibration all with the same fre-
quency, like that shown for the single oscillator of Fig. Id. After
coupling there are six normal modes all having different frequencies;
the standing wave patterns corresponding to these are shown in Figs.
1 \i to 1 In. A similar splitting of frequencies occurs when the members
of a set of electrical circuits are placed in close proximity as indicated
in Fig. Wo. For them the situation is more complicated than for the
mechanical oscillators; each mechanical oscillator has but a single
frequency, whereas each circuit has a fundamental and a sequence of
overtones. Each possible frequency for the electrical circuits is
split by coupling into a set of six.

In Figs. \\b to llg are shown the proper electron wave functons
which arise from the \s atomic states. These wave functions have
different energies. When the atoms were separated there were six \s
wave functions for the six atoms and each of these gave two states —
one for each spin. After coupling we find six crystal wave functions
and twelve crystal quantum states, the same number of states for each
spin as before. This illustrates a fundamental theorem concerning
wave functions in crystals which holds for two and three dimensions
as well as for one and is true no matter how large the number of atoms
in the crystal. This theorem, which we shall refer to as the "conserva-
tion of states," may be stated as follows: consider a set of N similar
isolated quantum mechanical systems; they may be single atoms or
molecules. Any particular quantum state is then repeated N times
over, once for each system. Now bring the systems together so that
the energy levels have split up. Then for each AT^-times-repeated
quantum state of the isolated systems, we find a set of N crystal quan-
tum states. In other words, putting the systems together may change
the energies and wave functions of the quantum states but no states
are gained or lost in the process.

In Fig. 12 we indicate how the energy levels of the states depend
upon the lattice constant. Each energy level in the figure corresponds
to two states, one for each spin. For simplicity only two atomic
levels are shown here. Higher energy levels split appreciably at
larger lattice constants because of the greater spatial extension of their
wave functions. For any particular lattice constant the energy levels
arising from a given atomic state lie in a certain band of energy. The

THE QUANTUM PHYSICS OF SOLIDS

673

number of states in the band is, of course, proportional to the number
of atoms; however, if the number of atoms is large, the width of the
band is independent of the number of atoms. This concept of allowed
bands of energies for the crystal states plays the same role in crystals
as the concept of energy levels in the atom. We shall refer to 3^ bands

LATTICE CONSTANT (OR STRENGTH OF COUPLING)

Fig. 12 — Dependence of energy levels upon lattice constant or frequency
of vibration upon strength of coupling.

and M bands of energy levels in crystals in much the same way as we
refer to the Zs and Zd atomic energy levels from which these bands arise.

We must emphasize that like the molecular states, the crystal states
do not belong to the atoms individually but instead belong to entire
system of atoms.

Before proceeding with the application of these ideas to crystals
with large numbers of atoms, we shall digress by anticipating several
subjects to be taken up in the next paper. For the energy levels of
isolated atoms the quantum numbers n, I, m, and Ws were satisfactory.
For a crystal, however, there will be many crystal quantum states
in an energy band all arising from atomic levels having the same values
of n, I, m, and Ws. A new quantum number is therefore needed to dis-
tinguish the various crystal states in an energy band one from another.
In Fig. 11 we see that the wave function of each crystal state is asso-

674 BELL SYSTEM TECHNICAL JOURNAL

dated with a wave form, shown dashed. This wave form is in every
case of such a wave-length that it has an integral number of half wave-
lengths along the edge of the crystal.^" The number of half wave-
lengths is a suitable quantum number for the wave functions in the
crystal and a more general consideration of it in the next paper will
lead us into the theory of the "Brillouin zone" and the zone structure
of energy bands. The second subject concerns the transmission prop-
erties of the crystal. The set of coupled circuits of Fig. 11 constitutes
a length of transmission line. A line of this type is a simple filter net-
work and as such it has bands of frequency in which power will be
transmitted and bands in which it will not. The allowed frequencies
lie in the transmitting bands. The system of coupled mechanical
vibrators likewise constitutes a mechanical filter. Just as the mechan-
ical and electrical systems can transmit power in their allowed bands,
a crystal can transmit an electron whose energy is in an allowed band.
The electrons in an allowed band, however, can produce a net current
only if the band is partially filled. Electrons in wholly filled energy
bands, although individually representing tiny currents to and fro in
the crystal, can produce — we shall find — no net current as their indi-
vidual currents cancel out in pairs. On this basis the theorist ex-
plains the difference between metals and insulators as follows: in a
metal some of the energy bands are partly filled, but in an insulator
each energy band is either completely filled or completely empty.

Distributions of Quantum States in Energy Bands

When there are a very large number of atoms in the crystal, it is
impractical to represent the energy levels by distinct lines as was done
for the case of six atoms in Fig. 12 and another scheme must be used.
For a crystal of macroscopic dimensions the number of levels in the
band is of the order of 10^*, that is a million million million million.
When so many levels are placed so close together, a continuous band of
allowed energies is suggested. Actually, of course, only a discrete set
of allowed energies is possible, the total number in the band being
that required by the conservation of states. We shall now consider
the distribution in energy of these quantum states; that is, how many
lie in a given range of energy between E and E + dE. Let us call

^» For a three-dimensional crystal having the external shape of a cube, the three-
dimensional wave function has an integral number of half wave-lengths along lines
parallel to each edge of the crystal. This condition is illustrated in a simplified
form by the wave patterns for the two-dimensional drum head shown in Fig. 7;
for each normal mode, there is an integral number of half wave-lengths parallel to
each boundary of the membrane, and, in fact, the values of these numbers are given
by p and q.

THE QUANTUM PHYSICS OF SOLIDS

675

this number dN] it will depend upon E and be proportional to dE and
we may write

dN = N{E)dE, (3)

where the function N{E) represents the "number of quantum states
per unit energy" at E. This equation, like many in statistical mechan-
ics requires special interpretation, because if dE is small enough — less
than the spacing between levels in the band — it may include no levels.
If, however, we always use small but not infinitesimal values for dE,
so many levels will be included in it that equation (3) is quite satis-
factory. In Fig. 13(2 we represent qualitatively the distribution in

N(E)

^ 0 N (E) ^ 0

NUMBER OF QUANTUM STATES PER UNIT ENERGY

Fig. 13 — Distribution of energy states in energy.

(a) For two separate energy bands.

(b) For overlapping energy bands.

(c) For free electrons.

N (E)

energy for two energy bands. We plot N(E) horizontally so as to
retain the vertical scale for E. The area under the curve for the 2p
levels is three times that for the 2^. This is because the number of
states in the 2p and 2^ bands are respectively six times and two times
the number of atoms in the crystal. The Is band lies too low to be
shown on this figure; its levels will be concentrated over a.very narrow
range in energy in keeping with the small splitting suggested in Fig. 12.
It is possible for the energy band arising from one atomic energy
level to overlap the energy bands arising from other atomic levels.
We shall be concerned below with several cases where this occurs for
various crystals. When it does occur the states in the bands become
mixed up and it is no longer possible .to decide which atomic level was

676 BELL SYSTEM TECHNICAL JOURNAL

the parent of each state in the band. This confusion is of no conse-
quence, however, for it does not interfere with using the distribution
in energy curves when they are obtained. Furthermore, the conserva-
tion of states holds when the bands overlap so that the total number of
states per atom in the combined bands is the sum of the number of
states per atom in the separated bands. In Fig. 136 we represent a
distribution qualitatively similar to that occurring in various metals
where 5 and p bands overlap. The number of states per atom in the
combined bands is eight, four for each spin.

A very important distribution-in-energy curve is that of the case of
"free electrons." This is the distribution one obtains by imagining
that the electrons in a crystal are perfectly free — that is, subjected to
no electrostatic forces whatever — but that they are required to remain
within a certain prescribed volume. The distribution of quantum
states in energy for this case is represented in Fig. 13c. At low tem-
peratures the electrons tend to occupy the lowest states consistent with
Pauli's principle and the system is referred to as a "degenerate electron
gas." With the aid of the distribution curve, the energy and pressure
of this gas can be calculated. We shall require its energy for a discus-
sion of the binding energy of sodium, but we shall give here only
the equation of the curve, leaving the calculation of the energy until
later.* According to the theory, then, for the case of free electrons
the number of states per unit energy is given by

iV(£) =^(2m)3/2£i/2, (4)

where V is the volume of container, h is Planck's constant, ni the
mass and E the energy of the electron; for free electrons E is all
kinetic energy, there being no potential energy. For the case of
the alkali metals, calculations show that the wave functions for the
valence electrons are very similar to the wave functions for free elec-
trons. For these metals we can use Eq. (4) to calculate energies.
Before utilizing the concepts of energy bands in a discussion of the
binding energies of crystals, we must define two symbols to be used in
describing the energy of a state in the band. For this purpose we
arbitrarily separate the energy E of a crystal state into two parts:
one of these is denoted by Eo and stands for the energy of the lowest
state in the band and the other is Em which stands for the energy which
the state possesses in excess of Eq — that is, its energy above the bottom

8 The reader will find a derivation of this curve given in K. K. Darrow's article
"Statistical Theories of Matter, Radiation and Electricity," Bell System Technical-
Journal, Vol. VIII, 672, 1929 or Physical Review Supplement, Vol. I, 90 (1929), and
in various texts on quantum statistics and the theory of metals.

THE QUANTUM PHYSICS OF SOLIDS 677

of the band. We shall find in the next paper that the quantum states
in a band represent electrons traversing the crystal with various aver-
age speeds. The state Eo has an average speed of zero. The sub-
script " M" has been assigned with these ideas in mind and stands for
"motion," implying that an electron with energy greater than Eo has
an energy of motion Em. In general both Eo and Em are actually
composite energies containing both kinetic and potential energy; only
in the case of free electrons is Em purely an energy of motion. We
shall not use in this paper the property of motion connected with the
values of Em; however, we shall use the division of the energy into
two parts, Eo and Em, and we shall for convenience refer to the latter
as an "energy of motion."

We shall next apply the concept of the energy band to a determina-
tion of the binding energies of several types of crystals. It is one of
the principal merits of the theory of energy bands in crystals that we
can treat many different crystal types on the basis of the same set of
ideas. As we shall point out later, however, the band theory is most
appropriate for metals: for ionic and valence crystals other theories
are better suited.

Energy Bands and Binding Energies of Metals

For several metals the wave functions and distribution of states in
energy have been found by solving Schroedinger's equation for the
electrons in the metal. We shall discuss sodium since it constitutes
one of the simplest cases and is the first metal for which good calcula-
tions were carried out.

A sodium atom, Na, contains ten electrons in filled K and L shells
and one valence electron in the M shell; its electron configuration is
Is^ 2s^ 2p^ 3s. When the atoms are assembled together as in the
metal, the 3s atomic state gives a wide band which overlaps the 3p
band while the lower levels widen only very slightly.

The formation of the energy bands ^ is shown in Fig. 14. Since the
K and L bands are very narrow, it is possible to neglect the changes
in the wave functions of the electrons occupying them and to concen-
trate upon the valence electrons. The valence electrons then move
in a potential field produced by the Na+ ions and the other electrons.

It can be shown by a lengthy argument that for the case of a mono-
valent metal, the energy of the metal as a whole is very nearly equal
to the sum of the energies of the valence electrons.^" It is rather

» J. C. Slater, P/jy^. i?ez;., 45, 794 (1934).

J" An exact statement of the situation is too involved for this paper. The reader
can find a more complete discussion in Mott and Jones "The Properties of Metals
and Alloys," Chapter IV.

678

BELL SYSTEM TECHNICAL JOURNAL

natural that the valence electrons should contribute so largely to
the binding since the complete shells of electrons making up the Na+
ion, that is the K and L electrons, are only slightly affected by bring-
ing the atoms together to form a metal. The result that the energy
of the metal is the sum of the energies of the valence electrons is

ao

LATTICE CONSTANT IN ANGSTROMS

Fig. 14 — Energy bands for sodium versus lattice constant.

of great importance in applying the theory. We shall discuss below
how the energies of the various states in the band depend upon the
arrangement of the atoms; some of these states are occupied and
the energy of the crystal can be found by adding the energies of
the occupied states. In this way we can find how the energy of the
crystal depends upon the arrangement of the atoms and can find
what arrangement makes the energy least. According to theory the
arrangement of least energy is the stable one and the one which
should be found in nature. The remainder of this section will be
devoted to discussing the energies of the quantum states in metals and
the energies of the electrons which occupy them.

The first satisfactory solutions of Schroedinger's equation for elec-
trons moving in the field of a metal were obtained for sodium by
Wigner and Seitz." They assumed, in keeping with the findings of
experirnent, that the sodium atoms were arranged on a body-centered

11 E. Wigner and F. Seitz, Phys. Rev., 43, 804 (1933) and 46, 509 (1934) and E.
Wigner, Phys. Rev., 46, 1002 (1934).

THE QUANTUM PHYSICS OF SOLIDS

679

cubic lattice. They did not, however, assume that the lattice con-
stant was that given by experiment but instead carried out calculations
for each of several assumed values for the lattice constant lying on
both sides of the experimental value. The results of their calculations
are shown in Fig. 15. The curve marked Eq is the energy of the lowest

0123456789 10

LATTICE CONSTANT IN ANGSTROMS

Fig. 15 — Energy for sodium versus lattice constant.

level in the valence band. Only two electrons, one with each spin,
can occupy this energy level and all others must occupy states of
higher energy — that is, only two electrons can have zero value for the
"energy of motion" Em and all others must have larger values. By a
method of calculation described below, it can be shown that the
average energy of motion of a valence electron is given by the curve
marked Ef in the figure. Hence the total energy per valence electron
in the metal, which for a monovalent metal is equal to the energy per
atom, is represented by the curve marked E in the figure; £ = £o + Ep.
Figure 15 exhibits the dependence of this energy upon the lattice
constant. The abscissa of the minimum in the E curve gives the
theoretically predicted value for the equilibrium lattice constant. The
binding energy or heat of sublimation is defined as the energy required
to separate the metal into isolated atoms; it is the difference in energy
between the minimum of the curve and the value of E for infinite
lattice constant — that is, for free atoms. Finally, the curvature of the
curve at its minimum is a measure of the energy required to compress
or expand the crystal and from it a value for the compressibility can

680

BELL SYSTEM TECHNICAL JOURNAL

be obtained. In Table I, we compare theoretical and experimental
values of lattice constant, binding energy, and compressibility calcu-
lated by the method described above. The theoretical values were
computed by Bardeen ^^ who has added some refinements and correc-
tions to the original calculations.

TABLE I

Li

Na

Calc.

obs.

Calc.

obs.

Lattite Constant (angstroms) . . .
Heat of Sublimation (Kg. cal./-

gm. atom)

Compressibility (cm'' /dyne)

3.49

34
8.4X10-12

3.46

39
7.4X10-12

4.53

23
12.0X10-

-12

4.25

26
12.3X10-12

Although the theory can give quite satisfactory values for the
various physical quantities shown in Table I, it cannot as yet predict
precisely what crystalline form a metal like sodium will take. In
carrying out the calculations discussed above, it was assumed that the
atoms were arranged in a body-centered cubic lattice. Now the cor-
rect theoretical procedure would be to calculate the energy for all
conceivable arrangements of the atoms and then to select that arrange-
ment giving the least energy of all as the theoretically predicted
equilibrium arrangement. This program is, of course, too laborious
to be practical^ — furthermore experience shows that metals, with but
few exceptions, crystallize in one of three forms : body-centered cubic,
face-centered cubic, and hexagonal close-packed. For this reason it
might be regarded as sufficient to calculate the energies for the face-
centered cubic and hexagonal close-packed and to compare these with
that for the body-centered cubic. When such calculations are carried
out, however, it is found that the minimum energies calculated for
the three forms differ among themselves by amounts which are negli-
gible in view of approximations necessary in making the calculations.
Hence the theory cannot predict with any certainty which form really
has the lowest energy; it does predict, however, that all three forms
do have nearly the same energy and gives a value for this energy.
Actually the binding energy of sodium must be greatest for the body-
centered cubic lattice because this form is the one that occurs in nature
and so must be the form of lowest energy. However, it is probable
that the diff'erence in energy between the various possible allotropic

12 J. Bardeen, Jour. Cheni. Phys., 6, 367, 372 (1938).

THE QUANTUM PHYSICS OF SOLIDS 681

forms for sodium is really very small — so small that we should not
expect the present theory to evaluate it. Some indication that the
energy of caesium is very nearly the same in the body-centered form
and face-centered form (or possibly the hexagonal close-packed form)
is furnished by a transformation at high pressures observed by Bridg-
man. In the next paper we shall meet a case where the theory does
seem able to differentiate between the energy of face-centered and
body-centered structures. In general, however, the procedure is to
use the crystal structure found by x-rays and to calculate the energy
for a series of values of the lattice constant as was done for sodium.
We must now return to a discussion of the curves Eo and Ep of
Fig. 15. About the curve £o we shall only say that it is obtained by
solving Schroedinger's equation for and finding the energy and wave
function of an electron in the lowest state in the energy band. The
wave function for this state, however, possesses the interesting feature
of being very nearly the same as the wave function for a free electron
having zero energy of motion. From this fact it is possible to draw
the conclusion that the distribution in energy of motion of the valence
electrons in sodium is the same as the distribution in energy of free
electrons in an electron gas. Accepting this conclusion, we can then
use the formulas given for the distribution of states for free electrons
in order to calculate the mean energy of motion of the valence electrons
in sodium. The results of this calculation, which we give in a foot-
note,^* lead to the energy curve Ef- This energy curve is, from its

^3 We shall first derive a general expression for Ep without specifying the particular
form of N{E). Since in this footnote all energies are measured from £o, we shall
omit the subscript M from Em and use simply the symbol E in the equations. The
total number, denoted by n, of atoms in the crystal is equal to the total number of
valence electrons. Let the volume of the crystal be V. Because of the duplicity
due to the spin there are 2n states in the band, and half of them will accommodate
the n electrons so that the band will be filled only up to a certain energy £max. We
must therefore have

r^""' N{E)dE. (i)

Once the distribution function N{E) is known, this equation serves to determine
-Emax. The average energy of motion of an electron in these occupied states is, from
the definition of an average, the total energy of motion divided by the total number
of electrons:

Ef = - r^""' EN{E)dE. . (ii)

Substituting the value of N{E) for free electrons into the first equation gives

rt = I VilmE^^^Jh-^yi^ (iii)

The quantity Vj-n is the volume per electron which in the case of a monovalent metal

682 BELL SYSTEM TECHNICAL JOURNAL

definition, the average energy per electron of a degenerate electron
gas. In a degenerate electron gas the electrons have the least possible
energy consistent with Pauli's principle and with the distribution of
quantum states in energy. For reasons associated with the origin
of the statistical mechanics of electrons — that is, with the Fermi-Dirac
statistics — the energy Ep is called the "Fermi energy" and given the
subscript F. The energy Ef is far greater than the average energy
per particle of an ordinary classical gas. We shall see below how this
fact accounts for the very small specific heat of the electron gas.
From the dependence of the energy upon volume, the pressure of the
electron gas can be calculated. It is usually very large, for sodium it
is about 50,000 atmospheres. The force that prevents this pressure
from blowing the metal apart is represented by the Eq curve, which
gives decreasing energy with decreasing lattice constant and corre-
sponds to a force pulling the atoms together. A more detailed dis-
cussion of these forces will be taken up in the third paper of this series.

Other Metals

Calculations similar to those for sodium can be carried out for other
metals. The band structure as calculated for copper by Krutter i* is
shown in Fig. 16. Ten electrons per atom can be accommodated in
the M band and two per atom in the 45. For copper the 2>d band is
filled — in keeping with the fact that the Cu+ ion consists of filled
K, L, and M shells. From the discussion of molecules given above

is the same as the volume per atom. Denoting by fl the value of F/w, we find

/ 2 \ 2/3 hi
£max. = f^) ^12-=/" = Se.lflo-^/'eV (iv)

where fio is the volume per atom in cubic Angstroms. For a body-centered cubic
lattice with lattice constant a Angstroms, Oo = a^l2. Substituting the expression
for N{E) into the equation for Ep gives

Ef = \ Sraax. = 21.6fio-2/3ev. (v)

Expressing Ef in atomic units and fto in terms of the lattice constant, we find

Ef = 2.54a-2. (vi)

This is the equation of the curve for Figure 15. The values of Emax. calculated from
the above equations for a series of metals are

Metal Li Na K Rb Cs Cu Ag Au

£max.(ev) 4.74 3.16 2.06 1.79 1.53 7.10 5.52 5.56

" H. M. Krutter, Phys. Rev., 48, 664 (1935).

THE QUANTUM PHYSICS OF SOLIDS

683

we should expect encroachment repulsions between these Ions when
their wave functions begin to overlap. In the band picture this repul-
sion results from the spreading of the 3d band; since the band spreads
more to higher energies than to lower energies and since it is full, the
average energy of an electron in it increases as the lattice constant
decreases. Thus the same result, repulsion between closed shells, is

0 3d I 2

-0.1
12-0.2 -

O -0.3

5

,-0.6
-0.7 -
-0,8 -
-0.9

0 I 2 3ao4 5 6 7 8 9 10 II

LATTICE CONSTANT IN ANGSTROMS

Fig. 16 — Energy bands for copper versus lattice constant.

found for the ions in a metal as for the rare gas atoms. For elements
whose atoms have partially filled 3d levels the situation is quite differ-
ent. For them only part of the levels of the 3d band will be filled
and there will be a decrease in the energy of the 3d electrons in the
metal as compared to the atom. This has been proposed by Seitz and
Johnson as an explanation of the fact that the highest binding energies
for the metals of a transition series occur for those that have approxi-
mately half-filled 3d bands and for which consequently nearly all of
the 3d electrons have lower energies than in the atomic state. ^^ The
very high melting point metals — columbium, molybdenum, tantalum,
and tungsten — come approximately at the middle of their transition
series. In Table II we give the binding energies for a number of the
transition elements.

15 F. Seitz and R. P. Johnson, Jour. App. Phys., 8, 84, 186, 246 (1937).

684

BELL SYSTEM TECHNICAL JOURNAL

TABLE II

Heats of Sublimation for Several Metals Including the Transition Elements
IN Kilocalories per Gram Atom *

K
19.8

Ca

48

Se
70

Ti
100

V
85

Cr

88

Mn

74

Fe
94

Co
.85

NI
85

Cu

81

Zn

27.4

Rb
18.9

Sr
47

Y

90

Z

110

Cb

Mo
160

Ma

Ru

120

Rh
115

Pd
110

Ag
68

Cd
26.8

Cs

18.8

Ba
49

La
90

Hf

T

185

W
210

Re

Os

125

Ir
120

Pt

127

Au
92

Hg
14.6

* Taken from F. R. Bichowsky and F. D. Rossini "The Thermochemistry of the
Chemical Substances," Reinhold (1936), except for T which was taken from D. B.
Langmuir and L. Maker, Phys. Rev. 55, 1138 (1939).

Energy Bands of Diamond
In Fig. 17 we show the band structure for diamond as calculated by
Kimball. ^^ The configuration of the carbon atom is Is^ls^lp^ and

ao

5 6 7 8 9 10 II 12

LATTICE CONSTANT IN ANGSTROMS

Fig. 17 — Energy bands for diamond versus lattice constant.

all four of the L shell electrons are involved in the binding. At large
lattice constants the lower band contains two states per atom and the
upper six. The lower band is completely filled, the upper only one-

1® G. E. Kimball, Jour. Chem. Phys., 3, 560 (1935). Some unimportant features
resulting from approximations in Kimball's work have been modified in this figure.

THE QUANTUM PHYSICS OF SOLIDS 685

third filled. To the left of the crossing of the bands, Kimball finds
that both bands contain four states per atom so that the lower is filled
and the upper is empty. The actual spacing in diamond occurs to
the left of the crossover and, as we shall see in the next paper, the
resultant filled band and empty band arrangement explains the ab-
sence of electrical conductivity for diamond. The diagram suggests
an explanation for the conductivity in graphite; one of the lattice
constants of graphite is known to be larger than the abscissa of the
crossover of Fig. 17; hence in graphite there are partially filled bands
and conduction.

The general downward trend of the bands in Fig. 17 indicates a
strong binding energy for diamond; but quantitative calculations of
the total energy have not been made.

The type of binding involved in diamond is quite like the binding
of metals save that, owing to the absence of partially filled bands,
there is no electrical conductivity. In both cases the energy arises
from the lowering of energy levels as the atoms come together. In
chemical terminology the binding of diamond is referred to as "ho-
mopolar" signifying that the atoms are all similarly charged, or rather
uncharged. In crystals containing ions rather than neutral atoms,
the cohesion is due largely to electrostatic forces and one refers to
binding as " heteropolar " or "ionic."

Energy Bands and Binding Energies of Ionic Crystals

The energy band theory can be applied to the calculation of the
binding energy of ionic crystals. Before discussing this application,
however, it will be instructive to examine a somewhat simpler ap-
proach to the problem.

A sodium chloride molecule consists of a sodium ion and a chlorine
ion. These ions have charges of +e and —e respectively and have a
mutual electrostatic energy of

-J. (5)

where r is their distance of separation. This electrostatic energy,
which we shall refer to as the "coulomb energy," decreases with de-
creasing interatomic distance. If the ions are close together, as they
are in a molecule, the energy of encroachment due to the overlapping
of their closed shells must be considered; this energy increases with
decreasing interatomic distance. The equilibrium distance is the one
that makes the total energy, coulomb plus encroachment, a minimum.

686 BELL SYSTEM TECHNICAL JOURNAL

Closely similar calculations can be carried out for a crystal. One
finds the total coulomb energy of all the ions and the total encroach-
ment energy; and then one finds the lattice constant that makes the
total energy a minimum. The total encroachment energy is easily
found; only atoms which are nearest neighbors in the lattice have
appreciable overlapping with each other and it is therefore a straight-
forward and simple calculation to find the total number of encroach-
ments in the crystal. The coulomb energy is not quite so simply
found, however, because the electrostatic interaction of a given ion
with its nearest neighbors is no more important than its interaction
with its vastly larger number of more distant neighbors. The electro-
static problem is solved as follows : one considers a NaCl lattice which
is perfect except for the absence at one lattice point of a Na+ ion ; one
finds by known techniques of electrostatics the value at the vacant
lattice point of the electrostatic potential due to the remaining ions;
this potential is negative and has a value

Me SA9e .,.

where a is the lattice constant and M is a numerical constant known
as Madelung's constant, which has a particular value for any special
lattice; for the NaCl lattice, M = 13.94. If now a Na+ ion is placed
in the vacant lattice point, its electrostatic energy will be — e<i). Sim-
ilarly the electrostatic potential at a vacant Cl~ lattice point is +0 and
the electrostatic energy of a Cl~ placed there is —€({>. The total
electrostatic energy per NaCl molecule in the lattice, however, is not
— 2e(f) but only —ecj); the factor 2 does not occur since otherwise the
electrostatic interaction between each pair of ions would be included
twice. ^^ The total energy per molecule for the crystal can be found
by combining the coulomb and the encroachment energies, and the
equilibrium lattice constant and binding energy per molecule thence
can be derived.

Using wave functions for Na+ and Cl~ ions obtained by D. R. Har-
tree, who has found solutions of Schroedinger's equation numerically, the
encroachment energies in NaCl have been evaluated by R. Landshoff.^^
For the lattice constant and binding energy for NaCl he obtains 5.8 8 A
and 165 Kg.-cal./gm. atom while experiment gives 5.63A and 183
Kg.-cal./gm. atom.

Some very important theoretical work of a semi-empirical nature has

1* To see that this is true in a simple case, use the procedure described above to
calculate the electrostatic energy of an isolated NaCl molecule.
'^Zeits.f. Phys., 102, 201 (1936).

THE QUANTUM PHYSICS OF SOLIDS 687

been carried out for the alkali halides. In it an analytical expression
suggested by theory and containing adjustable constants has been used
for the closed shell repulsions. The adjustable constants have been
determined from certain data and then used for predictions which can
be compared with other data. Using a relatively small number of
adjustable constants, Born and Mayer.^" Mayer and Helmholz,^^ and
Huggins and Mayer ^^ have calculated a much larger number of values
for lattice constant and binding energy for many alkali halides with
an agreement with experiment of the order of one per cent.

Let us now consider NaCl using the band picture. We shall reach
the rather surprising conclusion that there is no fundamental differ-
ence between the results obtained from it and those just deduced from
the ionic picture described above.

In Fig. 18 we show qualitatively the behavior of the bands for NaCl.^^
In the ionic state, an electron is transferred from the Na Zs to the CI Zp.
The general shifting of the bands is explained as follows. The wave
functions corresponding to the Cl~ Zp band, like all energy band wave
functions, are distributed over the whole crystal. They are not,
however, equally intense at Na+ and at Cl~ ions; instead they are defi-
nitely concentrated about the Cl~ ions. The electrostatic potential
at a Cl~ ion, due to the remainder of the crystal, has the same value
(6) as was found in discussing the ionic method. Since the charge on
the electron is —e, the energy of each of the states in the Cl~ 3p band
varies with a in the same manner as does —ecf). A similar argument
shows that the Na+ energy bands vary as +e</). At a certain lattice
constant, the Cl~ d>p and Ss bands and the Na+ 2p and 2s bands begin
to widen. Since these bands are full, this widening gives the cus-
tomary encroachment energy just as it was obtained in the ionic
picture. The shifting of the bands similarly gives the coulomb energy.
To see this we note that per NaCl molecule there are 18 electrons
in the Cl~ bands where energies vary as — 18e0 and that there is also
one chlorine nucleus with charge +17e whose energy varies as -\-17 ecj).
This leaves a net effect of —ecj) for the Cl~ ions. Similarly a net effect
of —e(f> comes from the electrons and nuclei of the Na+ ions. As in
the case of the ionic method the sum, — 2e</>, of these energies really
contains each ionic energy twice and the total electrostatic energy per
NaCl molecule is —ecf). So far as calculating energies is concerned,
the two methods give equivalent results; the advantage, if any, lies

^''Zeits.f. Phys., 75, 1 (1932).
^^Zeits.f. Phys., 75, 19 (1932).

22 Jour. Chem. Phys., i, 643 (1933).

23 J, C. Slater and W. Shockley, Phys. Rev., 50, 705 (1936).

688

BELL SYSTEM TECHNICAL JOURNAL

with the ionic method rather than the band method because of the
more immediate physical interpretation of the former.

We may remark that in the discussion of metalHc sodium, it was not
necessary to consider the potential energy of the nuclei and the closed

u ^ •« an^ ® '° '2 '"* '^ '^ 20

LATTICE CONSTANT IN ANGSTROMS

Fig. 18 — Energy bands for sodium chloride versus lattice constant.

shell electrons as was done in NaCl. This is because sodium metal is
not ionic — although we think of it as consisting in part of Na+ ions,
the electrostatic forces between them are suppressed by the shielding
effect of the electron gas. In an ionic crystal, like NaCl, there is no
electron gas and the coulomb energy must be considered in the manner
described above.

Energy Bands for Other Crystals

There are chemical compounds which lie between the homopolar

and ionic types. For example in the sequence of compounds NaF,

MgO, AIN, SiC the compounds are progressively less and less definitely

ionic — the least ionic, SiC or carborundum, being homopolar. Simi-

THE QUANTUM PHYSICS OF SOLIDS 689

larly there are compounds, in particular intermetallic compounds,
which are more like metals than like either ionic crystals or valence
crystals. Thus there is an intermediate field which connects all three
of the simple types of binding. Good computations are lacking for
these intermediate cases; we shall return to a discussion of some aspects
of them in connection with semiconductors in the next paper.

Concerning a Classification of Crystals
In the last section we saw how the concept of the energy band can
explain the binding energies of a number of different types of crystals.
Although the band theory has the merit of being very general it has
the disadvantage of being at the same time rather abstract. Other
theories have been developed to explain the cohesion of particular types
of crystals; and, while lacking the generality of the band theory, they
have the advantage of a more immediate physical interpretation in
their own particular fields. In this section we shall digress from the
exposition of the band theory in order to describe briefly some of the
simpler viewpoints of the other theories.

We have discussed in the last section three types of binding. Sodium
exemplified the metallic type; diamond, the homopolar or valence type;
and sodium chloride, the ionic type. The distinction between the
valence bond and the metallic bond is not very clearly indicated in the
band theory; the only difference there had to do with the degree of
filling of the bands. There is another difference, however, which has
been long familiar to chemists. The homopolar compounds are usually
characterized by "directed valence." Thus the "tetrahedral carbon
atom" is a familiar concept of organic chemistry. In crystals in
which homopolar binding is dominant the atoms are arranged so that
each atom has the proper valence bonds with its neighbors. In dia-
mond each carbon atom is tetrahedrally surrounded by four other
carbon atoms. In silicon carbide, carborundum, a similar situation
prevails: each carbon is tetrahedrally surrounded by four silicons and
vice versa. These crystals are said to have a "coordination number"
of four, or z = 4, meaning that each atom has four nearest neighbors. In
crystals of the divalent elements— sulphur, selenium and tellurium —
each atom has two near neighbors and the valence condition is satis-
fied; these crystals have a coordination number of two. The mono-
valent halogens form crystals in which each atom has one near neigh-
bor, coordination number one. In the metals, however, the neighbors
of a given atom are as many as eight or twelve — do these large coordi-
nation numbers imply that the metals have eight or twelve electron
pair bonds with their neighbors?

690 BELL SYSTEM TECHNICAL JOURNAL

According to the quantum mechanical theory of valence, which in
itself forms a theory with as many ramifications as the band theory,
the electron configuration U'^ls'^lp'^ of carbon is especially suited for
forming "electron pair bonds" with other atoms. In forming these
bonds the wave functions from one atom and another become dis-
torted so as to overlap and form a high electron concentration along
the line between the atoms; the energy levels being incompletely filled
for the atoms, this overlapping does not produce a repulsion but in-
stead a binding together like that produced by the overlapping wave
function in Fig. 9b in the hydrogen molecule. The carbon atom is
capable of forming four such bonds and forming them most effectively
along four lines, making the tetrahedral angles with each other.

Recently Brill ^^ and his collaborators using x-ray analysis have
determined the electron concentration in diamond, in which the car-
bon atoms are arranged in a tetrahedral manner. The results of their
investigations are shown in Fig. IQA.^^ It is easily seen that the
electrons are concentrated in the bonding directions forming homopolar
bonds between the atoms.

The energy band theory, we have said, does not give the clearest
picture of the valence crystals; it is, however, especially suited to
treatments of the metallic bond. According to the band theory the
valence electrons constitute an electron gas — that is, instead of forming
electron pair bonds with localized overlapping of the wave functions,
they form instead a more or less uniform region of negative charge.
In this negative charge the positive ions float. Since the ions repel
each other they tend to arrange themselves so as to use their space to
best advantage and this requires that they take up one of the "close-
packed" arrangements. Let us see why this is true. The close-
packed arrangements are those obtained by trying to pack rigid
spheres as compactly together as possible. For these arrangements
then, the volume per sphere is less than for other arrangements; that
is, the close-packed arrangements are the ones which give a minimum
volume per sphere for a prescribed value for the distance between
sphere centers. Conversely, the close-packed arrangements must be
the ones which give a maximum value for the distance between neigh-
boring sphere centers for a given value of the volume per sphere.
Since the energy of motion, Ep, of the electron gas and, although we
have not shown why, the energy Eo, depend for a metal mainly upon
the volume, in metals we are interested in cases where the volume per

" R. Brill, H. G. Grimm, C. Hermann and CI. Peters, /1km. d. Physik, 34, 393 (1939) .
^5 The writer is indebted to Professor Grimm for his permission to reproduce Fig.
19 from his article: Naturwissenschaften 27, 1 (1939).

THE QUANTUM PHYSICS OF SOLIDS

691

atom is closely prescribed. For a given volume per atom, as we have
seen above, the close-packed arrangements are the ones which give
the largest separation between neighboring positive ions; and since the
positive ions repel each other, the close-packed arrangements will
give the lowest energies. This accounts for the fact that the custom-

k

3/.

CL-

%

Fig. 19 — Electron charge densities in crystals. The numerical values give the
number of electrons per atom in the space corresponding to each intensity of shading.

(A) In diamond.

(B) In magnesium.

(C) In sodium chloride,

ary metallic lattices are the body-centered cubic lattice, the face-
centered cubic, and the close-packed hexagonal. A further discussion
of this physical picture of the nature of the metallic state will be given
in the third paper of this series. In Fig. 19B we show qualitatively
the electron density of metallic Mg according to Grimm.^^ It is seen
that the valence electrons give a uniform negative charge in which
the positive ions are embedded.

We have seen in the preceding section that the band theory of the
alkali halides is essentially equivalent to the ionic theory. A large
fund of evidence attests to the validity of the ionic theory, one item
being the electron concentrations determined for sodium chloride by
BrilP^ and his collaborators. These are represented in Fig. 19C; we

^^ Loc. cit.
2* Loc. cit.

692 BELL SYSTEM TECHNICAL JOURNAL

see that the electrons are closely held about the ions with very little
overlapping of the closed shells.

In addition to the metallic, homopolar, and ionic bonds, there is still
another interatomic force known as the Van der Waals force — a very
weak force compared to the other three. We shall not discuss its
origin here except to say that it arises from the spontaneous and
mutual polarization of two atoms or molecules when in the neighbor-
hood of each other. It is responsible for the "a" term in the Van der
Waals equation for gases. When a crystal is formed from organic
molecules, such as a crystal of benzene, the forces holding them to-
gether are the weak Van der Waals forces. This is the reason why
"molecular crystals" have low melting points and binding energies.
Although the Van der Waals forces are much smaller than the other
three, they are not entirely negligible in comparison and in some of the
calculations referred to in the last section, their effects are included.

It is interesting to note that in a single crystal of a given chemical
compound, several of the various forces may be operative at once in a
rather separable way. A classification of this sort for crystals has been
discussed by Grimm.^^ For example the crystal mica, which cleaves so
naturally into sheets, consists of planes of atoms bound together chiefly
by valence forces, the binding between the planes being due to ions
lying between and in the planes. Thus mica is held together in two
directions by strong valence forces and in the other by weaker ionic
forces. In asbestos the atoms are arranged in parallel rows, being held
together in the rows by valence forces; the rows, on the other hand, are
held to each other by ionic forces. The ionic bonds are more easily
broken and asbestos crystals exhibit a typical fibrous structure. Mica
and asbestos are intermediate members of a sequence of which diamond
with all valence binding and sodium chloride with all ionic binding
constitute the extremes. We shall give one more example: cellulose
consists of long chains of carbon, oxygen and hydrogen, the chains
held to each other by Van der Waals forces ; it is an example of valence
binding in one direction and Van der Waals binding in the other two.

This section has been a digression, as the main purpose of these
papers is to illustrate the band theory of solids. It would hardly be
fair to concentrate on this, however, without pointing out, as has
been done in this section, that, although the band theory has great
generality, it is best adapted for a certain class of solids and that other
viewpoints are^more natural for solids outside of this class.

25 Naturwissenschaften, 27, 1}_(1939).

THE QUANTUM PHYSICS OF SOLIDS 693

Thermal Properties of Crystals

In this section, as in the last, we shall digress from a straightforward
exposition of the theory of energy bands and discuss the theories of
specific heat and thermal expansion. These theories are well worth
discussing on their own merits and furthermore their results and
methods can be applied later to other topics. Thus the thermal vibra-
tions that account for the specific heat will be shown in the second
paper of this series to account for the resistance of metals. The dis-
cussion of thermal expansion given here will in the next section on
magnetism be extended to an explanation of the unusual expansion
properties of magnetic materials, in particular to an explanation of
the very small expansion of invar. We shall, however, make use of
the band theory once in this section by showing why the free electrons
in a metal do not normally make an appreciable contribution to the
specific heat.

In the introduction to this paper we pointed out that the specific
heat per gram atom of a solid should be by classical theory 2)R —
coming half from the kinetic energy and half from the potential energy
of the atoms. This prediction is in reasonable agreement with ex-
periment for many crystals at high temperatures. As the temperature
is lowered, however, the observed specific heat decreases in such a way
as to approach zero when the absolute zero of temperature is ap-
proached. This decrease in the specific heat at low temperatures, as
well as the value 3i? at high temperatures, is readily explained by
quantum mechanics. In order to understand the explanation we must
inquire into the atomic vibrations of a crystal.

In considering atomic vibrations we are really concerned with the
motions of the nuclei. The electrons act as a cement to hold the nuclei
in their equilibrium positions and exert restoring forces on them when
they are displaced. (We shall see below why the electrons do not par-
take of the thermal energy.) The nuclei are eff"ectively mass points in
this theory and for quantum mechanical reasons, which we shall not
discuss, they are incapable of acquiring thermal energy of rotation;
hence so far as the crystal vibrations are concerned, we need consider
only their translational or rectilinear motions. A crystal containing
N atoms has 3iV degrees of freedom since each nucleus can move
in three dimensions. In order to find the specific heat of a crystal
we must find the normal modes of vibration. The system of coupled
oscillators in Fig. 11 represents reasonably well the normal modes
of vibration for a one dimensional crystal whose atoms have only
one degree of freedom. There is a similar set of normal modes for

694 BELL SYSTEM TECHNICAL JOURNAL

a three dimensional array of atoms and, once the forces between the
atoms are known, the frequency of vibration of each of the modes can
be found. This means that so far as thermal vibrations are concerned,
we can consider the crystal as equivalent to a set of 3iV oscillators
whose frequencies are those of the normal modes. We must next dis-
cuss the specific heat of a single oscillator.

According to classical statistical mechanics, a harmonic oscillator
in a temperature bath at absolute temperature T will have an average
thermal energy equal to kT, where k is Boltzmann's constant. The
value kT is only an average value, we emphasize, and the oscillator
will have other energies some of the time, the probability of each
energy being given by known equations. The probability is very
small, however, that the oscillator acquires more than two or three
times kT of thermal energy. In a very large system of oscillators,
the fluctuations of energy of the oscillators tend to cancel out and the
probability of any appreciable fractional deviation of the total energy
from its mean value is very small. If N is the number of mole-
cules in a gram molecule {N = 6.06 X 10-^), then Nk = R, the gas
constant, = 1.99 cal. per gm. molecule per degree C. Hence the
energy of 2>N oscillators is E = 3NkT = 3RT and the specific heat is
C = dEjdT = 3R] this classical result that the specific heat of one
gram atom of solid is 3R is known as the DuLong-Petit Law.

According to quantum mechanics, an oscillator of frequency v has a
set of quantum states whose energies are }4hv, (1 + /4)hv, (2 -|- y2)hv,
etc. The oscillator can take on only these energies. If it is in a heat
bath of temperature T, however, it will sometimes have one allowed
energy and sometimes another and as for the classical case we shall
be concerned with its average energy. At absolute zero, the average
energy is, of course, }4hv. Now the probability of the oscillator gain-
ing much more than kT of thermal energy is very slight. Hence the
average energy of the oscillator remains at y2hv until thermal energy
becomes large enough to excite it to the next state which is hv higher,
and consequently so long as kT is much less than hv the quantum
oscillator acquires much less thermal energy than would a classical
oscillator. For kT much greater than hv, the oscillator will spend an
appreciable fraction of its time in many of the quantum states and,
as may be shown mathematically, the quantum restriction is no longer
of importance so far as the average energy is concerned and the value
kT is obtained just as in the classical case. In Fig. 20 the dependence
upon temperature of the average energy and the specific heat for a
quantum oscillator are shown.

THE QUANTUM PHYSICS OF SOLIDS

695

The specific heat of the crystal is just the sum of the specific heats
of its oscillators. Since the oscillators have different frequencies they
have different specific heats and in order to add up the specific heats of
all of them it is necessary to know how the various frequencies of the

J

/

I.O

ok
<

^0.5
o

u.
o

UJ

Q.

CO

0

/

/

^

/

(a)

Cb)

2.0

kT

TEMPERATURE, 7—-

Fig. 20 — Thermal behavior of an oscillator according to quantum mechanics.

(a) Energy versus temperature.

(b) Specific heat versus temperature.

oscillators are distributed. Once this distribution in frequencies is
known it is merely a matter of summation to find total specific heat.
The problem of finding the distribution in frequency of the oscillators
was first solved by Debye. The low-frequency vibrations are very
simply found for they are merely the acoustic vibrations of the crystal ;
they are very similar to the normal modes shown for the square mem-
brane of Fig. Ig. For these low-frequency vibrations it can be shown
by a straightforward argument, which is too long to give here, that
the number dNoi oscillators whose frequencies lie between v and v + dv
is

dN=VA.{' + '

v^dv,

(7)

where Ct and Cl are the velocities of transverse and longitudinal
waves in the solid and V is its volume. ^^ Debye assumed that this
distribution held for all the normal modes. There is of course a highest
frequency of vibration, i^max, and the total number of normal modes
must be 3N; hence Debye concluded that

1 Ct' ^ Cl'\ ■

Cj}\ 3
26 For a derivation see P. Debye, Ann. d. Physik, 39, 789 (1912).

(8)

696 BELL SYSTEM TECHNICAL JOURNAL

From this equation v^ax can be found if NIV and the velocities Ct
and Cl are known. Knowing j/max and the distribution in frequency,
Debye summed the specific heats of all the oscillators and obtained
the specific heat of the solid. According to this theory the specific
heat vanishes at T = 0 and is proportional to T^ near T = 0. At high
temperatures it approaches the classical value of 3)R. A measure of
the temperature at which the classical value is closely approached is
given by the maximum frequency of atomic vibration j'^axi when ^T is
greater than Ai'max, all the modes of vibration including the highest
make substantial contributions to the specific heat. The temperature
at which this occurs is known as the Debye temperature and denoted
by the symbol Qd] obviously Od = hv^^jk. The specific heat given
by Debye's equation is a function of TJOd only and can thus be rep-
resented by the expression CiT/dD); so that by this theory all crystals
should have the same curve for specific heat versus temperature except
for changes in the temperature scale corresponding to the different
values of their Debye temperatures.

TABLE III
Debye Temperatures in Degrees Kelvin Used in Figure 21

Pb

88

Tl
96

Hg
97

J
106

Cd
168

Na
172

KBr
177

Ag
215

Ca
226

KCI
230

Zn

235

NaCl
281

Cu

315

Al
398

Fe
453

CaFj

474

FeS2
645

C

1860

In Fig. 21 is shown a compilation of specific heat data." For each
substance a value of do (given in Table III) has been chosen so as to
obtain the best agreement with experiment and the values of the specific
heat have then been plotted as a function of T/do- The Debye theory
relates to specific heat at constant volume and in it no allowance is
made for the energy due to thermal expansion. The experimental
points are derived from measurements of specific heat at constant
pressure which have been transformed by using a thermodynamical
relationship so as to give specific heat at constant volume.

For these curves 6d was chosen so as to obtain the best fit. It is,
however, possible to calculate do from theory by using the elastic
constants of the material to evaluate Ct and Cl and then substituting
in Eq. (8). For sodium the elastic constants have been calculated
entirely from theory by the methods described in the section on

"Taken from E. Schroedinger, Handbuch der Physik, Vol. X, p. 307 (1926).

THE QUANTUM PHYSICS OF SOLIDS

697

^\§-

'

+

J

+

lo

1

- 1 ■■ I 1

SEPARATE PLOT FOR HIGHER

TEMPERATURES FOR;

o Tl X J ^ Na

o Hg + cd • KBr

\

•\

\.

1

-*^

^

>^

■'"^-.^J 1

^•^-^

» a

>.

^-*

n

o o

"~^

-^

^'^^

isl O
D <3

O^'HlCK,

--^

-<»

^^

• +

"^^

"^i;,

"^<>

Q- 0
X 0

■«»te.,^_^

^

a

S
o
U

SPECIFIC HEAT AT CONSTANT VOLUME, Cy, IN CALORIES PER GRAM ATOM PER DEGREE CENTIGRADE

698 BELL SYSTEM TECHNICAL JOURNAL

"Electrons in Crystals" and extensions of them* to be discussed in the
third paper of the series. Using the theoretical values one obtains
a value of 143° K for 6d, whereas the value that fits experiment best
is 172° K.

Recently calculations have been made from a model of the crystal
as an assemblage of atoms rather than as a continuum as postulated
in deriving Eq. (7) — that is, a model like the coupled oscillators, rather
than like the stretched membrane, is used. These calculations, prin-
cipally by Blackman, have explained some discrepancies between the
Debye theory and experiment.

The Specific Heat of the Electrons

We must now see why the electrons contribute only slightly to the
specific heat. Let us consider a case like that of sodium where we have
a partially filled band. At the absolute zero of temperature, the elec-
trons will fill all the levels below a certain energy £i and all the higher
levels in the band will be empty (Fig. 22a). Now at temperature T
some of the electrons will be excited to higher states; since, however, an
electron cannot gain more than about kT of energy thermally, only
those electrons whose energies lie in a range kT below Ei can be excited.
Electrons occupying states farther down in the band cannot acquire
kT of thermal energy for, if they did so, they would have to move to
states already occupied and such an act is forbidden by Pauli's prin-
ciple. In order to demonstrate what a small fraction of the electrons
can gain energy thermally, we point out that the width of the energy
band is usually 4 or 5 ev while the value of kT in electron volts is
r/1 1,600 and room temperature corresponds to a kT of about .03 ev.
The electrons which do gain thermal energy have a normal value for
the specific heat but constitute only about one per cent of all the
valence electrons.

It might be maintained that the above argument is specious and
that the electrons could all gain energy kT; this would not violate
Pauli's principle because the electrons would move upward in the
band as a unit, each moving into a state vacated by another elec-
tron. This contention is found to be wrong; one finds by using the
statistical mechanics appropriate to electrons that the distribution of
the electrons among the energy levels is given by the Fermi-Dirac
distribution function. ^^ According to this, the distribution of the elec-
trons among the levels would be as indicated in Fig. 22b. The proba-

* K. Fuchs, Proc. Roy. Soc. 157, 444 (1936).

2* For a discussion of the Fermi-Dirac statistics see K. K. Darrow, The Bell System
Technical Journal, Vol. VIII, p. 672, 1929, or The Physical Review Supplement, Vol. I,
p. 90, 1929.

THE QUANTUM PHYSICS OF SOLIDS

699

0.5

FERMI FUNCTION, f (E)

Fig. 22 — Specific heat of the electrons.

(a) Distribution of electrons in energy for the absolute zero of temperature.

(b) Enlargement of part of (a) but for room temperature; each unit of area rep-
resents a quantum state.

(c) The Fermi distribution function.

(d) A water tank analogue.

700

BELL SYSTEM TECHNICAL JOURNAL

bility that any particular energy state be occupied is given by the
Fermi-Dirac factor/

1

/

E — Ei
g JcT _ I

(9)

This factor is shown in Fig. 22c and the corresponding filling of energy
levels is shown schematically in 22b. A physical picture which is
helpful in understanding this result may be obtained by considering the
distribution of energy levels, Fig. 22a, to be the cross-section of a
trough or tank. If we pour water into this tank it will fill to a certain
level, El. If we let each molecule of water in the tank represent an
electron in the crystal, then the distribution in energy of the electrons
is correctly represented by the distribution in height of the molecules.
Thermal agitation is represented by shaking the tank; this will produce
surface ripples as in Fig. 22d which represent crudely the Fermi-Dirac
distribution.

0.05

Q 0.04

uj O
a. t-

^<
iU5
a < 0.03

^ *" 0.02

^ 0.01

/

/

f^

1i
>2

/

^

/"

//

/

c

CSUM OF a AND 6)

^

3

^

^

ifra^^

^^0= 1.20 X 10-3 T

6=4.70XI0-^T3^^

0 2 4 6 8 10 12 14 16 18 20

ABSOLUTE TEMPERATURE IN DEGREES KELVIN

Fig. 23 — Specific heat of iron at low temperature.

Under certain conditions, however, the electronic specific heat is not
negligible. We have seen that the number of electrons participating in
specific heat is proportional to ^T and that these have a more or less
normal specific heat. Hence the electronic specific heat is proportional
to T. On the other hand, at low temperatures the Debye specific heat
is proportional to T^. Hence for sufficiently low temperatures the
electronic specific heat is the larger. In Fig. 23 we give the specific

THE QUANTUM PHYSICS OF SOLIDS 701

heat of iron near absolute zero.^^ The theoretical curve c, which is
seen to represent the experimental data quite well, is the sum of two
terms represented by curves a and b. a is linear in the temperature
and represents the electronic specific heat while h is cubic and repre-
sents that due to lattice vibrations. Numerical calculations from
theory of the slope of curve a which could be compared with the
observed slope are not available. Curve h, we have said, is just the
Debye curve and is drawn as if the Debye temperature were 462°,
a value which is in good agreement with 453°, the value deduced from
the specific heat at higher temperatures in connection with Fig. 21.
At very high temperatures the electronic specific heat will again be
of importance. But at high temperatures it is necessary to apply
corrections to the Debye theory and the writer is not acquainted with
any unambiguous evidence for electronic specific heat in that case.

Thus we see that only a very small fraction of the electrons of a
partially filled band contribute to the specific heat. It is the Pauli
principle which restrains the remainder. We shall see in the next
paper why the Pauli principle does not interfere with the conduction
of electricity. For the case of an insulator — that is, a crystal each
of whose bands is either wholly filled or wholly empty — it is still harder
for electrons to arrive at empty states and the electronic specific heat
is quite negligible. Hence all of the specific heat for an insulator is of
the atomic vibration type discussed in the Debye theory.

The Theory of Thermal Expansion

In order to understand the theory of thermal expansion we must
study the curve representing energy versus lattice constant for the
solid. This is shown qualitatively in Fig. 24. We note that the
energy curve is unsymmetrical about its minimum. We may describe
its behavior by saying that it is harder to compress than to expand the
solid. This statement is illustrated by a comparison of the expansion
and the compression which can be produced by a given energy E; it is
seen that the asymmetry of the curve causes the expansion produced
by this energy to be greater than the compression. Now the origin of
thermal expansion is as follows: owing to thermal agitation — that is,
atomic vibrations — regions of the crystal are alternately expanding and
contracting; since the expansions occur more readily than the con-
tractions, there is on the average a net expansion. The greater the
temperature the greater this net expansion ; hence we find that the size
of the solid increases with increasing temperature. This explanation
of thermal expansion can be made clearer by considering, not a solid,

29 W. H. Keesom and B. Kurrelmyer, Physica 6, 633 (1939).

702

BELL SYSTEM TECHNICAL JOURNAL

but a diatomic molecule. Suppose Fig. 24 gives the dependence of
the energy of a molecule upon the internuclear distance. Suppose the
molecule is given vibrational energy corresponding to E on the figure.

ao

LATTICE CONSTANT

60
TEMPERATURE

Fig. 24 — The theory of thermal expansion. The asymmetry of the curve for
the energy of a crystal versus the lattice constant is responsible for the thermal
expansion.

Then the nuclei will vibrate between positions h and c on the figure.
Since c lies more to the right of the equilibrium position than h does to
the left, the mean distance of separation, a, lies to the right of ao.
Increasing the vibrational energy to E' increases the mean separation
to a'. This shows that the asymmetry of the potential curve results in
a continuous increase in mean internuclear separation with increasing
energy of vibration. A crystal is, in a sense, an assemblage of diatomic
molecules, each pair of nearest neighbors having a potential energy
curve like that of Fig. 24, and its expansion is explained in the same
way.

The theory outlined above can be made quantitative. From it we
obtain the interesting result that the thermal expansion coefficient is
proportional to the specific heat. This is a rather natural result:
we have seen that the total expansion is proportional to the thermal
energy; hence the rate of expansion with increasing temperature, i.e.
the thermal expansion coefficient, should be proportional to the rate of
increase in thermal energy with increasing temperature, i.e. to the
specific heat. The relationship embodying this statement is known
as Griineisen's law and is expressed by the equation

a = 7-p.CF,

(10)

where a is the volume coefficient of thermal expansion (three times the
linear coefficient) , K is the compressibility, V the volume of one gram

THE QUANTUM PHYSICS OF SOLIDS

703

atom, and Cv the specific heat per gram atom at constant volume. 7 is
a parameter which measures the asymmetry of the curve and is defined
as follows : if we think of the solid as being compressed by an external
pressure, the forces between the atoms will change and the Debye
temperature will increase. If the curve were a parabola — ^that is,
perfectly symmetrical — the Debye temperature would not change.
7 is defined by the relationship

aln«. (U)

7 =

a In V

The 7, K, and V are nearly constant for a given substance. Hence the
thermal expansion curve is practically the same as the specific heat
curve except for a constant factor. In Fig, 25 we give the thermal

XI0"6

UJ 8

O

0 50 100 150 200 250 300 350 400 450 500 550 600

ABSOLUTE TEMPERATURE IN DEGREES KELVIN, T

Fig. 25 — Coefficient of thermal expansion versus temperature for copper.

expansion of copper.^" The Debye temperature was chosen to give the
best fit. We see that the theory of thermal expansion gives as good
agreement with experiment as does the theory of specific heat. If
Griineisen's law were perfectly satisfied, the same Debye temperature
would be found for both the thermal expansion and the specific heat
curves. The relatively small difference between the two values, 325
for expansion and 315 for specific heat, is a measure of the validity of
Griineisen's law.

5° E. Griineisen, Handbuch der Physik, X, p. 43 (1926).

704 BELL SYSTEM TECHNICAL JOURNAL

Griineisen's law applies only to simple crystals; we shall see in the
next section that it is not applicable to the anomalous expansion asso-
ciated with ferromagnetic transformations nor is it applicable to the
abnormal expansions of the order-disorder transformations in alloys.

Magnetic Effects

In this section we return to a discussion of the energy band theory
and this time introduce the magnetic moment associated with the spin
of the electron. It is the spin magnetic moment which when added
to the concept of energy bands leads to explanations of para and
ferromagnetism.

When a body is placed in a magnetic field it becomes magnetized;
in other words it acquires a magnetic moment. Ferromagnetic ma-
terials become very easily magnetized in the field with their magnetic
moments parallel to the field and they may remain magnetized after
the field is removed. Paramagnetic materials are also magnetized in
the direction of the field but only very weakly compared to ferro-
magnetic materials and only while they remain in the field. Diamag-
netic materials are magnetized in a direction opposite to the field and,
like paramagnetic substances, only weakly and while in the field.
These magnetic effects are produced by the electrons in two distinct
ways. In the first place, the motion of the electron as a whole pro-
duces a current and this current, like the ordinary macroscopic currents
in a wire, produces a magnetic field. Conversely, an externally ap-
plied magnetic field affects the motions of the electrons in a body and
can thereby magnetize it; this process accounts for the diamagnetism
of diamagnetic bodies but it may contribute to the paramagnetism as
well. It is not with this first way in which electrons can behave mag-
netically but rather with the second way, described below, that we
shall be concerned. The first way, which is mentioned for complete-
ness, involves a theory too complicated for treatment in this article.
In the second place, an electron can behave magnetically by virtue
of its spin : the rotation of the electron about its own axis produces
a magnetic moment which is anti-parallel — because the charge of
the electron is negative — to the angular momentum due to the spin.
A magnetic field tends to align the spin magnetic moments of the elec-
trons and to make them contribute to the paramagnetism. We shall
see below that this process accounts for the paramagnetism of non-
ferromagnetic metals. We shall see also that the magnetism of ferro-
magnetic bodies is due to the magnetic moment of the electron spin
but that the energy involved in the theory of ferromagnetism is not
an interaction betw^een the magnetic dipoles of the electrons but is

THE QUANTUM PHYSICS OF SOLIDS 705

instead an electrostatic exchange energy like that discussed for atoms
in connection with Figs. 4 and 6.

Paramagnetism and Diamagnetism
Let us consider first the so-called "weak spin paramagnetism."
This occurs in metals, since they have partially filled bands. In the
presence of a magnetic field the spin of the electron is quantized so that
the component of its angular momentum in the field direction is either
-\-}^h or —}/2^i where h = h/lw {h = Planck's constant) is the quan-
tum mechanical unit of angular momentum. The corresponding com-
ponents of magnetic moment along the field are — M/s and -f At/s where
fi^ is the quantum mechanical unit of magnetic moment known as the
Bohr magneton. Letting — e be the charge and m the mass of the
electron and c be the speed of light, we have from the quantum theory

M/3 = ehjlmc. (12)

The ratio of mechanical moment (i.e. angular momentum) to magnetic
moment, taken without regard to sign, is called the "gyro-magnetic
ratio." For the spin of the electron its value is mc/e, but for the motion
of the electron as a whole, its value is Imcje. Because of the difference
between these two values, experimental measurements of the gyro-
magnetic effect play a decisive role in the experimental verification of
the electron spin theory of ferromagnetism in a way which we shall
describe below.

Half the quantum states in an energy band of a crystal have angular
momentum components along the magnetic field of J^i/ and the other
half of —]/2^i. In Fig. 26a, we have divided the states in the band into
two groups, corresponding to the two spins. We shall refer to one of
these as "the band with plus spin" and to the other as "the band with
minus spin." When a magnetic field is applied, the energies of the
electrons are changed. Thus if an electron in the lowest state of the
band with minus spin has an energy £o before the field is applied, it
has an energy of Eq — n^H afterwards; the second term represents,
of course, the energy of the magnetic dipole jji^ when parallel, as dis-
tinguished from anti-parallel, to the field — the situation for minus
spin. All the states in the band with minus spin will be thus altered in
energy. Similarly all the states in the band with plus spin are dis-
placed upwards in energy by jjl^H. This is the situation represented in
Fig. 26h. After the displacement we find that some of the electrons
in the band with plus spin have higher energies than empty states in
the band with minus spin ; such an arrangement is not stable and the
electrons will change their quantum states so as to produce the lowest
energy possible consistent with the distribution of energy levels shown

706

BELL SYSTEM TECHNICAL JOURNAL

in Fig. 26& and with Pauli's principle. The arrangement of lowest
energy is shown in Fig. 26c; electrons have shifted from the band of
plus spin to states of lower total energy in the band of minus spin until
the two bands are filled to the same energy level, indicated by the
solid horizontal line. As the figure shows, the number of electrons
shifted will be the number lying in the energy range bE = tx^H}^

(a)

-SPIN + SPIN

(b)

-SPIN + SPIN

(c)

SPIN + SPIN

— iN(E) 0 0 ^N{E)-*

NUMBER OF QUANTUM STATES AND ELECTRONS PER UNIT ENERGY

Fig. 26 — The paramagnetism of free electrons.

(a) Distribution of electrons in energy.

(b) Displacement of levels by a magnetic field.

(c) Distribution of electrons in energy in a magnetic field.

The number of states, bN, lying in this energy range in the band of
plus spin, which contains of course half the states in the band, is ac-
cording to equation (3)

m = }4N{Ei)8E = y2NiEi)npH.
The magnetic moment of these states is

8M+ = - fi^m = - y2N{Ei)ix^''H.

(13)

(14)

The minus sign occurs because the angular momentum and the mag-
netic moment of an electron are in opposite directions; the states of
plus spin have minus moments in Fig. 26.

The electrons that occupied these states before the field was applied
now occupy states with minus spin and produce a magnetic moment of

bM- = }4N{E,)tx^m.

(15)

Hence the minus band gains a plus moment and the plus band loses a

" We have here assumed that the fractional change in N{E) in the interval n^H
is negligible; this assumption is reasonable. For a field of 10,000 gauss, fi^H is only
5.77 X 10~^ ev while £i — £o is of the order of several ev.

THE QUANTUM PHYSICS OF SOLIDS 707

minus moment and, since the net moment of Fig. 26a is obviously
zero, the net moment produced by the magnetic field is

8M = 8M- - 8M+ = N{Ei)fxpm. (16)

The susceptibility of a material, denoted by x> is defined as the mag-
netic moment produced per unit volume per unit field:

The subscript "s" is a reminder that this susceptibility was produced
by the spin magnetic moment of the electron.

Since the moment produced is in the direction of the field, Xs is
positive; the susceptibility is of the paramagnetic type. As for its
magnitude: in the monovalent metals, as we have said before, the
distribution of levels in the bands is well approximated by the free
electron formula (4). Using this, we find

X. =^(2m)3/2(E^ax)^W. (18)

where £max (= -Ei — -Eo) is the maximum kinetic energy in the band.
Before comparing susceptibilities calculated from this expression
with experimental values, we must discuss diamagnetism. The elec-
trons in the partially filled band of Fig. 26 give formula (18) because of
their spin magnetic moments. They give a susceptibility also because
of their motion through the crystal. For the case of free electrons,
this susceptibility is negative — that is, it is a diamagnetic susceptibility,
and, according to a theory we cannot discuss here, in magnitude it is
one third of Xs- Denoting it by Xm ("w" for motion of the electron
as a whole), we have

Xm= - (1/3)X.. (19)

The electrons in the filled bands, corresponding to electrons in closed
shells in the ionic cores of the metal, also give rise to diamagnetism.
They can give no spin paramagnetism because there is no possibility of
transferring electrons from a filled band of one spin to a filled band of
the other spin — this would require putting more electrons in the band
of one spin than it has quantum states, a violation of Pauli's principle.
Denoting by xi the susceptibility of the ionic cores of the metal, we
have for the net susceptibility x the equation

X = Xs + Xm + Xi- (20)

Specializing this for the case of free electrons in the valence electron

708

band gives

BELL SYSTEM TECHNICAL JOURNAL

= (2/3)xs + Xt = y ( -^ ) iipKEm..y" + Xi-

(21)

In Table IV we give theoretical and experimental values for the sus-
ceptibilities of the simple metals. The values of Xt are obtained from
theory for lithium and by experiment for the other metals.

TABLE IV
Magnetic Susceptibilities *

Li

Na

K

Rb

Cs

1.5

-0.1

0.9

0.5

0.68
-0.26
0.2
0.51

0.60

-0.34

0.06

0.40

0.32
-0.33
-0.12

0.07

0.24

-0.29

X = fx. + x<

X observed f

-0.15
-0.10

* This Table is taken from N. F. Mott and H. Jones, "The Theory of the Proper-
ties of Metals and Alloys," Oxford 1936, p. 188.

t K. Honda, Ann. d. Physik 32, 1027 (1910) and M. Owen, Ann. d. Physik 37, 657
(1912).

Although equation (17) for the spin susceptibility Xs in terms of
N{Ei) is generally true, the relationship that Xm = — Xs/3 is true
only for the case when N{E) is the free electron distribution. ^^ For
some metals N{E) differs greatly from that for free electrons and then
larger values of Xm may occur. The high diamagnetism of bismuth is
explained in this way. In the next paper, we shall discuss the mean-
ing of the freeness of electrons; however, a discussion of electron
diamagnetism lies beyond the scope of this paper.^^

Ferromagnetism

The shift of electrons from one band to another for the paramagnetic
behavior shown in Fig. 26 persists only so long as the magnetic field
is applied. When the magnetic field is removed, the stable arrange-
ment is as shown in Fig. 26a, equal numbers of electrons having each
spin. The situation is quite different in ferromagnetic materials and,
for reasons discussed below, in the stable arrangement there are many
more electrons of one spin than of the other.

Two things are important for the occurrence of ferromagnetism :
the exchange effect as illustrated in Figs. 4 and 6 and the structure of
the bands arising from the 3d levels. The 3d levels, as is shown in

^ An even more stringent condition is actually required.

33 For the diamagnetism of electrons in closed shells the reader is referred to K. K.
Darrow's article, "The Theory of Magnetism," Bell System Technical Journal, Vol.
XV, 1936, and in particular to Page 247.

THE QUANTUM PHYSICS OF SOLIDS

709

Fig. 6, are only partially filled for free atoms of the ferromagnetic
elements iron, cobalt, and nickel. We shall show first how the par-
tially filled 2)d bands together with exchange forces can produce ferro-
magnetism and later discuss the theory of why only the last three of
the eight transition elements are ferromagnetic.

The splitting of the atomic energy levels into bands is shown in

0

y.

1--12--

3d

-0.1

1

-0.2

--1I--

•

-0.3

-

z

y-0.4

o

-

--I0--

5

"""*— ■■— --■^

z

^

>

£-0.5

z

UJ

-

-8--
--7--

...

-0.6

-

- 6--
.- 5--

-0.7

-_3_.

h-2 —

^

-0.8

-

NUMBER OF QUANTUM STATES PER UNIT ENERGY

Fig. 27 — Distribution of states in energy for copper. The distribution is prob-
ably quite similar for iron, cobalt, and nickel and in the absence of calculations for
these other metals, this figure will be used for them. The total number of quantum
states per atom in the 4s and 2>d bands having energies less than the ordinates of the
dashed lines are given by the corresponding integers.

710

BELL SYSTEM TECHNICAL JOURNAL

Fig. 16. The 3d levels give a band capable of containing ten electrons
per atom, five with each spin ; and the 45 band can hold two electrons
per atom, one with each spin. Curves representing N{E) for these
bands, calculated for the case of copper by Slater and Krutter, are
shown in Fig. 27. We see that the 45 band is much wider in energy
than the M and that it contains only one-fifth as many electronic states.
The band structure will be similar for all the transition elements; the
energy scales, however, will be different. As is shown in Fig. 6 the Zd
electrons are more tightly bound for copper than for nickel or chro-
mium. Corresponding to this tighter binding, the d>d wave functions
of copper extend less in space than those of nickel and chromium and
consequently they overlap less between atoms and the Zd band is
narrower for copper. Progressing towards decreasing atomic number
in the sequence of elements from copper to scandium, the ?>d band will
continually widen; and this widening, as we shall see later, can help
account for the absence of ferromagnetism for the elements before
iron in the periodic table.

(a)

+ SPIN

(b)

-SPIN + SPIN

ELECTRONS

PER ATOM

= 5

UNMAGNETIZED STATE MAGNETIZED STATE

NUMBER OF QUANTUM STATES AND ELECTRONS PER UNIT ENERGY

Fig. 28 — The ferromagnetism of nickel.

In Fig. 28, we give a simplified representation of the 45 and M bands
split into two sets according to the spin. (We may, if we wish, sup-
pose that a magnetic field is applied along which the spin is quantized,
but that the field is so weak that the displacement of the energy bands
produced by it is negligible; this supposition is not necessary, however,
for regarding the spin we shall need only the fact that all the electrons
in the + spin band have parallel spins which are anti-parallel to those
in the — spin band.) For the element nickel there are 28 electrons, 10
of which are in the M and 45 bands. They can fill the bands as indi-
cated in Fig. 28a. Let us compare this distribution with the electron

THE QUANTUM PHYSICS OF SOLIDS 711

configuration of the atom, Fig. 6; we see there that there are unequal
numbers of electrons of the two spins. This inequality is produced by
the exchange effect which lowers the more occupied set of 3J levels in
respect to the less occupied set and produces a stable arrangement with
the ?)d levels of one set completely filled. This exchange effect oper-
ates in the same way in metallic nickel. In Fig. 28& we show the
distribution which results when electrons are shifted from the Zd band
of plus spin to that of minus spin until the latter is filled. The ex-
change effect produces the displacements of the bands as shown. The
arrangement in Fig. 2%h is stable; in order for electrons to be trans-
ferred from the filled minus 3d band to the plus band, they would
have to increase their energy, a fact which is expressed by drawing
the diagram so that the lowest vacant quantum states are appreciably
above the highest energy state of the filled d>d band. Thus for nickel
an unbalanced distribution of spins prevails both for the free atom
and the metal.

The Energy of Magnetization

The argument presented above for the stability of the magnetized
state shown in Fig. 286 is not really rigorous. We saw that if one
electron was transferred from the filled 3J band to one of the vacant
states, its energy and, therefore, the energy of the crystal would be
raised. In other words, the magnetized state has less energy than a
state which is slightly less magnetized. This fact in itself does not
prove that the magnetized state is stable; it proves only that it is
metastable — i.e., that its energy is less than the energy of other states
which differ from it slightly; in order to establish the stability of the
magnetized state, it is necessary to prove that its energy is less than
the energy of any other state including that of the unmagnetized state
shown in Fig. 28a. We may illustrate this necessity by considering
the following hypothetical behavior: as the magnetization is reduced
from that of Fig. 28Z> to zero (the value for Fig. 28a), the energy might
at first increase and then decrease — decreasing so much finally that
the energy would be lower for the unmagnetized than for the fully
magnetized state. We shall, therefore, discuss the difference in energy
between the fully magnetized and unmagnetized states; theory shows
that this quantity is the fundamental one whose value determines
whether or not ferromagnetism occurs.

Let us consider the change in energy in going from the unmagnetized
state to the magnetized state in Fig. 28. This change in energy can be
separated into two contributions, one positive and one negative. The
positive contribution comes from an increase in "Fermi energy" or

712 BELL SYSTEM TECHNICAL JOURNAL

"energy of motion," which was discussed in connection with the bind-
ing energy of metals. This energy is positive because after the shift
to the magnetized state, electrons have moved from states in the band
of plus spin to states which lie higher — in respect to the bottom of the
bands in both cases — in the band of the minus spin ; that is, the elec-
trons which have moved from one band to the other have all gained
"energy of motion." The negative contribution to the energy comes
from the exchange effect. This causes the lowering of the filled band
and the raising of the unfilled band; since there are more electrons in
the lowered band than in the raised band, there is a net decrease in
energy due to this exchange effect. Thus we have a positive change in
Fermi energy and a negative change in exchange energy in going from
the unmagnetized to the magnetized state. If the exchange energy
has a greater change than the Fermi energy, the energy of the mag-
netized state is lower and the metal is ferromagnetic.

No satisfactory calculations have as yet been made for these energy
differences. In order to calculate them, accurate values for the dis-
tribution of states in the M band are needed, and the mathematical
methods available for computing this distribution are not as yet very
satisfactory. Next the exchange effect energy must be found; this is
also difficult to calculate accurately. Finally, the description given
here is over-simplified; in particular another energy term, known as the
correlation energy, must be included; this energy acts somewhat like
an exchange energy but between the bands of different spins and it
tends to cancel out the exchange energy. Although these difficulties
greatly mar the usefulness of the theory of ferromagnetism repre-
sented in Fig. 28, this theory is able to correlate a large amount of
experimental material in a very natural way; and since it is the theory
based on the concepts of energy bands, it is the one that we shall dis-
cuss in this paper. In passing, however, we must state that there are
other theories of ferromagnetism which in some ways are more suc-
cessful and in other ways less successful than the band theory. Some
of these are atomic rather than band theories. An example of this type
of difference in method of attack was given in the discussion of the
binding energy of sodium chloride; two treatments were given: for one
the basis being the ions and for the other the energy bands. In the
case of sodium chloride, however, the theoretical equivalence of the
two methods is easily demonstrated. In the case of ferromagnetism,
the two theories are not equivalent and are both simplifications of a
more complex and as yet unsatisfactorily explored intermediate case.

Although no satisfactory calculations of the energy difference be-
tween the magnetized and unmagnetized states of metals exist, the

THE QUANTUM PHYSICS OF SOLIDS 713

theory must be regarded as representing great progress over non -wave-
mechanical theories. The reason is this: in older theories of ferro-
magnetism the energy was supposed to come from the magnetic inter-
action between the magnetic dipoles, and it turned out that the ener-
gies calculated in this way were at least a thousandfold too small.
The energies calculated in the new theory are adequate in magnitude
but have nothing to do with the magnetic moment of the electron;
they arise from the exchange energy, which is, as we have said before,
an electrostatic energy resulting from the wave-mechanical treatment
of Pauli's principle. It is the laws governing the spin quantum num-
ber of the electron, not the magnetic moment, which are responsible
for the energy of magnetization; the externally observed magnetic
field of a ferromagnetic material is merely a superficial indication of
more fundamental electrostatic forces.

Intrinsic Magnetization

According to our theory, the low energy state and therefore the
stable state of metallic nickel is a magnetized one. If one picks up a
piece of nickel at random, however, it may not appear to be magnetized.
This apparent absence of magnetism is due to the presence of "do-
mains." According to the domain theory — which is a very well estab-
lished branch of magnetic theory — a block of nickel will consist of a
number of microscopic domains, each highly magnetized, but having
their magnetic moments pointing at random in a number of directions
so that on the average there is no magnetism. The application of a
magnetic field aligns the magnetic moments of these domains and,
since they are then all parallel, one can measure the total magnetization
of the sample. A field strong enough to line up all the domains is said
to produce "saturation" because a further increase in field will give no
further increase in magnetization. It is customary and convenient to
divide the total or saturation magnetic moment of the material by
the total number of atoms, thus finding the average magnetic moment
per atom, and to express this value in Bohr magnetons. The resultant
value is called the intrinsic magnetization per atom and is denoted by
/3.'^ For example, if a crystal had one electron per atom and all the
electrons had their spins parallel, then all their magnetic moments
would be parallel, too, and the intrinsic magnetization would be
unity, /S = 1.

For nickel the intrinsic magnetization is 0.6 Bohr magnetons per

atom. The following argument shows how easily such a fractional

number can be accounted for by our theory. Nickel has 10 elec-

^ The "intrinsic magnetization" is customarily defined as the magnetic moment
per unit volume when the moments of the domains are parallel.

714 BELL SYSTEM TECHNICAL JOURNAL

trons per atom in the d>d and 4^ bands. The 2)d band with minus
spin is supposed full, containing five electrons per atom. The 4^
band (both spins) can contain two electrons per atom, and from
Fig. 27 we see that it is about one-fourth full; suppose it contains
0.6 electrons per atom; the remaining electrons go to the 2>d band
with plus spin which is not quite full but has a "hole" in it of 0.6
electrons per atom. There are equal numbers of electrons of each
spin in the 4^ band and their magnetic moments cancel. ^^ The net
magnetic moment arises from the unbalance of 0.6 electrons per
atom between the two parts of the 3)d band. This unbalance will
correspond to a magnetization of 0.6 Bohr magnetons. The theory is
not capable of predicting the number 0.6 exactly; however, this number
is entirely consistent with what can be said about the distribution of
levels in the band. In the "atomic" theories of magnetism, it is sup-
posed that each atom has a certain magnetic moment. From the
results of the gyromagnetic experiments,'® one concludes that the
magnetization is due to electron spin. Since an atom whose magnetism
is due to electron spin must have a magnetic moment equal to an
integral multiple of the Bohr magneton,^'' the "atomic" theory is
forced to assume that 40 per cent of the nickel atoms are unmagnetized
and that 60 per cent have one Bohr magneton, or else that 70 per cent
are unmagnetized and 30 per cent have two Bohr magnetons or at any
rate that there are at least two kinds of atoms. These rather awkward
assumptions are not required in the band theory, the reason being, as is
suggested in Fig. 28, that the electrons are not thought of as belonging
to the atoms individually but to the crystal as a whole.

The intrinsic magnetization of ferromagnetic material decreases with
increasing temperature. In the band theory this is explained as fol-
lows: at a temperature T some of the electrons are excited from the
filled band to the partially filled band; as the temperature is increased
more are shifted. Furthermore, if we compare the effects of two equal
increments of temperature, one occurring at a higher temperature than
the other, the one at the higher temperature will have the greater
effect. This is because at the higher temperature more electrons have
been shifted; hence the exchange effect displacement of the band of one
spin in respect to the band of the other spin is less and electrons need

^ Actually there will be a slight exchange effect in the 45 band; however, it will be
so slight that the magnetic moment produced can be neglected

"If a piece of iron is suspended so that it can rotate and then is magnetized, it
will acquire an angular momentum. The ratio of angular momentum to magnetic
moment should be mcje if the magnetization arises from electron spin and 2mc/e if it
arises from motion of the electron as a whole. Experiment gives the following
fractions of the former value: for iron 1.03, for cobalt 1.23, for nickel 1.05.

^'' For a discussion of this theorem see K. K. Darrow's article, "Spinning Atoms
and Spinning Electrons," Bell Sys. Tech. Jour., XVI, 319 (1937).

THE QUANTUM PHYSICS OF SOLIDS

715

not gain so much energy to shift from the more full to the less full
band. Hence at the higher temperature there is more decrease in
magnetization per degree rise in temperature than at the lower tem-
perature. A logical consequence of this reasoning is that the magnet-
ization decreases more and more rapidly as the temperature increases

0.2

+•

^

^-^

-^^.

•

^>S4-

\ +

\

+

\

+

+ = Fe

• = CO

o = Nl

\

O +

V ^

\ +

\

1 +

1

TEMPERATURE, -r-

ec

Fig. 29 — Intrinsic magnetization versus temperature. The horizontal scale rep-
resents the temperature divided by the Curie temperature and the vertical scale,
the intrinsic magnetization divided by the intrinsic magnetization at absolute zero.
The theoretical curve is derived from quantum mechanics.

and becomes zero at a certain critical temperature, which is known as

the Curie temperature and denoted by dc. A more complete discussion

of the theory of the temperature dependence of magnetism would

belong in a paper devoted solely to the theory of magnetism.^* In

38 See, for example, K. K. Darrow, Bell Sys. Tech. Jour. XV, 224 (1936), R. M.
Bozorth, "The Present Status of Ferromagnetic Theory," Bell Sys. Tech. Jour., XV,
63 (1936) and texts such as J. H. Van Vleck, "The Theory of Electric and Magnetic
Susceptibilities," Oxford, 1932, E. C. Stoner "Magnetism and Matter," Methuen and
Company, Ltd., London, 1934, and F. Bitter "Introduction to Ferromagnetism,"
McGraw-Hill Book Co., New York, 1937.

716 BELL SYSTEM TECHNICAL JOURNAL

this paper we shall use the fact that the magnetism changes with the
temperature to explain the anomalous expansion of ferromagnetic
materials. In Fig. 29 we show the variation in intrinsic magnetization
with temperature as observed for iron, cobalt and nickel.

Variation of Intrinsic Magnetization with Composition

Let us consider how the intrinsic magnetization should vary from
element to element in the transition series, supposing always that the
temperature is so low that thermal effects can be neglected. The ele-
ment next to nickel is cobalt; cobalt has one less electron than nickel
so that the Zd band and partially filled 4^ band for it will have one
less electron in them. Because of the relatively small number of
quantum of states in the 45 as compared to the 2>d band, this deficit
will be made up mainly by the 3rf band which will therefore contain
not 4.4 as for nickel but instead 3.4 electrons leading to an unbalance
of 1.6 Bohr magnetons per atom. The observed ^ for cobalt is 1.7 in
good agreement with this.

One can obtain electron atom ratios intermediate between cobalt
and nickel by forming alloys. We shall speak of the electron concen-
tration, C, of these and other alloys, meaning by this term the total
number of electrons available for the 3>d and 4^ bands divided by the
total number of atoms. So long as the minus spin half of the Zd band
remains full and so long as the number of electrons in the 45 band does
not vary much, the value of /S will be a linear function of the electron
concentration varying from ~ 1.6 to ~ 0.6 as the concentration varies
from 9 for cobalt to 10 for nickel. In Fig. 30 are given the intrinsic
magnetizations plotted against electron concentration for a series of
alloys. It is seen that from cobalt to about halfway between nickel
and copper, an increase in C produces, very nearly, a numerically equal
decrease in /S. This means that the increase in C goes toward filling
up the holes in the Zd band and reducing the unbalance and hence jS.
Some alloys are included in Fig. 30 for which the two elements are not
adjacent in the periodic table; their values of /S also conform to the
values predicted from their electron concentrations.

The very natural way in which the band theory accounts for the
results shown on Fig. 30 is its principal success in the theory of fer-
romagnetism.

The bend in the curve between iron and cobalt is not very satis-
factorily explained at present. One theory is that for iron neither Zd
band is entirely full; but this explanation is said to be inconsistent with
the observed dependence of magnetization upon temperature at low

THE QUANTUM PHYSICS OF SOLIDS

717

temperatures. Another theory is that there are only 0.2 electrons in
the 45 band, thus leaving the remaining 7.8 electrons of iron distributed
5 to one 3d band and 2.8 to the other, leaving an unbalance of 2.2; this
theory is unsatisfactory because it would require an inexplicable dis-
placement upwards of the 4s band compared to the 3d in going from

? 2

• Fe
+ Fe
o Fe

-V

-Cr

-NL

- rr\

M

^

^

a Nl- Co
^ Nl-Cu

▼ NL-Zn

V PURE
METALS

Pauling's

THEORY

/f

Y\

'i^

V

/

/

V

\

^v

■''A

\

'i

/
/

\

Cr

Mn

Fe Co

Nl

Cu

6

7

8 9
ELECTRON CONCENTRATION , C

10

II

Fig. 30 — Intrinsic magnetization versus electron concentration.

The data for this figure were obtained from the following sources:
Fe-V and Fe-Cr M. Fallot Ann. de Physique 6, 305-387 (1936).
Fe-Co R. Forrer J. de Physique et le Radium, 1, 325-339 (1930).
Fe-Ni M. Peschard Comptes Rendus 180, 1836 (1925).

Ni-Co P. Weiss, R. Forrer, and F. Birch Comptes Rendus 189, 789-791 (1929).
Ni-Cu and Ni-Zn V. Marian Ann. de Physique 7, 459-527 (1937).

cobalt to iron. Another theory has been proposed by Pauling ^' ; he has
stated it in the "atomic" language but it can be translated into the
band language as follows: the 3d band is broken into two parts, an
upper part containing 4.88 levels per atom, 2.44 for each spin, and a
lower part separated from the upper by an energy gap and containing
5.12 levels per atom, 2.56 for each spin. A number of electrons per
atom varying from 0.6 for nickel to 0.7 for cobalt are in the 45 band;
for simplicity we shall suppose that this number has a constant value
of 0.65 electrons per atom. According to this simplification, one of the
upper parts of the 3d band has 0.65 holes for nickel. This band will
become empty if the electron concentration is decreased by 1.79
(= 2.44 - 0.65)— that is, for a concentration of 10 - 1.79 = 8.21.

39 L. Pauling, Phys. Rev., 54, 899 (1938).

718 BELL SYSTEM TECHNICAL JOURNAL

If the concentration is decreased below 8.21, electrons will be removed
from the upper part with the other spin ; this will result in a decrease in
the unbalance and hence in (3, which has for C = 8.21, a value of 2.44 —
corresponding to one filled and one empty upper part ; and this decrease
will be numerically equal to the decrease in C. Accordingly, the value
of iS for iron, C = 8, is 2.44 - 0.21 = 2.23. The numbers 2.44 and
2.56 were, of course, chosen so as to obtain this agreement for iron.
This theory of Pauling expresses reasonably well the variations in )8 for
all the alloys of Fig. 30.

Criterion for Ferromagnetism

We must now see how the theory explains the absence of ferro-
magnetism for the remaining transition elements. We have seen that
the exchange energy lowers and the Fermi energy raises the energy of
the magnetized state compared to the unmagnetized state. These two
effects very nearly cancel even for the magnetic elements iron, cobalt,
and nickel. For the other elements in the transition series, which are
not ferromagnetic, the Fermi term apparently exceeds the exchange
term. We shall give a theoretical reason for expecting this result.

In the first place we must indicate how nearly the efifects cancel.
Let us take cobalt, which has nine electrons in the ?>d and 4^ bands, as
an example. From Fig. 27 we see that for cobalt in the unmagnetized
state both 2>d bands are filled to about — 0.46 atomic units. In the
magnetized state one band is filled by electrons which have come from
levels with less energy of motion in the other band. Since the top
of the Zd band comes at about — 0.42 units on Fig. 27, the average
gain in energy for each transferred electron is about 0.04 units. Since
the number of electrons transferred is 1.7 per atom, the increase in
Fermi energy is 0.068 atomic units or 0.9 ev per atom. From an
analysis of thermal measurements the value for the actual energy of
magnetization is found to be about 0.2 ev per atom; a value which is
only about one fourth of the predicted increase in the Fermi energy.
Hence the exchange energy exceeds the Fermi energy by only 25 per
cent and the two energies nearly cancel.

The variation in the structure of the Zd band from element to ele-
ment was discussed in connection with Fig. 27; we concluded then that
the bands become wider as we recede in the periodic table from nickel
towards scandium. Greater band width means greater Fermi energy
in the magnetized state and this effect opposes the occurrence of ferro-
magnetism. The exchange energy can also change. Calculations by
Slater,*" which unfortunately are too over-simplified to bear much

« J. C. Slater, Phys. Rev., 49, 537, 931 (1936).

THE QUANTUM PHYSICS OF SOLIDS

719

weight, show that for manganese the Fermi energy outweighs the ex-
change energy so that manganese is not ferromagnetic at all . In Fig. 3 1
we represent the state of affairs predicted for chromium; the exchange

+ SPIN

- SPIN

+ SPIN

UNWAGNETIZED STABLE STATE MAGNETIZED UNSTABLE STATE

NUMDER OF QUANTUM STATES AND ELECTRONS PER UNIT ENERGY

Fig. 31 — The absence of ferromagnetism for chromium.

energy is over-balanced by the Fermi energy and for this metal the
unmagnetized arrangement has the least energy and is the stable state.
A very instructive curve can be drawn to illustrate the criterion for
the occurrence of ferromagnetism. It is shown in Fig. 32. The
vertical scale is the energy of the unmagnetized state, Eu, minus the
energy of the magnetized state, E^^. When Eu - E^ is positive, the
magnetized state has the lower energy and will be the stable state,

-I

< UJ
2 I

MANGANESE

RADIUS OF 3d ORBIT

Fig. 32 — Criterion for the occurrence of ferromagnetism.

720 BELL SYSTEM TECHNICAL JOURNAL

and when Eu — Ej^ is negative, the reverse is true. Hence a positive
value for Ev — Ej^ is a necessary and sufficient condition for ferro-
magnetism. The variable on the horizontal scale is ra (the distance be-
tween nearest neighboring atoms in the crystal) divided by Td (the aver-
age radius for the ^d wave function). Small values of rajra mean
crowding together of the atoms, large values of the Fermi energy, and
no ferromagnetism. Certain values of rajrd, such as are found for iron,
cobalt, and nickel, favor ferromagnetism. Very large values of Valrd
mean widely separated atoms and low Fermi energy and, conse-
quently, ferromagnetism; however, for very widely separated atoms,
the energy of interaction between them is small and so is the energy of
magnetization. The curve shown in Fig. 32 is only qualitative. The
theory that the curve should have this form was first worked out by
Bethe using the "atomic" rather than the band theory of magnetism;
for the reasons discussed above, however, no quantitative theoretical
curve is available. Ratios of raird have been calculated by Slater *
and occur as indicated for several elements. This curve can be con-
sidered from either of two viewpoints. We may imagine that ta re-
mains constant, as it does approximately for the transition elements,
and that ra varies from element to element; we then get the result
shown in Fig. 32. On the other hand we may consider a definite
chemical element thus fixing r^; then Fig. 32 tells us how the energy
of magnetization depends on the lattice constant or volume of the
sample. We shall use this in the following paragraphs to explain the
effects of magnetism upon thermal expansion.

Magnetism and Thermal Expansion
In Fig. 33a we show a solid curve which represents for iron in the
magnetized state the dependence of the energy Ej^j upon the lattice
constant a. In Fig. Z2>h is shown, on a relatively enlarged energy
scale, the value of Ev — Em as taken from Fig. 32 with rd thought of
as fixed, and a the lattice constant in place of Ta- The position of
curve {b) has been adjusted so that the point marked O , corresponding
to iron in Fig. 32, comes at the equilibrium distance or minimum of
the Em curve. Adding the solid curves of (a) and (h) (adjusting the
energy scales, of course) gives the dashed curve representing the energy
Ev of the unmagnetized state shown in Fig. 33a. We are now in a
position to make predictions about the thermal expansion of iron.

Let us imagine that the iron is somehow made to stay in the mag-
netized state. Then its expansion curve, lattice constant versus
temperature, will be shown as in Fig. Zic by the solid heavy line. Next

* J. C. Slater, Phys. Rev., 36, 57 (1930).

THE QUANTUM PHYSICS OF SOLIDS

721

imagine it maintained in the unmagnetized state; in this state the
equilibrium lattice constant is smaller than for the magnetized case
and the expansion curve is shown dashed. The curves for fixed

il

-*^

xx

'A

u^^/ 1

\\

•

/

\\

•

/

\V

/ /

'M

\\

/ /

\\

\
— \

(a)

y/ / / /

^ X y / /

^KyWy ^

o

(0

^yyyyp'Z

^^^^^,,.^^^^^y^^^

<

^»^^/']^/]^/^£:^

Q.

_.rr-<^^^^^^

UJ

-■'^'^^^I--^'I--^''^ "^ 1

:::>C^-''' 1 (c)

"

LATTICE CONSTANT

ec

TEMPERATURE

Fig. 33 — Theory of the thermal expansion of iron.

(a) Energy in magnetized (M) and unmagnetized {U)

states versus lattice constant.

(b) Difference in energies versus lattice constant.

(c) Lattice constant versus temperature.

(d) Thermal expansion coefificient versus temperature.

intermediate degrees of magnetization are shown as light lines. Now
as the iron is heated the magnetization does not stay constant but
decreases with temperature and becomes zero at the Curie temperature
Q^. In Fig. ZZc this corresponds to a continuous shifting from the
line of higher magnetization to the lines of lesser magnetization with
increasing temperature as indicated by the curve with circles. We see
that the rate of expansion — that is, the thermal expansion coefficient,
which is defined as the derivative of the curve divided by a — should
have an irregular form as shown in Fig. TfZd.

In Fig. 34 we show observed thermal expansion curves for a series of
iron nickel alloys,*^ showing that the expansion for iron rich alloys agrees
with that predicted from Fig. ZZ. The reader may verify that had
the curve of Fig. ZZh been adjusted to correspond to nickel, the anom-
alous expansion would have been in the opposite direction, as is found
experimentally for the nickel rich alloys.

The more rapid the transition from the magnetized to the unmag-

" Figures 34 and 35 are taken in a modified form from J. S. Marsh, " Alloys of
Iron and Nickel," Vol. I, Special-Purpose Alloys, 1938, McGraw-Hill Book Co.

722

BELL SYSTEM TECHNICAL JOURNAL

netized curve, the greater will be the anomaly in expansion. For the
alloy invar the Curie point occurs at about 200° C. and the transition is
so rapid that the magnetic effect nearly cancels the normal expansion.

^y^

^

/

'

''^'

^

t-

/

\

^^

^'a

f

<'

NICKEL
PER CE^

N

y

/

-•'','•

*

r

99^

y^

J

^^'^

/
/

1/

^

/

66.8

^--'

^■^

t
I

J

^

^"^

59.2

-j

^^

1

•^

U-— ■

I

J

47.1

h

/

/

38.2

/

/

r

/

V

/

r

V

y

0 100 200 300 400 500 600 700 SCO

TEMPERATURE IN DEGREES CENTIGRADE

Fig. 34 — Coefificients of expansion for iron-nickel alloys versus temperature.

Figure 35 shows a curve for the thermal expansion of an iron-nickel
alloy containing 36.5 per cent Ni, corresponding to Fig. 33c. The
flat region implies an expansion coefficient of nearly zero.

Griineisen's law is definitely violated by metals having expansion
effects of the sort associated with ferromagnetic changes. Griineisen's
law, it will be recalled, states that the thermal expansion coefficient is
proportional to the specific heat. For all ferromagnetic transforma-

THE QUANTUM PHYSICS OF SOLIDS

T23

tions, the specific heat has a peak at the Curie temperature. For invar,
however, the thermal expansion suffers a dip at the Curie temperature.
Hence the proportionaUty between specific heat and thermal expansion
coefiicient does not hold. Even for cases where the expansion coei^-

< 1.0

I

i

/

/

f

V

y

0'<i>-0-

^wq£>^

k

/

-^

..Jitp^

-100 -50 0 50 100 150 200 250 300 350 400 450

TEMPERATURE IN DEGREES CENTIGRADE

Fig. 35 — Expansion of invar versus temperature.

cient has a peak, as in nickel for example, the proportionality does not
hold. The reason for the failure of Griineisen's law is easily found
and reflects in no way upon validity of the law for the cases to which
it is intended to apply. Griineisen's law is derived by assuming that
the crystal has a single definite energy versus volume curve. For
ferromagnetic materials this is not true as is evinced by the two
curves of Fig. TfTta.

In this paper we have been concerned with the important but inactive
attributes of electrons associated with their energies. We have seen
how the variations of the electronic energy levels can be used to explain
a number of the important properties of solids. In the next paper, we
shall discuss the more dynamic subjects of electron velocities and
accelerations.

ACKNOWLEDGMENTTS

The writer would like to express his gratitude to Dr. R. M. Bozorth
for discussions of the section on magnetism, to Dr. K. K. Darrow for
criticisms and suggestions, to Mr. A. N. Holden for many valuable
comments on the manuscript and for the preparation of the crystal
of Fig. 1, and to Mr. B. A. Clarke for much valuable advice and
assistance with the figures.

Dial Clutch of the Spring Type *

By C. F. WIEBUSCH

The mathematical theory is developed for the spring clutch
which consists of two coaxial cylinders placed end to end and
coupled torsionally by a coil spring fitted over them. Relations
are derived whereby it is possible to design spring clutches in terms
of the requirements and the constants of the spring material. Ex-
perimental verification of the relations is given. The theory of
residual and active stresses as applied to the springs is discussed.

THE operation of all present day machine switching telephone
systems depends on the use of the telephone dial. The dial
originates the current pulses required to operate the step-by-step,
panel, or crossbar switching equipment and for the reliable functioning
of this equipment the pulses must occur within a closely limited
frequency range. The stepping pulses are produced during the un-
winding of the dial from the position to which it has been wound by
the subscriber and it is this unwinding which must occur at a constant
speed. To accomplish the speed control a governor depending on
centrifugal force is used. It is not desirable that the governor come
into action on the windup of the dial as this would put an extra load
on the user's finger and slow up the operation of dialing. A clutch
which holds in one direction of rotation and is free in the other direc-
tion is therefore interposed between the governor and the finger wheel
with its associated circuit interrupting mechanism. In the past, the
most commonly used clutch consisted of a pawl and ratchet, but this
has now been replaced by the spring clutch because of its quietness
and lower cost. A partially assembled dial using a spring clutch is
shown in Fig. 1.

The ideal clutch for a dial governor would be one offering zero cou-
pling torque during dial windup and an infinite positive coupling in
the other direction. In practice the free torque in the windup direction
need only be small compared to the torque of the main spring, while
the holding torque in the other direction need only be great enough
to withstand the main spring torque plus any helping torque that a

* Essentially the 'same material was presented at National Meeting of Applied
Mechanics Division of The American Society of Mechanical Engineers, New York,
N. Y., June 14-15, 1939, and published in Journal of Applied Mechanics, September
1939, under the title of "The Spring Clutch."

724

THE SPRING CLUTCH

725

Fig. 1 — Dial governor find front and back view of partially assembled dial.

subscriber may impatiently exert. The first limit is easy to set up
on the basis of the mechanical constants of the dial; the fixing of the
latter limit required measurements on the strength of a considerable
number of persons. It was found that the maximum force that an
ordinary man can exert with any finger at the finger hole of a dial
is about six pounds. When the proper factors of safety have been
added to these limits it is possible to specify exactly the requirements
on the dial clutch. The remainder of this paper is devoted to the
development of the relations and a discussion of the problems involved
in designing a spring clutch to meet a given set of requirements.

I™3.

wsWi'SI^ JL

Fig. 2 — Telephone-dial clutch.

The type of spring clutch to be discussed here consists of two cylin-
ders placed end to end, rotating on a common axis, and torsionally
coupled by the friction between the cylinders and a coil spring fitted
over the cylinders. A photograph of such a clutch, assembled and
apart, from a telephone dial is shown in Fig. 2. In spite of widespread
use there seems to be little theoretical discussion of this device in
the literature.

726

BELL SYSTEM TECHNICAL JOURNAL

It is obvious that if the driving drum be rotated in the direction to
wind up the spring and decrease the diameter, the spring will grip the
cylinders and will be capable of exerting more torque than it would in
the direction of rotation which tends to unwind the spring. Equations
are to be developed which will permit the calculation of these two
torque values in terms of the physical dimensions and the material
constants of the clutch.

Torque of Spring Clutch in the Free Direction
In Fig. 3 assume that the spring is fastened to the left-hand arbor in
order that any slipping which may take place must occur on the driving
drum on the right. Assume also that the spring is so formed that the

Fig. 3 — Diagram of spring clutch.

inward radial force on the drum per unit length of the material is
constant when no torque is applied.

Notation
/ = length along the line of contact of the spring on the arbor,

measured from the free end to any point, in.
ju = coefficient of friction between the spring and the arbor
^2 = radius of the arbor, in.
R2 = radius to the neutral bending axis of the spring when on the

arbor, in.
N == number of turns on the right-hand arbor
P = compression in the spring wire at any point due to the applied

torque; this is not the stress in the material but the resultant

force acting across the entire cross section of the wire, lb.
/o = radial force of spring on arbor when no torque is applied, lb. per

in. of contact line.

THE SPRING CLUTCH 727

As compression exists in the spring wire at any point when the arbor
is turned to make the spring unwind, there will be a radial force sub-
tracting from /o at every point. This subtracting force is Plr^. The
increase of compression in the wire along the length of the line of
contact due to friction is

dP = m(/o - PlrMl (1)

which upon integration gives

/ = - (r^/M) In [/o - (P/r2)]C,

where C is a constant of integration equal to I//0 since P = 0 at ^ = 0.
Hence

P = rMl - e-^'/'-^). (2)

Since / = I-kYiN,

P = rMl - e-2-^''). (3)

Since the torque is equal to Pr2

T = r^Joil - e-2-^M) (in. -lb.). (4)

It will be observed that for any but fractional values of N/j. the ex-
ponential term becomes very small and

T = r2% (A^M > 1). (5)

If Nn =1.0 this expression is in error by only 0.2 per cent. It can
thus be seen that provided N/j. does not become too small, variations
in A^^ or M do not affect the torque exerted. The torque will depend only
on the radius of the arbor and on the force /o which is controlled
entirely by the dimensions and the elastic properties of the spring.

Torque of Spring Clutch in the Gripping Direction
If the torque is applied to the clutch in the direction to wind up the
spring, instead of unwind it as in the previous case, the force P'Jr2
due to the tension P' in the spring wire adds to the inward force /o and
the relation corresponding to equation (1) is

dP' = m(/o + P'lr2)dl. . (6)

From which by the same method as before

P' = r2/o(e2-VM _ 1). (7)

The corresponding torque is

T' = rif,{e''^^'>^ - 1) (in.-lb.). (8)

728

BELL SYSTEM TECHNICAL JOURNAL

In this case the torque increases rapidly with an increase in either
N or n especially for large values of Nijl. The coefificient of friction is
in general a rather variable factor. It is to be expected that the
slipping torque will also be variable, but since a lower limit can in
general be set for this coefficient it will always be possible to make the
number of turns of the spring such as to give any desired lower limit
of torque.

The Radial Force on the Arbor

One method of evaluating the force /o occurring in the torque rela-
tions depends on equating the potential energy of strain per unit
length of the wire when on the arbor to the work done in expanding
the spring from its free diameter to the diameter of the arbor.

Let

E = Young's modulus for the spring material, psi

/ = the area moment of the wire section, in.^

h = the radial thickness of the wire, in.

Ri = free radius to the neutral axis, in.

;'i — free inner radius of the spring, in.

Fig. 4 — Element of spring in initial and expanded condition.

Consider the portion of spring wire shown in Fig. 4 straightened
out from the initial radius of curvature Ri to the radius Ro. The

THE SPRING CLUTCH , 729

fibers above the neutral axis will be compressed while those below
the neutral axis will be stretched. Let y be the distance of any given
fiber from the neutral axis. The length of the undistorted fiber will
be L = {Ri + 3')^! while after bending this same fiber will have the
length L' — {Ri + y)Qi- The strain or the change in length per unit
length is

L-V ^ _ {R2 + y)d,

L (R, + y)e, ^""^

Since along the neutral axis there is no change in length, 9i = L0/R2
and 61 — Lq/Ri. Substituting these values in equation (9) gives

Strain = {y/R2)(R2 - Ri)/{Ri + 3')- (10)

The potential energy per unit volume in a material strained in tension
or compression is

W/V = (E/2)(Strain)2. (11)

Substituting the value of strain from equation (10) in equation (11)
the energy density at any point of the deflected wire will be

W E

y{R2 - Ri)

V 2 I R^iRi + y) J

(12)

Let b represent the width of the wire at the point y. Then for a wire
symmetrical about the neutral axis the strain energy per unit length
of the wire becomes

r^l^ET y(Ro - RQ

'^bdy, (13)

where the factor (Ri + y)/Ri represents the ratio of the length of the
fiber at the point y to the length along the neutral axis. If all values of
y, and hence also h/2, are small compared to Ri there will be little error
made in neglecting the y, which carries both positive and negative
values, in the expression Ri + y. Hence

W C''^E(R^- R,\\ ,^ ,.,.

T = l^,,2[-R^)'y''y- ^''^

The integral of hyHy is the area moment / of the section and therefore

T=l-(^')-

This must be equal to the work done per unit length of the neutral

730 BELL SYSTEM TECHNICAL JOURNAL

axis, by the force per unit length F{AR) working through the distance
AR where AR = R2 - Ry. That is

F(AR)dAR = \eI

AR

R,{R, + AR)

(16)

Differentiating both sides with respect to AR gives F{AR) for the left-
hand side, and after simplification

^(^«' = f (sr^3- (17)

Substituting for AR its value R^ — Ri gives

F{AR) = EI{R2 - Ri)/RiRoK (18)

The equivalent force per unit length measured along the surface of the
arbor must be larger than this value in the ratio of i?2/^2 since the
same total force is here distributed over a shorter length. This latter
force is/o; hence

/o = ^ F(AR) = EI ^^' lb. per in. (19)

The value of /o calculated from this equation in terms of the constants
of the spring material and the dimensions of the spring may be used in
equations (4) and (8) to calculate the free torque and the slipping
torque of the clutch.

Experimental Check of the Free-Torque Relation
In order to check the validity of the relation for the free torque,
equation (4), and that for the radial force on the arbor, equation (19),
the free torque of a given spring on arbors of various diameters as well
as the torque for different numbers of turns on the same arbor was
measured. The spring of 0.0085 X 0.022-in. phosphor-bronze ribbon
was attached to a short vertical shaft suspended by a torsion fiber of
measured torsional stiffness. The free end of the spring was placed
over a vertical arbor capable of rotation. The arbor was rotated and
the angle of twist of the torsion fiber was measured thus giving a
measure of the slipping torque. The precision of the measurements of
torque was about 0.5 per cent although the sensitivity to small changes
was about 0.2 per cent. No measurable increase of torque occurred
by increasing the number of turns on the arbor beyond six. This is
to be expected if the coefficient of friction exceeds about 0.12.

For all succeeding measurements seven to eight turns were used.
As a further check on the independence of the torque and the coefficient

THE SPRING CLUTCH

731

of friction for this number of turns a measurement was made before
and after oiling the arbor and spring with a Hght lubricating oil.
There was a decrease in torque of approximately 0.25 per cent.

The inside diameter of the spring as measured by a taper gage was
0.180 in. ± 0.001 in. The torque for arbors ranging in size from 0.182
to 0.193 in. was determined and is shown in Fig. 5. This curve ex-

Z 0.008

^ 0.005

y^

y

»

y

y^
y

y

/

y

>

/

/

/

Y

Ji^

y

y

/

fo ,

V

/

'A

f TORQUE

•

'A

V

y'

'A

Y

<y

f

//

■y

/

^

0.6 O

0.180 0.182 0.184 0.186 0.188 0.190 0.192 0.194

DIAMETER OF ARBOR IN INCHES

Fig. 5 — The free torque and the radial force on the arbor for a phosphor-bronze
spring on arbors of different diameters.

trapolated to zero torque gives, for an accurate measure of the inside
diameter of the spring, 0.1794 in. Using this value and the quantity
£/, determined by obtaining the resonant frequency of a straight short
length of the ribbon, of which the spring was made, vibrating as a
fixed free reed, the radial force on the arbor as calculated by equation
(19) is shown by the dotted curve as a function of the arbor diameter
Iri. The points indicate values of /o obtained from the measured
values of torque by the use of equation (5). The two sets of values
agree within about 2 per cent.

As a further check on the validity of the calculations under practical
conditions, the free torque of a phosphor-bronze spring on a dial-
governor arbor was measured for various numbers of I urns of the
spring engaging on the slipping arbor. The torque due lo bearing
friction alone with no spring in place was also measured and found to

732

BELL SYSTEM TECHNICAL JOURNAL

be approximately 0.001 in. -lb. This constant value was subtracted
from the other measured values of torque. The resulting values of
free spring torque are plotted as a function of the number of turns in
Fig. 6. The torque values calculated by eciuations (4) and (19) and

6

1

/

2

^/

slipping] f^EASURED — no LU
TORQUE 1 MEASURED— OILED

BRICANT-

0.8
0.6

[^MEASURED — WAX COATED^,

,- — °

/

X ^

//

>>

0.2

//

0.1
0.06

0.06
0.04

0.02

0.01
0.008

0.006

^«

Ki'

#

J

r

fy

//

FREE fCALCULATEC
TORQUE \ MEASURED

/

/

J

0.002

0.001

/
/

^^

/

2 3 4 5
TURNS OF SPRING ON ARBOR

Fig. 6 — Dependence of torque on the number of turns of the spring engaging the arbor.

using the value oi ix — 0.165 obtained as described in the next section,
are shown on the curve to indicate the agreement.

Experimental Check of the Holding-Torque Relation

It is to be expected that any relation for which the coefficient of
friction is a controlling factor will be difficult to check accurately.
Equation (8) for the slipping torque is of this type. It is possible
however by taking a large number of measurements to establish the

THE SPRING CLUTCH 733

validity of the equation and then by determining Hmiting values for the
coefficient of friction, to use this equation as a design relation, especially
if only a minimum torque limit is set. Measurements of the slipping
torque, as a function of the number of turns, were made on the same
dial clutch that was used for checking the free torque.

This slipping torque was not steady as was the case in the free direc-
tion but varied as much as ± 20 per cent. An average value was taken
in each case. An uncertainty also existed regarding the number of
turns engaging the rotating arbor. Since the crossover from one arbor
to the other requires practically one whole turn, slight differences in the
arbor diameters may result in a gain or loss of almost half a turn. In
addition to these factors there was an end effect due to the fact that
the free end of the spring wire was cut off square rather than beveled
but this factor although calculable was neglected in view of the other
uncertainties. The results of these measurements are shown in Fig. 6.

From equation (8) it can be seen that for large values of N the plot
of T' versus N will be a straight line provided /z is independent of the
force between the spring and the arbor. The slope of this straight
line when multiplied by the proper constant, which can be shown to be
0.368, gives the coefficient of friction. For the experimental points
shown in Fig. 6 this value of /i is 0.165. Using this value of m in
equation (6) the calculated curve was plotted. Considering the un-
certainties involved the calculated and measured curves are in good
agreement.

The dotted curve of Fig. 6 shows the effect of lubricating the clutch
with a light machine oil. This resulted in only a small decrease of the
coefficient of friction. The curve shown by the dashes illustrates the
effect of lubricating a clutch with spermaceti. The coefficient was no
longer a constant but decreased with an increase in load.

Spring Stresses

In determining the load that a spring clutch will withstand, first
without stretching which will result in backlash, and second without
breaking, initial as well as load stresses must be considered. The
initial stresses are made up of the residual stresses due to forming the
spring, plus the stresses due to expanding the spring to fit the arbor,
that is from an inner radius Vi to an inner radius r^.

Of these limiting load values the easiest to calculate is the torque
required to break the spring. This is given by the product of the
radius of the spring and the breaking strength of the spring wire.
Loads much smaller than this value would stretch some of the fibers
of the spring, especially those in which a high initial stress already

734 BELL SYSTEM TECHNICAL JOURNAL

existed. As will be shown, such stretching will cause the radius to
increase at those portions of the spring where the applied stresses are
highest, that is, for those turns near the dividing line of the arbor.

Substituting for y, in equation (10), the distances from the neutral
axis to the extreme inner and outer fibers will give the strain in these
fibers. Provided Ri is considerably larger than /?/2, half the thickness
of the material, the distance to these extreme fibers becomes hjl and
the y in the denominator can be neglected in comparison to i?i. The
maximum fiber stress due to placing the spring on the arbor is this
value of strain multiplied by Young's modulus. Then

This stress is in the form of compression for the outer fibers and tension
for the inner. Since a load on the clutch results in a tension in the
spring, the stress given by equation (20) must be added to the load
tension stress to get the total stress on the inner fibers of the spring.
This initial stress therefore reduces the load-carrying capacity of the
clutch.

Residual Spring Stresses
When a straight wire is wound upon an arbor to form a coil spring
the strain on the inner and outer fibers must exceed that corresponding
to the yield-point and plastic-flow results. To simplify the discussion
assume the idealized stress-strain curve shown by the heavy lines of
Fig. 7(a). The stress distribution across any section of the wire while
wound on the winding arbor will be as shown by the heavy lines of
Fig. 7(b) where Syp is the yield-point stress, the maximum stress that
the material will sustain. The moment, across the section, required
to produce this bending is

fft/2
Shydy (21)

h/2

where h is the width of the wire at any point of y distance from the
neutral axis and 5 is the stress at the same point. If the spring is
released, it expands to a radius R\ in which condition the external and
the internal moments are both zero. It is now possible by applying
the same moment as was given by equation (21) to reduce the radius
of curvature again to Rq but without causing additional plastic flow.
The added stress distribution produced by this second bending must
therefore follow a straight line as shown by 52-52, which together
with the residual stresses in the relaxed condition (radius R^ must

THE SPRING CLUTCH

735

Q.

>

.""

1 L

^^

V^'

x:

^^^

Q.

.-"

</)

1'

a

en

u
3

NOISS3adlA|03

% q: i^

^ > i

736 BELL SYSTEM TECHNICAL JOURNAL

equal the distribution Syp-Syp resulting from the original forming
operation. Therefore the stress distribution in the relaxed condition
(radius R\) must be the difference between Syp-Syp and S1-S2. or as
indicated in Fig. 7(c). The value of ^2 is of course so determined that
the moment as specified by equation (21) is the same for the dotted-
line as for the solid-line stress distribution.

The value of Sr = S2 — Syp is relatively easy to determine for
rectangular and round wire on the basis of the straight-line stress-strain
characteristic if the bending has been sufficiently severe to have caused
plastic flow almost to the neutral axis. The moment given by the
actual stress distribution will then differ but little from that obtained
by equation (21) with 5 replaced by Syp, a constant. The values of 5
corresponding to the S2.-S2. distribution are given by

5 = 2S2ylh. (22)

For a rectangular wire 6 is a constant and equating the moments corre-
sponding to the two stress distributions gives

I SYpbydy = I l^hyHy,

»ft/2 /ift/2 C

SYpbydy =1

-ft/2 J-hj2

from which S^ = (3/2) Syp or

Sr = S2 — Syp — (l/2)5rp (rectangular wire). (23)

Similar integrations in the case of a round wire of radius h/l for
which b = 2V[(/i/2)2 - /] gives

Sr = 0.7 Syp (round wire). (24)

These equations give the residual fiber stresses in the extreme inner
and outer fibers under the assumed conditions. In any case where the
stress-strain characteristic is known a correct value for the residual
stress can be obtained by graphical integration. The values given by
equations (23) and (24) will, however, be fair approximations even in
cases where the stress-strain characteristic is curved provided it does
not exhibit strain hardening to a decided extent. Since a limited
amount of plastic flow takes place for any stress above the proportional
Hmit, which is generally far below the yield point, the residual stress
may be sufficient to cause a small amount of creep. Any additional
stresses will then cause permanent deformation of the spring.

The analysis will be continued on the basis of the idealized straight-
line characteristic. Figure 7(d) shows the result of placing the spring

THE SPRING CLUTCH 737

on the clutch arbor. The line ^o-vSo shows the stresses added by this
expansion where ^o is given by equation (20). The sum of these
stresses and those shown in Fig. 7(c) gives the total stresses as shown
by the solid line of Fig. 7(d). If now a load be put on the clutch a
uniform stress Sl will be added but this stress for even relatively light
loads may be sufficient to cause the total stress on the inner fibers to
exceed the yield point as is indicated in Fig. 7(e). The inner fibers are
consequently stretched and when the load is released and the spring
taken from the arbor it will be found that the center turns of the spring
have expanded. Even with the spring on the arbor if the clutch is
turned in the free direction it will be noticed that these center turns
raise off the arbor. It was shown in the paragraphs on the clutch
torque in the free direction that the torque did not increase appreciably
after the first few turns. This can be explained by the fact that as
soon as the outward radial force due to the compression along the wire
is equal to the initial inward radial force of the spring on the arbor the
friction on these turns vanishes. The value of the compression will be
fixed by a relatively few end turns. Hence if the inward force of some
of the center turns decreases due to their stretching this compression
will be sufficient to expand the turns to clear the arbor. If Sl is still
further increased the stretch will be sufficient to cause the diameter
of the center turns to exceed the arbor diameter even when no torque
is applied in the free direction.

Since the yield point of metals decreases at higher temperature it is
possible to produce a spring having lower residual stresses by the
proper heat-treatment. If the wire is wound on an arbor and then
heated, additional plastic flow takes place since the maximum stress
that can be sustained at the high temperature is that shown in Fig. 7(a)
as the high-temperature yield point. If the spring is then cooled and
released the expansion will not be as great as for the untreated spring.
The residual stresses will again be given by equation (23) or (24) where
Syp is taken as the lowest yield point reached in the temperature cycle.
In Fig. 8, (a), (b), and (c) show the stresses in the heat-treated specimen
corresponding to those shown in Fig. 7, (c), (d), and (e), for the un-
treated spring. Figure 8(c) shows that for the same load stress as for
Fig. 7(e) no permanent deformation has taken place. It is of course
important that the strain-relieving temperature should not go high
enough to lower permanently the strength of the material. This
limit ^ for phosphor bronze is about 320" C.

To determine the stress-temperature characteristics of 18-8 stainless

1 "Better Instrument Springs," Robert W. Carson, Trans. A.I.E.E., vol. 52,
September, 1933, p. 869.

738 BELL SYSTEM TECHNICAL JOURNAL

(a) (b) (c)

z
o

Syp

V)

?

Mi

^

^

^,

^^

7

^

V-

y^

O

lO

n

Ui

nr

a.

>

o

o

h

So

S'So

Fig. 8 — Stress conditions in a strain-annealed clutch spring.

steel ^ a number of springs of 0.0068 X 0.021-in. ribbon were wound on
0.1486-in. arbors and given various heat-treatments. They were then
cooled, released from the arbors, and measured for inside diameter.
Table 1 gives the results of these measurements.

TABLE 1

Effect of Heat-Treatment on Springs

Ribbons of 18-8 stainless steel, 0.0068 X 0.021 in., heat-treated on

0.1486-in. winding mandrels

Heat-treatment temp., °C.

Time, hr.

Diam. after release, in.

Residual stress, psi

25

0.228

111000

100

4

0.206

88000

200

4

0.188

66000

300

4

0.182

58000

400

4

0.175

47000

470

4

0.169

37000

500

4

0.166

33000

400

}i

0.177

51000

400

V2

0.176

49000

400

1

0.176

49000

400

2

0.175

47000

400

3

0.175

47000

400

4

0.175

47000

The residual stresses were calculated by noting from equation (23)
that Sr = S2IS and then obtaining ^'2 from equation (20) rewritten as

h Ri - Rt

2R\ Rq

' 8 per cent nickel, 18 per cent chromium.

E.

(25)

THE SPRING CLUTCH

739

Straight pieces of the stainless-steel ribbon were given the same series
of heat-treatments as the springs. Young's modulus was determined
for each of these samples and a bending test was also applied to de-
termine whether the wire had been permanently annealed. No ap-
preciable effect was noted. The proportional limit and the ultimate
tensile strength of this ribbon at room temperature as measured on a
tensile-testing machine were 41,600 and 252,000 psi, respectively. It
is thus seen that except with the high-temperature anneals the residual
stress alone exceeds the proportional limit and any additional stress
will cause a permanent deformation.

It is also possible to obtain a favorable residual-stress distribution,
that is, an initial compression on the inner and a tension on the outer
fibers. If the released spring having the stress distribution shown in
Fig. 7(c) is expanded until considerable plastic flow takes place on the
inner and outer fibers the stress distribution of Fig. 9(a) is obtained,
which on release results in the residual-stress distribution as shown in
Fig. 9(b).

(b) SPRING
RELEASED

(C) SPRING ON
CLUTCH ARBOR

(d) CLUTCH
UNDER LOAD

■* h *■ •* h *■ •* h "

Fig. 9 — -Stress conditions in an expanded clutch spring.

To verify the validity of these arguments three springs of stainless-
steel ribbon with different preliminary treatments and one of heat-
treated phosphor bronze were tested for backlash as a function of
previous loading. The backlash angle was measured from a point of
slipping in the free direction to the point in the holding. direction at
which it would sustain a load of 0.05 in. -lb. An initial load of 0.5 in. -lb.
was then applied and removed and the backlash measured as before.
This was repeated for various loads up to the breaking point of the
spring. The results are shown in Fig. 10. In the case of the untreated
stainless steel the backlash began to increase immediately. Its higher
initial value was probably due to the unavoidable stressing occasioned

740

BELL SYSTEM TECHNICAL JOURNAL

by assembling the spring on the clutch arbor and to the 0.05-in.-lb.
testing torque. The backlash of the other three samples remained
constant to slightly above 0.5 in. -lb. and then began to rise. At low
loads the phosphor bronze was better while at higher loads the heat-
treated stainless steel had the advantage; the breaking load for the
latter was also about 30 per cent higher.

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

MAXIMUM PREVIOUSLY APPLIED TORQUE IN INCH POUNDS

Fig. 10 — Effect of overload on clutch backlash. Arbor diameter, 0.190 in.

(a) Phosphor-bronze-ribbon spring, 0.0085 X 0.022 in., heat-treated 4 hr. at 230° C,
0.1835 in. ID.

ib) 18-8 stainless-steel ribbon, 0.0068 X 0.021 in., wound on 0.127-in. mandrel
and released, 0.183 in. ID.

(c) 18-8 stainless-steel ribbon, 0.0068 X 0.021 in., wound on 0.120-in. mandrel
and released, 0.170 in. ID, mechanically expanded to 0.183 in. ID.

(d) 18-8 stainless-steel ribbon, 0.0068 X 0.021 in., wound on 0.157-in. mandrel,
heated 4 hr. at 470° C, cooled, and released, 0.182 in. ID.

THE SPRING CLUTCH 741

Conclusion

The relations developed in the preceding sections are sufficient to
determine uniquely the correct spring dimensions for a spring clutch
of specified free and gripping torque provided the material constants
and the cross-sectional shape (round or rectangular) of the wire, as well
as the length and diameter of the clutch arbor, are specified. Choice
of values for the last two factors is based largely on permissible heating
resulting from the slipping in the free direction. Furthermore, as
would generally be the case, if only maximum values of the free torque
and minimum values of the gripping torque are given a number of
solutions can be obtained from which to choose the most convenient.
By combining the relations derived, in a manner to permit step-by-step
calculation, the design of spring clutches is reduced to a simple routine.

Abstracts of Technical Articles from Bell System Sources

Recent Observations on the Relation between Penetration, Infection and
Decay in Creosoted Southern Pine Poles in Line} C. H. Amadon.
The relation between poor penetration and decay, and the necessity
for rational and adequate penetration requirements in treating
specifications, are now fairly well understood by producers and users
of creosoted southern pine poles. The purpose of this brief paper is
to supplement the information presented in the Proceedings for 1936
and 1937 on the behavior of these poles in line under actual service
conditions.

Tarnish Studies. The Electrolytic Reduction Method for the Analysis
of Films on Metal Surfaces} W. E. Campbell and U. B. Thomas.
A method is described for analysis of tarnish films on metals by
electrolytic reduction at the cathode. Its suitability is demonstrated
for the rapid and accurate measurement of oxide films on copper
varying in average thickness from monomolecular layers to 1000 A.
It is shown to be useful for reduction of mixed oxide-sulfide films on
copper and silver. The method is used to measure the oxide films
on freshly reduced copper after one-half hour's exposure to oxygen
or air. Such films are shown to be 10-20 A thick. A thicker film,
measuring 30-70 A is found to be produced by abrasion of copper in
air, water, benzene or toluene. Adaptations and modifications are
discussed which give wide analytical application to the method.

An Electrochemical Study of the Corrosion of Painted Iron? H. E.
Haring and R. B. Gibney. The corrosion protective value of
approximately 50 difi^erent paints was determined by means of an
electrochemical method which has been previously described. This
determination involved the measurement of the change in the potential
of the painted iron with time when wet with water for 24 hr. or less.
It was found that the interpretation of the time-potential curves
which were automatically plotted by a recording vacuum tube elec-
trometer, was facilitated if the test was conducted in a nitrogen
atmosphere. The results obtained with the electrochemical or
potentiometric method compared favorably with those obtained in a

1 Proc. American Wood-Preservers' Association, 1939.

2 Electrochemical Society Preprint 76-25.
^ Electrochemical Society Preprint 76-24.

742

ABSTRACTS OF TECHNICAL ARTICLES 743

one-year outdoor exposure test. Such differences as were found were
shown to be due either to deterioration or improvement in the paint
film as the result of weathering.

Characteristics of Modern Microphones for Sound Recording.^ F. L.
Hopper. Factors influencing the choice of a microphone for sound
recording are considered. The characteristics of a new miniature
condenser transmitter and amplifier, as well as a number of other
types of microphones now in use, are included.

Cold-Cathode Gas-Filled Tubes as Circuit Elements.^ S. B. Ingram.
The application of electronic devices to the local systems plant is
still in its infancy. One of the first of these devices to receive extensive
use is the cold-cathode gas-filled tube. As a sensitive relay it is
beginning to make its appearance in a number of telephone control
and signaling circuits, being best known for its use in the standard
four-party subscriber set where its rectifying property enables it to
discriminate between positive and negative polarity for selective
ringing. Compared with other types of vacuum tubes the cold-
cathode tube has the advantages that it operates without cathode
heating power, has the ability to start immediately when a signal is
applied, and does not deteriorate when not passing current. These
advantages make it particularly suitable for use in telephone circuits
where intermittent service is common and long life and economical
operation are required.

The paper describes the structure and electrical characteristics of
cold-cathode tubes. Their properties as circuit elements are then
illustrated in a number of typical basic circuits.

Indufftive Coordination with Series Sodium Highway Lighting Circuits.^
H. E. Kent and P. W. Blye. This paper describes the wave-shape
characteristics of the sodium-vapor lamp and discusses the relative
inductive influence of various series circuit arrangements in which
such lamps are employed. A method is outlined by means of which
the noise to be expected in an exposed telephone line may be estimated.
Measures are described which may be applied in the telephone plant or
in the lighting circuit to assist in the inductive coordination of the
two systems. These measures need be considered only when a con-
siderable number of lamps is involved, since noise induction is negligible

* Jour. S.M.P.E., September 1939.
6 Elec. Engg., July 1939.
^ Elec. Engg., ]\x\y 1939.

744 BELL SYSTEM TECHNICAL JOURNAL

when there are only a few lamps as, for instance, at highway inter-
sections.

A Cardioid Directional MicroplwneJ R. N. Marshall and W. R.
Harry. A microphone is described which has uniform directivity
over a wide frequency range. This is made possible by placing in a
single instrument a dynamic type pressure microphone element and a
ribbon type "velocity" element, and electrically equalizing the out-
puts before combination. The resultant directional pattern is a
heart-shaped curve or cardioid, giving a fairly wide pick-up zone in
front and a substantial dead zone at the back of the instrument.
Because of the unusually rugged ribbon employed, the new microphone
is much less susceptible to wind noise than ordinary ribbon types.
Housed in an aluminum case, the microphone weighs only 3j lbs.
High output level, low impedance, and high quality, together with
the excellent directivity, promise to make the cardioid microphone an
important tool for the motion picture sound engineer.

Fractional- Frequency Generators Utilizing Regenerative Modulation.^
R. L. Miller. By the application of the principle of regeneration to
certain modulation systems, a generator of submultiple or other
fractional-frequency ratio may be obtained.

A simple example is obtained by considering a second-order modu-
lator whose output is connected back to a conjugate input by means
of a feedback loop including an amplifier and a selective network.
If an input frequency /o is applied, it is found that a frequency com-
ponent fo/2 appearing in the feedback path will modulate with the
applied frequency to produce sidebands of fo/2 and 3/o/2. The net-
work and amplifier, being especially efficient for the frequency fo/2
and having a gain higher than the modulator loss, will reinforce this
component causing it to build up to some steady-state value. Similar
processes are possible by which greater submultiple ratios may be
obtained.

Since the output wave is obtained by a modulation process involving
the input wave, it will appear only when an input is applied and then
bears a fixed frequency ratio with respect to it. Experiments show
that the ability of the generator to produce a fractional frequency is
independent of phase shift in the feedback path. Circuits are possible
in which the amplitude of the fractional-frequency wave will bear a
linear relation to the input wave over a reasonable range and at the

^ Jour. S.M.P.E., September 1939.
8 Proc. I.R.E., July 1939.

ABSTRACTS OF TECHNICAL ARTICLES 745

same time maintain a constant phase angle between the two waves.
Typical circuits are discussed which make use of copper oxide as the
modulator elements.

Seasonal Cosmic-Ray Effects at Sea Level.^ R. A. Millikan,
H. V. Neher and D. O. Smith. By sending a Neher self-recording
electroscope in a 10-cm lead shield repeatedly on a slow Norwegian
steamer over the route Vancouver-Los Angeles, around South America
and return to Los Angeles and Vancouver, we find (1) as heretofore
an equatorial dip measured from Los Angeles of seven per cent on the
western side of South America, eight per cent on the eastern side;
(2) no measurable seasonal effect, or winter-summer differences, at all
in the voyage from Los Angeles to the Straits of Magellan; (3) as
heretofore constancy in cosmic-ray intensity in summer and fall,
within the limits of uncertainty imposed by fluctuations estimated
at not over one per cent, on the voyage between Los Angeles and
Vancouver; (4) but in winter and spring an increase of as much as
two or three per cent between Los Angeles and Vancouver. This is
interpreted as the atmospheric-temperature effect earlier studied by
Hess, Compton, and their respective collaborators.

Some Engineering Considerations in Loading Circuits}^ J. A.
Parrott. This paper describes the various loading arrangements
used on toll entrance and intermediate cable circuits and discusses the
transmission benefits obtained by loading and some of the important
problems in the consideration of loading railroad entrance and inter-
mediate cables. In addition to voice frequency loading, loading for
the lower frequency carrier systems such as the Type H is also
discussed.

The Formation of Metallic Bridges between Separated Contacts}^
G. L. Pearson. Low resistance bridges were formed between gold,
steel and carbon electrodes having separations of 2-70 X 10~'^ cm by
applying voltages less than the minimum sparking potential. For a
given pair of electrodes the field required to form the bridges is a
constant and is 5-16 X 10^ volts per centimeter. Measurements of
the temperature coefficient of resistance of the bridges identify them
as consisting of the material of the electrodes. A study of their re-
sistance as a function of the displacement of one of the electrodes
shows that they may be pulled out as well as crushed. At voltages

" Phys. Rev., September 15, 1939.

^'' Proc, Assoc. Amer. R.R., Telegraph and Telephone Section, April 1939.

11 Phys. Rev., September 1, 1939.

746 BELL SYSTEM TECHNICAL JOURNAL

less than those required to form the bridges, field currents exist.
These increase rapidly as the field is raised and attain a value around
10"^" ampere before the bridges are formed. Calculation of the
maximum electrostatic stress on the electrodes at the time of break-
down gives a value 0.05 to 0.0005 times the tensile strength of the
electrode material at room temperature. The field is locally higher
than that calculated because of surface roughness and the tensile
strength is probably lowered by the local heating known to accompany
field currents. The data therefore indicate that electrostatic force
pulls material from the electrodes to bridge the gap.

Measuring Transmission Speed of the Coaxial Cable}"^ J. F. Wentz.
Time of transmission of carrier currents over high speed lines is dis-
cussed. A method of measuring this time delay as used on the
1000-kc system of the New York-Philadelphia coaxial cable is de-
scribed and the results are given for the television band transmitted
over it experimentally.

12 Bell Labs. Record, June 1939.

Contributors to this Issue

M. J. Aykroyd, B,S. in Civil Engineering, Queen's University, 1913.
Bitulithic and Contracting Company, Edmonton, 1913-14; Depart-
ment of Public Works, Ottawa, 1915-16; Imperial Ministry of Muni-
tions, Montreal and New York, 1916-18; Manager and Director,
Export and Import Company, Montreal and London, England,
1919-23. Bell Telephone Company of Canada, Plant Department,
Montreal and Toronto, 1923-34; Outside Plant Engineer, Bell Tele-
phone Company of Canada, Toronto, 1934r-.

D. G. Geiger, Queen's University: B.S. in Electrical Engineering,
1922; B.S. in Mechanical Engineering, 1923; Department of Electrical
Engineering, 1923-24. Bell Telephone Company of Canada, Montreal,
Transmission Division of General Engineering Department, 1924r-26
and 1928-29. Lecturer in Electrical Engineering, Queen's University,
1926-28. Transmission Engineer, Bell Telephone Company of
Canada, Toronto, 1930-.

Eginhard Dietze, B.S. in Electrical Engineering, University of
Michigan, 1917. American Telephone and Telegraph Company,
1917-34; Bell Telephone Laboratories, 1934-. Mr. Dietze has been
engaged in transmission studies of telephone stations, including room
noise conditions at telephone locations. He is co-author of "Indi-
cating Meter for Measurement and Analysis of Noise."

Walter D. Goodale, Jr., E.E., Lehigh University, 1928; M.E.E.»
Polytechnic Institute of Brooklyn, 1937. American Telephone and
Telegraph Company, Department of Development and Research,
1928-34; Bell Telephone Laboratories, 1934-. Mr. Goodale has been
engaged in studies of various factors affecting telephone station
transmission.

W. B. Bedell, Ohio Northern University, U. S. Army, 1917-1919
(Lieutenant, Infantry) ; American Telephone and Telegraph Com-
pany, Long Lines Engineering Department, 1919-. Mr. Bedell is
engaged in equipment engineering work involving broad-band carrier
telephone systems.

747

748 BELL SYSTEM TECHNICAL JOURNAL

Glen B. Ransom, B.S. in Electrical Engineering, University of
Minnesota, 1921. American Telephone and Telegraph Company,
Long Lines Department, at Chicago, 1922-27; District Engineer at
Indianapolis, 1927-28; Division Transmission Engineer at Cleveland,
1928-30; Long Lines Engineering Department, Transmission Branch,
1930- Appointed to present position, Circuit Layout Engineer,
1932.

W. A. Stevens, B.S. in Electrical Engineering, Bucknell Uni-
versity, 1925. New York Telephone Company, Engineering Depart-
ment, 1925-28. American Telephone and Telegraph Company, De-
partment of Operation and Engineering, Transmission Engineering
Group, 1928-. Mr. Stevens' work has largely dealt with toll trans-
mission matters.

B. D. HoLBROOK, A.B., Stanford University, 1924; A.M., 1925.
University of Chicago, 1926-30. Bell Telephone Laboratories, 1930-.
Mr. Holbrook has engaged in research on broad-band carrier telephony
and on signaling systems.

J. T. Dixon, B.E. in Electrical Engineering, Johns Hopkins Uni-
versity, 1924; S.M. in Electrical Engineering, Massachusetts Institute
of Technology, 1926. American Telephone and Telegraph Company,
Department of Development and Research, 1926-34; Bell Telephone
Laboratories, 1934-. Mr. Dixon has been engaged in development
work on carrier systems.

W. Shockley, B.Sc, California Institute of Technology, 1932;
Ph.D., Massachusetts Institute of Technology, 1936. Bell Telephone
Laboratories, 1936-. Dr. Shockley 's work in the Laboratories has
been concerned with problems in electronics.

C. F. Wiebusch, B.A., 1924, M.A., 1925, University of Texas.
Instructor, Department of Physics, University of Texas, 1925-1927.
Bell Telephone Laboratories, 192 7-. Mr. Wiebusch was involved for
a number of years in the development of disc recording and repro-
ducing apparatus and loud speakers and for the past few years has
been engaged in the development of telephone signaling and registering
apparatus.

•^