This Volume is for REFERENCE USE ONLY I(^[^t^(ty8?i(^f^(^i^(yi?ir)rsti{^r)fsvi^ • • • • • «• THE BELr'SrstEM* TECHNICAL JOURNAL A JOURNAL DEVOTED TO THE SCIENTIFIC AND ENGINEERING ASPECTS OF ELECTRICAL COMMUNICATION EDITORIAL BOARD F. R. Kappel O. E. Buckley H. S. Osborne M. J. Kelly J. J. PiLLioD A. B. Clark • R. BOWN D. A. QUARLES F. J. Feely P. C. Jones, Editor M. E. Strieby, Managing Editor TABLE OF CONTENTS AND INDEX VOLUME XXX 1951 AMERICAN TELEPHONE AND TELEGRAPH COMPANY NEW YORK « • • t* V • • • •• '•- < « » « « PRINTED IN U.S.A. VOLUME XXX JANUARY 1951 no. i THE BELL SYSTEM TECHNICAL JOURNAL DEVOTED TO THE SCIENTIFIC AND ENGINEERING ASPECTS OF ELECTRICAL COMMUNICATION The Type N-1 Carrier Telephone System: Objectives and Transmission Features R. S. Caruthers 1 Television by Pulse Code Modulation W. M. Goodall 33 Prediction and Entropy of Printed EngUsh . C. E. Shannon 50 A Submarine Telephone Cable with Submerged Repeaters /. J. Gilbert 65 Theory of the Negative Impedance Converter J. L, Merrill 88 The Ring Armature Telephone Receiver E. E. Mott and R. C. Miner 110 Internal Temperatures of Relay Windings R. L. Peek 141 The Evolution of Inductive Loading for Bell System Tele- phone Facilities T. Shaio 149 Technical Publications by Bell System Authors Other Than in The Bell System Technical Journal 205 Contributors to this Issue 211 30^ Copyright, 1951 $1.30 per copy American Telephone and Telegraph Company p^^ Year THE BELL SYSTEM TECHNICAL JOURNAL Published quarterly by the American Telephone and Telegraph Company 195 Broadway, New York 7, N. Y, Leroy A. Wilson Carroll O. Bickelhaupt Donald R. Belcher President Secretary Treasurer EDITORUL BOARD F. R. Kappel O. E. Buckley H. S. Osborne M. J. Kelly J. J. Pilliod A. B. Clark R. Bown D. A. Quarles F. J. Feely J. O. Perrine, Editor P. C. Jones, Associate Editor SUBSCRIPTIONS Subscriptions are accepted at $1.50 per year. Single copies are 50 cents each. The foreign postage is 35 cents per year or 9 cents per copy. PRINTED IN U. S. A. The Bell System Technical Journal Vol. XXX January, ig§i No. i Copyright, 1951, American Telephone and Telegraph Company The Type N-1 Carrier Telephone System: Objectives and Transmission Features By R. S. CARUTHERS {Manuscript Received Oct. 17, 1950) The Nl Carrier System is a 12-channel, double-sideband system for single cable application. It provides low loss, stable, high velocity service for toll and exchange circuits in the range from 15 or 20 miles to 200 miles. Units and sub- assemblies are miniaturized and arranged on a plug-in basis. Emphasis has been placed on reduction in cost of components, as well as simpUfication of manufacturing methods, engineering, installation and maintenance. Economy is achieved by many novel features, principal among which is a built-in low cost compandor. By compressing and expanding the volume range of speech, the compandor permits much higher tolerance of noise and crosstalk, thereby substantially lowering the cost of both line and terminal facilities. Other impor- tant features are self-contained dialing and supervisory signaling, an individual channel regulator, and automatic equalization through the use of "frequency frogging," or interchange of high- and low-frequency groups at each repeater. T Introduction and General Technical Description HE N-1 Carrier System is the most recent addition to the alphabetic list of carrier telephone systems which began in 1918 with the A system. This and many other systems produced since then have passed into obscurity. Others like the C, H, J, K, and L Systems* carry the majority of telephone traffic for distances exceeding 100 miles. Even though carrier has been the backbone of all the longer-haul telephone service in the country, these systems, and in particular the terminals, have been too expensive for short-haul use. This has prevented tapping the great mass of circuits owned largely by the Associated Companies and extending into nearly every city and town. The M system, developed primarily for power line use, has found limited appUcation in this field. The objective in the design of the N system has been to provide a single cable carrier facility which, without special cable treatment, will be eco- nomical for distances as short as 15 to 20 miles and which will be technically satisfactory in performance for a nominal maximum of 200 miles. Relaxa- * See Ust of references at end of article. 1 2 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 tion of requirements, made possible by limiting the system to 200 miles (instead of the usual transcontinental 4000 miles), has been an important factor in helping to meet the low-cost objective. Elimination of the need for two cables permits use of a large part of the five million miles of toll and exchange circuits in Associated Company voice frequency cables for carrier operation. An important aim of type N carrier is directed at the exchange plant where, even though the mileage is less, the number of circuits for exceeds that in toll use. Here the benefits of a high grade carrier facility are numerous. Exchange Plant makes use of a large percentage of small-gauge, high- capacitance cables, heavily loaded to reduce the net loss. Economically it is difiicult to apply carrier or voice repeaters to these relatively short- length circuits. Many circuits to suburban points are now routed over toll trunks, because of the high loss of the exchange type circuits. Type N can be used to afford a low-loss, high-grade exchange circuit which can be switched in the manner usual for tandem and similar circuits. Low-loss trunks employing type N will be of great benefit in the ever increasing distances in the suburban areas between satellite points and their outlets. Direct, high-grade trunk groups, always at a premium and first selection of automatic switching equipment, can be increased in number. Another important objective, in addition to the provision of a stable, low-loss, high-velocity talking circuit, is that of providing built-in signaling arrangements suitable for dialing and supervision. Such a system is urgently needed to meet the rapidly expanding demands of toll line dialing, as well as for exchange circuits. Such a signaling channel has been made available at a frequency just above and directly associated with the voice channel which it serves. The emphasis placed on economy in the development of the N system has not resulted in a marked lowering of standards of performance. On the contrary, the N system, within its range of operation, sets new standards in many respects, notable among which is stability of net loss. The ob- jectives have been met rather by a combination of new approaches and new circuit elements, backed up by closely coordinated cooperative effort in cost reduction of components, assemblies, and finally, of the complete system. Among the many features making possible such a development as Nl Carrier, certain are outstanding. The most important of these is the com- pandor, a device for compressing and expanding the volume range of sj)eech, thereby affording an improvement in the amount of noise and cross- talk which can be tolerated. The effects of the compandor are far reaching, both in the line and in the terminals. The need for expensive line treatment, THE N-1 CARRIER SYSTEM 3 such as crosstalk balancing, is eliminated; band filter discrimination can be reduced; and signal levels can be raised without undue interference. The N system employs a cable pair in each direction. In order to operate in a single cable the two directions are further separated by the use of different frequency bands; 44-140 kc for one direction on one pair; and 164-260 kc for the other direction on the other pair. Double-sideband, carrier transmitted operation, very similar to that of a radio system, is used, with channels spaced 8 kc apart. The voice channel bandwidth is 250-3100 cycles. The dialing and supervisory control frequency is at 3700 cycles. Frequency frogging, involving interchange and inversion of frequency bands at each repeater, is accomplished by modulation with a 304 kc carrier, and serves two important purposes: Circulating crosstalk paths around the repeater are blocked; and the system is made self -equalizing for as many as ten repeater sections, having a gross loss of between 400 and 500 db. Either paired or quadded, 16, 19, 22, or 24-gauge cable conductors can be employed, with suitable variation in repeater spacing. The nominal spacing of repeaters is 8 miles for 19-gauge and 6 miles for 22-gauge con- ductors. No limitation is placed on the percentage of cable conductors on which N carrier can be applied in a toll cable. Accordingly, as many as 1800 channels can be obtained from a 300-pair cable. For built up connections, two N systems can operate in tandem to make up a toll trunk. At the most, not more than 4 to 6 links of N are expected in tandem in a long multilink connection. Many additional transmission features are listed and briefly described in Table I. Frequency Allocation The frequency allocation of the system is shown in Fig. 1. In order to coordinate system frequencies in the same cable some with odd numbers of repeaters, some with even numbers, and some circuits starting or stopping at intermediate repeater points of other systems, it is necessary to arrange the terminals to transmit and receive either high or low group frequency bands. The channel modulators and demodulators in the terminals, how- ever, use carriers only in the high group band at 8 kc intervals between 168 and 256 kc. Thus, when transmitting high group frequencies to the line and receiving low group frequencies, the high group transmitting unit (HOT) merely amplifies the channel frequencies. The associated low group receiving unit (LGR) however, employs a group modulator with 304 kc carrier that inverts the received low group of line frequencies into the upper band for channel separation in the receiving channel band filters. When 4 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 transmitting low group to the line and receiving high group, the group modulator and 304 kc oscillator are used in the transmitting side of the circuit. Similarly, in the repeater, low and high group bands are interchanged between input and output lines through use of group modulators with 304 kc carriers. Choice of the one group alone for prunary modulation and demodulation of the speech bands stems largely from the desire to use only 12 designs of Table I Transmission Features of N1 Carrier Telephone System 1. Built-in compandor affording an effective signal-to-noise improvement of 20-25 db. 2. Frequency frogging and inversion to improve crosstalk and furnish automatic equalization. 3. Built-in signaling equipment in each channel to provide supervision and dial puls- ing. Tone on-tone off operation employing 3700 cycles, 4. Message channel bandwidth 250-3100 cycles. Transmission of special services (telegraph and telephoto) through standard message channel equipment. 3500 cycle program channel plus 11 message channels, or 5000 cycle program channel plus 9 message channels provided by special program channel equipment. 5. Automatic regulation of each channel at the receiving terminal by the individual channel carrier. 6. All alarms built in with special carrier system failure alarm operating on trans- mitted carriers automatically freeing subscriber dial equipment. 7. Use of noise generator where needed to mask inteUigible crosstalk and obtain satis- factory performance in exchange type cables. 8. Built-in resistance hybrid arrangements for 2-wire termination at non-gain switch- ing points or alternative use of 4- wire termination at —16 and 4-7 levels for standard interconnection to existing broadband intertoll carrier systems. As much as -{-10 level is permissible for special purposes. 9. Repeaters spaced at 8-mile intervals on 19-gauge toll cable and at shorter dis- tances on high-capacity or smaller-gauge exchange cable. 10. Power fed to pole mounted repeaters 8 miles (19-gauge toll cable) on either side of an office repeater, thus requiring power supply stations about 24 miles apart. Power is fed over the cable pairs by simplex connection and use of +130 volt and —130 volt batteries. 11. Automatic regulation of line repeaters by thermistor flat gain adjustment, con- trolled by total output power of the 12 transmitted carriers. 12. In service switching of repeater and terminal circuits. 13. Small, lightweight, portable transmission measuring equipment for ofl&ce and pole cabinet use. 14. Simple order wire and alarm equipment provided to alarm power failures at un- attended power offices and to permit communication with all repeater points. channel band filters rather than 24. Easier filter requirements, occasioned by the use of double-sideband operation and the compandor, together with the fact that, for the high group, all harmonics fall outside the useful band, result in the elimination of the need for transmitting band filters. Thus, the only filter needed in the 12-channel group of sidebands and carriers is a common filter to suppress transmission of speech sidebands on harmonics of the channel carriers. An important factor in the choice of the high group for receiving channel band filters was the better performance obtained in the simple radio type slug-tuned coils in this frequency range, and the smaller size of condensers needed for tuning. the n-1 carrier system 5 Compandor While the compandor principle is not new, it is believed that, for the first time, full advantage of the compandor has been taken in the design of a carrier system. To assist in explaining these advantages, general com- pandor principles will be reviewed in the light of the present development. The 1 A compandor \ designed more than ten years ago, has had considerable usage in open-wire carrier systems in reducing crosstalk, but in the N GROUP CARRIER 304 KC 260 KC— 12p-»-256 11'DU. 248^5 HIGH-GROUP 10[>y 240 2(0 BAND /9[>V232^y OF LINE / vrWpiR ^>: TRANSMISSION/ l^f^'^^^'^ 6[}*^208i 5 [>♦ 200 ct; 40-^192 y / 3[>*184 ^? / 2CK176 < ' 1&^168 ^ 164KC-I \ \ / VOICE TO CARRIER MODULATION AND DEMODULATION IN CHANNEL UNITS / / VOICE / CHANNELS ODDDDDDDDDDD 12 10 8 6 4 2 \ \ 140\KCa- , \ 1tl—136>- \ 2D-^128 5^ \ 3[>*120SI2 \ 4D-»-I12 3-1 5[>*104 0(J \6D-*-96 DCO \7[>*88 "^g >l>*80 ^E 9D— 72 s iqD-^64 oc- 120-^48 44 KC — LOW-GROUP BAND FREQUENCIES OF LINE TRANSMISSION CH 12|-k260KC 260 KC/ EAST-WEST OUT---"^ LOW-GROUP CH)2 CH 12 WEST- EAST IN--^^^^ — HIGH-GROUP CH 1 \ 44 KC 44 KC^ LOW-HIGH REPEATER ,260 KC CH 1 EAST-WEST OUT-— "^ LOW-GROUP CH 12 I-K44 KC 44 KC HIGH-LOW REPEATER LOW-GROUP CH 12 Fig. 1 — N-1 carrier frequency allocations for terminals and repeaters. system a more compact and cheaper unit was needed with requirements revised to match the reduced maximum length of circuits. The word com- pandor is a contraction of compressor and expandor — the compressor in the transmitting terminal compressing the input range of speech volumes for passage over a wire or radio transmission medium where a variety of noise and crosstalk interferences are present — the expandor in the receiving terminal expanding the received range of compressed speech volumes to the original range. A 20-28 db noise advantage is derived, and can be explained as follows: Weak speech volumes most susceptible to system disturbances are lifted and carried at higher level over an intervening noisy medium. 1 Application of Compandors to Message Circuits, C. W. Carter, Jr., A. C. Dickieson and D. Mitchell— ^./.£.E. Trans., Vol. 65, pp. 1079-1086. 6 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 The stronger volumes need less increase in proportion to the volume. When the circuit is idle 28 db gain is introduced by the compressor and 28 db loss by the expander. Any disturbance in the transmission medium in the absence of speech receives 28 db attenuation in the expandor. Loss is removed from the expandor as the speech volume increases and the noise increases correspondingly. In a well designed compandor with proper time constants the increased noise will tend to be continuously masked by the increased speech volume. Interferences to the listener during silent speech periods, such as intelligible crosstalk or audible tones, receive the full 28 db of noise suppression in the expandor. Interference in the presence of speech receives less than full suppression in the expandor the stronger the speech. Table II shows test results of noise advantage of the N-1 compandor at several noise values and speech volumes. In Fig. 2(a) a level diagram shows the gain and loss introduced by the compressor and expandor for signals of different strengths. A signal of 5 db Table II Compandor Noise Advantage Thermal Noise Speech Volume at 0 Level (dba at 0 level) None -30VU -lOVU 0 vu 53 58 63 68 28.0 27.0 24.0 18.5 24.7 22.2 20.0 17.8 24.0 22.2 17.8 14.6 20.3 19.9 17.2 13.7 above 1 milliwatt (-1-5 dbm) is shown as unmodified by compressor and expandor. A signal input to the compressor of —50 dbm receives 27.5 db gain and the resulting —22.5 dbm signal input to the expandor receives 27.5 db loss. For each signal input to the compressor weaker than -|-5 dbm by 2 db, the compressor introduces 1 db more of gain and the expandor 1 db more of loss to a maximum of 28 db gain and loss respectively at —51 dbm input to the compressor or —23 dbm input to the expandor. In Fig. 2(b) input vs output is plotted for compressor, expandor and the combina- tion. The slopes of these input-output plots are 1/2 for compressor and 2/1 for expandor. In Fig. 3, (a) and (b), compressor and expandor circuit schematics are shown for the N-1 Carrier System. Compressor input and expandor output are connected to the resistance hybrid circuit at the left of the compressor schematic for conversion to the 2-wire voice circuit input. Alternative connections for 4-wire operation and an adjustable gain control to establish over-all circuit net loss also are shown. Input voice signals to the compressor pass through the germanium variolosser, are compressed to half the input THE N-1 CARRIER SYSTEM 20 10 -10 -20 -40 -50 -70 -80 -60 -50 -40 -30 -20 -10 0 ZERO LEVEL INPUT POWER IN DBM (h) -IDEAL - ACTUAL yy' y ^^^ ^ '- ,^---- ::>; / COMPRE, 5S0R^,^^^ ^ ^^ // ^^^ "^^^ ^ // // // / 1^^" ^^ y^EXPANDOR ^^^^ANDEM ^ COMPRESSOR AND EXPANDOR ^4 ^'/ / ^ ^ ^^^ ^;^ 20 Fig. 2 (a)— Compandor action on steady tones of different levels, (b) — Input-output load characteristics of N-1 compandor. s THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 volume range, then are amplified in a 2-stage feedback amplifier. Most of the amplifier output is fed through the control circuit where it is rectified in a germanium bridge circuit. A condenser-resistance filter in the control VOICE AMPLIFIER TRANSMITTING LOW-PASS FILTER 2W0R 4W IN 2W0UT VOICE FREQUENCY TO MODULATOR INPUT VIA EXPANDOR SIGNALING SUBASSEMBLY lu^-wiKt ^ \AA/— OUTPUT ^G vvv--^ CONTROL AMPLIFIER Fig. 3 (a) — Channel compressor circuit, (b) — Channel expander circuit. circuit output passes only the rectified syllabic envelope of the speech frequencies. The control circuit filter output current is fed to the midpoints of the germanium variolosser bridge arrangement. The time constants of the control circuit filter are chosen for fast attack (3-5 milliseconds)* * 90% of final value reached in time indicated. THE N-1 CARRIER SYSTEM 9 to prevent syllabic speech bursts from overloading circuits following the compressor, and for slow recovery (30-50 milliseconds)^ so that the vario- losser will introduce fixed loss over a syllabic interval. Too slow a recovery time also is harmful, tending to leave the expandor at low loss after the speech burst is over. Thus, the noise can be heard at the end of each syllable. The expandor in Fig. 3(b), like the compressor, consists of a variolosser, an output amplifier, and a control circuit which rectifies the compressed range of speech signals. Thus, the expandor control circuit is operated by the expandor input speech signal and is called forward acting, while the compressor control circuit is operated by the compressor output signals and is called backward acting. The rectified syllabic envelope control circuit currents in the compressor and expandor are made as near alike as possible through choice of like circuit constants and levels, so that good tracking of compressor and expandor variolossers will result. Integration of the compandor into the design of the N-1 system from the start has yielded many advantages both from a line standpoint, and in repeater and terminal circuit and equipment design. A listing of these advantages follows: Line Operation to frequencies as high as 260 kc without need for far-end crosstalk balancing. Crosstalk in cable increases about 6 db as the fre- quency doubles and the ability to balance crosstalk becomes rapidly unsatisfactory above 60 kc. The N system with satisfactory crosstalk for 200 miles would be satisfactory for only one or two miles without com- pandors. Repeater spacing can be about 25 db longer (40% more miles) than with no compandor, without limitations from near-end crosstalk or line noise. Less precise balance in line and equipment against longitudinal noise can be tolerated. Longitudinal noise suppression coils are eliminated in voice pairs not used for carrier at repeaters in telephone offices. Reflected near-end crosstalk requirements are eased markedly, thus '^ permitting much less precise equipment impedances. Repeater Poorer modulation can be tolerated, thus allowing 25 db less feedback, 25 db less non-regenerative gain and fewer repeater tubes. As many as 25 repeaters can be tolerated in tandem. Without the compandor even one repeater would make the system unsatisfactory from this standpoint. Repeater directional filter discrimination requirements are reduced by about 25 db. 10 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 Use of small and cheap filter coils and repeater transformers with per- malloy cores is possible without harmful modulation. Less precise transformer impedance and balance requirements, in con- junction with reduced size, eliminates the need of electrostatic shields between windings. Terminal Aids in elimination of transmitting channel band filter, and in large reduction of receiving band filter requirements. Permits higher levels of carrier, speech and signaling tone without in- tolerable noise, crosstalk or interchannel modulation effects. Equipment Much more freedom is allowed in equipment layout and wiring, per- mitting more compacting, miniaturizing and less use of shield plates, shielded cans, and shielded wiring, without harmful noise pickup and crosstalk couplings. Operation is feasible from common office battery with large reduction in individual circuit filtering. Signaling and speech circuits can be used on the same ofiice battery without need for separate office wiring, fusing and alarms. Frequency Frogging Like the compandor, frequency frogging is vital to the N system, and numerous benefits result from its use. Primarily the purpose was to eliminate interaction crosstalk, i.e., crosstalk from the output of one repeater into a paralleling voice pair and thence back into the input of other repeaters. In K carrier cables this crosstalk path was eliminated by using two cables and at a repeater point connecting one cable to repeater inputs and the second cable to repeater outputs. The voice pair passing by the repeater point and remaining in the one cable thus was not exposed to both repeater inputs and outputs. In the N system in a single cable a modulator in each repeater frogs the frequency band from low group to high group, and in the following repeater back again from high group to low group. Thus, repeater outputs are always in one frequency band, and repeater inputs in the other, so that the crosstalk through the paralleling voice path can always be blocked by a filter at the repeater input. This approach is invaluable in N carrier where the alternative to frequency frogging is to use a second cable or to add suppression filters in all the paralleling voice pairs. In Fig. 4, cable frogging in K carrier and frequency frogging in N carrier are illustrated diagrammatically. In addition to frequency frogging, the two frequency bands are inverted THE N-1 CARRIER SYSTEM 11 in passing through the N repeater. Thus, the highest frequency channel in one line section becomes the lowest frequency channel in the succeeding line section. So nearly constant are the sums of the losses in two line sections for all channels for the frequency range chosen, that equalization is provided without resort to any major slope correction in the repeaters. The small amount of slope and bulge remaining are easily taken care of in the repeater through use of a few shaping elements in the feedback circuit. TYPE K REPEATER STATIONS CABLE B REPEATER STATIONS -^\ /^Z 12-60 KC ^ .^ /Si E-W CABLE A — {> HIGH GROUP 7H> fHD>T LOW GROUP W-E i^-- ^^-- — <^ — ^ LOW GROUP 8 MILES TYPE N HIGH GROUP E-W SMILES -•1 Fig. 4— Cable frogging and frequency frogging. In Fig. 5(a) the sum of the line losses is shown for two successive 7.5 mile cable sections. The residual slope of only 3.7 db is in contrast to about 34 db of slope in two successive low-group sections in an unfrogged system. The flat line loss of about 90 db is accompanied by only about 0.4 db of bulge. Also shown in Fig. 5(a) is the summation of LH and HL repeater gains. The difference in slope between line and repeater amounts to about 1.5 db and is taken care of by a small range slope control in the repeater. The remaining difference between line and repeater is nearly flat with frequency and is compensated for either through use of flat pads in the line (span pads) or through use of the repeater flat gain regulators. At about each tenth repeater enough frequency distortion has accumulated through lack of match between repeater and line to require use of a deviation equal- 12 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 izer. The anticipated shape of this characteristic, shown in Fig. 5(b), is based on 19-gauge cable and the deviations among the first 46 factory made 95.0 94.5 CO |94.0 ^93.5 2 Z93.0 < 92.5 92.0 88.5 88.0 87.5 V LOSS OF TWO CABLE SPANS ^ (7.5 MILES EACH) ^? \ s. ^X \ ■s. X "^N "v ^V \ \ 3 4 5 6 7 8 9 CHANNEL NUMBER 10 11 i: 10 'pe N Link -1-1 ± 2% Pulse Link -1 zh 1.5% 2nd Type N Link -f 1 =fc 2% 58.5 ± 11.5% During extreme battery and level conditions on one N circuit link about =t 2% more pulse distortion can be expected. Carrier Frequency Transmitting and Receiving Circuit The third part of the channel unit is the carrier subassembly. It contains a germanium varistor modulator and individual channel crystal carrier oscillator in the transmitting circuit and the channel band filter, an auto- matic gain control or channel regulator and a germanium varistor de- modulator in the receiving circuit. Figs. 7(a) and 7(b) show the carrier THE N-1 CARRIER SYSTEM 17 channel circuits. At the input of the transmitting circuit, the output of the compressor LPF and the signal keyer are connected. At the output all 1 + 130 V MODULATOR UNBALANCING CIRCUIT \ (a) (b) 8 10 12 14 16 18 20 22 OUTPUT OF EACH FUNDAMENTAL IN DBM 24 26 28 (C) <(0 O-l UJ z5 UJUJ Is I o ■^ / 1 \ 12 20 21 IN DBM 22 23 24 25 Fig. 14 15 16 17 18 19 SINGLE FREQUENCY OUTPUT 10(a) — Low-high repeater modulation. (b) — High-low repeater modulation. (c) — Gain-load characteristics of high-low and low-high repeaters maintained at a nominal or thermostated temperature which, in general, is from about 135° to 185°F. This allows operation of the regulator with repeater temperatures from about — 20°F to 130°F with little change in its control range. Beyond these temperatures the performance deteriorates slowly. The low level operation of the modulator and repeater amplifier combined with the high level of carrier in the modulator and large amplifier feedback, result in low interchannel modulation. In Fig. 10, (a) and (b), one- and two- 24 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 frequency modulation curves are shown. Figure 10(c) shows the single- frequency load characteristic. Most of the modulation crosstalk results from the many third-order combinations of carriers and speech sidebands in a repeater. Third-order products of this type add in phase in a string of repeaters. Twenty repeaters are 26 db worse in modulation crosstalk than one repeater. Repeater and Terminal Levels The operating levels of the system are all referred to the strengths of the individual carriers which are each made 15 db above one milliwatt (+15 dbm) at reference 0 level of one sideband. Thus, a + 5 dbm signal at 0 level + 10 0 -10 -20 5 m -30 o -40 -50 -60 -70 TERMINAL A HIGH-GROUP TRANSMITTING UNIT OUTPUT +4- ■53 INPUT 168 KG 256 + 10 0 -10 20 TRANSMISSION A TO B HIGH-LOW REPEATER -^OUTPUT .136 "~"*"«*^ *^^ 48 KG 12 +10 0 -10 -20 CD -30 Q -40- TERMINAL B HIGH-GROUP RECEIVING UNIT OUTPUT -5.5 -53 INPUT 12 1 CHANNEL NUMBER Fig. 11(a) — N-1 repeater and group unit level diagrams. in the voice circuit is modulated to produce two sidebands each of +5 dbm at 0 single sideband level in the carrier part of the system. Six db of loss must be inserted between 0 single sideband level and 0 voice level at the output because of the in-phase addition of the two sidebands upon demodulation. Thus, the two +5 dbm sidebands become +5 dbm at 0 voice level in the output. Zero dbm of 3700 cycle tone is used for signal- ing at 0 level and, since it is inserted after the compressor and removed before the expandor, each sideband is 15 db below the carrier. Limiting of speech peaks in the compressor restricts maximum values to about +9 dbm at 0 level. In-phase addition of the maximum speech sideband peaks nearly 100% modulate the carrier (+15 dbm at 0 level). In Fig. 11, (a) and (b), carrier level information is given for repeaters and terminals. High-group output repeaters and terminals have carrier outputs sloped from —3 to +4 dbm with a total of +12 dbm of carrier THE N-1 CARRIER SYSTEM 25 r" Q2j: tiJ3D -JQCO % HOC iu< tr q:±oo Ijcro -tzzTzz^zz^^zSZ | / L IL / / / / 0 - 3 1 P + !3 1 1 \ / / / / b^ b Ca) LOW-HIGH 1 / ( fi / G\ ®/ y y ^ % ^^^ 1^' ^^^^ y X / / / IL + LL / / k 1 ''^® h + ■? w 1 b| 1 1 Cb) ■14 -12 ■10 -8 -6 -4-2 0 2 4 6 REPEATER INPUT IN DECIBELS 10 12 16 Fig. 13 — Regulation characteristics of ,high-low and low-high repeaters. to values below those used in telephone offices. As a result an appreciable increase in tube life is obtained compared to that obtained in offices under ordinarily regulated battery conditions. 28 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 System Regulation The regulating characteristics of the LH and HL repeaters are shown in Fig. 13, (a) and (b). The channel unit regulating characteristic is shown in Fig. 14. The solid curves in Fig. 13, (a) and (b), show change in repeater -J lU S Z-0.5 i-,.o > g-1.5 t- 2-2.0 1- O -2.5 ^ ^ y y / / / ■10 -8-6-4-2 0 2 4 6 8 INPUT DEVIATION FROM NOMINAL IN DECIBELS Fig. 14— Regulation characteristic of channel unit regulator. 9 8 !3 St o Z O ^ z < 1- 1- °2 WITHIN 0.10 DB Q Ol CO a III n (0 " .35 ' J UJ 1 1/ ^1 o i \l 1 / 1 / 1 / / 1 / 1 1 1 y f 1 / / / ' 1 y / / / 1 1 t 0 ,_L_ 1.5 2 3 4 5 6 8 10 15 20 30 40 60 80 100 TIME IN MINUTES Fig. 15 — Stabilization time of repeater or group unit regulator. output when the total carrier input power is subjected to flat gain line changes as shown by the abscissa. The dotted curves show the regulation of a long string of repeaters, each regulating for the same line change, as well as for the residual output change passed on into successive line sections. The circled numbers indicate the number of the repeater at which the output will depart no further at the indicated input regardless of how many follow- THE N-1 CARRIER SYSTEM 29 ing repeaters there may be. The arrows at "a" and "b" show the line change expected for extreme ranges of ambient temperature for 8 miles of 19-guage toll cable. The group terminal regulators have characteristics about like those of the HL repeater. It can be seen that it would take a most extra- ordinary set of line conditions to require the channel regulator to com- pensate for as much as ±5 db change at its input. Despite the doubling of 5cn (a) ^ \ \ 1 0.5 1.0 1.5 2.0 2.5 3.0 FREQUENCY IN KILOCYCLES PER SECOND 3 O a. u 4 z m O 5 Z < X «-> 6 **^"~— -, -COMPRESSOR (b) \: \ s \ V \ EXPANDOR ^ 1 1 OVERALL 5 6 7 8 9 10 11 12 1000 CYCLE OUTPUT AT "O" LEVEL IN DECIBELS ABOVE 1 MILLIWATT Fig. 16(a) — T)^ical channel net loss frequency characteristic, (b) — Typical channel limiting characteristics. circuit variations by the expandor circuit, Fig. 14 indicates that the overall channel net loss can be expected to stay within about d=2 db. Figure 15 shows the speed with which the thermistor regulator in the repeater restores the output to normal when subjected to a line change. An increase of input from the line of 6.5 db, for example, requires a 5-minute wait for the output to get within .25 db of its final value. The regulator operates more slowly on decreasing line input. It is essential that the regula- tor move rather slowly to avoid false regulation on accidental short-dura- tion line hits. 30 the bell system technical journal, january 1951 Over-all System Performance Various means are used to describe the over-all performance of a carrier system such as type N. Subjective tests show, as in other carrier systems, that noticeable deterioration in speech quality occurs when many links are connected in tandem. Satisfactory conversation has been carried on between Milwaukee and Madison, Wisconsin over nine such links, representing a total circuit length of about 750 miles. In this circuit connection, speech passed through 9 compandors, 108 group repeaters and 117 stages of modula- tion. Practically all of the speech impairment occurred in the 9 compandors. 100 90 Z 70 o to 52 60 «0 <50 cc »- a. Ui ^30 90 DBA 82. 72 54 DBA +8VU (3 10 DBA (NOTE 2) 10 DBA (NOTE 4) J-'^^-'-i^'^V-^M^RT^ -^PM^^^-^^^ 7 DBA — NOTES — 1. BEATS BETWEEN LISTENING CHANNEL 3. +4VU INTERFERING TALKER. r^^T^^^liJS^,^ ^^^ "^"^^ °^ ^^^^~ 4. +4VU INTERFERING TALKER, CENT CHANNEL. p/^p END. 2. SIGNALING TONE ON LISTENING CHANNEL. 5. 10-REPEATER SYSTEM Fig. 17 — Relative levels of speech and interference on N-1 carrier. When only six links were used (which is about the maximum likely to be encountered in service) little impairment was observed. Generally even a critical observer cannot distinguish between a single N channel link and a direct circuit connection between the transmitter and the receiver of the same noise and bandwidth. In Fig. 16, (a) and (b), the frequency character- istic and limiting characteristic of the channel are shown. The useful band of speech frequencies passed is considered to be between 10 db points in four links or about 200 cycles to 3100 cycles. In the N system, because the compandor control circuits are particularly wide-band, the frequency re- sponses are substantially alike when measured with single frequencies or when actuated by speech. THE N-1 CARRIER SYSTEM 31 ORDER WIRE JACKS, TEL SET & AUX SIG 5 -I 1 OQ. OOL 1 {>J kS^Mj iZ - oa uj X Z 32 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 Noise and crosstalk in the over-all system come from many causes. Figure 17 shows relative levels of principal contributions. Order Wire and Alarm Circuit Two spare pairs in the cable along an N carrier route are provided for testing and maintenance purposes. One pair, either 16- or 19-gauge with B88 or HI 72 loading, is used for order wire. Signaling uses either 1900 cycles or 1000-20 ringing. A cableman's whistle is used at pole repeaters to signal attended points. A second pair of conductors is used to bring alarms to attended points from unattended repeater power points. Tones at 700, 1100, 1500 or 1900 cycles are provided for alarming four separate points. Tone is normally on the line and is removed by a relay during a trouble. A 5-second delay in the alarm circuit prevents false operation on line hits. D-C. power is simplexed over the alarm and order wire pairs to pole repeaters as a power source for switching in a spare repeater. Figure 18 shows the order wire and alarm circuit arrangement. References 1. "Improved Three-Channel Carrier Telephone System," J. T. O'Leary, E. C. Blessing and J. W. Beyer, Bell Sys. Tech. Jour., Jan. 1939. 2. "New Single Channel Carrier Telephone System," H. J. Fisher, M. L. Almquist and R. H. Mills, A.I.E.E. Trans. 57, 25, (1938); also Bell Sys. Tech. Jour., Jan. 1938. 3. "Twelve Channel Carrier Telephone System for Open Wire Lines," B. W. Kendall and H. A. Affel, AJ.E.E. Trans. 58, 351 (1939); also Bell Sys. Tech. Jour., Jan. 1939. 4. "Some Applications of the Type J. Carrier System," L. C. Starbird and J, D. Mathis, AJ.E.E. Trans. 58, 666 (1939); also Bell Sys. Tech. Jour., Apr. 1939. 5. "Carrier Telephone System for Toll Cables," C. W. Green and E. I. Green, Elec- trical Engineering, 57, 227 (1938) ; also Bell Sys. Tech. Jour., Jan. 1938. 6. "Cable Carrier Telephone Terminals," R. W. Chesnut, L. M. Ilgenfritz and A. Ken- ner, Electrical Engineering, 57, 237 (1938); also Bell Sys. Tech. Jour., Jan. 1938. 7. "Crosstalk and Noise Features of Cable Carrier Telephone Systems," M. A. Weaver, R. S. Tucker and P. S. Darnell, Electrical Engineering, 57, 251 (1938); also Bell Sys. Tech. Jour., Jan. 1938. 8. "Experience in Applying Carrier Telephone Systems to Toll Cables," W. B. Bedell, G. B. Ransom and W. A. Stevens, Bell. Sys. Tech. Jour., Oct. 1939. 9. "An Improved Cable Carrier System," H. S. Black and others, A.I.E.E. Trans., 66, 741 (1947). 10. "A Million-cycle Telephone System," M. E. Strieby, Bell Sys. Tech. Jour., Jan. 1937. 11. "Frequency-Division Techniques for a Coaxial Cable Network," R. E. Crane and others, AJ.E.E. Trans., 66, 1451 (1947). 12. "Progress in Coaxial Telephone and Television Systems," L. G. Abraham, AJ.E.E. Trans., 67, 1520 (1984). 13. "Stability of Tandem Regulators with L-1 Carrier Systems," J. P. Kinzer, AJ.E.E. Trans. 6S (pt. 2), 1179 (1949). 14. "Attenuation and Delay Equalization for Coaxial Lines," W. R. Lundry, AJ.E.E. Trans. 68 (pt. 2), 1174 (1949). 15. "Equalization of Coaxial Lines," K. E. Gould. AJ.E.E. Trans. 68 (pt. 2) 1187 (1949). 16. "Carrier Telephone System for Rural Service," J. M. Barstow, A J.E.E. Trans. 66, 501 (1947). 17. "Application of Rural Carrier Telephone System," E. H. Bartelink and others, AJ.E.E. Trans. 66, 511 (1947). Television by Pulse Code Modulation* By W. M. GOODALL Transmission by pulse code modulation presents inviting possibilities in the field of television in that information may be relayed by many repeater sta- tions without deterioration. In a PCM system, the information signal is periodic- ally sampled and its instantaneous amplitude described by a group of pulses according to a pre-set code. These pulse groups occur at the sampling rate and constitute the transmitted signal. In this process an operation known as ampli- tude quantization is required. This paper will include a discussion of time sampling, amplitude quantization, binary coding and decoding of a television signal. The operation of the equip- ment used to perform these functions is described. The results obtained with an experimental system for different numbers of digits (i.e., maximum number of pulses per group) from one to five are illus- trated by photographs. The television signal used in these tests was obtained from a special low noise film scanner. As was expected, the number of digits required depends upon the amount of noise in the test signal. THE papers that have so far appeared on pulse code modulation have dealt primarily with the transmission of speech. The present work deals specifically with the problems involved in the transmission of television, but in its general aspects it is pertinent to the transmission of any broadband signal by PCM. The chief difference between a system for telephony and one for television resides in the required speeds of operation. The use of the wide band required for this system would be justified by the well known ad- vantages of a pulse-code system which have been pointed out by Oliver, Pierce and Shannon^ Regenerative repetition of the on and off binary pulses at repeater points permits the relaying of the signal to great distances with- out introducing any significant degradations due to noise or distortion aris- ing in the medium. In addition, the coding process permits the trading of bandwidth for noise advantage on a very favorable basis. General Considerations As is well known, PCM is a form of time-division modulation. The in- formation to be transmitted is sampled at regular intervals. This process results in a definite and limited number of amplitudes per unit of time which replace the original wave in subsequent operations. When the sampling frequency is at least twice the highest frequency present in the original wave, the resulting distortion falls outside the desired band and can be re- moved by a low-pass filter in the output of the system. For a system of fixed * Presented orally before the I.R.E. National Convention, New York City, March 1949. II See "Philosophy of PCM"— OHver, Pierce and Shannon— Proc. I.R.E., Nov. 1948. 34 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 sampling frequency it is also desirable to band limit the input signal to avoid undesirable distortion products due to extraneous frequency components which may be present in the original wave. For a nominal 5 mc television channel the sampling rate used in these experiments was 10 mc per second and the input and output filters passed components of 4.3 mc and atten- uated components of 5.0 mc. The sampling process produces a discrete number of samples to be transmitted. For the present case this number is 10 million per second. QUANTIZED NUMBER BINARY NUMBER WEIGHTED EQUIVALENT I I 1 1 1 I 1 I 1 ; 1 I 0 1 0 ; 1 I 0 0 : 0 1 0 1 1 ! 1 16 I 8 1 4 i 2 I 1 16 I 0 I 0 i 2 I 0 i 0 I 0 I 0 I 2 I 1 DECODED NUMBER = 31 = 18 J=l =3 0;0i0]0;0j lojolololo Fig. 1 — Five-digit code groups. Each of these samples may have any value in a continuous range between 0 and a maximum value set by the amplitude range which the system is designed to transmit. In binary PCM each of these amplitudes is transmitted by a code group of binary digits. As an example, consider a five-digit code which is illustrated in the second column of Fig. 1. Here we have five digits or on-and-off pulses. The maximum number of values that can be represented by these five two- position pulses is 2^ or 32 values. Examples shown are for amplitudes of 31, 18, 3 and 0. It is easy to see that any other integer value greater than 0 and less than 31 can also be represented by one of the combinations of pulses and spaces. It is also apparent that when all the combinations have been used up ne other values can be obtained. r TELEVISION BY PULSE CODE MODULATION 35 If it were necessary to transmit all of the continuous values present in the sampled wave, it would be necessary to use a large, or even worse, an infi- nite number of digits. Of course, this is not done. Instead the sampled wave which momentarily may have any value is represented by one of the 32 values that are permitted by the five-digit code. This process is known as amplitude quantization. The quantized amplitudes are shown in the first column of Fig. 1. In the examples shown any number between 17.5 and 18.5 would be represented as 18 and likewise for the other values shown. There is some uncertainty as to the correct value exactly one-half way be- tween permitted values. Here an arbitrary choice is much to be preferred to faulty operation which may give a large error signal. More will be said about this point later. H-(C) CODE GROUPS t--f-(e) AUDIO WAVE UULJi 25 \aT~ 4 4 ^d) DECODED PAM PULSES Fig. 2 — PCM wave forms. Ul 25 28 Each of these code groups, here illustrated as a 5-digit group, represents a single sample of the ten million per second that are needed to represent the television signal. These digits may be transmitted over a single circuit. Figure 2 is an example of this method of transmission for an audio wave a. The samples are represented by the PAM wave b. The code groups are shown in the wave c while the decoded pulses are shown on the wave d. The original audio wave, delayed by one sampling interval, is shown as wave e. It will be noted that the quantized PAM pulse waves d do not fit exactly on the curve. This is the result of the quantization process previously mentioned. For a five-digit 4 kc telephone channel forty thousand digit pulses per second are used in the transmission medium. For television, the same wave forms apply, and a five-digit 5 mc signal uses fifty million pulses per second in the transmission medium. Figure 2 illustrates a PCM system where the 36 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 digit pulses are sent on a time-division basis. It is not necessary to do this, however, since the digit pulses may be sent over separate wire or frequency- division carrier circuits. In the experimental setup used in these studies each of the five digits is transmitted over a separate wire circuit. The total bandwidth required in the transmission medium is essentially the same for both methods of transmission. A single one-way television circuit for five digits would require from 50 to 100 megacycles bandwidth in a microwave system. The actual required band would depend upon the state of the art and the complication permitted in the repeater equipment. From many points of view the transmission medium is the most important part of the system. In non-regenerative systems, for example in the carrier system used in present day coaxial cable transmission, most of the distortion and noise that appears in the final output is the additive resultant of a large number of small contributions arising in the individual repeater links that make up the complete transmission medium. It is easy to see that, for this method of transmission, each repeater link must be much better than the overall system. For a signal that is sampled and quantized in amplitude, however, it is possible to generate a new signal at each repeater which is essentially perfect. In the absence of noise the quantized signal would have one of the permitted amplitudes at the sampling time. A small amount of noise will change this situation so that the ampUtude will not be exactly the correct value at the sampling time. As long as the noise or other disturbance is not too great, it is possible to requantize the signal and to transmit the correct amplitude at the sampling times. This process which is known as regeneration can be used for any type of signal that has been sampled and quantized in amplitude. For a system using binary pulses where only two levels are present, the regenerative process is technically possible. Regenerative repeaters would transmit new pulses, which would be accurately timed and properly shaped. As long as the noise is kept below a threshold value, the noise would not accumulate from link to link and the final decoded signal would be of the same quality as one ob- tained from a monitor located at the transmitter. This means that the quality of the final output of the system depends upon the size of the time and amplitude quanta used in the PCM system. In other words, the final quality depends upon the sampling rate and the number of digits used and not upon the length of the system. The last two columns of Fig. 1 show how the digit pulses can be decoded to produce the output signal. The decoder produces the weighted equivalents of the digit pulses which are then added for each code group. Each of these summation pulses represents one of the input samples in a quantized form. These summation pulses are then passed through an appropriate low-pass filter to the output of the system. TELEVISION BY PULSE CODE MODULATION 37 Description of Experiments The experiments to be described were confined to tests with a transmitting terminal connected to the receiving terminal by short coaxial transmission lines. The transmitting terminal performed the functions of sampling, quan- tizing and coding, while the receiving terminal decoded the PCM signal. No regenerative repeaters were included since they are not necessary in tests designed to evaluate the fundamental limitations of sampling and quantizing of a television signal. Figure 3 gives a block diagram of the system used in these experiments. The input filter band limits the signal so that the highest frequency is less than one-half of the 10-megacycle sampling rate. The input sampler sam- ples the wave and holds the amplitude value obtained until the next sam- pling interval. It uses the same type of circuit as that described in the paper by Meacham and Peterson in The Bell System Technical Journal for January CODER AND QUANTIZER TRANSMISSION MEDIUM DECODER ^-^ — *. INPUT SAMPLER OUTPUT SAMPLER INPUT FILTER OUTPUT FILTER t \ Fig. 3 — Block schematic of PCM system. 1948. In general, much of the circuitry described by them has been used in this equipment, but the units of course function at greatly increased speeds. The coder and quantizer use a coding tube which produces the code simul- taneously in five-digit output circuits. Quantization is accomplished by using a special code, together with suitable slicing units in the output of the digit amplifiers. Further discussion of the coder and quantizer will be given in connection with Fig. 4. In these experiments the transmission medium consisted of an appropriate number of wire circuits, no regenerative repeaters being used. At the receiver, a decoder regenerates the pulses and adds the weighted digits to obtain the quantized PAM signal, as already shown in Figs. 1 and 2. The output sampler is similar to the one used at the input. It will be recalled that step samples are produced, i.e., the signal is sampled at the beginning of each interval and this value is held until the next sampling time. The output filter band limits the signal and removes extraneous components above 5 mc, particularly the 10 mc sampling frequency. As is well known, these I 38 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 filters should have good phase response if they are to be used for a television signal. The physical equipment used in this experiment is housed in three seven- foot cabinet relay racks. One bay contains the sampler, the push-pull am- plifier for driving the deflection plates of the coding tube, the coding tube, the digit amplifier and slicers, and finally the translator. Another bay con- DIGITS 12 3 4 5 DIGITS D □■=■ □ -23 DS -15- ^D □ □ n CONVENTIONAL REFLECTED Fig. 4— PCM code plates. tains the decoder, output sampler, attenuators, patching panel, output filter and other test gear. The last bay contains the regulated power supplies. Coders and Quantizers We return now to further consideration of the coder and quantizer. The coding tube used in these experiments was developed by Mr. R. W. Sears. It is similar in many respects to one previously described by him in The Bell System Technical Journal for January 1948. The older tube produced the code on a time-division basis, while the new tube produces the code simultaneously on a plurality of output digit collectors. The time-division coding tube which was used by Meacham and Peterson in the 96-channel multiplex system first quantized and then coded the signal. The simultaneous coding tube uses a different code which does not require TELEVISION BY PULSE CODE MODULATION 39 a quantized input. The encoded signal is subsequently translated into the conventional binary code. The coder and quantizer are probably the most important parts of the terminals of a PCM system. The following discussion of the two types of coding tubes will illustrate how they function and show how the new tube can function at the greater speeds necessary for television. Consider the code plate on the left side of the next figure (4) . This plate gives the conventional binary code as discussed in connection with the first figure. In a time-division coding tube a point beam is used. It is deflected vertically by the output of the sampler. After the beam has settled down to its proper position, which corresponds to the quantized signal amplitude it is swept across the code plate. An output collector is used which covers the back of the code plate. If the beam goes through a hole in the code plate a pulse is produced; if it is stopped by the code plate no pulse is produced. By this means a code group is produced on a time-division basis for each sample. As long as the beam does not fall on the edge of a hole, this arrangement functions satisfactorily. Now consider the case where the beam sweeps across the set of edges corresponding to the amplitude 15.5. It is seen that, by a slight misalignment of the code plate and the horizontal deflecting plates, the beam could produce either the code group corresponding to 31 or to 0 depending upon the way the deflection axis is tilted with respect to the code plate. This would result in an error equal to one-half of the total amplitude range of the system. Corresponding errors of smaller magnitude are possible for other levels. In all cases this type of error results for signals which have amplitudes one-half way between values permitted by the code. Errors of this sort can be avoided by quantization of the signal before the coding. This is accomplished in the earlier tube by using the output from a mesh of grid wires in a feedback arrangement. The wires of the grid overlap the edges of the holes in the code plate. When the beam hits one of these grid wires, a current is fed back into the input which causes the signal am- plitude to change in such a way as to move the beam between the grid wires. After a short interval the beam settles down in a quantized condition. Then the beam is swept across the code plate. If the beam tends to become mis- aligned during the deflection process, the feedback from the grid wires cor- rects this condition and an accurate code is produced. Because of the time required for the feedback process, this method of quantization limits the number of samples that can be coded in a given time. Another factor which limits the speed of this type of coder is the time re- quired to sweep the beam across the code plate. It is apparent that the time required to register the code could be reduced I 40 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 if all digits were produced simultaneously. In this type of coder a line beam is used which covers the full width of the code plate and the code is registered simultaneously on a plurality of digit collectors, one collector being used for each digit of the code. This is one of the features that was included in the coding tube used in these experiments. In the new tube the time required for quantization by feedback has been avoided by using a different type of code which avoids the large errors which are present in the conventional binary code for amplitude values one-half way between the integer values permitted by the code. This new code, here called the reflected binary code, is shown on the right side of Fig. 4. For present purposes it should be noted that at points one-half way be- tween integer values the beam intersects only one edge in any code group. Further, if the deflection axis is tilted so that an incorrect code group is in- dicated, the resulting error is only one quantum level, instead of a much larger value possible with the conventional binary code. In practice, even if the beam is properly lined up, there wdll be times when the output for the digit in which the beam intersects an edge will be between zero and full output. Since this digit must be unambiguously represented either by a full pulse or no pulse, it is necessary to make a choice and quantize the particular output under discussion. The output of the digit collectors is amplified and the final quantization of any uncertain digit is done by a slicer which is in the output of each digit amplifier. Use of this code thus localizes final quantization to within a single digit, and an arbitrary choice results at most in an error of one quantum level. The use of the reflected binary code for PCM applications was suggested to the writer by Mr. F. Gray. As mentioned before, this code is translated to the conventional binary code. The translator used in these tests was designed by Mr. R. L. Carbrey w^ho developed it specifically for this ex- periment. Results of Experiments We now pass on to some of the results obtained with this system. Figure 5 should help in understanding the results shown in the remaining figures. It shows a triangular wave which has been analyzed into the three ''on" and ''off" rectangular waves shown in the bottom part of the figure. In this paper we shall follow the convention that the digit of largest am- plitude is the first digit, the next largest digit is the second digit and so on. By this convention the first digit is J of the total amplitude range, the second digit § of the first, or } of the total range. Thus, the amplitude of any given digit would bejn of the total amplitude range. It is convenient to think of the first digit as a first-order approximation to TELEVISION BY PULSE CODE MODULATION 41 the original in terms of the rectangular waves. The second digit gives a sec- ond-order correction to add to the first digit, and the third digit gives a third-order correction to add to the first and second digits. The rectangular waves, of course, are the envelopes of the pulses that are transmitted over the various digit channels. Because the respective values represented by the various digits are once and for all known, it is not neces- sary that the amplitudes with which the pulses are transmitted be equal to the values which they represent, but they may to advantage be sent with the same amplitude in all of the digit channels. At the decoder the relative -'1^^- KTn.-'I^I 1 ST DIGIT I I I I I I I 2 ND DIGIT 3 RD DIGIT R^ 1^ ^ 1^?^ 1^ 1^ ^ [x1 N [XI P?^ [^ ^ N I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I Fig. 5 — Rectangular wave approximations. amplitudes of the digit channels are restored according to the coding con- vention and the results added to obtain the rectangular wave approxi- mation to the original wave. It is seen that the first three digits give a fair approximation to the original wave. More digits, of course, would improve this approximation. In general terms, from this point of view, the coder is an analyzer which determines the best approximation to the information wave in terms of a series of rectangular waves of decreasing ampHtudes. The decoder is a syn- thesizer which approximates the original wave by adding the rectangular waves obtained from the coder. The coding convention allows the derived rectangular waves to be transmitted with the same amplitude for all the ( 42 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 ONE DIGIT TWO DIGITS THREE DIGITS FOUR DIGITS FIVE DIGITS ORIGINAL Fig. 6 — Test signal, Density wedge: one to five-digit transmission. digits. The remaining figures show some results obtained by transmitting a television signal through the PCM system described in the first part of the paper. Mr. B. M. Oliver and others of the television group of The Bell Telephone Laboratories have developed a special low-noise film scanner that provides an excellent test signal. This cquii)ment includes a rooter which, in com- TELEVISION BY PULSE CODE MODULATION 43 bination with the expansion of the kinescope, results in an overall linear system. This method of operation, as is well known, results in a wide range of tone values between black and white. The PCM system used, employed steps of equal size; in other words, within the limits of the quantum steps it is a linear system. The combination of the signal from the film scanner, including the rooter, and the linear PCM system, followed by an expanding viewing tube, results in an overall system which employes the limited num- ber of steps in the PCM system to essentially optimum advantage. Fig. 7 — Test signal, RMx\ test chart: five-digit transmission. While in practice, synchronization would probably be derived from the code pulses, for the purposes of this experiment it was not necessary to trans- mit the synchronizing pulse through the PCM system. Synchronization of the monitor was obtained by a separate path. This was done, since in an operating system it would not be necessary to use more than one or two levels to send the synchronizing pulse as compared with 25% or more of the levels that would be necessary in an unmodified standard television wave-form. The pictures shown on the figures were taken with a one-second exposure. It will be realized that in a photographic still picture obtained in this manner the exact effect in the viewing tube cannot be conveyed because it is not possible to see motion due to noise. 44 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 Figure 6 shows the results obtained using a special test signal for five different PCM systems. The five PCM systems are those which result for ONE DIGIT TWO DIGITS '^^J? THREE DIGITS FOUR DIGITS FIVE DIGITS ORIGINAL Fig. 8~Test signal, model: one to five-digit transmission. one digit, for two digit, for three, four and five-digit transmission. The test signal for these pictures was an electrical saw tooth wave derived from the TELEVISION BY PULSE CODE MODULATION 45 horizontal sweep generator. It will be noted that the linear input signal re- sults in an amplitude quantized output signal. The one- digit system sends ONE DIGIT TWO DIGITS THREE DIGITS FOUR DIGITS FIVE DIGITS ORIGINAL Fig. 9 — Test signal, boy and bird: one to five-digit transmission. two levels, black and middle grey. The two-digit system sends four levels, the three-digit system sends eight levels and the four and five-digit system 46 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 SUM OF FIVE DIGITS FIRST DIGIT SECOND DIGIT THIRD DIGIT FOURTH DIGIT FIFTH DIGIT Fig. 10— Test signal, boy and bird: single digits, one through five. sends sixteen and thirty-two levels. The original, of course, is not quantized and shows a smooth graduation from black to white. It is, however, band limited by the input filter. The steps in the five-digit system are even more clearly visible on the picture tube. During some tests in which random noise was added to the TELEVISION BY PULSE CODE MODULATION 47 test signal, it was found that the sharpness of the contour edges was destroyed by random noise when the ratio of the peak-to-peak signal to rms noise was 60 db. For the five-digit picture the smearing of the edges was about one- tenth of the distance between the contours. Other tests which will be de- scribed later suggest that the contours for the five-digit thirty-two level system would be masked with an input peak-to-peak signal to rms noise ratio of 40 db. The writer is not aware of a television system that is capable of generating a signal with a peak-to-peak signal to rms noise ratio of 60 db. However, if such a system were available, these results indicate that an eight- or nine- digit PCM system would be needed to avoid appreciable degradation of the 60 db signal. Figure 7 shows the results for an RMA test chart with five-digit PCM transmission. The resolution is limited by the input filter, the film scanner having a resolution corresponding to about 10 megacycles. Using the test pattern for a signal, careful comparison of the band limited transmission with and without the PCM system showed only small defects in the PCM transmission. When the PCM transmission is seen on the television screen, the contour effects which are strikingly apparent for one, two, and three digits are hardly noticeable for five digits. Figure 8 illustrates this performance as well as is practical with photographic reproduction. About one digit is lost, and the three-digit printed reproduction shows the contours with about the same distinctness as four digits when viewed on the television screen. This state- ment applies in general to all of the printed reproductions. Figure 9 shows the same results for a different subject. The contour effects for a transmission system using a small number of digits are particularly apparent in the sky. Another method of presenting the results is shown in Fig. 10. In the pre- vious pictures the results have been presented for complete systems using one, two, etc., up to five digits. In Fig. 10, however, the transmission of each of the five digits is separately illustrated. Except for the 5th digit, for which this was not possible, an attempt was made to reproduce the pictures with equal contrast between black and white. The large amount of detail present in the fourth and fifth digits is particularly striking. The sum picture was obtained with proper weighting of the all five digits as discussed earlier in the paper. The remaining figure (11) illustrates the effect of adding noise to the input to reduce the contour effects. From these photographs it appears that add- ing noise has been definitely helpful in this respect. However; a penalty is paid for this result. The photographic process reduces the effect of noise by I 48 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 FOUR DIGITS FOUR DIGITS PLUS NOISE Fig. II — Test signal, boy and bird: with and without added noise. TELEVISION BY PULSE CODE MODULATION 49 integration and the picture observed on the monitor for the added noise case was definitely more "noisy" than the other picture. Even so, most observers agreed that in general the adding of noise was desirable for a system using a small number of digits. Acknowledgments * Many people contributed to the success of this experiment. Mr. O. E. DeLange and Mr. A. F. Dietrich worked along with the writer in the design, building and testing of the equipment. Mr. R. W. Sears, Mr. R. L. Carbrey and Mr. L. A. Meacham should be specially mentioned in connection with the design of the equipment, and Mr. B. M. Oliver assisted in the television tests. Mr. J. C. Schelleng assisted with suggestions and guidance. L Prediction and Entropy of Printed English By C. E. SHANNON {Manuscript Received Sept. i^, igso) A new method of estimating the entropy and redundancy of a language is described. This method exploits the knowledge of the language statistics pos- sessed by those who speak the language, and depends on experimental results in prediction of the next letter when the preceding text is known. Results of experiments in prediction are given, and some properties of an ideal predictor are developed. 1. Introduction IN A previous paper^ the entropy and redundancy of a language have been defined. The entropy is a statistical parameter which measures, in a certain sense, how much information is produced on the average for each letter of a text in the language. If the language is translated into binary digits (0 or 1) in the most efficient way, the entropy H is the average number of binary digits required per letter of the original language. The redundancy, on the other hand, measures the amount of constraint imposed on a text in the language due to its statistical structure, e.g., in English the high fre- quency of the letter E, the strong tendency of H to follow T or of U to follow Q. It was estimated that when statistical effects extending over not more than eight letters are considered the entropy is roughly 2.3 bits per letter, the redundancy about 50 per cent. Since then a new method has been found for estimating these quantities, which is more sensitive and takes account of long range statistics, influences extending over phrases, sentences, etc. This method is based on a study of the predictability of English; how well can the next letter of a text be pre- dicted when the preceding N letters are known. The results of some experi- ments in prediction will be given, and a theoretical analysis of some of the properties of ideal prediction. By combining the experimental and theoreti- cal results it is possible to estimate upper and lower bounds for the entropy and redundancy. From this analysis it appears that, in ordinary literary English, the long range statistical effects (up to 100 letters) reduce the entropy to something of the order of one bit per letter, with a corresponding redundancy of roughly 75%. The redundancy may be still higher when structure extending over paragraphs, chapters, etc. is included. However, as the lengths involved are increased, the parameters in question become more ^ C. E. Shannon, "A Mathematical Theory of Communication," Bell System Technical Journal, v. 27, pp. 379-423, 623-656, July, October, 1948. 50 I PREDICTION AND ENTROPY OF PRINTED ENGLISH 51 erratic and uncertain, and they depend more critically on the type of text involved. 2. Entropy Calculation from the Statistics of English One method of calculating the entropy ^ is by a series of approximations Fq , Fi , F2 , • • ' , which successively take more and more of the statistics of the language into account and approach ^ as a hmit. Fn rnay be called the X-gram entropy; it measures the amount of information or entropy due to statistics extending over T adjacent letters of text. Fat is given by^ = -Z p{^i , j) log2 p{bi , i) + Z p{b^) log p{b^). i,j i in which: ^^ is a block of X-\ letters [(iY-l)-gram] j is an arbitrary letter following hi p(bi , j) is the probability of the iV-gram bi , j pbiU) is the conditional probability of letter j after the block bi, and is given hy p{b^, j)/p(bi). The equation (1) can be interpreted as measuring the average uncertainty (conditional entropy) of the next letter 7 when the preceding iV-1 letters are known. As .V is increased, Fy includes longer and longer range statistics and the entropy, H, is given by the limiting value of i^jv as iV ^ x : H = Lim Fn . (2) N-*oo The X-gram entropies Fy for small values of N can be calculated from standard tables of letter, digram and trigram frequencies. If spaces and punctuation are ignored we have a twenty-six letter alphabet and Fq may be taken (by definition) to be log2 26, or 4.7 bits per letter. Fi involves letter frequencies and is given by 26 Fi = -Z p(i) log2 p(i) = 4.14 bits per letter. (3) The digram approximation F2 gives the result ^2 = - Hp(i,j) \og2 pi{j) = - Z) pii,j) log2 p(i,j) + E p(d log2 pit) (4) i,j 1 = 7.70 - 4.14 = 3.56 bits per letter. 2 Fletcher Pratt, "Secret and Urgent," Blue Ribbon Books, 1942. 52 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 The trigram entropy is given by F3 = - Z) p{hj, k) log2 pij{k) i,j.k = - E pihj, k) logo p{i,j, ^) + Z p{i,j) log2 p(i,j) (5) i,j,k i,j = 11.0 - 7.7 = 3.3 In this calculation the trigram table^ used did not take into account tri- grams bridging two words, such as WOW and OWO in TWO WORDS. To compensate partially for this omission, corrected trigram probabilities p(i^ j, k) were obtained from the probabilities p'{i, j, k) of the table by the folk - ing rough formula: Pii,h *) = Jl P'^i'h *) + ^ '•(^)^O; *) + 4^ p{i,Mli) where r{i) is the probability of letter i as the terminal letter of a word and s{k) is the probability of k as an initial letter. Thus the trigrams withi:^ words (an average of 2.5 per word) are counted according to the table; the bridging trigrams (one of each type per word) are counted approximately by assuming independence of the terminal letter of one word and the initial digram in the next or vice versa. Because of the approximations involved here, and also because of the fact that the sampling error in identifying probability with sample frequency is more serious, the value of F3 is less reliable than the previous numbers. Since tables of .Y-gram frequencies were not available for N > 3, F4 , F^ , etc. could not be calculated in the same way. However, word frequencies have been tabulated^ and can be used to obtain a further approximation. Figure 1 is a plot on log-log paper of the probabilities of words against frequency rank. The most frequent English word "the" has a probability .071 and this is plotted against 1. The next most frequent word ''of" has a probability of .034 and is plotted against 2, etc. Using logarithmic scales both for probability and rank, the curve is approximately a straight line with slope — 1 ; thus, if pn is the probability of the nth most frequent word, we have, roughly /.„ = -. (6) n Zipf* has pointed out that this type of formula, />„ = k/n, gives a rather good approximation to the word probabilities in many different languages. The ' G. Dewey, "Relative Frequency of English Speech Sounds," Harvard University Press, 1923. " G. K. Zipf, "Human Behavior and the Principle of Least Effort," Addison-Wesley Press, 1949. PREDICTION AND ENTROPY OF PRINTED ENGLISH 53 formula (6) clearly cannot hold indefinitely since the total probability S^„ 00 must be unity, while S A/n is infinite. If we assume (in the absence of any 1 better estimate) that the formula pn = .1/w holds out to the n at which the 5 z ■UJ a a 0.001 u. o ca o 0.0001 \ 1 — — ""~~' —" ■~~" "~~ ^^=^THE \. r°j = ^ ^ ro I ^J "n^ y ^ ff-^ N\, ^v X \x >> m:*" -OR ^> N ^^ ^ ^ ir-sA Y \ \ ^ V H REA LU f ^ ^ >^QU/ \LITY \ \ \ \ > s \ L r 0.00001 1 2 468 10 20 4060 100 200 400 1000 2000 4000 10,000 WORD ORpER Fig. 1 — Relative frequency against rank for English words. total probability is unity, and that pn = 0 for larger n, we find that the critical n is the word of rank 8,727. The entropy is then: 8727 — 12pn log2 pn = 11.82 bits pcr word, (7) 1 or 11.82/4.5 = 2.62 bits per letter since the average word length in English is 4.5 letters. One might be tempted to identify this value with 7^4.6 , but actually the ordinate of the Fn curve at N = 4.5 will be above this value. The reason is that F^ or F5 involves groups of four or five letters regardless of word division, A word is a cohesive group of letters with strong internal Fi F2 ^3 Fword 4.14 3.56 3.3 2.62 4.03 3.32 3.1 2.14 54 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 statistical influences, and consequently the A^-grams within words are more restricted than those which bridge words. The effect of this is that we have obtained, in 2.62 bits per letter, an estimate which corresponds more nearly to, say, Fb or Fe . A shnilar set of calculations was carried out including the space as an additional letter, giving a 27 letter alphabet. The results of both 26- and 27-letter calculations are summarized below: Fo 26 letter 4.70 27 letter 4.76 The estimate of 2.3 for Fg , alluded to above, was found by several methods, one of which is the extrapolation of the 26-letter series above out to that point. Since the space symbol is almost completely redundant when se- quences of one or more words are involved, the values of F^ in the 27-letter 45 case will be — or .818 of Fy for the 26-letter alphabet when N is reasonably large. 3. Prediction of English The new method of estimating entropy exploits the fact that anyone speaking a language possesses, implicitly, an enormous knowledge of the statistics of the language. Familiarity with the words, idioms, cUches and grammar enables him to fill in missing or incorrect letters in proof-reading, or to complete an unfinished phrase in conversation. An experimental demon- stration of the extent to which English is predictable can be given as follows: Select a short passage unfamiliar to the person who is to do the predicting. He is then asked to guess the first letter in the passage. If the guess is correct he is so informed, and proceeds to guess the second letter. If not, he is told the correct first letter and proceeds to his next guess. This is continued through the text. As the experiment progresses, the subject writes down the correct text up to the current point for use in predicting future letters. The result of a typical experiment of this type is given below. Spaces were in- cluded as an additional letter, making a 27 letter alphabet. The first line is the original text; the second line contains a dash for each letter correctly guessed. In the case of incorrect guesses the correct letter is copied in the second line. (1) THE ROOM WAS NOT VERY LIGHT A SMALL OBLONG (2) ----ROO NOT-V I SM----OBL---- ^^^ (1) READING LAMP ON THE DESK SHED GLOW ON (2) REA 0 D SHED-GLO--0-- (1) POLISHED WOOD BUT LESS ON THE SHABBY RED CARPET (2) P-L-S 0— BU-L-S-0 SH RE-C PREDICTION AND ENTROPY OE PRINTED ENGLISH 55 Of a total of 129 letters, 89 or 69% were guessed correctly. The errors, as would be expected, occur most frequently at the beginning of words and syllables where the line of thought has more possibility of branching out. It might be thought that the second line in (8), which we will call the reduced text, contains much less information than the first. Actually, both lines con- tain the same information in the sense that it is possible, at least in prin- ciple, to recover the first line from the second. To accomplish this we need an identical twin of the individual who produced the sequence. The twin (who must be mathematically, not just biologically identical) will respond in the same way when faced with the same problem. Suppose, now, we have only the reduced text of (8). We ask the twin to guess the passage. At each point we will know whether his guess is correct, since he is guessing the same as the first twin and the presence of a dash in the reduced text corresponds to a correct guess. The letters he guesses wrong are also available, so that at each stage he can be supplied with precisely the same information the first twin had available. ORIGINAL COMPARISON COMPARISON ORIGINAL TEXT REDUCED TEXT TEXT *- ^ »- *• ^ ► 1 V PREDICTOR -3r V ^ PREDICTOR J Fig. 2 — Communication system using reduced text. The need for an identical twin in this conceptual experiment can be eliminated as follows. In general, good prediction does not require knowl- edge of more than N preceding lehers of text, with TV fairly small. There are only a finite number of possible sequences of N letters. We could ask the subject to guess the next letter for each of these possible iV-grams. The com- plete list of these predictions could then be used both for obtaining the reduced text from the original and for the inverse reconstruction process. To put this another way, the reduced text can be considered to be an encoded form of the original, the result of passing the original text through a reversible transducer. In fact, a communication system could be con- structed in which only the reduced text is transmitted from one point to the other. This could be set up as shown in Fig. 2, with two identical pre- diction devices. An extension of the above experiment yields further information con- cerning the predictability of English. As before, the subject knows the text up to the current point and is asked to guess the next letter. If he is wrong, he is told so and asked to guess again. This is continued until he finds the correct letter. A typical result with this experiment is shown below. The 56 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 first line is the original text and the numbers in the second line indicate the guess at which the correct letter was obtained. (1) THERE IS NO REVERSE ON A MOTORCYCLE A (2)1115112112 1115 117 1112132122711114111113 1 (1) FRIEND OF MINE FOUND THIS OUT (2)861311111111111621111112111111 (1) RATHER D RAMATICALLY THE .OTHER DAY (2) 4 1 1 1 1 1 1 11 5 1 1 1 1 1 1 1 1 1 1 1 6 1 1 1 1 1 1 1 1 1 1 1 1 1 (9) Out of 102 symbols the subject guessed right on the first guess 79 times, on the second guess 8 times, on the third guess 3 times, the fourth and fifth guesses 2 each and only eight times required more than five guesses. Results of this order are typical of prediction by a good subject with ordinary literary English. Newspaper writing, scientific work and poetry generally lead to somewhat poorer scores. The reduced text in this case also contains the same information as the original. Again utilizing the identical twin we ask him at each stage to guess as many times as the number given in the reduced text and recover in this way the original. To eliminate the human element here we must ask our subject, for each possible iV-gram of text, to guess the most probable next letter, the second most probable next letter, etc. This set of data can then serve both for prediction and recovery. Just as before, the reduced text can be considered an encoded version of the original. The original language, with an alphabet of 27 symbols, A, B, — , Z, space, has been translated into a new language with the alphabet 1, 2, • • • , 27. The translating has been such that the symbol 1 now has an extremely high frequency. The symbols 2, 3, 4 have successively smaller frequencies and the final symbols 20, 21, • • • ,27 occur very rarely. Thus the translating has simplified to a considerable extent the nature of the statisti- cal structure involved. The redundancy which originally appeared in com- plicated constraints among groups of letters, has, by the translating process, been made explicit to a large extent in the very unequal probabilities of the new symbols. It is this, as will appear later, which enables one to estimate the entropy from these experiments. In order to determine how predictability depends on the number N of preceding letters known to the subject, a more involved experiment was carried out. One hundred samples of EngHsh text were selected at random from a book, each fifteen letters in length. The subject was required to guess the text, letter by letter, for each sample as in the preceding experiment. Thus one hundred samples were obtained in which the subject had available 0, 1, 2, 3, • • • , 14 preceding letters. To aid in prediction the subject made such use as he wished of various statistical tables, letter, digram and trigram PREDICTION AND ENTROPY OF PRINTED ENGLISH 57 tables, a table of the frequencies of initial letters in words, a list of the fre- quencies of common words and a dictionary. The samples in this experiment were from "Jefferson the Virginian'' by Dumas Malone. These results, to- gether with a similar test in which 100 letters were known to the subject, are summarized in Table I. The column corresponds to the number of preceding letters known to the subject plus one; the row is the number of the guess. The entry in column N at row S is the number of times the subject guessed the right letter at the 5th guess when (iV-1) letters were known. For example, Table I 1 2 3 4 5 6 7 8 9 66 10 67 11 62 12 58 13 66 14 72 15 60 100 1 18.2 29.2 36 47 51 58 48 66 80 2 10.7 14.8 20 18 13 19 17 15 13 10 9 14 9 6 18 7 3 8.6 10.0 12 14 8 5 3 5 9 4 7 7 4 9 5 4 6.7 8.6 7 3 4 1 4 4 4 4 5 6 4 3 5 3 5 6.5 7.1 1 1 3 4 3 6 1 6 5 2 3 4 6 5.8 5.5 4 5 2 3 2 1 4 2 3 4 1 2 7 5.6 4.5 3 3 2 2 8 1 1 1 4 1 4 1 8 5.2 3.6 2 2 1 1 2 1 1 1 1 2 1 3 9 5.0 3.0 4 5 1 4 2 1 1 2 1 1 10 4.3 2.6 2 1 3 3 1 2 11 3.1 2.2 2 2 2 1 1 3 1 2 1 12 2.8 1.9 4 2 1 1 1 2 1 1 1 13 2.4 1.5 1 1 1 1 1 1 1 1 1 14 2.3 1.2 1 1 1 15 2.1 1.0 1 1 1 1 16 2.0 .9 1 1 1 17 1.6 .7 1 2 1 1 1 2 2 18 1.6 .5 1 19 1.6 .4 1 1 1 1 20 1.3 .3 1 1 1 21 1.2 .2 22 .8 .1 23 .3 .1 24 .1 .0 25 .1 26 .1 27 .1 ' the entry 19 in column 6, row 2, means that with five letters known thfi cor rect letter was obtained on the second guess nineteen times out of the hun dred. The first two columns of this table were not obtained by the experi- mental procedure outlined above but were calculated directly from the known letter and digram frequencies. Thus with no known letters the most probable symbol is the space (probabihty .182); the next guess, if this is wrong, should be E (probability .107), etc. These probabilities are the frequencies with which the right guess would occur at the first, second, etc., trials with best prediction. Similarly, a simple calculation from the digram table gives the entries in column 1 when the subject uses the table to best 2 3 4 5 6 7 8 >8 10 7 2 2 3 3 0 4 7 4 4 6 2 1 2 9 58 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 advantage. Since the frequency tables are determined from long samples of English, these two columns are subject to less sampling error than the others. It will be seen that the prediction gradually improves, apart from some statistical fluctuation, with increasing knowledge of the past as indicated by the larger numbers of correct first guesses and the smaller numbers of high rank guesses. One experiment was carried out with "reverse" prediction, in which the subject guessed the letter preceding those already known. Although the task is subjectively much more difficult, the scores were only slightly poorer. Thus, with two 101 letter samples from the same source, the subject ob- tained the following results: No. of guess 1 Forward 70 Reverse 66 Incidentally, the TV-gram entropy Fn for a reversed language is equal to that for the forward language as may be seen from the second form in equa- tion (1). Both terms have the same value in the forward and reversed cases. 4. Ideal TV-Gram Prediction The data of Table I can be used to obtain upper and lower bounds to the A^-gram entropies Fn . In order to do this, it is necessary first to develop some general results concerning the best possible prediction of a language when the preceding N letters are known. There will be for the language a set of conditional probabilities ^ij , i2 , * • • , t>r_i 0"). This is the probability when the (A^-l) gram ii , ^2 , • • • , is-i occurs that the next letter will be j. The best guess for the next letter, when this (A-1) gram is known to have oc- curred, will be that letter having the highest conditional probability. The second guess should be that with the second highest probability, etc. A machine or person guessing in the best way would guess letters in the order of decreasing conditional probability. Thus the process of reducing a text with such an ideal predictor consists of a mapping of the letters into the numbers from 1 to 27 in such a way that the most probable next letter [conditional on the known preceding (A-1) gram] is mapped into 1, etc. The frequency of I's in the reduced text will then be given by qi = Xp{ii,i2, ••• ,iN-i,j) (10) where the sum is taken overall (A-1) grams ii , 12 , • • • , iw-i the 7 being the one which maximizes p for that particular (A-1) gram. Similarly, the fre- quency of 2's, qi , is given by the same formula with j chosen to be that letter having the second highest value of p, etc. On the basis of A-grams, a different set of probabilities for the symbols PREDICTION AND ENTROPY OF PRINTED ENGLISH 59 in the reduced text, gf "^^ , q2'^^ , . • . , ^2?"^ , would normally result. Since this prediction is on the basis of a greater knowledge of the past, one would ex- pect the probabilities of low numbers to be greater, and in fact one can prove the following inequalities: tgr>tq': 5 = 1,2,.... (11) This means that the probability of being right in the first S guesses when the preceding N letters are known is greater than or equal to that when only (iY-1) are known, for all S. To prove this, imagine the probabilities pdi , ^2, ' ' ' , iN , j) arranged in a table with j running horizontally and all the iV-grams vertically. The table will therefore have 27 columns and 27^ rows. The term on the left of (11) is the sum of the S largest entries in each row, summed over all the rows. The right-hand member of (11) is also a sum of entries from this table in which 5 entries are taken from each row but not necessarily the S largest. This follows from the fact that the right-hand member would be calculated from a similar table with (N-l) grams rather than .¥-grams listed vertically. Each row in the N-1 gram table is the sum of 27 rows of the i\^-gram table, since: 27 pik, h, • • • , iifj) = J2 piii ,^2, " , (nJ). (12) The sum of the S largest entries in a row of the N-1 gram table will equal the sum of the 276* selected entries from the corresponding 27 rows of the X-gram table only if the latter fall into S columns. For the equality in (11) to hold for a particular S, this must be true of every row of the N-1 gram table. In this case, the first letter of the .Y-gram does not affect the set of the 5 most probable choices for the next letter, although the ordering within the set may be affected. However, if the equality in (11) holds for all S, it follows that the ordering as well will be unaffected by the first letter of the Y-gram. The reduced text obtained from an ideal .Y-1 gram predictor is then identical with that obtained from an ideal .¥-gram predictor. Since the partial sums ea = i:?r 5 = 1,2,..- (13) are monotonic increasing functions of N, < 1 for all N, they must all ap- proach limits as .Y -^ oc . Their first differences must therefore approach limits as N -^ x> ^ i.e., the gf approach limits, q'? . These may be interpreted as the relative frequency of correct first, second, • • • , guesses with knowl- ,. edge of the entire (infinite) past history of the text. b 60 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 The ideal iV-gram predictor can be considered, as has been pointed out, to be a transducer which operates on the language translating it into a sequence of numbers running from 1 to 27. As such it has the following two properties: 1. The output symbol is a function of the present input (the predicted next letter when we think of it as a predicting device) and the preced- ing (iV-1) letters. 2. It is instantaneously reversible. The original input can be recovered by a suitable operation on the reduced text without loss of time. In fact, the inverse operation also operates on only the (A^-1) preceding sym- bols of the reduced text together with the present output. The above proof that the frequencies of output symbols with an N-1 gram predictor satisfy the inequalities: tq'!>tqr' 5 = 1, 2, • • • , 27 (14) 1 1 can be applied to any transducer having the two properties listed above. In fact we can imagine again an array with the various (N-l) grams listed vertically and the present input letter horizontally. Since the present output is a function of only these quantities there will be a definite output symbol which may be entered at the corresponding intersection of row and column. Furthermore, the instantaneous reversibility requires that no two entries in the same row be the same. Otherwise, there would be ambiguity between the two or more possible present input letters when reversing the transla- tion. The total probability of the S most probable symbols in the output, 8 say z2^i , will be the sum of the probabilities for 5 entries in each row, summed 1 over the rows, and consequently is certainly not greater than the sum of the S largest entries in each row. Thus we will have t,q''i>'Eri 5= 1,2, •••,27 (15) 1 1 In other words ideal prediction as defined above enjoys a preferred position among all translating operations that may be applied to a language and which satisfy the two properties above. Roughly speaking, ideal prediction collapses the probabilities of various symbols to a small group more than any other translating operation involving the same number of letters which is instantaneously reversible. Sets of numbers satisfying the inequalities (15) have been studied by Muirhead in connection with the theory of algebraic inequalities.^ If (15) holds when the qi and r,- are arranged in decreasing order of magnitude, and •* Hardy, Littlewood and Polya, "Incfiualities," Cambridge University Press, 1934. PREDICTION AND ENTROPY OF PRINTED ENGLISH 61 27 also 2 9? = 12^1, (this is true here since the total probability in each case is 1), then the first set, q^ , is said to majoriz3 the second set, fi . It is known that the majorizing property is equivalent to either of the following properties: 1. The fi can be obtained from the q^ by a finite series of ''flows." By a flow is understood a transfer of probability from a larger ^ to a smaller one, as heat flows from hotter to cooler bodies but not in the reverse direction. 2. The ri can be obtained from the qi by a generalized "averaging" operation. There exists a set of non-negative real numbers, aij , with /! dij = 22 (^ij = 1 a-nd such that ri = Haij{q^j). (16) ► 5. Entropy Bounds from Prediction Frequencies If we know the frequencies of symbols in the reduced text with the ideal A-gram predictor, qi , it is possible to set both upper and lower bounds to the iV-gram entropy, Fn , of the original language. These bounds are as follows: 27 27 X) i(gf - gf+i) log i < Fn < - Jl q^ log q^. (17) t=i t=i The upper bound follows immediately from the fact that the maximum possible entropy in a language with letter frequencies q^ is — ^ gf log q^ . Thus the entropy per symbol of the reduced text is not greater than this. The iV-gram entropy of the reduced text is equal to that for the original language, as may be seen by an inspection of the definition (1) oi Fn . The sums involved will contain precisely the same terms although, perhaps, in a different order. This upper bound is clearly valid, whether or not the pre- diction is ideal. The lower bound is more difficult to establish. It is necessary to show that with any selection of iY-gram probabilities _^(ii , ^2 , • . . , ^jv), we will have 27 Zl i{qi — gf+i) log i < X pih • ' ' ^n) log pi, • • • tN-iiiN) (18) The left-hand member of the inequality can be interpreted as follows: Imagine the qi arranged as a sequence of lines of decreasing height (Fig. 3). The actual qi can be considered as the sum of a set of rectangular distribu- tions as shown. The left member of (18) is the entropy of this set of distribu- tions. Thus, the i*^ rectangular distribution has a total probability of 62 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 Kq^ — Qi+i)' The entropy of the distribution is log i. The total entropy is then 27 Jliiq^ - q^+i) log i. The problem, then, is to show that any system of probabilities piii , ... , is), with best prediction frequencies qi has an entropy Fn greater than or equal to that of this rectangular system, derived from the same set of qi . 0.60 0.20 ORIGINAL DISTRIBUTION 10.05 10.05 0.025 0.025 0.025 0.025 qi q L2 ^3 q* qs ^6 ^7 qe 0^0 (qi-q2) RECTANGULAR DECOMPOSITION 0.15 0'5 (qz-qa) 1 0.025 1 0.025 1 1 1 1 , 0.025 j(q4-q5)j , , ,0 025qe Fig. 3 — Rectangular decomposition of a monotonic distribution. The qi as we have said are obtained from the p{ii , . . - , iN) by arranging each row of the table in decreasing order of magnitude and adding vertically. Thus the qi are the sum of a set of monotonic decreasing distributions. Re- place each of these distributions by its rectangular decomposition. Each one is replaced then (in general) by 27 rectangular distributions; the qi are the sum of 27 X 27^ rectangular distributions, of from 1 to 27 elements, and all starting at the left column. The entropy for this set is less than or equal to that of the original set of distributions since a termwise addition of two or more distributions always increases entropy. This is actually an application PREDICTION AND ENTROPY OF PRINTED ENGLISH 63 of the general theorem that Hy{x) < n{x) for any chance variables x and y. The equality holds only if the distributions being added are proportional. Now we may add the different components of the same width without changing the entropy (since in this case the distributions are proportional). The result is that we have arrived at the rectangular decomposition of the qi , by a series of processes which decrease or leave constant the entropy, starting with the original iV-gram probabilities. Consequently the entropy of the original system Fn is greater than or equal to that of the rectangular decomposition of the qi . This proves the desired result. It will be noted that the lower bound is definitely less than Fn unless each row of the table has a rectangular distribution. This requires that for each V \\ VN 1 \ \ N 7 N -UPPER BOUND \ \J !^' k I ^ N X / k**" k ^ I f > i i ( w ) c > I ^ H LOWER BOUND- >J ^ < > ( r c , ^ 3 \ I s ~~i L — ■ p < > 0 12 3 5 6 7 8 9 10 11 12 13 14 15 NUMBER OF LETTERS 100 Fig. 4 — Upper and lower experimental bounds for the entropy of 27-letter English. possible (iY-1) gram there is a set of possible next letters each with equal probability, while all other next letters have zero probabiHty. It will now be shown that the upper and lower bounds for Fn given by (17) are monotonic decreasing functions of N. This is true of the upper bound since the ql^^ majorize the q^ and any equalizing flow in a set of probabilities increases the entropy. To prove that the lower bound is also monotonic de- creasing we will show that the quantity U =Y^ i(qi - qi+i) log i (20) is increased by an equalizing flow among the qi . Suppose a flow occurs from qi to ^,+1 , the first decreased by Aq and the latter increased by the same amount. Then three terms in the sum change and the change in U is given by A^ =[-{i- 1) log (i - 1) + 2i log ^ - (^ + 1) log {i + 1)1A^ (21) 64 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 The term in brackets has the form —f{x — 1) + 2f{x) — f{x +1) where f{x) = X log X. Now/(x) is a function which is concave upward for positive x, since/" (x) = l/o; > 0. The bracketed term is twice the difference between the ordinate of the curve Sit x = i and the ordinate of the midpoint of the chord joining i — 1 and i + 1, and consequently is negative. Since A^ also is nega- tive, the change in U brought about by the flow is positive. An even simpler calculation shows that this is also true for a flow from qi to ^2 or from ^26 to ^27 (where only two terms of the sum are affected). It follows that the lower bound based on the iV-gram prediction frequencies q^ is greater than or equal to that calculated from the 7\^ + 1 gram frequencies q^'^^ . 6. Experimental Bounds for English Working from the data of Table I, the upper and lower bounds were calcu- lated from relations (17). The data were first smoothed somewhat to over- come the worst sampling fluctuations. The low numbers in this table are the least reliable and these were averaged together in groups. Thus, in column 4, the 47, 18 and 14 were not changed but the remaining group totaling 21 was divided uniformly over the rows from 4 to 20. The upper and lower bounds given by (17) were then calculated for each column giving the following results: Column 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 100 Upper 4.03 3.42 3.0 2.6 2.7 2.2 2.8 1.8 1.9 2.1 2.2 2.3 2. 1 1.7 2.1 1.3 Lower 3.192.502.11.71.71.31.81.01.01.01.31.31.2 .91.2 .6 It is evident that there is still considerable sampling error in these figures due to identifying the observed sample frequencies with the prediction probabilities. It must also be remembered that the lower bound was proved only for the ideal predictor, while the frequencies used here are from human prediction. Some rough calculations, however, indicate that the discrepancy between the actual F^ and the lower bound with ideal prediction (due to the failure to have rectangular distributions of conditional probability) more than compensates for the failure of human subjects to predict in the ideal manner. Thus we feel reasonably confident of both bounds apart from sampling errors. The values given above are plotted against N in Fig. 4. Acknowledgment The writer is indebted to Mrs. Mary E. Shannon and to Dr. B. M. Oliver for help with the experimental work and for a number of suggestions and criticisms concerning the theoretical aspects of this paper. A Submarine Telephone Cable with Submerged Repeaters By J. J. GILBERT {Manuscript Received Sept. ii, ig^d) The paper describes the recently installed Key West-Havana submarine cable telephone system in which repeaters designed for long life are incorporated in the cable structure and are laid as part of the cable. IN APRIL of last year there was installed between Key West, Florida, and Havana, Cuba, a submarine telephone cable system involving a radi- cal departure from the conventional art of long distance submarine teleph- ony. This departure consisted of the inclusion within the armor of the sub- marine cable of electron tube repeaters which are designed to pass through the cable laying machinery and sink to the ocean bottom like a length of cable, and which, over an extended period of perhaps twenty years, should not require servicing for the purpose of changing electron tubes or defective circuit elements. The repeater has the appearance of a bulge in the cable about three inches in diameter and tapering off in both directions to the cable diameter of a little over an inch. The total length of the bulge including the taper at each end is about 35 feet. The bulge is flexible enough so that it can conform to the curvature of the brake drum and of the various sheaves in the laying gear on the cable ship. A repeater, with stub cables, is shown in Fig. 1. Historical The new cable system, comprising cables Nos. 5 and 6 of the Cuban- American Telephone and Telegraph Company, represents another step in the development of telephonic communication between the United States and Cuba, which has presented many interesting problems. Natural con- ditions make it difficult, if not impossible, to employ some of the usual methods of communication. One such condition is the absence of high ground in Florida that would permit the use of economic radio systems. Another is the stretch of water between Florida and Cuba, which, in places, is as much as 6,000 feet in depth and which restricts the type of cable that can be used. The practical solution has been to go from the point of contact with the Bell System toll lines at Miami, over the Keys to Key West by land line (with some water crossings), thence to Havana, an air line distance of about 100 n.m., by submarine cable of the deep sea type of construction, having a single coaxial circuit, insulated with water resistant material. There 65 66 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 are problems involved in building and maintaining the Miami-Key West connections but these are outside the scope of the present article. Telephone communication between the United States and Cuba was initi- ated in 1921, when three submarine cables were laid between Key West and Havana.^ Each cable provided a telephone circuit, operated on a two-wire basis, and two or more telegraph circuits, d-c. and a-c. The cables were con- tinuously loaded with iron wire, insulated with gutta-percha and had return conductors consisting of copper tapes laid on the insulated core and exposed P'ig. 1 — Submarine cable repeater. electrically to the sea water. These cables were the first ones to employ the copper return conductor, which has also been used in subsequent cables. The copper return was employed after a theoretical study had indicated that the armor and sea water, which for the low frequencies then involved in cable telegraphy furnished a low resistance return conductor, would not be satisfac- tory at voice and higher frequencies. At these frequencies skin effect causes the return current to concentrate in the armor wires, which are naturally poor iW. H. Martin, G. A. Anderegg, B. W. Kendall, Key West-Havana Submarine Tele- phone Cable System, AJ££. Transactions, Vol. 41, pp. 1-19, February 1922. A SUBMARINE TELEPHONE CABLE WITH SUBMERGED REPEATERS 67 conductors for alternating currents, and this makes the resistance of the return path rise to undesirable values. The copper return effectively removes the armor wire and sea water from the transmission circuit at all but very- low frequencies. This has the further advantage of reducing the exposure of the circuit to static noise. Although the iron wire loading was very effective in reducing attenuation in the voice range, the eddy current resistance due to the loading wire made itself felt to a rapidly increasing degree for frequencies above the voice band. Consequently, when additional circuits were required some years later and it was decided to extend the frequency range in order to make use of newly developed carrier frequency equipment, it was necessary to dispense with magnetic loading. In 1930 the Key West-Havana No. 4 cable was laid em- bodying new materials and novel principles of design.^ The insulating ma- terial in this case was paragutta, which had been recently developed by the Laboratories, and which possessed electrical characteristics and stability much superior to gutta-percha. An intensive study had been made of the design of coaxial cables for carrier frequencies with the aim of obtaining optimum electrical performance by proper proportioning and construction of the conductors and these principles were employed in the new cable. Initi- ally, three carrier telephone circuits were obtained on the No. 4 cable using the equivalent four-wire method, with separate frequency bands for trans- mission in opposite directions. The cable had been designed with considerable transmission margin and in 1940 the need for additional circuits to Cuba resulted in the installation of new terminal equipment which enabled it to provide seven two-way high quality circuits on an equivalent four-wire basis. The Key West-Havana No. 4 cable design has proved very popular in other parts of the world. Several such cables have been laid between England and the Continent and between England and Ireland, between Australia and Tasmania, and others were used in connection with the war effort. A cable of this design has also been laid between two of the Japanese islands. Submerged Repeaters The demands for circuits to Havana continued to grow, and, after the close of World War II, the time appeared ripe for making use of a new development which had just come to a head in the Laboratories after a period of experimentation.^ This development was the submerged repeater. The need for periodic strengthening of signals transmitted over con- siderable distances is about the same in submarine cables as it is in land m. A. Affel, W. S. Gorton, R. W. Chesnut, New Key West-Havana Carrier Telephone Cable, B.S.TJ., Vol. 11, pp. 197-212, April 1932. ^O. E. Buckley, The Future of Transoceanic Telephony, Thirty-Third Kelvin Lecture, B.S.TJ., Vol. 21, pp. 1-19, July 1942. 68 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 lines and, as in land lines, the permissible spacing between repeaters usually diminishes as the desired frequency increases. The great difficulty in the case of submarine cable routes is that there are usually no land sites on which repeaters can be located. Artificial islands consisting of floating platforms or buoys have been proposed as a solution, but ocean currents and storms have disastrous effects on such structures. Interruptions due to such causes would make it difficult to meet the requirement on continuity of service which is necessary in the case of important telephone circuits. Therefore, it appeared that the safest place for a submarine cable repeater is on the ocean bottom. Requirements on Repeater The decision to place the repeater on the ocean bottom resulted in special requirements on the structure the first of which is that it be capable of re- sisting the considerable hydrostatic pressure that is encountered in deep water. It also seemed desirable that the operation of getting the repeater overboard from the cable ship should not impede the smooth functioning of the laying process. The best way of meeting this requirement appeared to be to make the repeater structure flexible, within practicable limits, and as small as possible in diameter so that it could pass around the drum and sheaves of the laying gear like any length of cable. In order to make such a repeater attractive from operating and commercial points of view another requirement was necessary, namely, that the electrical circuit elements of the repeater, including electron tubes, resistances, con- densers and coils be designed for long life under operating conditions, so that there would be assurance of freedom from trouble or need of replacement of parts over a long period, perhaps twenty years or more. Servicing of the repeater would be in the nature of a cable repair, and the repair of a submarine cable is something not to be sought after. The procedure is apt to be expensive and time consuming, due to circumstances beyond con- trol such as bad weather or lack of availability of a repair ship; and the dis- turbance of the cable involved in lifting it to the surface and dropping it again, possibly in something of a heap, is not desirable. It is obvious that the requirement on long life of circuit elements presents a difficult problem, especially in view of the fact that the space available for these elements is minimized in order to keep the repeater diameter small. There was still another requirement on circuit elements, that of rugged- ness. The stresses involved in laying cables in deep waters are quite con- siderable. The cable is under a tension of several thousand pounds and ''incidents" might occur which would have no effect on an ordinary cable but which might result in dangerous shocks to the delicate elements of the repeater. A SUBMARINE TELEPHONE CABLE WITH SUBMERGED REPEATERS 69 Also, as a consequence of the cable tension, the armor unlays somewhat; and this imposes twist and elongation on the interior structure, either coaxial circuit or repeater housing. The cable circuit can be designed to withstand this distortion, but the repeater housing is much more susceptible to damage from this cause. The Repeater Housing The requirements on flexibility and water-tightness under ocean bottom pressures were the factors of outstanding influence in the design of the re- Fig. 2 — Steel rings and copper envelope of repeater. peater housing and of the end seals by means of which the cable enters and leaves the housing. In the present form the housing consists of a long tube of soft copper If inches in diameter and .03 inch thick, supported internally against collapse under sea bottom pressure by an assemblage of abutting steel rings, each f '' wide, and given a degree of rigidity by means of thinner steel rings of the same width overlaying and staggered relative to the thicker rings. When this structure is sealed at the ends it is capable of withstanding pressures as high as 10,000 pounds per square inch and it can be bent to a radius as small as three feet without undue distortion of the copper envelope. Details of the structure are shown in Fig. 2. Into each end of the housing is led the insulated conductor of the cable by 70 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 means of a series of seals. The inner or vapor seal is of the glass-metal type especially developed for this particular purpose and capable of withstanding considerable hydrostatic pressures. Next in line there is a seal comprising a central brass tube and an external brass member, both vulcanized to rubber, which is joined to the insulating material of the cable. These seals are co- axial in form, the outer member in each case being brazed to the copper tube of the housing or an extension thereof. Finally a closely fitting "core tube" of copper, extending over the cable insulation for a distance of about seven feet, is brazed to an extension of the copper envelope of the housing, filled with vistac and sealed at the distant end by means of a neoprene sleeve joined firmly to the core tube and to the cable insulation. The repeater housing and core tube are provided with corrosion protective layers and a bedding for the armor wires, the bedding over the core tube being built up in the form of a taper. The armor is a continuation of the cable armor wires with additional wires interspersed on account of the larger diameter of the repeater. To prevent twisting of the container due to the. unlaying of the armor wires under tension, a second layer of wires with a direction of lay opposite to that of the main armor is employed. The repeater may be armored as part of the cable or it may be armored separately, with a stub on each end, and spliced into the cable. The components of the housings and seals, as well as the complete armored housing, have been subjected to exhaustive tests of various sorts. The rubber- brass seal, for instance, was tested for penetration of moisture vapor over long periods of time. Methods of making this seal were checked by tension tests until a uniformly high degree of adhesion was obtained. Armored hous- ings were tested on a laboratory setup in which laying conditions could be simulated by bending the structure under tension and in motion around a six foot diameter drum. The Repeater Circuit The diameter of the housing had been chosen originally on the assumption that the bulge caused by the repeater should not be more than two or three times the diameter of the cable proper in order to reduce the possibility of over-riding turns on the brake drum during laying. Mechanical tests indi- cated that this diameter was also safe from the standpoint of deformation of the copper envelope during bending. Accordingly, it was required that the repeater structure should be restricted in cross-section so as to fit inside this tube, with as much length as would be needed. The problem then became one of packaging the elements involved in a high gain electron tube amplifier in the restricted space available. The method finally adopted is shown in Fig. 3. The completed amplifier consists of an A SUBMARINE TELEPHONE CABLE WITH SUBMERGED REPEATERS 71 articulated assemblage of composite lucite cylinders, each about five inches long, successive units being held together by a spring assembly. Each lucite cylinder contains the related electrical elements of a particular part of the repeater circuit. The groups of smaller elements are mounted rigidly in a lu- cite form which slides into an insulating envelope consisting of two close fitting lucite shells and is held in place by end pieces of lucite. Eight copper tapes laid in axial slots between the shells and extending over several sections, where necessary, permit electrical interconnection of the various parts. A representative assemblage is shown in Fig. 4. In the case of the Key West- Fig. 3 — View of repeater assembly. Havana repeater the complete assemblage is eighty-four inches long and com- prises fifteen sections. Circuit Elements Early in the development general principles were developed regarding the type of circuit best suited for underwater repeaters and on this basis require- ments were established on the characteristics necessary for the circuit ele- ments, including electron tubes, and on their arrangement in the repeater. Decisions in such matters could not be arbitrary of course, but had to be carefully worked out in order to freeze designs as early as possible so as to facilitate the start of significant life tests. The electron tube is the most important of the elements. Work had been 72 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 begun on a tube suitable for this use as far back as 1933. Thus, when a deci- sion was made to lay the new cables, a long background of experience was drawn on in the manufacture of the tubes. Early models of the type had been operated on continuous life test for as long as ten years. Designed primarily for long life, the tube is a suppressor grid pentode with an indirectly heated cathode. Of rugged design to withstand the shocks of cable laying, the spac- ings between electrodes are relatively large. Unusual care was taken in manufacture to insure solid welds and to avoid the presence of loose particles. During various stages of assembly, rigorous inspections were made on all tubes by engineering personnel. Selection of tubes for use in the cable was based on a thorough examination of all details in the history of each tube. Fig. 4 — Repeater network assembly. as well as the history of the group in which it was manufactured. All tubes which were candidates for the cable were aged several thousand hours before preliminary selection was made. In addition, other tubes from the same pro- duction group were further life tested several more thousand hours to estab- lish the quality of the group. One early decision was to power repeaters by direct current fed from land over the cable conductor. The tube heaters con- nected in series would furnish plate and grid potentials. This was an impor- tant factor in setting the nominal power requirements for the tube, which are about J ampere at 20 volts for heater supply and plate potentials of 40 to 60 volts. While the electron tube is usually the most vulnerable element in electrical circuits from the standpoint of life, attention must be given to other ele- A SUBMARINE TELEPHONE CABLE WITH SUBMERGED REPEATERS 73 ments — condensers, resistances, and coils — especially where they are subject to long continued application of electrical potentials, as in the case of power separation filters. The factors that determine the life and performance of these elements are not completely under control. It was felt, however, that the best assurance on dependability could be obtained by careful, conserva- tive design and by manufacturing and assembling the elements into repeaters under the best possible conditions of cleanliness. An air conditioned space was provided for this purpose at the Murray Hill Laboratory. In addition to cleaning the air in this space, precautions were taken against the entrance of dirt by other means, for example, on the clothing or persons of operators. Fig. 5 — Assembly of the repeater. The humidity of the air was carefully controlled to prevent contamination from perspiration during handling of the parts. Manufacture was carried out by selected workmen, and the product was inspected at various stages by engineers. A view of one of the operations is given in Fig. 5. Field Trials Simulated laying tests in the laboratory covered a period of several years. Special pains had been taken to include as far as possible all aspects of the laying operation, even those which were judged to be free of hazard to the repeater. Tests were also made to determine the effect, if any, of the laying operation upon the electrical transmission characteristics of the cable. Like- wise, comprehensive electrical tests had been made to insure that no unex- 74 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 pected effects would be encountered due to the immersion of the repeater in water. A large scale test was needed, however, to establish the practicability of the repeatered cable. This is because of the fact that during the laying opera- tion the suspended length of cable trailing the ship may be as great as ten nautical miles or more, and in this length there occur complex mechanical phenomena which cannot be simulated in the laboratory with a great degree of assurance. After preliminary trials from a barge in Long Island Sound, a deep water test of the repeatered cable was made in 1948 in the Bahamas. The cable ship LORD KELVIN of the Western Union Telegraph Company was chartered for the purpose. Lengths of cable up to 15 n.m. were paid out along with repeaters in depths of water up to 2 n.m. Several repeaters were laid, measured while on the ocean bottom and then hauled back to the ship, a procedure that involves much more severe treatment than a mere laying operation. The repeater shown in Fig. 1 experienced this treatment. Tests were also made with repeater housings containing specially designed acceler- ometers to determine the shocks resulting from possible abuse during laying. The results indicated that the repeaters as well as the cable could take the punishment with considerable margin of safety. The Transmission System Designing the electrical circuit of the repeater was largely a matter of getting the most out of the long life electron tube in the way of stability of repeater gain and low modulation while obtaining as much gain as the system permits. For most efficient use of tubes and to simplify the structure a uni- directional repeater design was decided upon. The repeater employed in the Key West-Havana cables has three stages with negative feed back, the circuit being as shown in Fig. 6. The gain fre- quency characteristic is shown in Fig. 7. The transmission band is from 12 kc. to 120 kc. The insertion gain at 108 kc, the top frequency employed in traffic, is 65 db. The repeater gain equalizes the loss of about 36 n.m. of cable, the attenuation frequency characteristic of which is shown in Fig. 8. For com- parison the characteristics of the earlier cables are also shown. The layout of the new repeatered cable installation is shown in Fig. 9. There are two cables, one for each direction of transmission. The East, or No. 5 cable, transmitting South, is 114.55 n.m. in length. The West, or No. 6 cable, transmits north and is 124.97 n.m. in length. Each cable has three repeaters spaced approximately 36 n.m. apart. Two of the six repeaters are in a depth of .9 n.m. and two in about .35 n.m. The last repeater in each cable is located as close as* possible to deep water so as to strengthen the signal before it enters shallow water and land sections of cable where static -\sm^ vw en iDi WW ^\AAr-viKl^L/~t-A/V\^ r^WV- ^i^^VW vQ^ Fig. 6 — Circuit of repeater. 75 76 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 noise and crosstalk might be picked up. In Havana the last repeater is located in a large vault on the beach. At Key West the last repeater is located close to Sand Key Light where the water begins to deepen. 70 65 60 55 I 50 O UJ O 45 Z •7 40 35 30 25 20 y — ^, ■ y y \ y y y / / / / / / / / / / / / 2.4 S 2.0 O UJ ^p,.2 Ouj o z Ui 0.6 0.4 20 30 40 50 60 70 80 90 100 110 120 FREQUENCY IN KILOCYCLES PER SECOND Fig, 7 — Gain characteristic of repeater. / / / % / y^ y ^•1930 i92iy " ^■' ,•" __ ==- -^ O.I 0.2 0.4 0.6 1.0 2 4 6 8 10 20 40 60 FREQUENCY IN KILOCYCLES PER SECOND 200 Fig. 8 — Attenuation frequency characteristics — Key West-Havana Cables. At manholes near the shore at both ends the cables are spliced directly to underground cables running in ducts to the terminal equipment at the offices, a distance of three miles at Havana and one mile at Key West. The under- A SUBMARINE TELEPHONE CABLE WITH SUBMERGED REPEATERS 77 78 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 ground cables have the same coaxial circuit as the submarine cables but in place of the mechanical protection of jute and armor they are provided with electrical protection of helical steel tapes, layers of paper and over all a lead sheath. The 12 kc. to 108 kc. passband yields 24 channels in each cable, each chan- nel occupying a band of 4 kc. The signal-to-noise ratio for these channels is about the same as for the same length of high grade carrier frequency circuit on land. The Cable The cable has a copper return, as in the case of the earlier installations, but differs from them in being insulated with polyethylene. It also involves some new principles of design that render the cable circuit less subject to change of electrical characteristics due to laying stresses. This is a matter of considerable importance in the case of a system with submerged repeaters, since after the cable has reached the bottom it is impossible to adjust the repeater to compensate for changes in cable attenuation during laying, a mat- ter that in ordinary cables is taken care of by adjusting the equipment on shore. In order to avoid undesirable irregularities in transmission characteristics special precautions were taken during manufacture to obtain a higher than usual degree of uniformity of the cable impedance as seen by a repeater. Because of the wide transmission band, schemes heretofore employed for re- ducing the effect of the variation of impedance among the core lengths con- stituting the cable would have called for core lengths so short as to seriously increase the number of joints. The irregularities were therefore minimized by careful control of conductor and insulation diameters and by continuously insulating lengths of the order of 12 n.m., cutting them only as was necessary for handling, and reassembling the shorter lengths as far as possible in insulat- ing order to assure random addition of reflections due to impedance irregu- larities. The success of this technique is evidenced by the impedance devi- ation curves shown in Fig. 10. The structure of the cable is shown in Figs. 11 and 12. The central conduc- tor consists of a solid wire .131 inch in diameter on which are laid three copper tape surrounds each .0145 inch thick and .148 inch wide, closely conforming to the solid wire. The interstices of the conductor are filled with polyethylene. The stranded conductor, .160 inch in diameter, is insulated with polyethylene to a diameter of .460 inch. Directly on the polyethylene insulation is laid the return conductor com[)rising six copper tapes, each approximately .016 inch thick by .241 inch wide, preshaped so that when in place they conform to the surface of the insulation. Both the return tapes and the tape surrounds of the central conductor have left hand lay. Over the return conductor is wound a teredo tape approximately .003 inch thick with overlap. Over all is the A SUBMARINE TELEPHONE CABLE WITH SUBMERGED REPEATERS 79 cutched jute, the armor and the outer jute serving, to which are appHed the usual cable compounds. Four types of armor are employed in the cable for use in various depths of water or for special shore conditions. -0.5 0.5 CO UJ "^-0.5 0.5 0 -0.5 36N.M. LENGTH. AUTOMATICALLY CONTROLLED INSULATION DIAMETER. MANUFACTURING ORDER CORE ASSEM. 0.5 2: AR MEAN OF THE DEVIATIONS OF ALL ARMORED CABLE MEASURED. TOTAL OF 9 CABLE LENGTHS , 18 ENDS -0.5 -0.5 10 20 30 40 50 60 FREQUENCY 70 80 90 100 110 120 IN KILOCYCLES PER SECOND 130 140 150 Fig. 10 — Impedance deviations of cable lengths from average of all armored cable impedances. The lengths of the various types, in nautical miles, as they appear in the two cables, starting at Key West are as follows: Type No. 5 Cable No. 6 Cable A 14.31 12.65 B 25.60 31.22 D 72.73 76.17 B 1.44 4.39 A .16 .18 AA .31 .36 80 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 TYPE NOMINAL OUTSIDE DIAMETER CENTER CONDUCTOR 0.13 (COPPER) 3 SURROUND TAPES 0.160 (0.148 X 0.0145 COPPER) POLYETHYLENE 0.460 (0.150 THICK) 6 RETURN TAPES CO.241 X 0.016 COPPER) TEREDO TAPE (1.750X0.003 COPPER, OVERLAPPED) RAYON TAPE (1.750 X 0.007) 1 SERVING CUTCHED JUTE (100 LB) ARMOR WIRE (22 NO. 14 H T., 0.083 EACH WIRE BRAIDED, 0.107) 2 SERVINGS 1.00 IMPREG. JUTE 1.12 C17/3) CENTER CONDUCTOR (COPPER) 3 SURROUND TAPES (0.148 X 0.0145 COPPER) POLYETHYLENE (0.150 THICK) 6 RETURN TAPES (0.241X0.016 COPPER) TEREDO TAPE (1.750X0.003 COPPER, OVERLAPPED) RAYON TAPE (1.750 X 0.007) 2 SERVINGS CUTCHED JUTE (125 LB) ARMOR WIRE (11 N0.1 MILD STEEL) 2 SERVINGS IMPREG. JUTE (28/3) CORROSION PROTECTION 1 WRAP 2 INCH PAPER R.H. LAY 1 WRAP 2 INCH PAPER L.H. LAY 1 WRAP 3 INCH SHEETING R.H. LAY (EACH WRAP FLOODED WITH TAR) EXTERIOR NON-ADHESIVE WASH 1.630 1.780 2.280 2.430 2.580 0.131 CENTER CONDUCTOR (COPPER) 3 SURROUND TAPES 0.160 (0.148 X 0.0145 COPPER) POLYETHYLENE 0.460 (0.150 THICK) 6 RETURN TAPES 0.492 (0.241X0.016 COPPER) TEREDO TAPE 0.501 (1.750 X 0.003 COPPER, OVERLAPPED) 2 STEEL TAPES 0.524 (5/16 WIDE & 0.006 THICK) PAPER INSULATOR 0.600 /2 WRAPS 5 MILR.H.LAYA V2 WRAPS 7 MIL L.H. LAY/ LEAD SHEATH 0.760 (0.08 NOM. THICKNESS) Fig. 11 — Cable structures. A SUBMARINE TELEPHONE CABLE WITH SUBMERGED REPEATERS 81 During the course of manufacture and in splicing on board ship, joints in the copper conductors were silver soldered. For joining the polyethylene in- sulation a special molding machine was designed and built by means of which polyethylene under high pressure and an elevated temperature was applied to the surfaces to be joined. The cable was manufactured by the Simplex Wire & Cable Company of Cambridge, Mass., and incorporated the results of a cooperative develop- ment program conducted by this Company and the Bell Telephone Labora- UNDERGROUNO TYPE D TYPE B TYPE TYPE AA Fig. 12 — Cable types. tories. The excellent quality of the cable is a tribute to the manufacturer in this very difficult and exacting field. Terminal Equipment The transmission apparatus at Key West and Havana is mostly standard equipment employed in land line carrier systems, and the operations involved in combining the twenty-four voice circuits into one band and separating them again are largely conventional. Special equalizers, power separation fil- ters and an auxiliary amplifier had to be designed and the standard transmit- ting amplifier used in the J system was modified to accommodate the lower frequency band. A feature of particular interest is the equipment for testing the electrical condition of the repeaters from measurements at Key West. Each repeater contains a sharply tuned circuit by means of which the gain 82 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 Fig. 13 — Terminal power supply. of the repeater is increased above normal at a distinctive frequency outside the transmission band of the repeater. With the aid of a loop circuit at Ha- A SUBMARINE TELEPHONE CABLE WITH SUBMERGED REPEATERS 83 vana the gain with reduced feed back of the individual repeaters can be measured by scanning the test frequency region with an oscillator and detec- tor at Key West. An indication of incipient decay of gain of any repeater is thus given. The power for the repeaters is supplied over the cable conductor from Key West. A positive potential of about 250 volts is applied to one cable and — 250 volts to the other, with a loop connection between the two cables at Havana to complete the d-c. circuit. This neutral point is also connected to ground. The current in the cable conductors is at present maintained at 0.23 ampere. A view of the rectifying and control equipment for one of the polari- ties is given in Fig. 13. Precautions are taken against interruption of the power supply to the cable, and sensitive controls are provided to maintain the current constant in spite of earth currents and to guard against excessive currents or potentials in the cable system in case of trouble in the power supply or in the cable itself. Laying the Cables The laying of the cables was completed without undue incident by the Cable Ship LORD KELVIN. The task was one of unusual difficulty since modifications had to be made in the cable laying gear, some of them untried, and it was particularly desirable that the prescribed lengths and courses be realized. Modifications were made in the cable laying gear in order to obtain an additional margin of safety in laying repeaters. As was previously indicated, the repeater is capable of bending without harm on a diameter of approxi- mately 72 inches; and the existing cable drum, approximately 68 inches in di- ameter, would have been adequate. It was felt desirable, however, to build the drum on the LORD KELVIN out to an 85-inch diameter to match the diameter of the bow sheaves. The dynamometer sheaves and the sheave lead- ing the cable off from the brake drum presented more of a problem. The lead off sheave was replaced by a ring sheave, 85 inches in diameter, supported on wheel bearings. The frame supporting these bearings was hinged at one end and the pressure on the other end of the frame, due to the tension of the cable passing over the sheave, offered a ready means for measuring this ten- sion. For this purpose a resistance pressure cell was employed with a recorder, which not only gave a continuous record of tension but also relayed the sig- nals to a vertical indicator on deck for the guidance of the brake operator, and to a smaller indicator on the bridge. This arrangement is shown in Fig. 14. It is felt that it has much to recommend it over the conventional dyna- mometer from the standpoints of sensitivity and quickness of response. It was important to measure the transmission characteristics of the re- 84 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 Fig. 14 — Ring sheave and dynamometer scale. Fig. 15— EiecLrical laboratory on shipboard. A SUBMARINE TELEPHONE CABLE WITH SUBMERGED REPEATERS 85 peatered cable before, during and after laying, and the special equipment needed for this purpose was more than could be contained in the electrician's room usually provided on cable ships. The jointers' store room was accord- ingly taken over and converted into an electrical laboratory, shown in Fig. 15. The cable, loaded on board the LORD KELVIN, with the deep sea re- peaters spliced in and stowed away in the tanks, arrived off Key West on April 21, 1950. Courses had been laid out for the two cables with the idea of keeping five-mile separation between the two most of the way, and five-mile separation from the nearest of the cables that constitute the rather compli- cated network between Key West and Havana. It is hoped thereby to avoid having the new cables picked up by mistake in connection with the repair of other cables and to avoid confusing the two cables in case either one of them is in need of repairs. The stretch of water between Key West and Sand Key Light, a distance of about 8 n.m., is too shallow for the operation of a ship of the size of the LORD KEL\TX so the sections of the two cables in this area had been laid from barges by the Long Lines Department of the American Telephone and and Telegraph Company. At Havana a new landing place had been selected. Experience with existing cables which land in Havana Harbor indicate that considerable deterioration of armor takes place in this locality and there is also the anchor menace. In addition, closeness to an existing carrier fre- quency cable might have given rise to undesirable crosstalk. The new landing place at the foot of B Street in Havana is about three miles from the harbor. Figure 16 shows the landing site as viewed from the cable ship during the laying operation. A view of the interior of the vault on the Havana shore is given in Fig. 17. After putting out mark buoys at strategic points and at intervals of about 12 n.m. along the course of the cable, the Key West shore end of No. 5 cable was picked up at Sand Key and spliced on to the cable in the tanks. Then 32 n.m. of this cable were paid out, and the end buoyed at the point of final splice. The ship then proceeded to Havana, and landed the manhole repeater which was spliced to the underground cable to the office. The ship then floated the end of the cable ashore on barrels with the aid of a line operated by a winch manned by Cuban Telephone Company personnel. As soon as the end reached shore it was spliced to the repeater, the barrels were cut off, the cable dropped to the bottom and the cable on shipboard was paid out until the point of final splice was reached, where the end on board was spliced to the previously buoyed end to complete the connection between Key West and Havana. The ship then returned to Havana, landed the end of No. 6 cable by means 86 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 WF Fig. 16 — Havana landing site. Fig. 17— Repeater vault. A SUBMARINE TELEPHONE CABLE WITH SUBMERGED REPEATERS 87 of barrels and winch line and paid out cable to the point of final splice, which in this case was about four miles from Sand Key. The end of No. 6 at Sand Key was then picked up, a repeater spliced to it and to the end of the cable in the tank, and the latter was paid out to the point of final splice. Within a short time after completing this splice, insulation measurements had been completed on the two cables, the power supply was connected in to activate the repeaters, and conversation over the cable system took place. Careful attention was given to the amount of slack paid out, that is the excess of cable length over the actual distance traversed. This latter distance is usually determined by observing the length of a taut wire paid out con- tinuously during the laying. In the absence of taut wire gear other methods had to be devised. Observations on buoys by radar and range finder provided almost continuous information regarding the position of the ship and gave satisfactory information on slack. The conditions for cable laying between Key West and Havana are far from good. The Gulf Stream is swift and er- ratic. The velocity of the current at any particular point as indicated by the stream at the buoys was found to vary considerably over a fairly short period of time. As an indication of the degree of precision obtained by careful navi- gation of the ship, the final results show that in each of the cables the speci- fied length was missed by only .2 n.m., which is quite an unusual achieve- ment. Acknowledgment is made to the Western Union Telegraph Company, the owners of the LORD KELVIN, for their cooperation in providing the special equipment for the ship and to the Captain of the LORD KELVIN, his staff and crew, for the very satisfactory performance of the laying operation. Since the installation of the new system, it has been subjected to compre- hensive tests involving measurement of noise and intermodulation between channels as well as precise measurements at numerous frequencies of net loss of the repeatered cables at intervals of time. The system has proved to be very stable and has met the requirements laid down for it. This was as ex- pected. Nothing unfavorable to the submerged repeater has made itself felt; but, in accordance with conservative submarine cable tradition, its perform- ance will be critically observed over a period of time. Activity in the development of the repeatered cable and the conduct of the Key W^est-Havana project centered in a small group of Bell Telephone Lab- oratories' engineers specializing in submarine cable work and drawing on the advice and help of other groups of various backgrounds. At times, espe- cially when troubles were encountered, the contributions of these groups were of tremendous importance and considerable in extent. The writer, as project engineer, takes this opportunity of acknowledging the assistance of the nu- merous individuals involved in the success of the undertaking. Theory of the Negative Impedance Converter By J. L. MERRILL, Jr. {Manuscript Received July j, iQ^o) This paper presents a relatively new approach to the solution of negative im- pedance problems related to vacuum tube circuits. The approach consists of reducing the vacuum tube circuit of a device for producing negative impedance to an electrically equivalent four-terminal network from which the stability and the operation of the device as an element in a system can be predicted accurately. The theory is of interest at this time because a negative impedance repeater, the El, has recently been developed for use in the exchange plant. It has been found that such a repeater can be placed in series with a voice frequency telephone line to provide transmission gains which are ample for many purposes. Introduction A NEW type of telephone repeater known as the El has been developed -^ ^ recently to meet the large demand in the exchange area for an eco- nomical means of providing transmission gains of about 10 db in tw^o-wire telephone lines. This repeater costs less than the 22 type v^hich has been the standard tvi^o-wire, tv^o-vs^ay means of amplifying voice currents in the Bell System. The difierence in cost is made possible by a difference in operating principle. The El repeater employs a type of feedback amplifier the action of v^hich can be said to have the properties of a negative impedance converter. It is the purpose of this paper to describe the operation of the negative im- pedance converter, which is a device for transforming positive impedance into negative impedance. Negative impedance like positive impedance can have two components: reactance and resistance. The reactance component can be either positive or negative. However, for an impedance to be negative the resistance compo- nent should be negative at some frequency in the range from zero to in- finity. The idea of negative resistance originated over 30 years ago, and in the beginning was associated with the concept of resistance neutralization. This concept grew from the observation that a two-terminal device could be found which had an unusual property when inserted in series with a single mesh circuit : it could produce the same flow of current as would flow other- wise at some frequency provided a resistance R were removed from this mesh. Apparently, the addition to a circuit of a two-terminal element could neu- talize an amount of resistance equal to R. Thus within certain frequency limits this two-terminal device could be treated as a negative resistance equal in magnitude to — R. 88 THEORY OF NEGATIVE IMPEDANCE CONVERTER 89 In the early days of vacuum tube development the negative resistance effect was considered to be an important one. Possibly the regenerative vac- uum tube circuits associated with the early radio receivers stimulated interest in the subject. One of the first text books on the theory of vacuum tube cir- cuits^ devoted about as much space to regenerative means for producing negative resistance as it devoted to the theory relating to any one of the more conventional devices — namely: amplifiers, oscillators, modulators and detectors. In spite of the interest in the subject, little practical use was made of the negative resistance theory. Negative resistance cannot be completely disassociated from reactance. A vacuum tube circuit arranged to develop negative resistance will present reactance as well at some frequencies, and the effect on an external circuit at these frequencies will be that of taking away resistance and adding or subtracting reactance. At high and low frequencies the circuit may present a positive impedance. Consequently, the term negative impedance is used herein to designate the effect produced by a two-terminal device which has the property of negative resistance at some frequency or frequencies, nega- tive resistance plus reactance at other frequencies and positive impedance at still other frequencies. The Negative Impedance Converter Heretofore, many vacuum tube circuits have been devised for converting positive impedance into negative impedance. All known simple circuits employing vacuum tubes for obtaining negative impedance, as distinguished from the combination circuits which can be made up either of vacuum tubes or of negative elements found in nature, have much in common and can be treated as the same type of arrangement. Essentially, this type of arrange- ment is a feedback amplifier and can be treated as such. Recently, a new method of handling these devices has been developed which has the merit of simplifying computations in many cases. This method is based upon the fact that vacuum tube circuits devised for converting positive impedance into negative impedance can be reduced to an electrically equivalent, four- terminal network consisting of a combination of positive impedance ele- ments together with an ideal negative impedance converter. This ideal converter. Fig. 1(a), resembles a form of transformer: it has a ratio of transformation of —k:l, can have four terminals and is capable of bilateral transmission. Assume that a positive impedance Zn is connected to terminals 3 and 4 and —HZn is seen at terminals 1 and 2, Fig. 1(b). Then it must follow from the theory described herein that if a positive impedance ^L. J. Peters — Theory of Thermionic Vacuum Tube Circuits — McGraw-Hill Book Company— 1927. 90 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 Zl is connected to terminals 1 and 2, a negative impedance Zl/— ^ will be seen at terminals 3 and 4, Fig. 1(c). George Crisson stated^ that there are two types of negative impedance which he defined as the series type and the shunt type respectively. His series type is the reversed voltage type of negative impedance — kZt^ equiva- lent to — F//; and his shunt type is the reversed current type Zif—k equivalent to V/—I. This is a logical development considering that impe- dance Z equals F//, and therefore negative impedance (— Z) equals either — V/I or V/—I where V is the voltage measured across the impedance and / is current flowing through it. c 1 3 2 o— -k'.\ 4 (a) c -k :i _ J- ; 3 4 ^ 1 3 c kZ^-^ -k:\ Zn^ 2 4 (b) (c) — N, C -k : 1 N2 (d) Fig. 1 — The negative impedance converter. It is important to note that k, the ratio of transformation, is of the form A/Q where both the magnitude A and the angle 9 are changing, however slowly, with frequency This follows from the fact that, as will be shown, k contains a term (/xi — 1) where jui is a voltage ratio the magnitude and phase of which can change with frequency. The ratio of transformation k can be made to have a magnitude closely approaching unity, and at some frequency or frequencies the angle can be made zero. If k equals 1/0 the series type negative impedance seen at ter- minals 1 and 2, Fig. 1(b), will be equal to — Zn, — V/I, where the voltage V is reversed by 180 degrees from the voltage which would appear across ter- minals 1 and 2 were the impedance here the positive impedance Zjv- and the voltage to current ratio the conventional V/I. Likewise, the shunt type negative impedance seen at terminals 3 and 4, Fig. 1(c), would be ZJ — 1^ V/—I, where here it is the current which is reversed by 180 degrees from the current which would flow through the positive impedance Zl. Thus a strange fact is noted: multiplying a positive impedance by — / does not yield the ' George Crisson — Negative Impedance and the Twin 21-Type Repeater — B.S.T.J.- July, 1931. THEORY OF NEGATIVE IMPEDANCE CONVERTER 91 same result from a circuit viewpoint as dividing a positive impedance by — 1. A positive impedance multiplied by —i is a series type negative im- pedance. A positive impedance divided by —i is a shunt type of negative impedance. A practical (i.e., real or actual) converter circuit can be represented by Fig. 1(d). A vacuum tube circuit contains positive impedance elements. Some of these will show up in the equivalent circuit on the left-hand side of the ideal converter; others will show up on the right-hand side of the ideal converter. This will be clarified in the discussion of the El circuit which follows. The equivalent circuit of any practical negative impedance converter of this type can be represented by the equivalent circuit of Fig. 1 (d) which shows the positive impedance elements associated with the vacuum tube in *z, kz kZ^ kZz -kZ2 -kZ^ kZ^ ? — VW -kZ^ ■VA — \ kZ^ >-kZ^ [c) c ■k:^ o 3 O— 1 C 3 4 i -k:\ 4 (d) Fig. 2 — Equivalent circuits. the form of two equivalent networks (iVi and N2) arranged one on each side of the ideal converter (C) having a transformation ratio of —k:l. It should be noted that should the series arms of i\^i equal k times the series arms of N2 and should the same relationship exist for the shunt arms then the effect of these networks is cancelled, except for power dissipation, and Fig. 1(d) is equivalent to Fig. 1(a). This is illustrated in Fig. 2 where Xi and iY2 have been represented by equivalent T networks as shown specifi- cally in Fig. 2(a). Network X2 can be multiplied by — ^ and transformed to the left-hand side of the ideal converter. Fig. 2(b). The adjacent series arms of these two networks cancel each other as shown in Fig. 2 (c) . The shunt arms go to infinity and the other series arms also cancel leaving Fig. 2(d). It is not possible to cancel Xi and N2 perfectly in a practical circuit design. But over the frequency range of interest this could be closely approxunated by making all impedances shunting the ideal converter as large as possible, and by cancelling all resistances in series in .Yi by a resistance added in N2. 92 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 As a physical concept the idea of negative impedance is difficult to visual- ize because this type of impedance supplies power to an external circuit rather than dissipates it. This power is supplied either by the application of a reversed voltage or a reversed current. In spite of the difficulty which may be experienced in attempting to visualize the feedback action that takes place inside a negative impedance converter, if its equivalent circuit is known then its stability can be determined readily and its operation as a device for producing negative impedance becomes obvious. Stability Like any amplifier whose output connects back to its input, the negative impedance converter if not properly terminated can run away with itself and oscillate. Stability can be determined by conventional feedback theory^; fortunately, there is a simpler criterion for determining stability. Consider again the ideal converter. Fig. 1(b). Assume that Zl^ not shown on Fig. 1(b), is an impedance connected to terminals 1 and 2. Consider the circuit mesh formed on the left-hand side of the ideal converter by the connection of Z^ to terminals 1 and 2. Here a negative impedance {—kZji) is seen looking into terminals 1 and 2, and a positive impedance {Zl) is seen looking away from them. The total impedance in this mesh is Zi,— kZ^. If k Zn should equal Zl then the total impedance would be zero; and a voltage inserted in series with this mesh would call for infinite current, a situation obviously impos- sible. Thus it becomes evident that kZ^ should not equal Zl; or, what is the same thing, the ratio UZn/Zl should not equal 1/0 if the system is to be stable. Furthermore, it can be shown that for an ideal converter the ratio UZn/Zl contains the characteristics of the feedback factor (iu/3) of the am- plifier in the converter. In view of this fact, it might be expected that Nyquist's rule* for stability in feedback amplifiers could be paraphrased as follows: To obtain stability in an ideal negative impedance converter the locus oj the ratio UZs/Zl over the frequency range from zero to infinity must not en- close the point 1/0. The same general rule for stability can be arrived at by connecting an impedance Zn to terminals 3 and 4 of Fig. 1 (c) and by considering the circuit mesh formed by {Zl/ —^ + Zs. It should be noted in this case that Zl/—^ calls for a flow of current 180 degrees out of phase from that which would flow through Zu/k. This means that where the phase angle of Z^ijk equals that of Zjv the magnitude of Zl/^ must be greater than that of Zat, which is another way of saying that at this phase angle the magnitude of kZs/ZL must be less than unity. 'H, W. Bode — Book — Network Analysis and Feedback Amplifier Design — D. Van Nostrand Company, Inc. — 1945. * H. Nyquist— Regeneration Theory— 5.5. r./.— Jan., 1932. THEORY OF NEGATIVE IMPEDANCE CONVERTER 93 From a practical engineering viewpoint there is a simple criterion for judging stability. It can be stated as follows: The ideal negative impedance converter will be unconditionally stable provided that the magnitude of ^Zat/Zl is less than unity at any frequency where the angle of this ratio is zero. These same conditions for stability apply to any practical (i.e., real or actual) converter circuit, Fig. 1(d). However, Zl must be taken as the im- pedance seen looking into the network N\ from the position of the ideal converter C, and Zs must be taken as the impedance seen looking into the network .Vo from the ideal converter C. In other words, the effect of N\ must be included in Zl and the effect of Ni must be included in Zjv. Negative Impedance Converter Circuits Negative impedance can be produced by connecting the output of an amplifier back in series or in shunt with the input in the right phase rela- tionship. This type of circuit can be considered as a negative impedance converter similar to Fig. 1(d) where the ratio of transformation — ^ is of the form — (/ii — i), in which ii\ represents a function of the voltage amplifica- tion of the amplifier. The disadvantage of a transformation ratio of this kind is that it changes markedly with variations in tube constants and battery supply voltage. Such circuits present a stability problem. One solution to this problem has been described by E. L. Ginzton^. He reduced variations in the amplifier gain by stabilizing the amplifier itself with negative feed- back and thus reduced variation in /xi. Note that if jUi is set equal to 2, then — k becomes equal to —1. There is another method of using negative feedback to stabilize a circuit for producing negative impedance. This method was used in the El circuit and will be described in detail in connection with it. Essentially, here nega- tive feedback is arranged together with positive feedback to produce a trans- formation ratio for the ideal converter of the form — {\i\ — 1)/(m2 + !)• The symbol /X2 represents a voltage ratio. Furthermore, /X] equals /3du2. If |3 approximates unity and if y.^ is very much larger than one, — k approaches — 1 in value and is relatively independent of variations in tube constants and battery supply voltage. In order to illustrate how the equivalent circuit of a negative impedance converter can be derived, consider a circuit credited to Marius La tour about the year 1920, Fig. 3(a). Figure 3(b) is a schematic representation of Fig. 3(a) in the manner originated by G. Crisson. With reference to Fig. 3(b), the polarity of amplifier A is assumed such that, at the instant the a-c current /i flows in the direction indicated, the current /o will flow in the direction ^ E. L. Ginzton — Stabilized Negative Impedances — Electronics — July, 1945. 94 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 shown and the voltages V2 and jjlIiZn will have the polarities shown. For the moment it will be assumed that the input impedance of amplifier A is infinitely high, an assumption which will be modified later to agree with actual circuits. The symbols Zn and Zi represent impedances, Rp represents the plate resistance of the output tube {T2) and tiliZw represents the voltage produced in the plate circuit of the output tube of amplifier A, the tube Fig. 3 — Latour's circuit. 7*2 of Fig. 3(a), by the voltage drop IiZn across the input, grid to cathode of Ti, Fig. 3(a). The mesh equations for Fig. 3(b) can be written as follows: Vi = {Zu + Zi) 7, -Z1/2 0 = - (Zi + nZ^) h + {Rv + ^1) h The current h becomes: V,{Rp + Zi) {Zs + Z,){Rp + Zi) - (Zi + ixZ^)Z, ^^- ^^^ The impedance seen looking into terminals 1 and 2 caA be written: Z12 = THEORY OF NEGATIVE IMPEDANCE CONVERTER 95 Thus the impedance Z12 equals the impedance Z\ in parallel with Rp which combination is in series with impedance Zn multiplied by 1 — \ixZ\liRj, + Zi)]. An equivalent circuit for Z12 is illustrated in Fig. 3(c). Next, assume that Zl^ not shown on Fig. 3(b), is connected to terminals 1 and 2 of Fig. 3(b) and that Zn is removed from across terminals 3 and 4. The mesh equations can be written as follows: -72= (Zi + Zz.)/i -Zi/o MF2 = -Zi/i +(i?p + Zi)/2 The current /i can be written: J - - ^2 [Rp + Zi - fiZi] , V ^' - (Z, + Z,KR, + zo - z\ ^- ^^^ The impedance looking into terminals 3 and 4, Fig. (3b), with the changes listed above is: z. + ^-^' y _ ^2 Rp -\- Zi . . Z34 = -— = -, r Eq. (4) \ Rv + Zj Hence, if the circuit of Fig. 3(b) is redrawn as a four- terminal network as shown in Fig. 4(a) with Z2 added to represent the input impedance of ampli- fier A the equivalent circuit of this network can be represented by Fig. 4(b). The equivalent circuit consists of two positive impedance networks, one on each side of an ideal converter. The ratio of transformation of this ideal converter is of the form — ()Ui — 1):1. Looking into terminals 1 and 2, Fig. 4(b), a series type negative impedance will be seen and looking into terminals 3 and 4 a shunt type negative impedance will be seen. The proof that these impedances are negative and of the reversed voltage or reversed current type has been established by H. W. Dudley, F. H. Graham and R. C. Mathes for similar circuits and will not be taken up here, although the fact could be derived simply from equations (1), (2), (3) and (4). The purpose of this discussion is to illustrate the simplicity with which an equivalent circuit can be derived, and to point out the value of the concept of the ideal negative impedance converter. A well known circuit which can be used as a negative impedance converter is the circuit of the 21 type repeater. In this circuit the output of the ampli- fier is connected back to the input through a bridge type of arrangement referred to as a hybrid coil. Negative feedback and positive feedback can be developed across this coil between the amplifier output and the amplifier input. This device was used as a negative impedance converter by Crisson in his twin 21-type repeater. 96 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 There is another type of negative impedance converter circuit which should not be confused with the converter circuits mentioned heretofore. This type was disclosed by Charles Bartlett in the March 1927 issue of the z, IDEAL CONVERTER OF RATIO Rp+Z, (a) (b) Fig. 4 — A negative impedance converter and its equivalent circuit. (a) f=o f=oo -Ri- -JX (b) jX f= — L o-AAA^ -* :i R'< Lg c^ 1 1 — I (g) -J 1 ; X W=oo \l 7 I R2 *RrR2 <- (h) Fig. 5 — Impedance loci. -jX Journal I.E.E. pages 373 to 376. The Bartlett converter consists of a T network of equal resistances, one of them negative. To construct such a converter there must be available a negative resistance element. Over a THEORY OF NEGATIVE IMPEDANCE CONVERTER 97 finite frequency band this negative resistance can be produced by a converter circuit such as that of Fig. 4. However, in this case Bartlett's circuit becomes in a sense, a converter within a converter. The Negative Impedance Locus Before the El type of converter is described, it would be well to con- sider, in general, the impedance characteristic which can be produced by a negative impedance converter. The shape of the impedance characteristic over the frequency range, zero to infinity, looking into terminals 1 and 2 or into terminals 3 and 4 of a negative impedance converter will be called the negative impedance locus. It is convenient to plot this locus in the polar form with frequency as a ''running" parameter. The locus can be derived for any circuit by means of the theory outlined by K. G. Van Wynen for positive two- terminal impedances.® For example, consider the converter of Fig. 4. Assume that an impedance such as that shown in Fig. 5(a) is connected to terminals 3 and 4 of Fig. 4; assume Zi of Fig. 4 is a capacitance and that both Rp and Z\ are resist- ances. Now Fig. 5(a) represents a two- terminal network made up of a resistance shunted by an inductance. The locus of this positive impedance plotted on the R and jX plane over the frequency range from zero to in- finity is shown in Fig. 5(b). At zero frequency the impedance is zero; at infinite frequency the impedance is i?i. If to the network of Fig. 5(a) a ca- pacitance C is added, to represent Zi of Fig. 4, the impedance of the net- work so formed. Fig. 5(c), follows the circle of Fig. 5(d). At zero frequency the impedance is zero, at the resonant frequency the impedance is i?i, and at infinite frequency the impedance is zero again. If the impedance of this network. Fig. 5(c), were viewed through an ideal negative imped- ance converter. Fig. 5(e), having a ratio of transformation of —k\\ where, for the moment, k is assumed to be a numeric over the entire frequency range, the impedance locus can be represented by Fig. 5(f). Of course, k will always have an angle at high and low frequencies but, to a first approximation, at least, it can be assumed that over most of the frequency range shown in the impedance diagrams of Fig. 5(f) and Fig. 5(h) k ap- proaches a numeric. If the circuit configuration of Fig. 5(g) is created by adding resistance Ri in series with Fig. 5(e) the impedance locus looks like that of Fig. 5(h). This is a series type of negative impedance and simulates the impedance seen over a large portion of the frequency range looking into terminals 1 and 2 of Fig. 4 with the two- terminal network of Fig. 5(a) con- nected to terminals 3 and 4. ^ Design of Two-Terminal Balanciner Networks — K. G. Van Wynen — B.S.TJ. — Oct., 1943. 98 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 By a similar analysis, the locus of the shunt type of negative impedance can be derived. With the proper choice of an impedance connected to terminals 1 and 2 of the negative impedance converter the locus of the impedance seen at terminals 3 and 4 can be made to follow a circle in the clockwise direction (at least as long as k approximates a numeric). Thus, over a portion of the frequency range the series and shunt type of negative impedance can be made to have very similar impedance characteristics. At very high or low frequencies where k has an appreciable angle there will be a distinct difference between the locus of the series and the corresponding shunt type of negative impedance. This would be expected because in one case the network impedance is multiplied by — ^; and in the other it is divided by — k. The El Converter The circuit of the negative impedance converter used in the El telephone repeater is shown in Fig. 6(a). It consists of a transformer, two triode tubes, an RC network and an inductor. The transformer T couples the cathodes of the two tubes to terminals 1 and 2. The tubes while apparently in push-pull are biased for Class A operation. The RC network couples the plate of each tube to the grid of the other. The inductor L supplies plate current. The equivalent circuit of Fig. 6(a) is shown in Fig. 6(b). In obtaining this equivalent circuit the two tubes have been assumed to be identical. Thus the converter used with the El repeater can be reduced to a four- terminal network consisting of (reading from left to right) : the equivalent circuit of the line transformer T; the two biasing resistances R^', the two plate re- sistances Rp divided by (1 + /X2) ; the ideal negative impedance converter C of ratio — (mi — 1)/(m2 + 1) to 1; the elements of the RC coupling arrange- ment which appear in shunt across terminals 3 and 4; the inductor L also shunted across these terminals; and the capacitor Cx which has been added to represent both the distributed capacitance of the windings of L and the capacitance between vacuum tube plates. It should be noted that 1x2 is the amplification factor of each tube; and that Ml equals j3ijU2 where jSi is a proportionality factor representing the fraction of the voltage, between the plate of one tube and ground, which is fed back to the grid of the other tube. The value of ^i depends upon the values of Ci, i?3, -^6 and C2 of the RC coupling circuit. If ^i approaches unity in value then /xi approximates /U2. If this is so and if both /ii and iU2 are relatively large in magnitude compared to unity then the ratio of transformation, — (mi — 1)/(m2 + 1) to 1, approaches although it cannot equal —1:1. As an illustration of how the elements in the El circuit may be propor- THEORY OF NEGATIVE IMPEDANCE CONVERTER 99 tioned, consider the practical design of the El converter. Here the ratio — (ni — 1)/(m2 + 1) to 1 is —0.9: 1 over most of the voice frequency range. This is not the over-all ratio of transformation of the device, but only the ratio of the ideal converter C, Fig. 6(b). The ratio of transformer T and the effect of the other circuit elements must be considered in determining the over-all effect of the converter from terminals 1 and 2 to terminals 3 and 4. The transformer ratio is 1:9 from terminals 1 and 2 to the tube '? Ri L R ?"* EQUIVALENT CIRCUIT OF TRANS- FORMER 1+//2 Fig. 6 — The El converter circuit. cathodes. The shunt arms of the networks on both sides of the ideal con- verter C are relatively high compared to the impedances between which this converter has been designed to operate at voice frequencies. Therefore, these shunt arms can be disregarded at voice frequencies although at fre- quencies above and below the voice band these shunt arms represent a problem for the circuit designer from the viewpoint of stability. In the actual El circuit the series arms such as 2Rp/{l + fi2) and 2i?2 could be ^xancelled out by adding in series on the right-hand side of the ideal con- b 100 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 verter a resistance of 1800 ohms (not shown in Fig. 6). The final result is that the impedance seen, looking into terminals 1 and 2 of the El converter when 1800 ohms plus a network Zn is connected to terminals 3 and 4, equals — O.lZjv within a reasonable percentage of error over the frequency range from about 300 to 3500 c.p.s. for values of negative impedance from about 100 to 2000 ohms. In the practical design two line windings instead of the one shown con- nected between terminals 1 and 2 in Fig. 6(a) are provided on transformer T. In practice one of these windings is inserted in each side of the telephone line in a balanced arrangement. Terminals 1 and 2 are thus effectively con- nected in series with the line, and the El repeater presents to the telephone line a reversed voltage type of negative impedance (— F/I), which is the means of introducing additional power in the line thereby providing a transmission gain. The value of the negative impedance is controlled by a NETWORK EH AMPLIFIER ImJ ■^w^ LINE 1 TRANSFORMER LINE 2 rw^ Fig. 7 — El telephone repeater. network connected to terminals 3 and 4. Thus the El repeater consists of a transformer, an amplifier unit and a gain adjusting network (Fig. 7). The transformer, the amplifier unit and part of the network make up the nega- tive impedance converter under discussion. For overload conditions the action of a repeater of this kind differs markedly from what might be expected from a conventional amplifier. What can be expected of a conventional amplifier is well known. An idea as to the performance of a negative impedance converter under overload conditions can be had from the following example: Assume that terminals 1 and 2 of the converter are connected in series with a telephone line and a network is connected to terminals 3 and 4 so that a reversed voltage type of negative impedance of a value less than the line impedance is inserted in the line. The combination described will be stable, and some transmission gain will be provided by this negative impedance. If now the volume of speech on the line is increased beyond the overload point the result will be a noticeable reduction in the amount of negative impedance, and a conse- i THEORY OF NEGATIVE IMPEDANCE CONVERTER 101 quent reduction in gain. Under excessive overload conditions the negative impedance becomes small; and the effect of the converter is scarcely dis- cernible on the transmission of speech as far as gain is concerned. The harmonic distortion introduced on the line by the vacuum tubes overloading will increase to a maximum and then decrease with further increase in volume. The constants of the circuit coupling the plate to the grid of the vacuum tube or tubes in the converter will determine the maximum amount of distortion. A push-pull circuit is better from this standpoint than a single sided one. In the El repeater harmonics are not particularly ob- jectionable under any condition of overload. The El repeater employs a single 407 A vacuum tube which is a twin triode of the 9-pin miniature type. When operated on a plate voltage of 130 volts this repeater will pass speech volumes of +10 vu before com- pression begins because of overloading in the vacuum tube. Development of the El Equivalent Circuit One purpose of this paper is to prove that Fig. 6(b) is equivalent to Fig. 6(a) Assume that an impedance Zn is connected across terminals 3 and 4. Assume, furthermore, that the elements Ci, C2, i?3 and R^, which also connect across terminals 3 and 4, are all included in impedance Zn. Assume an impedance Zl is connected to terminals 1 and 2. The circuit of Fig. 6(a) then can be represented by Fig. 8 where the vacuum tubes have been replaced by their plate resistances (Rp) and their equivalent circuit voltages Miei and /X2^2- The voltage /xi^i is that voltage which appears in the plate circuit of each tube as a result of the action on the grid of all voltages between the tube plates and ground. The voltage ^2^2 is that which appears in the plate circuit of each tube as a result of the voltages between the cathode and ground. Fig. 6(a). The resistors Ri, R2 and Rg designate the resistance in the various coil windings plus other circuit resistance which might be inserted at the points indicated. The reactances Xi, X2 and X3 represent the effect of the self -inductance in the coil windings. The react- ances Ml, M2 and M^ represent the effect of the mutual inductances between coil windings. The numbers on a coil winding determine the polarity of the winding with respect to other windings on the same core. As mentioned previously the vacuum tubes are operated Class A. The basic circuit equations can be written as follows for Fig. 8: 0 = P7i + Qh - M3(l + H2)h - S(l - ni)h 0 = e/i -f PI2 - M,{1 + M2)/3 - 5(1 - /Xl)/4 £3 = -M3/1 - if 3/2 + {Zl + R, + X^)h + 0 £4 = -Sh - 5/2 + 0 + (Z^ + 25)/4 102 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 Where P= Ro-\-Ri+ Xi(l - MlW +^2 (1 + M2) Q = -Mii?i + Xi(^i - Ml) + X2O + fl2)k2 5 = i?i + Xi(l + ^1) i?o = i?p + i?2(l + M2) ^1 = coupling factor = Mi/Xi h = " " = M2/X2 £3 and £4 = applied voltages While the derivation of most of the coefficients in these mesh equations is obvious, the derivation of P and Q may require further explanation. Co- efficient P can be considered as follows : 1 — The term Rq equals Rp + -^2(1 + ^2)- The plate resistance Rp is in the plate circuit and hence stands alone. The resistance R2 being between cathode and ground. Fig. 6(a), produces negative feedback and must be multiplied by (1 + /X2). 2 — The resistance Ri is in the plate circuit, and here as in the case of Rp the flow of current in Ri does not produce a voltage across the grid of the same tube through which this current flows. 3 — The reactance Xi is in the plate circuit of each tube, and by means of the mutual reactance (Afi) is coupled to the respective grid of the other tube. This coupling provides positive feedback for current flowing through X\ which can be expressed as —fxiMi or — mi^i^i- Thus the term Xi(l — Mi^i) is derived. 4 — The reactance X2 being between cathode and ground, Fig. 6(a), provides negative feedback. Hence X2 must be multiplied by (1 + ^2). Coefficient Q can be explained in similar fashion: 1 — Although the flow of current through Ri does not produce a voltage across the grid of the same tube through which this current flows, a voltage drop is produced across the grid of the other tube because of the cross coupling of these grids, Fig. 6(a). Thus voltage drop in one plate circuit appears between grid and ground of the other tube in the direction to aid the flow of current in this other mesh; hence the term — mi^i- 2 — Likewise, the reactance Xi acts in the same manner as Ri in aiding the flow of current in the other tube circuit. Furthermore, Xi is coupled by the mutual reactance to this other mesh. These effects can be expressed as Xi(^i — Ml). 3 — The reactance X2 is coupled by mutual reactance to both tube circuits. It appears in each circuit between cathode and ground in the polarity to produce negative feedback equal to ^2(1 -|- ^2)^2. THEORY OF NEGATIVE IMPEDANCE CONVERTER 103 In order to establish the fact that Fig. 6(a) can be represented by the equivalent circuit of Fig. 6(b) the basic mesh equations will be developed in the following manner: First — The impedance seen looking into the converter from terminals 1 and 2, Z12, will be found. Second — An equivalent circuit which will provide this impedance will be drawn. Third — The impedance seen looking into the converter from terminals 3 and 4, Z34, will be obtained. Fourth — The equivalent circuit for Fig. 6(a) should be the logical result. Zi2 = .Ez ^ Eq. (5) P Q -s Q p -s -S{\ - Ml) -S{\ - Ml) (Z^ + 2S) E q.(6) J^z A where: A = -Mz Q p -5 -Mz{l + M2) -M,(l + M2) 0 -S(l - Ml) -5(1 - Ml) Z^+25 +M3 p Q -s -^3(1 + M2) -M3(l+M2) 0 -5(1 - Ml) -5(1 - Ml) Z.r+25 ^ + {Zl + i?6 + X3) p Q -s Q p -s -5(1 - Ml) -5(1 - Ml) Z^+26' Solving for I3 ^ E^jP - (2)[(P + Q){Z^ + 2S) - 2(1 ^ Mi)5'] {P - Q)[[Zl + i?6 + X,]l{P + Q){Z^ + 2S) Eq. (7) - 2S\l - Ml)] - 2^3^(1 + M2)(Z^ + 25)] -' = (Zx, + R, + X3) - i3 /i: = /?6 + .Y 2Ml{l +M2)(Z^.4-25) {P + Q){Z,^ + 2S) - 2(1 - Mi)52 2M^(1 + M2)(Z.v + 25) {P + QKZn + 25) - 2(1 - Mi)52 Eq. (8) Eq. (9) 104 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 where P + Q = Ro+ {1 - n{)S + X2(l + M2)(l + k2) Eq. (10) Substituting for P + ^ a-nd rearranging Zi2 = Rq -\- Xz R, + X,{1 + M2)(l + fe - 2kl) + ^^^ ^^ff" Z,N -f- ZO Ro + X,(l + M2)(l + fe) + ^\ ^'^^^^ Eq. (11) Equation (11) can be rewritten in a form from which the equivalent circuit can readily be constructed. This form is given below in Equation (12) 1 Zi2 = i?6 + Xs + 1 L2£JU(i+iU2)J Xsd + k. 2kl) .m + M2) + 2^1 [1 - Ml] r X3 1 r 252^ "I Li + M2jL4^i^2jU^ + 25j Eq. (12) From Equation (12) the equivalent circuit of Fig. 9(a) can be developed. Starting at the lower right-hand side of Equation (12) it will be observed that 2SZn/{Zn + 25) represents Zn and 2S in parallel. This parallel combination is multiplied by (1 — jUi)^3/(l + M2)(4^3 ^2)- In series with the parallel combination is the leakage inductance of transformer T equal to X3(l + ^2 — 2^3)72^3; and the term containing Rq, which stands for Rp -\- i?2(l + M2). In parallel with all of this is X3. The resistance Re is simply a series resistance as evident from Fig. 8. It can be seen from Fig. 9(a) that X3 14X2^3 is the impedance ratio of transformer T, and that — (jui — 1)/()U2 + 1) is the transformation ratio of an ideal converter. The resulting circuit can be represented by Fig. 9(b). Next consider the impedance Z34, which is seen looking into terminals 3 and 4 of Fig. 8. £4 Z34 — Zn Eq. (13) I A = p Q -Mad + M2) Q P -Mad + M2) -Ma -Ma Z,. + IU + Xa £4 Eq. (14) (Zs + 25) [(Zz. + i?6 + X3)(P + 0 - 2M3'(1 -h M2)] E, __ - 2(1 - ixi)S\Zj^ + R, + X3) Eq. (15) h~ (P + Q){Z!. + i?6 + X3) - 2^3^(1 + M2) THEORY OF NEGATIVE IMPEDANCE CONVERTER 105 + -AAAr-^WT^-L^nW^-^VV^ :w-Ae,+/^2e2 ;7*^^^W0^^ M, ^ X3 6 M. r X3-^ ■AAAr ^ Fig. 8 — Schematic of El repeater. M\^k2-2ki) 1 1-^6 0 vw ■nm^ 2X33 U-/ly X3ZN 4*1X2 1-/Z, +A2 (a) -AA/V X3R2 AAAr (sXaj^/O +/^2) Z,2-^ EQUIVALENT CIRCUIT OF TRANSFORMER MULTIPLY BY X3_ 4X2*3^ HVW-AAAH 2R2 2Rp 1+/Z2 MULTIPLY — *► BY U2+V (b) 25 ^34 — 2o — Fig. 9 — Equivalent circuit of equation (12). 2(1 - n,)SKZ^ + i?6 + X3) Zn. (p + (3)(Zz. + i?6 + X3) - 2^3^^2X3(1 + M2) Substituting for P + (2 and rearranging Eq. (16) 106 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 Za4 = 25 + 2R, (1 - Ml) + 2X2(1 + M2) (1 - Ml) 4klX, (1 + M2) + [1 + ^2 - 2kl] X, (1 - Ml) (Zl + i?6 + X3) Eq. (17) From Equation (17) the circuit of Fig. 10(a) can be developed in a manner similar to the way Fig. 9(a) was developed from Equation (12). Furthermore, Fig. 10(a) can be rearranged in the forxH shown in Fig. 10(b) . 4)^3^X2 Re Xa 2R2 AkjXzZL g 4*32X2X3 X3 (a) 2X2(1 + ^2-2^3^) 2R T EQUIVALENT CIRCUIT OF TRANSFORMER MULTIPLY-*— BY 1 / X3^ /4X2/fe3' (b) Fig. 10 — Equivalent circuit of equation (17). A comparison of Fig. 9(b) with Fig. 10(b) shows these two circuits to be essentially the same except for the point of view. If it is remembered that Zn in Figs. 8, 9 and 10 has been chosen to include the elements in the RC network which couples the plate of one vacuum tube to the grid of the other, then from consideration of Figs. 9(b) and 10(b) it is obvious that Fig. 6(b) is the equivalent circuit of Fig. 6(a). If Equation (6) or Equation (7) were studied it would be found that for all conditions of circuit stability the current h would flow in the same general direction in which it would be expected to flow in any circuit mesh where all impedances were positive. But Zn can equal a negative impedance. Hence, Zn must be a reversed voltage type of negative impedance equal to — VII. For an impedance to be negative either the voltage V at some frequency must be the reverse in polarity of that measured across a like positive impedance or the current must flow in the reverse direction. If the THEORY OF NEGATIVE IMPEDANCE CONVERTER 107 current does not reverse direction the voltage must, to produce a negative impedance. If Equation (14) for the current U were studied it would be found that all conditions which meet the requirement for circuit stability when the impedance Z34 is negative would produce a flow of current through this mesh with a phase impossible to realize were Z34 positive. Hence, if im- pedance Z34 is to be negative the current must be reversed and the im- pedance must be of the reversed current type equal to V/—I, where here V is the voltage across Z34 and / is the current flowing through it. Design Considerations If a resistance were connected to the network terminals 3 and 4 of Fig. 6(a) the impedance seen at the line terminals 1 and 2 would follow a locus Fig. 11 — Impedance locus of El repeater. similar to that shown in Fig. 11 for the frequency range from zero to in- finity. At zero frequency this impedance would be a small positive resistance equal to the d-c resistance of the primary windings of transformer T. At some low frequency /i (Fig. 11) the locus would show a positive im- pedance. In the El repeater it is this portion of the impedance characteristic which is used for the passage of low frequencies such as ringing, diahng and the like. Between the frequencies of /2 and/3 (Fig. 11) is seen an im- pedance which approximates a negative resistance. At high frequencies the locus would approach the origin again. In Fig. 11 this approach is shown through the first and then the fourth quadrant. At frequencies above the speech band passed by the telephone line a negative impedance is not wanted for the El repeater because it is of little value for voice transmission and may be detrimental in adding to the difficulty of obtaining stable operation. 108 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 In the design of the El repeater it is desirable for the network to have control of the impedance presented at the Hne terminals over the voice frequency range (/2 and /a of Fig. 11). To accomplish this all impedances shunting the converter circuit are made as large as possible and all impe- dances in series are made as small as possible at these frequencies. Further- more, Ml is made as close to fi2 as practical, and large enough so that the factor (ni — 1)/(m2 + 1) is made as close to unity as possible. If this factor approximates unity and if the series term Rp/{1 + 112) is relatively small with respect to impedances between which the converter is operating, it can be seen from the equations that battery supply variations and tube changes should have little effect upon the negative impedance presented by the converter at these frequencies. The retard coil and transformer inductances should be considered at low frequencies as a possible source of instability. At low frequencies the in- ductance of the retard coil shunting terminals 3 and 4, and the inductance of the transformer shunting terminals 1 and 2 materially affect the im- pedances facing the ideal converter. Another important consideration in the design is the ratio of the line transformer. The ratio must be such that the tubes will operate efficiently with the normal network, line load, and plate supply voltages. This part of the design follows conventional methods. The distributed capacitances of the line transformer windings should be taken into account. In general, these are large compared to the tube capac- itances between cathodes and between ground and each cathode. These interelectrode capacitances can be neglected at voice frequencies, but at the higher frequencies all of them should be considered, and conventional methods of suppression of parasitic oscillations should be applied. Also, the distributed capacitance of the retard coil must be considered from the standpoint of stability at the higher frequencies. Conclusion A vacuum tube arrangement for producing negative impedance can be represented by an equivalent four-terminal network consisting of an ideal converter having a ratio of transformation of —k'A and two positive im- pedance networks located one on each side of the ideal converter. In these two networks some of the elements can be cancelled in effect by balancing those in one network against corresponding elements in the other. Elements which cannot be balanced can be made either relatively large or relatively small compared to the impedances between which the converter is designed to operate. Across one pair of the four terminals of a practical converter can be seen a reverse voltage type of negative impedance; across the other pair THEORY or NEGATIVE IMPEDANCE CONVERTER 109 can be seen a reversed current type. This device can be made to approach the ideal only over a finite frequency range. At some frequencies k will not be a numeric. Likewise, at some frequencies the two internal networks will produce appreciable effect. Stability can be ascertained readily from a working knowledge of the components of the equivalent circuit. Designs are practical wherein variations in battery voltages and vacuum tube constants are second-order effects. Acknowledgements The writer acknowledges the help of Messrs. K. G. Van Wynen, K. S. Johnson and F. B. Llewellyn with the concept of negative impedance and the contributions of Messrs. J. A. Weller, H. Kahl and W. J. Kopp relating to the practical design of negative impedance converters. He is also in- debted to Miss A. B. Strimaitis for the many computations which were required in this development and to Messrs. R. Black, J. A. Lee and J. M. Manley for their comments on this paper. In recent years there has been a growing need for an inexpensive two- wire repeater having a cost lower than that of the 22 type for use in the exchange plant. Mr. G. C. Reier encouraged the study of negative impedance devices as a possible way of meeting this need. Had it not been for his encouragement the El repeater development might not have been under- taken. The Ring Armature Telephone Receiver By E. E. MOTT and R. C. MINER {Manuscript Received Aug. 15, 1950) A new type of telephone receiver is described, in which the permanent magnet, the pole piece and the armature, which drives a light weight dome, are all ring-shaped parts. This structure exhibits a substantially higher grade of performance than present receivers of the bipolar type, with regard to efficiency, frequency range, leakage noise level, and response when held off the ear. In addition to showing the characteristics of this new receiver, an analysis of the various losses is given, and ideal performance limits are estabhshed. The advantage of providing an aux- iliary path for the air gap flux is indicated, and other applications of the device as a transducer are described. Introduction tHE ring armature receiver is a new type of telephone receiver de- veloped for use in the subscriber's telephone set. It differs from other types in that the diaphragm consists of a thin, lightweight, dome- shaped central portion made of low density, non-magnetic material whose function is to radiate sound energy, surrounded by a narrow ring-shaped armature to which it is attached. The ring armature is not clamped at the outer periphery, but is held in place solely by magnetic attraction. It is driven at its inner periphery by the magnetic force. A ring-shaped pole and magnet structure serves as the motor element to drive the diaphragm. The new receiver is shown in sectional view in Fig. 1. The advantage of the composite diaphragm construction in the new receiver is that the central portion moves almost wholly Uke a piston and is therefore nearly 100% effective and that its contribution to the total moving mass is small, being of the order of \. For these reasons it has been found possible to reduce the mass per unit area to approximately \ of that of the diaphragm of the bipolar receiver. Because of the large effective diaphragm area and the low mass, the acoustic impedance of the new receiver is low, being about \ of that of the earlier receiver. Although the motor efficiency is approximately equal to that of the bipolar receiver, the improved dia- phragm construction yields a receiver of higher available power response,^ wider frequency range, improved characteristic when the receiver is held ofT the ear, and having greater discrimination against room noise. The ring armature construction is also applicable to devices other than earphones, such as microphones and loudspeakers. ^A.S.A. Standard Z24.9-1949 "Coupler Calibration of Earphones." 110 THE RING ARMATURE TELEPHONE RECEIVER 111 Early Steps in the Development It has long been evident that the effective mass of the magnetic disc type diaphragm used in the bipolar receiver is high, and is therefore a serious limitation to obtaining an extended frequency range without sacrificing efficiency. Attempts were made to reduce this mass by using lightweight cone type radiators driven by relatively small magnetic discs at the center as in Fig. 2(a). The difficulties, however, of controlling the vibrational stabihty MEMBRANE FERRULE -GRID APHRAGM MAGNET DIAPHRAGM SEAT COIL POLE PIECE TERMINAL PLATE ^- ACOUSTiC RESISTANCE Fig. 1 — Sectional view of the ring armature receiver in a handset. of such structures made them impractical. Moreover, the mass of the arma- ture was 100% additive to the moving system. By reversing the positions of the armature and the light-weight portion of the diaphragm, putting the latter in the middle and using a ring of mag- netic material around the outside edge as shown in Fig. 2(b), much better results were obtained. ^-^ The armature, having one edge resting on a seating surface, added only 30% of its mass to the moving system. Also, since the large central portion of the diaphragm carries no flux, it could now be re- placed by a lightweight non-magnetic material instead of the relatively 2U. S. Patent No. 2,170,571, E. E. Mott, Filed August 12, 1936. 3U. S. Patent No. 2,171,733, A. L. Thuras, Filed October 6, 1937. 112 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 heavy magnetic material needed for armatures. These two factors permitted a very substantial reduction in the effective mass to be made in the moving system. In addition it has been observed that the peripherally driven diaphragm moves as a piston over a wide frequency range, while a centrally driven cone type diaphragm, as in Fig. 2(a), is more likely to have parasitic modes of vibration in the frequency range of interest. However, the re- ceivers of the type shown in Fig. 2(b) needed small air gaps in order to get the force factor necessary to attain a high efficiency. Moreover, the thin (a) COIL -f — POLE PIECE Tfj- MAGNET (b) Fig. 2 — (a) Early composite diaphragm receiver. (b) Simple ring armature receiver. (c) Ring armature receiver with auxiliary magnet. magnet mounted between the inner and outer pole pieces presented manu- facturing problems because of curved surfaces that had to be ground to close tolerances. The magnet in this case had to be of low reluctance and large section area, and this resulted in a rather tall structure. By adding an auxiliary ring magnet overlying the front of the diaphragm, as in Fig. 2(c), radially magnetized in aiding relation to the lower magnet, a large increase in force factor was attained with larger air gaps than in Fig. 2(b).'*' ^ In addition an upright main magnet, as shown, could then be ^U. S. Patent No. 2,249,160, E. E. Mott, Filed May 19, 1939. »U. S. Patent No. 2,249,158, L. A. Morrison, Filed July 15, 1941. THE RING ARMATURE TELEPHONE RECEIVER 113 used to advantage, even though it had a relatively higher reluctance. With this design, magnetic fields were produced in the two air gaps above and below the diaphragm. In addition, the auxiliary ring magnet acted to shunt a portion of the d-c. flux around the armature, which resulted in reduced saturation in the middle portion of the armature, which permitted increased flux density in the air gap below the diaphragm. This partially separated the paths of the a-c. and d-c. flux in the magnetic structure, and adjusted the magnetic forces exerted on the diaphragm, so that lower stiffness armatures VARISTOR TERMiNAL PLATE Fig. 3 — i'hotograph of the ring armature receiver and its parts. could be used than in the structure of Fig. 2(b). Application of the auxiliary ring magnet in front of the diaphragm contributed very substantially toward the development of a suitable motor element. The coil and magnet relationship shown in Fig. 2(c) also resulted in a lower axial height and a more compact structure. Description of the Production Design The main and auxiliary magnets of the early designs were Alnico castings, and were expensive to produce. In the production design, they have been combined into a single L-sectioned remalloy ring magnet, and the diaphragm 114 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 seat has been transferred from the main magnet to a non-magnetic nickel - chromium alloy ring. The details of this construction are shown in Figs. 1 and 3. The diaphragm consists of a flat ring-shaped vanadium permendur^ armature, to the inner periphery of which is cemented a lightweight, plastic-impregnated and molded cloth dome. The dome is placed in a concave downward position with respect to the receiver cap, which greatly enhances its strength with respect to suddenly applied air pressures. At the outer periphery, the arma- ture rests on the non-magnetic seat, and is driven at the inner margin by the magnetic field produced at the tip of the ring-shaped pole piece. The 45% permalloy^ pole piece, at its end opposite the air-gap, has an integral flange extending outward, to which the armature seat is welded. The magnet also rests on the pole piece flange, outside of the armature seat. This magnet is made of a material similar to remalloy,** but of a modified composition in which the molybdenum content is increased, which results in a higher co- ercive force but lower residual induction. It is hot formed from sheet material into the shape of a cup and then punched to provide an opening in the base of the cup, the diameter of the opening being slightly smaller than the inner diameter of the cylindrical portion of the pole piece. The inwardly extending flange of the magnet forms the auxiliary portion. Acoustic controls of the response-frequency characteristic of the receiver are provided in the same manner as in former telephone receivers of the controUed-diaphragm type,^ except that lower values of acoustic impedance are used which are easier to control. CoupHng chambers on each side of the diaphragm connect to constricted passageways having acoustic mass and resistance. The coupling chamber under the diaphragm exhausts into the handset handle cavity through four holes, molded in the phenol plastic terminal plate, which are covered with an acoustic resistance fabric ce- mented to the terminal plate. This acoustic mesh serves to extend the fre- quency range of the receiver because of its negative reactance character- istics, and the acoustic resistance damps out the diaphragm resonance. The coupling chamber above the diaphragm exhausts into the listener's ear cav- ity through the acoustic mass and resistance of the holes in the receiver cap. Proper selection of the acoustic impedances of the elements of this mesh serves still further to extend the frequency range of the receiver. The rela- tionships of all the acoustic and mechanical elements is such as to produce the desired response frequency characteristic (See section entitled "Network Representation"). There are several parts of the ring armature telephone receiver whose •"Survey of Magnetic Materials and Applications in the Telephone System," V. E. Legg, The Bdl System Technical Journal, Vol. XVIII, July 1939. instruments for the New Telephone SeU, W. C. Jones, The Bell System Technical Journal, Vol. XVII, July 1938. THE RING ARMATURE TELEPHONE RECEIVER 115 functions are almost completely mechanical, as compared with the mag- netic, electrical, or acoustical functions of other parts. The armature seat, which already has been mentioned, is one of these. An interesting design feature of this part is the necessity for high electrical resistivity since most of the a-c. flux links the seat and it is therefore subject to eddy current losses. A nickel-chromium alloy has been found suitable for this part. Another part having a purely mechanical purpose is the coil stop. This part consists of a flat strip of metal punched in a curved shape so as to fit on top of the coil, and having three prongs bent at right angles to the strip. The tips of the prongs pass through slits in the pole-piece flange and are bent over in assembly to hold the coil in place. A membrane is mounted between the protective grid and the magnet flange to keep dust and other foreign sub- stances out of the instrument. In this receiver the protective grid and the clamping ferrule, which is crimped over in the final assembly, are combined into one part. Low manufacturing costs are realized by the use of multiple-purpose parts. Some examples have been noted already. The single magnet serving as both main magnet and auxiliary magnet is an example. The combined ferrule-grid, which eliminates the fabrication, finishing, and handling of one part as compared with previous designs, is another. The terminal plate also falls into this class of parts. It not only serves as an electrical termination for the receiver, but also is molded in such a way as to provide the correct coupling air volume in back of the diaphragm; it contains the acoustic passageways leading out of the back of the instrument and provides a mounting surface for the acoustic resistance fabric cemented over these passageways; it mounts and protects a click-reduction varistor which is made a part of the receiver; it is molded with projections which prevent the spade tip terminals of the handset cord from shorting against the varistor case or turning in such a manner as to cause the cord conductors to be pinched between the receiver and its handset seating surface; it has other projections which key into the coil lead holes of the pole-piece and provide insulation between the wires and the pole-piece and at the same time orient and prevent rotation of the terminal plate with respect to the pole-piece; and it is provided with two slots into which the crimped edge of the ferrule is staked to prevent rotation of the ferrule. Perhaps the most interesting example of a multiple-purpose part is the diaphragm dome. Its primary purpose is, of course, to radiate sound energy in its capacity as a lightweight, rigid closure for the central opening of the armature. In addition, it has six small projections molded to its top surface just outside of the dome portion, which will touch the inner edge of the magnet flange if the diaphragm is lifted upward off of its seat by mechanical shock. Thus the projections prevent the armature from coming close enough 116 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 to the auxiliary magnet to be held there by magnetic attraction and insure that the armature will always return to its seat in case it is dislodged by mechanical shock. Another function which is built into the dome serves to prevent the outside edge of the armature from coming into contact with the inside surface of the cylindrical main portion of the magnet. Contact of this nature has been found to produce irregularities in the response-frequency characteristic of the receiver and a variability of the output level of a few- decibels. These undesirable variations are controlled by six spokes of the dome material which extend outward beyond the edge of the armature a few thousandths of an inch and thus tend to prevent contact between the arma- ture and magnet. Finally, the dome contains a small hole which introduces a low frequency cut-off in the response-frequency characteristic of the re- 250 500 750 1000 1500 2000 FREQUENCY IN CYCLES PER SECOND 3000 Fig. 4 — Available power response-frequency characteristics measured with a source impedance of 128 ohms on a 6 cc. coupler, except as noted. ceiver, which has been found to be desirable to reduce interference picked up in telephone circuits from electrical power circuits. Performance Characteristics A partial evaluation of the performance improvements of the ring arma- ture receiver as compared with its predecessor is illustrated in Fig. 4, which shows available power response-frequency characteristics** for the two re- ceivers. The two solid curves in this figure show the relative sound pressure output of the new Ul receiver and the present standard HAl receiver over ^Response-frequency characteristics in this article are shown on a new frequency scale which gives a well balanced visual emphasis to the various frequency bands. The scale is linear from 0 to 1000 cycles per second, and logarithmic from 1000 to 10,000 cycles per second, the two sections having a dimensional ratio of 4 to 9. See "A New ?>equency Scale for Acoustic Measurements", W. Koenig, Bell Laboratories Record, August 1949. THE RING ARMATURE TELEPHONE RECEIVER 117 their frequency ranges. These solid curves were measured with the receiver on a standard closed coupler^ of six cubic centimeters volume, using a source impedance of 128 ohms, and the ordinate scale is given in terms of the square of the pressure generated in the coupler per unit of electrical power available to a pure resistance of 128 ohms substituted in the electrical cir- cuit in place of the receiver. The new receiver shows 5 decibels improvement in output level and about 500 cycles per second extension in the frequency range. This represents a very substantial increase in transducer efficiency, and the increase in range results in a quite noticeable improvement in the quality of speech sounds. The low frequency cut-off obtained by a hole in the diaphragm of the Ul receiver, mentioned in the preceding section, ap- pears in the response-frequency characteristic below 350 cycles per second. The irregularities in the characteristic of the Ul receiver at 450 and 1200 cycles per second are not inherent in the receiver, but are acoustical effects of the passageway molded in the handset handle, which serves as a conduit for the wires connected to the receiver unit. This is indicated by the dashed line curve, which shows the response-frequency characteristic of the receiver when the passageway is plugged at the receiver bowl of the handset. No adverse effect of these irregularities has been discerned. For comparison with the closed coupler characteristic, the dotted curve in Fig. 4 shows the pressure generated by the Ul receiver at the entrance to the human ear. This curve is an average of 90 observations on 30 subjects measured by a small diameter search tube inserted into the outer ear cavity through the receiver cap and connected to a microphone external to the handset, so that the ear is used as a passive coupler. Figure 5 shows the manner of using the apparatus, which includes a 640AA condenser trans- mitter mounted on the handset and coupled to the search tube through a very small chamber. It will be noted that the curve of Fig. 4 taken on a human ear shows increased low frequency cutoff because of leakage be- tween the receiver cap and the ear, but that otherwise the 6 cc. closed coupler response is a good representation of the data taken on the ear. Con- siderable deviations from the average curve were observed from person to person, as illustrated in Fig. 6 which shows the maximum and minimum values of all measurements at various frequencies and the standard deviation of the measurements at three frequencies. An interesting comparison of the performance of the Ul and HAl re- ceivers is made by holding the receivers slightly away from the ear. It is observed that the degradation in response caused by this condition, which represents a very large amount of acoustical leakage between the ear and the receiver cap, is much greater in the HAl receiver. The effect is illus- 9T;^e 1 coupler per A.S.A. Standard Z24.9-1949. 118 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 trated by Fig. 7, which shows available power response-frequency character- istics for the two receivers when they are raised one-eighth of an inch from the normal sealed position on a standard coupler. The Ul receiver shows better response than the HAl receiver at both high and low frequencies. The low frequency end is cut off less in the Ul receiver, because it has 2.5 Fig. 5 Mclhod of luta.^uiii microphone. rt-Ciivcr res[)Orise on a liuiuan car, usin^ a sc irch tube times larger effective area and therefore is a better radiator of sound at low frequencies. The high frequency end is better because of the inherent exten- sion of frequency range in the Ul receiver. Another interesting characteristic of the new receiver is its performance under conditions of high ambient noise levels. Noise leakage between the receiver cap and the external ear generates an acoustic noise pressure in the ear cavity which may mask the sound signal from the receiver. This leakage THE RING ARMATURE TELEPHONE RECEIVER 119 1- tib i Q. Its O tr LU Q- 70 III z e 65 II CD Q o 60 ■-X^ ^'^^^^ \ •-— ^ •''""""•^^^ -^-A \ f 1 /~~ *^— .^ \, ^\ U ^' ^ \ / ' / / / r \' / / 1 1 / Q ^50 III MEASUREMENTS 1 BA — AVbKACab Ul- ALL MbAiUKbMbN 1 is RS SHOW STANDARD DEVIATIONS \ Q. to LU a 40 1 250 750 1000 2000 FREQUENCY IN CYCLES PER SECOND 3000 4000 Fig. 6 — Available power response-frequency characteristics of Ul receiver, measured withe a source impedance of 128 ohms, on human ears as passive couplers. 60 S75 a. m -5 Q O ? cr LU LU CL in Z ^ 70 65 55 750 .N^- PRESENT STANDARD / RECEIVER (HA1) 4000 1000 1500 2000 3000 FREQUENCY IN CYCLES PER SECOND Fig. 7— Available power response-frequency characteristics, with receivers raised i inch from normal position on coupler. noise is predominantly low frequency noise not only because typical room noise characteristically decreases with increase in frequency,io b^t also because the leakage path has an acoustic impedance which rises with fre- lo^Room Noise Spectra at Subscribers' Telephone Locations," D. F. Hoth, Journal of Acoustical Society of America, Vol. 12, April 1941. 120 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 quency. The Ul receiver has considerably lower acoustic impedance than the HAl receiver and, since the acoustic impedance of the receiver shunts the ear coupling chamber impedance, the same degree of noise leakage under the Ul receiver generates a lower noise pressure in the ear cavity with a resultant decrease in the masking effect on a given signal. Figure 8 shows data on this characteristic. Tests were made by measuring the pressure in a 6 cc. coupling chamber closed by the receiver except for a leakage path having acoustic resistance and mass values approximating those of the worst leakage condition shown by the data presented in Fig. 6. The measurements were made in a highly absorbent room, with a loud-speaker as the sound source. The curves show that below 1500 cycles per second the noise leakage sound pressure generated in the coupler when the Ul receiver is used is less than that of the HAl receiver by as much as 5 db over a considerable portion a -20 PRESENT STANDARD RECEIVER (HAl) 1 " "*•«•, 'x^^ x ^> ^^ / / / / NEW RECEIVER (Ul)'" ^y \ \ ■'-\ ^ ^ \ \ 400 600 800 FREQUENCY IN CYCLES PER SECOND 2000 Fig. 8 — Relative noise leakage sound pressure in a 6 cc. coupler having a simulated ear leak. Reference level is the pressure at the coupler with the receiver removed. of the frequency range. The effect of this difference has been observed in listening tests using real voices* and in subjective tests] while measuring the shift in the threshold of intelligibility between the two receivers under quiet and noisy conditions. Since under certain conditions a reduction in the noise may be equivalent to a corresponding gain in signal strength, this feature of the ring armature receiver represents a distinct improvement. A characteristic of considerable importance in the development and de- sign of a telephone receiver is the manner in which the receiver output level varies with direct current superimposed on the alternating current flowing in the receiver coils. The direct current may be applied in such a way that it develops flux in the magnetic circuit which either aids or opposes the polar- *Unpublished work by W. D. Goodale, Bell Telephone Laboratories, t Unpublished work by R. H. Nichols, Bell Telephone Laboratories. THE RING ARMATURE TELEPHONE RECEIVER 121 izing flux of the permanent magnet. Superimposed direct-current character- istics are shown for both the Ul and the HAl receivers in Fig. 9. The verti- cal Une in the plot labeled zero represents the normal operating condition of the receiver with no direct current in the coils. Increasing values of opposing current are plotted to the left and increasing values of aiding current are plotted to the right of this axis. In order that such curves may be compared fairly, they have been plotted on the basis of equal impedances for the two instruments, and each receiver has been referred to an impedance of 100 76 74 72 Sn_ 70 hi Q o ? a III ai Q. X NEW RECEIVER (Ul) N: N, •" , 'n V ^ X T'^ — >i — \ \ \ y .y \ \ / / PRESENT STANDARD^^ RECEIVER (HAl) ^-^. •>»^^^ f — OPPO SING Al[ )ING — ->- 1 60 0.20 0 16 0.12 0.08 0.04 0 0.04 0.08 0.12 0.16 0.20 0.24 0.28 SUPERIMPOSED DIRECT CURRENT IN AMPERES Fig 9— Available power response versus superimposed direct current characteristics measured from a source impedance of 128 ohms on a 6 cc. coupler at 1000 cps. Each re- ceiver has been referred to 100 ohms impedance by multiplying its current values by /■^lOOO. y 100 ohms. Thus, if both receivers were of 100 ohms impedance at a frequency of 1000 cycles per second the curves would be compared directly. If an instru- ment has an impedance differing from 100 ohms, its direct current values along the scale are multiplied by a suitable scale factor as follows: 1 r ^ . /^lOOO Current scale factor = /!/ -^ where Ziooo is the magnitude of the receiver impedance at 1000 cycles per second. 122 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 The superimposed direct-current characteristics are an indication of the stabihty of the receivers. SHght changes in the air-gap of a receiver may occur during its Hfe due to external mechanical stresses, extreme tempera- ture variations, or magnetic influences. The application of direct current to the receiver winding produces such changes in the air-gap artificially in a controllable and reproducible manner, and shows that within a certain range there is no serious effect on the response level to be expected from slight alterations in the air-gap. The curve also shows that there is an optimum magnetization for the instrument at which the response is a maximum, and the sharpness or bluntness of the response peak is a measure of the stability. 500 450 400 350 300 250 200 150 100 50 A / \ \ / V ^ -~^ / \ / 'phase angle \y \ / \ ^ ^ '' y^ IMPEDANCE — >/ 1 ^.y^ --^ /■ / / 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 FREQUENCY IN CYCLES PER SECOND Fig. 10 — Impedance of ring armature receiver, measured on a closed chamber of 6 cc volume. The comparison between the two receivers shows that the Ul receiver is less sensitive to changes in superimposed direct current than the HAl receiver. The impedance-frequency characteristic of a typical Ul ring armature receiver, measured on a closed chamber of 6 cc. volume, is shown in Fig. 10. The magnitude of the impedance rises with frequency because of the in- ductance of the instrument. The departures of the impedance curve from a smooth upward sweep with frequency represent the contributions of the mechanical and acoustical elements of the receiver to the electrical im- pedance, that is, the motional impedance. The phase angle of the ring armature receiver averages 40°, which is somewhat lower than that of bi- polar receivers such as the HAl because of the larger part played by eddy currents in the impedance of the former. THE RING ARMATURE TELEPHONE RECEIVER 12.^ Network Representation The representation of electro-acoustical transducers as electrical networks has long been a useful tool.^^- ^^ Extensive use of this analogy has been made in the development and design of the ring armature receiver. The saving of time and increase in accuracy and completeness of analysis possible with this technique is apparent when it is realized that a complete family of re- sponse-frequency characteristics, showing the effects of variation of one or more of the mechanical or acoustical constants of the instrument, can be obtained by electrical measurements of voltage on an electrical network for various settings of variable inductances, capacitances, or resistances which simulate the mechanical or acoustical constants of interest. The amount of work required to obtain the same information by building and testing me- chanical and acoustical models is such that in many cases it would be im- practical or impossible within a reasonable time interval. ■ Ze — L_ ht 1 ""^^ 1 ' ^i 1 Fig. 11 — Block diagram network representation for receivers. A complete generalized representation of the ring armature receiver is shown in Fig. 11 in block diagram form. Ze is the electrical impedance of the instrument with all motion of the armature blocked mechanically. Z^ in- cludes a mesh which simulates the effects of eddy currents in the metallic structure of the instrument, r is the force factor, defined as the force applied to the armature per unit of current flowing in the receiver winding. Zm is the mechanical impedance of the mechanical and acoustical portion of the receiver at the point of application of the force, F. The relationships in this diagram are and Z = Ze + The term ^ is the motional impedance of the instrument. Zm ""High Quality Recording and Reproducing of Music and Speech," J. P. Maxfield and H. C. Harrison, Bdl System Technical Journal, July 1926 t> • . o«^ 12-Theory of Magneto-Mechanical Systems as apphed to Telephone Receivers and Similar Structures," R. L. VVegel, Am. Inst, of Elec. Eng., October 1921. 124 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 In studying the performance of an instrument the three elements in the above block diagram, Ze , r, and Zm are considered separately, and a difTer- MEMBRANE-DIAPHRAGM GRID-MEMBRANE EAR COUPLING ^CAP GRID HOLES, CHAMBER, Sm -- CHAMBER, Sq CHAMBER, Sc /^ Rg^g X / membrane, ^ RmMm DIAPHRAGM, - SdMq Rd AIR GAP, RaMa COIL CHAMBER; — Sa back chamber,- Sb HOLE, RhMh" ACOUSTIC RESISTANCE - ELEMENT, Rx Mx HANDSET HOUSING CHAMBER Sx 2m So Rd Md -|( — v\A^ — nm^ .Ml •Rh M» Rg Mg Sm zi=Z^G :i:SA Ra Ma :4^Sb l-AAA^^Wy^ ^AAr^^W^ :Sc ^Sx Rx Mx Fig. 12. — Zm. Equivalent network of mechanical and acoustical elements of ring arma- ture receiver. ent type of analysis applied to each. These three elements and their analyses and uses will be discussed separately below : (a) Mechanical and Acoustical Elements The element of the block diagram represented by Zm is the portion of the network representation of most use in the development and design of re- peivers. Figure 12 shows an expansion of Zm into an equivalent electrical teE RING ARMATURE TELEPHONE RECEIVER 125 network which has been used extensively in the study of the ring armature receiver. The cross-sectional drawing of the receiver and associated handset handle and cap is labeled to indicate the various acoustical and mechanical elements which are represented by the electrical circuit in the lower portion of the figure. Thus Sd , Md and Rd represent the stiffness, mass, and me- chanical resistance of the diaphragm; Mh and Rh represent the mass and resistance of the hole in the diaphragm which provides the low-frequency cut-off in the receiver, etc. One item of interest in this circuit representation, which differs from that of previous receivers, is the division of the chamber in back of the diaphragm into two parts, Sb and Sa , connected by the air passageway RaMa of the magnetic air-gap between the armature and the pole-piece tip. Under certain conditions, particularly those representing the receiver with some of the acoustical controls removed, the acoustical con- stants of the air-gap have been found to be of sufficient magnitude to war- rant this division of the total back chamber into two connected parts. An approximation is involved in this representation of the back chamber in that the force applied to the coil chamber, Sa , by the motion of the armature is ignored, but this approximation is justifiable through a consideration of the relative magnitudes of the effective areas and volumes involved, and the representation has been found to be in good agreement with measurements on the actual physical structures. The constants of the equivalent circuit are determined by various physical measurements and computations. For example, the effective mass of the diaphragm, Md , is estimated from the weights and the integrated vibratory kinetic energy of its various parts. The diaphragm stiffness, Sd , is then computed from its resonant frequency. The diaphragm resistance, Rd , is determined from a circle diagram analysis. The various chamber stiffnesses are computed from their air volumes, knowing the integrated effective area of the diaphragm. The acoustical resistances and masses are obtained from a combination of theoretical computations and special tests on the network, using circuit conditions in which these constants play the predominant role. In setting up this equivalent circuit for analysis and study, mechanical resistances are replaced by electrical resistances; masses are replaced by inductances; and compliances, the reciprocal of the stiffnesses, are replaced by capacitances. Response-frequency characteristics may then be deter- mined by applying a constant voltage to the input terminals and noting the voltage across Sc , which is proportional to the pressure generated in the ear coupling chamber for constant force applied to the armature. The effects of changes in any of the elements can be determined by simply changing the electrical value of the equivalent network element and repeating the measurement. In this manner, optimum values or combinations of values jmay be determined to provide the desired response-frequency character- 126 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 istic, the effect of proposed design changes may be predicted, and other characteristics determined without building large numbers of physical models. (b) Damped Electrical Impedance The damped electrical impedance of the receiver, that is, the electrical impedance when the armature is blocked so that it cannot move, is repre- sented by Ze in the block diagram of Fig. 11. The damped impedance of the ring armature receiver plotted against frequency is shown in Fig. 13. The 240 2 O200 160 120 80 ^ REACTANCE ^ ,^--"'" r"' -.--'' RESISTANCE / -' ,'-' .•^' / C'-' ,'' 7 „ 40=^ 400 800 1200 1600 2000 2400 2800 3200 3600 4000 4400 FREQUENCY IN CYCLES PER SECOND Fig. 13 — Damped impedance of ring armature receiver without varistor. i-^M0^ r I \I\N — ^KJ^y^' R Fig. 14 — Ze. Network representation for the damped impedance. rise in resistance and the departure from linearity of the reactance are due to the effects of eddy currents in the metallic parts of the instrument. A circuit representation for Ze is shown in Fig. 14. This circuit is derived on the assumption of a single eddy current path coupled to the receiver winding. The electrical resistance and inductance of the winding are repre- sented by r and ^, and the eddy current circuit by R and L. Analysis of this circuit is useful in determining the extent to which eddy currents have a detrimental effect on the efficiency of the .receiver. In general, the effect of eddy currents is greater in the ring armature receiver than in the bipolar types, largely because of the toroidal form of the motor element. Slotting of the ring-shaped parts has been found to be ineffective in reducing the eddy THE RING ARMATURE TELEPHONE RECEIVER 127 currents. However, with the low effective mass and large effective area of the diaphragm, the constants of the acoustical elements shown in Fig. 12 can be adjusted to compensate almost completely for the effects of eddy currents, even up to quite high frequencies. (c) Force Factor The third element in the block diagram of Fig. 11 is r, the force factor, defined as the force on the armature per unit current flowing in the receiver <: 5 q: Q < a jo^xa IN PHASE COMPOhJENT 6 7 8 9 10 14 15 lexto® A 1 /3 ; / ^ r / V, 3. 60'^- ^^ ^^ ^ r/ ^ ~-~* / J V o30^ 232C \^9 30'^ y / — 01710'^ (a) XIO^ 400 800 1200 1600 2000 2400 2800 3200 3600 FREQUENCY IN CYCLES PER SECOND Fig. 15— Force factor plots of ring armature receiver, (a) Force factor circle, (b) Magnitude and angle of force factor. winding. This is a complex quantity whose angle between force and current is designated by the symbol /?. In magnetic receivers like the ring armature receiver, the force factor varies with frequency, both in magnitude and in phase. Fig. 15(a) shows a vector plot of this quantity, and indicates how the terminus of the vector follows an approximately circular path with change in frequency. Figure 15(b) is a chart showing the magnitude of r and the angle /3 as functions of frequency. 128 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 The force factor diminishes with increasing frequency, and is largely dependent upon the alternating component of flux in the field of the air-gap. The presence of eddy currents produces a component of flux there also, which is usually in opposition to that produced by the current in the coil winding. The net amount of flux is thus diminished with increasing fre- quency as the effect of eddy currents becomes greater. It has been shown^^ that, for a single eddy current path, the locus of the vector plot such as that of Fig. 15(a) would be a semicircle with its center on the horizontal axis. The fact that the center of the circular locus shown here is somewhat below the horizontal axis indicates a departure from the simple theory. It seems likely, however, that if two or more eddy current paths exist having sub- stantially different time constants, the departure shown here might be explained. The values of force factor are obtained from a circle diagram analysis with the diaphragm resonated at different frequencies in the middle and upper frequency range. For very low frequencies, the mechanical impedance of the receiver is determined by the stiffnesses of the system, provided the hole in the diaphragm is closed, and a simple expression for the force factor at low frequencies can be derived in terms of the pressure generated by the receiver in a closed coupler for a given current in the receiver. This expres- sion is TO = Y¥\ ' -^~~^ — ^ ' ^ dynes per abampere. where Tq is the low frequency force factor, po is the low frequency pressure generated in a closed coupler for current I in the winding, Sr is the total mechanical stiffness of the diaphragm and acoustic chambers back of the diaphragm referred to the effective diaphragm area A , and Sf is the mechani- cal stiffness of the closed coupling chamber in which po is measured. Since the force per unit current will depend on the number of turns in the coil, force factor is not independent of receiver impedance. Thus, when comparing the force factors of receivers, it is necessary to refer the measured values of force factor to a common value of impedance by introducing a factor based on the ratio of the square roots of the impedances of the re- ceivers being compared. Such comparisons between the ring armature re- ceiver and its bipolar predecessor show approximately equal values of force factor at low frequencies, with the ring armature receiver force factor falling off more rapidly at higher frequencies. Limits of Receiver Efficiency and Distribution of Losses AT Low Frequencies In the design of this receiver, an object has been to make the efficiency as high as practicable over the frequency range from 350 to 3500 cps. Since THE RING ARMATURE TELEPHONE RECEIVER 129 there are theoretical limits to the level of efficiency which cannot be sur- passed even in the ideal case where there are no losses, it becomes of interest to determine the magnitude of these upper limits. It is also of interest to determine the amount and origin of the various types of losses that occur, and to what extent they can be minimized. In the case of a telephone receiver, the character of the ear load is pre- dominantly a reactance, corresponding to the stiffness reactance of an ear cavity of about 6 cc. volume. The power transfer to such a load is not ordi- narily used to denote the efficiency, as may be done for a resistance termi- nated device such as a loudspeaker for example. Instead, the available power response is taken as a measure of relative efficiency of receivers, and it is defined as follows:* 1 'b\^ Response = 10 log 77 = 10 log ^^ (1) Where 10 log T) = available power response in db referred to (1 dyne/cm^)^ per watt. p = pressure developed in the ear cavity in dynes/cm^, E = voltage of source in volts. Ro = source resistance in ohms; chosen in this discussion to be equal to the receiver impedance at the midband frequency /« , 1000 cps. In this expression, the numerator 1^1^ is proportional to the acoustic power output, while the denominator E^I^Ro is the available power input. Low Frequency Loss Analysis It will now be shown that the available power response approaches a theoretical limit which is about 17 db higher than the response level of this receiver at low frequencies, and that this expression may be arranged to give five loss factors, each of which has an important physical significance. For this purpose we need to consider only the stiffness, force factor, and inductance of the receiver working into a closed chamber representing the ear load. It is well known that in this instance for frequencies below 500 cps, with the receiver working out of a source of constant voltage E, and resist- ance Ro , the equations of motion are: {Ro + R+joiL) I +jo)T .10-7 ^ = £ - r/ + (^r + Sf)x = 0 (2) where L = low frequency inductance of receiver winding in henries R = low frequency resistance of receiver winding in ohms r = transduction coefficient or force factor in dynes per ampere Sr = Stiffness of receiver diaphragm, including the rear chamber, negative field stiffness, etc. in dynes per cm. 130 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 Sf = Stiffness load of coupler and front volume in dynes per cm. / = current in amperes X = displacement of diaphragm in cms. The solution of these equations for the displacement is tE ^ " (i?o + i? + jo^L) {Sr + Sf) + icor' . 10"' ^^^ For an adiabatic change, the pressure p in the chambers in front of the diaphragm due to a small displacement x is where y = ratio of specific heats of air = 1 .405 Po = atmospheric pressure = 1.013 x 10^ dynes/cm- A = effective area of diaphragm in cm^ Vg == receiver front volume beneath the grid holes, in cm*"^ Ft, = coupler volume = 6 cm^ Combining equations (3) and (4) we have yPpA tE ^ Vg+Vc' (Ro + R){Sr + Sf) + Mr' 10"' + L{Sr + Sf)] (5) Substituting equation (5) in equation (1) and expressing 77 as a power ratio we obtain '^ " F, + Vc'""'' {Ro + R)\Sr + Sfy + <.VlO-' + LiSr + Sf)f' ^^^ Let K = ^^^^^_^ ^^^ or r' = KL{Sr + ^/)10^ Then _ 47P0 .10^ Vc . RoKLiSr + Sf) (Ro + R)'{Sr + Sf)' + c^-^lKLiSr + Sf) + L(Sr + Sf)Y and factoring ^ 47P0 .10' Vc Sf K '^ coVc ' Vg + Vc ' Sr + Sf ' 1 + K R^L{1 + K) (7) (i?o -I- Rf + cu2L^(l + K)' (8) THE RING ARMATURE TELEPHONE RECEIVER 131 At low frequencies, the reactance of the receiver as seen from the electrical side is X = o}L{].-\-K). Hence the last factor of the above equation becomes RqX (R -\- RY + X^ Takmg the case of a pure reactance receiver first, we may place R = 0, and if we further match Rq to X at the midband frequency /o , and then denote the value of X at/o as Xq , we have R,X XqX f/fo ~ v2 {Ro + RY + X' xi -^ X' 1 + {f/foY 95 o>-< Z^< 80 <^ I- Ziup oak 75 ct UJ o crz 70 (i< 65 COUPLING LOSS=7.0DB £1 RES. L0SS = 1.1DB (a) ^U ACTUAL RESPONSE CORRESPONDING LEVEL AND RANGE LIMITS ^CALCULATED RESPONSE (b) 400 600 1000 2000 FREQUENCY IN CYCLES PER SECOND 4000 6000 10,000 Fig. 16— (A) Low frequency loss distribution of ring armature receiver. (B) Theoretica limits of response level and frequency range, for receivers with uniform response down to zero frequency. The latter step assumes that the low frequency reactance X is a linear func- tion of frequency. For the pure reactance receiver, the response then becomes 2tPo.10^ Vc Sf K 10 log 77 = 10 log (-» "•" Fc7r/o( - , r Vc Sr-hSf 1+K (9) Thus it is seen that the expression for the efficiency may be factored into four terms, each of which has a significant physical interpretation. A plot of these factors versus frequency is shown in Fig. 16(a). Curve (1) represents the first term only, the others are assumed to be equal to unity. This may be called the ideal response, where no loss occurs and it has a level of 91.7 db vs. (1 dyne/cm2)2 per watt for a 6 cc. front volume and a matching frequency of 1000 cps. Curve (2) represents the product of the first two terms; added is the volume loss Vc/Vg -\- Vc , which is the effect of introducing additional front volume between the diaphragm and cap, thus increasing the total front chamber volume of the load. Curve (3) includes the effect of the third term of the equation, which may be called the stiffness 132 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 loss, because it adds a diaphragm stiffness Sr , in series with the load stiff- ness, Sf . Curve (4) includes the coupling factor, K/1 -{- K^ which depends on the force factor that can be developed in relation to the inductance and stiff- ness of the system. This factor contains the term K — r— — — -— - which is a sort of coefficient of coupling, analogous to the electrical coupling coeffi- cient of a transformer, except that it may exceed unity. The whole factor, however, K/l+K, can never exceed unity, and we may call it k^, defining k as the "coupling f actor.'' Thus each term of this equation may be associated with some physical part of the receiver, which contributes to the losses. A fifth term will now be developed, which may be called the resistance loss, due to the electrical resistance of the receiver. If the receiver has a RoX resistance R, the last term of equation (8) may be written as /„" ^24!' ya where R and X are taken as the measured low-frequency resistance and reactance of the receiver. In equation (9) however, the term "" /.//.no was factored out of this expression and included as part of the first term. To take account of this, the remaining term for the resistance loss becomes Resistance Loss — ~ {Ro + RY + X' JIU If this remaining factor is included, the expression for the response of the receiver with resistance becomes 10 log r? = 10 log 2tPc 10^ \ / Fe \ I ^s \ A-^A'i ^ ^_±fll^ (10) This is the equation of the curve (5) shown in Fig. 16a. This curve checks quite closely with the measured response of the actual receiver, shown by the dashed curve (5). The close coincidence of the solid and dashed curves constitutes a check on the accuracy of both the theoretical and measured response of the receiver. The slight divergence of these curves in the range from 300 to 500 cps is due to the effect of the mass of the diaphragm, which was neglected in the calculations. While the above analysis is limited to low frequencies, it gives one an indication of the magnitudes of the various types of losses. It shows that, of THE RING ARMATURE TELEPHONE RECEIVER 133 these, the stiffness loss and coupUng loss are the greatest. Considerable progress has been made in the design of this receiver in reducing the stiff- ness loss from 11.3 db for the HAl receiver to 6.9 db. This is due largely to the increased effective area and low acoustic impedance of the diaphragm. Receiver Efficiency Limits In the analysis above, it is shown that for an ideal receiver having no losses, operating into a 6 cc. chamber, and matched at 1000 cps, the re- sponse approaches an upper limit of 91.7 db vs. (1 dyne per cm^)^ per watt. In other words, this is the limit which the low-frequency response of an idealized receiver approaches when the diaphragm stiffness Sr , the front chamber Vg , and the coil resistance R all approach zero, and the coupling factor k approaches unity. However, in addition to the level limit there exists a frequency range limit which lowers the level of the former limit. The curve labelled ''Locus of Performance Limit" of Figure 16(b) determines both these boundaries. Thus, if any point is selected on this curve, a horizontal and a vertical line through it determine shnultaneously the maximum response level and the highest frequency range obtainable. The calculation of both SOURCE RESISTANCE Ro A 1 N (NETWORK) I 1 E - 1 Or) 1 V EAR CAVITY COMPLIANCE c Fig. 17— Network of an ideal receiver having a uniform response over a given band of frequency. limits may be based on H. W. Bode's resistance integral theorem.^^ In ac- cordance with this theorem, when an ideal coupling network N, shown in Fig. 17, is used to give the maximum performance between a resistance source Ro and a capacitative load C, we have the general formula r 2a do3 = 2CRo (11) where e - = (i)' Eo = the source voltage and E = the voltage developed across the load C. ""Network Analysis and Feedback AmpUfier Design/' H. W. Bode-D. Van Nostran^ Co.— p. 362, 134 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 If a flat transmission is required over a given band of frequencies we may replace the limits of integration by coi and C02 , these quantities representing the edges of the useful band, which yields 2CRo or £2 2r 1 (12) El/iRo C(C02 - COi) C(/2 - /l) Translating this expression into the equivalent acoustical system, where C represents the compliance of the human ear cavity, it may be shown* that, Vc by substituting C = ~^ , replacing the voltage E by the pressure p de- veloped in the cavity, and by using the factor of 10^ to convert from practical to c.g.s. power units the following equation results This is the expression for the available power response of an ideal receiver which is assumed to have a flat response over the band of frequencies ex- tending from /i to /2 . The plot of this equation expressed in decibels, and marked "Locus of Per- formance Limit" is shown in Fig. 16(b) taking Vo as 6 cc and /i as zero. From this curve, an ideal receiver having a bandwidth of 3500 cps would have a response level of 88.3 db. It is also evident that the low frequency analysis given in the preceding section corresponds to a receiver with a range of approximately 1600 cps, while for wider ranges the response level would be lower, corresponding to the three other bands shown in the figure. From the analysis given above, it is clear that the 88.3 db level limit super- sedes the 91.7 db value based on the low frequency losses alone, because the former value takes account of the frequency range over which a receiver is designed to operate. A complete loss theory would undoubtedly arrive at the lower limit. However, because of the reactive load, it has not been possible to derive a suitable formula which includes the dependence on frequency range, and at the same time shows the character of the losses. The utility of the low frequency analysis lies in the fact that it shows the relative impor- tance of the various losses, and where the most opportunity for improve- ments lies, and their likely magnitudes. It must be realized that although ring armature receivers may be built in the laboratory, which have smaller losses than the receiver discussed, the present design is a compromise chosen to be most suitable for use in the subscriber's telephone set. •Unpublished work by T. J. Pope, Bell Telephone Laboratories, Inc. THE RING ARMATURE TELEPHONE RECEIVER 135 Magnetic Circuit The essentials of the magnetic structure of the ring armature receiver, including an equivalent circuit, are shown in Figs. 18(a) and 18(b). As ex- plained earlier, the magnetic structure includes an L-sectioned ring pole- piece of 45% permalloy having an outwardly extending flange which carries a non-magnetic ring, the latter acting as a support for the permendur dia- phragm. The remalloy magnet, which is also an L-sectioned ring, is assem- bled over the pole-piece assembly so that its inwardly extending flange overhes the diaphragm. This overlying portion of the magnet plays an important part in that it enhances the force factor of the device by securing some of the advantages of a balanced armature type of receiver in a simpler •MAGNET (, 'DIAPHRAGM UPPER AIR GAP ^g2 LOWER AIR GAP ^g, NON-MAGNETIC ^COIL SUPPORT (a) (b) Fig. 18— Magnetic circuit analogy, (a) Physical arrangement of magnetic structure- (b) Equivalent magnetic circuit, type of structure. The auxiliary magnet principle shown here was first used on the simple bipolar receiver,^ and later was applied to the ring armature type structure.^ In both cases, gains in force factor of 3 to 6 dh were realized The equivalent magnetic circuit of Fig. 18(b) shows to a first approxima- tion the relations of the physical elements of Fig. 18(a), neglecting the leakage paths. As shown, the overlying portion of the magnet provides a shunt path so that a part of the d-c. flux flows around the armature and only through its inner marginal portion, while the lower portion of the magnet carries additional flux to the armature and through the main air gap. The magnetic circuit is a type of partially balanced circuit which, if fully bal- anced, will have no d-c. flux flowing through the armature provided the following relations are satisfied: 5- 9^2 + «,2 136 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 Where ^i = M.m.f. of lower cylindrical part of magnet fFi = M.m.f. of flanged portion of magnet G(mi = Reluctance of lower cylindrical part of magnet 9^2 = Reluctance of flanged portion of magnet 9igi — Reluctance of main air gap (a variable modulating reluctance) 9ig2 = Reluctance of auxiliary air gap 9ld = Diaphragm reluctance The above relationship can be derived by placing the flux through the diaphragm reluctance did equal to zero in the circuit shown. Under these conditions, the armature carries no d-c. flux over its middle portion and will be operating at maximum permeability to a-c. flux. Moreover, the d-c. air gap flux density in the lower air gap where most of the field of force resides can be made higher before saturation begins to degrade the permeability of the inner marginal portion of the armature, than if all of the armature had to carry d-c. flux. The above factors tend to increase the a-c. and d-c. flux, and, since the force factor is a function of the product of these two quanti- ties, a higher force factor will result from the addition of the overlying portion of the magnet. ^ In order to maintain the position of the freely supported diaphragm on its seat at the outer periphery, it has been found desirable to have only a partial balance of the circuit. This is accomplished by making the upper air gap approximately five times larger than the lower one. Thus the field in the upper air gap is weaker, so that a 25 to 50% unbalance in flux exists. Under these conditions, the flux component in the diaphragm due to the upper portion of the magnet only partially cancels that due to the lower portion. However, the resulting flux density in the diaphragm is such that the per- meability will be only slightly below the maximum permeability which obtains for the perfectly balanced condition. The reluctance of the upper mesh to a-c. flux is so high, that the a-c. flux flowing in this branch can be neglected, hence the lower mesh carries substantially all of the a-c. flux, as shown in the figures. Thus, a partial separation of the a-c. and d-c. flux paths is accomplished. The magnetic materials which comprise this structure include a remalloy magnet, a vanadium permendur diaphragm, and a 45% permalloy pole- piece. Some of the considerations which led to the choice of these materials are indicated below. The remalloy magnet can be formed from sheet material while at elevated temperatures, is machinable prior to the final heat treat- ment, and has good magnet properties. Although Alnico could be used as magnet material, it would not lend itself to forming, and the result would be a more expensive magnet. The vanadium permendur diaphragm has a higher permeability at the higher flux densities than other materials, and THE RING ARMATURE TELEPHONE RECEIVER 137 this results in a higher force factor. The high yield point and high modulus of elasticity of permendur give better elastic properties so that the diaphragm will restore over a wider range of deflections to which it may be subjected. The 45% permalloy pole-piece has a high resistivity, resists corrosion with- out the need of a finish to protect it, and is easily formed to the desired shape. Since it has a high permeability, and is not too sensitive to strains, it is well suited for pole-piece material. Application of Ring Armature Receiver to Other Sound Devices Several other applications of the ring armature transducer have been made on an experimental basis in addition to that of the handset receiver, K 70 W.E. CO. 711 -A !5 S UJ 1- m -. 60 ««^ \ \ -^ ^ LU -5 y :>* ^*^ r^ A ? a: LU UJ 0. 50 "^ g|45 to Q Ul — Q O 35 RING ARMATURE \ \ \ \ \ i V 1000 2000 4000 FREQUENCY IN CYCLES PER SECOND 6000 10,000 F.g. 19 — Available power response-frequency characteristic of an experimental wide- range ring armature receiver, compared to a W.E.Co. 711-A moving coil receiver, measured on a 6 cc. closed coupler. such as its use as a wide-range receiver, as a miniature horn-type loudspeaker, and as a microphone. By narrowing the ring armature and suitably proportioning the acoustic networks, the receiver may be made to operate over a much wider frequency range at some sacrifice of efficiency, and may thus be used for high quality monitoring and audiometric work. A response characteristic of such a unit is shown in Fig. 19. The response compares favorably with the Western Electric 711-A moving coil type receiver used for the same purpose. Being comparable in efficiency, it has also a similar frequency range of about 7000 cps. More important, however, are the greater ruggedness and sim- plicity of the ring armature type receiver. Moreover, the impedance may be made to suit the application over a considerable range of impedance values, whereas the moving coil type is limited to a coil of about 25 ohms. While somewhat less pure in tone than the moving coil type the harmonics are 50 db below the fundamental at a sound pressure of 20 dynes per cm^ in the 138 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 coupler, and therefore are not noticeable under ordinary listening conditions. The attainment of wide frequency range in magnetic type units is unique, and is due in part to the use of a peripherally driven diaphragm. Centrally driven diaphragms used in magnetic type receivers usually have parasitic modes of vibration at these frequencies, which places a limit on the frequency range for which they can be designed. As a loudspeaker, the ring armature structure has been found to have some experimental application when used with a horn, both for speech and as a sound source for measuring purposes. Response characteristics of such 15" ■1 ? 640 AA MICROPHONE UJ (^ ?w UJ 5 Q o ? cr Ui UJ Q. z i^ 25 20 15 10 5 0 -5 > '-I0 ) > »-15 -20 \ /^\^ ywiTH HORN \ \ / \ / ^ \ \ / / — \ \ \ / / / \ \ v., / / y^ WITHOUT HORN \ \ / \ s "^ \ 500 1000 2000 4000 6000 10,000 FREQUENCY IN CYCLES PER SECOND Fig. 20 — Available power response-frequency characteristic of a ring armature receiver, measured as a loudspeaker with and without a horn. a unit are shown in Fig. 20 for the instrument with and without a horn. In the case of the unit without a horn the unit had a receiver cap as used in the handset receiver, and the acoustic circuits were similar to those of the normal receiver. For the case of the horn attached to the unit a spherical plug was used to couple the horn closely with the diaphragm, and no acoustic damping circuits beneath the diaphragm were necessary. The horn pictured in the sketch was spaced 15 inches away from the measuring microphone, and the same distance was used for the curve without a horn. It is apparent that, with the horn, 15 db is added to the sound level on the axis, and the fre- quency is widened by a factor of 2 or more. The efficiency shown in Fig. 20 THE RING ARMATURE TELEPHONE RECEIVER 139 compares favorably with similar devices of the moving coil type. The maxi- mum acoustic output, however, is lower, because the amplitude of the diaphragm is limited by the air-gap. As a microphone, the ring armature structure may be modified to have characteristics which are quite favorable for certain types of applications. Figure 21 shows the field response of a ring armature unit modified for use as a microphone and measured on an open circuit voltage basis. A special housing of 30 cc. rear volume was used in this case, with a | inch diameter orifice in the rear of the housing to act as a resonant circuit to produce the low frequency resonance shown with a desirable cut-off at 250 cps. By lowering the acoustic damping resistance of the unit, a second resonance was produced in the middle of the frequency range as shown. The peak at the upper end of the range is the normal characteristic of the instrument, but it may be enhanced somewhat by the use of a cavity in front of the diaphragm. 2 en u CD Z -55 -60 QCC -65 Z Q. o > ^2 ■75 -80 IMPEDANCE AT 1000 CPS = 300 OHMS ^ ^ — ^ y^ ^^ — N, pv y S k \ s ,. v 500 1000 2000 4000 FREQUENCY IN CYCLES PER SECOND 6000 10,000 Fig. 21 — Free field response-frequency characteristic of an experimental ring armature microphone, at normal sound incidence. The output level of this microphone is about 9 dh above the Western Electric 633A moving coil type at the same impedance level, but over a more limited frequency range. Conclusions It has been shown in the preceding sections that, by the use of the ring armature structure, it has been possible to realize a substantially higher grade of performance with regard to efficiency, frequency range, and leakage noise level, as compared to other types of telephone receivers in current use. To summarize, the ring armature receiver has been found to have the fol- lowing advantages from a performance standpoint: 1 . A gain in conversion efficiency of the order of 5 db as compared to the HAl receiver and a corresponding increase in output capacity. 2. A wider frequency range, with an upper frequency of 3500 cps as compared to 3000 cps for the HAl receiver. 140 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 3. A flexibility in frequency range, permitting the extension of the fre- quency range to approximately 7000 cps. 4. A broader superimposed direct current characteristic resulting in greater stability from a mechanical as well as an electrical standpoint. 5. A lower acoustic impedance, resulting in an improvement of the signal to ambient leakage noise ratio. 6. A substantial increase in the transmitted bandwidth when the receiver is held at small distances away from the ear. Other advantages from a mechanical standpoint are: 1. A simple mechanical structure of ring-shaped or circular parts. 2. A low mechanical impedance, permitting the use of large air cavities and elements of low acoustic impedance for response control. 3. A concave, spherical dome-shaped diaphragm withstanding high tran- sient pressures. This work was carried on under the supervision of Messrs. W. C. Jones, F. F. Romanow, and W. L. Tuffnell, from whom many valuable suggestions were received. We also wish to acknowledge the valuable assistance of Messrs. P. Kuhn, L. A. Morrison, R. E. Polk, W. C. Buckland, R. R. Kreisel and R. E. Wirsching during the development of this receiver. Internal Temperatures of Relay Windings By R. L. PEEK, JR. {Manuscript Received Aug. i8, igso) The steady state temperature distribution of a relay winding depends upon the power supplied and upon the rates of heat removal at the inner and outer surfaces. This is analyzed in terms of a more general form of the temperature distribution relation discussed by Emmerich {Journal of Applied Fhysics)K This analysis is used to determine empirical constants for the rates of heat removal at the surfaces. Illustrative data are given for a stepping magnet. Introduction EMMERICH^ has developed an expression for the steady state tem- perature distribution in a magnet coil when the heat flow is wholly radial, and the temperatures of the inner and outer surfaces are the same. A more general problem arises in the case of relays and other electromagnets used in telephone switching apparatus. In these cases, the coil is mounted on an iron core. Heat is withdrawn from the coil partly by conduction through this metal path, and partly by radiation from the outer surface. In consequence of this, the temperatures of the inner and outer surfaces are in general different. In the relay and switching magnet problem, primary interest attaches to the rate at which heat is withdrawn through these two paths, as their combined effect determines the maximum temperature attained within the coil. The analysis outlined below has been employed to determine the division of heat between these two paths, and for the evaluation of em- pirical constants of heat removal. These constants are used in estimating the relation between the temperature of the winding and the power sup- plied to it. Theory As in Reference (1), it is assumed that there is no heat loss through the ends of the coil, so that the temperature gradient is wholly radial, and that the actually heterogeneous coil structure can be treated as homogeneous. Then if Q is the heat supplied per unit volume per unit time, and K is the thermal conductivity, the radial distribution of temperature is the solu- tion to Poisson's equation: dr' ^ r dr ^ K 1 C. L. Emmerich, Steady-State Internal Temperature Rise in Magnet Coil Wind- ings, Journal of Applied Physics, 21, 75, 1950. 141 142 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 where r is the co-ordinate of a surface of temperature T. The general solu- tion to equation (1) is given by the equation: T = A^B\ogr-^, (2) where A and B are constants determined by the boundary conditions. The temperature has a maximum value T ' at some radius r', at which the temperature gradient dT/dr = 0. Substituting the expression for T given by equation (2) in this condition, it is found that: r-=^. (3) If the expression for B given by equation (3) is substituted in equation (2), and if A is taken as given by the resulting expression for T^ when r = r' , equation (2) may be written in the form: . = r' + ^i^(i + 2iog-^-(,:J). (4) This equation gives the general expression for the temperature distribution in terms of the radius r' at which the temperature has its maximum value T' . In the special case in which the temperature Ti at the inner radius ri is the same as that at the outer radius ^2 , substitution in equation (4) of r = ri and r = r2 gives two expressions for Ti . From these there can be obtained the same expression for the radius / of maximum temperature as is given in Reference (1) for this special case. In the notation used here this expression is: 2 2 r" = 'A:^^. (5) Substitution of this expression for / in equation (4) gives an expression for T — Ti which is identical with that given by equation (18) of Reference (1). Using the expression for T given by equation (4), integration of Zir rTdr over the interval ri to ^2 , and division of this integral by it {r\ — rj), the coil volume per unit length, gives the following expresson for the mean coil temperature T : ^,.A|iogp^-nogp ^.^A Experimental By means of equation (4), coil temperature measurements may be ana- lyzed to determine the thermal conductivity and the rates of heat removal INTERNAL TEMPERATURES OF RELAY WINDINGS 143 from the inner and outer surfaces of the coil. If the heat flow is wholly- radial, all the heat supplied must pass through one or the other of these surfaces. The division of the heat between the two paths is determined by the radius r' of maximum temperature. The rate of heat flow to the core is therefore the rate of heat supply per unit volume Q, multiplied by the volume of the coil inside the radius r\ or tt {r'^ — r\) per unit length of coil. Similarly, the rate of heat flow through the outer surface per unit length of coilisg.TT {r\ - /2). It is therefore formally possible to determine the heat division by measur- ing the temperature distribution, and reading the radius of maximum tem- perature directly from it. When this is done it is found that the tempera- ture gradient is comparatively flat in the vicinity of the maximum, and that it is therefore difficult to measure r' directly. An indirect determination of the radius / may be made, however, by determining the maximum temperature T' and the temperatures Ti and T2 at radii ri and r^ respectively. Expressions for Ti and Ti are obtained from equation (4) by letting r = ri in the one case and ^2 in the other. Then from these two expressions: --^' i + 2iogp-(p;- Knowing Ji, Ti, T\ and the radii ri and ^2, r' may be evaluated by nu- merical or graphical solution of equation (7). This solution is facilitated by the use of a table or plot of the function F (X) = 1 + log X^ - X^. The numerator of the right hand side of equation (7) is Y {ri/r'), and the de- nominator is Y ir^lr'). A convenient procedure for determining the temperature distribution within a coil is to measure the resistance changes in different layers, tapping the coil between these layers. If there is more than one layer between taps, the resistance change measures the mean temperature of the layers included. For an accurate determination of the gradient, it is convenient to make the resistance measurements on a comparative basis, as by use of the bridge circuit shown in Fig. 1. Here the terminals marked 0 and 6 are the inner and outer ends of the winding, while terminals 1 to 5 denote taps at intermediate layers. With the key i^ in Position 2, the bridge circuit may be balanced to establish the resistance between terminals 0 and 3, for example, relative to that between terminals 3 and 6. The resistance of the whole winding may be determined with sufficient accuracy (about one per cent) by voltmeter-ammeter readings made with K in Position 1. With this known, the resistance of the layers between taps, and hence the tem- perature differences, can be computed from the bridge readings. 144 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 The temperature corresponding to the resistance between taps may be taken as the temperature at the mean radius of the layers included. The ih e K o—-<>^ooo^<>^i)0(y\<>Jiy^ — o K 2' ■Wv WV IH Fig. 1 — Circuit for measuring temperature differences in tapped coils. 140 uj 120 o < g 110 z UJ 100 90 70 60 50 40 1 1 . -=f "^"'sigS WATTS k- _l 1 1 ^^^ PER COIL 1 1 1 I / / ff MEAN TEMPERATURE 1 1 1 1 1 1 1- '~J^^ 6.04 ^- J "O^ '" .^ I 1 1 31 ^^^ 1(0 SI lUl l< |Cr: |DC lUJ 1 3.00 3^ 1 1 1 ^^>^— 1 1 1 1 1.07 1 1 1 .^^<>— 0.5 0.6 0.7 0.8 0.9 1.0 1.1 RADIUS IN CENTIMETERS Fig. 2— Temperature distribution in coil of 197 switch magnet. results of such measurements may be plotted as shown in Fig. 2. The results given in this figure were obtained with a sample of the Vertical Magnet of the Western Electric Company's 197 (Step-by-Step) switch. INTERNAL TEMPERATURES OF RELAY WINDINGS 145 The plotted points show the mean temperature of the layers between taps plotted against their mean radius; the dashed boundary lines show the inner and outer radii of the coil. The different curves correspond to the different levels of steady state power input indicated. It is apparent in Fig. 2 that the central part of each curve is comparatively flat, and that it would therefore be difficult to determine the radius of maximum temperature directly. It may be noted in passing that the maxi- mum temperature is not greatly in excess of the mean temperature. This justifies the usual engineering practice of taking the mean temperature as a criterion of whether the coil is overheated or not. Table I Heat Distribution in 197 Switch Coils Total Heat Input (Watts) Q (watts per Cm.^) . . . Max. Temperature T' (°C) Temperature Ti (°C) . . Temperature T^ (°C) . . K (Calories/°C/sec./ cm.) r' (Cm.) Heat to Core (Watts) . Heat to Cover (Watts) (Per Cent.) Inner Surface Temper- ature (°C) Outer Surface Temper- ature(°C) 3.00 0.268 0.69 X 10-3 0.93 1.39 6.04 0.540 105 95 102 0.79 X 10-3 0.95 2.99 3.05 51 91 99 8.98 0.802 139 124 132 0.82 X 10-3 0.94 4.37 4.61 51 119 130 From each curve in Fig. 2 there was read the maximum temperature T and the temperatures Ti and Ta at n = 0.622 cm. and ri = 1.156 cm. re- spectively, corresponding to the inner and outer points plotted. These temperatures are listed in Table I together with the corresponding values of Q, the power input divided by the volume of the coil (11.2 cm^). From these data, the radius r' of maximum temperature has been computed by the Q A procedure described above. With r' known, the quantity - was computed from equation (4) for the case r = n , T = Ti. The resulting values of / and K are included in Table I. Using the value of r' thus determined, the division of the heat between that going to the core and that going to the cover was computed with the results shown in the table. The values of n and ^2 used in the above computation are, as indicated in Fig. 1, internal to the coil. Taking new values of n and rz corresponding to the core and cover radii respectively, the temperatures at these surfaces were computed 146 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 from equation (4), using the values already found for r' , T and — . These A core and cover temperatures are included in Table I. It is of some interest to examine the observed values of apparent con- ductivity K. As the temperature differences for the two lower input meas- urements are small, the results for the other two cases are more accurate. The latter give a value for K of approximately 0.8 X 10~^ calories per °C per sec. per cm. In this form wound coil using No. 29 wire, the volume occupied by the insulation is approximately 36 per cent. As the conductivity of the copper is very large compared with that of the insulation, the con- ductivity of the latter may be estimated as of the order of K multiplied by the fraction of the volume occupied by the insulation. This gives an indicated conductivity for the insulation of the order of 3 X 10~^ calories per °C per sec. per cm. which is about the same as that of dry paper. 0.4 CORE SURFACE 0.0045 WATTS/CMyOEGREE C ^ ^ ¥^ >- y^ ^ ^ .^ ^ Y' ^ ^ ^TICOVER SURFACE 0.0020 watts/cmVdegree C , 1 1 1, 1 1 1 30 40 50 60 70 80 90 100 110 120 130 140 temperature in degrees centigrade Fig. 3 — Rates of heat removal from coil of 197 switch magnet. For engineering purposes the results of major interest are those for the quantities of heat leaving the core and the cover. The results in Table I show that the heat flow is about equally divided between these two paths. As the core radius is about half the cover radius, the rate of heat flow to the core per unit area of surface is about twice that leaving unit area of the cover surface. The rates of heat removal per unit area through the inner and cover surfaces are shown plotted against the corresponding temperatures in Fig. 3. It will be seen that the relation between the rate of heat removal per unit area and temperature is approximately linear, and intersects the tempera- ture axis at 38°C (100°F), which was the ambient temperature in these tests. It follows that for engineering purposes the rate of heat removal per unit area through either the inner or cover surface may be taken as proportional to the difference between the surface and ambient temperatures. A similar linear approximation has been found to apply for other relay and switch coils when mounted under conditions representative of telephone apparatus. Because of the multiplicity of mounting conditions and the complexity of INTERNAL TEMPERATURES OF RELAY WINDINGS 147 conducting and radiating paths by which heat is removed, it is difficult to estabUsh a relationship of the type shown in Fig. 3 by analysis of the paths of heat removal. For given mounting conditions, however, this relationship can be determined empirically by the procedure outlined above and used to estimate the heat removal from a given coil mounted under conditions for which such measurements have been made. The rate of heat removal is thus measured by the slopes of the heat flow vs. temperature curves, which may be designated ki and ^2. Thus ki is the time rate of heat flow to the core per square centimeter of surface per °C difference between the inner coil surface and the ambient temperatures, while ^2 is the corresponding coefficient for the cover surface. For the case shown in Fig. 3, ki = 0.0045 watts per cm^ per °C, and ^2 = 0.0020 watts per cm^ per °C. This observed value of ^2 is characteristic of the cover sur- faces of coils mounted as in telephone apparatus, where the heat removal is primarily by radiation to surfaces at or near the ambient temperature. While the value of h observed for this case is representative of that applying to inner coil surfaces, the values of h for such surfaces vary widely, and are particularly sensitive to variations in the clearance between the metallic core and the interior surface of the coil. Prediction of Coil Temperatures If values for the heat removal coefficients are known, the distribution of temperature within the coil for a given steady state power input may be determined from equation (4). The power input and the coil volume deter- mine the rate of heat supply per unit volume Q. The rate of heat flow to the core per unit length of coil is therefore tt (/^ - rl) Q. The core area per unit length through which this heat passes is 2 irri. So from the empirical linear relation between the heat removed and the surface and ambient tempera- tures : r, - To = '^^^j^, (8a) where To is the known ambient temperature. Similarly, for the cover surface : Zk2r2 By substituting these expressions for Ti and T2 for T in equation (4), with r taken as n in one case and r2 in the other, there is obtained an ex- pression for / which reduces to the following equation: 2 2 ri rp , ^2 - ri n _ ki h 2K (Q) ^ J^ I 1 . 1 1 !?' 148 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 If r' is thus determined, and K is known from measurements of similar coils, V can be determined by means of equation (4) from the values of T\ or Ti given by equations (8). If desired, the mean temperature T can then be determined by equation (6). Conclusions In most relay and switch magnet coils, of the type used in telephone apparatus, the heat flow under steady state conditions can be considered as wholly radial, and the temperature distribution conforms approximately to equation (4) above. In this expression, T' is the maximum temperature, and r' the radius at which this occurs, so that heat generated inside the surface of radius r' passes to the core, and that generated outside this radius passes to the cover. The rate of heat removal per unit area at either of these surfaces is found experimentally to be approximately proportional to the difference between the surface and ambient temperatures (for the temperature range of normal operation). The proportionality constant is the heat removal coefficient (^i or ^2 of equations (8)). Under conditions typical of telephone apparatus, this coefficient is of the order of 0.002 watts per cm^ per °C for a cover surface, and 0.005 watts per cm^ per °C for an inside surface in close proximity to the metal core. The heat removal coefficient for an inner surface is much more variable than that for a cover surface. The coil temperature distribution [equation (4)] depends upon the rate of heat supply per unit volume Q, and upon the effective heat conductivity K. Q may be taken as equal to the total steady state power input divided by the coil volume. Correction might be made for the radial variation in Q resulting from the variation in copper resistivity with temperature. The relatively small temperature range observed in practice, as illustrated by the results of Fig. 2, makes this an unnecessary refinement. The heat con- ductivity constant K is an effective average value, applying to the coil as though it were a homogeneous structure. It is conveniently evaluated by measurements of actual coils, and is approximately a constant for a given wire size and type of insulation. By measurement of the resistance changes in tapped coils, the internal temperature distribution can be determined. From this, values of the effective heat conductivity K and of the heat removal coefficients k\ and ki can be determined by the use of equation (4), as described above. Con- versely, if K and the heat removal coefficients are known, equation (4) may be used to estimate the internal temperature distribution, and thus the mean and maximum coil temperatures. 1.03 !N. (O.D.) 0.06 LB Headpiece. — A panorama of loading coils 1904-1948. The Evolution of Inductive Loading for Bell System Telephone Facilities By THOMAS SHAW Introduction THIS is the story of the contributions of inductive loading in the growth of the Bell Telephone System to its present great stature. In particu- lar, it tells how these contributions have been made. We see in it the great economic value of organized research, of research scientists and design and development engineers, of manufacturing skill and care, and of the applica- tion of sound engineering principles to the design of the telephone plant. The story told here is almost entirely concerned with series inductance coil loading, since other types of loading have had very little use in the Bell System. To make the story more complete, however, a brief account is included of Bell System developments and applications of continuous load- ing. The main story starts soon after the turn of the century, following the development of the first standard loading coils and loading systems, and carries through to the end of 1949. In the beginning of this period emphasis was placed on urgently needed increases in the range of telephone trans- mission over open-wire lines and cables, and in the use of cheaper cables. In this connection it should be remembered that a really satisfactory type 149 150 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 of telephone repeater did not become available for general use until 1915, about 15 years after the invention of loading. The commercial limit in the economical use of loading to extend the transmission range of open-wire lines was reached in 1911, several years before the vacuum-tube repeater became available. Then, repeaters and loading had to be used as teammates to conquer the transcontinental distances. Subsequent improvements in repeaters, auxiliary equipment and circuits eventually made it advantageous to discontinue open-wire loading, and simultaneously opened an important new field for impedance-matching loading on the entrance and intermediate cables that unavoidably occur in open-wire lines. When different types of carrier systems became available for open-wire facilities, several new types of impedance-matching loading suitable for these carrier systems were developed. The early efforts to extend the transmission range of long-distance cables in competition with open-wire lines, so as to obtain increased stability of service and lower facility costs, reached a climax during the period 1911- 1915 in the use of composite, quadded, 10 ga. and 13 ga. cables, and of load- ing coils nearly as large as the open-wire loading coils. This trend slowed down shortly after vacuum-tube repeaters became commercially available. During the next fifteen years or so, intensive development work on improved repeaters, on equalizing and regulating networks, and on higher velocity, higher cut-off loading, made it feasible to use 19-gauge conductors and loading coils no larger than the initial standard cable coils for distances ranging up to about 1500 miles. In the exchange area cable plant, coil loading has made it possible at a low cost to meet the needs imposed by geographical factors, with as yet very little competition by telephone repeaters. Large reductions in the costs of the trunk plant have resulted from the extensive utilization of 22- and 24-gauge cables, made feasible by the use of inexpensive loading. The substantially continuous transmission developments in exchange area serv- ices also made possible important improvements in the intelligibility of transmission by using higher cut-off loading to transmit wider speech- frequency bands. The important loading apparatus developments in the period covered by the review have taken full advantage of the development at fairly even- spaced intervals of a series of successively better magnetic core-materials to improve the transmission service performance or reduce loading costs, sometimes combining these features. The loading coil cost-reductions which resulted from the large size-reductions made possible by the standardization of compressed permalloy-powder core loading coils during the late 1920's were especially important in influencing the growth of the long distance and INDUCTTIVE LOADING FOR TELEPHONE FACILITIES 151 exchaYige area cable plant, and in leading to important service improve- ments. As described, step by step, in the present story, coil loading has been a very important factor in making possible the provision of satisfactory telephone service at reasonable rates which have encouraged a continually increasing use. Important elements in the public satisfaction to which loading has made fundamental contributions are: (1) high-quality trans- mission, and (2) high-speed service facilitated by the provision of relatively large groups of relatively low-cost facilities. In the extensive utilization of the long-distance service over repeatered, loaded, voice-frequency toll cable facilities, loading must of course share the credit for the improved trans- mission, plant cost-reduction, and speed of service with the telephone repeaters and associated equalizing and regulating networks, where in- volved. All of the coil loading development work for Bell System needs, including the specific developments described in the present review, has been done by Bell System people without outside aid. Coil loading was independently invented by Dr. G. A. CampbelP of the headquarters staff of the American Bell Telephone Company, and by Professor M. I. Pupin^ of Columbia University, at nearly the same time, in 1899. The patent interference pro- ceedings made necessary by the conflicting claims of the Pupin and Camp- bell applications resulted in a priority award to Pupin during April 1904, on the basis of a few days' earlier disclosure. The prompt purchase of Pupin's rights in the invention before the interference action had gone far assured the Telephone Company complete freedom to develop the new loading art in the most advantageous ways. The improvements worked out and applied over the years are principally due to groups of scientists and engineers working as teams on various phases of the transmission research, development, and engmeering problems; on the magnetic materials research and development problems; on the ap- paratus-design and manufacturing problems; and on the field-construction and traffic problems. Nearly all aspects of telephone systems' development have been involved to a greater or less extent. In the aggregate, a large number of individuals have made important contributions to the advancement of the loading art. The writer of this review is to be regarded as a spokesman for his co-workers. Since the assign- ment of a fair measure of personal credit to each individual who has been involved would be extremely difficult, it is not attempted in the present review. 152 THE BELL SYSTEM TECHNICAL JOURNAL, JANU/VUY 1951 PART I: THE BEGINNINGS OF COIL LOADING • General Theory For present purposes, a rigorous presentation of the mathematical theory of coil loading is unnecessary/^^ A simple description and a brief statement of theory is sufficient. The primary purpose of coil loading is to improve the transmission of intelligence by substantially reducing the circuit attenuation, and by making the circuit attenuation approximately uniform throughout a predetermined frequency-band. These transmission benefits are obtained by serially in- serting coils having uniform inductance values at regularly recurring inter- vals along the circuit, but are limited to a frequency-band below the loading cut-off frequency. This is an inverse function of the square root of the product of the coil inductance and of the mutual capacitance of the loading sections between successive coils, as determined by the coil spacing and unit-length capacitance of the circuit. Above the loading cut-off frequency, there is a substantial suppression of transmission. For more than a decade prior to Campbell's and Pupin's 1899 researches, the theoretical possibility of improving transmission over telephone lines by artificially increasing their inductance had become known from the mathematical studies of Vaschy and Heaviside. Also there had been con- siderable speculation by them"*- ^, and by others, regarding the practicability of approximating the advantages of uniformly distributed inductance by inserting low-resistance inductance coils along the line. Rules for spacing the lumped inductances had not been worked out, however, nor had suitable coils been developed. The requisite coil-spacing turned out to be such that there are several coils per wave length at the highest frequency which should be efficiently transmitted to obtain satisfactory intelligibility. Here, "several" means more than two, since at the theoretical cut-off frequency there are two coils per wave length. In terms of the nominal velocity of propagation of the "corresponding smooth line" (a hypothetical line having the same total inductance and capacitance) there are tt coils per wave length at the cut-off frequency; expressed in "loads-per-second," this nominal velocity is exactly w times the cut-off frequency in cycles per second. The attenuation improvement obtainable with loading corresponds some- what to the increase in impedance that results from the increase in induct- ^> Readers interested in the rigorous mathematical theory are referred to Bibliography items (1) and (2), Campbell's treatment has been extensively used by communication engineers l)ecause of its comprehensive coverage of the frequency band concept in which the cut-ofT effects on propagation and impedance are emphasized. Also, his disclosures include explicitly the effects of conductor resistance and ratio of coil resistance to con- ductor resistance. His general formulas include the distributed inductance and leakage. INDUCTIVE LOADING FOR TELEPHONE FACILITIES 153 ance. This can be understood from the fact that in the (low-impedance) non-loaded circuit, the series dissipation losses which are proportional to the square of the line current are ordinarily very large relative to the di- electric dissipation (i.e. shunt) losses which are proportional to the square of the line potential. When the line impedance is increased a suitable amount by the loading, the decrease in series losses is much greater than the increase in shunt losses. In commercial practice, economic considerations generally prevent the use of high loading impedances which would result in the shunt losses becoming as great or greater than the series losses. In situations where voice frequency attenuation improvement is the principal objective, the unit transmission loss can usually be reduced to the order of one-third to one-fourth of the non-loaded value. The loss reduction is less than this at low voice frequencies and more at high frequencies, resulting in a much more uniform transmission of the important frequencies that are required for intelligibility and naturalness. In certain situations which will be discussed later a lower ratio of attenuation reduction is ac- cepted in order to obtain other, more important, transmission advantages. Pioneering ^ Developments General A full account of the pioneering research and development work would take much more space than is available in a review devoted primarily to the evolution of the loading art. The present account is therefore limited to a brief description of the first loading systems and apparatus standards that resulted from the pioneering work.^^^ Although the success of the 1899 laboratory investigations, and the Bell System's 1900 experimental installations on exchange cables and on open- wire lines, quickly built up a substantial demand for loading, the com- mercial applications had to be deferred pending the development of satisfactory types of loading coils. Then there followed a series of what should be considered as trial installations of different types of loading, tailored to the specific needs of particular projects. Analyses of the per- formance characteristics of these installations, supplemented by continuing experimental work ui the laboratory and by engineering cost-studies, re- sulted in the establishment of a series of standard cable loading systems for general use late in 1904. The commercial development of satisfactory open- wire loading encountered many even more complicated problems than those involved in cable loading, and in consequence the standard loading for 104-mil lines did not evolve until 1905. This same type of loading be- (b) A more complete description of these standards is given in Bibliography Reference (6). Reference (7) is also of interest. Reference (1) gives some details of Campbell s early work. 154 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 came standard for 165-mil lines in 1910, after a long period of additional development work to get better line-insulation. All of this early loading development work was for non-quadded cables and for non-phantomed open-wire lines. Loading Coils The earliest speculative suggestions regarding coil loading recognized the critical need for obtaining a low ratio of coil resistance to circuit re- sistance, and by implication a low ratio of coil resistance to coil inductance. As was expected, this turned out to be a difficult design and manufacturing problem, especially with open-wire loading which was given development priority. By April 1901, a very satisfactory coil-design had been worked out for open-wire loading by Mr. H. S. Warren, an associate of Dr. G. A. Campbell. It had a toroidal core, formed by winding a bundle of insulated mild-steel wires, 4 mils in diameter, on a suitably shaped spool, several miles of wire being used in each core. The manufacturing process of the outside supplier Fig. 1 — Non-phantom type loading coils. Coil winding schematic and method of con- nection into circuit. included cold drawing to obtain a magnetically hard wire having an initial permeability of about 65. The two line-windings, each confined to separate halves of the core winding-space, made use of insulated, stranded wire. The fine subdivision of the magnetic material and of the copper conductor was essential to the satisfactory control of eddy current losses. This coil. Code No. 501, was the first standard loading coil. It remained standard for about a decade, until a redesign became necessary to facilitate an extensive commercial exploitation of phantom working. Because of the very low-resistance design objective, it had to be a large coil. Some of its dimensional and electrical characteristics are included in Table I. In size, it was approximately 25% larger than the largest coil shown in the head- piece. The cable loading coils listed in the table were standardized for general use during 1904, following occasional use of other types of coils having different inductances and in some instances using a different core material. These coils were generally similar in their basic design features to the open- wire loading coil, but for economic reasons were much smaller in size.^*'^ ^•^ Core weight 3.5 lbs., 69000 turns iron wire; length 11 miles. INDUCTIVE LOADING FOR TELEPHONE FACILITIES 155 Also, their ratios of resistance to inductance were considerably higher. In size, these coils are typified by Coil B in the headpiece. The 4-mil (No. 38 A.W.G.) wire used in these cable coil cores had a nominal initial permeability of 95, nearly 50% higher than that of the open-wire loading coil core-material. The differences in magnetic perform- ance characteristics, including permeability, core losses, and certain other features subsequently discussed, resulted solely from differences in the annealing treatments during the wire-drawing process. Additional important differences between the cable coils and the open- wire coil were: (1) the use of non-stranded conductors in the windings of the cable coils, and (2) the use of lower dielectric-strength insulation in the cable coils. Table I Characteristics of First Standard Loading Coils Code No. Nominal Inductance (henry) Resistance (ohms) Use Over-all Dimensions (inches) d.c. 1000 cycles Diameter Axial Height 501 506 508 507 0.265 0.250 0.175 0.135 2.5 6.4 4.2 3.2 5.9 22.3 13.0 9.1 Open-Wire Lines Cables 9 4i 4i 4i 4 2i Loading Coil Cases The open-wire loading coils were individually potted in cast-iron rases designed for mounting on pole fixtures. The coil terminals issued from the case in individual rubber-insulated leads. The cable loading coils were assembled in multi-coil groups on wooden spindles, and potted in cast-iron cases, suitable for installation in cable manholes and on pole fixtures. Intercoil crosstalk was controlled: (1) by mounting adjacent coils so there would be approximately a minimum coupling between their (small) magnetic-leakage fields; (2) by using iron shielding-washers between adjacent coils; and (3) by placing the spindle groups of coils in individual compartments cast in the cases. The coil- terminal leads issued from the cases in a twisted-pair, lead-covered, stub cable. Prior to potting, the coils were thoroughly dried out under vacuum, and were impregnated with moisture-proofing compound. Loading Systems As previously mdicated, the standard practices for cable loading were established in advance of those for open-wire loading, notwithstanding an 156 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 earlier commercial beginning. ^^^ Three different cable loading standards were adopted, to provide for a range of attenuation-reduction performance. Some data regarding these systems are given in Table II. The transmission data apply to the early types of cable having an average mutual capacitance of about 0.070 mf/mi. The theoretical loading cut-off frequencies were approximately 2300 cycles (about 7000 loads per second). This initial standard was the result of extensive series of speech transmission tests to determine the minimum cut-off frequency that would be commercially satisfactory with respect to intelligibility. A materially higher cut-off would have increased the loading costs by requiring the loading coils to be more closely spaced. Table II First Standard Cable Loading Systems (Using Coils or Table I) Loading Designation Coil In- ductance (henry) Coil Spacing (miles) Nominal Impedance (ohms) Nominal Velocity (mi/sec.) Attenuation Loss (db/mile) 19 A.W.G. 16 A.W.G. 13 A.W.G. Heavy Medium 0.250 0.175 0.135 1.25 1.75 2.5 1800 1300 900 8750 12200 17500 0.28 0.39 0.51 0.16 0.21 0.27 0.11 0.14 Light . . . 0.17 Non-Loaded Cable 1.05 0.74 0.59 Note: The figures given in the columns headed "nominal impedance" and "nominal velocity" apply for the nominal impedances and the nominal velocities of the hypothetical "corresponding smooth Hnes," having the same total inductance and total capacitance. The first standard open-wire loading used No. 501 coils at about 8-mile spacing, giving an impedance of about 2100 ohms and a cut-off frequency close to the standard cut-off frequency for cable loading. Under dry-weather insulation conditions (5 megohm-miles or better) the attenuation losses in the 104-mil and 165-mil lines were about 0.031 and 0.014 db/mi, re- spectively. The corresponding losses without loading were 0.075 and 0.033 db/mi, respectively. The approximate 8-mile spacing fitted in with the open-wire transposition arrangements and gave a satisfactory attenuation- loss reduction. The earlier attempts to secure a much greater attenuation reduction had involved shorter spacings, ranging down to 2.5 miles, and were unsuccessful. At extended periods of low line-insulation caused by wet weather, these higher-impedance loading arrangements had poor trans- mission, sometimes worse than non-loaded lines. Excessive noise, crosstalk, and reflection losses also were unfavorable factors. (•*> N. Y.-Chicago, 165-mil open-wire line, November 1901 ; New York-Newark cable, August, 1902. inductive loading for telephone facilities 157 Preview of Subsequent Developments General Outline For convenience in discussion and ease of understanding it has been found desirable to divide the remaining subject matter of this review into several parts, each covering a particular phase of the evolution of the loading art, as follows: Part II — Loading for Long Distance Circuits. Ill — ^Loading for Exchange Area Cables. IV — Cable Loading Coil Cases. V — ^Loading for Incidental Cables in Open- Wire Lines. VI — Continuous Loading. VII — Extent of Use and Economic Significance. VIII — Summary and Conclusion. Parts II, III, IV, V, and VII are wholly concerned with coil-loading. In Parts II, III and V, specific coil loading systems and loading apparatus developments are separately considered under headings which indicate the development emphasis. In general, the individual developments are discussed in chronological sequence so as to tie closely together the interrelated systems and apparatus developments. The chronological procedure also applies in Parts IV and VI. The dates which are given and the cross references from section to section permit the reader to fit the important developments into a definite time pattern. Although the review is primarily concerned with the evolution of loading, and its contributions to the growth of the Bell System, appropriate references are also included regarding other related advances in the telephone art which have influenced the design and performance of the loading systems and apparatus, and the extent of use. Loading Systems The changes in voice-frequency loading systems have been primarily for the purpose of improving the service performance, including the trans- mission of wider frequency-bands to improve intelligibility. The loading changes for repeatered circuits have catered to the various special problems that arose in consequence of the great increase in circuit lengths. The loading systems for cable circuits transmitting radio broadcasting programs and those for voice-frequency and carrier-frequency impedance- matching in incidental cables that occur in open-wire lines also had their own individual requirements to meet the specific service needs. Loading Coils The loading coil developments substantially paralleled the loading systems developments in variety and scope. In many instances, new loading coils 158 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 were developed to take advantage of the availability of (new) superior materials, improved design techniques, and fabrication methods, for cost reduction or service improvements. In other important instances, new types of loading coils were necessary to provide for new types of facilities; for example, (1) to permit the commercial exploitation of phantom working, (2) for a network of coarse-gauge, long-distance cables, (3) for facilities Table III Loading Coil Core-Materials Item No. Type of Material Vol- ume Perme- abiUty Approx. Period Commercial Mfg. Principal Fields of Use Bibliography References -Prior Publications (1) (2) (3) (4) (5) (6) (7) (8) 65-permeability, 4-mil, iron wire. 95-permeability, 4-mi!, iron wire. Annealed, compressed, powdered iron. Unannealed, com- pressed, powdered iron. Compressed, powdered permalloy. Compressed, powdered molybdenum - perm- alloy. Compressed, powdered molybdenum - perm- alloy. Non-magnetic. 36 52 55 35 75 125 60 1 /1901-1924 \191 1-1927 /1904-1911 \1904-1916 /1916-1927 \1916-1924 /1918-1928 \1924-1928 /1927-1937 \1927-1938 /1937- \1938- 1948- 1920- Open- Wire Lines\ Toll Cables / Early Toll Cables) Exchange Cables J Exchange Cablesl Toll Cables / Toll Cables \ Exchange Cables/ Exchange Cables\ Toll Cables / Exchange Cables\ Toll Cables j 15 kc Cable Program Transmission Carrier Loading Coils for Incidental Cables Open Wire Lines (6) & (8) (6) & (8) (6), (8) & (13) (6), (8) & (13) (24) (26) (26) (8) (a) Initial permeability. to transmit programs for radio broadcasting stations, and (4) for incidental cables in open-wire carrier systems. Certain economic concepts have dominated the design work on the indi- vidual loading coils. In the introductory section of the review, the general need for having the loading coil resistance low relative to that of the circuit resistance \yas mentioned. In applying this design rule, the principle of cost-equilibrium^*^ has been a basic criterion. It has resulted in the de- ^') This is a condition of cost-balance in which a small transmission improvement can be made by improving the coils at al)out the same cost as would be involved in improving the circuit in other ways — for example, by using a slightly larger size of conductor. INDUCTIVE LOADING FOR TELEPHONE FACILITIES 159 velopment of: (1) large-size, very low resistance coils for open-wire lines and for 10 ga. and 13 ga. long-distance toll cables, (2) smaller-size, higher- resistance coils for smaller-gauge toll cables, and (3) still smaller size of coils having still higher resistances for fine-wire exchange cables. Over the years, the progressive use of superior core-materials has made possible several successive, substantial size-reductions in the cable coils, with some- what larger-ratio size-reductions in exchange area loading coils than in the toll cable coils, because of their less complex service-requirements and also in conformity with cost-equilibrium criteria. These progressive size- reductions are well illustrated in the headpiece. Improved magnetic materials have been very important factors in the loading coil development work. The different magnetic materials which have been used in standard loading coils are listed in Table III with ap- proximate dates, in terms of the beginning and end of manufacture, and other pertinent data. PART II: LOADING FOR LONG-DISTANCE CIRCUITS The early applications of standard open-wire loading made loaded 104- mil circuits about as good from the attenuation standpoint as non-loaded 165-mil circuits of equal length. When this loading was later applied to 165-mil circuits, the first New York-Denver loaded 165-niil line (1911) was approximately equivalent in transmission performance to the original non- loaded New York-Chicago 165-mil line (1892). Large economies also resulted from the application of the first standard cable loading to suburban trunk cables and toll connecting trunks in ex- change areas, and to interurban toll cables. Notable examples of the latter were the Boston-Worcester (1904), New York-Philadelphia (1906), and New York-New Haven (1906) cables. The toll cables used heavy loading. Considerable medium loading was used in long exchange cables. (1) Phantom Group Loading This was the first major new loading development to follow the pioneer- ing standardization work. Beginning late in 1907, it culminated in com- mercial applications on open-wire lines and on new quadded cables during 1910. ^f) Entirely new types of coils were developed for loading the phantom circuits. Each of its four line-windings comprised a tandem connection of an inner-section winding located on one core-quadrant and an outer-section winding located on the opposite core-quadrant, the two line windings associated with the same side circuit being distributed over the same pair (« A much more comprehensive story of the phantom loading development and its relation to the development of quadded cable and to phantom working on open-wire hnes is given in BibUography items (8) and (9). 160 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 of opposite core-quadrants. The line windings were inserted in the four line wires of the phantom circuit and connected to have all of the mutual inductances aid the self inductances. In the individual side circuits the mutual inductances opposed the self inductances, and in consequence the coils contributed negligible leakage inductances to the circuits. The phantom coils were about twice as large in weight and volume as the associated side circuit coils, for cost-equilibrium reasons. The side circuit coils were closely similar in size to the existing standard non-phantom coils. Each of their two line windings consisted of an inner- section winding on one half-core and an outer-section winding on the other SIDE CIRCUIT COILS PHANTOM CIRCUIT COIL INNER WINDINGS OUTER WINDINGS Fig. 2 — Phantom group loading. Coil winding schematics and method of connection into circuit. half-core, and thus in effect were evenly distributed about the entire core. The close magnetic-coupling thus obtained resulted in a negligible leakage inductance to the phantom circuit in the parallel-opposing connections of line windings. The mutual inductances aided the self-inductances in the side circuits. Figure 2 schematically illustrates the coil winding arrangements. The general design symmetry of the individual coils also included essential symmetry in the distribution of the direct admittances among the line windings and from the line windings to the core and the case. The initial designs so well satisfied the service needs that only a very few minor design refinements were subsequently required from the crosstalk standpoint. The real difficulties encountered in meeting the service crosstalk-require- INDUCTIVE LOADING FOR TELEPHONE FACILITIES 161 ments were in controlling or correcting the small accidental unbalances that were unavoidable in manufacture. The transmission performance in loaded side circuits was about the same as that of loaded non-phantom circuits on similar-size conductors. A slight attenuation impairment resulted from the non-inductive resistance of the phantom coils. The phantom coils were located at side circuit loading points and the phantom inductance was chosen to give a cut-off frequency of about 2300 cycles, the same as in the side circuits, and in non-phantomed circuits. In consequence, the nominal impedance of the loaded phantoms was ap- proximately 60% of that of the associated side circuits. The attenuation Fig. 3— An early installation of open-wire phantom group loading. Individually potted coils; phantom coil on pole; side-circuit coils on crossarms. was about 13% better than that of the associated side circuits of open-wire lines, and from 15 to 20% better in loaded cables, depending upon con- ductor size. The great commercial unportance of the phantom-group loading de- velopment is indicated by the fact that nearly two-thirds of all the voice- frequency loading coils installed on quadded toll and toll entrance cables are coils of side circuit type, and nearly one-third are phantom loading coils. Over the years during which phantom loading and quadded cable have been available, only a relatively small amount of non-phantom type loading has been used in voice-frequency toll cable facilities. Important facilities in this special category are the loaded cable program-transmission circuits subsequently described and the "order wire" maintenance circuits in coaxial cables. Also, during the 1940's, there was some occasional use of 162 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 non-phantom type coils on non-quadded exchange type cables for short haul toll facilities, in place of phantom group loading on quadded toll cables. (2) Loaded Coarse-Gauge Quadded Toll Cables The need for extending the telephone transmission range in storm-proof toll cable, and the unavailability of telephone repeaters suitable for use on loaded circuits, led to a great activity in the development of composite coarse-gauge quadded cables and of entirely new loading coils for these cables, beginning during 1910. The first application (1911) was the new Philadelphia- Washington Section of the Boston- Washington underground cable system. ^«^ The new coils for the 10 AWG sides and phantoms were generally similar in design to the open-wire loading coils, even in their use of stranded copper conductors, and were only about 20% smaller. The coils for the 13-gauge conductors were intermediate in size (approx. geometrical mean) between the coils for the 10-gauge conductors, and the coils previously developed for 19 and 16 ga. cables. The size and efficiency relations among these three series of coils were approximately in cost-equilibrium for the grades of cable involved. In new underground sections of these coarse-gauge cables a new standard * 'medium-heavy" weight of loading was used, the coil spacing and inductance being midway between those for standard heavy and medium loading and having the same cut-off frequency. The new weight of loading was nearly as good in transmission performance as the heavy loading that was used in old parts of the Boston- Washing ton route and other routes where the loading vaults had been laid out for heavy loading, and was considerably less expensive. In the medium-heavy loaded 10-gauge circuits, the attenua- tion was 0.050 and 0.040 db/mi, respectively for the sides and phantoms; the corresponding values in the 13 ga. circuits were 0.069 and 0.085 db/mi, respectively. The 10 ga. loaded circuits were designed for service between Boston and New York, and between New York and Washington. On an emergency basis, the phantoms could be used for Boston- Washington service. It is appropriate at this point to mention the substantial reduction in toll cable dielectric losses that was worked out in the period under discus- sion. The extensive use of loading for the first time on long 10 gauge and 13 gauge circuits greatly increased the importance of reducing the amount of moisture that unavoidably accumulated in the conductor insulation during («> A more comprehensive account of this development and associated quadded cable developments is given in References (8) and (9). INDUCTIVE LOADING FOR TELEPHONE FACILITIES 163 the early stages of cable manufacture. This was done by refinements in the cable drying treatments. (3) Changing Fields of Use for Iron-Wire Core Loading Coils The new coarse-gauge cable loading coils, above referred to, marked the beginning of the use of 65-permeability iron-wire in place of 95-perme- ability wire in the cores of standard cable loading coils. In every respect except permeability, the 65-permeability wire was su- perior to the higher permeability wire. The lower permeability was relatively disadvantageous as regards d-c resistance per unit inductance in coils of a given size. On the other hand, the core-loss resistance was substantially sihaller, by virtue of the lower permeability and the superior hysteresis characteristics. In consequence, the total effective resistance of the 65- permeability core coils was lower at the upper speech-frequencies and nearly the same at the important middle frequencies, so that there was considerably less attenuation-frequency distortion. Other even more important service advantages of the 65-permeability core toll cable loading coils resulted from their much greater magnetic stability. D-c signaling currents caused smaller temporary changes in in- ductance and effective resistance, in consequence of the superimposed d-c magnetization. Also, the residual effects of strong superimposed currents, manifested as permanent or semipermanent changes in inductance and effective resistance, were much smaller. A specially valuable advantage of the 65-permeability wire core-material was in the substantially smaller amount of telephone transmission distortion caused by the operation of superposed composite telegraph systems. The transient core-magnetization caused by the telegraph currents caused small transient changes in the inductances of the coils, and relatively very large transient changes in the effective resistances. The resulting non-linear distortion became known as "telegraph flutter." It varied as a function of telephone frequency and telegraph speed, the size of the core, the inductance of the windings, and the ratio of the amplitudes of the telephone and tele- graph currents. It was accumulative in effect as the circuit lengths increased. Since simultaneous telephony and telegraphy was very general and was important from the revenue standpoint in the open-wire and cable long- distance facilities, the control of "telegraph flutter" became an increasingly important requirement in the development of new loading coils. (The need for satisfactory control of "telegraph flutter" eventually led to the development of the improved cable telegraph systems which are described in Section 8 of this review.) By 1912, the use of 95-permeability core-material in new toll cable coils 164 tHE BELL SYSTEM TECHNICAL JOUKNAL, JANUARY 1951 had stopped. However, since exchange area circuits and suburban trunk cables were seldom used for composite telegraph working, the use of 95- permeability iron-wire continued standard until 1916, when compressed, powdered-iron, core coils became available. (4) Loaded Repeatered Open-Wire Lines The pioneering phases of the development of better lines and better loading coils for use on repeatered long-distance facilities had their first commercial application in the transcontinental open-wire circuits between New York and San Francisco, January 1915. The adaptation of the lines to the requirements of repeater operation was secondary in importance only to the development of satisfactory repeater elements, and of circuits for associating the repeater elements with the line. A comprehensive ac- count of all phases of the very important transcontinental telephony-de- velopment project has been published in an article, "The Conquest of Distance by Wire Telephony."^ Accordingly, the account in the present review is limited to the loading for the line. Comprehensive information regarding telephone repeaters is given in a 1919 paper by B. Gherardi and F. B. Jewett.ii Since the lines were used for two-way transmission, a high degree of impedance balance between the line and the repeater balancing-network circuit was necessary in order to obtain satisfactory repeater gains. This problem involved the construction of lines having a new order of regularity and stability in their impedance characteristics over the working frequency- band, to make feasible the design of simple types of balancing networks^^ for adequate simulation of the line impedances. The requirements just stated involved a much greater degree of uniformity in the loading coil spacing than was necessary in non-repeatered circuits, and a corresponding reduction in the coil inductance deviations. This latter requirement meant that the new coils must have a much greater resistance to the magnetizing effects of superposed steady and transient line-currents, especially since exposure to lightning surges had to be accepted as a normal service experience. The new requirement for high magnetic stability in the loading coils was met by using short air-gaps at diametrically opposite points in their toroidal- type 65-permeability iron-wire cores. This construction feature also resulted in a substantial reduction in (but not the elimination of) telephone trans- mission distortion caused by ''telegraph flutter" phenomena, when com- posite telegraph circuits were superposed on the loaded circuits. The new side circuit and phantom circuit loading coils were coded 550 and 549, respectively. They were a little smaller than the coils which they super- seded, and had somewhat higher resistances. The resulting attenuation im- INDUCTIVE LOADING FOR TELEPHONE FACILITIES 165 pairments, however, were negligible in the repeatered circuits. The headpiece includes a 550 coil (the largest coil, designated A). During the decade that followed the beginning of transcontinental tel- ephony, a large enough quantity of Nos. 549 and 550 coils were installed to load approximately 300,000 circuit miles. In the beginning, the improved loading was concentrated on parts of a proposed backbone-network of re- peatered 165-mil lines. Soon it became apparent from: (a) the continuing Fig. 4— Typical installation of high stability open-wire loading coils. Note the three phantom loading unit combinations in 3-coil cases supported on the poles; other m- dividually potted side-circuit and phantom coils are supported on the crossarms. development work on telephone repeaters, repeater circuits and auxiliary apparatus and transmission networks, and from (b) field experiments sup- plemented by theoretical cost studies, that non-loaded 165-mil liiies with additional repeaters would have much more satisfactory transmission char- acteristics than repeatered loaded Hnes, and would be less expensive. The principal transmission advantages were: (1) the practicability of securing materially lower net losses, in consequence of the effect of the higher velocity of transmission in reducing echo-current disturbances, (2) more uniform attenuation and impedance characteristics under varying weather condi- 166 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 tions, (3) reduced delay-distortion because of the more uniform velocity- frequency characteristics at the upper speech frequencies, (4) complete elimination of telegraph-flutter impairments, and (5) better quality of speech transmission by the effective transmission of a much wider frequency- band. In this latter connection, it is of interest that the transmission band which was effectively transmitted over the loaded, repeatered, transcon- tinental circuits ranged from about 350 to 1250 cycles, defining the band as that between the lowest and highest frequencies whose transmission was not more than 10 db higher than that of the 1000-cycle transmission. At the higher frequencies, the line losses and the loading coil losses piled up so as to effectively suppress transmission. The excess losses at the low voice- frequencies were due to the line terminal apparatus and the repeater auxiliary apparatus. The rapidly growing appreciation of these advantages led initially to a curtailment in the installation of new loading on 165-mil circuits, and subsequently to the removal of the existing loading and the installation of additional repeaters. ^^^ By this time, the vacuum-tube repeater had been accepted in its own right as an independent instrumentality for improving transmission. On 104-mil lines, the economic competition between loading and repeaters was much closer than that on 165-mil line, and for a period of several years the aggregate mileage of loaded 104-mil lines increased substantially while the mileage of loaded 165-mil lines decreased at an accelerating rate. In this connection the transmission disadvantages of loading on repeatered 104-mil lines were not so serious as those on repeatered 165-mil lines, partly because of the much shorter lengths involved and partly because of their more stable transmission performance under varying weather conditions. During the early 1920's, the commercial exploitation of open- wire carrier telephone and carrier telegraph systems became an increasingly important factor in the removal of loading from open-wire lines. About 1924, the practice of installing new loading on 104-mil lines was stopped in order to increase the plant flexibility for the more extensive use of repeaters and of carrier systems, and accordingly the production of new open-wire loading coils was discontinued. The removal of the existing load- ing, however, was not completed until about 1934. (5) High Stability Type Coils for Coarse-Gauge Toll Cables The use of improved telephone repeaters started on a small-scale basis on loaded coarse-gauge circuits along the Boston-Washington route even <•>) The unloading of the original transcontinental circuits was completed early in 1920. The net loss was reduced from about 20 db to 1 1 db, and the width of the effective trans- mission band was doubled. INDUCTIVE LOADING FOR TELEPHONE FACILITIES 167 before the loaded, repeatered transcontinental open-wire circuits were ready for service. To permit more satisfactory repeater operation in the remaining loading complements of these cables, and in many more coarse-gauge toll cables which were installed during the next few years, a series of high- stability type of loading coils was standardized during 1916/'^ The coils in this series used air-gaps in their 65-permeability, iron-wire cores. Since the availability of satisfactory types of telephone repeaters had reduced the need for 10-gauge conductors, the new coils were "compromise" designs, suitable for either 10 ga. or 13 ga. conductors. Accordingly they were inter- mediate in size between the two different series of coarse-gauge cable coils that were developed in the 1911-1913 period. These new loading coils remained standard for toll cable uses for only a few years. The practice of installing 10 ga. and 13 ga. toll cables substantially stopped before 1920, because theoretical studies of the possibilities of improving repeaters and loading systems were indicating that it should ultimately be possible to usp repeatered, loaded 19-gauge or 16-gauge conductors for spanning the longest distances likely to be involved in the long-distance cable plant. The use of 4-wire repeatered facilities became a very important objective in the new development plans, making necessary an intensive development of transmission equalizing and regulating net- works and practices. (6) Compressed Powdered-Iron Core Loading Coils for Repeatered AND Non-Repeatered 19 AND 16-Gauge Toll Cables 6.1 Compressed Powdered-Iron Core-Material General This was the first new loading coil core-material to be developed since the establishment of the first loading standards. Many other possibilities had been considered on a number of occasions, notably silicon steel in fine- wu-e form, but no core-material had been discovered that was superior to the 65-permeability iron-wke in its major performance characteristics. The compressed powdered-iron development was the pioneering begin- ning of an entirely new and very important art in the design of high-stability, low-loss, magnetic core-materials. It was started by the Engineering Dept. of the Western Electric Co. as an independent project, alongside the basic research work on various phases of transcontinental telephony, and reached the first stage of commercial fruition during 1916. An important objective was to obtain much better magnetic stability than that of iron-wire cores, and at a lower cost than that of wire cores having series air-gaps. Also, from <0 Additional information regarding this development is given in References (8) and (9). 168 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 the manufacturing standpoint it was desirable to have a better control of the magnetic properties of loading coil core material, and to be free from limitations on quantity such as were occasionally experienced in obtaining iron core wire from outside manufacturers. These particular difficulties were very serious during the First World War in consequence of the greatly increased demand for loading coils and the impossibility of securing an adequate supply of diamond dies for drawing the 4-mil core wire. (In normal times, all dies were imported from Europe.) Incidentally, the supply limitations on diamond dies made it necessary to permit the use of over- size core wire even though this resulted in an impairment in transmission per- formance due to the abnormal (eddy current) core losses. Fortunately, the compressed powdered-iron core material became commercially available in time to be of great value in helping the Western Electric Co. to increase the output of loading coils. ^ The success achieved in this development subsequently led to the applica- tion of the compressed, insulated, magnetic-powder technology to magnetic alloys, for use in the cores of loading coils and of other types of coils used in various types of transmission networks, including electric wave filters. Initially worked out for voice frequency applications, the new technology expanded to become an important factor in the design economy of carrier and radio transmission systems. The low eddy current losses made possible in large part by the use of very small, insulated, magnetic particles, were inherently important elements in the high frequency applications. Following its development in the United States, the compressed, magnetic powder core, in one form or another, spread to Europe, and became important in world wide communications. The prior art is of historical interest, in that experiments with finely divided magnetic particles had extended over a period of several decades. As an early example, Oliver Heaviside described in his ''Electrical Papers" some work on magnet cores with magnetic powder embedded in wax. It is also of interest that during the Bell System pioneering efforts to obtain satisfactory loading coil cores, considerable experimental work was done (1901) on magnetic oxide cores involving high temperature heat treatments of loosely formed iron wire or iron tape core structures in an oxygen atmos- phere. (U. S. Patents Nos. 705,935, and 705,936, July 29, 1902.) ^ The total output, however, could not be increased sufficiently fast to meet the high 1917-1918 demand for loaded facilities. This resulted in a temporary practice of what came to be known as "omitted-coil loading" on a substantial mileage of toll cable facilities. In the initial installation of loading on these particular facilities, the coils were placed at alternate load points along the line; — for example, at 12,000 ft. spacing instead of the standard 6,000 ft. spacing. The resulting transmission impairments were accepted as being tolerable under war emergency conditions. As soon as practicable, however, the "omitted loads" were "filled in," so that shortly after the end of the war the coil spacing conformed to the established standard practices. INDUCTIVE LOADING FOR TELEPHONE FACILITIES 169 None of the early work by these and other investigators, however, had resulted in commercially usable iron powder cores. It was not until the Western Electric concept of pressures sufficient to deform the magnetic particles, and of an insulating medium of such character as to withstand these high pressures and provide an exceedingly thin insulating film be- tween particles, was developed, that commercially usable results were ob- tained. The Western Electric compressed powdered-iron development was carried out in two distinct steps, one after the other, using the same basic magnetic material. In the early work, consideration was given to the use of chemically produced iron powder. Then, mainly for cost reasons, the development Fig. 5— Early cable loading coils and their cores. At left: Iron wire core coil; core has insulating-binding tape partly removed to show core construction. At right: Compressed iron powder core coil; 7-ring core has binding tape partly removed. Also 2 individual core rings. efforts were concentrated upon the use of electrolytically deposited iron which was processed so that it could easily be ground into particle sizes of the required fineness. The iron particles were thoroughly mixed with suit- able insulating material and then moulded into thin core rings of desired over-all dimensions under moulding pressures of about 100 tons per square inch. These core rings were stacked vertically and bound with insulating tape for use as loading coil cores. In the first commercially usable product, the iron-powder was annealed prior to the insulating and ring-moulding operations. When a higher-grade loading coil core material became necessary for reasons subsequently dis- cussed, the iron-powder annealing process was omitted and a larger amount of insulation was mixed with the magnetic material, which changes resulted in a substantial reduction of effective permeability. Other process dif- 170 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 ferences were also involved. These two magnetically different, compressed loading coil core-materials were sometimes known as ''soft-iron dust" and ''hard-iron dust" or as "compressed annealed iron-powder" and "com- pressed unannealed iron-powder," respectively. In the Speed-Elmen classic paper^' on "Magnetic Properties of Compressed Powdered Iron," these two materials are referred to as "Grade A" and "Grade B", respectively. A still lower permeability core material, known as "Grade C", was developed primarily for use in carrier frequency inductance coils. In this material, a larger amount of particle insulation than that in the "A" and "B" grades was used, and the average size of particle was smaller. In commercial production the "Grade B" cores consisted of a mixture of 90% unannealed powder and 10% annealed powder, the latter com- ponent being included to obtain the desired value of permeability, and to increase the mechanical strength of the core rings. The different magnetic characteristics of the "A" and "B" grades of compressed, powdered iron were basic factors in the evolution of the loading practices for the new loading coils that used them in their cores. A brief review of these practice differences follows, and includes some additional general data regarding the coils themselves. ^''^ 6.2 Compressed, Annealed, Powdered-Iron Core Loading Coils Referring to Table III, it will be noted that cores using this new material had nearly the same effective volume-permeability as the cores of 95- permeability iron-wire. By using similar-size cores, and closely similar windings, it was found possible to obtain effective resistance-frequency characteristics close to those of the standard small-gauge cable loading coils using 95-permeability wire cores, as typified in the 508 coils of Table I, and corresponding grades of side circuit and phantom loading coils. Also the new potting developments were minimized. An outstanding service advantage of the new "soft-iron dust" core loading coils was in their very high stabiUty of residual inductance, by virtue of the self-demagnetizing action of the very large number of very small series air-gaps in the cores. After a temporary exposure to magnetiza- tion by abnormally large superimposed currents that might be caused by accidental grounds on superposed d-c signaling circuits or by induction from outside sources (lightning, power-line shorts or grounds), the coil inductance would return to within a few per cent of the initial value. On the other hand, after extreme exposure to strong magnetic shocks the residual induct- ance in the 95-permeability wire-core coils might be as much as 40% below the initial inductance, the high retentivity of the magnetic circuit being an important factor in this performance. *' Some additional detailed data regarding these two series of loading coils were pub- lished in Reference (8). INDUCTIVE LOADING FOR TELEPHONE FACILITIES 171 The new coils also were considerably better than the 95-permeability wire- core coils in the following important features: (a) Their susceptibility to changes in inductance and effective resistance during service intervals involving the superposition of steady d-c signaling currents; (b) Their susceptibility to the transient magnetizing effects of superposed composite-telegraph currents, i.e., "telegraph flutter". The relative performance characteristics, above described, resulted in the "soft-iron dust" core coils superseding the standard 95-permeability wire- core coils in the fields of use in which these older standard coils had been used. As an important example, the original standard 508 coil, used princi- pally for medium loading in exchange cables, was superseded in 1916 by the 574 coil, which remained standard for about a decade. The telegraph-flutter characteristics. Item (b) above, prevented the new coils from being used generally in place of 65-permeability wire-core coils on toll cables quads having all four wires composited for grounded telegraph operation. However, for a few years there was a "compromise" practice of combining "soft-iron dust" side circuit loading coils with 65-permeability wire-core phantom loading coils in 19 and 16-gauge toll cable projects where the needs for superposed grounded-telegraph operation could be satisfied by compositing the phantoms, and the demands for repeatered facilities could be met by luniting repeater operation to the side circuits. In this special loading setup, the transmission distortion by "telegraph flutter" was controlled in the phantoms, and was completely avoided in the side circuits because the grounded telegraph currents, flowing in parallel through the side circuit coil windings, neutralized each other's effect in magnetizing the cores. With respect to regularity in circuit impedance-frequency characteris- tics in relation to repeater gains, the high residual-inductance stability of the soft-iron dust-core loading coils made them distinctly preferable to the 65-permeability wure-core coils in the repeatered side circuits. During 1917-1918, when the subsequently described work on improved loading systems for long repeatered toll cables got well under way, theoretical studies of the use of soft-iron dust core loading coils on such facilities dis- closed seriously objectionable non-linear transmission distortion that had not been bothersome on short circuits. This was due to the relatively large hysteresis losses m the leading coil cores, which cause the effective resistances of the coils and the circuit attenuation loss to mcrease appreciably in mag- nitude as a function of line current ampUtude. The effects of these losses are much more serious in the repeatered circuits, because of the larger line currents, and because of the much greater circuit lengths. Since the hystere- sis losses also vary in durect proportion to the telephone frequency , the result- ant coil-resistance increments and attenuation increments are greater at the high-speech-frequencies than at low frequencies. 172 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 As none of the other energy losses in the core or winding vary with line current strength, it became convenient to consider the attenuation loss caused by hysteresis as an ''excess" loss, when referred to the attenuation that would result if the hysteresis should be vanishingly small or zero. The theoretical studies above mentioned not only showed the "excess" attenua- tion in long loaded, repeatered, circuits to vary as a function of the magni- tude of the input current and frequency, as above noted, but also showed it to vary as a function of the length of repeater section, the position of the repeaters in the line, the weight of loading, and the over-all circuit length. Since it is not possible to offset the effects of loading coil hysteresis by means of distortion corrective or equalizing networks at repeater stations or circuit terminals, the piling up of the "excess" losses along the line in very long loaded, repeatered, circuits could reach values that would be large relative to the desired over-all working equivalent, if the individual loading coils should have large hysteresis losses, as did the soft-iron dust-core loading coils. Comparative theoretical studies of the excess loss due to hysteresis effects in 65-permeability core loading coils showed these coils to be greatly superior to the soft-iron dust-core coils in this feature. On the other hand, the wire- core coils were relatively unsatisfactory from the inductance-stability stand- point for use on long repeatered circuits. 6.3 Compressed, Unannealed, Powdered-Iron Core Loading Coils It was very fortunate that the development work on the compressed, unannealed, powdered-iron core-material, previously mentioned, approached commercial fruition at about the time the unsuitability of the soft-iron dust-core loading coils for very long repeatered circuits became apparent. As noted in Table III, the effective volume permeability of this improved core-material was closely that of the 65-permeability wire-cores. The new standard loading coils using this improved material had cores generally similar in dimensions to those of the older coils used on 19 and 16 ga. toll cables, and their over-all dimensions were sufficiently similar to avoid the need for developing new loading coil cases. In general terms, the new coils combined the best qualities of the soft- iron dust-core loading coils with the best performance characteristics of the 65-permeability wire-core loading coils. Actually, they were much better than the soft iron-dust core coils with respect to stability of residual induc- tance, and susceptibility to magnetization by superposed steady currents. In these respects they were also substantially superior to the 65-permea- bility wire-core loading coils. However, they were not quite so good as the low permeability wire-core coils with respect to hysteresis losses and telegraph flutter transmission impairments. On the other hand, they were substan- INDUCTIVE LOADING FOR TELEPHONE FACILITIES 173 tially as good in their efifective resistance-frequency characteristics. The above summarized advantageous electrical and magnetic properties resulted during 1918 in the standardization of the new compressed, annealed, pow- dered-iron core loading coils for general toll cable use in place of the 65- permeability wire-core coils and soft-iron dust-core coils. The availability of the improved loading coils quickly stopped the previously mentioned temporary, compromise practice of using soft-iron dust side circuit loading coils in combination with 65-permeability wire-core phantom loading coils. After the hard-iron dust-core loading coils became commercially available, the remaining development work on improved toll cable loading systems described in the following pages was in terms of these coils. (7) New Loading Systems for Repeatered 19 and 16 Ga. Toll Cables 7.1 General The basic problems of learning how to use telephone repeaters most advantageously on long cable circuits began to receive serious attention soon after the completion of the open-wire transcontinental telephony proj- ect, along with the repeater development work that ultimately resulted in the obsolescence of open-wire loading, as previously mentioned. During the decade or more of intensive, continuous development activity on the repeatered toll cable problem that followed, it was found highly advan- tageous to work loading and repeaters together as equal partners in a team, each making its contribution according to its own nature. The important contributions of loading were the substantial reductions of attenuation and of frequency distortion at a cost (for voice-frequency transmission) much lower than the cost of the additional repeaters and the distortion corrective- networks which would have been required on non-loaded cables. Incidentally, the use of loading substantially simplified the solution of the important equalization and regulation problems. The attainment of the good working partnership between loading and repeaters involved the development of new loading systems having sub- stantially improved transmission characteristics, and the development of improved repeaters and improvements in repeatered circuits, including equalizing networks and arrangements for controlling the cable transmission- performance changes that result from seasonal and daily changes in tem- perature. A classic report on these related developments is given in a paper^"' by A. B. Clark, entitled, 'Telephone Transmission over Long Cable Cir- cuits." ^^^ The present discussion is primarily concerned with the features of the improved loading that were essential to satisfactory transmission- performance in long repeatered cable circuits. <^> Reference (15) is also of interest with respect to engineering aspects. 174 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 The compressed, unannealed, powdered iron-core loading coils previously- described were found to be satisfactory with respect to inductance stability and other properties, including hysteresis effects for use in the improved loading systems. New smaller inductance values were necessary, however, for the coils used in the longest circuits. It was of course necessary to con- trol the geographical spacing deviations, and the factory deviations in cable capacitance and in the loading coil inductances, so as to obtain a satis- factory degree of "regularity" in the impedance characteristics of the loaded circuits. 7.2 Transmission Limitations of Existing Loading Systems (a) General: As the lengths of loaded cables progressively increased beyond 'those involved in the establishment of the first standard loading systems, certain transmission effects which were initially unnoticed or comparatively unimportant became very noticeable as objectionable transmission impair- ments. By increasing the electrical lengths of the circuits, the use of repeaters greatly aggravated these impairments and it became very desirable to correct them so far as feasible at their source. Complex problems thus arose in providing better quality of transmission over much greater distances. The impairments referred to above were directly related to the band width of frequency transmitted by the line, which is determined by the cut-off frequency, and to the velocity of transmission. They are discussed briefly in the following paragraphs. (b) Attenuation-Frequency Distortion: At frequencies above about 70% of the theoretical cut-off frequency, the attenuation increases with rising fre- quency at a continuously accelerating rate, in consequence of the accumu- lation of the effects of internal reflections at the individual loading points. At lower frequencies where these so-called 'lumpiness of loading" effects are not of dominating consequence, the attenuation increases with rising frequency are largely due to the energy losses in the loading coils. (Usually the eddy-current losses in the cores are the most important component loss, since they are proportional to the square of the frequency.) It thus happens that the attenuation losses may pile up in long loaded cables in such a way as to substantially suppress the transmission of the higher- frequency components of speech, even when the attenuation losses are tol- erable at lower frequencies. In consequence, the width of the transmission band which is effectively transmitted over a long loaded cable becomes narrower and the quality of transmission progressively deteriorates as the circuit length increases, unless suitable auxiliary equalizing networks and additional repeaters are utilized. The large amount of attenuation-frequency distortion which occurred in the first transcontinental telephone circuits was previously commented upon. INDUCTIVE LOADING FOR TELEPHONE FACILITIES 175 The attenuation-frequency distortion in long loaded cables can be reduced by raising the theoretical cut-off frequency. As a secondary factor, the re- duction of core losses in the loading coils is advantageous. (c) Velocity Distortion: This became noticeable as peculiarly disturbing, transient distortion in the intervals when spoken syllables were building up or dying down, prior to, or after, then* steady-state transmission. It is most disturbing at the upper speech-frequencies where the steady-stage velocity of wave propagation varies at an accelerating rate as the cut-off frequency is approached. It can be particularly disturbing in very long 0.60 0.87 1000 1500 2000 2500 3000 FREQUENCY IN CYCLES PER SECOND Fig. 6— Attenuation frequency characteristics toll cable loading. 3500 circuits where repeaters are used to reduce the over-all loss, and in extreme cases it could make the circuits unusable for commercial service. These transient distortion impairments may be reduced by raising the loading cut-off frequency, and by increasing the velocity of wave propagation. The loading design changes that were made in these features gave a satisfactory control of the velocity distortion in the longest loaded cables used commer- cially, without requiring the use of velocity-distortion corrective networks in the lines or at repeater stations. (d) Echoes: Echo effects also were found to be potentially limiting factors in providing satisfactory transmission-performance over long loaded cable 176 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 circuits. They are due to the transmission of reflected energy from points of impedance irregularity. They are troublesome factors whenever the time of transmission between the point of reflection and the disturbed subscriber is appreciable, especially when the use of repeaters prevents the attenuation of the reflected energy from being negligible in magnitude. Increasing the velocity of wave propagation is a sure procedure for reducing echo effects. Control of the impedance irregularities which cause them is also important, but cannot be carried to a sufficiently fine degree in long, low- velocity cir- cuits. For the satisfactory control of echo effects in very long, four-wire type, high- velocity, (H44-25) loaded circuits, the use of auxiliary devices known as "echo suppressors" was found to be very advantageous.^^ (e) Basic Networks and Filters: The previously mentioned basic networks^^ which simulate the impedances of the loaded circuits are vitally necessary features of the balancing lines that are used with the repeaters employed on two-way speech circuits. Relatively simple types of networks provide satis- factory impedance simulation up to a high fraction of the cut-off frequency, in loaded circuits having regular coil spacing and uniform coil inductances. At frequencies near the loading cut-off, however, it is not feasible to provide basic networks which satisfactorily simulate the impedances of the loaded circuits. Consequently, in order to avoid large repeater unbalances which would cause objectionable singing at these frequencies, it is necessary to associate with the repeaters low-pass type electric wave filters^^ which have cut-off frequencies appreciably lower than the loading cut-off frequencies. Usually this cut-off frequency differential is of the order of 10% or more of the loading cut-off. The reduction of transmitted band width caused by these filters aggravates the frequency attenuation distortion effects pre- viously discussed. This use of filters with the repeaters thus became a contributory factor in the need for raising the loading cut-off frequency in long repeatered circuits. By reducing the transmitted frequency band width, however, the filters used with the repeaters have favorable effects in reducing the high-frequency velocity distortion caused by the loading. The filters used with the repeaters on long H44-25 circuits, subsequently described, had cut-off frequencies substantially below the loading cut-off frequencies primarily for the purpose of controlling velocity distortion impairments. 7.3 Improved Loading Systems (a) General: To sum up the foregoing, the theoretical analyses of the limi- tations of the standard toll cable loading pointed definitely towards an in- crease in cut-off frequency and in the velocity of wave propagation. Since the state of the art was such that theoretical studies"- '^ alone could not determine the magnitudes of the changes that would be required, extensive INDUCTIVE LOADING FOR TELEPHONE FACILITIES 177 investigations of experimental installations also became necessary. For cost reasons, it seemed desirable that the improved loading should be used at standard ''heavy loading" spacing, i.e., 6000 ft. In consequence, the increase in cut-off was proportional to the increase in velocity. Also, there was a proportional reduction in the nominal impedance, accompanied by an in- crease in the unit-length attenuation. Loading Systems- Table IV -Small Gauge Repeatered Toll Cables Item No. Loading ^*^ System Circuit Coil (b) Code No. Nomi- nallm- pedance (ohms) Theo- retical Cut-off Frequency (cycles) Nomi- nal Vel- ocity (mi/ sec.) Attenuation Loss<«> (db/mile at 1000 Cycles) Maxi- mum ^'l) Geographi- 19 A.W.G. 16 A.W.G. cal Length (miles) (1) (2) (3) (4) (5) (6) (7) (8) H174-106 H44-25 (I H174-63 << H245-155 Side Phantom Side Phantom Side Phantom Side Phantom 584 583 590 589 584 587 582 581 1550 950 800 450 1550 750 1850 1150 2800 2900 5600 5900 2800 3700 2400 2400 10000 10000 19000 20000 10000 13000 8000 8000 0.28 0.22 0.48 0.40 0.28 0.28 0.25 0.20 0.16 0.13 0.25 0.21 0.16 0.16 0.16 0.12 500 500 2000 2000 500 1500 250 250 Notes: (a) Nominal coil spacing is 6000 feet in cable having a capacitance of 0.062 mf/mile in the side circuits and 0.100 mf/mile in the phantom circuits. (b) The code numbers of the first standard compressed, unannealed, powdered- iron core coils used in the loading systems. (c) These attenuation values apply at 55°F. Under extreme high or low tem- perature conditions, the actual attenuation may be approximately 12 per cent larger or smaller, due principally to changes in conductor resistance with temperature. In long repeatered cable circuits these variations of attenuation with temperature require special corrective treatment by means of automatic transmission regulators. (d) These particular length-limitations were set by velocity-distortion effects. By using velocity-distortion corrective networks in the Hnes or at repeater stations, it would have been possible to extend the circuit lengths beyond the listed limits, provided also that adequate steps could be taken to con- trol echo currents. Under actual service conditions, however, echo currents might Hmit the circuit lengths to considerably lower values than those listed above, depending upon the grade of balance of the lines and the permissible overall loss. The transmission development work resulted in the standardization of two new phantom-group loading systems, designated HI 74-106 and H44-25('"> in Table IV. Several years later (1923), a new H63 phantom («") The letter-number loading designations used in Table IV, and in the remainder of the text, were simplifications adopted for general use in 1923. The letter prefix symbolizes the geographical spacing in feet; the numbers correspond to the nommal mductances (in milUhenrys) of the associated side circuit and phantom loading coils, m the sequence noted. The letter "H" designates "Heavy" loading spacing. In the early days this was about 1.25 miles; later it became 6(XX) ft. 178 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 loading was substituted for H106 phantom loading, to provide HI 74-63 phantom-group loading as a successor standard for HI 74-106 loading. (b) E 174-106 Loading: The development work on HI 74-106 loading pre- ceded that on the H44-25 system. By using available standard ''medium" loading coils at standard "heavy" spacing, the transmission velocity and the cut-off frequency were raised to values about 20% higher than those of the H245-155 loading which had been, by far, the most widely used loading on 19 and 16 gauge toll cables. The new combination of inductances and spacings became widely known in the early installations as "medium-heavy, high cut-off" loading. This designation called attention to the first change in standard loading cut-off frequency since the establishment of the initial load- ing standards in 1904. When used in conjunction with improved repeaters, the HI 74-106 load- ing enabled satisfactory transmission to be obtained over circuits about twice the length of the longest H245-155 repeatered circuits which were satisfactory from the transmission standpoint. In the beginning, HI 74-106 loading was extensively used on 4-wire repeatered circuits. After the new transmission systems using H44-25 loading came into general use, HI 74-106 (and HI 74-63) loading was largely restricted to short haul two-wire circuits. The 1917 trial installation tests showed H174-106 loading to be a substan- tial step forward in the struggle to extend the transmission range in re- peatered 19 and 16-gauge toll cables, but far from a big enough step to satisfy the transmission requirements in very long cables such as the New York-Chicago cable project which had been accepted as a definite develop- ment objective. The continuing studies which considered other combina- nations of lower inductances and of standard and new spacings ended in the decision to standardize H44-25 toll cable loading. (c) H44-25 Loading: Although these inductance values had been used for impedance matching loading on entrance cables, they had not previously been used on toll cables. The initial designation for the improved loading was "extra-light, very high cut-off " loading. The cut-off frequency and transmission velocity were about twice as high as those in HI 74- 106 loading, and the nominal impedance was 50% lower. H44-25 was necessary for the longest repeatered circuits. It was developed primarily for use on 19-gauge 4-wire circuits in which large repeater gains could be obtained by the repeaters in the one-way paths, to offset the rela- tively high bare-line attenuation. The first installation of H44-25 loading was made during 1919 on circuits in the New York-Philadelphia-Reading Cable. Trial service of a complete four-wire system, including new regulating and equalizing arrangements, and an echo suppressor, started during 1923. In October 1925, commercial service between New York and Chicago started over a H-44-25 four-wire repeatered system. It had taken a long time to work out the necessary improvements in the INDUCTIVE LOADING FOR TELEPHONE FACILITIES 179 repeaters and their associated distortion-corrective networks, and to learn how to use regulating repeaters to control satisfactorily the very large transmission changes that resulted from temperature variations in long cir- cuits. During the mid 1920's aerial cable came into use extensively along new cross-country routes where underground cable conduits would have been unduly expensive. Such cables, however, presented added difficulties and expense in transmission regulation since the temperature range variations are about three times as great as in underground cable. During 1930 the use of buried cables started. With respect to transmission regulation and service continuity, they compare well with cables in underground conduit and are less expensive, when the number of cables along the route is small. However, buried toll cable generally tends to be more expensive than aerial cable. At the end of 1949 the aggregate wire mileage in buried toll cables was nearly one-third of that in aerial toll cables. A substantial amount of H44-25 loading was also used on 16-gauge 2-wire repeatered facilities, for circuit lengths intermediate between the trans- mission limits of HI 74-106 and HI 74-63 loading and lengths where echo- impairment difficulties made necessary the use of 19-gauge 4-wu-e facilities. In such two-wire circuits, very good line-balance was of course required at the intermediate repeaters. An important economic factor in this "medium" long-haul practice was the 50% lower loading cost per unit of facility length of the two-wire circuits. This intermediate-length usage of 16-gauge 2-wire circuits, however, tapered off in the long-distance plant of the A.T.&T.Co. during the late 1920's, so as to obtain the important plant flexibility and operating advantages that were inherent in the general use of 19-gauge 4-wire circuits for medium-haul and long-haul toll cable facilities. Notwithstanding the 2 : 1 ratio in loading cut-off frequencies, the width of the frequency-band transmitted over long H44-25 circuits was not much wider than that transmitted over the much shorter HI 74-106 facilities. This was largely due to the filters which were used to suppress the upper half of the H44-25 transmission band, primarily for the purpose of reducing the very serious velocity-distortion transmission impairments that would have otherwise resulted in very long circuits. This suppression of the higher frequencies also eased the transmission equalization and regulation problems. The attenuation-frequency distortion characteristics of the old and new toll cable loading are shown in Figs. 6 and 7. Figure 6 (p. 175) shows the attenuation in db per mile. Figure 7 (p. 180) gives the bareline attenuation-frequency curves under specified circuit length and repeater conditions hi which the total 1000-cycle attenuation is 10 db. The effect on frequency distortion of raismg the loading cut-off fre- quency, and of usmg distortion corrective-networks, is clearly indicated, (d) H 174-63 Loading: Before concluding this summary of the basic develop- 180 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 ment work on improved loading for long repeatered circuits, it is opportune to include some detailed information on the previously mentioned improve- ment of phantom loading for the so-called "medium-heavy" loading system, i.e., the combination of new H63 phantom loading with the existing HI 74 side circuit loading to constitute the HI 74-63 phantom-group loading system, data for which are included in Table IV. The practical importance of this development was in the substantial reduction it permitted in loading costs. It marked the beginning of commercial use (1923) of phantom loading coils having cores similar in size to those of the associated side circuit coils. The cost savings resulted directly from the coil size-reduction, and from the increased size of loading complements that could be placed in standard-size 0.001 3000 3500 1000 1500 2000 2500 FREQUENCY IN CYCLES PER SECOND Fig. 7 — Attenuation frequency characteristics of short and long loaded toll cable cir- cuits having a net attenuation loss of 10 db at 1000 cycles per second. pots, and from the simplification of pot assembly and cabling arrangements. The choice of phantom coil inductance (63 mh) was such as to make the phantom circuit 1000 cycle attenuation the same as that on the associated side circuits, without increasing the side circuit attenuation above that in HI 74-106 loading. This reduction in the loading inductance substantially improved the phantom circuit's transmission performance-characteristics by virtue of the substantial increase in cut-off frequency and transmission velocity, and made the repeatered phantom circuits electrically suitable for much greater distances than their side circuits. This superiority was seldom utilized, however, because of the practical operating flexibility advantages inherent in the established practices of using the associated side circuits and phantoms interchangeably between the same operating or switching centers. In due course, the sizes of the other toll cable phantom loading coils were INDUCTIVE LOADING FOR TELEPHONE FACILITIES 181 reduced to side circuit coil size, for cost-reduction reasons. The resultant economies were large relative to the value of the small attenuation impair- ments which resulted from this change. (8) New Telegraph Systems for Loaded Cables At several points in this review references have been made to the transient telephone transmission impairments which resulted from the operation of separate, superposed, grounded telegraph circuits over the individual line- wires of the loaded telephone circuits. ^''^ These ''composite" telegraph sys- tems had originally been developed for use on non-loaded open-wire lines Fig 8— Reduction of cable ohantom coil size to that of associated side circmt cods. Large No. 581 Phantom Coil (106 m.h.) at left. Small No. 587 Phantom Coil (63 m.h.) at right. N.B. These phantom coils had compressed unannealed iron-powder cores. and consequently required the utilization of telegraph currents of very large amplitude relative to the telephone currents. The great extensions in the lengths of 19-gauge repeatered loaded cable that were to be expected from the use of the improved loadmg and repeaters, previously considered, put great emphasis upon a much better control of the telegraph-flutter interference, and led to the development of improved cable telegraph systems, along with the improved telephone transmission systems. In one of these, known as the ''Metallic Polar Duplex Telegraph System,"i9 ^^e superposed telegraph current was of the same general order («») Reference (10) gives a comprehensive discussion of telegraph-flutter phenomena. 182 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 of magnitude as the telephone current. This permitted a much greater reduction of the telegraph-flutter impairments than that which could have been obtained at a reasonable cost by using larger coils, A disadvantage of this system, however, was that it halved the number of superposed telegraph circuits per toll cable quad. The other new telegraph system was a voice-frequency carrier system^^ which became commercially available during 1923 soon after the direct current metallic system just mentioned. This provided a total of 10 inde- pendent telegraph channels over the side circuits of special groups of H174- 63 4-wire circuits used exclusively for telegraph service, and consequently there could be no telegraph-flutter reactions on telephone transmission. On the other hand, the need for controlling intermodulation effects among the associated carrier-telegraph channels imposed limits upon the allowable non- linear distortion in the loading coils. The loading coils then standard (hav- ing compressed, unannealed, iron-powder cores) satisfactorily met the re- quirements, and with a greater margin than did the repeaters which were standard at that time. Interference considerations, however, prevented the general use of the metallic polar telegraph systems on loaded cable pairs used for carrier telegraphy. The voice-frequency carrier-telegraph system soon became the most widely used telegraph system in the long distance toll cables. It did not require special facilities, but made effective use of the whole frequency- band provided for voice telephony. The initial number of channels was expanded to 12 on HI 74-63 facilities, and subsequently to a total of 24 channels by using the wider-band H44-25 facilities, previously described. The present-day system is limited to 18 channels, however, in order to permit the ready interconnection of loaded cable and broad-band telephone facilities in tandem. A detailed account of these and other telegraph improve- ments is given in a 1940 B.S.T.J. paper^i. The strong-current, composite-grounded d-c telegraph system is very seldom used on modern toll cables. There is, however, a considerable use of the strong-current grounded d-c telegraph system on a simplex-phantom basis. Under this service condition, the telegraph current does not magnetize the loading coil cores and consequently there is no telegraph-flutter inter- ference with telephone transmission. The metallic polar d-c telegraph system is usually limited to a few voice repeater-sections, because of the modern severe limits on telegraph-flutter impairments upon telephone transmission, and partly for economic reasons. The improvements in telegraphy over loaded toll cables also included arrangements which were developed in 1922 for the purpose of reducing interference between d.c. telegraph circuits when superposed by the com- positing method on wires of the same loaded cable quad.^ This interference, INDUCTIVE LOADING FOR TELEPHONE FACILITIES 183 known as telegraph crossfire, is mainly due to capacitance coupling between the cable conductors and in the central office equipment. In long circuits, the inductive coupling between the two line windings of each side circuit coil, and among the four line windings of each phantom loading coil, are important factors in the over-all crossfire between the telegraph circuits that are associated with the same cable quad. (9) Compressed Permalloy-Powder Core Loading Coils Since the transmission characteristics of the compressed, unannealed, powdered-iron core coils, which became available for general use in toll cables during 1918, were as satisfactory as was expected for the rapidly expanding repeatered toll-cable plant, greater emphasis was placed on cost reduction than on transmission improvement, in the continuing studies of new loading coil design-possibilities. 9.1 Core-Material Development It was inevitable that permalloy^ should be considered. This remarkable new nickel-iron alloy, invented by Mr. G. E. Elman of Western Electric research department, had important early applications in thin-tape form for continuous loading of deep-sea telegraph cables. Some early studies and experiments indicated interesting possibilities of using it in thin sheets in non-toroidal type loading coil cores, but the pros- pects were much more intriguing if permalloy could be made available in compressed-powder toroidal cores. However, the initial experimental results with powdered-permalloy were disappointing. When the processes used in making compressed powdered-iron cores were employed, the permeability was unsatisfactorily low in consequence of the magnetic changes caused by the severe mechanical treatment involved in the embrittlement processes. The development moved forward rapidly after experiments with a physically sturdy type of ceramic-powder insulation for the permalloy particles proved that an annealing treatment after the core rings were pressed could erase the objectionable magnetic effects of the powderizing process and raise the permeability to desirable, high values. A complete account of this very im- portant development is given in an A.I.E.E. paper^ by W. J. Shackelton and I. G. Barber, "Compressed Powdered Permalloy, Manufacture and Magnetic Properties." In the form developed for voice-frequency loading coil cores, the effective volume-permeability of the improved core-material was 75, more than twice that of the standard compressed, unannealed, powdered-iron core-material, and the intrinsic permalloy characteristic of very low hysteresis was retained. The combination of magnetic and electrical properties was such that large size-reductions could be made in the loading coils without degrading the 184 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 important transmission-performance characteristics, relative to those of the standard powdered-iron core loading coils. 9.2 Permalloy Core Loading Coils The coils standardized for toll cable loading were in volume and weight about one- third as large as the superseded types previously described. Coils C and B in the headpiece exemplify the coils under comparison. The direct- current resistances of the new coils were slightly lower than those of the superseded designs, their hysteresis losses were substantially lower, but their eddy-current losses were somewhat greater, because of the higher permea- bility. In consequence, their effective resistances were more favorable at the important low and middle speech-frequencies, than those of the compressed annealed iron powder core coils but not quite as good at the top frequencies. The stability of residual inductance after magnetization by strong super- posed currents was appreciably better than that of the superseded designs. The hysteresis advantages included a substantial reduction in non-linear distortion effects and about a 50% reduction in the transient distortion effects that are unavoidable in the operation of grounded telegraph over composited circuits. Their telegraph-flutter rating was considerably better than that of any of the prior standard cable loading coils, excepting only the large-size "high-stability" type of coarse-gauge cable coils, previously de- scribed. (Subdivision 5.) With the standardization of the permalloy-core loading coils there started the practice of coding the combination of two side circuit coils and the associated phantom coil as a phantom-group ''loading unit." The letter "P" was used in the code designations; a code number associated with the code letter recognized the different inductances of the different loading units, the complete codes being PI, P2, etc. The coil size-reduction resulted in a 2 to 1 reduction in the potting-space requirements and permitted twice as many coils to be potted in standard- size cases, thus reducing potting costs. The cost savings in potted coils ranged from 30 to 40%. Additional savings resulted in the installation costs, including the space costs in the loading vaults in underground cable projects. The development was very timely, in that the much cheaper coils became available during 1928 for use in the unprecedented expansion of H44-25 four-wire repeatered facilities that started that year and built up to a very high peak during 1930. In the period 1928-1931, over 4,000,000 permalloy- core toll cable loading coils were manufactured for Bell System uses. The lower costs of these coils encouraged the provision of larger circuit-groups in the long-distance cable plant which made possible substantial improvements in the speed of service. This, in combination with excellent transmission INDUCTIVE LOADING FOR TELEPHONE FACILITIES 185 performance, greatly increased the demand for service, up to the beginning of the business depression in the early 1930's. CABLE A CABLE B Fig. 9— Installed aerial toll cable loading. Four different methods of supporting the loading-coil cases are used in this installation, which provides loading for two cables: (a) On the platform of a 2-pole "H" fixture. (1 large welded steel case, and 5 large cast iron cases.) (b) A pole balcony supporting a large welded steel case. In this installation, it provides an extension of the "H" fixture, (c) A small welded steel case equipped with brackets, and fastened directly to pole, (d) Clamping a small lead-sleeve case to the main cable and its supporting strand. (This case contains program circuit loading coils.) Around 1930, improved assembly-arrangements were worked out for the permalloy-core loading units. These involved the assembly of the individual loading units in individual unit-containers, and the code designations were changed. These used the letters 'TB", and the same numbers as in the P- type units; the complete designations being PIB, P2B, etc. 186 THE BELL SYSTEM TECHNICAL JOUBNAL, JANUARY 1951 The compressed powdered-permalloy core toll cable loading coils remained standard until 1938, when much cheaper and slightly better compressed, powdered molybdenum-permalloy core coils became available, as discussed in subdivision 11. S INDUCTANCB COILS USiD FOR CROSSTALK ADJUSTMENTS SIDE CtRCUlT COILS PHANTOM COIL Fig. 10 — P-B type loading unit potting assembly prior to placement in unit shielding container. Phantom coil is below the two side circuit coils. Midget inductance coils are used in phantom-to-side crosstalk adjustments. (10) Improved Loading Standards for Two- Way Repeatered Toll Cables During the late 1920's considerable attention was given to the improve- ment of transmission standards made possible by the use of the improved repeaters and the improved loading. This included reductions in the allow- able net losses between terminals and improvements in crosstalk perform- ance. Also, steps were taken to obtain better control of attenuation- frequency distortion, the important objective being to provide fairly uniform transmission in the frequency-band between 250 and 2750 cycles per second.^^ The transmission requirements over the frequency-band just mentioned INDUCTIVE LOADING FOR TELEPHONE FACILITIES 187 could be met without undue difficulty on the H44-25 four-wire and two-wire facilities, but were not feasible on the HI 74-63 facilities then being used mainly on a two-wire basis. The work on the improved standards problem resulted in the development of the B 88-50 and H88-50 toll cable loading systems, data for which are given in Table V. In effect, this development established a new minimum cut-off standard of about 4,000 cycles per second for loading used on repeatered circuits. Also, as noted in the table, the transmission velocity was increased in H88-50 loading. B88-50 loading, using a coil spacing of 3,000 ft. (i.e., one-half of H-spacing), was originally intended for use in "long" repeater sections. The cheaper H88-50 loading was used on "short" repeater sections, and in con- sequence some facilities had tandem combinations of the two new types of loading. In the early applications H88-50 loading was used in repeater sec- tions ranging up to about 45 miles in length and the more expensive B 88-50 Table V H88-50 AND B88-50 Loading Loading System Circuit Nominal Impedance (ohms) Theoretical Cut-off Frequency (cycles) Nominal Velocity (mi/sec.) Attenuation Loss (db/mile at 1000 Cycles) 19 A.W.G. 16 A.W.G. H88-50 B88-50 Side Phantom Side Phantom 1100 700 1550 950 4000 4200 5600 5900 14500 15000 10000 10500 0.35 0.30 0.25 0.23 0.19 0.16 0.16 0.14 loading was used on longer sections. Later, improvements in the control of crosstalk and special procedures for reducing loading section capacitance- deviations made 1188-50 loading suitable for longer repeater sections. Dur- ing recent years, the voice frequency repeater points have usually been laid out to permit the use of H88-50 loading, and at present there is little use for new B88-50 loading. New loading coils were developed for the new loading systems, and were coded in the "PB" loading unit series, pw-eviously mentioned. This apparatus development included substantial improvements in crosstalk performance obtained by new assembly-methods, and refinements in the crosstalk adjust- ments and test circuits. These new assembly-methods were applied to all standard toll cable and toll entrance cable loading units and provided flexibility for potting different types of loading units in the same case, and for identification of their terminal leads in the stub cables. The new H88-50 and B88-50 loading became available for general use during 1932, 188 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 Fig. 11 — Potting assciiil)l> lo.s I' i; i \ |,r hjadinj^' units in large welded steel case. As- sembly ready for lowering into casing. Half of loading units are on far side of assembly frame, not visible in picture. The large number of loading coils makes necessary the use of 2 stub cables. inductive loading for telephone facilities 189 (11) Compressed Molybdenum-Permalloy Powder Core Loading Coils 11.1 The Improved Core-Material The continuing search for still better core-materials culminated during the middle 1930's in the development of the 125-permeability compressed molyb- denum-permalloy material, described in an A.I.E.E. paper^^ by V. E. Legg and F. J. Given, "Compressed Powdered Molybdenum-Permalloy for High- Quality Inductance Coils." In its intrinsic magnetic and electrical properties as used in voice-frequency loading coils, the improved permalloy-material is nearly as much superior to the old standard 75-permeability permalloy as this latter material was to the 35-permeability compressed powdered- iron which it superseded as standard during the late 1920's. The improved permalloy owed its superior characteristics mainly to the inclusion of molybdenum in the alloy, the principal constituents of which are approximately 2% molybdenum, 81% nickel, and 17% iron. The molyb- denum component substantially raises the permeability and the specific resistance, and materially reduces hysteresis. The eddy-current losses are much lower than in the 75-permeability permalloy material, because the effect of the higher permeability in increasing these losses is more than offset by the effect of the higher intrinsic resistance in reducing them. In developing the material, it was considered to be very important to go as far as possible in improving the intrinsically favorable hysteresis prop- erties. This was accomplished without adverse effects on permeability and eddy-current losses and other important properties, by annealing the pressed core rings in hydrogen at a much higher temperature than that previously used with material under treatment while exposed to the atmosphere. Also an improved type of particle insulation was developed. AU in all, a large number of unusually difficult processing problems had to be solved in the research and development stages. Also, some of the processes required considerable additional attention during the manufacturing preparations for quantity production. In the voice-frequency loading applications, the successful efforts to reduce hysteresis to a minimum fitted in with the preliminary economic design studies, which indicated it would be deskable to take advantage of the superior intrinsic properties of the new magnetic material by using it in smaller cores, so as to reduce loading-apparatus costs as much as possible without appreciably degrading transmission performance. In this connection, it is noteworthy that with any given magnetic-material the hysteresis losses become greater as the core size is reduced, in consequence of the greater intensity of magnetization. The 125-permeability molybdenum-permalloy core material under dis- 190 THE BELL SYSTEM TECHNICAL JOUBNAL, JANUARY 1951 cussion was developed primarily for voice-frequency uses. At much higher frequencies, lower permeabiUties are necessary to prevent the core losses from becoming too high. Accordingly, other grades of compressed molybdenum- permalloy powder having lower permeability values are available. These are obtained by diluting the molybdenum-permalloy powder with inert material before pressing. Also, smaller-size particles are used. A new grade not de- scribed in the Legg-Given paper,^^ previously referred to, which has an effective permeability of 60, was used in small carrier loading coils for the Army spiral-four field cable during the war,^^ and is now being used in the cores of cable loading coils for 15-kc program transmission circuits which are described in Subdivision 13.3. 11.2 M-type Molybdenum-Permalloy Core Loading Units ^ The initial standard, molybdenum-permalloy core, phantom loading units which were coded in the M-series became available for commercial use during 1938. The individual coils were about 60% smaller than the standard, 75-permeability, permalloy-core coils which they superseded for use in new plant. In the headpiece, these size-relations are typified by coils D and C, respectively. By design, the new coils had about the same d-c resistance and hysteresis loss as the superseded designs. Their eddy-current losses were considerably lower than those of the 75-permeability permalloy designs, and in conse- quence the total effective resistance was lower at the upper frequencies, thereby improving the steady-state frequency-distortion characteristics of the circuits in which they were used. In plant-design engineering, the new coils were accepted as being equivalent to the older coils. The residual inductance stability was a little better, and the telegraph-flutter distortion characteristics were considerably better. The susceptibility to superposed d-c magnetization, however, was worse. This minor impairment was the only adverse effect of the substantial increase in permeability, and the substantial reduction in coil size. The development was timely in that the new coils were available for use in meeting the accelerating demand for toll cable loading that started in 1939 and continued for several years. In the five-year period 1938-1942, a total of about 800,000 side and phantom toll cable loading coils were manu- factured for Bell System use notwithstanding the large installation of Type K carrier systems on non-loaded and unloaded cables that occurred in this period, thereby reducing the demand for additional, repeatered, loaded cable voice-frequency facilities. The economic advantage of the broad-band carrier system is largely due to the fact that the cost of the conductors and the repeaters and of the distortion corrective-networks and regulating devices which are used to INDUCTIVE LOADING FOR TELEPHONE FACILITIES 191 shape and control the transmission medium is shared by all of the transmis- sion paths. Very valuable transmission advantages result from the rela- tively very high velocity of transmission over the non-loaded conductors/"^ One of the effects of the new carrier systems' competition was to more than reverse the relative amounts of loading for new installations of 4-wire and 2-wire circuits — somewhat less than ^ the total being provided for 4-wire circuits, during the period under consideration. The substantial cost- reductions, resulting from the introduction of the 75-permeability permalloy coils, of course materially limited the additional savings that could be realized by further size-reduction. Notwithstanding this, and taking into account also the declining demand for toll cable loading, the development of the M-type loading units turned out to be a very profitable operation, in terms of the reduced costs of new plant. 11.3 SM and MF-type Molybdenum-Permalloy Core Loading Units These war-emergency designs owed thek existence to the necessity for conserving strategic materials, especially nickel. They use half as much molybdenum-permalloy as the M-type loading units. The use of a new type of insulation, Formex enamel, ^p^ on the conductors in place of a combination of cotton with an older type of enamel, greatly improved the winding space-factor and minimized the increase in d-c resistance that necessarily followed from the 50% reduction in coil size. In the frontispiece. Coil E is one of these new coils. Coil D being the superseded coil. To minimize delays in introducing the war-emergency designs into com- mercial use, which began during 1942, they were (initially) assembled in the unit-containers and potted in the loading coil cases that had been designed for the M-type loading units. They were initially coded as the SM-type loading units. Subsequently, to conserve steel, entirely new unit-assembly arrangements were made in new smaller-size unit containers and new smaller-size loading coil cases were developed to take full advantage of the loading coil size- reduction. The coils themselves were not changed but new code-designations were assigned in the "MF" series, in conformity with the long established practice of coding phantom loading units in their unit containers. The d-c resistances of the SM and MF loading units are about 25% higher than those of the corresponding M-type loading units, and the hysteresis effects are about 40% greater, under similar operating conditions. The other core-losses are unchanged in magnitude because they do not vary as ^°^ Published information regarding the cable carrier systems is given in Bibliography References (28) and (29). (p) This improved wire-insulation had already found valuable uses in new exchange area loading coils, as discussed in Section 22. 192 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 Fig. 12 — M-type and MF type phantom loading units. Before and after placement in their unit shielding containers. M-type unit above the MF-type unit, "a" designates mid- get inductance coils (used in crosstalk adjustments); "r" designates midget resistors (used in crosstalk adjustments). The loading units shown outside the containers are not the same as those shown inside the containers. , a function of coil size. For the most important types of loading, the increases in attenuation that result from the higher coil resistances are in the range INDUCTIVE LOADING FOR TELEPHONE FACILITIES 193 1 to 3% at 1000 cycles on 19 ga. cables. At the top voice-frequencies, the attenuation increments are less than twice as large as the 1-kc increments. In 50-mile repeater sections, the resulting increases in the bare-line attenua- tion are of the order of 0.2 to 0.4 db at 1000 cycles depending on the type of loading and much of this increment-loss usually can be recovered by raising Fig. 13— Potting assembly methods— medium and large size complements of MF- type units. For placement in cylindrical, thin steel, casings. the repeater gains. The stability of residual inductance is as good as that in the M-type loading units. The unpaired hysteresis effects, above mentioned, are accompanied by increased non-linear distortion, including telegraph-flutter effects. Also the smaller coils are somewhat more susceptible to changes in inductance and effective resistance when the circuits in which they are used have steady currents superposed upon them during talking intervals. Additional information regarding the smallest loading units is included 194 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 in an A.I.E.E. papei^° by S. G. Hale, A. L. Quinlan, and J. E. Ranges, "Recent Improvements in Loading Apparatus For Telephone Cables." The various relative transmission-impairments, above mentioned, were accepted in advance as being tolerable from the service standpoint under war conditions, considermg the types of circuits required and their probable relatively short lengths. At that time it was thought possible that better loading units, not necessarily as good as the M-type units, might be war- ranted in the post-war period. Meanwhile, the service experience with the Fig. 14 — Potting assembly methods — small complements of M-type and MF-type loading units. Note use of lead sleeve casing for MF type units, and relatively large welded- steel casing for M-type units. small loading units has been reasonably satisfactory, largely because of the easing-up of performance requirements that is resulting from the restriction of toll cable loading to short-haul facilities. These seldom have more than two repeater sections, in consequence of the economic competition offered by present standard and proposed new, cheaper, carrier systems on non- loaded cable. Under these circumstances, the cost of developing better loading units which would probably increase the loading costs would be hard to prove in. Thus, the MF-type war-emergency loading units became post-war loading standards. INDUCTIVE LOADING FOR TELEPHONE FACILITIES 195 It should not be inferred from the foregoing that the MF (and SM) loading units have unimportant significance in the economy of Bell System toll cable plant-design. For example, during the period 1942-1949, a total of about two million side and phantom coils were manufactured for assembly in these smallest, standard, phantom loading units. A large majority was installed subsequent to VJ-day, as part of the Bell System program of plant expansion to meet the greatly increased demand for long-distance telephone service, and to restore the speed of service to the pre-war standards. Table VI Electrical Data — Most Important Voice- Frequency Phantom Loading Units Nominal Inductances W — mh Approx. Avg. Resistances (») — Ohms Loading Unit Code Nos. Side Circuits Phantoms Side Phantoms d-c Ikc d-c Ikc PI, PIB Ml MFl, SMI 172.4 172.4 172.4 63.6 63.6 63.6 10.7 10.8 13.8 13.6 13.0 16.4 5.3 5.4 6.9 6.2 6.0 7.6 P2, P2B M2 MF2, SM2 43.5 43.5 43.5 25.1 25.1 25.1 3.8 3.6 4.5 4.4 4.0 5.0 1.9 1.8 2.2 2.2 2.0 2.5 P4, P4B M4 MF4, SM4 30.9 30.9 30.9 17.8 17.8 17.8 2.7 2.4 3.1 3.0 2.7 3.4 1.3 1.2 1.5 !;; PUB Mil MFll.SMU 88.7 88.7 88.7 50.2 50.2 50.2 6.1 6.3 7.9 7.0 7.2 9.1 3.05 3.1 4.0 3.5 3.6 4.6 Notes: (1) The listed inductance values are the mean specification inductance values (at 1800 cycles). (2) The coil resistance values allow for 19-gauge stub cables of 7.5-ft. external length. (12) Comparative Electrical Data, Voice-Frequency Phantom-Group Loading Units Comparative electrical data regarding the commercially most important, former standard and present standard, voice-frequency phantom-group loading units are given in Table VI, above. Those coded in the "F" and "PB" series used compressed permalloy-powder cores; the M, SM, and MF- type units used compressed, molybdenum-permalloy powder cores. Prior to the standardization of the P and PB-type units, the side circuit and phantom circuit coils had their own individual code numbers. They were intercon- nected in loading unit formation during the case assembly and cabling pro- cedures. 196 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 The loading units having the digit 4 in their code designations are "full- weight" units for H31-18 voice-frequency entrance cable described in Part V of this review. The loading units having the digit 2 in their designations are used in H44-25 four-wire repeatered circuits. The other loading units are used in two-wire repeatered circuits, and also in circuits not long enough to require repeaters. (13) Improved Loading eor (Long-Distance) Cable Program Transmission Circuits 13.1 General In the early days of radio chain-broadcasting (during the early 1920*s), the links which connected the broadcasting stations with the studios where the programs originated usually were open-wire voice-frequency telephone circuits modified to meet the special requirements of this new type of service. In some instances, toll cable circuits were used for links not more than a few hundred miles long. Where available, side circuits of H44-25 facilities, previously described, were preferred for the cable program-transmission service because of their high cut-off frequency. By using suitable equalizing and regulating net- works in conjunction with modified one-way amplifiers, a fairly satisfactory transmission-medium could be obtained, providing a frequency-band ranging from about 100 cycles up to about 4000 cycles. While these circuits were adequate for speech broadcasting they were not equally satisfactory for classical music programs by symphony orchestras. As early as 1924, some preliminary studies were started on entirely new types of loaded cable facilities primarily for use in transmitting the highest grade of radio-broadcast program material. These studies showed 16 ga. cable pairs to be desirable for long program circuits. At the time, however, there was considerable question as to what the ultimate performance- requirements should be, and some doubt as to whether the commercial demand would be sufficiently large to warrant the high cost of developing and providing a suitable new type of facility. During the following years, there was a large increase in the number of broadcasting stations and in the need for inter-connecting links. Also the toll cable network expansion had commenced to accelerate rapidly. Be- ginning about 1926, the new toll cables that were installed usually included a small complement of 16-gauge non-quadded pairs (generally 6) in anticipa- tion of their ultimate use for improved program facilities, if the then ex- p>ected demand should eventually materialize. Studies of improved loading, and of the very important equalization and temperature regulation problems were renewed. This work progressed sufficiently so that early in 1927 a trial INDtJCTlVE LOADING FOB TELEPHONE FACILITIES 197 installation of H22 loading was planned for program facilities in a new ca- ble between New York and Philadelphia. This loading had a 40% higher cut- off frequency than the H44 loading previously mentioned, and a 30% lower nominal impedance. It was expected that the program frequency-band could be stretched to a 6000-cycle top. It used a new loading coil described later on. 13.2 B22 Program Facilities f While the preparation for the H22 trial installations was still under way, further experimental and theoretical studies showed it would be desirable to provide an equalized transmission-band from about 50 cycles to about 8000 cycles, so as to obtain a margin for probable future improvements in broad- casting services. Accordingly, a decision was reached in September 1927 to develop a new type of cable program facility that would be satisfactory for lengths of 2000 miles or more. A new type of loading, designated B22 (22 mh loading coils at 3000-ft. spacing), was authorized and a trial in- stallation on cable circuits looped back and forth between New York and Pittsburgh was planned. The development of the new loading was only a small part of the total development effort. The equalizing and temperature-regulation problems were much more difficult than those previously encountered in the development of long-distance telephone message facilities, partly because of the much wider transmission-band and partly because of the more severe Hmits necessarily imposed. Improved repeaters were required and crosstalk and noise problems demanded very serious attention. A comprehensive account of the development work and a detailed description of the B22 cable program-facility is given in an A.I.E.E. paper^^ by Messrs. A. B. Clark and C. W. Green. Accordingly, the remaining discussion herein is limited to the loading. The theoretical cut-off frequency of B22 loading is a Uttle over 11,000 cycles; its nominal impedance is closely equal to that of H44 loading, previ- ously mentioned. The theoretical nominal velocity of wave propagation is about 20,000 miles per second. The use of phase equalization networks of 8 kc band width, however, slows down the actual velocity to about 13,000 mi/sec. The attenuation on 16 ga. pairs at average temperature is about 0.24 db/mi at 1000 cycles, and ranges from about .14 db/mi at 35 cycles to about .38 db/mi at 8000 cycles. The new 22 mh non-phantom type loading coils used compressed, permalloy-powder cores similar m size to those of the toll cable side circuit and phantom loading coils previously described in general terms. Non- linear distortion in the line was satisfactorily low m consequence of the favorable hysteresis characteristics of the permalloy-core coils. 198 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 The satisfactory completion of the system's trial-installation tests in 1929 resulted in a large amount of B22 loading being installed during 1930 and 1931 on 16-gauge pairs in cables that had been installed in advance of the facility development work, as previously mentioned, and in new cables. During 1936, compressed, molybdenum-permalloy powder-core program loading coils became available for use in place of the permalloy-core coils above described. The new coils were smaller than their predecessors, and were substantially as good or better in the lower half of the working frequency band. At the high frequencies they were better than the permalloy-core coils, because of the lower eddy-current losses previously mentioned. An Fig._ 15 — Molybdenum -permalloy core program circuit loading coil potted for installa- tion within cable splice sleeves. The canvas bag shown in the picture is used to prevent the metal shielding-container of the coil from damaging the insulation of nearby con- ductors in the cable sphce. The fabric strips are used to tie the coil case to the cable core at the splice. important factor in the choice of coil size was to make the coil suitable for installation within the loading splice-sleeves so as to reduce potting and installation costs. This practice became quite general, especially at the "B" loading points intermediate between the "H" loading points where phantom loading units were installed on telephone message circuits in the same cable. In these "splice installations," the per-coil savings in potting and installation cost were large relative to the direct savings in loading coil costs resulting from size reduction. In order to realize these substantial combined savings as quickly as possible, the new program coils were given priority in the commercial exploitation of the molybdenum-permalloy core-material. As an indication of the commercial importance of the program circuit INDUCTIVE LOADING FOR TELEPHONE FACILITIES 199 loading above described, it is of interest to note that enough program coils were manufactured during the period 1928-1948 to provide loading for more than 100,000 pair-miles of B22 facilities. The demand for the new B22 loading is rapidly declining however, in consequence of the post-war de- velopment of program transmission facilities using combinations of channels in non-loaded cable carrier systems. From now on, it seems probable that new B22 loading will largely be limited to short extensions of existing loaded facilities, and to short links between cable carrier-system terminals and the points where broadcasting programs are picked up or delivered. 13.3 15-kc Program Transmission Circuits The development of new loading for use on cable facilities transmitting FM broadcasting material was completed early in 1948. It provides a trans- mission band extending up to 15 kc and is suitable for use on circuits that connect FM broadcasting transmitters with their studios, in situations where its use will reduce costs as compared with the use of intermediate amplifiers. Two weights of 15-kc loading are available, one having a nominal im- pedance equal to that of B22 loading (800 ohms), and a lighter-weight loading having a nominal impedance of about 480 ohms. The 800-ohm loading generally uses 1 1 mh coils at spacings which give a theoretical cut-off frequency of about 23 kc, and a nominal velocity of about 20,000 miles per second. In 0.062 mf/mi cables the coil spacing is 1500 ft. and in "high-capacitance" exchange cables, it is 1100 ft., in order to obtain closely the same total loading section capacitance and similar values of nominal impedance and cut-off frequency. Since studio-transmitter circuits usually include tandem combinations of component cables which have appreciably different unit-length mutual capacitances, this loading plan minimizes reflection effects which would otherwise result from impedance differences at the junctions of the component cables. 800-ohm loading is sometimes provided on program pairs in coaxial cables by using 7.5 mh coils at 1000 ft. spacing. When the coaxial cables are installed in 1000 ft. lengths, this loading arrangement avoids the need for making the (expensive) extra cable splices that would be required if 1500 ft. spacing should be used. Although 50% more program loading coils are required, the small additional cost of the loading is negligible in relation to the savings in cable splicing costs. This 7.5 mh, 800-ohm loading has a nominal velocity of about 20,000 mi/sec, and a theoretical cut-off frequency of about 34 kc. The 480-ohm loading uses 7.5 mh coils at spacings twice as long as those for the 800-ohm loading using 11 mh coils. The theoretical cut-off is a little over 19 kc and the nominal transmission velocity is about 36,000 miles per second. The 800-ohm loading is superior in all transmission features to the 480- 200 THE BELL SYSTEM TECHNICAL JOUENAL, JANUARY 1951 ohm loading, especially at low frequencies. It is an acceptable substitute for B22 loading for transmission of AM broadcasting material, being appreciably better in the frequency range 4 to 8 kc, because of its much higher cut-off frequency, and it is substantially as good at low frequencies. Accordingly, to provide plant flexibility for possible future broadcasting service require- ments, this 800-ohm 15-kc loading is being installed on short-haul program pairs in new toll cables in situations where the anticipated initial needs are for AM broadcast programs. When the loading is installed in the course of the cable installation, the slightly higher cost of the broader-band loading is negligible in comparison with the plant flexibility-advantage above cited. The field of use for the 480-ohm 15-kc program loading is in short repeater sections where the transmission requirements permit its use, and where it is desirable to take advantage of its lower cost, relative to the 800-ohm loading. This cost advantage is maximum when the loading has to be applied to cables previously installed. The loading coils for the new 15-kc program loading are of the same size as the molybdenum-permalloy core coils developed for B22 loading. Accord- ingly, when installation conditions are favorable, economies can be achieved by placing the coils within the loading splices. The new program loading coils use 60-permeability, compressed, molybdenum-permalloy powder cores. This relatively new grade of molybdenum-permalloy has much lower eddy- current losses than the 125-permeability grade used in voice-frequency loading coils (and in B22 program loading), and is very advantageous in the reduction of attenuation over the upper two-thirds of the 15-kc trans- mission-band. The 60-permeability cores also have superior non-linear dis- tortion-characteristics. (14) Control of Crosstalk The control of crosstalk between adjacent telephone circuits has been a very important problem from the beginning of the use of loading, especially in loaded cables, and has been most difficult in long loaded, repeatered, quadded toll cables. 14.1 Cable Unbalances The effect of loading in increasing the circuit impedance raises the voltages which act upon the unavoidable cable capacitance-unbalances, and reduces the magnitudes of the line currents which act upon the series resistance (and inductance) unbalances. Consequently, with the introduction of load- ing, it became necessary to improve the design of the cables so as to materi- ally reduce the capacitance unbalances. This was accomplished by using different lengths of twist in adjacent pairs and in adjacent layers, and by using different lengths of lay in adjacent layers. INDUCTIVE LOADING FOR TELEPHONE FACILITIES 201 The development of quadded cable and of phantom-group loading during the period 1908-1910 introduced especially difficult requirements in the control of crosstalk between the phantom circuits and their side circuits, and to a lesser degree between the associated side circuits. Notwithstanding further improvements in design and great care in manufacture, it became necessary during the installation of the quadded cables to resort to the use of special splicing procedures which reduced the total capacitance-unbalance per loading section to satisfactory values. For nearly a decade it was the practice in the control of phantom-to-side and side-to-side crosstalk to make the capacitance-unbalance test-splices at seven approximately even-spaced intermediate splicing-points in each load- ing section. By about 1919, further improvements in design and in manu- facturing processes made it feasible to reduce the number of test splices per loading section to 3. This practice is still general for quadded cables used principally for two-wire repeatered facilities. In the period of very rapid extension of the installation of long repeatered, loaded four-wire circuits (1929-1931), it was found feasible to limit the number of test splices per loading section to one, by using supplementary balancing-condensers to reduce the high residual capacitance-unbalances on two-wire circuits, and by using additional balancing-condensers at one end of each repeater section on four- wire circuits, when required to obtain satisfactory low over-all crosstalk. The one-way transmission in the individual, oppositely-bound, paths of the four-wire circuits was a basic factor in making feasible these field-adjustment simplifications, thereby reducing installation costs. 14.2 Loading Coil Crosstalk Although the side circuit and phantom loading coils never had objec- tionable design unbalances, it has always been difficult in manufacture to realize the inherent symmetry of their design. The series inductance un- balances have been the most troublesome accidental unbalances. In the early days, reasonably satisfactory control of crosstalk between circuits in the same phantom-group was obtained by care in manufacture, and by adjusting the inductance unbalances to the nearest turn. A general, substantial, tightening of the crosstalk limits became necessary when repeaters came into general use, because of the effect of the repeaters in amplifying the unwanted crosstalk along with the wanted conversation, and because of the great increases in circuit length that the repeaters made feasible. During a period in the early 1920's, when intensive development was under way to reduce the loading apparatus crosstalk, the over-all repeater-section crosstalk was controlled by poling the unbalances of the coils against the cable unbalances in the loading sections near the repeaters. The new development work, above referred to, included greater refine- 202 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 ments in the manufacturing processes, including greater accuracy in the subdivision of the core winding-space, more uniform winding-arrangements in layer formation by automatic winding-machines, and the use of external series-inductance adjustments by means of preselected, miniature, inductance coils, which resulted in much smaller residual unbalances than could be obtained by the nearest full-turn adjustments. More precise crosstalk measurement-circuits were developed, and the practice started of making the crosstalk adjustments and measurements in test circuits having, at the test frequency, impedance characteristics approximating those of the lines in which the coils under test are used. (Previously a relatively insensitive test-circuit having "compromise" impedance characteristics had been used for all types of side and phantom coils.) Also, the factory crosstalk adjust- ments were concentrated on minimizing near-end crosstalk in loading units intended for two-wire circuits, since in such circuits the far-end crosstalk is relatively unimportant. In loading apparatus intended for use on four-wire circuits, the crosstalk adjustments were made to minimize far-end crosstalk because the associated phantom-group circuits are always used in the same direction of transmission and the one-way repeaters associated with them block the propagation of near-end crosstalk. The external inductance ad- justments, above referred to, were especially designed for the reduction of phantom-to-side crosstalk. Other adjustments and assembly processes con- trolled crosstalk between associated side circuits. As a result of the various improvements above referred to, the average phantom-to-side crosstalk in the loading apparatus was reduced to about one-fourth of the earlier values. These reduced values were of the same order as the cable crosstalk in the individual loading sections after the completion of the capacitance-unbalance test-splicing. In the late 1920's and early 1930's, when the need for improved trans- mission systems on two-wire repeatered circuits resulted in the development of the H88-50 and B88-50 facilities previously described, another develop- ment campaign was started to improve loading apparatus crosstalk-per- formance. This resulted in the reduction of the average loading coil crosstalk to values much smaller than those caused by the cable residual capacitance- unbalances after test splicing, so that the effective repeater-section crosstalk is not significantly larger than that which would result if it were possible to manufacture perfectly balanced loading coils. Important factors in this improved performance were the use of series, external, resistance adjust- ments in particular loading units where worth-while crosstalk reduction could be thus obtained, and the use of a new series of inductance elements having closer gradations in their inductance values to more closely approach the theoretical optimum adjustments. More compact assembly-arrangements of the phantom loading units in individual shielding containers also con- INDUCTIVE LOADING FOR TELEPHONE FACILITIES 203 tributed to the more favorable crosstalk-performance, along with other process improvements. (Refer to Fig. 10, page 186.) The improved crosstalk-performance above discussed, which was achieved in the development of the PB-type permalloy-core phantom loading units, previously described, was maintained in the commercial production of the smaller-size M-type molybdenum-permalloy core loading units which super- seded the PB-type loading units, and in the present standard MF-type loading units. (Refer to Fig. 12, page 192.) It seems improbable that additional improvements in loading unit cross- talk-performance will be needed in the future, in view of the trend during recent years of restricting voice-frequency phantom-group loading to short- haul facilities. A more comprehensive account of the successful struggle to control cable crosstalk in loaded toll cables is given in a 1935 Bell Telephone Quarterly article^^ by Mr. M. A. Weaver. An A.I.E.E. paper,^ previously referred to, includes considerable additional information on the crosstalk-reduction work on the loading coils, up to 1926. Bibliography 1. George A. Campbell, "Collected Papers," A.T.&T.Co., New York, 1937. Introduc- tion by E H. Colpitts; see also "Three Early Memoranda on Loading," page 10. 2. M. I. Pupin, "Wave Transmission over Non-Uniform Cables and Long Distance Air Lines," Trans. A.I.E.E., Vol. XVII, 1900, p. 445. Also, Pupin U. 5. Patent Nos. 652,230 and 652,231, June 19, 1900. 3. George A. Campbell, "On Loaded Lines in Telephonic Tvdinsmission"— Philosophical Magazine, March 1903 (reprinted in Reference No. 1, based entirely on 1899 the- oretical studies and experiments). 4. Vaschy, La Lumiere Electrique, Jan. 12, 1889. 5. O. Heaviside, "Electromagnetic Theory," Vol. 1, 1893, p. 441. 6. B. Gherardi, "Commercial Loading of Telephone Circuits in the Bell System," Trans. A.I.E.E., Vol. XXX, 1911, p. 1743. 7. Roger B. Hill and Thomas Shaw, "Hammond V. Hayes: 1860-1947," Bell Telephone Magazine, Vol. XXVI, Autumn 1947, pp. 150-173. 8. Thomas Shaw and William Fondiller, "Development and Application of Loadmg for Telephone Circuits," Trans. A.I.E.E., Vol. XLV, Published in Bell System Tech- nical Journal, Vol. V, April 1926, pp. 221-281. 9. Thomas Shaw, "The Conquest of Distance by Wire Telephony," Bell System Tech- nical Journal, Vol. XXIII, October 1944. 10. W. Fondiller and W. H. Martin, "Hysteresis Effects with Varying Superposed Mag- netizing Forces," Trans. AJ.E.E., Vol. XL, 1921. 11. B. Gherardi and F. B. Jewett, "Telephone Repeaters," Trans. AJ.E.E., Vol. XXX- VIII, Nov. 1919. , ^. , . 12. R. S. Hoyt, "Impedance of Loaded Lines and Design of Simulatmg and Compensat- ing Networks," B.S.T.J. April 1923. . ^ ^ ^ 13. Buckner Speed and G. W. Elmen, "Magnetic Properties of Compressed Powdered Iron," Trans. AJ.E.E., Vol. XL, 1921, p. 596. . . r- i. 14. A. B. Clark, "Telephone Transmission Over Long Cable Circuits, Trans. AJ.E.E., Jan. 1923; B.S.T.J., Jan. 1923; Electrical Communication, Feb. 1923. 15. H. S. Osborne, "Telephone Transmission Over Long Distances," Trans. AJ.E.E., Oct. 1923; Electrical Communication, Oct. 1923. ^ , , „. . „ 16. A. B. Clark and R. C. Mathes, "Echo Suppressors for Long Telephone Circuits, rm«5..4./.E.E.,Junel925,p.618. . » r c t r v.i i 17. G. A. Campbell, "Physical Theory of the Electric Wave Filter, B.S.T.J. Vol. 1, Nov. 1922. 204 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 18. J. R. Carson, "Theory of the Transient Oscillations of Electrical Networks and Transmission Systems," Trans. A.I.E.E., Vol. XXXVIII, 1919, p. 345. 19. J. H. Bell, R. B. Shanck and D. E. Branson, "Metallic Polar-Duplex Telegraph System for Cables," Trans. A.I.E.E., Vol. XLIV, 1925. 20. B. P. Hamilton, H. Nyquist, M. B. Long and W. A. Phelps, "Voice-Frequency Carrier Telegraph Systems for Cables", Trans. A.I.E.E., Vol. XLIV, 1925. 21. A. L. Matte, "Advances in Carrier Telegraph Transmission," B. S.T.J. , April, 1940. 22. R. B. Shanck, "Neutralization of Telegraph Cross Fire," B.S.T.J., July, 1926. 23. H. D. Arnold and G. W. Elmen, "Permalloy, An Alloy of Remarkable Magnetic Properties," Journal of the Franklin Institute, Vol. 195, 1923. 24. W. J. Shackelton and I. G. Barber, "Compressed Powdered Permalloy, Manufacture and Magnetic Properties," Trans. AJ.E.E., Vol. 47, 1928, p. 429. 25. W. H. Martin, "Transmitted Frequency Range for Telephone Message Circuits," B.S.T.J., Vol. IX, July 1930. 26. V. E. Legg and F. J. Given, "Compressed Powdered Molybdenum-Permalloy for High-QuaUty Inductance Coils," Bell System Technical Journal, Vol. XIX, 1940, p. 385. 27. J. E. Ranges, "Loading The Spiral-4 for War," Bell Labs. Record, Oct. 1946. 28. A. B. Clark and B. W. Kendall, "Carrier in Cable," B.S.T.J., July 1933. 29. C. W. Green and E. I. Green, "A Carrier Telephone System for Toll Cables," B.S.T.J., Jan. 1938. 30. S. G. Hale, A. L. Qumlan and J. E. Ranges, "Recent Improvements in Loading Ap- paratus for Telephone Cables," Trans. A.I.E.E., Vol. 67, 1948. 31. A. B. Clark and C. W. Green, "Long Distance Cable Circuits for Program Trans- mission," Trans. AJ.E.E., Vol. 49, 1930, p. 1514. 32. M. A. Weaver, "The Long Struggle Against Cable Crosstalk," Bell Telephone Quar- terly, Jan. 1935. Technical Publications by Bell System Authors Other Than in The Bell System Technical Journal Generalizations of the Weiss Molecular Field Theory of Antiferromagnetism* P. W. Anderson.i Fhys. Rev., v. 79, pp. 705-710, Aug. 15, 1950. Abstract — A Weiss field calculation has been carried out for antiferro- magnetism in more complicated structures than the usual calculation allows and has been shown to give results more detailed and more consistent with experimental evidence on the magnetic properties of such structures than does the simpler theory. Atomic Moments of Ferromagnetic Alloys. R. M. Bozorth.^ Letter to the editor. References. Fhys. Rev., v. 79, p. 887, Sept. 1, 1950. Domain Structure of a Cobalt-Nickel Crystal. R. M. Bozorth^ and J. G. Walker.^ Letter to the editor. Fhys. Rev., v. 79, p. 888, Sept. 1, 1950. Recording Fluxmeter of High Accuracy and Sensitivity.* P. P. Cioffi.^ Rev. Sci. Instruments, v. 21, pp. 624-628, July 1950. Abstract — A recording fluxmeter has been developed which employs one or two integrators and a double element L and N Speedomax recorder for tracing magnetization curves directly on standard coordinate paper. The response of the recorder pen drive mechanism is proportional to the flux density, B, and is controlled by the B integrator. The response of the paper drive mechanism is proportional to the magnetizing force, H, and is controlled either by the magnetizing current, when the specimen is in the form of a ring, or by the H integrator when the specimen is in the form of a bar. Ayrton shunt networks provide flexible B and H scale adjustments. High accuracy and sensitivity are obtained by minimizing the causes of drift. At maximum sensitivity, four interlinkages give a deflection of one mm, Young^s Modulus and Its Temperature Dependence in 36 to 52 pet Nickel- Iron Alloys.* M. E. Fine' and W. C. Ellis.^ //. Metals, v. 188, pp. 1120- 1125, Sept. 1950. Abstract — Young's modulus and its temperature coefficient in 36 to 52 pet Ni-Fe alloys depend upon composition and also the straining-anneal- ing history. Alloys near 42.5 pet Ni, when worked cold and then annealed at 400° or 600°C, have nearly zero mean thermoelastic coefficients between — 50° and 100°C. A discussion of the theory is given. * A reprint of this article may be obtained on request to the editor of the B.S.TJ. 1 B.T.L. 205 206 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 Ultra-High Vacuum Ionization Manometer. J. J. Lander.^ Rev. Sci. In- struments, V. 21, pp. 672-673, July 1950. Abstract — This note describes an ionization menometer which indicates pressures more than two decades below the lower limit usually encountered at about 1 X 10"^ mm of Hg with other manometers. This limit depends on the design of the gauge; however, values reported for various gauges do not differ much from that given above. Commonly the limit is observed as a lowest reading obtained despite recourse to more or less drastic methods of producing lower pressures, or a variety of changes in gauge design. The flash filament method of pressure measurement has been used to measure lower pressures and at the same time to indicate the lower limit of an ioniza- tion guage. Metallized Paper for Capacitors.* D. A. McLean.^ I.R.E., Proc, v. 38, pp. 1010-1014, Sept., 1950. Abstract — Metallized capacitor paper is attracting widespread interest as a way of reducing capacitor size. In metallized paper capacitors, the usual metal foil is replaced by a thin layer of metal evaporated onto the surface of the paper. Lacquering the paper prior to metallizing increases the dielec- tric strength and insulation resistance, reduces atmospheric corrosion of the metal, and diminishes the rate of loss of electrode metal by electrolysis. Owing to the extreme thinness of the metal layer, metallized paper capacitors are subject to a type of failure not ordinarily found in conventional capaci- tors. This type of failure consists of the loss of electrode by electrolysis and occurs under d-c. potential when the ionic conductivity is high, as results, for example, from the presence of moisture. For this reason, it is recom- mended that special precautions be taken to keep the ionic conductivity low, in particular with respect to thorough and effective drying and sealing of the capacitor units. Thernwelastic Stress Around a Cylindrical Inclusion of Elliptic Cross Section. R. D. Mindlin^ and H. L. Cooper.^ //. Applied Mech., v. 17, pp. 265-268, Sept. 1950. Abstract — ^The two-dimensional equations of thermoelasticity are solved for the case of a uniform temperature change of an infinite medium con- taining a cylindrical inclusion of elliptic cross section. The problem is treated as one of plane strain in elliptic co-ordinates, and the solution is given in closed form. Formulas and curves are given for the maximum values of various components of stress at the interface between the inclusion and the surrounding medium. Magnetostriction of Permanent Magnet Alloys.* E. A. Nesbitt.^ Bibliog- raphy. Jl. Applied Phys., v. 21, pp. 879-889, Sept. 1950. * A reprint of this article may be obtained on request to the editor of the B. S.T.J. » B.T.L. ARTICLES BY BELL SYSTEM AUTHORS 207 Abstract — In order to obtain a better understanding of the mechanism of coercive force in modern permanent magnets, magnetostriction measure- ments have been made on various alloys having coercive forces from 50 to 600 oersteds. The results can be summarized by discussing two types of alloys. First are the older carbon-hardening permanent magnets, and for these alloys high coercive force and high magnetostriction occur together. Second are the new carbon-free permanent magnets and for these alloys high coercive force does not occur with high magnetostriction. In fact for the Mishima alloys having compositions near 29 per cent nickel, 12.5 per cent aluminum, and 58.5 per cent iron, cooled at the rate of 3°C per second (coercive force 400 oersteds), the magnetostriction actually passes through zero. This is contrary to the classical strain theory of coercive force which states that the latter is proportional to the product of the magnetostriction and internal stress. To explain the mechanism of coercive force for these alloys it is necessary to resort to more recent theories. Stress Analysis for Compressible Viscoelastic Materials * W. T. Read, Jr.' //. Applied Phys., v. 21, pp. 671-674, July 1950. Abstbact — ^Mathematical methods of stress analysis are presented for linear, compressible, viscoelastic, or anelastic, materials such as metals at high temperatures or high polymers with small strains. For such materials stress, strain and their time derivatives of all orders are related by linear equations with coefficients which are material constants. Fourier integral methods are used to show that static elasticity solutions can be used to de- termine the time dependent stresses in viscoelastic bodies with any form of boundary conditions. If stress and double refraction and their time derivatives are also linearly related, the standard photoelastic techniques can be used to determine the directions and difference in magnitude of the time dependent principal stresses, even though the principal stress axes do not coincide with the polarizing axes and both vary with time. When viscoelastic models are used in photoelastic studies, the time variation of the stress distribution in the model represents a first approximation to the dependence of the stress in the elastic prototype on Poisson's ratio. Metallurgy Behind the Decimal Point.* E. E. Schumacher.' //. Metals, V. 188, pp. 1097-1110, Sept. 1950. Abstracts — No one property has a monopoly as to being disproportion- ately affected by minor elements. Nearly all properties are affected, but there is time here to mclude only a selected few. I have chosen, therefore, three of general mterest: strength, magnetic, and electrical properties. I shall inquire into both the mechanisms and consequences of these dispro- * A reprint of this article may be obtained on request to the editor of the B.S.T.J. 1 B.T.L. 208 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 portionate efifects and try to share with you the fascination and challenge of this field. Chain Feed Carries Springs Through Forming Die. J. D. Thompson^ arid G. W. Rada.2 Am. Mach., v. 94, pp. 86-87, Oct. 2, 1950. Punch-Press Tooling Works from Cams, Makes Cams. J. H. Tomlin.^ Am. Mach., v. 94, pp. 106-108, Sept. 18, 1950. Abstract — Literally millions of cam-shape combinations are possible in the telephone-exchange contact cams made for Bell Telephone; yet only two punches and two dies do all the work . . . Two cams are cut at a time from same-size master cams in a punch-press setup that allows a switch to a new cam shape in a matter of seconds. Construction of Cold-Cathode Counting or Stepping Tubes.* M. A. Town- send.^ Elec. Engg., v. 69, pp. 810-813, Sept. 1950. Abstr.\ct — Electronic digital counters are capable of performing at high speeds many of the functions which are performed at low speeds by chains of relays and mechanical stepping switches. Here is described a new principle of tube construction by means of which the position of a glow discharge can be made to step along a row of cold cathodes under the control of input pulses. Ferromagnetic Domains.* H. J. Williams.' References. Elec. Engg., v. 69, pp. 817-822, Sept., 1950. Abstract — Ferromagnetism is based on the property of domains. These are tiny regions within a magnetic substance. They have this special char- acteristic : most of the elementary atomic magnets contained in a particular domain have their spins oriented in the same direction. Domain sizes and shapes are the result of an attempt of the ferromagnetic system to reach a state that minimizes the magnetostatic, magnetostrictive, domain-boundary, and other energies. 416A-Tubefor Microwave Relays. K. P. Dowell.^ FM, v. 10, pp. 20-22, Aug., 1950. Abstract — For construction of its cross-country microwave relay chain, the Bell System required a 4,000-mc. amplifier tube having a greater gain- bandwidth product than any available at the time. The 41 6A planar triode, shown in Fig. 1, was developed especially for this application. Because of its exceptionally close interelectrode spacing, new techniques were necessary for factory production of the tube. It is the purpose of this paper to show some of the unique operations employed in its manufacture and assembly. On the Acoustics of Coupled Rooms.* C. M. Harris' and H. Feshbach. Acoustical Sac. Am., JL, v. 22, pp. 572-578, Sept. 1950. * A reprint of this article may be obtained on request to the editor of the B.S.T.J. » B.T.L. «W.E.Co. ARTICLES BY BELL SYSTEM AUTHORS 209 Abstract — In many acoustically coupled systems the methods of geo- metrical acoustics do not apply. Reverberation formulas as ordinarily used would lead to incorrect results. This paper approaches the problem of coupled rooms from the 'Vave" point of view, treating the coupled rooms as a boundary value problem in obtaining an approximate solution. The results explain some discrepancies noted by earlier researchers between experiment and predictions from geometrical acoustics; for example, the dependence of absorption in a room on the position of the open area which couples the room to an adjacent one. For the case where the window area which couples one room to another is comparable in size with the partition which separates the rooms, the effect of the partition will be least when it is at a particle- velocity node. For the case where the window area is small compared with the partition which separates the two rooms, the effect of the coupling window depends on the square of the unperturbed pressure at the window. Thus the effect of the window varies with position and is least at a pressure node. Experimental data on isolated modes of vibration of a coupled system are given which check the results predicted by this applica- tion of the wave theory. Quantitative Spectrochemical Analysis of Ashes, Deposits, Liquids, and Miscellaneous Samples."^ E. K. Jaycox.^ References. Anal. Chem., v. 22, pp. 1115-1118, Sept. 1950. Abstract — A general technique is described which is appHcable to the quantitative spectrochemical analysis of a wide variety of materials. Sample preparation, the incorporation of spectrochemical buffers, and excitation procedures are discussed for typical cases which illustrate the scope and possibilities of the method. Examples include the analysis of the ashes of rubber, plastics, paper, and cloth; deposits on walls of vacuum tubes and other surfaces; water, oils, and other liquids; and miscellaneous solid ma- terials. Response Peaks in Finite Horns* C. T. Molloy.^ Acoustical Soc. Am., Jl., V. 22, pp. 551-557, Sept. 1950. Abstract — It is the purpose of this paper to discuss the theory of the axial response curves of the class of acoustical systems comprising a driv- ing unit and a finite "Hyperbolic Horn". The term "Hyperbolic Horn" as used in this paper denotes horns of the type first discussed by Salmon. It is proposed to derive an expression from which the response curve may be calculated. A method will also be given by means of which the peaks in this response curve may be located without the necessity of computing the whole curve. Finally the converse problem will be discussed, namely, how to * A reprint of this article may be obtained on request to the editor of the B.S.T.J. 1 B.T.L. 210 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 choose the driving unit and horn parameters so that one of the response peaks will occur at a predetermined frequency. Eard Rubber. H. Peters.' Bibliography. Ind. & Engg. Chem., v. 42, pp. 2007-2019, Oct. 1950. Abstract — The chemical engineer who picks hard rubber for various special uses usually does so on the basis of its availability, its relatively reasonable cost, its good physical and chemical properties, its ease of machin- ing and fabrication, and its excellent resistance to a great variety of chem- icals. This annual review of 1949, like the previous one in 1948 (32), deals with the above in addition to some fundamental studies on natural and synthetic hard rubbers. Heretofore, these basic investigations were usually centered around hard rubber prepared from natural rubber; now there is a decided interest in hard rubber prepared from the synthetics. While ad- mittedly this interest is at a very low ebb, the trend is definitely upward and probably will continue that way for years to come. Holes and Electrons.* W. Shockley.^ Physics Today, v. 3, pp. 16-24, Oct. 1950. Abstract — Some new experiments in transistor electronics are described here in which concepts suggested by theory have been verified directly by experiment. Metallized Paper Capacitors."^ J. R. Weeks.^ I.R.E., Proc, v. 38, pp. 1015-1018, Sept., 1950. Abstract — Metallized paper capacitors are being introduced into tele- phone apparatus wherever size is of prime importance. It is shown that low- voltage metallized paper capacitors with about half the volume of a foil- paper capacitor of conventional design have about the same characteristics as the latter. Performance data are discussed which indicate that such capaci- tors will give long service when used within their voltage rating and when well-protected against moisture. It is pointed out that this type of capacitor should be used within its voltage rating if sparking with its attendant circuit noise is to be avoided. When sparking does occur due to abnormal voltage conditions no permanent damage results. * A reprint of this article may be obtained on request to the editor of the B. S.T.J. 1 B.T.L. Contributors to this Issue R. S. Caruthers, B.S., University of Maryland, 1926; E.E., 1930; M.S., Massachusetts Institute of Technology, 1928. General Electric Com- pany, 1926-28; U. S. Bureau of Standards, 1928-29. Bell Telephone Labora- tories, 1929-. Prior to the war Mr. Caruthers was engaged chiefly in the development of the C, J and K Carrier Telephone Systems. During the war he was engaged in the design of radar equipment. Since the war his principal activities have been as project engineer for the Nl and O Carrier Telephone development. J.J. Gilbert, A.B., University of Pennsylvania, 1909; Harvard, 1910- 11; University of Chicago, 1911-12; E.E., Armour Institute, 1915; Instruc- tor of Electrical Engineering, Armour, 1912-17. Captain, Signal Corps, 1917-19. Bell Telephone Laboratories, 1919-. Mr. Gilbert's work with the Laboratories has been concerned with submarine cable problems. William M. Goodall, B.S., California Institute of Technology, 1928. Bell Telephone Laboratories, 1928-. Mr. Goodall has worked on research problems in connection with the ionosphere, radio transmission and early radio relay studies, radar modulators, microwave radio relay systems, and Pulse Code Modulation. J. L. Merrill, Jr., Pennsylvania State College, B.S. in Electrochemistry, 1928; Elliot Research Fellow, 1928-30; M.S., 1930. American Telephone and Telegraph Company, Department of Development and Research, 1930- 34; Bell Telephone Laboratories, 1934-. With the American Telephone and Telegraph Company Mr. Merrill worked on transmission problems related to the exchange area. After coming to the Laboratories he continued to work on exchange area transmission projects such as the transmission features of the Time and Weather Announcement Systems, Service Ob- serving, Operator Training and like systems. During the war he was en- gaged with a group planning system operation of air raid warning and of tactical wire and radio networks. Since the war his efforts have been directed toward the design and application of repeaters for the exchange area plant. Russell C. Miner, B.S. in Electrical Engineering, University of Cali- fornia, 1929. Bell Telephone Laboratories, 1929-. Mr. Miner has been engaged in work chiefly concerned with the development of acoustical instruments. 211 212 THE BELL SYSTEM TECHNICAL JOUENAL, JANUARY 1951 Edward E. Mott, B.S. and M.S. in Electrical Engineering, Massachusetts Institute of Technology, 1928. General Electric Company, 1926-28. Bell Telephone Laboratories, 1928-. Mr. Mott has been engaged in telephone instruments research and development, particularly in connection with various types of telephone receivers and related devices. During the war he was engaged in underwater sound studies. R. L. Peek, Jr., Columbia College, A.B. 1921; School of Mines, Columbia University, Met. E., 1923. Bell Telephone Laboratories, 1924-. From 1924 to 1936 Mr. Peek was engaged in studies of materials and materials testing. Since 1936 he has been engaged in the development of electromagnetic switching apparatus and (in 1941 to 1945) other applications of magnetics and magnetostriction. Claude E. Shannon, B.S. in Electrical Engineering, University of Michi- gan, 1936; S.M. in Electrical Engineering and Ph.D. in Mathematics, M.I.T., 1940. National Research Fellow, 1940. Bell Telephone Laboratories, 1941- Dr. Shannon has been engaged in mathematical research principally in the use of Boolean Algebra in switching, the theory of communication, and cryptography. Thomas Shaw, S.B., Massachusetts Institute of Technology, 1905. Ameri- can Telephone and Telegraph Company, Engineering Department, 1905-19; Department of Development and Research, 1919-33. Bell Telephone Labora- tories, 1933-48. Mr. Shaw's active telephone career was mainly concerned with loading problems in telephone circuits, including the transmission and economic features of the loading apparatus. The article now being published was started shortly before his retirement in 1948. VOLUME XXX APRIL 1951 no. 2 THE BELL SYSTEM TECHNICAL JOURNAL DEVOTED TO THE SCIENTIFIC AND ENGINEERING ASPECTS OF ELECTRICAL COMMUNICATION The Seventy-fifth Anniversary of the Telephone 213 Seventy-five Years of the Telephone: An Evolution in Technology W. H, Martin 215 An Improved Telephone Set A. H. Inglis and W. L. Tuffnell 239 Pyroljrtic Film Resistors : Carbon and Borocarbon R. 0. Grisdale, A. C. Pfister, and W. van Roosbroeck 271 The Potential Analogue Method of Network Synthesis Sidney Darlington 315 Zero Temperature Coefficient Quartz Crystals for Very High Temperatures W. P. Mason 366 Duality as a Guide in Transistor Circuit Design R. L. Wallace, Jr. and G, Raisbeck 381 Some Design Features of the N-1 Carrier Telephone System W. E. Kahl and L. Pedersen 418 The Evolution of Inductive Loading for Bell System Tele- phone Facilities (Continued) Thomas Shaw 447 Abstracts of Bell System Technical Papers Not Published in this Journal 473 Contributors to This Issue 488 50i Copyright, 1951 $1.50 per copy American Telephone and Telegraph Company per Year THE BELL SYSTEM TECHNICAL JOURNAL Published quarterly by the American Telephone and Telegraph Company 195 Broadway, New York 7, N. Y. Leroy A. Wilson Carroll O. Bickelhaupt Donald R. Belcher President Secretary Treasurer EDITORIAL BOARD F. R. Kappel O. E. Buckley H. S. Osborne M. J. Kelly J. J. Pilliod A. B. Clark R. Bown D. A. Quarles F. J. Feely P. C. Tones, Associate Editor SUBSCRIPTIONS Subscriptions are accepted at $1.50 per year. Single copies are 50 cents each The foreign postage is 35 cents per year or 9 cents per copy. PRINTED IN U. 8. A. The Bell System Technical Journal Vol. XXX April, /pj/ No, 2 Copyright, 1951, American Telephone and Telegraph Company of t(\o (Jcfemonc It was on the 10th of March in 1876, seventy-five years ago, that understandable speech was first sent over a wire. Perhaps the words spoken were not so pro- foundly important as Mr. Bell might have wished for such an historic occasion, but they were important at the moment. He had spilled soms acid and needed Watson^ s help. More significantly, the words ushered in a new era in communi- cation, an era that as Bell envisioned would see the growth of a vast network of wires connecting people together in their own communities, and connecting the communities to each other. The short span of seventy -five years immediately behind us has seen his great vision more than fulfilled. Progress has been achieved step by step and, although many of the steps were small, their cumulative effect over the past seventy-five years is tremendous. Today, hundreds of millions of people take for granted the ability to converse with almost any one, anywhere. The two following papers, one by W. H. Martin, and one by A. H. Inglis and W. L. Tufnell, clearly illustrate this accumulation of technological progress. They deal with the telephone itself, the instrument that Mr. Bell invented. In other fields of telephone development — switching, repeaters, signaling, and now video transmission — the same story emerges. It is a story of steady application of new ideas, improved materials, and improved techniques of measurement and design, applied to making communication faster, easier, and better. And the end is not yet in sight. 213 214 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 A "still" from the sound picture "Mr. Bell" made for the Alexander Graham Bdl centen- nial in 1947. Shortly before the scene depicted above, Mr. Bell had spoken the historic words: "Mr. Watson, come here; I want you." At the time of the photograph Mr. Watson has just rushed in excitedly crying out: "Mr. Bell, I heard every word you said, distinctly." Seventy-five Years of the Telephone: An Evolution in Technology By W. H. MARTIN SEVENTY-FIVE years ago— on March 10, 1876— the inventor spoke and his assistant heard the first sentence to be transmitted by tele- phone: ''MR. WATSON, COME HERE; I WANT YOU." Three days earUer, U.S. Patent No. 174,465 had been granted to Alexander Graham Bell for his concept of means for making the conversion between the air vibrations of an uttered sound and their corresponding electrical undulations. On this historic occasion, Bell talked into his liquid transmitter, and Thomas A. Watson listened to a tuned-reed receiver. In this receiver, shown at the right of Fig. 1, the free end of a steel armature was caused to vibrate by the undulatory currents through an electromagnet. Bell's famous patent showed such a structure with the free end of the reed attached to the middle of a stretched membrane, as at the left of Fig. 1 . In Bell's liquid transmitter, in the middle of Fig, 1, a wire attached to a sound-vibrated diaphragm varied the length of its contact with some acidulated water, and thus produced a resistance changing in accordance with the impinging sound waves. This sound-controlled variable resistance in a battery circuit provided a means of associating amplification with the conversion of speech waves into their electrical counterparts. Thus, the first telephonic transmission of informa- tion demonstrated the two general principles of making the conversion be- tween sound and electricity which have continued to be embodied uni- versally— after much evolution through invention, research and development — in the transmitters and receivers of commercial telephony. Today Bell would be called a scientist. He had been trained for work in the field of speech and hearing. He set himself the problem of transmitting and reproducing speech, which he approached analytically and experi- mentally. Where he thought more knowledge would help him in the solution, he tried to get it. Watson was the engineer of the team; he expressed Bell's ideas in forms for further experimentation and for use. The telephone busi- ness came into being out of such procedures and in a laboratory; that lab- oratory was the progenitor of the Bell Telephone Laboratories. In this anniversary article, it has been deemed appropriate to portray the evolution of the methods and technology, and the scope of the activities in Bell Telephone Laboratories and its predecessors in the line of descent, which have been applied to the development of Bell's telephone instruments to bring them to their present state. This portrayal will show that Bell's 215 216 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 --T^\\-->»?jX. c3 C J^ In Is a"" SEVENTY-FIVE YEARS OF THE TELEPHONE 217 vision of the telephone and his precepts and practices in following it have guided the scientists and engineers who have followed him and still live in the expansion of his activities in these Laboratories which bear his name. Before moving into this evolution of devices, methods and technology, it should be recalled that Bell's vision covered not only the devices which he invented and which formed the basis of telephony, but extended also to the manner of providing a communication system extending throughout the land. While in England in 1878 Bell wrote: ''...it is conceivable that cables of telephone wires could be laid underground, or suspended overhead, communicating by branch wires with private dwellings, country houses, shops, manufactories, etc., etc., uniting them through the main cable with a central office where the wires could be connected as de- sired, establishing direct communication between any two places in the city. Such a plan as this, though impracticable at the pres- ent moment, will, I firmly believe, be the outcome of the intro- duction of the telephone to the public. I believe, in the future, wires will unite the head offices of the Telephone Company in different cities, and a man in one part of the country may com- municate by word of mouth with another in a distant place. . . . Believing, however, as I do, that such a scheme will be the ultimate result of the telephone to the pubhc, I will impress upon you all the advisability of keeping this end in view, that all present arrange- ments of the telephone may be eventually reaUzed in this grand system "^^^ In Bell's prophetic conception of the telephone system, it is evident that there was then in his mind a reaUzation of the invention and development that would be required beyond his work on the telephone itself to make pos- sible the kind of communication system which he envisioned. In "keeping this end in view," there has been a continuing activity over the years to make Bell's telephone perform better and better to meet the requirements of the "grand system." An important factor from this standpoint was em- bodied in Bell's hquid transmitter. It has been the continued development of the variable resistance transmitter that has made available at the talker's position a thousand-fold amplification of the small amount of energy in speech sounds. This has made it possible to use lower cost, smaller wires in the extensive network connecting private dwellings, shops, manufactories and central offices as contemplated by Bell. For the "outside plant" and "central office" portions of Bell's 1878 con- ^"^ This and other information about the early years of the telephone are taken from the well documented book "Beginnings of Telephony" by F. L. Rhodes. Item 1 in Bibliog- raphy at end of this article. 218 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 cept of the "grand system" for local and toll service, there has likewise been continuing invention, research and development over the years for their advancement in performance and application. While it would be necessary to include also these portions of the telephone system to show the extent of the influence on technology of Bell's vision, the activities covered here will be those in the "station" portion of the plant, and primarily those on the transmitter and receiver. In looking back over the progressive development of the telephone, the four factors — invention, experiment, theory, and measurement — may be noted as tending to be dominant in turn for a period. It is perhaps unneces- sary to state that the claimed dominance of any one of these factors in a period does not imply there were not important contributions from the others. It should be added that this succession of dominant factors is not confined to the development of the telephone but exemplifies the progress in adapting other contemporary devices to man's use. It is thought, how- ever, that the development of the telephone has certain distinctions, pos- sibly in degree of complexity and appUcation, and of the effects of subjective performance. After discussing these four factors with respect to the development of the telephone instruments, some brief indications will be given of the great effects of the work on the last two — theory and measurement— on the per- formance and design of these devices in the latter part of this seventy-five year period. Invention Following the transmission of the first sentence, Bell continued to experi- ment in his Boston laboratory and Watson to make models embodying the ideas coming out of this work. By May of 1876, Bell had devised the "iron box"^''^ receiver with its permanent magnet and peripherally supported diaphragm of iron. In October 1876, these two ideas were incorporated in the first "box" telephone^^^ and in May 1877 in the wood-encased hand telephone. ^'^^ This 'box' telephone was used to introduce commercial teleph- ony but was followed soon by the hand-held type. ^^^ Bell's invention stimulated others to work and invent in this field. A series of variable resistance transmitters quickly followed Bell's liquid type. In 1878 Blake invented the platinum-carbon contact transmitter, Edison patented his compressed lamp-black carbon transmitter and Runnings ap- plied for a patent in England on a transmitter containing a pulverized form of carbon to secure a large number of microphonic contact points. Edison's ^^^ Bibliography item 1, p. 30. <«) Ibid., p. 176. W) Ibid., p. 43. («> Ibid., pp. 176, 177. SEVENTY-FIVE YEARS OF THE TELEPHONE 219 patent application on granules of carbonized hard coal was filed in 1886/'^'^ As early as 1878, the idea of mounting both the transmitter and the re- ceiver on a common handle had been invented and such "handsets" were used by boy operators in the 'Gold and Stock' telephone exchange in New York City .3 In 1878, Watson patented his polarized two-gong ringer and designed the hand-cranked magneto for its actuation. The receiver-operated switch- hook was invented in 1877. Patent applications were filed in 1877 covering the association of an induction coil with the transmitter. Thus, by the end of 1878, the general nature and principles of operation of most of the components of the present-day telephone set had been in- vented. One of them, the ringer, has come through the years in a form very similar to its original design. Other components, such as the carbon trans- mitter and the handset, have called for a large amount of research and de- velopment to make the appHcation of the general principles satisfactory for the conditions of modern commercial telephony. Other important inventions which affected the telephone set were the centralized battery for signahng in 1880 and the common battery for both talking and signaling purposes in the latter part of that decade. The bi- polar hand receiver came into use in 1890 and the White solid-back carbon transmitter was invented in 1890. The rotary dial was first used by the Automatic Electric Company in 1896. Figure 2 shows telephone equipment manufactured in 1882 by Charles Williams, Jr., in whose shop Bell had met Watson. This represents an early idea of combining in a unit-mounting the various pieces of apparatus for the use of the telephone. This unit — suitable for installation on the premises of a telephone subscriber — may be taken as typifying the first step toward the telephone station set as we know it. This 1882 telephone set included the Blake transmitter, single-pole hand receiver, ringer, magneto, switch- hook and induction coil. Incidentally, this arrangement of apparatus was later produced by the Western Electric Company which became the manu- facturing organization of the Bell System in 1882. Many changes have taken place in the elements and form of the station sets used in the Bell System since this 1882 set. Certain outstanding steps are illustrated in Fig. 3, showing a deskstand of 1919, the handset of 1927, the combined set of 1937, and the set on which production started in 1950. The 1919 set used a solid-back transmitter and a bipolar hand receiver which were the results of several stages of improvement of the types intro- duced in the 1890's. The 1927 handset required the invention of important changes in the granular carbon transmitter. The 1937 set introduced a new « Ibid., Chap. V. ^> Numbers refer to items in the Bibliography. 220 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 Fig. 2 — Telephone equipment manufactured by Charles Williams, Jr. in 1882. SEVENTY-FIVE YEARS OF THE TELEPHONE 22 1 Fig. 3 — The telephone deskstand of 1919, at top; the handset of 1927, left center; the combined set of 1937, right center; and the 500-type set of 1950, bottom. 222 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 principle of receiver operation and the 1950 set incorporated the invention of a radically new receiver structure. Experiment The solid-back granular-carbon transmitter and the bipolar hand re- ceiver which were introduced in the last decade of the nineteenth century typify in their general structures the telephone instruments of the first quarter of the twentieth, in the Bell System and elsewhere. Throughout most of this period the progress made in telephone instruments may be characterized largely as improvements determined by experiments on modi- fications in details of form. Many important results were obtained in this field by this empirical or "cut and try" method, as was also the case with the other elements of the telephone set and with apparatus in many other fields in this period. That was generally the technology of the time. Progress by "cut and try," however, tends to be cumbersome, slow and unsystematic. The vibrating diaphragms of both transmitter and receiver had their primary resonances in the transmitted range of voice frequencies. By Hsten- ing to the speech sounds reproduced by various structures, judgments w^re made as to their relative merits on the sources of loudness, intelligibihty and naturalness. By such quaUtative tests, the primary resonances of these structures were moved to around one thousand cycles as being the most advantageous location in the audible frequency range. Since the resonance of the vibratory elements of these instruments con- tributed so much to their overall conversion efficiencies, the changes in the design tended to enhance these resonance effects. Improvements came in efficiency, reUability and form, but the resonance effects remained peaked around one thousand cycles. Loudness of the sounds reproduced at the other end of the circuit was of great importance and it was early realized that the ear and mind of the listener can do an amazing job in associating distorted reproduced sounds with those spoken by the talker. So amplifica- tion by the granular carbon in the transmitter and the fostering of efficiency by resonances in both instruments were features of development in this period and played a large role in keeping down the cost of the circuits re- quired for the expansion of telephony. The undesirable effects of resonance were increasingly appreciated throughout this period of experiment, but no practicable means were dis- covered of reducing resonance without sacrificing unduly the loudness of the sounds reproduced in the ear of the listener. Since resonance had to be — and the importance of the loudness was so readily recognized — the efforts were directed to making the most of resonance. An outstanding feature of this period in the progress of the telephone was the difficulty of measuring performance. The technical people then working SEVENTY-FIVE YEARS OF THE TELEPHONE 223 in telephony strove to be quantitative. In their judgments of the relative talking performance of two instruments or circuits, percentage figures were used to show degree of difference. Later the length of trunk in one of the circuits was adjusted to get judged equality of performance and, at the be- ginning of the century, there was adopted the Standard Cable Reference System, with an adjustable network representing a 19-gauge cable pair in the trunk connecting commercial type common battery station sets.* By comparisons and substitutions, numbers of "miles of cable" were associated with relative performances on the basis of effect on the loudness of the re- produced sounds. In 1912, a bulletin was issued for the use of the Bell System Operating Companies — largely the work of O. B. Blackwell — in which quantitative ratings in terms of the cable reference system were placed on the perform- ances of various instruments and sets, and loops and trunks of different gauges of conductors. Theory Around the beginning of the 20th century, the "theory" factor began to Increase significantly. Prior to that, the theoretical material appHcable to telephony was very limited — such as that produced in Europe by Helm- holtz. Hertz, Rayleigh, Poincare and Heaviside. Within a decade, there was produced a wealth of theoretical material dealing specifically with the prob- lems of telephone transmission. This is exemplified outstandingly by the work of G. A. Campbell— his theory of loading,^ from which he developed the theory of the electric wave filter,^ theories of electrical networks as pubHshed in his article "Cisoidal Oscillations"'^ and his exposition of maxi- mum output circuits^ covering aU ways of achieving, with one transformer and one balancing impedance, what has come to be called the "anti-side- tone" station circuit. While some of this work of Campbell's was not pub- lished until later, it was available to his colleagues. The results of these theoretical studies of Campbell and those of his con- temporaries of that time, notably Blackwell, were utilized to explore by computation the transmission of telephonic currents over lines and through the various circuits associated with these lines in central oiOSces and at tele- phone stations. Because of the complexity of many of these circuits and the need for ex- ploring them for the range of frequencies involved in telephonic transmis- sion, use developed of the equivalent network for computing the transmission effects of circuits consisting of pieces of open wire and cable, with the trans- formers, relays and networks associated with them at terminal or switching points. The application of these theories to the solution of telephone net- work problems was presented in books by K. S. Johnson^ and T. E. Shea.^® 224 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 While much of this theoretical material had very little effect at the time upon the development of telephone instruments, it provided a storehouse to be drawn upon later for that purpose by the brilliant concept of an analogy. A further pubUcation to be noted in that first decade of this century is another by Campbell on the use of syllables to measure the efficiency of telephone circuits in reproducing intelUgible speech.^^ Measurement With this sketch of the roles of invention, experiment and theory, the stage is set for the great part to be played by measurement and what it fostered. The major theme of this part may be briefed as the role of measure- ment in promoting and implementing the application of theory to design. In communication by telephone, the performance of the telephone system is inextricably combined with the performances of its users. This relation- ship is close for all the devices of the telephone set which directly involve the user, but is especially so for the instruments. This means that not only are physical measurements needed of instrument performance — input and output sounds and corresponding electrical counterparts — but also subjec- tive measurements of performance involving the talkers and Hsteners — the generation and understanding by them of speech sounds and their reactions to the conditions of telephony. Until the early part of the 20th century there was no means of measuring electrical currents or voltages of the magnitudes and frequencies involved in telephony. Progress in the field of acoustics also had been small because the means for quantitative measurement there were Hmited. For the design of telephone instruments there was little quantitative information as to the relations which should be maintained between the original sounds and the reproduced sounds to provide for their recognition. This situation tempers any criticism against the lack of great progress in the period which was necessarily Hmited to development by "cut and try" and crude qualitative judgments of performance. Physical Measurements The electronic vacuum tube — the epochal invention of Lee DeForest — was first welcomed into telephony as the long-sought means of stretching the toll fines across the country and thus making Bell's ''grand system" cover the nation. Soon after this accomplishment, however, it was recog- nized that the vacuum tube had other important appUcations — as an ampli- fier for measuring the currents and voltages^- of telephony and as an oscil- lator in generating currents of the frequencies in the voice range. For a short time prior to the availability of the vacuum tube, the Vreeland mer- SEVENTY-FIVE YEARS OF THE TELEPHONE 225 cury-arc oscillator^^ was used as a source of currents for measurement with a thermocouple operating a galvanometer. Telephone circuits were measured by these cumbersome means but there were limitations to the range of fre- quencies and levels. This oscillator was used also with various forms of bridges for measuring the impedances of lines and apparatus. The vacuum tube amplifier and oscillator quickly opened up the electrical measurement of telephone circuits at the levels of speech current and re- placed the laborious computation of circuit performance. Also the amplifier made it possible to use the oscillographs of the time to make photographic records of speech currents and of single frequency currents of corresponding levels.^'*' ^^ These measurements and records revealed a lot about telephone transmission properties of lines and apparatus and put the design of trans- formers^® and other circuit elements on a better basis. In 1915 a proposal was made by Dr. H. D. Arnold, the carrying out of which had momentous effects. The proposal was that the vacuum tube amplifier be associated with as nearly perfect devices as could be developed to carry out the functions of transmitter and receiver and by these means to create a practically perfect telephone transmission system which would approach air transmission. With the large amplification available, it would be possible to utilize transmitters and receivers in which efficiency of con- version could be sacrificed to the extent necessary to approach freedom from distortion. Arnold also had the conception that, with this nearly perfect transmission system, the effects of distortion on the intelligibility of reproduced sounds could be studied in a controlled manner — that is, distortion could be in- troduced into the electrical part of this transmission system by electrical networks and therefore be specifiable and reproducible. In carrying out this proposal, Crandall and then Wente worked on the development of the required transmitters and receivers and from this work came the condenser transmitter^"^ ■ ^^ and later the high quaUty moving coil receiver.^ ^ From this activity then came some more important concepts and results. A transmitter of the condenser type which was stable and uniform in re- sponse over a wide range of frequencies was used with an amplifier operating into a meter to give a direct-reading indication of the magnitude of sounds even at quite low levels. With this there was developed^o- 21. 22 the theory of the thermophone as a means of setting up, in a specified closed chamber associated with the condenser microphone, an absolute level of sound, so that the combination of the condenser transmitter and amplifier could then be used to give an absolute measurement of the intensity of a sound field at a point. This made possible the absolute measurement of sound over the range of intensities and frequencies involved in speech and hearing. By 226 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 associating a probe tube with the condenser transmitter, absolute measure- ments of sound intensity could be made in the ear canal. This method of sound measurement led also to the closed-coupler artificial ear^' ^'* means of measuring the acoustic output of a telephone receiver under specified conditions approximating those of a typical human ear. Another important measuring device derived from this work was the volume indicator^^' ^^ whose rate of response to the fluctuations of speech sound energy was made to approximate the ear in this respect. This indicator when connected through a suitable amplifier to a telephone circuit could be used to measure the level of speech currents at that point. When a volume indicator was associated through an amplifier with a suitable pickup micro- phone it became a sound level meter for giving a measurement of the level of the complex tones of speech, music and noise. Another device made practicable by the availability of the vacuum tube amplifier was the loudspeaker. This permitted suitable sound levels to be delivered by loudspeakers^^- ^^' ^^ which were progressively freed from dis- tortion as the theory and technique of electroacoustic devices was advanced. The loudspeaker was employed in the artificial mouth^'* as a means of pro- ducing speech sounds of prescribed character and level for the testing of transmitters. This combination of sound and electrical level meters, artificial mouth and ear, provided for the measurement of the physical performance of trans- mitters and receivers over the frequency range involved in telephony, for the levels at which they were operated and with both speech sounds and single frequency tones. The overall physical performance of these devices were thereby brought to quantitative determination. With this situation the "standard cable system" was replaced as a refer- ence system in the latter part of the twenties by what wafe termed the "Master Reference System for Telephone Transmission. "^ 9 This system — an outgrowth of Arnold's "perfect" transmission system — with the thermo- phone means for absolute calibration of the transmitter and the closed coupler arrangement for absolute calibration of the receiver, provided a telephone reproducing system, the performance of which was specifiable in absolute physical terms. Means were furnished in this Master System for including distortion networks to make the idealized instruments of the reference system approximate the characteristics of the instruments used commerically; this distortion facilitated loudness balances with commercial instruments and circuits. This reference system became the reference for expressing loudness reproducing efficiency of commercial circuits and their components. It was adopted as a standard by the Bell System and by the CCLF.t t Comite Consultatif International Telephoniquc. SEVENTY-FIVE YEARS OF THE TELEPHONE 227 Siibjective Measurements We come now to the carrying out of Arnold's concept of using this refer- ence system as a means of investigating the effects of distortion on the recog- nition of reproduced speech sounds. This was first started in the Laboratories under Crandall and then continued under Fletcher and his associates. This work involved the use of people as meters, with the problems of their cali- bration. For such tests, lists of monosyllables were prepared which went far be- yond the simple lists proposed by Campbell. A large amount of work was done in the determination of the basic sounds to be used, the most suitable form of syllables and the arrangement of syllables in groups to have balance with respect to their content of basic sounds.^ ° Starting with the earlier versions of the Master Reference System, the effects were measured by these articulation tests of changes in loudness, distortion and accompanying noise, on the understanding of the reproduced sounds and syllables. This study of distortion included resonance such as characterized commercial instruments and the variation of response with frequency as encountered in commercial circuits. Also, extensive articulation tests and analyses were devoted to the fundamental investigation of the effects of bandwidth as provided by electric wave filters of the Campbell type, and from these was derived a quantitative determination of the im- portance of the different parts of the transmitted band on the recognition of the reproduced sounds of speech. This work is described in Fletcher's book "Speech and Hearing"^^ and in many papers Hsted in the bibliog- raphv ^^' ^^' ^^' ^^' ^^' ^^ From this work there was developed also a procedure for computing the articulation of a telephone circuit from the physical characteristics of the circuit. With the availabihty of this computational method^^- ^^ it has been practical to discontinue articulation testmg itself except for special purposes. Another factor which comes into telephony as an important effect in the use of the telephone is "sidetone." The speaker's voice reaching his own ear through the sidetone path of the telephone set reacts on his loudness of talking, this loudness being decreased unconsciously as the sidetone is increased. Also, in Hstening, sidetone introduces into the listening ear the room noise picked up by the transmitter. Both of these effects of sidetone were studied in the laboratory under controlled conditions, so that an ap- preciation was obtained of the magnitude of their effects. There still remain the question as to applicability of the effects of vol- ume, distortion, noise and sidetone as determined in the laboratory to com- mercial telephony with the conditions uncontrolled at the telephone stations and the users untrammeled in their habits and reactions. Information re- 228 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 garding this extension was obtained by observations on circuits covering a range in the various factors affecting transmission, and a count made of the number of repetitions which were requested per unit time by the users in carrying on normal telephone conversations. This repetition-rate method of measuring performance of telephone circuits bridged the gap between the laboratory and the plant, and established a relation between physical and subjective measurements in the laboratory and subjective results in service. '*°''^^ In fact, the rating method derived from the repetition count observations was needed to prove that the effect of the reduced sidetone of the anti-sidetone circuit was sufficient to offset the additional circuit losses, complexity and cost of that circuit and so to justify its general use. The development of the idealized transmission system and of the devices for measuring the electrical and acoustic inputs and outputs of telephone instruments, and the carrying out of the articulation and repetition rate measurements, together with the analyses of their results and deduction of relationships, required a large amount of activity for about fifteen years from the time of Arnold's concept, to cover the scope outhned here. Sub- sequent work has been directed to refining the devices and the results. This work of physical and subjective measurement produced the knowl- edge of the performance characteristics which telephone transmitters and receivers should have and also the way to specify and analyze their per- formance— in other words, what to strive for in the development of new designs and how to determine the degree to which it has been attained. Design Theory The work which was done in developing the transn^itters and receivers for the idealized transmission system promoted an evolution of the theory of the vibratory elements of such devices, including the effects of the as- sociated air chambers. From this came large advances in the theoretical understanding of electro-acoustic converters, as exemplified by the book of Crandall "Theory of Vibrating Systems and Sound"^^ ^nd pubhcations by Wegel,^^ Wente^^' ^ and others. One further concept was necessary to bring the design theory on instru- ments to its present level. As has been discussed earlier, the analysis of telephone circuits from the electrical standpoint made extensive application of the idea of the equivalent network. The new concept involved two steps: One was that the theory of electro-acoustic devices could be reduced to the simplicity of electrical network theory by using electrical analogs for the vibrating system. This was well brought out by R. L. Wegel in his paper of 1921«. The second step, promoted by H. C. Harrison,^^' *^ E. L. Norton and others, was that mechanical wave transmission systems could be de- signed as analogs of electric circuits. SEVENTY-FIVE YEARS OF THE TELEPHONE 229 This concept brought to bear on the development and design of electro- acoustic devices all the wealth of electrical transmission theory and meas- urement techniques, and especially the Campbell filter idea of designing a system to transmit efficiently a band of frequencies. With this analytical method, the means of controlling resonance could be explored quantitatively and systematically. Also thereby, means could be studied of compensating for limitations in the behavior of one part of the network by corrective measures elsewhere. This electrical analog equivalent network concept not only facilitated the analysis of the overall performance of electro-acoustic devices but also made possible the study of the contribution of each element and of changes in each characteristic of each element to that performance. This could be done, mathematically or by measurement, on the simulating electrical network. Such studies promoted the understanding of the functioning of such devices and indicated what needed to be done to improve their performance. This method of analysis made it readily possible to determine the effect of modi- fications in the material properties and dimensions of the mechanical and magnetic parts, and of damping and dissipation in the acoustic elements. This pointed the way to meeting the response characteristics which were shown to be desirable by the subjective measurements on the intelligibility of reproduced sounds. With this technique, advances can be made intelUgently in the kinds of materials*^ used for the diaphragms of instruments and for the other mag- netic parts of receivers; and the designer has been put in the position not solely of considering the materials that are offered to him by the metal- lurgist and other material engineers, but also of giving to them the speci- fications of desired properties. Incidentally, this specific tailoring of the characteristics and dimensions of the material to the performance require- ments of the part in which it is used is an important factor in the miniaturi- zation of apparatus and in minimizing in its design the old "factor of safety" (or "factor of ignorance" as it might be termed with present technology). Design for Performance With this evolution, the technology of telephone transmitters and re- ceivers has made great progress since the beginning of the era of measure- ment. The situation will be indicated by considering the development and design of these instruments from several aspects and by noting certain salient accomplishments. By "design for performance" is meant the process of determining the per- formance characteristics to be striven for, then developing systematically the means for meeting them and embodying these means in a suitable op- erating design. In selecting the performance objectives, due regard must of 230 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 course be given to the likelihood of their achievement. In the era when ex- periment was the dominant factor in development, advancement in per- formance was largely expressed in terms of the modification which was tested. The results of this era of measurement began to have their effect on the design of commercial telephone instruments about twenty-five years ago. Though the idea of a handset goes back to the early days of telephony^ it was not found out until the middle 1920's how to get, in the instruments of a handset, service performance comparable to that afforded by the then available instruments when supported and separated as they were in the wall set and deskstand set. There were two important limitations to achieving this result — one, the so-called "howling" resulting from the coupling be- tween the diaphragm of the transmitter and the diaphragm of the receiver; and the other, the degradation of the performance of the granular carbon transmitter with position. The importance of the amplification provided by this granular carbon on the design of the telephone plant has been indicated and it was the magnitude of this amplification and the resonances in the instruments that caused the howling difficulty in the handset. With such instruments directly coupled mechanically, the howling problem was diffi- cult to solve .^^ In the early twenties, in the development of the handset which was made available in 1927, the coupling factor between the diaphragms of the two instruments was measured for a variety of proposed designs of handle; and the development and selection of the design was dn the basis of a handle having resonance out of the range of the instruments used and of such ma- terial as to provide dissipation of energy in this mechanical transmission path.49 The other factor that made possible the solution of this problem was the development of a transmitter in which the vibratory system was essentially free from resonance and the positional effect of the carbon chamber was materially reduced. This transmitter — the first non-resonant transmitter^^ in commercial telephony — gave a decrease in the magnitude of the electrical output. It was demonstrated, however, by articulation and repetition-rate tests, that the reduction in loudness output was compensated for by the lower distortion of the reproduced sounds; and hence the combination of higher quality with decreased loudness gave a resultant intelligibility in service comparable to that obtained with the then available deskstand trans- mitter. The change in transmitter response is shown by a comparison of curves A and B of Fig. 4(a). The elimination of sharp resonances gives an additional improvement in transient response. A comparison of curves A and B of Fig. 4(b) shows that the small receiver of the 1927 handset was made to give the same performance as the preceding SEVENTY-FIVE YEARS OF THE TELEPHONE 231 ^5 UJ z Q (n> (/).Q - tro cr 11^ CD Qt- ^^ -20 -25 -30 -35 TRANS- MITTER 323 (1919 DESK STAND) (a) Fl (1937 COMBINED SET) lD 1 \ r^/^ \ N >^/ ■^' \ \ 1 » • / V / J\ \ \ 1, \ V 1 1 / / / \ \ ^ \ x^ / \ \ \ \ \ A/. X^ ^^ \ \ \ / / / , / V 1 1 1 1 1000 FREQUENCY IN 1500 2000 2500 3000 CYCLES PER SECOND 4000 5000 Fig. 4 — (a) Artificial mouth response of the station set transmitter; (b) available power response of station set receiver. larger hand-held receiver. This was the result of improved magnetic circuit and materials. The handset of 1937^°- " included a new design of transmitter which was made available about 1934 for use in the earlier handset. In this transmitter the freedom from resonance was preserved and the effect of the improving 232 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 analytical and quantitative approach is demonstrated by the much higher electrical output than that of the 1927 transmitter. This is shown by the comparison of Curves B and C of Fig. 4(a). For the 1937 handset, the objective was set of making the receiver also free of resonance. The method of obtaining this result in terms of the equiv- alent electrical circuit is discussed in the W. C. Jones paper^^ of 1938, which shows also the electrical analog for the transmitter of this handset. A com- parison of the receiver of the 1927 and 1937 handsets is given by Curves B and C of Fig. 4(b). It is seen that the diaphragm resonance is completely eliminated. The Jones paper indicates how the air spaces associated with the diaphragm and an acoustic resistance element are employed to control the motion of the diaphragm. In the 1937 receiver, three special magnetic alloys are employed — per- mendur for the diaphragm, 45 percent permalloy for the pole pieces and remalloy for the magnets. In the manufacture of these receivers, each one is magnetized to its optimum value. ^° In the instruments of the telephone set of 1950, the appUcation of these design procedures has been carried still further. As brought out in a cur- rently published paper,^^ the performance requirements for these instruments were set on the basis of what it was desired to have in the way of bandwidth, frequency characteristics, and efficiency. The instruments were then devel- oped to attain these characteristics. The response of the 1950 transmitter is shown by Curve D in Fig. 4(a). The shape of this response was deliberately planned to be as shown in order to approach the characteristic of the air transmission path. The gain over Curve C of the 1934 transmitter is obtained with a decreased size of dia- phragm and unit. Also in the 1950 transmitter, a further improvement has been made in the granular carbon to increase its stabihty with time. For many years, in- tensive studies^^' ^ have been made of the performance of granular carbon in the telephone transmitter to understand the contact action and to deter- mine the causes of aging with use and time, and the means of alleviating these effects. From these and other studies of the structure of the chamber containing the carbon, have come remarkable results in improving the per- formance of this very critical mass of loose granules. It has been stated that the telephone system is built around a loose contact which is a thing that the electrical engineer hopes to avoid. The fact is that, today as a result of all this work which has been done on the use of granular carbon in the trans- mitter, Uttle of value would be gained in the quality of reproduction in commercial telephony by the replacement of the current desgins of this simple low-cost means of making the conversion between acoustic and elec- trical energy, by a combination of a passive device with a vacuum tube form SEVENTY-FIVE YEARS OF THE TELEPHONE 233 of amplification. Furthermore, the carbon transmitter has been made to behave well with respect to position, use and time. The 1950 receiver, invented prior to World War II, involves a radically new structure — a receiver having a composite diaphragm with an outer an- nular portion of magnetic material and an inner circular part of domed impregnated fabric. This invention was stimulated by the analytical demon- stration of the benefits of a diaphragm of low dynamic mass. A paper^^ published in the January 1951 issue of this Journal gives the theory of this receiver and describes the manner in which it was developed and designed to have the projected performance. That presentation shows the high level which the technology of the design of such devices has now reached. From Curve D of Fig. 4(b), it is seen that this latest receiver is 5 db more efficient than the 1937 design and reproduces a wider frequency range. The dropping of the response at the lower end is intentional to avoid increasing the interference from power systems. ^^ By these extensive studies in theory, the development and application of physical and subjective measurements, and the advanced technology of de- sign, the present generation of the descendants of Bell's transmitter and receiver approach in their performance the inherent limitations of the struc- tures and materials, with the compromises that are chosen in the interests of quaUty and cost of production, and ruggedness and uniformity in use. As embodied in the 1950 set, the efficiencies of conversion of the transmitter and receiver are now so high that, on the shorter loops, losses are automat- ically introduced in order to avoid the delivery of sounds of too great loud- ness to the ear of the listener. Design for Production Since the war, production of the instruments of the 1937 type handset reached a rate of around five million a year apiece. This production has demonstrated that devices of such sensitivity and refinement in design can be made in large quantity with closely controlled quaUty and at low cost. The analytical quantitative approach to design in the case of these instru- ments has been an important factor in the adaptation of these designs to quantity production with present manufacturing techniques. Such produc- tion may call for changes from the designer's ideas as to the properties of the materials, their fabrication or the tolerances to be met. With the ana- lytical quantitative approach to design, the effect of such changes can be readily evaluated, and proper judgments reached as to whether such com- promises with the design are justified in the interests of control of product and lower costs. Such judgments can be made without the necessity of ex- ploring the range of possibihty by a series of models. Furthermore, to carry out such kind of production, many of the meas- 234 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 uring devices, such as the artificial mouth, artificial ear, with calibrated condenser transmitters and oscilloscopes, are carried to the factory assembly line to measure precisely each instrument as produced. In the case of the instruments of the 1950 set, knowing that they were destined for large scale production by modern machines, tools, processes and assembly lines, the design for production was carried along with the design for performance. Thus the dictates of theory and laboratory per- formance were being continuously matched with those of fabrication and cost. Design for Service It has long been the practice in the Bell System to make trials in the operating plant of laboratory models or samples from the initial production of new designs. This has two major purposes — one to determine functioning under service conditions and the other to detect if there are weaknesses which may result in unexpected deterioration or failure. In addition, routine and special studies are made of service performance and troubles through- out the use of a device or system. As a result, information is continually being supplied to the designers to show the benefits of improvements and the needs for changes. This knowledge of service functioning and main- tenance can thus be coordinated with the procedures which have been termed "design for performance" and "design for production." In the de velopment of new designs or the modification of current ones, the Bell Tele- phone Laboratories designer is in a position to integrate concurrently the dictates not only of the laboratory and of the factory, but also those of service performance. This "design for service" can be carried out in the interest of getting the optimum ratio of service for the users, to the cost of employing the device in the plant, including not only the carrying charges on the initial price but also the cost of its operation and maintenance. Since the customers of the telephone system are paying for service and not buy ing equipment, the purpose of "design for service" is directed toward the goal of giving the most service for the money. One result of this integration of plant experience into design has been a reduction in the last fifteen years of four to one in the service troubles with telephone instruments in the Bell System plant. These devices now approach the performance in this respect of many passive circuit elements. Conclusion In closing this scant presentation of the scope and results of the ac- tivities which have been carried on in Bell Telephone Laboratories primarily to improve the telephone devices invented by Alexander Graham Bell, men- tion should be made of the many important benefits which have been de- SEVENTY-FIVE YEARS OF THE TELEPHONE 235 rived from this work in other fields. The condenser transmitter developed for the ideal telephone transmission system was the pickup microphone used in the introductory period of public address systems, radio broadcasting, electrical recording for phonograph reproduction and both disc and film recording for sound pictures. Subsequent other high quaUty micro- phones^^~^^ in these fields and the succession of loudspeakers^^"^ of increasing quality of reproduction owe their development to the same techniques which were evolved to improve Bell's instruments. The same techniques of design were applied also to the light valve^- ®^ for film records, the electrical re- corders^- ^^' " for disc records and to the many types of reproducers.^^ Thus this technology of telephone instruments has had widespread application in the mass use of sound reproduction in the phonograph, sound pictures and broadcasting. Another application which would have been especially pleasing to Dr. Bell was that to the microphones and receivers of hearing aids^^"'^^ and to the measurement of hearing impairments^ ^'^^. Also of interest to him would have been the contributions which these measuring techniques have made to the work on the nature of speech and hearing. In addition, these measurement tools and devices derived from them have provided solutions to many problems of architectural acoustics, and of noise and vibration reduction. In World War II, this technology made it possible to determine quickly the desirable performance characteristics of microphones and receivers suit- able for the high noise conditions of military applications such as in planes and tanks, and to develop the structures to provide this performance and meet the other miUtary requirements. In the submarine field, this tech- nology was applied to develop rapidly the instruments and methods for the measurement of underwater sound and to design and improve the various acoustic devices employed in that field.^^ The analytical quantitative equivalent network method of design for per- formance, which has been applied in such a refined manner and so success- fully to electro-acoustic devices, has been extended to mechanisms outside the acoustic field. Many of those who participated in pioneering this kind of design in acoustic devices are now engaged in the Laboratories on the development of improved mechanical devices. This method is a powerful tool but requires a type of training which is beyond that generally offered to mechanical designers; their studies might well be directed along the lines of the material in some of the articles cited here. All this constitutes a wonderful illustration of the manner in which the results of research and fundamental development in a particular field and for a particular purpose can ramify into other fields, and have as by-prod- 236 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 ucts many other important applications. One indication of this ramification is the widespread use of the "db", the unit which was originally adopted for telephone transmission work. While this evolution in technology, which has been outlined here, has been presented in its application to the telephone transmitter and receiver, it is in keeping generally with the progress of the technology of the times. To expand a previous statement, this apphcation has claims to distinction in the degree to which it has been necessary to go in measuring subjective performance, and in the degree to which it has been possible to go in inte- grating the dictates of the laboratory, factory and field in making "design for service" approach its goal of maximum ratio of service to cost. Although only a few have been named here, many have taken part in this evolution in technology. These many are collaborators in this anniver- sary article and in furthering Bell's vision of the "grand system." Bibliography 1. Beginnings of Telephony, F, L. Rhodes, Harper & Bros., New York and London, 1929. 2. The Development of the Microphone, H. A. Frederick, Bell Tel. Qiiarterly, V. 10, July 1931, pp. 164-188. 3. Early Handsets, H. A. Frederick, Bell Lab. Record, V. 12, July 1934, pp. 322-326. 4. The Transmission Unit and Telephone Transmission Reference Systems, W. H. Martin, A.I.E.E. JL, V. 43, June 1924, pp. 504-507. 5. On Loaded Lines in Telephonic Transmission, G. A. Campbell, Phil. Mag. V. 5, March 1903, pp. 313-330. 6. Physical Theory of the Electric Wave Filter, G. A. Campbell, Bell System Tech. Jour., Nov. 1922, V. 1 pp. 1-32. 7. Cisoidal Oscillations, G. A. Campbell, A.I.E.E. Proc, V. 30, April 25, 1911, pp. 789- 824. 8. Maximum Output Networks for Telephone Sub Station and Repeater Circuits, G. A. Campbell and R. M. Foster, A.I.E.E. Trans. V. 39, Part 1, Feb. 1920, pp. 231- 290. 9. Transmission Circuits for Telephonic Communication, K. S. Johnson, third printing, Van Nostrand, N.Y., 1927. 10. Transmission Networks and Wave Filters, T. E. Shea, Van Nostrand, N. Y., 1929. 11. Telephonic Intelligibility, G. A. Campbell, Philosophical Mag., 6th Series, V. 19, January 1^10, pp. 152-159. 12. Historic Firsts— Vacuum Tube Voltmeter, Bell Lab. Record, V. 24, July 1946, pp. 270 and 274. 13. Patenls 829,447 and 829,934 issued to F. K. Vreeland. 14. A Dynamical Study of the Vowel Sounds, I. B. Crandall, and C. F. Sacia, Bell Sys. Tech. Jour., V. 3, April 1924, pp. 232 to 237. 15. The Sounds of Speech, I. B. Crandall, Bell Sys. Tech. Jour., V. 4, October 1925, pp. 586 to 626. 16. Telephone Transformers, W. L. Gasper, AJ.E.E. Trans., V. 43, February 1924, pp. 443-456. 17. A Condenser Transmitter as a Uniformly Sensitive Instrument for the Absolute Measurement of Sound Intensity, E. C. Wente, Phys. Rev., V. 10, pp. 39-63, July 1917. 18. Historic Firsts— The Condenser Microphone, Bell Lab. Record, V. 21, July 1943, p. 394. 19. Moving Coil Telephone Receivers and Microphones, E. C. Wente and A. L. Thuras, Bell Sys. Tech. Jour., V. 10, October 1931, pp. 565-576. 20. The Thermophone as a Precision Source of Sound, H. D. Arnold and I. B. Crandall, Phys. Rev., V. 10, July 1917, pp. 22-38. 21. The Thermophone, E. C. Wente, Phys. Rev., V. 19, April 1922, pp. 333-345. SEVENTY-FIVE YEARS OF THE TELEPHONE 237 22. Historic Firsts— The Thermophone, Bell Lab. Record, V. 22, November 1943, p. 105. 23. Telephone Transmission Reference System, L. J. Sivian, Elec. Comm., V. 3, October 1924, pp. 114-126. . 24. A Voice and Ear for Telephone Measurements, Inglis, Gray and Jenkins, Bell Sys. Tech. Jour., V. 11, April 1932, pp. 293-317. 25. Public Address Systems, I. W. Green and J. P. Maxfield, A.I.E.E, Trans., V. 42, February 1923, pp. 64-75. 26. Speech Power and Its Measurement, L. J. Sivian, Bell Sys. Tech. Jour., V. 8, October 1929, pp. 646-661. 27. New 548 Type Loud Speaking Telephone, Bell. Lab. Record, V. 6, December 1925, pp. 160-163. 28. A High Efficiency Receiver for a Horn Type Loudspeaker of Large Power Capacity, A. L. Thuras and E. C. Wente, Bell Sys. Tech. Jour., January 1928, pp. 140-153, V. 7. 29. Master Reference System for Telephone Transmission, W. H. Martin and C. H. G. Gray, Bell Sys. Tech. Jour., V. 8, July 1929, pp. 536-559. 30. Articulation Testing Methods by Fletcher and Steinberg, Bell Sys. Tech. Jour., V. 8, October 1929, pp. 806-854. 31. Speech and Hearing, H. Fletcher, D. Van Nostrand, N. Y., 1929. 32. The Nature of Speech and Its Interpretation, H. Fletcher, Bell. Sys Tech. Jour., July 1922, V. 1, pp. 129-144. 33. Physical Measurements of Audition and Their Bearing on the Theory of Hearing, H. Fletcher, Bell Sys. Tech. Jour., V. 2, October 1923, pp. 145-180. 34. The Physical Properties of Speech, Music and Noise and Their Relation to Transmis- sion Problems, H. Fletcher, B.T.L. Reprint B-94-1. (An address before N.Y. Tel. Soc. and N.Y. Elec. Soc, February 1924.) 35. The Dependence of the Loudness of a Complex Sound Upon the Energy in the Various Frequency Regions of the Sound, Fletcher and Steinberg, Fhys. Rev., V. 24, Sep- tember 1924, pp. 306-317. 36. Effects of Distortion upon the Recognition of Speech Sounds, J. C. Steinberg, Acousti- cal Soc. of America Jl., V. 1, October 1929, pp. 121-137. 37. Developments in the Application of Articulation Testing, T. G. Castner and C. W. Carter, Jr., Bell Sys. Tech. Jour., V. 12, July 1933, pp. 347-370. 38. Factors Governing the IntelligibiHty of Speech Sounds, French and Steinberg, Acous- tical Soc. Am. JL, V. 19, pp. 90-119, January 1947. 39. The Perception of Speech and Its Relation to Telephony, Fletcher and Gait, J.A.S.A., V. 22, No. 2, March 1950, pp. 89-151. 40. Rating the Transmission Performance of Telephone Circuits, W. H. Martin, Bell Sys. Tech. Jour., V. 10, January 1931, pp. 116-131. 41. A System of Effective Transmission Data for Rating Telephone Circuits, F. W. McKown and J. W. Emling, Bell Sys. Tech. Jour., V. 12, July 1933, pp. 331-346. 42. Theory of Vibrating Systems and Sound, I. B. Crandall, D. Van Nostrand, N.Y., 1926. 43. Theory of Magneto-Mechanical Systems as Applied to Telephone Receivers and Simi- lar Structures, R. L. Wegel, AJ.E.E. JL, V. 40, October 1921, pp. 791-802. 44. Acoustical Instruments, E. C. Wente, Bdl Sys. Tech. Jour., V. 14, July 1935, pp. 388^12. 45. Methods of High Quality Recording and Reproducing of Music and Speech Based on Telephone Research, J. P. Maxfield and H. C. Harrison, Bell Sys. Tech. Jour., V. 5, July 1926, pp. 493-523. 46. Historic Firsts— The Orthophonic Phonograph, Bell Lab. Record, V. 24, August 1946, pp. 300-301. 47. Magnetic Materials in the Telephone System, V. E. Legg, Bell Sys. Tech. Jour., V. 18, July 1939, pp. 438-464. . . 48. The Theory of the Operation of the Howling Telephone with Experimental Confirma- tion, H. Fletcher, Bell Sys. Tech. Jour., V. 5, January 1926, pp. 27-49. 49. The Development of a Handset for Telephone Stations, A. H. Inglis and W. C. Jones, Bell Sys. Tech. Jour., V. 11, April 1932, pp. 245-263. 50. Instruments for the New Telephone Sels, \V. C. Jones, Bell Sys. Tech. Jour., V. 17, July 1938, pp. 338-357. 51. Transmission Features of the New Telephone Sets, A. H. Inglis, Bell Sys. Tech. Jour., V. 17, July 1938, pp. 358-380. 52. An Improved Telephone Set, A. H. Inglis and W. L. Tuffnell, Bell Sys. Tech. Jour., V. 30, April 1951. 238 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 53. Microphonic Action in Telephone Transmitters, F. S. Goucher, Bell Lab. Record, V. 8, August 1930, pp. 566-569. 54. The Carbon Microphone: An Account of Some Researches Bearing on Its Action, F. S. Goucher, Bell Sys. Tech. Jour., V. 13, April 1934, pp. 163-194. 55. The Ring Armature Telephone Receiver, E. E. Mott and R. C. Miner, Bell Sys. Tech. Jour., V. 30, No. 1, January 1951, pp. 110-140. 56. A Moving Coil Microphone for High QuaUty Sound Reproduction, W. C. Jones and L. W. Giles, //. ofSoc. of Motion Pic. Engrs., V. 17, December 1931, pp. 977-993. 57. An Efl&cient Miniature Condenser Microphone System, H. C. Harrison and P. B. Flanders, Bdl Sys. Tech. Jour., V. 11, July 1932, pp. 451-461. 58. A Non-Directional Microphone, R. N. Marshall and F. F. Romanow, Bell Sys. Tech. Jour., V. 15, July 1936, pp. 405-423. 59. A Tubular Directional Microphone, W. P. Mason and R. N. Marshall, //. A.S. of A., V. 10, January 1939, pp. 206-215. 60. New Microphone Providing Uniform Directivity Over Extended Frequency Range, R. N. Marshall and W. R. Harry, //. A. S. of A., V. 12, April 1941, pp. 481-498. 61. An EflBicient Loudspeaker at the Higher Audible Frequencies, L. G. Bostwick, //. A.S. of A., V. 2, October 1930, pp. 242-250. 62. Auditory Perspective — Loudspeakers and Microphones, E. C. Wente and A. L. Thuras, Bell Sys. Tech. Jour., V. 13, April 1934, pp. 259-277. 63. Modem Theater Loudspeakers and Their Development, C. Flannagan, R. Wolf and W. C. Jones, S.M.P.E. Jl., V. 28, pp. 246-263, March 1937. 64. Patents 1,638,555 and 1,656,255 issued to E. C. Wente. 65. The Principles of the Light Valve, Shea, Herriot and Goehner, Soc. of Motion Picture Engineers Journal, V. 18, pp. 697-731, June 1932. 66. Recent Developments in Hill and Dale Recorders, L. Vieth and C. F. Wiebusch, S.M.P.E. JL, V. 30, January 1938, pp. 96-104. 67. Lateral Feedback Disc Recorders, G. A. Yenzer, Audio Engineer, V. 33, September 1949, pp. 22-26, 44-45. 68. Universal Phonograph Reproducer, H. A. Henning, Bell Lab. Record, V. 19, October 1940, pp. 57-60. 69. Two Inventions Aid Hard of Hearing, W.E.Co. News, V. 14, November 1925, pp. 24^29. 70. Hearing Aids and Deafness, H. Fletcher, Bell Lab. Record, V. 5, October 1927, pp. 33-37. 71. Audiphones, W. L. Betts, Bell Lab. Record, V. 10, June 1932, pp. 362-366. 72. A Modernized Hearing Aid, R. Nordenswan, Bell Lab. Record, V. 15, January 1937, pp. 163-166. 73. The Orthotechnic Audiphone, W. L. Tuffnell, Bell Lab. Record, V. 18, September 1939, pp. 8-11. 74. Bone Conduction Receiver, M. S. Hawley, Bell Lab. Record, V. 18, September 1939, pp. 12-14. 75. Models 65-66 Hearing Aids, J. R. Power, Bell Lab. Record, V. 26, January 1948, pp. 30-33. 76. Audiometric Measurements and Their Uses, H. Fletcher, Volta Rev., V. 26, January 1924, pp. 10-14. 77. 5A Audiometer, L. G. Hoyt, Bell Lab. Record, V. 5, January 1928, pp. 159-162. 78. The 6BP Audiometer, A. H. Miller, Bell Lab. Record, V. 23, December 1945, pp. 464-465. 79. Historic Firsts— The Audiometer, Bell Lab. Record, V. 24, February 1946, pp. 57-58. 80. Scientists Against Time, J. P. Baxter, 3rd. Little, Brown and Company, Boston 1946, pp. 175-176. An Improved Telephone Set By A. H. INGLIS and W. L. TUFFNELL A new common battery telephone set has been developed and is now in produc- tion which is materially better than previous types in performance and conveni- ence to the user. This paper describes this set, and discusses, as typical of Bell System dleveopment processes, the contributions of the operating, development, and manufacturing organizations to the final design. It also describes the evalua- tion of the design by the controlled service trial, in terms of the results produced in actual service in the hands of the pubUc. THE Bell System is now introducing a new and improved common bat- tery telephone set, intended to supplement the present well known combined set first introduced in 1937.^' ^ In view of the established merits of the earlier set, of which something like 25,000,000 are now in the plant, it is of obvious interest to point out the nature and magnitude of the improve- ments represented in the new set which justify the effort and expense of such a change, to discuss some of the factors influencing its introduction at the present time, and to describe the set itseff and its characteristics. Before proceeding with this, it is pertinent to define what is meant by an improvement, what sort of changes come under this heading, and what means are available for appraising them. In the Bell System the answers to these questions are looked for in a combination of laboratory and field experience using the effect on service as a major criterion. Design for Service Improvements may be classified under two general headings. First, there are changes in form and in technical characteristics which improve the quality of the service and increase the satisfaction of the subscriber; the new design may be more acceptable in appearance, easier and more convenient to handle and manipulate, and provide easier and more natural conversa- tion with less effort. Such factors, however, valuable as they are in them- selves, cannot be considered apart from the second important kind of im- provement, which is cost reduction. An improvement, ideally, should offer possibility both of better service and of lower cost. Furthermore a new set may have improved features but, in addition, must offer all the essential service facilities that are currently offered, and work with the existing oper- ating conditions of the plant as it finds them. This sort of objective poses important problems of design coordinated with economy which require for a successful solution the knowledge, effort and teamwork such as is provided by the close cooperation developed over 239 240 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 the years among the operating, development and manufacturing organiza- tions. An important phase of the development of the new telephone set has been the contribution made by the Western Electric Company. Many of the parts for the development models were made by the Western so that the skills or faciUties at the manufacturing plant could be brought to bear on the projects at the earliest possible date. As a result of this activity on Western's part, many changes in design important in large scale manu- facture were introduced in the development stage so that later tooling for production could proceed with directness and assurance. During the course of the development of the various components and assembly of these into a set, joint studies by the Western engineers and the Laboratories were made to bring about a set that would not only meet the basic objectives but that would also be suitable for large scale manufacture at the lowest possible cost. From the field, the laboratory, and the factory comes knowledge of service needs, systematic advances in technical knowledge of structures and ma- terials, invention, and production skill. This reservoir of knowledge is ordi- narily tapped deeply to produce a new telephone set which can fully satisfy the severe requirements imposed. The reservoir must be refilled to permit further significant and worthwhile improvement, and can be profitably tapped only as this has occurred. Both these processes were delayed some five years by the war. Toward the end of that time comparison of technical possibilities with service needs gave promise of worthwhile accomplishment, with one im- portant proviso: the design would have to be completely integrated and considered as a unit structure. Each component would thus be considered only on its merits in contributing to the overall result. The development was undertaken on this basis and its justification is embodied in the values produced and demonstrated in the 500- type set. This set is new in concept, in execution, and in performance. Broadly the new set provides improved technical performance in all functions: transmission, diahng and ringing. It is compatible with existing plant operating conditions, needs fewer codes to provide the same scope of plant and commercial flexibiUty, and, as far as experience so far can deter- mine, in laboratory test and in the field requires less maintenance effort. These performance advantages are accompanied by better appearance and by added general convenience and ease of use to the subscriber. These are large claims, and it is only reasonable to ask how they can be substantiated and evaluated at such an early stage of actual experience with the set. The answer can be given with considerable confidence because teamwork, consistently applied, has evolved continually improved attack AN IMPROVED TELEPHONE SET 241 on such problems at all stages. A thorough knowledge of the field needs, a pyramiding technical know-how of physical principles, materials, and struc- tures, and their application in design and in production, and an increasingly comprehensive grasp of measurement technology, guided systematically by correlation with effects on performance in the hands of the public, provides a solid foundation for this confidence. By no means the least important factor in this result is that of measure- ment in its broad aspects, conceived and developed as a method of evalua- tion of design in terms of realized performance. Methods of Evaluation The invention of the vacuum tube gave great impetus to quantitative physical measurement in all phases of the telephone art, as pointed out in W. H. Martin's article in this issue of the Journal.^ Along with this, develop- ment and application of statistical and sampling theory and analysis, and continuing use of the so-called psychophysical test — a big new name for the traditional Bell System habit of remembering the human factor — have pro- vided increasingly powerful tools for laboratory test of new designs. It should be reaHzed that the value of such tests is only in direct proportion to the deliberate effort made to correlate their results, as well as those of the tradi- tional laboratory ''life" test, with effects in actual service. It is, perhaps in this grafting of newer measurement technology on the sturdy and depend- able stock of the "trial installation" that resides the greatest assurance of the significance of the answers. A further assurance that the subscriber gets what he wants is the increasing practice of asking him directly, by means of carefully constructed opinion surveys. All of these techniques of evaluation, plus the inevitably intense self criticism which is a matter of course in all Bell System projects, has been applied in the evolution of the new set from the first model to service trial and production. General Features The illustrations (Figs. 1 & 2) show the new set to be of completely new form, inside and out, low and sweeping in its lines and pleasing to the eye of the great majority of users. On the appearance design, laboratory engi- neers worked with Mr. Henry Dreyfuss, one of the country's leading ex- ponents of functional design. The handset is smaller, and some twenty-five per cent lighter than the existing type. The dial characters are external to the periphery of the fingerwheel where they are more easily seen over wider angles of vision, and are not subject to the inevitable wear of the surface which occurs under the fingerwheel. The cords are jacketed with neoprene, grommeted at the handset end for longer trouble-free life, and are less subject 242 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 to twisting. The ringer is provided with a manually adjustable volume con- trol which permits the subscriber to change the loudness over a considerable range. Less evident at first glance, but of greater importance both to user and Telephone Company are some of the more technical aspects of the electrical and mechanical design features. A schematic circuit of the set is shown in Fig. 3. This circuit is a varia- tion of one of the commonly used Campbell anti-sidetone circuits^ long ■p_ r^v Fig. 1 — External view of 500-set. Standard in the Bell System, with improvements added to meet tougher requirements in all functional categories. The mechanical arrangement of components in the assembly is entirely new, and is built around several concepts arising directly from service and manufacturing experience. In general, controls and adjustments are reduced or eliminated, and parts are enclosed and protected wherever possible against effects of dirt, moisture or mechanical damage. Where field or repair shop replacement of components is to be anticipated, as in the dial, ringer, handset, and cords, removal and replacement are de- AN IMPROVED TELEPHONE SET 243 signed to be easy. Other components are permanently mounted, and are re- placeable only in a shop. Switch assembly and transmission circuit com- ponents are so mounted and are completely enclosed and protected. The dial has no adjustments to be made in the field, and the ringer only one, bias tension which is rarely changed. The set functions completely with the cover removed. No parts or wiring are attached to the cover. This facilitates both production assembly and field servicing. i*^s# Fig. 2 — Internal view of 500-set. The success of such a design depends, of course, on precise knowledge of the service conditions to be met, how to meet them technically, and how to design and manufacture a set so it will keep on meeting them with the minimum of attention or expense thereafter. Functional Design in Relation to Objectives The main objective of the new set design was to reaUze acceptable per- formance requirements over longer distances from the central office, or with finer gauge cable conductors, and to do this with existing central office facil- 244 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 ities. This means of course that all the functional characteristics of the set must realize this objective. If, for example, extended range of transmission were not accompanied by a corresponding increase in dialing and ringing range, the entire potential value would not be reaHzed. A second objective was to reduce the transmission variations now experi- enced between individual users, and between the station most distant and that nearest the central office. A related objective of minimizing the variety of sets needed suggested the desirability of combining in one set, in so far as was economic, the required number of circuit arrangements to satisfy individual, party line, and measured service. DIAL EQUALIZER Fig. 3 — Circuit schematic of 500-set. There was, of course, plenty of incentive to incorporate in the design whatever experience had indicated might be done to retain or better the excellent maintenance performance of the current standard combined set. With these general objectives in mind somewhat more detailed descrip- tion of the circuit and design is in order. It will perhaps be somewhat clearer to take up each of the main functions in turn and to show for each how the specific objective was approached. It might be stated at this point that the description is based of necessity on the design as it was in the early pro- duction. The usual Bell System process is underway to find more economical and reliable ways to accomplish the objectives. The characteristics described herein will in general apply equally to any such modifications. Transmission The general objective called for the maximum usable increase in transmit- ting and receiving volume on long loops. This meant gains in each direction AN IMPROVED TELEPHONE SET 245 not to exceed about 5 db, due primarily to noise and crosstalk problems in- troduced with larger values. Along with this volume gain, improvements in quality were desirable. Any such volume gains over present levels would of course be intolerably loud on short loops, so if limitations in the variety of sets and the attendant administrative, production, and merchandising benefits were to be retained, it meant designing a set with transmission performance suitably adjusted for short and long loops. Inasmuch as on cu to vers and on P.B.X. extensions and the like, the same set would be at times on long and at others on effectively short loops, it also meant that this change in performance should auto- matically take place with change in connection rather than require manual reconnection or adjustment. Fig. 4 — View of equalizer. This has been achieved in the present design by including an automatic transmission equalizer. Fig. 4, which is adjusted in its inserted loss charac- teristics by the magnitude of the d-c. line current through the set. One element of the initial design (other preferable methods may develop in the future) provides a tungsten ballast filament in series with the transmitter so proportioned that the effect on transmitting on long loops is small, but on short loops with high values of d-c, the combined battery supply and a-c. circuit loss inserted is about 5 db. A corresponding graduated receiving loss is obtained by including a thermistor bead thermally coupled to the tungsten filament in the same structure. This bead, in series with a loss limiting resistance, is bridged across the receiver. The filament is protected against abnormal voltages by a bridged silicon carbide varistor. The resistance current characteristics of the elements of this equalizer are shown in Fig. 5. The required gains in transmission called for completely new transmitter 246 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 and receiver design. In the case of the receiver, the design was new in basic principles and resulted in the so-called "ring armature" structure which was discussed in the January 1951 issue of the Bell System Technical Journal.^ This structure is not only five db more efficient than the present handset receiver, but also permits extending the upper frequency range by some 500 cycles. For compatibility with existing plant characteristics the general response of the new receiver was kept flat as measured on a standard 6 cc coupler as in the present receiver. 2000 - ---- ^, VAR I FILAMFNJT S \ ■ * ^ - 1 ^ 1000 800 STORWV ( s'^^^VtHERM- - \ 1 V7 ?yj?r 1 - \ 1 r-f —3 500 ^ 400 O 300 ^ 200 ID 5 100 Id 80 \ 311A EOUALI7FR \ ' 1 \ \ ^—THERMISTOR PLUS 50A K: '^ ^ - / ^-^ ^^_ CC 60 50 40 30 9n - 1 r^-FILAMENT PLUS VARISTOR y / L^-^ ^ 10 0 O.OI 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 O.Il 0.12 0.13 0.14 0.15 CURRENT IN AMPERES Fig. 5 — Equalizer characteristics. While the transmitter design resembles superficially the current design, it differs in many important respects. To get the required 5 db volume gain on long loops required taking advantage of every design expedient in the transmitter itself, as well as in the handset in which it was mounted. Modu- lation of the carbon was increased, and the effective working acoustic pres- sures were raised by using smaller parts and locating the transmitter more advantageously with respect to the mouth. This is of particular benefit to women, whose transmitted levels have hitherto been considerably less than for men. Advantage was taken of new knowledge of granular carbon processing to get initial d-c. power gain over present type transmitters, and by a new AN(, IMPROVED TELEPHONE SET 247 preconditioning and heat treatment, to maintain the improved modulating performance better over longer periods. At the same time the rate of resist- ance increase with age is markedly reduced. Along with these several factors contributing to increased volume output of the transmitter, the response was altered in an attempt to provide more nearly orthotelephonic overall response. To assure that these instrument gains would be realized in actual service introduced one of the principal technical problems of the transmission de- sign, the better control of sidetone. Without a better job on sidetone, much TRANSMITTER /input pressureA from artificial y MOUTH /"output pressure'^ \\N 6 CC coupler J ]^l^ ^ TELE- H NO. 26 - ^'^^IL^^ GAUGE ^"^^ PHONE SET I— I LOOP 1—1 CORD CIRCUIT STEP BY _ 1000 FT STEP CORD CIRCUIT NO. 26 GAUGE LOOP M TELE- PHONE M SET RECEIVER LOOP RESISTANCE IN OHMS 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 J—, 1 1 I ^_l L oc -20 2000 4000 6000 8000 10,000 12,000 LENGTH IN FEET (NO. 26 GAUGE LOOP) Fig, 6 — Comparative sidetone levels. 14,000 16,000 of the value of the higher instrument efficiencies on long loops would fail of realization because of resulting lower acoustic talking levels, and increase of the masking effect on incoming speech of room noise picked up by the transmitter. The solution adopted for the initial design lay in choosing a more complex impedance to give the best overall balance over the frequency range for the loop and trunk conditions with which it must function. The relative sidetone of the two sets as a function of loop length for a typical circuit is shown in Fig. 6. The solution has given a set with essentially the same side- tone as the present set in spite of a ten db increase in instrument efficiencies, thus assuring the full effective gain represented by this increase. Typical loop loss characteristics for the 500-type set compared to the 302- 248 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 set are shown on Fig. 7 which also illustrates the effect of the equalizer. Overall air-to-air frequency responses of the two types of set are shown on Fig. 8 for long and short loops. The broader frequency range and the notable reduction in spread between long-and short-loop performance are evident. Subsidiary but essential transmission features of the new set include a copper oxide click reducer across the receiver particularly desirable for a re- ceiver of such high efficiency; low susceptance to power interference on party lines by the high impedance of the ringer and by shaping the receiver re- sponse below 300 cycles;^ and effective suppression of dialing interference LOOP RESISTANCE IN OHMS 500 600 700 800 900 1000 UJ (O UJ a. -20 500 TYPE SET ■500 TYPE SET (NO EQUALIZER) ■302 TYPE SET 1100 1200 1300 J 4000 6000 8000 10,000 12,000 LENGTH IN FEET (nO.26 GAUGE LOOP) Fig. 7 — Relative volume levels. 14,000 16,000 with radio and television reception by a small capacitance and resistance associated with the inductance of the line winding of the induction coil. The integrated design employed assures these features at minimum cost. Dialing A controlling limitation on dialing range is to be found in the degree to which the pulse characteristics vary from the optimum value from dial to dial and from time to time over the period of service. The new dial design by better governing and cam control of the individual pulse form provides the required improvement in loop range by assuring much better uni- formity in every respect. Service experience has shown that the better visibility and greater con- AN IMPROVED TELEPHONE SET 249 venience of operation are in fact realized and appreciated by most users, and that accuracy and speed of dialing by the subscriber have not been sacrificed. / input pressure \ ^from artificial mouthj /trans- Y MITTER [tt= RECEIVER TELE- PHONE SET 10 DECIBEL TRUNK NO. 26 GAUGE LOOP 48V STEP y —I BY STEP WrW OR J> CROSS- > BAR ^ M CORD VvHV CIRCUIT 48 V STEP BY STEpH OR CROSS- BAR CORD CIRCUIT NO. 26 GAUGE LOOP ^OUTPUT PRESSURE^ y^ IN 6CC COUPLER ) TRANS- \ MITTER \ TELE- PHONE SET RECEIVER -5 -10 -15 -20 25 -30 / \ /'\ 500 TYPE SET 302 TYPE SET f \ \/\ y '^ SHORT LOOP ^ 1000 FT. 26 GA. X \ \ \ \ \ \ ^*<»' :>'' \ \ \ 1 \ r- ^ ^ \ 1 A \ ^A J LONG LOOP / 15,000 FT. 26 GA. "^x > / / / \ \ ■^ \ \ \ 1 ,/ "'\ \ -J5 40 45 -SO i / ^^., ^ ^^ \ \ \ \ 11 / / ' / / / \ \ \ \ ] / / / / \ \ \ \ \ 0 200 400 600 800 1000 1500 2000 2500 3000 4000 FREQUENCY IN CYCLES PER SECOND Fig. 8 — Overall frequency response. Ringing The new ringer design offers a particularly interesting example of the impact of field experience and knowledge of service requirements on station apparatus design. Acoustic surveys of typical subscribers' premises have furnished data on the acoustic transmission losses for ringing sounds, caused by interfering noise, the absorption of walls and hangings, and by doorways, both open 250 THE BELL SYSTEM TEC3miCAL JOURNAL, APRIL 1951 and closed. These data indicated that for a satisfactory minimum audibility of the ringing signal at positions where the ringer should be heard, over the range of conditions encountered in service, a louder ringing signal than that of the present station ringer would be desirable. A lower pitched signal was also indicated as carrying better, particularly for that considerable portion of the population whose hearing has deteriorated with age. It was also known, however, that any such increase in ringing level, if not adjustable at will, would increase the all-too-frequent requests for the telephone man to come and adjust the sound to suit the subscriber's needs at the moment. The new ringer, by combination of magnetic design skill with mechanical ingenuity, has succeeded in apparently meeting all these requirements most satisfactorily to all concerned. It is lower pitched, and more efficient as well as more effective. The easy volume adjustment provided the sub- scriber has in fact nearly eliminated his requests for such readjustment by the maintenance man. In view of the lower pitch of the signal, and the mini- mum level which can be set by the subscriber, the manual adjustment feature apparently has not increased the number of cases where the bell cannot be heard. The ringer electro-magnetic design provides a structure which is more efficient and higher in impedance than previous designs. This permits ade- quate loop range with greater numbers of connected extension or party line stations. The higher impedance at audio frequencies combined with a re- duction in low frequency receiver response limits the inductive susceptive- ness of the set to as low values as with previous sets having 5 db less re- ceiving sensitivity. The foregoing description of general objectives, methods and results provides some background for more detailed consideration of the design of the components of the set and of the contributions of the Western Electric Company manufacturing department in working out with the development engineers practical methods and designs for efficient quantity production. Each of the components of the set as well as the over-all assembly has novel and valuable features contributing to the final results. It is these significant features, rather than the complete design of each component, which are discussed in the following paragraphs. Component Design Handset As already pointed out the handset. Fig. 9, is of a radically new form, smaller, lighter and easier to use than previous types. As in the case of its predecessor, it is made of phenol plastic, a molded-in cavity through the handle serving as a conduit for the separate leads to the receiver. Contact AN IMPROVED TELEPHONE SET 251 Fig. 9— Cross-section of new handset. 252 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 to the transmitter terminals is obtained by means of contact springs sup- ported in a separate plastic cup which serves also as a controlled acoustic cavity for the transmitter and as an acoustic shield between the transmitter and receiver. Such a shield is necessary, as otherwise the transmitter and receiver would be directly coupled acoustically. Transmitter While the transmitter unit is similar in structural design in some ways to the transmitter of the previous handset/ it differs in many important details. The diaphragm of the new unit is rigidly clamped at its periphery, thus increasing the output in the upper frequency range as compared to the paper clamped diaphragm transmitter of previous design. This is essential, to achieve a quality of transmission that approximates the orthotelephonic objective. The simple conventional system, consisting of a clamped diaphragm, back cavity and carbon chamber, has a response characterized by a single sharp resonant peak; whereas it was desired to provide a gradual increase in output with frequency with a broad maximum in the region of 3000 cps. This might be accomplished by a sufficiently damped structure with its resonance in the region of 3500 cps, but only at the expense of efficiency. In the new transmitter the desired response is obtained with high efficiency by coupling the diaphragm to a doubly resonant system composed of the cavity within the unit behind the diaphragm and the chamber between the unit and the plastic cup. These two cavities are connected by holes covered by woven fabric having carefully controlled resistance to the flow of air. The equivalent circuit of such an acoustic system and its acoustic im- pedance characteristic as a function of frequency for some limiting and typical values of the component impedances are shown on Fig. 10, where 53 is the stiffness of the chamber in the transmitter behind the dia- phragm, 54 is the stiffness of the chamber formed by the plastic cup, M4 is the mass of the air in the holes coupling the two cavities, R4 is the acoustic resistance of the coupling holes. The stiffness impedance of the cavity S3 behind the transmitter dia- phragm acting alone is shown by Curve 1. Curve 2 shows the impedance of both cavities S3 and S4 combined, with zero leakage impedance between them. Curve 3 shows the impedance of the acoustic system composed of both cavities coupled together by an impedance having typical value of mass but zero damping resistance, while Curve 4 shows the characteristic of the same system with coupling impedance having zero mass and a typical AN IMPROVED TELEPHONE SET 253 value of damping resistance. Finally, Curve 5 shows the acoustic impedance of the two-cavity system in which values are assumed for both the mass and resistance of the coupling impedance, such as would occur in the trans- mitter. The acoustic design of such a system requires exact control of the indi- v^idual elements to prevent large irregularities in the overall transmitter response. The control of R4 is particularly critical as illustrated by Curve 3, 200 100 80 60 l40 O 2 30 20 ' \ \ /\ - v '>4 . \, / \ - ^ k ■^^^ -.^ -^ \ \ \\ --^, ^k^ ,-----v i.'^*^ \ ^ \ >i V N \ \^ k 1 ^: N<^ s \ \, 1 1 \! N - z R* M4 TfTVTPu— \ \ s \ 1 r V ^ V vv z::^ :^S3 54- \ =\. _J \ 1 s. \ 1 \ \ 1 \ s N k S \ 1 1 1 1 1 1 _ 1 -J. 30 40 0 200 400 600 1000 2000 FREQUENCY IN CYCLES PER SECOND Fig. 10 — Transmitter acoustic impedances. 4000 6000 10,000 which shows the large decrease in acoustic impedance at resonance with a corresponding increase at anti-resonance of the system when the damping resistance R4 becomes very small. This will cause a sharp peak and dip respectively in the transmitter response at these frequencies. Correct balance of the acoustic impedances, as illustrated in Curve 5, will result in an acoustic network having an impedance at low frequencies approaching that of the combined cavities, Curve 2, with gradual trans- formation as the frequency increases, reaching the impedance of the single smaller cavity, Curve 1, at high frequencies. 254 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 By combining this acoustic system with a diaphragm and associated car- bon chamber that resonates at the anti-resonant frequency of the acoustic network, it is possible to obtain an overall response free from resonances with uniformly rising output with frequency to about 2500 cps, followed by a broad maximum output extending to approximately 3500 cps, then dropping off in output at higher frequencies as shown in Fig. 11. This shows the complete equivalent circuit, the computed response and the response measured with constant sound pressure at the diaphragm. The carbon chamber of the new transmitter unit, although similar in general to previous designs, has been modified in many important details in order to decrease the mechanical impedance of tl>e carbon in the interest of higher modulating efficiency. Also, better positional performance has been obtained by changes in the carbon chamber contour and effective head of carbon. Receiver The receiver unit of the new handset, as shown in Fig. 9 differs radically in design from any previous commercial receiver. It is referred to as a "ring ar- mature" receiver and employs a completely new magnetic and vibratory sys- tem.^ The diaphragm, which in previous receivers has been a simple disc of magnetic alloy, is now a composite design consisting of a ring of magnetic material (permendur) with a center of phenolic impregnated fabric material formed in the shape of a dome. This required, of course, an entirely new type of magnetic circuit. The magnetic ring or armature is supported at its outer edge on a ring of non-magnetic material which provides the diaphragm seat. The inner edge of the armature is associated in the design with a ring pole piece which carries the flux from a ring-shaped permanent magnet. The use of the composite diaphragm in the new receiver results in a lower mechanical impedance and an appreciable increase in the ratio of effective area to effective mass. This accounts for an improvement in receiving efficiency as compared to the previous handset receiver of approximately 5 db along with an extension of the frequency range. Also, because of the lower mechanical impedance of the diaphragm system, the loss in intelligibihty when it is held off the ear, as may occur in service, is greatly reduced. Because of the higher efficiency and greater power output capacity of the new receiver as compared to its predecessor, a peak limiting device (click reducer) is provided to prevent the user from receiving uncomfortably high acoustic levels. A copper oxide varistor element is therefore incorporated in the design as an integral part of the receiver. This varistor also protects the receiver magnet from possible demagnetization caused by transient electri- cal disturbances. Less magnet material is therefore needed. AN IMPROVED TELEPHONE SET 255 - •^1 .1^ 278 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 zone, prevents entry of the coating gases into the preheating zone either by flow or by diffusion. From the coating zone, the coated rods enter a ''coohng" or ''after-heat- ing" zone, during passage through which they are brought very nearly to room temperature. Through this zone, in a direction countercurrent to that of the rods, there is maintained a flow of oxygen-free nitrogen, or of this with small additions of hydrogen, since it has been found virtually impossible adequately to deoxidize commercial nitrogen except by the addition of a small amount of hydrogen and passage over a catalyst such as palladinized alumina prior to thorough drying and admission to the cooling zone. To prevent entry of coating-zone gases into the coohng zone, the counterflow of gas through this zone is maintained at a higher linear velocity. All gases admitted to the furnace are exhausted at the junction between the coating and cooling zones. To produce circumferentially uniform films on the rods they are rotated about their axes as they advance through the furnace. At reasonably high hydrocarbon concentrations in the atmosphere, an opaque fog is formed over most of the coating zone cross-section in both the batch and continuous furnaces. Immediately surrounding the rod surfaces or other surfaces on which deposition takes place, however, there is a fog- free region, called the conduction zone, which is the zone in which the trans- fer of heat from the surfaces to the gas occurs by conduction rather than by convection. The well-defined outer edge of this conduction zone is thus con- sidered to be the boundary of the region of generally streamline flow in the body of the furnace atmosphere, with the conduction zone, contiguous to the hot surfaces, being a more viscous, stationary region in which diffusion proc- esses are operative. The fog consists of minute particles of sooty and tarry substances which do not penetrate the conduction zone appreciably and which, therefore, do not deposit appreciably on the rod surfaces. The cause of this behavior is that the surface temperature of the rod exceeds that of the body of the gas; and, under the influence of this temperature gradient and the associated viscosity gradient, the heavier particles of soot and tar tend to diffuse away from the surface. If this temperature gradient is re- versed, as by the introduction of a cool rod into a hotter gas, then there is produced on its surface a soft and easily removed sooty coating. It is for this reason that, in the continuous process, the ceramic rods are preheated before entry into the coating zone and that the carbon-coated rods are pro- tected in the cooUng zone from contact with furnace effluents of higher temperature. 2.2 Process Variables Controlling the Rate of Carbon Deposition The thickness of pyrolytic carbon films is dependent not only on the na- ture of the hydrocarbon employed, but also on its concentration in the PYROLYTIC FILM RESISTORS: CARBON AND BOROCARBON 279 gases admitted to the coating chamber, on the temperature of this chamber, and on the duration of pyrolysis. The rate of deposition of carbon is independ- ent of this duration except during the first moments of deposition when the initial deposits formed serve to catalyze subsequent reaction, whose steady state is ordinarily quickly achieved. In Fig. 3 the film resistance of carbon films produced in a batch furnace is shown as a function of the duration of deposition. Included in the figure is a scale giving the film thickness which, as discussed in a later section,* is inversely proportional to the film resistance over the range shown. The linearity of the relationship thus bespeaks a con- stant deposition rate. 400 300 zs|::z::::::z: 0.05 X 10" 0.1 a. UJ H lU 2 0,2 H 7 tu o z 0.5 ^ z x: o I 0.2 10 20 30 0.3 0.4 0.6 1.0 2 3 4 5 6 DURATION OF PYROLYSIS IN HOURS Fig. 3 — Dependence of the thickness of carbon films on the duration of pyrolysis at 1000 deg C and 30 per cent methane concentration. Film thickness expressed in terms of film resistance. The pyrolyzing temperature, more than any other single condition, de- termines the actual rate of deposition of pyrolytic carbon. Figure 4 gives the fihn resistance for a given duration of pyrolysis, inversely proportional to the deposition rate, in a continuous furnace as a function of temperature in dynamic equilibrium and illustrates the need for precise temperature control when films of constant and reproducible film resistance are to be produced. Increase in the hydrocarbon concentration in the furnace atmosphere increases the rate of carbon deposition, as is shown by Fig. 5 for the case of methane, which gives the dependence of fihn resistance on concentration for * See Section 5.4. 280 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 a fixed duration of pyrolysis. It will be noted that the rate of deposition is not proportional to the concentration, a change in concentration by a 7000 6000 5000 2000 1500 r~" ■ 1 ! ~ s 1 - ^ \ - ^ ^^ - i ^^ =10.002x10-* - 0.003 p 0.004 965 970 975 980 985 990 TEMPERATURE OF PYROLYSIS IN DEGREES CENTIGRADE Fig. 4 — Dependence of the rate of carbon deposition on pyrolyzing temperature at 4.5 per cent methane concentration and for constant duration of pyrolysis. Rate of deposition expressed in terms of film resistance. 8000 < 2000 1500 800 600 500 400 - ^ — ^ - — ^ h^ %. - Si^ *^i^ - ^ - ^^^ ^^"^--5^ 0.002X10-* z 0.005 IJJ 0.02 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 METHANE CONCENTRATION IN COATING GASES IN PER CENT Fig. 5 — Dependence of the thickness of carbon films on hydrocarbon concentration in continuous furnace. Film thickness expressed in terms of film resistance. given percentage producing a greater change in rate of deposition at low concentrations than at high. The rate of carbon deposition with temperature, concentration, and dura- tion of pyrolysis all held constant is a function of the geometry of the system, being dependent, for example, on the distance between the furnace wall and PYROLYTIC FILM RESISTORS: CARBON AND BOROCARBON 281 the object being coated, and particularly so if this distance is less than the thickness of the conduction zone. While the rates of deposition associated with the film resistances of Fig. 4 and Fig. 5 are related to the corresponding absolute rates of hydrocarbon pyrolysis in the furnace atmosphere, they cannot be identified with them because of the important influence of the conduction zone, and because the rate of flow of the gases through the furnace is not specified. In fact, the rates of carbon deposition in individual furnaces are virtually independent of the rates of flow of the furnace atmospheres over wide limits, but they may differ appreciably from one furnace to the next. The viscosity in the conduction zone is so great that the rotation of an object in the furnace can be seen to drag with it the immediately surrounding gas; and it appears unlikely that this viscous gas layer is greatly altered in its thickness or other properties by any reasonable change in flow conditions of the furnace at- mosphere. The rates of carbon deposition were determined by weighing ceramic blanks before and after deposition of carbon films and are expressed in terms of weight deposited per unit area and unit time. This procedure is best suited to the thicker fikns, and for thin films or low rates of deposition large errors may obtain. For this reason, it has proved desirable to determine the rate of deposition from the film resistance, for which is required knowledge of the relationship between the fihn resistance and its thickness, and between its thickness and its mass, which involves a knowledge of the density of the carbon fihn. The determination of the density is discussed in a later section. 3. The Mechanism by Which Pyrolytic Carbon is Produced It seems reasonably weU estabhshed that the mechanism by which pyro- lytic carbon is produced is not simply a surface reaction, but is related to that of the gas phase dehydrogenation and polymerization of hydrocarbons. Thus, in the case of methane, the simplest hydrocarbon, it is found that, among others, free radicals such as methyl and methylene are present in the gas phase. These combine or polymerize and the resultant products lose hydrogen to yield radicals and molecules of increasing size and com- plexity. Analysis of the furnace gases from the pyrolysis of methane has shown the presence of acetylene, ethane, ethylene, benzene, napthalene, anthracene and a long series of more C9mplex materials of decreasing hydro- gen content up to pure "carbon" soot itself. It thus appears that pyrolysis of a gaseous hydrocarbon involves the formation of an entire series of molec- ular species of progressively decreasing hydrogen contents, which are inter- mediates in the formation of carbon. Chemical, structural, and physical tests are, ui fact, incapable of distinguishing between some of the higher members of this series and pyrolytic carbon.^^ 282 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 While the deposition of pyrolytic carbon fibns is not a surface reaction in the usual sense, the nature of the substrate surface can profoundly affect the reaction through its catalytic influence. For a ceramic surface contami- nated with iron or other heavy metals or their oxides this influence is evi- denced by the production of soft, sooty, easily removed deposits which can be formed at temperatures considerably below those normally required. There is evidence that these loosely adherent films may result through the formation of the metal carbides as intermediates. A great variety of catalytic influences on the deposition of pyrolytic carbon films has been observed: For instance, fingerprints are very clearly ''devel- oped" by deposition of thin fihns, the salts in them appearing to inhibit carbon deposition. If there is back diffusion of gases from the coating zone into the preheating zone and end chambers of a continuous furnace, then several phenomena may be observed: Colloidally dispersed complex hydro- carbons may deposit on the cooler ceramic rod surfaces from the gas phase or they may be mechanically transferred to the rods by contact with already contaminated portions of the furnace mechanism. In either event, their dis- tribution is nonuniform and the contaminated areas provide catalytic nuclei which accelerate carbon deposition in their immediate vicinities, resulting in a pyrolytic film with locally thicker areas. On the other hand, if these complex materials come into contact with certain metallic portions of the mechanism, complex organo-metallic compounds are occasionally formed, and transfer of these to the rod surface generally results in a local inhibition of deposition and hence in films with locally thin areas. For the production of uniform films of pyrolytic carbon it is generally necessary to employ a substrate which is uniformly clean. Chemical methods of cleaning contaminated surfaces have not proved generally feasible, and to achieve the requisite cleanliness firing of the ceramics at high tempera- tures in air is usually required. Even this may not be adequate, however, and it is occasionally necessary to reject ceramics with badly contaminated surfaces. Since the production of pyrolytic carbon involves the synthesis of progres- sively more complex hydrocarbons, it is natural to expect that the nature of the hydrocarbon employed would be of considerable significance. As discussed in a later section, pyrolytic carbon is graphitic in nature and thus can be considered as originating from aromatic hydrocarbons which possess similar hexagonal carbon ring structures. Isolation of benzene, napthalene, anthracene and other more complex aromatic compounds from the pyrolysis of methane is evidence that the aromatization of methane is probably an intermediate step in the production of carbon. It is therefore to be expected that the use of benzene should increase the rate of carbon deposition and this increase is observed. Similarly, the use of toluene or xylene, leading to PYROLYTIC FILM RESISTORS: CARBON AND BOROCARBON 283 the more rapid formation of aromatic radicals, should, as is observed, pro- vide even more rapid deposition than does the use of benzene. Rapid generation of free radicals, whether by catalytic surface reactions or through use of easily "ionized" hydrocarbons, is necessary for rapid dep- osition of pyrolytic carbon films. However; an excessive rate of generation, as from large concentrations of acetylene, leads to so rapid a gas phase polymerization that coherent surface films can be formed only with difficulty, the principal product being an "aerosol" of soot. Methane is employed in most instances because, being the most thermally stable hydrocarbon, the deposition from it can be so controlled as to yield thin and coherent films INTERPLANAR DISTANCE Fig. 6 — Structure of the most abundant form of graphite. 4. The Structure of Pyrolytic Carbon Films X-ray and electron diffraction analysis of pyrolytic carbon has shown clearly that its fundamental structure is similar to that of graphite, although it differs in two respects: The lattice constants are not quite the same, and the structure possesses a greater randomness, in a sense which will presently be specified. The hexagonal structure of the most abundant form of graphite" is shown in Fig. 6. The carbon atoms are arranged in parallel plane sheets, being located at vertices of hexagons in these sheets. The interatom separation in the sheets is 1.415 A and the separation between neighboring sheets is 3.345 A. Alternate sheets of atoms are so displaced that the repeating dis- tance perpendicular to the layers, or along the c-axis of the crystal, is twice the interplanar spacing, or 6.690 A. Other relatively rare forms of graphite 284 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 differ from this form only in the way successive planes are displaced or in the repeating distance.^^ Pyrolytic carbon consists of minute crystal packets composed of parallel plane sheets of carbon atoms in hexagonal arrays as in graphite.^^ The areas of these planes are, however, very small, their diameters generally being less than 50 A. Associated with their small size, there are differences in lattice constants, the interatom distance within the planes being less than in graphite and the interplanar spacing being greater. The extent of these differences is dependent on the size of the crystal packet. The interplanar 120 110 100 90 80 70 60 50 Ui }C 40 o t 30 10 — 1 PACKET SIZE - N BASE PLANE -HOFMANN AND WILM \ 1 ! - ALONG C-AXIS -BLAYDEN, RILEY AND TAYLOR 1 1 \ 1 \1 \ \ \ \v \ ^ *'"^, \^ ^\ \ N ^-^ "*■' MACROCRYSTAL GRAPHITE -~- -^ ^^_ 1 ■ — - 3.30 3.55 3.60 IN ANGSTROMS 3.65 3.35 3.40 3.45 3.50 INTERPLANAR DISTANCE Fig. 7 — Dependence of the interplanar separation in crystallites of pyrolytic carbon on crystallite size. separation as determined in the present work and by other investi- gators^^ . 14, 15, 16 js given as a function of the packet size in Fig. 7. The average crystal packet size in pyrolytic carbon appears, for a given parent hydrocarbon, to depend principally on the rate of carbon deposition whether this rate is altered by change in pyrolyzing temperature or in hydrocarbon concentration. When the rate of deposition is changed through use of other hydrocarbons there appears also to be a correlation with packet size. Pyrolytic carbon differs from graphite in another important respect: Whereas in graphite the atom layers lie one above the other with the atoms in successive layers in a definite relationship, those in pyrolytic carbon are PYROLYTIC FILM RESISTORS: CARBON AND BOROCARBON 285 randomly stacked, the only crystallographic order along the c-axis being the uniform separation of the layers. ^^•^'* The carbon atom has four valence bonds and, in graphite, these valences are completely satisfied within the plane hexagonal network. There is no valence bonding between successive atom layers, these being held together only by relatively weak van der Waals forces. The valence bonding between carbon atoms within any one plane is of the resonance-stabilized type, with the result that there is effectively one electron from each atom left over. Some such electrons are free to move over the entire extent of the atom plane, and these provide metaUic conductivity. With the larger interatomic spacing along the c-axis, many fewer electrons move from one plane to the next and along the c-axis, accordingly, the conductivity of graphite is much smaller. H H^^.^^H i^^y CxHy CxHy CxHy Fig. 8 — Two resonance forms of the valence structure in the carbon atom layer, showing the free valences at the crystal periphery with possible bonding of hydrogen and a hydro- carbon. Any single plane of carbon atoms in graphite may be considered to be a single giant molecule. Examination of such a plane of carbon atoms will show, however, as in Fig. 8, that it could better be considered as a free radical since there are free valences at its periphery; and these valences are quite probably satisfied by hydrogen or hydrocarbon fragments, as shown. Since the number of free valences in a graphite crystal is small relative to the total number of carbon atoms, the actual percentage of hydrogen is very small. Nevertheless, each plane of carbon atoms may be considered to be surrounded by a ''hydrocarbon skin." In pyrolytic carbon, the atom planes may likewise be considered to be surrounded by hydrocarbon skins. However, with an average diameter for these planes of approximately 25 A, the number of free valences is appreci- able relative to the total number of carbon atoms, so that the hydrogen content of pyrolytic carbon may be greater than that of graphite. This hydrogen content is primarily dependent on the temperature at which the 286 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 carbon is produced, and Fig. 9 shows the hydrogen content of pyrolytic carbon fihns produced from methane as a function of the deposition tem- perature. While the atom planes within a crystal packet are parallel to each other there is, in general, no regularity in the relative angular orientation of adjacent packets, which are randomly oriented. However, under some cir- cumstances, films can be produced in which the individual packets tend to be oriented with their atom planes parallel to the substrate,^^ the degree of orientation depending on film thickness and on the conditions of pyrolysis. 0.18 2 0.16 lU o tr u; 0.14 2 2 0.12 O a 0.10 2 UJ ^0.08 O ^ 0.06 O g Q 0.04 I 0.02 0 \ \. N, X \ ^ \ ^ 900 925 950 975 1000 1025 1050 1075 1100 1125 1150 1175 TEMPERATURE OF PYROLYSIS IN DEGREES CENTIGRADE 1200 1225 Fig. 9 — Dependence of the hydrogen content of pyrolytic carbon films on the temper- ature of formation. Under these circumstances, when pyrolytic carbon is produced at constant methane concentration, the degree of orientation at the surfaces of films greater than 3 X 10~^ cm in thickness passes through a maximum value as the pyrolyzing temperature increases. This maximum orientation occurs at 1025 deg C, regardless of hydrocarbon concentration. For deposition at constant temperature, the degree of orientation increases with the methane concentration. Pyrolytic carbon can thus be pictured somewhat as in Fig. 10, which is drawn approximately to scale and which shows the orientation of the crystal axes within the packets and the orientation of the packets in the carbon films. PYROLYTIC FILM RESISTORS: CARBON AND BOROCARBON 287 5. The Physical Properties of Pyrolytic Carbon Films The physical and chemical properties of graphite are different in its basal plane and along its c-axis.^^ As one common example, it is the ease with which shear occurs perpendicular to the c-axis which is fundamental to its value as a lubricant, even though in the base plane its hardness is great enough to warrant, in principle, its use as an abrasive. This pronounced anisotropy extends to other properties of graphite as well; and, since the crystals of pyrolytic carbon are very probably even more anisotropic because of the structural differences noted above, it is reasonable to expect that the properties of pyrolytic carbon will depend on the relative orientations of its constituent crystals. Though in some instances this expectation is con- 10"® CM 3xtO"^CM THE APPROXIMATE SIZE OF A SINGLE CRYSTALLITE, SHOWING THE ORIt.NTATION OF CRYSTAL AXES RANDOM ORIENTATION PREFERENTIAL ORIEN- TATION WITH BASE PLANE PARALLEL TO SURFACE Fig. 10— Crystallite size and orientation in pyrolytic carbon. firmed, as measurements to be described show, the influence of the inter- crystal boundaries is always present and, in many cases, it is controlling. 5.1 Density The density of pyrolytic carbon fihns composed of crystals about 25 A in diameter was determined, by flotation in a mixture of bromoform and carbon tetrachloride, to be 2.07 d= 0.04 gm^ cm-^ Since the interplanar spacing in the crystal packets averages 3.59 A and the interatom distance within the base plane is 1.40 A, the computed density, accepting that of graphite as 2.26, is 2.15 d= 0.04 gm cm"'. The value 2.07 gm cm-^ was employed in determinations of the thicknesses and specific resistances of all carbon fihns, since there was no observable systematic variation of density with change in the conditions under which the carbon was prepared, despite 288 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 the dependence of lattice constants on crystal size.^^-^^ The difference be- tween the measured density and that computed from lattice constants in- dicates that pyrolytic carbon is slightly porous, and this porosity obscures the correlation otherwise to be expected between density and crystal size. 5.2 Hardness The scratch hardness or micro-hardness of carbon films deposited on fused silica plates was determined with the Bierbaum Micro-character^^. Fused siUca, with a Moh's hardness of 7, has a microhardness of 1980, while silicon carbide with a Moh's hardness of 9-\- gave an average value of 7000. Re- 20,000 18,000 16,000 14,000 tn ^ 12,000 Q cr < I o o 10,000 4000 y ~^ \ / \ / / \ / \ / \ \ ^ 9.5 / / 1 X 1 x / \ 9 / \ S^ N >8 7 6 925 950 975 1000 1025 1050 1075 TEMPERATURE OF PYROLYSIS IN DEGREES CENTIGRADE Fig. 11 — Dependence of the hardness of pyrolytic carbon films on the temperature of formation. peated measurements of thick films of carbon produced at 1000 deg C and a 37 per cent methane concentration gave values for the micro-hardness ranging from 19000 to 19300, practically equivalent to diamond, or about 9.8 on Moh's scale. The hardness of pyrolytic carbon is dependent on the pyrolyzing con- ditions. Figure 1 1 shows the dependence of hardness on pyrolyzing tempera- ture for a 37 per cent methane concentration and illustrates the distinct maximum between 1000 deg C and 1025 deg C. When the temperature of the furnace is held fixed and specimens are prepared at progressively higher hydrocarbon concentrations, the micro-hardness increases monotonically. Values as high as 50,000 have been observed, and, in some instances, no perceptible mark was produced by the diamond point. The hardness was PYROLYTIC FILM RESISTORS: CARBON AND BOROCARBON 289 found to be independent of thickness above 6 X 10~^ cm, but for thinner films it is probable that the true hardness is greater than that observed, and the hardness shown in Fig. 1 1 for 950 deg C is probably low for this reason. Through this observed dependence of hardness on the conditions of pyrolysis, it appears that the hardness of pyrolytic carbon is correlated with the extent to which its crystals are preferentially oriented. It has been shown previously that the hardness of pyrolytic carbon is a function of crystal size^^, but these measurements were made on dendritic growths of carbon, in which the crystals are randomly oriented. It is prob- ably significant that the hardness according to these earlier measurements increased with decrease in crystal size and reached a maximum value for the crystal size at which, according to X-ray data" •^®, the lattice expansion along the c-axis begins to manifest itself. This may be an indication that the anisotropy in hardness of graphite crystals" is accentuated as the inter- planar spacing increases, thus facilitating shear parallel to the basal plane. Were it not for the expansion of the lattice along the c-axis, it is not im- probable that the hardness would increase monotonically with decrease in crystal size, since slip would be confined to progressively smaller and more perfect domains. The hardnesses of several specially selected specimens of crystal graphite were determined by the rocking pendulum method^'', employing a 90° diamond prism. The apparatus was insensitive for measurement of hard- nesses greater than 7 on Moh's scale, but the hardness of clean basal surfaces of graphite was found to lie between 6.5 and 7. The pendulum method does not eliminate purely elastic effects which may be appreciable in view of the large compressibility along the c-axis. For this reason the true hardness of the basal plane may considerably exceed this figure, which is, however, in agreement with published values". In view of the interatomic contraction in the base plane of pyrolytic carbon crystals it is probable, also, that the hardness of their basal planes exceeds that of the basal plane of macrocrystal graphite. With the prism edge oriented on the side of a relatively perfect graphite crystal so as to produce shear parallel to the base plane, the observed hard- ness was 0.5 on Moh's scale. Values of hardness on this scale from 1.0 to 1.5 were obtained for polycrystal graphite, these values being in agreement with other measurements. In view of the pronounced anisotropy in the hardness of graphite and the probably greater anisotropy of individual crystal packets of pyrolytic carbon, the apparent relationship between scratch hardness and the degree of pre- ferred crystal orientation is that to be expected, since preferential orienta- tion of the type observed exposes the hardest surfaces of the crystals to the scratching tool. 290 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 5,3 Thermal Conductivity A comparison method was employed to determine the thermal con- ductivity of the carbon films^^ The conductivity of a carbon film deposited on a flat silica plate was compared to that of an identical silica plate to the surface of which a thin foil of lead or other metal was fastened with glycerine. One end of each of these plates was securely clamped to a heavy copper base and to the opposite ends were clamped identical copper blocks supphed with heater windings. Differential thermocouples permitted determination of temperature differences between the two heated blocks and of the temp- erature drops along the specimens. The temperature drop along the speci- mens which were about 3 cm in length, never exceeded 12 deg C, and the entire apparatus was contained in a heavy copper cyHnder immersed in a constant-temperature oil bath. Calibration of the apparatus with foils of different metals and of various thicknesses showed that the relative thermal conductivities of the two specimens were accurately proportional to the powers dissipated in the two heaters when the temperatures and temperature drops were the same. By comparison with pure lead, iron, copper, nickel, and aluminum, the thermal conductivity of carbon films about 1 X 10~^ cm thick was found to be 0.08 watt cm-^ deg C~^ This value is in good agreement with the con- ductivity of black carbon determined by other methods^^, and it was in- dependent, within the limits of accuracy of the method, of the conditions under which the carbon was deposited. Specimens cut from samples of crystal graphite with their base planes parallel to their lengths were found by the same method to have thermal conductivities greater than that of pure copper, 4.0 watt cm-^ deg C~^ with a temperature coefficient of about — 0.0054 deg C~^ According to one series of measurements, the conductivity was greater than that of pure silver, this abnormally high conductivity of graphite along the base plane being in agreement with other measurements^^ Specimens suitable for the determination of thermal conductivity along the c-axis of graphite by this method could not be procured. However, specimens of like size cut from crystal graphite with their axes along the c-axis and the base plane, respectively, and oxidized to destroy any ori- entation produced at their edges by cutting, were clamped to the surface of a heated copper block with a small crystal of orthonitrophenol placed on the upper surface of each. The temperature of the block required to melt these crystals was noted and in this way it was found that the necessary temperature gradient along the c-axis was at least five times as great as that along the base plane, thus providing an approximate value of 0.8 watt cm~* deg C"^ for the thermal conductivity of graphite along the c-axis. The PYROLYTIC FILM RESISTORS: CARBON AND BOROCARBON 291 conductivity of poly crystalline Acheson graphite was found to be 0.4 watt cm-^ deg C~\ in agreement with published values^'*. The thermal conductivity of films of mesomorphic carbon is thus much smaller than those for single crystal or grossly polycrystalline graphite, and this is probably due to the definitive influence of intercrystal boundaries. As noted above, the crystals of mesomorphic carbon are more anisotropic than are those of graphite; but, despite this, the effect of the crystal boun- daries is sufficient to suppress any influence of crystal orientation on the thermal conductivity. 5.4 The Specific Resistance For determination of the specific resistance of pyrolytic carbon, silver electrodes were applied to the ends of films on rods or plates of fused silica and measurements were made at currents so small that there was no de- tectable joule heating. Comparative measurements made with and without potential probes showed no detectable contact resistance between these electrodes and the carbon film. Furthermore, the potential drop was linear along the specimens, thus indicating their uniform thicknesses. Within the limits of experimental accuracy, the specific resistance of pyrolytic carbon films is independent of film thickness: From the meas- urements of the weights and film conductances of carbon films discussed in Section 2.2, and using the value 2.07 gm cm~^ for the density, the data of Fig. 12 relating the film resistance to its thickness were obtained. Over the measured range from about 2.5 X 10"^ cm to about 2.5 X 10"^ cm thick- ness there is no change in resistivity and a strictly linear dependence of film resistance on thickness is obtained. While direct measurements of the thickness of still thinner films have not been made, the actual thicknesses have been approximated on the basis of the relationship between film thick- ness and duration of deposition given by Fig. 3. On this basis, films having resistances in excess of 2 X 10^ ohmfe for a square lie on an extrapolation of the curve of Fig. 12. These films are but a few Angstroms in calculated average thickness. The specific resistance does, however, depend on the conditions under which the carbon is prepared, and it decreases with increase in the degree of preferential crystal orientation for films greater than 3 X 10~^ cm in thickness. As a probable result of the influence of crystal orientation, the specific resistance of the carbon films measured parallel to the film surface passes through a minimum value at 1025 deg C as a function of increasing furnace temperature at constant methane concentration, while, with in- creasing methane concentration at a constant pyrolyzing temperature, it decreases monotonically. 292 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 Single crystal graphite has a specific resistance of about 3.9 X 10~^ ohm- cm parallel to its base plane^^, with a positive temperature coefficient^^ -^^ of 0.009 deg C~^, values confirmed by measurements made in the present study. Along the c-axis of the crystal, however, the specific resistance has been reported to range from 0.01 ohm-cm^^ to 1 or 2 ohm-cm^^, a value more than ten thousand times greater than that in the base plane. Measurements made in the present study show the specific resistance along the c-axis to lU ■' ^ ... ~ " 1 — " a - \ - \ - ^ \ 10--* \ - \ ft - - \ cc ly 9 - \ \ 2 ? \ - - > - \, z ^ 10-6 - N \ \ s X 8 - s^ ^ 0 - N ^ 4 - \ U. 2 - V \ 10-7 s - \ - \ - \, - N \ io-« 1 Ai 1 _^ J.J 1 _^ _LJ 1 _J_ ±. • — L_ _L N ■ 1 2 4 6 8 10 20 40 60 100 200 400 1000 4000 10,000 40,000 100,000 FILM RESISTANCE IN OHMS Fig. 12 — Relationship between the thickness of a pyrolytic carbon film and its film re- sistance. be approximately 0.01 ohm-cm, with a negative temperature coefficient of about 0.04 deg C-^ In view of the pronounced anisotropy in the specific resistance of crystal graphite, the relationship shown in Fig. 13 between the specific resistance of the carbon film and the degree to which its crystals are preferentially ori- ented with their base planes parallel to the direction of current flow is to be expected. Even in the most highly oriented specimens, however, the specific resistance is greater than 1 X 10~' ohm-cm, and this fact emphasizes PYROLYTIC FILI* RESISTORS: CARBON AND BOROCARBON 293 the role of intercrystal boundaries in determining the specific resistance of mesomorphic carbon. This influence is also evident from the dependence of the resistance on ambient gas pressure. After a carbon specimen is heated in vacuo to about 500 deg C in order to remove adsorbed gases, it is found on subsequent exposure to air that the resistance exhibits a gradual, relatively small in- crease with time. If, at any later time it is reheated in vacuo, the resistance returns to its original value. These changes in resistance are completely reversible and are presumably associated with the adsorption of atmospheric constituents at intercrystal boundaries. The influence of the intercrystal boundaries is further illustrated by the permanent decrease in film resistance by as much as 20 per cent, accompa- 0.0040 § 0.0035 g 0.0030 0.0025 0.0020 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 DEGREE OF PREFERRED ORIENTATION Fig. 13 — Dependence of the specific resistivity of pyrolytic carbon films on the degree to which the crystallites are oriented parallel to the direction of flow of the measuring cur- rent. Scale numeral "0" represents random orientation, while "10" represents perfect orientation. nied by a decrease in the temperature coefficient of resistance, which results from heating a pyrolytic carbon film in vacuo or in a neutral atmosphere to a temperature appreciably in excess of that at which it was deposited. These changes are presumably due to partial dehydrogenation at the boundaries with a partial intergrowth of adjoining crystals, an effect which has been confirmed by X-ray and electron diffraction examination. 5.5 The Temperature Coefficient of Resistance The temperature coefficient of resistance, a, for carbon films deposited on a suitable base depends on the thickness of the film, on the temperature of the fihn, and on the coefficient of thermal expansion of the base. As Fig. 14 shows, the value of a, defined as — dR/dT, where R is the resistance K. and T the temperature, decreases in magnitude with increasing film thickness 294 tHE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 and approaches a limiting value of about — 1.8- 10~^ deg C~^ which is found to be independent of the nature of the base. This value is, therefore, charac- teristic of the carbon fikn itself. The data illustrated in Fig. 14 were obtained over the temperature interval of 30 deg C to 60 deg C. Figure 15 shows the relationship between a and temperature for a typical film, the slope of which is common for all films deposited on the same base. As the coefficient of thermal expansion of the base increases, the value of a for any given film thickness less than 3 X 10~^ cm also increases, which serves to emphasize 10,000 6000 6000 1000 800 600 400 200 100 80 60 40 20 10 - 0.005 0.002 X 10-* 0.01 0.05 - 0.1 ^ - 0.5 1.0 -175 -200 -225 -250 -275 -300 -325 -350 -375 -400 -425 -450 -475 TEMPERATURE COEFFICIENT OF RESISTANCE IN PARTS PER MILLION PER DEGREE CENTIGRADE Fig. 14 — Dependence of the temperature coefficient of resistance of pyrolytic carbon films on film thickness. Thickness expressed in terms of film resistance. the role of the intercrystal boundaries in determining the properties of pyrolytic carbon, in suggesting that the resistances of these boundaries are dependent on pressure. The thermal coefficient of expansion for graphite crystals along the c-axis^ is 26 X 10-« deg C-^ and parallel to the base plane^^ is 6.6 X 10-« deg C-^; that for films of pyrolytic carbon was estimated to be of the order of this latter value. Carbon films which had stripped spontaneously from smooth cylindrical fused silica bases were found to curl away from them, the radii of curvature increasing with film thickness in the manner to be expected if PYROLYTIC FILM RESISTORS: CARBON AND BOROCARBON 295 the surfaces of the fibns originally contiguous to the bases had been de- formed largely in conformity with them according to the differential con- tractions during cooling. The thermal expansion coefficient of the pyrolytic carbon films was thus determined from measurements of their radii of curvature and of those of the bases from which they had stripped. This coef- ficient might be expected to depend on the nature of the intercrystal boun- daries. The anisotropy in the temperature coefficient of resistance of the con- stituent crystals of graphite might be expected to exist also in pyrolytic carbon, giving a dependence of a on the orientation of the crystallites. This dependence has not been observed, however, and the failure to observe it < (OUI lij ujq: ^^ ujO UJ< l-CL -375 -370 -365 ■360 -355 -350 -345 -340 t K \ S, \ N, \ \ >::», N \ \ N V t) -50 -40 -30 -20 -10 0 10 20 30 40 50 60 TEMPERATURE IN DEGREES CENTIGRADE Fig. 15 — Dependence of the temperature coefl&cient of resistance of a typical pyrolytic carbon film on temperature. may be due to the primary influence of the intercrystal boundaries in con- junction with the usual fluctuations in the value of a for a given set of coating conditions. 5.6 Summary Pyrolytic carbon, graphitic in structure as are most black carbons, has physical properties which can be correlated in part with the size and prop- erties of its constituent crystals and the way in which these crystals are arranged. While the lattice of these minute crystals differs in certain respects from that of graphite, it is probable that the metaUic character of the layer planes is retained, that the anisotropy in properties of the crystal packets is somewhat greater than for graphite, and, hence, that conclusions as to the properties of pyrolytic carbon based on this anisotropy are valid to good 296 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 approximation if the crystal packets are regarded as possessing the properties of macrocrystal graphite. While some definite correlations are observed between structure and properties, the intercrystal boundaries in pyrolytic carbon modify its bulk properties for two reasons: First, the effects of the interruption of lattice period at them are presumably greatly accentuated by the anisotropy of the graphitic crystals; and, second, there is an actual chemical contamina- tion at the intercrystal boundaries associated with the presence of peripheral hydrocarbon shells and of sorbed atmospheric constituents, as illustrated Table I Property Unit Polycrystal Graphite Graphite, Basal Plane Graphite, c-Axis »o'i^ Density Grams/cc 2.26 2.07 Hardness MOH's scale 0.5-1.0 >6.5 M).5 9.8 Thermal Co- (deg C-i)- 7.5 6.6 26.0 6.5-7.0 eflScient of io-« Expansion Specific Re- Ohm-cm 8 X 10-4 3.9 X 10-6 -'I X 10-2 1-1.8 X 10-3 sistance, p Temperature degC-i -1 X 10-3 -f 9 X 10-3 4 X 10-2 -1.8 X 10-" Coefficient of Resist- ance Thermal Watt cm-i 0.4 >4.0 M).8 0.08 Conduc- degC-i tivity, K Temperature Coefficient of Thermal deg C-i -1.1 X 10-3 ^-^-5.0 X 10-3 — -7.0 X 10-3 Conduc- tivity Wiedemann- (Watt Ohm 3.2 1.6 '-SO. 1.1 Franz Ra- degC-i)- tio, Kp 10* Rate of Oxi- Relative — 17. 1.0 — dation by the comparatively low thermal conductivity and by the changes in resistance and in temperature coefficient of resistance which heating the films in vacuo will produce. Some of the properties of the graphitic carbons are collected in Table I. 6. Pyrolytic Carbon Film Resistors 6.1 The Substrate or Core The influences of the supporting surface or substrate oh the properties of pyrolytic carbon films are both chemical and physical in nature. Mechan- ical perfection of the carbon films is essential to production of resistors and this perfection is determined in large part by that of the core surface. If PYROLYTIC FILM RESISTORS: CARBON AND BOROCARBON 297 there are cracks, pits, grooves or other mechanical imperfections in the core, these will result in corresponding imperfections in the carbon films. Various types of imperfections are shown in the schematic cross section of core and film in Fig. 16. Of the imperfections there illustrated, the thinner and thicker areas of the film are the result of the catalytic or chemical in- fluences described earUer, and, of these, the thin areas are the more harmful. If a continuous film covering the entire cylindrical core surface is employed as a resistive element by making suitable electrical connections to its ends, the effect of the imperfections is relatively small because each individual fault is shunted by a continuous and perfect film. However, it is common practice in resistor production to cut a helical groove through the film to provide, in effect, a carbon ribbon wound around a cylindrical core and thus to increase the resistance of the element. When this is done, the imperfec- tions may become series elements in the current path or shunt elements between turns, and their effects on resistor behavior are consequently greatly CRACK ^ LOOSE CONTACTS' THIN FILM BARE SPOT Fig. 16 — Types of faults in carbon film resistors. accentuated. Figure 17 shows photomicrographs of mechanical imperfections in the fihn both before and after the helixing operation. Carbon is deposited on the walls of cracks in the ceramic and over the surfaces of unvitrified grains in porous regions, and the contacts thus formed between carbon coated surfaces are similar to those in the carbon composi- tion resistor or those between carbon granules in a microphone. They are unstable with time, temperature and voltage; and this instabiUty is reflected in the behavior of the resistor. Microscopic count of such imperfections has been found to be qualitatively correlated with unfavorable effects on the temperature coefficient of resistance, the voltage coefficient of resistance, the noise level, and the stability of pyrolytic carbon resistors. While thor- oughly vitrified ceramic cores are desirable, it is nevertheless possible to employ sHghtly porous or imperfect cores under certain conditions, par- ticularly for thick fihns, since the depth of penetration of carbon into the ceramic can be controlled to some extent by proper choice of the pyrolyz- ing conditions. It appears that carbon is held to the substrate by a mechanical keying action, so that the surface geometry of the core is important: The scale of I 298 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 roughness required for good adherence generally increases with film thick- ness, the fihns invariably being under lateral compression at normal opera t- BEFORE HELIXING AFTER HELIXING Fig. 17 — Mechanical imperfections in ceramic rods, carbon coated. ing temperatures. It has been found that crystalline substrates such as porcelain, zirconium silicate and alumina, which may be made nonporous, provide excellent adherence. Vitreous surfaces such as those of overfluxed PYROLYTIC FILM RESISTORS: CARBON AND BOROCARBON 299 or over- vitrified porcelain, many steatites, and fused silica provide rela- tively inferior adherence, which can, however, be improved by chemical etching or by thermal oxidation of a previously deposited carbon film. Even though free from mechanical imperfections resulting from corre- sponding faults in the substrate surface, the carbon film may still exhibit local variations in thickness as a result of catalytic influences, as described earlier. The increase in resistance of a uniformly coated core or blank due to cutting a heUcal groove through the fihn can accurately be calculated when the helix angle and groove width are known, but if there are variations in fihn thickness, then the observed helixing increase is greater than that calculated, because the high resistance areas become series elements in the helix. Aside from the fact that such a variation would present production problems, an increase in temperature coefficient of resistance also results since, as shown in Fig. 14, this coefficient is larger the thinner is the film. This increase is particularly undesirable if resistors with closely reproduci- ble temperature coefficients are required. The core of a pyrolytic carbon resistor must, obviously, be a good in- sulator, particularly where very high values of resistance are obtained by helixing; and when extreme stabiUty of resistors under severe operating conditions is required, great care is necessary in the choice of the substrate material. Thus, the usual wet process electrical porcelain, when properly compounded from purified raw materials, can be made into resistor cores with very high surface perfection and good adherence for carbon films. However, it cannot be employed in resistor cores because at elevated oper- ating temperatures the mobihties of the alkafi ions in the glass matrix of this material are too great. The result of this mobility is that, under the influence of the fields between successive turns of a helixed resistor, electro- chemical migration sufficient to alter the shunting resistance between turns occurs even with the resistive element sealed in a thoroughly dry and evac- uated enclosure. To obviate these electrochemical effects, which are quaUtatively correlated with the analytically determined alkali concentrations, new alkali-free ceramic materials^*^ have been developed for use in fabrication of cores for pyrolytic carbon resistors. These materials are essentially porcelains in which all but small residual traces of sodium and potassium have been re- placed with alkaline earths such as magnesium, calcium, barium, and stron- tium. The ionic radii of these alkaUne earth metals are sufficiently larger than those of the alkaU metals that field migration is largely prevented. These alkahne earth porcelains show no evidence of electrochemical polari- zation when employed as resistor cores; and they have, in addition, high specific resistances and relatively low dielectric losses. I 300 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 6.2 Terminating and Adjusting to Value Transformation of a carbon coated ceramic rod into a completed resistor requires the application of low resistance contacts to the carbon film. Such electrodes may be applied directly to the carbon film by use of a water sus- pension of colloidal graphite (Aquadag) or of suitable metallic paints, or by other means. Except for resistors of low resistances, colloidal graphite, burnished and baked, provides an excellent termination. It is, however, susceptible to moisture; to provide greater stabiUty and to facilitate subse- quent manufacturing operations, metallic paints are generally preferred. To obtain resistors within given tolerances, it is necessary to adjust the resistances of the terminated units, since the statistical variation which the resistances would otherwise exhibit generally exceeds the allowable toler- ance. There are two reasons for this variation: First, there is, despite the most precise control of coating conditions in either the batch or the con- tinuous process, a statistical variation in film thickness; and, second, there are variations in the core surfaces and in the dimensions of the cores. Primary control of resistance tolerance is accomplished through control of the conditions of pyrolysis. The close control which is necessary in view of the great sensitivity of film thickness to the conditions of pyrolysis, as shown in Fig. 3, Fig. 4 and Fig. 5, requires careful attention to furnace design. The furnaces illustrated in Fig. 1 and Fig. 2 have proved satisfactory for resistor production: Either of them will furnish carbon films reproducible in film resistance to within about 7 per cent. The adjustment by means of which resistors with resistance tolerances as small as ±0.5 per cent or less are produced from coated blanks may be accomplished in two stages: if helixing is employed, by choice of the helix pitch and width; and by removal of a small amount of the carbon film by abrasion. The helix is ground through the carbon film by use of a water-cooled metal-bonded diamond cutting wheel. It is essential that the helical groove be smoothly ground in order to prevent the occurrence of cracks or fractures extending into the carbon ribbon, which lead to high noise levels and in- stability. The machines employed are so constructed that the carbon-coated blank "floats" against the abrasive wheel, thus providing a groove of es- sentially uniform depth and width regardless of any slight ellipticity in the cross-section of the core. Provision is made in the machines for continuously varying the helix pitch; and, over the range of pitch normally employed, the resistance of the coated blank can be increased by any desired factor from about 10 to about 8000. With uniformly coated blanks the helixing operation does not increase the spread of resistance values nor the value of the temp- PYROLYTIC FILM RESISTORS: CARBON AND BOROCARBON 301 erature coefficient of resistance. A typical helixing machine is shown in Fig. 18. Choice of film resistance and helix pitch is made to yield a resistor blank slightly lower in resistance than is ultimately desired, in order to permit final adjustment to tolerance. This final adjustment is ordinarily accom- plished by light and uniform abrasion over the entire surface of the resistor, through application of a cotton pad, moistened with an organic solvent, to the surface of the rotating resistor while the resistance is being measured continuously. Measurement has shown that the resistance stability of helixed resistors is slightly increased by this adjustment, probably in part because minute fractures of the film at the groove edges are partially eliminated. Fig. 18 — A typical variable pitch helixing machine with cover removed to show pitch- changing mechanism. Since the surface irregularities of the core are large relative to the carbon film thickness, abrasion does not remove carbon uniformly from the surface and large increases brought about in this way are often undesirable because of the resulting non-uniformity in film thickness. This non-uniformity re- sults in non-uniform potential gradients over the film surface and thus increases the distributed capacity of the film, which is undesirable in re- sistors to be used at very high frequencies. Non-uniformity in film thickness is also particularly undesirable in resistors designed to dissipate large amounts of power, which may be as great as 30 watts per square inch for hermetically enclosed types or 1000 watts per square inch for Hquid-cooled types. In such resistors, a small high resistance area may result in such pronounced local heating as to fuse the ceramic core locally with resultant progressive failure of a region across the entire conducting path if the power input is maintained. 302 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 6.3 Protection of the Carbon Film The conducting film of pyrolytic carbon is extremely thin and, unpro- tected, it is subject to change or damage from several causes. Principal among these are increases in resistance due to gas adsorption, oxidation, and physical damage as a result of unintentional abrasion or other rough hand- ling. To lessen or eliminate these causes of change, protection is given the film in various ways. The simplest and most generally accepted method of providing this pro- tection consists in the application of one or more coats of baking varnish over the carbon film. The application of the varnish causes an increase in resistance of the film which must be compensated for in adjusting the re- sistance to tolerance. This increase, which is generally less than one per cent, corresponds roughly to that observed over long periods of time in free air and is probably due to satisfaction by the varnish or its solvent of the adsorptive forces previously discussed. While an organic protective film over the carbon surface inhibits time aging of the resistance, it also introduces a complexity in resistor behavior. The varnish film is strongly adherent to the carbon and it has a thermal coefficient of expansion greater than either the carbon or the ceramic core. Further, thermal expansion of the varnish is subject to a form of hysteresis in that stresses introduced by a large temperature change relax only slowly with time after return to the original temperature. These properties have an important bearing on the change of resistance, with time and tempera- ture, of varnish-protected resistors, particularly when the carbon films are thin. As noted earlier, stresses set up in the carbon films due to the greater thermal expansion of the core produce changes in the resistance of the films. The stresses set up in the films by expansion or contraction of the protective layer do likewise. Figure 19 illustrates the fact that the stresses set up during curing of the varnish change subsequently with time in such a way that the resistance decreases, approaching an asymptotic limiting value. If the re- sistors are cycled in temperature, the immediate result is an increase in resistance followed by a slow decrease towards the initial value. Cycling of unvarnished resistor units sealed in vacuo or in helium, however, produces no change in resistance nor does shelf aging, thus leaving little doubt that the observed changes are due to the protective varnish finish. The carbon films are most stable and reproducible in properties when no solid material is in contact with their exposed surfaces. However, as discussed earlier, the resistance of a carbon film in free air increases with time, due to adsorption of atmospheric constituents. When resistor blanks are hermetically sealed in suitable enclosures filled with air at atmospheric pressure, the magnitude of the resistance increase with time due to the sorp- PYROLYTIC FILM RESISTORS: CARBON AND BOROCARBON 303 tion of atmospheric constituents is proportional to the enclosed volume of air. Hence, where high temperature operation is not necessary, hermetical sealing in air provides resistor units of relatively high stability free from any hysteresis in their resistance-temperature characteristics. When the carbon film is thick and the enclosed volume of air is small, such resistors can also be operated at higher temperatures if the permanent increase in resistance due to partial oxidation of the fibn and consumption of the en- closed oxygen can be tolerated. 6000 5500 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 0 -500 11 VACUUM SEALED RESISTORS 1. CYCLED -80"C TO +125°C VARNISHED RESISTORS: rr DUE TO CYCLING 2. 5HELP AGbU 3. CYCLED -80°C TO +125°C 4. CYCLED -80°C TO +25°C 5. CYCLED +25''C TO +125°C \ I ^ V \ \ V i\ \ S^ ii\ ^ "S '^ \ ■^ .,5 ^ "'s- "■"^ k — ^ I::^^ -^^ ^ _4 -^ ^ ^- -^ — — - in ^ =^» ^ 10 15 20 25 30 35 40 45 50 55 ELAPSED TIME IN DAYS 60 65 70 75 80 85 Fig. 19 — Resistance aging of varnished and hermetically enclosed pyrolytic carbon re- sistors as influenced by thermal cycling and time. The most stable pyrolytic carbon resistors are those in which the resistive unit is sealed in an hermetical enclosure which is baked and evacuated or filled with an inert gas. During the pumping and baking the resistance of such a unit decreases due to removal of previously adsorbed gases and residual low-molecular-weight hydrocarbons from the carbon film. Hence in contrast to the varnish-coated units, which are adjusted below tolerance before application of the finish, hermetically sealed units are adjusted to values somewhat above tolerance prior to sealing. To increase thermal dissipation over that which obtains with the evacu- ated unit, and to achieve rapid response of the resistor temperature to that 304 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 of the ambient, the hermetical enclosure is filled with an inert gas, oxygen- free nitrogen or helium normally being employed. Hydrogen is not used because it is not wholly "inert": Carbon films sealed in this gas increase in resistance with time, as if there were a tendency for them to revert to the hydrocarbons from which they were produced. Resistors sealed in vacuo or hehum exhibit a small initial aging, of the order of 100 parts per milUon (PPM) in resistance value, which can be completely eliminated by cycling them between —80 deg and 120 deg C. After this thermal cycling, the resistors do not change in resistance with time or further cycling. Measurements over more than seven years show the resistance to be stable to at least ±50 PPM and the temperature co- efficient of resistance to about 0.2 PPM deg C~^, within the limits of meas- uring accuracy^. For resistance values ranging from 100,000 ohms to tens of megohms, these stabilities are far greater than can be obtained in any other type of present-day resistor. Certain applications of these precision hermetically enclosed units have required that all resistors in a given network possess temperature coeffi- cients alike to within 1.0 PPM deg C~^ As illustrated in Fig. 14, the tem- perature coefficient of resistance of the film, a, depends on the film thickness, and hence all such "tracking" resistors are produced from a constant film thickness, different resistance values being obtained by the techniques of adjustment which have been described. The value of a for the films employed is 300 ± 35 PPM deg C~^ While this value is from 3 to 6 times larger in absolute magnitude than that for wirewound units, its statistical variation for these resistors is no greater. This statistical variation in a, however, makes it necessary to measure each resistor, if groups with values of a differing by no more than 1.0 PPM deg C~^ are required. Precision hermetically sealed resistors are very sensitive to faulty seals; and failure to reproduce resistance values at a constant reference tempera- ture after temperature change is a criterion of the effectiveness of the seal, resistance changes greater than 15 PPM in absolute value being sufficiently large to be significant in this respect, if this change occurs in a relatively short time. The resistance of the film attains a stable value in a given gaseous environment, but if this environment changes only very slightly in com- position or pressure it is necessary to restabilize once more by thermal cycling. If the composition changes with time, as in the case of a leaking envelope, stabilization to these accuracies is impossible. The sensitivity of resistance value of carbon films to their gaseous en- vironments would seem to be associated with adsorption equilibria, and there are data to show that adsorption of certain materials is more deleterious than that of others. There is evidence, moreover, that adsorption may not only change the number or mobility of the electrons in carbon, but that it PYROLYTIC FILM RESISTORS: CARBON AND BOROCARBON 305 may give rise to conduction by positive holes, which in the extreme case yields a positive Hall constant, rather than the negative Hall constant, indicating conduction by electrons, which carbon normally possesses. 6.4 Characteristics Figure 20 shows some types of pyrolytic carbon resistors produced, while Table II summarizes the essential characteristics of some of the more widely used varieties. Pyrolytic carbon resistors are compared in Table III with representative carbon composition and wire-wound resistors. These tables show that for many uses pyrolytic carbon resistors are superior to other available varieties. Thus, for high frequency applications, particularly when high values of resistance or large power dissipations are required, they are ahnost unique.^ Similarly, regardless of frequency or of resistance, they exhibit greater stability in all respects than do carbon composition types. The stabilities and the tolerances to which they can be held are such that they could well serve as replacements for wire-wound types in many applications if it were not for the numerically large values of their temperature coefficients of resistance. It has, however, been found possible to decrease the temperature co- efficients of resistance of resistors in all other respects equivalent to the pyrolytic carbon type to values smaller than are, on the average, available in wire-wound varieties. These are produced by modification of the pyrolytic carbon film by the addition of boron and are known as "borocarbon resis- tors "^^ The comparatively small temperature coefficients of these boro- carbon resistors are, of course, of considerable interest. Besides being in- creasingly requisite for applications in which appreciable amounts of high frequency power must be dissipated, they greatly simplify production of closely matched units for computer network and other applications, are of particular advantage for electronic equipment which is subject to extremes of temperature, and can be employed as replacements for wire- wound types in many applications. 7. BOROCARBON RESISTORS Investigations of the properties of carbon shortly after the turn of the century indicated that they could be greatly modified by the addition of boron.^2 So far as can be ascertained, however, the implications of this early work for the pyrolytic carbon resistor went unnoticed until, during the recent war, an investigation of the pyrolytic codeposition of carbon and boron was undertaken in these Laboratories. Results of this preliminary study indicated a good probabiUty 'that composite pyrolytic fihns of boron and carbon would have appreciably smaller temperature coefficients of resist- ance than films of carbon, as has been confirmed by subsequent development. 306 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 U 'o X to PYROLYTIC FILM RESISTORS: CARBON AND BOROCARBON 307 Table II Western Protective Enclosure Overall Dimensions (ins.) Resistance Range Power Rating in Air (Watts) Electric Type Number Dia. Length Min. (ohms) Max. (meg.) Free Convection (Normal) Forced Convection (200 ft/ min) 145 144 147 D-170000 152 153 154 Plastic Shell Varnish Varnish Glass Glass Glass Glass 0.219 0.281 0.281 0.438 0.615 1.25 1.25 0.781 0.938 2.063 3.25 4.63 8.75 14.75 1 50 200 200 20 10 40 5 5 50 15 10 1 10 0.5 1.0 2.0 10. 60 300 600 3.0 8.0 20.0 75. 500 2000 4000 Table III Pyrolytic Carbon Carbon Composition Wire Wound (144 Type) (RC-30) (107 Type) Nominal Power Rating 1 Watt 1 Watt i Watt to 1 Watt Resistance Range 50 ohms to 5 10 ohms to 22 0.4 ohms to 0.25 meg- megohms megohms ohms Tolerance ±1,±2,±5% ±5, ±10, ±20% ±0.1, ±0.25, ±1.0% % Resistance Change at -3.5 ±7.5 ±0.251 Rated Load ±1.02 Temp. Rise (°C) at 75 52 56 Rated Load Max. Cont. Voltage 1000 500 500 % Resistance Change per ±0.1 ±2 Negligible year (Shelf aging) Temperature Coeff. (ppm -250 to -540 -1200 to +2400 ±401 per°C) +30 to +1302 Approx. Ind. (/xH) for 0.26 <.02 125 0.1 Megohm 0.48 <.02 — 1.0 Megohn Approx. Cap. (ji/xi) for 0.02 Megohm <1 <5 1.0 0.1 Megohm <.l <2 1.5 Approx. Ratio of high frequency Res. (Re) to d-c Res. (Ro) for f Ro (megacycles x Megohms) of 1 0.95 0.5 too. 8 Not suitable for High 10 0.60 0.2 to 0.6 Frequency Use 1 For resistances of 0.4 ohms to 90,000 ohms 2 For resistances of 90,000 ohms to 0 . 25 megohms It is possible now to produce pyrolytic film type resistors with temperature coefficients as small as -20 PPM deg C-^ roughly one tenth the minimum value for pyrolytic carbon, and, indeed, lower than for many wire-wound types. Boron is incorporated in the carbon by the simultaneous pyrolytic de- position of carbon and boron from gaseous compounds of these elements. 308 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 It can be accomplished, for example, by pyrolysis of a single compound such as tripropylborane, or by use of a mixture of a boron hydride and a hydrocarbon such as methane or benzene. Usually, however, boron tri- chloride is employed as the source of boron and a suitable hydrocarbon as the source of carbon. The films produced by codeposition of carbon and boron are, in many respects, indistinguishable from carbon films of like thickness. z -3?f> _l -1 5 -300 a UJ 0. -?7S tf) h- a. < -?f)0 Ql 7UJ i -225 l- < a. -50 UJ Q. i -25 1 I ' \ \ \ V \ \ \ / \ \ \ 1100*0/ v \ s. ^^ ,y A y /1200'* c \^ ' / / — 1_ _L ^ 1 , 1 0.2 0.3 0.4 0.6 0.8 1.0 2 3 4 5 6 8 10 BORON CONTENT OF FILM IN PER CENT Fig. 21 — Dependence of the temperature coefficients of resistance of borocarbon films on boron content and temperature of formation As the boron content of thick films increases from zero in films of like thickness, however, the temperature coefficient of resistance, a, decreases through a minimum value and then increases, as shown in Fig. 21. The po- sition of the minimum value of a is essentially independent of the pyrolyzing temperature, but the magnitude of a at the minimum decreases, as shown, with increase in furnace temperature. It will be noted that, at its minimum, the magnitude of a is less than 20 PPM deg C"^ when comparatively high pyrolyzing temperatures are employed. The specific resistance of carbon films, except for the relatively smal' variations shown previously in Fig. 13, is independent of the pyrolyzing PYROLYTIC FILM RESISTORS.* CARBON AND BOROCARBON 309 conditions and of the nature of the parent hydrocarbon. The specific resist- ance of borocarbon films, however, is a function of boron content, and it can be varied over a wide range, as shown in Fig. 22. Associated with this dependence of specific resistance on boron content there is a corresponding dependence of a, the relationship between a and specific resistance being shown in Fig. 23. 1.0 0.8 0.6 0.5 0.4 0.3 0.2 0.08 I 0.06 O 0.05 > 0.03 H 0.02 IS) /), is applied to a given network consisting of a finite number of lumped linear elements, we can always calculate the corresponding output voltage, V exp {pt), in terms of the network constants. Then we define a transmission function F{p) as the logarithm of the ratio V/E. In general F{p) is an ana- lytic function in the complex ^-plane. Its value on the real frequency axis, p = io), defines the gain and the phase shift of the network. In the inverse problem we start with an assigned transmission function F{p) and are required to find a network for which F{p) is the transmission function. More frequently we have to design a network with assigned gain or phase characteristics over a prescribed frequency range. Obviously, there will be certain restrictions on the assigned transmission function if the network is to be physically realizable. Further, the solution will not be unique, though certain solutions may be more convenient than others. Engineering and cost requirements usually impose severe limitations on the number of elements that may be used in constructing a physical net- work, hence it may not be possible to match the given function exactly even within the prescribed range of frequencies. Thus from the practical design point of view the problem of network synthesis may be formulated as follows : To design a network with a reasonable number of lumped elements such that its transmission function approximates a given transmission func- tion to a prescribed tolerance in a given frequency range. The potential analogue method of network synthesis is a method of approximating to the prescribed transmission function by considering charge distributions in a complex plane and their associated potential and stream functions. In other words, the fact that the prescribed function is usually analytic means that its real and imaginary parts are potential functions 315 316 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 which satisfy Laplace's equation in two dimensions. Hence they may be interpreted as potential and stream functions (interchangeably) of certain charge distributions. In potential theory the problem of network analysis corresponds to the problem of determining the potential of a given charge distribution, while the problem of network synthesis corresponds to the problem of determining an appropriate charge distribution when the poten- tial is given. This is one of the fundamental problems of potential theory, and it has been widely discussed in the mathematical hterature of the subject. The usefulness of the potential analogue method of network synthesis derives primarily from the fact that we may use the whole background of our knowl- edge of potential theory and of the properties of electrostatic fields in for- mulating the solution of the charge distribution problem. A general solu- tion is obtained in terms of a continuous distribution of charge over a contour (C) in the complex plane. This is the mathematical part of the problem. Thereafter, the design problem is to approximate the continuous distribution by means of a set of lumped charges which will have approxi- mately the same potential function. The solution of this problem involves a certain amount of ingenuity, and may at times seem to be more of an art than a science. Once the lumped charge distribution has been determined, the locations of the charges are interpreted as corresponding locations of poles and zeros of the transmission function. Well-known methods of de- signing a network with assigned poles and zeros may then be used, and the problem regarded as solved. We may note that neither the lumped charge distribution nor the con- tour (C) is tmiquely determined by a given transmission function. Physical restrictions on the type of distribution which will lead to a realizable net- work usually impose sufficient limitations on the charge distribution, but the contour (C) remains to some extent at our disposal. If our first choice of contour proves unsatisfactory we can always try another contour which may give more suitable results. This introduces another important char- acteristic of the potential analogue method, namely that we may use the properties of conformal transformations to simplify the choice of contour. Thus any simple closed contour in the complex />-plane may be mapped on a unit circle in a second complex plane. The solution of the charge dis- tribution problem on the unit circle is particularly simple, but it may not lead to the most suitable network design formula. However, we may use the inverse transformation to map the unit circle on some more convenient contour and locate equivalent charges at corresponding points of the two contours. From the mathematical standpoint the use of continuous charge dis- tribution instead of lumped charges corresponds to the use of integrals POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 317 instead of finite sums. To the best of the author's knowledge, the first appli- cation of the continuous charge concept to network synthesis was by H. W. Bode, who used the so-called "condenser plate" analogue to design phase equalizers for experimental coaxial cable systems for television, in the late nineteen-thirties. An extension of the ''condenser plate" technique, combining gain and phase equalization, is described in a patent issued to Bode^ in 1944. The integration idea was used independently by W. Cauer,2 [^ connection with applications of Poisson's integrals to network problems. Development of the potential analogue method was interrupted by the war, but in the last few years there has been considerable activity in this field.^ The aim of the present paper is to systematize the development of the potential analogue method, and to extend it in various directions in order to obtain a more versatile design tool. Much of the material has been presented orally at meetings of the Basic Science Division of the A.I.E.E. In principle, at least, the method may be used to simulate or equalize, over a finite range of useful frequencies, any gain or phase characteristic Fig. 1- F(p)=flr+L/3=L0G -^ -A transducer used as a transmission circuit. which may be represented by an analytic function. Network types to which the method has been successfully applied include filters, equalizers, delay networks and combinations of networks required for long communication systems such as coaxial cables. As experience increases, the range of appli- cations is still being extended. 2. Analytic Properties of the Transmission Function We shall consider the transmission function of a typical transducer, Fig. 1. The absolute value of the ratio of the output voltage to the input voltage represents the gain in transmission through the network, while the phase of the ratio represents the phase shift. If a is the gain in nepers and j8 the phase shift in radians we have V/E = e"e^, (1) and we define the transmission function as the logarithm of this ratio, F{icc) = log (V/E) = « + t/8. (2) 318 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 For a finite network with lumped elements the ratio V /E is a rational fraction and the transmission function may be represented by an expres- sion of the form ^(^) = iogit;;-fiy-fi;-- \p - piAp - p2)--' (3) = log i^ + Z log {p - pi) -H log {p - pi), where K is a constant which may usually be ignored in the analysis since its value merely alters the U'^el of gain or phase and does not affect their variation with frequency. A/'e have introduced the complex oscillation constant /> = ^ + tw (4) instead of the real frequency variable, co, and equation (3) defines the trans- mission function in the complex />-plane. If we separate the real and imagi- nary parts of (3) we find analytic expressions for the gain and phase: « = ao + Z^ log I /> - :^1 I - X log I /> - /n I , i8 = /3o + Z PKP - K) - Z PKP - p"n)' The significance of the parameters pm. and p'n is easily understood if we note that when p — pm^^ have a: = — co and therefore V/E = 0. Hence the zeros of the rational fraction in (3) represent points of infinite loss of the network. Similarly if ^ = pn then a = oo and we may have a finite value of V when E is zero. Thus the poles of the rational fraction are the natural oscillation constants or natural modes of the network. For brevity we shall refer to pm and ^n as the zeros and poles of F(p) though they are really logarithmic singularities of the transmission function. The numerator and denominator of the rational fraction are finite poly- nomials in p. If the network consists of real elements the coefficients in the polynomials are real. Thus we have the first property of the transmission function. The zeros and poles must be either real or conjugate complex. A second essential property is that the real parts of the poles pn must be negative if the network is to be stable. And the third property that concerns us is that there must be at least as many poles as zeros, that is, as many finite natu- ral modes as points of infinite loss. This condition insures the proper be- havior of the transmission function at asymptotically high frequencies. Using these properties the gain and phase may be expressed in alterna- tive forms. From the first property it follows immediately that the con- jugate function [F(p)]* must be equal to the value of F when p = p*. But p* — —p when p = ioi, hence in this case [F(p)]* = F(-p) = « - z/3. (6) POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 319 On the real frequency axis, therefore, we have « = i[F{p) + F{-p)] = even part of F, I ip = ilFip) - Fi-p)] = odd part of F. Specifically we may write 2a = 2a„ + Z loglp'J - />' | - E log | /»' - / \pm + P/ \pn + P/ (7) (8) where the singularities occur in paurs, one of each pair being the negative of the other. (a) (b) Fig. 2 — A point charge in the potential plane; (a) at the origin, (b) at the point Zm . 3. Logarithmic Potentials In two-dimensional potential theory we are really concerned with uni- formly charged Une filaments whose potentials and intensities are the same in any plane perpendicular to the axis of the filament. Hence, it is conven- ient to speak of a point charge g in a two-dimensional plane (x, y) and re- gard the plane as the plane of a complex variable, z = x -\- iy. The poten- tial of a charge q at the origin in this plane. Fig. 2(a), is proportional to the magnitude of the charge and to the logarithm of the distance from the charge. F = — g log p + constant, (9) where the constant may have any convenient value. Note that we are using arbitrary units of charge and potential; in a coherent system of electro- magnetic units the logarithmic term would have a constant multiplier. 320 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 For present purposes this would merely lead to a complication of the argument. If we introduce polar coordinates, z = pe^^, we may consider a complex potential W = — 5^ log z + constant = — ^ log p — iq

i=^i(z) -^i(zo), (23) where ^1 is the stream function in the region on that side of (C). Since the total flux, *i 4- ^2 , is given by (21) we see that the stream function is discontinuous across the line charge, and the amount of the discontinuity is [^1(2) -^i(zo)] - [^2(2) -^2(zo)] = 27rg(z). (24) POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 323 If C is a closed contour, and if the above arc corresponds to passage from 00 to 2 in a counterclockwise direction around C, then ^i and ^2 in (24) cor- respond respectively to the interior and exterior of C. On the other hand the potential is continuous across the line charge. To prove this we note that the potential is the real part of the complex potential W in (13), and is therefore given by V= - f e(rt log I z - f I I ^rl + constant. (25) The integral depends on the distance | z — f | between a t)^ical point f on (C) and the given point z. For two points Zi and Z2 just on opposite sides of (C) the distance is the same, so that F(z2) = F(zi). 4. Analogy Between Transmission Functions and Logarithmic Potentials Comparing equations (3) and (12) we see that the transmission function F{p) in the complex />-plane may be identified with the complex potential W oi a, system of discrete charges. If we assume that unit positive charges are located at the natural modes, pn , of the network, and unit negative charges at the infinite loss points, pm , the complex potential in the ^-plane is W = - 12 log ip - p"n) + Z log {p - pL) + constant. (26) The real part of this function is the potential and its imaginary part is the stream function. Then, by the definition of gain and phase in equation (2), the gain of the associated network is given by the potential on the imaginary axis (the real frequency axis), and the phase by the corresponding stream function. The zeros and poles of F(p) locate the charges producing the complex potential W, and they form a discrete set of points. When F(p) corresponds to practical problems these points are usually arranged along well-defined lines in the complex />-plane and not distributed at random throughout a whole area. The corresponding potential W should then be that of a discrete set of charges arranged along corresponding fines in the charge plane. When the potential function is given in analytic form, however, it is usually simpler to use known methods of potential theory to determine a continu- ous charge distribution over a convenient contour. This continuous dis- tribution may then be approximated by a set of equal lumped units of charge spaced on the same contour. The difference between the actual 'sources' of F(p) and W is usually small, and by using distributed charges much of the algebraic complexity associated with the design of compHcated networks may be avoided, at least in the earlier stages. 324 THE BELL SYSTEM TECHNICAL JOIIRNAL, APRIL 1951 When the assigned gain or phase is represented in analytic form it is sometimes possible to determine a distributed charge over a suitably chosen contour which matches the desired characteristic exactly. Then the only approximations involved in obtaining a finite network are those which arise from replacing the continuous charge distribution by a set of lumped charges. The errors are easy to calculate and can usually be adjusted to meet the allowable network tolerance. It is important to stress that for physical networks the complex poten- tial W must be generated by unit charges. Hence, if we have determined a continuous charge distribution over a given contour in the complex />-plane, we must choose our unit of charge to make the total charge on the contour equal to an integral number of charge units. Then the contour can be divided into segments each carrying a unit charge, and the lumped charge distribution is obtained by locating one unit of charge at some convenient point on each segment, usually at or near the center. The total charge determines the number of lumped charges that may be used. This limitation is not so restrictive as it might appear at first sight, since the assigned transmission function frequently involves a constant parameter in terms of which the unit of charge may be defined. It is also possible, as we shall see later, to increase the total charge on the contour by special devices, appropriate to different types of problem. We assume that the gain, a, corresponds to the real potential, F, and the phase, jS, to the stream function '^; but it would be equally permissible to interpret a as the strea n function of another complex potential, iW, and then /8 would be the negative of the potential. It is usually more con- venient to equate gain and potential, in network synthesis problems, and we shall confine our analysis to this interpretation. The desired for n of gain and phase may be given as a condition on their variation with frequency. Since the electric intensity is the gradient of the potential, we see from equations (17) that da/doo is analogous to the elec- tric intensity in the direction of the negative frequency axis. Similarly, the variation of ^ with frequency is analogous to the electric intensity in the direction of the negative real p-Sixis, that is, at right angles to the frequency axis. Thus we may summarize the analogies we shall use most frequently: a) Transmission function and complex potential b) Gain and potential c) Phase and stream function d) — -;- and field along real frequency axis t) — -f- and field across real frequency axis. do) POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 325 The conditions imposed on the zeros and the poles of the transmission function to make it physically realizable have their counterparts which must be imposed on the charge distribution associated with the complex potential if it is to be equivalent to a realizable network. Using the above analogies they may be summarized as follows: 1) The charge distribution must be symmetrical about the real axis in the complex plane. 2) The positive charges must be in the negative haK of the plane. 3) The net charge must be non-negative. 4) If the contour is made up of disjoint curves in the plane there must be an integral number of units of charge on each segment. (28) The first three conditions correspond exactly to the zero and pole li nita- tions, while the last is a corollary of the unit charge limitation we have already discussed. 5. Condenser Delay Networks As a simple example of the potential analogy we shall consider the design of a network with constant phase delay in a prescribed frequency range. Analytically the condition is that d^/doi should be constant for | co | < coo , where c^o has an assigned value. The corresponding function in the potential plane is the field transverse to the imaginary axis. This suggests the field between the plates of a parallel plate condenser, and we construct im ne- diately the analogy illustrated in Fig. 5. The distributed charge is shown in Fig. 5a, where we assume a constant charge density on each plate of the condenser, the plates being parallel to the real frequency axis. The positive charge is placed on the left-hand plate to satisfy the second condition of the set (28). As long as the distance between the plates is small compared with their width the field between the plates is transverse, and substantially con- stant, except for an edge effect which will diminish as the dimensions of the plates are increased. If we could use infinite plates the field would be exactly constant, and the continuous charge distribution on the plates would match the network stipulation exactly. In practice we must use a finite number of lumped charges; hence we choose the charge points shown in Fig. 5b, where the crosses represent unit positive charges, the natural modes of the network; and the circles represent unit negative charges, the infinite loss points. To keep the end effects small it is desirable to extend the plates considerably beyond the frequency coo . We note that for the lumped charge distribution the field along the real frequency axis vanishes, since each unit positive charge contribution is 326 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 cancelled by the contribution from the opposite negative charge. Thus, by our analogy, da/do) vanishes, and the constant phase delay network has a constant gain at all frequencies. For the charge spacing illustrated in Fig. 5 the poles of the transmission function are located at the positive charge points, p'^ = —a-\- ivb, v = — w, • • • 0, • • • w, while the infinite loss points are located at the negative charge points, p^ = +o + ivh. Thus the required transmission function is — a — ifxb F(p) = constant + log H -m p -{- a — ifjib (29) 3 oc o -1 UJ u. REAL p 3 -1 < UJ oc X © X © X © X © X © X © X © X o REAL p X o X o X © f^r X © b X © \+^ X 0 (a) DISTRIBUTED CHARGE (b) LUMPED CHARGES NATURAL MODES Py= -a+it^b ^ = -m,---,o,---,+m 27r. INFINITE LOSS POINTS pj,= +a+L^b^ APPROXIMATE PHASE OF NETWORK At\ ^_ 27r., -^"^^ o.m 27r .. FREQUENCIES WELL INSIDE "PLATES" / /-* " b i)iN ^ u/ Fig. 5 — The condenser plate analogue; (a) distributed charge, (b) lumped charges. If we allow the number of charges to become infinite, but still with con- stant spacing by the infinite product may be recognized as the ratio of sine or cosine functions,* sm, cos F = constant + log (^•') sm, cos (^"') (30) *See, for instance, B. O. Pierce's "Short Table of Integrals," page 96, equations 816, 817. POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 327 where the sine or cosine is used according as the number of oscillation constants is odd or even. There are two sources of error in the finite representation (29) : The first is due to the finite extent of the charged plates, and may be called the "truncation error." Its effect will be important only near the ends of the plates, which explains why it is advisable to prolong the charges beyond the upper frequency bound coo . Its magnitude is exactly determined by integrating the effect of uniform charge density, of magnitude 1/&, over the region beyond the finite plates: d^ 2x [2^-1 « .2,-1 a 1 - -/i = — - - tan — — - + - tan , (31) where ±coe are the real frequencies at the ends of the plates. The bracketed expression represents the non-constant part of the phase delay, due to the finite extent of the plates. Note that 2coe = nb = total extent of natural mode intervals = plate width. The correction term becomes smaller as co, increases. The second source of error Hes in the use of lumped charges instead of a continuous charge distribution, and may be called the ^'granularity error." Its magnitude may be approximately determined from (30) if we replace the sines and cosines by their exponential equivalents, differentiate with respect to co, and assume that the error is small. We find. d^ do3 27r , 4x / liraA 2x0) /^^n -^±-^exp(^-— jcos — , (32) where the plus and minus signs refer respectively to odd and even numbers of modes. We may assume that both errors are small, and that they act inde- pendently, so that the total error is given approximately by the sum of the non-constant factors in (31) and (32). We note that if we increase the plate spacing, a, the granularity error becomes smaller while the truncation error increases. This increase may be offset by increasing a>e , but this means extending the condenser plates and therefore adding additional lumped charges, with consequent increase in network complexity. Thus the choice of specific spacing and dimensions is hkely to represent a balance between granularity errors, truncation errors and network complexity. The truncation errors may be somewhat reduced, with no increase in network complexity, by increasing the charge densities near the edges of the plates. Later we shall discuss a systematic method of adjusting the charge distribution. 328 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 6. Filters or Selective Networks Filters offer another particularly simple illustration of the potential analogy. The object of a filter is to transmit all frequencies in a prescribed range and to block all other frequencies. This means that the potential must be substantially constant in the pass-band, and large and negative in the stop-band. Now the potential inside a conductor is constant, hence charge distributions on conductors should yield transmission functions of filters. POSITIVE CHARGE DISTRIBUTED ON A CONDUCTING SHIELD 'FIELD OUTSIDE SHIELD DOUBLED DENSITY ON HALF CONTOUR X \ SYMMETRY RELATIVE TO EACH AXIS LUMPED 'charge APPROXIMATION \ GAIN UNCHANGED AT REAL OJ RFAL D (a) CLOSED CONTOUR (b) HALF CONTOUR Fig. 6 — Analogy between filters and conducting shields; (a) positive charge distributed on symmetric shield, (b) lumped charge distribution on half of contour. Figure 6 illustrates the analogy between filters and conductors, or shields. The first condition in the set (28) requires that the shield must be symmetric in the real />-axis. Symmetry about the co-axis is not necessary, but it i^ usually advantageous. The third condition of (28) requires that the charge on the shield should be positive, in the absence of external charges. Positive charges determine the poles of F(p), and must therefore he in the left half of the />-plane if the network is to be physically realizable. In the shield, on the other hand, there are positive charges in both halves of the />-plane, so that we cannot use the charge distribution on the shield without modi- POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 329 fication. The difficulty is readily resolved, however, if we note that the charge on the shield is symmetric about the w-axis, and that the charges on each half of the shield produce the same potential on the imaginary axis. Hence the gain will be unchanged, if we use only the left half of the shield and double the charge. Even if the shield is not symmetrical about the oj-axis we can still transfer the positive charges on the right half of the plane to their mirror images in the axis without changing the value of the potential on the axis. This REAL p (a) SYMMETRICAL REAL p .--^^ REAL p // U -X— X (b) DISSYMMETRICAL '^'^"xJ^ REAL p Fig. 7 — Lumped charge distribution for a given contour; (a) symmetrical, (b) dis- symmetrical. would give us a charge distribution over two separate contour branches, as in Fig. 7, and would thus increase the network complexity. This explains the desirabiUty of using the type of shield which is symmetrical relative to each axis. So far we have considered conductors in the absence of external charges (except at infinity). If the network is to have points of infinite loss at certain finite frequencies we must have negative charges outside the shield. Fig. 8. These charges alter the charge distribution on the shield, but the potential 330 THE BELL SYSTEM TECHNICAL JOURNAL, APRLL 1951 inside the shield is still constant. In the case of band-pass filters we can use disjoint contours as in Fig. 9. These must be symmetric about the ^-axis and again we shall find it advantageous to have them symmetric also about the co-axis. In all cases the net charge on the shield must be positive, and A^ ^> POSITIVE CHARGE DISTRIBUTED ON A CONDUCTING SHIELD \ \ L NEGATIVE r CHARGES NEGATIVE CHARGES Fig. 8 — Negative charges outside shield have no effect on potential inside. we can state as a general filter principle that: The natural oscillation con- stants '^shield'' pass-bands from infinite loss points. 7. Gain Invariant and Phase Invariant Transformations We have just seen that we can transfer positive charges (or poles) from the right half of the />-plane to the left without changing the value of the potential (or gain) on the real frequency axis. Similarly, there are trans- POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 331 formations which leave the stream function (or phase) unaltered. These invariant transformations are easy to understand if we consider the com- ponents of the field intensity. As shown in Fig. 10a the field of any given charge along the co-axis equals the field of an equal charge at the mirror image of the given charge in the real frequency axis. By (27d) these two charges thus give the same rate of change of a with frequency. Similarly two opposite charges, Fig. 10b, at mirror image points have the same REAL p Fig. 9 — A disjoint contour. transverse field intensity across the co-axis. Thus these charges produce the same rate of change of /3 with frequency. To sunmiarize in terms of the transmission functions: 1) the zeros and poles of F{p) may be moved from the right half of the />-plane to the left haK, and vice versa, without changing the gain; 2) a singularity of F{p) may be moved from one half of the />-plane to the other without changing the phase, provided the type of singularity is reversed (that is, a zero be- comes a pole and vice versa). 332 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 8. Green's Formula The simple examples we have just discussed could have been solved with- out recourse to the potential analogous method, since the charge distribu- tions were easy to recognize. In general, this is not the case, and we now turn to systematic methods of determining the charge distribution when the gain, a, is given as an analytic function of w in a prescribed frequency range, | w | < wo . The corresponding transmission function is obtained if we replace co by p/i and regard /> as a complex variable. Then the mathe- matical problem is to determine a charge distribution on some contour C which will have this function F{p) as its complex potential. The contour C is to a large extent arbitrary. We shall assume that it is a simple closed curve in the />-plane, enclosing the frequency band of in- REAL p REAL p (a) GAIN INVARIANT TRANSFORMATION ( b) PHASE INVARIANT TRANSFORMATION Fig. 10 — Illustrations for (a) gain invariant (b) phase invariant transformations. terest, and subject only to the imitations that it must be symmetric in the real />-axis, and that F(p) must be analytic inside C. Then one very general solution of the charge distribution problem in potential theory is given by Green's formula, f which has the form for the logarithmic potential in two dimensions. The integral expresses the potential at any point P inside C in terms of the values of V and of its normal derivative on C. The differential ds is an element of length on C and n is the normal drawn out of the region we are considering. At points tSee e.g. A. G. Webster, Partial Differential Equations of Mathematical Physics, G. E. Stechert and Co., New York, 1927, p. 210. POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 333 outside C the integral vanishes. In potential theory it is shown that the , potential F on C may be interpreted as a double layer of charge of strength ^ V, while the normal derivative of the potential on C may be interpreted as a single layer of charge of density dV/dn. Thus Green's formula ex- presses the potential inside C as due to a single and double layer of charge on C, the charges being determined by the known values of V inside C. Green's formula represents a very simple and general solution of the charge distribution problem. The simplicity is due primarily to the con- stancy of the potential outside C; and this in turn is made possible by the double layer of charge, which suppUes the discontinuity between the vari- able interior and constant exterior potentials. Unfortunately, from • the network synthesis point of view, it is not a practical solution, for double layers of charge lead to zero-pole combinations which are not easily realiza- ble. A double layer might be approximated by two closely-spaced strings of positive and negative charges, but the resulting zeros and poles would be in addition to the zeros and poles for the simple layer of charge. Hence the associated network would be difficult to design, and would also be unnecessarily compUcated and wasteful of network elements. It is well-known, however, that V and its normal derivative cannot both be assigned independently on C, and that the potential inside C is deter- mined when we know the values of V alone on C. This would make it pos- sible to eliminate the double layer of charge, if we could obtain the analytic continuation of V on both sides of C. Then we should have a potential which is continuous across C, and this would be consistent with the exist- ence of a simple layer of charge on C whose density is determined by the discontinuity in the associated stream function, as we saw in Section 3. We might remark that if V(P) is a given function of P outside C, the integral (33) will again express V{P) at points outside C in terms of the values of V and dV/dn on C. In this case V{P) must vanish at infinity at least as 1/p, and the value of the integral will be zero at all points inside C. Hence if we retain both single and double layers of charge it is possible to obtain a charge distribution on C for which the gain characteristics are assigned over the entire frequency axis. With simple layers the gain may be assigned only over that part of the frequency axis which Ues inside C. Then we must accept its values on the remainder of the axis, though it may be possible to control these values to some extent by varying the contour C. 19. The Exterior Transmission Function We have just seen that for a simple layer of charge on C we have to determine the analytic continuation of the transmission function on both 334 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 sides of C. Then the potential will be continuous across C while the stream function will be discontinuous by an amount which is determined by the charge on C in accordance with equation (24). If we write Fiip) = Viip) + i^i^iip) (34) for our known function inside C, and a corresponding expression Feip) = V,{P) + i^eiP) (35) for the complex potential outside C, then Ve is determined by F* , while ^e will be known if we know both^i and q. Conversely, q will be determined if we know both ^i and ^e . Thus the problem of determining the charge distribution on C may also be formulated as the problem of determining the exterior stream function "^'e . To make the function ^e unique we specify that it must be analytic outside C, and must vanish at infinity at least as l/p, except perhaps for a logarithmic term which corresponds to an equi- potential charge density on C. If the net charge on C is zero^e must vanish at infinity. Thus, if it is possible to solve this potential problem we have a corre- sponding solution of the charge distribution problem. The existence of a solution has been proved, and is known as Dirichlet's principle, but its solution has been formulated analytically only for circular contours. How- ever, for circular contours in the />-plane simple methods of determining ^e are available, and we shall discuss these before giving the general solution. 10. The Power Series Solution for a Circular Contour When the interior transmission function is given as an analytic function inside a circular contour, the exterior function may be determined by vari- ous methods. An elementary method is based on power series expansions. Since any analytic function of p can be expanded in a power series inside a certain domain of convergence the method has quite general application. To obtain the best form of power series applicable to our problem, we shall start by considering the expansion of the complex potential for a given set of lumped charges g„ located on the circle at points pn , F{p) = constant - S ^n log (p - pn). (36) n Inside the circle we have \ p\ < pniox each of the charge points />„ , and therefore each of the logarithmic terms may be expanded as convergent series in p/pn • Hence Fi{p) = constant - Z) ^n log (-/>n) - I] ?« log ( 1 - 7- ) n n \ pn/ = constant - YL qn\ - — - '^Tji - • • • \^ POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 335 and for the interior potential a suitable power series expansion is P Fiip) = oo+T.amP'^. (37) m=-l Outside the circle we have \ p \ > Pn , so that the logarithmic terms may- be expanded in convergent series of pn/p, Feip) = constant — 2^ ^n log ^ — £ ^n log ( 1 — ^) n n \ P / = .o-Mog.-i:.„(-^--|--). Hence a suitable power series expansion for the exterior potential is Feip) ^ bo-bo\ogp+ Z M"". (38) The constant bo represents the total charge on the circle. If there is no net charge the logarithmic term vanishes and Feip) is analytic outside C. It will vanish at infinity if we also have bo = 0, but for the moment we shall retain both constants, and apply the boundary conditions on C to determine the unknown constants bm from the known constants dm . On the circle of radius coo we have p = cooe^'', (39) so that just inside C the interior potential is Fm = ao+ Za^o)?^*"*", (40) w»=l while just outside C the exterior potential is FM =bo-bo log (a,o^*') + E bmc^o'^e-'"'', (41) In our apphcations the constants a and b are real, hence we may separate the real and imaginary parts of (40) and (41), and find Viii}) = oo + Z (^moy^ cos w^, ^ii^) = Z) ^m(^o slu Mt}, (42) Vei^) = &0 — ^0 log I COo I + Z bmOio"" COS M^, ^M = -&ot> - Z bmo^o"" sin mi}. (43) The condition that V must be continuous across C determines the b's: bo — bo log I coo I = flo , bm = o)Tam , m> 0. (44) 336 THE BELL SYSTEM TECHNICAL JOXIRNAL, APRIL 1951 Then the charge distribution is determined by the discontinuity in^ across C If we measure the charge from the real axis, t? = 0, we find from equa- tion (24), lirqid) = 2 OmOiS sin wt? — [— &o^ — S ^mco^"* sin md] Hence we have two alternative formulations for q: qW = -^ \- - zl bm coT^ sin m^ got? 1 A = — r> 1 I / / 1 + - 2l^ gmcoo sin wt? . ZtT log I OJo/Wo I TT m=l (45) We have substituted bo = bo log | coo | for the constant bo , where coo is an undetermined frequency. The total charge on the contour is q(2T) = bo = — flo/log I ojo/coo | • (46) Since the total charge must be non-negative this implies that bo ^ 0, but ao may be either positive or negative, according as coo is greater or less than coo . The gain and phase are determined by the values of F on the real fre- quency axis, p = io)j hence, inside C, «.• = oo + Z (-)" a2nCo^ /3, = E (-)" a2n+ico^"+' , (47) and outside C, 2/1+1 W n=l n=0 Oie = —^0 log I £0/C0o | + S (" )" ^2nC0 (48) ^. = ±*o ^ - Z (-)" *. -2n-l r, .^^ N X -'2n+lW -^ n=0 where the minus sign in /3e refers to points on the positive half of the co-axis, and the plus sign to points on the negative half. We note that a is an even function, of a> while /8 is an odd function. This agrees with equation (7) and it means that if only the gain is prescribed we know directly only the even coefficients, a2n , in the power series ex- pansion, oi Fi . Hence we know only the even part of Fi{p). But we have seen that the singularities in the logarithmic expression for a occur in pairs, one of each pair being the negative of the other. To determine the complete transmission function Fi(p) we must assign one of each pair of singularities to F(p) and the other F{—p) in such a way that equations (7) and (8) are satisfied. POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 337 For the unit circle the exterior potential and charge equations take very simple forms. Corresponding to the interior potential Fiip) = ao + Z OmP-, (49) we find F.{p) = -Q log (/./U) + E a„/.-", Q^ gW = ^ + - 2^ dm sin »«? , (50) where Q is the total charge on the unit circle, Q = ao/log | coo | . The coeffi- cients in all three series are identical. . x--^^ 2a: = -LOG[i + (a?/a;o)^"] Fig. 11 — Unit charges arranged symmetrically on a circle for the maximally flat filte approximation. As a simple example let us determine the charge distribution on the unit circle which corresponds to a constant gain for | co | < wo , and to a phase shift independent of co. By equation (49) this requires that a^ = 0 when m 7^ Oj and hence the continuous charge distribution on the circle is simply ,«, = g (51) where Q is the total charge on the circle. Equal increments in ?> give equal increments in the accumulated charge round the circle. If we ignore the requirements of reahzability this distributed charge may be approximated by simply dividing the unit circle into 2m equal parts, and placing a unit positive charge at each point of division, Fig. 11, p^ = g»*'/-, yfe = 0, 1, . . . 2m - 1. (52) 338 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 The total charge is Q = 2w, and the transmission function for the lumped charge distribution is 2m-l Fiip) = constant - 2 log(p - pk) . (53) Since {P - PoXp - Pl) '"{p- p2m-l) = f"" - 1, (54) this is equivalent to Fi{p) = constant - log {p^"" - 1), (55) at all points inside the circle \ p\ = 1. This is the transmission function for the Butterworth "maximally-flat" filter.^ As m increases Fi is more and more nearly constant inside C. But the objection to this solution is that it involves poles (or positive charges) in the right half of the ^-plane. If the phase is of no importance we may use the gain invariant trans- formation to transfer these poles to the left half of the plane, which is equivalent to using only the left half of the contour, and doubUng the charge at each charge point. Then we have a physically realizable charge distribution such that For integral values of Q we locate charge points at ^& = ^* * , where TT IT ^ ,» , TT ''»=i-2^' ..,. = ^. + ^. (57) The shape of the gain characteristic for small values oi Q = 2m is illus- trated in Fig. 12. It approximates zero gain at frequencies inside the circle, and the approximation improves as m increases, or as the frequency de- creases. At frequencies outside the circle the gain becomes a high loss, and the filter is of the low-pass type. The transfer of poles from the right to the left half of the />-plane leaves the gain unaltered, but it changes the phase delay, since the sign of the phase contribution from each transferred charge is reversed. It is possible to compensate for this change by adding a simple charge distribution such as that shown in Fig. 13. Here the positive charges on the left are matched by the negative charges on the right, so that the electrostatic field is zero along the real frequency axis and the charges merely add a constant gain. The contribution to the phase delay from each negative charge equals that from the corresponding positive charge. Just as in the condenser plate analogue POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 339 u UJ Q Z <0 to o 0 FREQUENCY, CO Fig. 12 — Curves showing successive approximations to zero gain with maximally flat filters K 0 X © X G X o X 0 X o REAL p X O X O X o X o y X o X o Fig. 13— A symmetrical charge distribution about the real frequency axis used to correct the phase delay. of Fig. 5 the two sets of charges can be interpreted as equal and opposite charge densities on the two halves of the contour, thus giving a constant 340 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 phase delay. This method is of general application in changing the phase delay, and the corresponding networks are easy to obtain. 11. The Inversion Theorem for a Circular Contour An alternative derivation of the exterior stream function for a circular contour of radius coo is based on the method of inversion, in which p is re- placed by oil/pj Fig. 14. This transformation maps the region inside C on the region outside C and vice versa. Points on the circle remain on the circle but are transformed to the conjugate complex points. Now suppose that the transmission function Yi{p) is defined inside the circle as an analytic function of p, and that it satisfies the conditions for physical realizability. Then if we have a unit charge at some complex point, Fe(P) = Fi,(a;g/p) Fig. 14 — The inversion theorem for a circular contour. p on the circle there must be a hke charge at the conjugate complex point, />*, while the total charge must be non-negative. For simpHcity we may assume that the total charge is zero and then the exterior function Fe{p) must be analytic outside C. We wish to show that Fi(col/p) may be inter- preted as the exterior function. Obviously since Fi{p) is analytic inside C we must have Fi{o}l/p) analytic outside C. Hence it will represent the ex- terior function outside C if it represents a function whose potential is the analytic continuation of the potential inside C. On the circle we have \p\2^ pp* = ^l ^ or /»* = cooV/'. (58) But we have akeady seen that when the complex zeros and poles occur in conjugate pairs we must have \Fi{p)]* = Fi{p*). Hence on the circle FiifA/p) = Fiip^) = \Viip)]* = Vi - i<^i . (59) POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 341 This is the value of the transformed function as we approach the circle from points just outside C, corresponding to the value Vi + i'^i for points just inside C. Thus the potential is continuous across C and consequently we have proved that for all points outside C, the function FeiP) = Fi(0,l/P) = Ve(P) + i^ifeip) (60) is the exterior function for the circle. We have just seen that on the circle ^e = —^i^ hence equation (24) for the integrated charge reduces to qW = -[^i(t?) - ^iiM + Qo , (61) TT where Qo is a constant charge density, and the charge is measured from t?o . 12. CONTORMAL TRANSFORMATIONS From the network point of view, unfortunately, the simple solution for a circular contour does not always lead to the best solution of the design problem. Hence we must also consider more general contours. The potential analogue method requires an ab initio choice of contour on which the zeros and poles of the approximating transmission function are to be located. Small changes in the contour shape should not be of great importance, but it may happen that our initial choice leads to a very complicated network when a much simpler one would satisfy the physical requirements. Experi- ence is required to make the most effective use of the method, and various simplifications may frequently be available. For instance, it may be possible to split the assigned gain or phase functions into components, for some of which the zeros and poles may be located by inspection. Then the potential analogue is used to synthesize the remaining components. There is, however, one limitation on the choice of contour which is inherent in the potential interpretation, namely, that the transmission function must be finite and analytic inside the contour. This is because the value of the po- tential on C defines its values at all points inside C only if these values, and their derivatives, are finite throughout the interior. We can see this intui- tively when we remember that for a given charge distribution the potential and its derivatives are finite at all points not occupied by the charges. It happens that the type of contour most frequently used up to the present has been the ellipse, and we shall discuss this contour in more detail later. For the present we shall consider more generally any simple closed contour in the complex p-p\a,ne, surrounding the frequency band of interest, I CO I < coo . The contour must be symmetric in the real />-axis, as we have seen, but we shall not impose any other restrictions except the fundamental one that the given complex potential must be analytic inside C. 342 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 We now introduce the theory of conformal transformations, and use the fundamental property that any simple closed curve in the finite />-plane may be mapped, by an analytic transformation, on the unit circle in a second complex plane, which we shall denote by the w-p\a,ne. Suppose that p = T{w) (62) is such a transformation. Primarily the transformation must be such that points on the contour C in the />-plane become points on the unit circle, Ci , in the 2£^-plane, but this is not sufficient to define T uniquely. To make the definition unique, in a way which we shall find convenient in solving our potential problem, we impose the following conditions: 1) T(w) maps Ci on C 2) T{w) maps the exterior of Ci on the exterior of C in a one-to-one analytic manner ,^^s 3) The point at infinity in the 7£;-plane corresponds to the point at infinity in the />-plane 4) r(+l) is real and positive. Now if our assigned transmission function in the />-plane is Fiip) = Viip) + i^iip) (64) the assigned transmission function in the ze;-plane is F'iiw) = Fi\T{w)] = V'iiw) + i^'iiw) (65) and our problem is to find the exterior function Fe{w) in the w-plane. Un- fortunately this problem cannot usually be solved by the simple inversion theorem for the circle in the />-plane, because the transformation (62) intro- duces singularities in F'i{w) which are in addition to the singularities due to the poles and zeros of the original function. The second condition of the set (63) requires that Feiw) must be analytic outside Ci , but in general Fi(w) is not analytic inside Ci and the inversion theorem will therefore not lead to an analytic form for F'e{w). The second condition of the set (63) was deliberately chosen to make the mapping Feiw) of the unknown exterior function Fe(p) analytic outside Ci . The extra complexity of the potential problem for the general contour C, as compared with the circle in the />-plane, arises because it is not usually possible to define the transformation in such a way that, simultaneously, the mapping Fi{w) of the known interior func- tion Fiip) is analytic inside Ci . Two exceptions are when Fi{p) is constant so that F'i{w) is also constant (the equipotential distribution), and when T(w) is a linear function (when the original contour in the p-plane is also circular). POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 343 Hence we must find a more general solution of the problem for the circle before we can use the potential analogue method to its fullest extent. This we shall do in the next section. For the moment let us assume that we have solved the problem for the unit circle in the Te;-plane, and thus determined a charge distribution on Ci for which the potential is continuous across Ci . Now, by our definition of T, points on Ci correspond to points on C. Hence we find the distribution on C by an inverse transformation in which the charge at any point on Ci becomes the same charge at the corresponding point on C. This charge distribution on C has the required potential inside C It may be simpler in practice to determine a convenient lumped charge distribution on Ci and then transfer these lumped charges to the corre- sponding points on C. It remains to determine T(w)j satisfying the conditions (63). One method is based on the remark above that if C is an equipotential in the />-plane then Ci is an equipotential in the w-plane. Hence T might be defined as the transformation that maps equipotential distributions on C as equipotential distributions on Ci . This transformation has been determined for many con- tour shapes in the classical theory of equipotential distributions. At the same time the precise shape of the contour is not usually critical for network purposes, so that it may be simpler to choose a T{w) directly and determine the corresponding shape of the contour. A simple functional form involving two or three parameters might be assumed, for example, riw) = aw -^+ -^ (66) W TiT where the parameters a, b, c will be sufl&cient to give C any length and breadth and a considerable further variation in shape. Illustrative shapes for transformations of the type (66) are shown in Fig. 15. In practice the special case of the ellipse, for which c = 0, is often adequate. 13. Poisson's Integrals We turn now to a general solution of the exterior potential problem for the unit circle in the w-plane, which may be used when the simple inversion theorem is not apphcable. For this purpose we start from Cauchy's integral, where C is a simple closed curve in the w-plane and the integration is taken clockwise round C It is assumed that Fe{w) vanishes at infinity at least as 1/w, and then the integral expresses the value of an analytic function Fg at any point outside C in terms of its values on C. 344 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 We are interested particularly in applying (67) to a point just outside the unit circle in the 2£;-plane. To do this we place the point w on the circle and then keep it just outside the actual contour by introducing an infinitesi- mal semicircular indentation as shown in Fig. 16. Over this semicircle the integral may be evaluated by writing \ — w = 8e^", where 5 is the infinitesi- mal radius, and assuming that FeiX) is practically constant; then its value is iFXwl (68) ' ^ r/- 16*' 16 W 16 w3 3r(w) = ^W-AJ.4.J5J5 Fig. 15 — Illustrative contours for the transformation. p = T(w) = aw 1 ; w vf Then over the contour C which is the unit circle excluding the indentation, (67) becomes in Jc'\ — w (69) If we now interpret Fe(X) as the exterior complex potential of our charge distribution problem, on the circle, and introduce angular coordinates X = e^\ w = e»>, (70) POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 345 the integral may be written v.W + i^M^.,^^ (71) where P denotes the principal valuef of the integral, corresponding to the contour C'\ that is, with an infinitesimal segment at the singularity ^ = (p \=eL<> Fig. 16 — Unit circle contour with semicircular indentation at p. omitted. In the integral (71) the value of VeW is known (since it is equal to F,(t?) on C ) and we shall now show how to determine "^e from Ve. If we separate the real and imaginary parts of (71) we find VM = -^ P f [VeW + ^eW cot i(^ - ^)] d^, Jtt Jo 'TT ^0 ,2)r "i^eM = ^ P [ [VeW cot i(^ - -plane ellipse C of Fig. 17 by the transformation p = T{w) = i^J''^ - -) , (84) where the major axis of the ellipse is along the real frequency axis with foci at ±/coo , the intercepts on the co-axis are at zhiioioii + k), and the inter- cepts on the ^-axis are at ±io;o(, — k). This transformation will map the outside of Ci on the outside of C if coo and k are real positive constants with 348 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 k < 1. The eccentricity of the ellipse varies with k; in the hmit ^ ^ 1 the elhpse degenerates to the segment of the real frequency axis | co | < coo . Now for a given transmission function inside C, Fi(p), the complex po- tential inside Ci is Fi{w) = Fi[T(w)]. In general this function will have singularities inside Ci , but when Fi(p) may be expanded in a power series in p we may use the separation theorem of the last section to obtain a simple formula for the charge distribution on Ci . For instance, let Fi{p) be a poly- nomial in p, Fi(p) = T.anp\ (85) n then .:.w = i:4»yt-y". (86) When the binomial is expanded in a power series the terms involving positive p PLANE Fig. 17 — Elliptic contour in the />-plane. powers of w will belong to Fa{w)f while the terms involving negative powers will belong to Fb(w). Hence the parts of Fi{w) analytic respectively inside and outside Ci are ..« = r..(|)-[©--.©-% n(n — 1) 2! (r-] n-2 + 2! POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 349 When n is odd each series ends in the first power of its argument; when n is even Fa ends in a constant (which may be ignored in determining the charge distribution) while Ft ends in a term in w~ . We have seen that the charge distribution on Ci is determined by Faiw), and from equation (78) we find fro\ ^ \^ /wo\Tsin M sin {n — 2)^ . ~| (88) Corresponding to each power ^" in Fi{p) we have a finite Fourier sine series for q\^). Conversely, the powers of p from 0 to n, for each value of it, may be summed in such proportions that the resulting w*^ degree polynomials, Fi(p), correspond to charge distributions sin nd^ on Ci . The actual form of these polynomials may be determined by considering the formulas we have just derived. sin n^ If the charge distribution is Cn — -. — , the corresponding term in Fa{w) is Cn{w/ky, and this is matched by the term Cn{—k/wY in Fb(w). Hence the interior function for this charge is *,=e.[©- +(-!)■ (89) Now on the real frequency axis, p = iw, the solution of equation (84) for w in terms of co is w = ke^, 6 = sin"'-. (90) coo This means that the real frequency axis in the />-plane in the region j u) | < ojo corresponds to a semicircle of radius k in the w-plane. Substituting from (90) in (89) we have F,M = CnW"' + (-)V-'»'|. (91) Hence, corresponding to a charge distribution //„\ ^ ^ sin w^ , ^/ in the w-plane, we have, on the real frequency axis in the /i-plane. Fi(to) = I Z CAe'"' + (-)" e-""] + Co 00 *o = 2 C2m cos 2md -i- iJ2 C2m+i sin (2w + 1) 5 m=0 rn=0 350 THF BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 We write this result alternatively in the form ^t(^) = JlC2mT2m{0)) + iJ2C2m+l T2m+l{oo) (93) where Tom is the Tchebycheff polynomial of even order, T2m(co) = COS \2m sin~\co/coo)] (94) and T2m+i may be interpreted as a modified Tchebycheff polynomial of odd order, particularly adapted to network synthesis problems, T2m+i{oi) = sin [(2m + 1) sin~\co/coo)]. (95) It is easy to verify that the T's are in fact polynomials in co/coo . For the first few values of n we find Wo \coo/ Wo \coo/ \wc/ \coo/ In deahng with prescribed gain and phase functions for elliptic contours, the simplest procedure is to expand the gain, not in an even power series, but in a series of even Tchebycheff polynomials, while the phase is expanded in a series of odd Tchebycheff polynomials. Such expansions are always possible for analytic functions, and it should be pointed out that their region of convergence is greater than that for a simple power series. An addi- tional advantage of using the polynomials instead of the power series is that the r's are orthogonal in the frequency range | co | < coo , while the various terms of the power series are not. This increases the rapidity of convergence and leads to a more efficient solution of the design problem. A simple illustration of the effect of contour shape on the accuracy of the lumped charge approximation to the transmission function is shown in Fig. 18. This refers to the constant gain filter we discussed, for a circular contour, in Section 10. The granularity error for the circle (curve 1) is very small at low frequencies, while for the two elHpses (curves 2 and 3) it is small, but oscillatory, and the oscillations become larger as the ellipse becomes nar- rower. On the other hand, at frequencies near the upper limit coo of the fre- quency band, the granularity error is much smaller for the ellipses than for the circle; in other words, the cut-off frequency is more sharply defined. 16. The Expansion Theorem for General Contours The term by term correspondence between the Fourier expansion of the charge on Ci and the expansion of the gain and phase functions as series of polynomials holds also for general contour shapes. In the general case POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 351 the polynomials are not of the Tchebycheff type, and as a rule they are not orthogonal. By its definition in (63) T(w) can always be expanded in a series of the form r(w) = TI,W + ^0 + JlgnW ", (97) valid on and outside Ci . It follows that ^", which transforms into [r(w)]", can always be expanded as an n degree polynomial in w plus a power series in 1/w, and these correspond to Faiw) and Fbiw) respectively. The charge FREQUENCY, UJ Fig. 18— Illustrating the effect of contour shape on the accuracy of the approximate transmission function for a flat filter. on C] corresponding to ^" is determined by Faiw) and is therefore a finite Fourier sine series, similar to (88) except for more general coefl&cients. Con- versely, we can always construct a polynomial in p of degree n, by choosing appropriate coefficients for the various powers of p, in such a way that the charge on Ci is merely sin nj^. In other words if then g'ii9) = sin ni^ F^(p) = Pvnip) 352 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 where Prnip) is a polynomial of degree n whose coefficients depend only on T(w), that is on the shape of the contour. By summing the above relations for all values of n we have the general expansion theorem, Fiip) = 11 Cn Frnip), ^ (98) q'W = ZjCn sin M. Thus if the assigned gain and phase functions can be expanded in terms of the polynomials Pvn{p), appropriate to the given contour, then the Fourier expansion of the charge on Ci can be written down immediately. 17. High-pass and Band-pass Filters So far we have assumed that the contour in the />-plane is a simple closed curve. This is adequate as long as the positive frequencies of interest extend REAL p Fig. 19 — Appropriate contour for a high-pass filter. from zero to a finite upper bound, ojo , as in low-pass filters. For high-pass filters, in which the positive frequencies extend from a lower bound, coo , to infinity, an appropriate shape of contour is shown in Fig. 19. However, high-pass problems can always be reduced to the low-pass type by simply using \/p as the variable instead of p. POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 353 In band-pass filters, whose positive frequencies of interest extend between two finite values, coo < oj < coi , we must be able to use a contour of the type shown in Fig. 20a. This consists of two disjoint closed curves, one above and one below the real axis (real p). The physical requirements are satisfied if the curves are symmetric about the real />-axis, but as usual it is advan- tageous to make them symmetric also about the real co-axis. For then, if a point py lies on one of the curves, the point — pv will lie on the other. This makes it possible to map the disjoint contour C on a single closed curve C2 in the ^^-plane, the ^'-plane of Fig. 20b, by means of the transformation P = ^/y- The single contour C2 may now be mapped on the unit circle in (a") p PLANE (b) y PLANE = p^ PLANE (C) w PLANE Fig. 20— Contours for a band-pass filter; (a) disjoint contour symmetric about both axes in ^-plane, (b) single contour in /)2-plane, (c) unit circle in tt'-plane. the w-plane. Fig. 20c, by means of a second transformation y = ri(w). Combining the transformations we have p = VFiW (99) P = TiW, as the transformation which maps C on Ci . The conditions on the function Ti(w) are the same as in (63) except that, since C2 is in the left half of the y-plane and does not cut the positive real axis, the fourth condition must be replaced by a similar requirement. ri(+ 1) — ri(— 1) is real and positive. Now the presence of the square root in the transformation (99) may introduce branch points in the w-plane corresponding to the branch points 354 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 at zero and infinity in the >-plane. There will be no branch points if the original transmission function Fi{p) is an even function of p, for then the exterior function Fe{p) will also be an even function. In this case the simple closed curve analysis does not have to be modified. The usual method can be used to determine ^e(w) in the le-plane, and the charge distribution on C\ determined. When Fi{p) is an odd function, however, we have to proceed more care- fully, since the transformation now introduces branch points in the ^e'-plane corresponding to a /ac/oy \/Ti{w). In this case we assume that Vi{w) is given in analytic form, and determine the root Wi of Ti{w) = 0 which lies outside Ci . Then it will be possible to express Fe(w) in the form V 1 — w/wi where G(w) is analytic outside Ci , and has the proper behavior at infinity. From the conditions imposed on Ti it can be shown that Wi is real; hence we introduce a rationalizinoj factor MM = a/(i-^-)(i-±), (101) y \ Wi/\ WWiJ and multiply both sides of equation (100) by M{w). This leads to M{w)F'e{u^ = A/l - — G{w) = H{w), (102) y wwi where H{w) is analytic outside Ci . On Ci , | w | = 1, so that M{w) is real and on Ci the potential and stream functions are defined by Miw) V[{w) = Re H(w), (103) M(w) "^eM = Im H{w). Thus the real part of H{w) is determined by the known potential Veiw); this determines in turn the imaginary part of H(w) and hence ^^(2^) is de- termined. When Fi{p) is neither even nor odd we divide it into even and odd parts and treat each part separately. If only the gain is important we need retain only the even part, or if only the phase is important we consider only the odd part. 18. Examples So far we have been describing the potential analogue method in general terms, and developing a systematic design procedure applicable to a wide range of problems. The method involves a certain arbitrariness, in the initial choice of contour, and there may also be some doubt in the reader's mind as POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 355 to the accuracy of the final result, since a general theory of granularity errors has not been developed. Hence in this section we shall consider the apphca- tion of the method to some actual engineering problems. This should aid the reader in using the method himself, and should also help to convince him of its validity. Example 1. The Gaussian Filter It is required to design a low-pass filter whose voltage transfer ratio is exp { — b(jy) and which has constant phase delay in the prescribed frequency range. For convenience we choose our unit of frequency to make the cut-off frequency equal to unity, and then we choose our contour C to be an ellipse in the /)-plane passing through the points p = d=|, d=?". The assigned transmission function in the />-plane is Fiip) = bp'' - I3P, and the transformation which maps C on the unit circle in the w-plane is p = Tiw) = - - — . In the w-plane the transmission function is and the part of Fi analytic inside Ci is r. f \ 9Z> 2 3|S 3 , FaKw) = — w "" ^^ ~ 8^* Hence, by the separation theorem, the required continuous charge distribu- tion on Ci is ,W = ^ sin 2.-1^ sin. + f!^, 16t 47r ZTT where we have assumed a total charge Q on the circle. In practice the values of b and Q are usually assigned, while the magnitude of the phase delay is at our disposal. Hence we choose /3 large enough to insure TT that ^'(^) is a mono tonic decreasing function for 0 < ?? < - . This makes it possible to divide the continuous charge into a set of unit steps, such that these steps are negative in the right half plane, and therefore correspond to zeros of the transmission function. A typical set of numerical values is b = l, e = 3, 5 = ^'. 356 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 For these values we find unit increments in q at the zeros (negative steps) 0,rb25°.47,±55°.76; and at the poles (positive steps) =tl20°.65, ±142°.89, ±158°.99 and =tl73°.17. These five zeros and eight poles on the unit circle in the w-plane are now mapped back to the corresponding points on the ellipse in the ^-plane, where they give the location of the zeros and poles of the approximate transmission function. Figure 21 illustrates the accuracy of the resulting approximation to the prescribed gain and phase. 1.0 0.9 0.8 0.7 0.6 z > >0.5 D >° — 0.^ 0-3 0.2 0.1 ^ \ • • \ x' y \ %nu^^ • y^^^^^ \ V >< -plane, so that Fi{p) = kpi/2 e'V/2, Vi{p) = kp'^' cos y, ^iip) = kp'i^ sin J^, and it is easy to see that the equipotentials are parabolas in the />-plane, as illustrated in Fig. 22a. Along the equipotential V i = k ■\/a the stream function is ^^Xp) = ± k\/p - a where the positive sign refers to that part of the parabola which lies above the real />-axis and the negative sign to the part below the real />-axis. The closure of the contour at infinity is shown in Fig. 22b. ^ N \ / \ / i \ r \ \ ' 1 / / (b) Fig. 22 — The cable transmission function K y/p ; (a) equipotential contours are parab- olas, (b) contour closed at infinity through a circular arc. If charge is placed on the equipotential in such a way that ^t/lir repre- sents the integrated charge density, then the correct potential and stream function will be produced everywhere to the right of the contour and the potential to the left of the contour will be the constant k\^a. To keep the contour from crossing the Im />-axis we must take a = 0. Then the parabola degenerates into the negative real />-axis and charge is distributed with inte- grated density function Q{p) = --V~P on the axis. The lumped charge approximation consists of placing zeros at points pn = —Pn where Q(p„) = w — J; i.e. zeros are to be placed at pn = - (n - 2)^^, n =, 1, 2, 3 358 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 The gain and phase for this infinite array of zeros are obtained from the function = kp'" + log (1 + e-^'"""") + const. Thus the correct function kp^''^ is obtained modified by a term of the order e~'^^^ representing ''granularity error". The solution as it stands is impractical for three reasons: (i) an infinite number of singularities are used, (ii) the singularities are all zeros so that one cannot satisfy the physical realizability requirements, (iii) the granularity error becomes appreciable at low frequencies. Objections (ii) and (iii) may be avoided by choosing two numbers ki , ^2 such that k = k2 — ki and making lumped charge approximations for kip^''^ and kip^'"^ separately. That is, we put zeros at — (/^ — J) VV^2 and poles at — {n — ^Yir/ki. By choosing ki and ^2 large enough we obtain a very fine-grained approximation to the ideal (continuous) charge distribu- tion and can make the frequency at which granularity effects become bother- some as low as desired. Moreover since poles as well as zeros are used, we are now in a better position to satisfy the physical realizability requirements. When designing the network in this way it is convenient to make ki/ki a rational number with numerator and denominator as small as possible. If the numerator and denominator are q^ and qi then every zero pn , for which 2n — 1 is a multiple of ^2 , is cancelled by a pole which falls at the same place. The most obvious way to remedy defect (i) is to use just the first .V zeros and the first N poles, picking N large enough so that the infinite set of zeros and poles which are being ignored produce only a negligible effect in the frequency band of interest | co | < 1. To get an idea of how large N must be, we evaluate the integral fip) = I k log (1 + p/r) 2. Vr '^'■' which represents the gain and phase contributed by all the charge from p = —R to p = — 00 in the continuous distribution. The substitution r = x^ transforms the integral into an easily handled form and we find /(/>) = - * [VR log (1 + 1) - 2V^ tan-' V/TAr], so that/(/>) is about k p/ir\/ R when | R/p \ is large. POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 359 In practice we soon find that we must use an unnecessarily large number N of zeros and poles to get good accuracy from the simple trick just described. A better plan is to keep just those zeros and poles which lie within some more moderate distance from the origin, say R = 2. Then the remaining gain and phase f(p) must be approximated by other means. This offers no special difficulty; the disagreeable p^^- type singularity at the origin has already been produced, leaving f(p) a relatively slowly varying function over the band I CO I < 1. One way of approximating /(^) by the log of a rational function with the desired number of zeros and poles is first to find a polynomial approximation to /^^^ and then pick the rational function which has the same first few terms in its power series as the polynomial. In the design carried out at BTL the polynomial approximation was performed by a method using Tchebycheff polynomials. This method will be the subject of a later paper. For purposes of illustration we may equally well imagine f(p) to be produced by placing charge on an eUiptic contour surrounding the interval | co | < 1. The following numerical example will give the reader some idea of how well the method works in actual practice. The cable had a loss of 5.368 nepers (46 db) at CO = 1 and it was required that the cable be equahzed to within .005 db from co = .02 to co = 1 . Using zeros only on the negative real axis, the granularity error would have been much too high. Sufficiently low granularity error was obtained by putting poles at p = -.0068498 (2n - 1)^ and zeros at p = -.0034948 (2n - 1)2. This choice of position of zeros and poles makes every seventh zero cancel every fifth pole. In the final design only 6 of these zeros and 6 of the poles were used. The remaining gain and phase were produced, to the desired accuracy, by a pair of real poles at /> = —1.5 and four pairs of conjugate complex poles lying close to an elliptic contour about the frequency band of interest. Example 3. Delay Equalizer A problem of frequent occurrence is that of ''delay equalizing" a given network with known singularities. From the potential analogue point of view the problem is, given the location and sign of certain lumped charges, to find a distribution Qi(s) of charge on a contour C which produces no other effect on the real frequency axis in the range of interest but to cancel the transverse component of the electric field of the given charges. The distribu- 360 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 tion of charge Qi{s) as it stands gives rise to non-physical networks with poles in the right half -plane. However it is possible to add to Qi(s) sl dis- tribution of charge producing a high enough uniform cross-axis field (flat delay) so that the total charge distribution Q{s) yields physical networks. For the time being consider just the equalization of one. singularity. If we solve this simple problem the Qi(s) for the general case of any number of singularities can be obtained by adding up the charge distributions for the individual singularities. For the sake of concreteness imagine the singularity to be a unit positive charge at ^o = —a-\r ih in the left hand />-plane. What is needed is a distribution q\{s) of charge on C which produces inside the contour the complex potential I'^'^p + pt corresponding to a charge — | at />o and a charge + J at — /)o . By the phase invariant transformation, these two charges give the same field across the oj-axis as a unit negative charge at pQ , while along the axis their fields cancel. Note that we have reversed the sign of the charge at pQ . This is because the shielding distribution on C due to any set of exterior charges must be such that its potential inside C exactly cancels the potential of the charges, that is, it matches the potential that would be obtained if the signs of all charges were reversed. Now the complex potential of a point charge Q at — />o , outside C, isF(p) = — Q log {p — po). When this is mapped on the w-plane by a transformation p = T{w) which maps C on the unit circle Ci the transformed function may be separated into two parts, analytic respectively inside and outside Ci , F.W = -Q log {w - w,), F,(w) = -Q log rW - rfae)^ W — Wq where Wo is the w-p\sine mapping of po , defined by po = r(wo), and Wo is outside Ci . We have seen that the mapping of the charge distribution q(p) on C into the charge distribution q'{w) on Ci is determined by Fa(w), and in the present case Faiw) represents the complex potential of a point charge Q located at Wo . It follows that the required shielding distribution on C in the presence of exterior charges maps into the shielding distribution on Ci in the presence of the mappings exterior to C\ of the exterior j>-plane charges. Thus in the w-plane our equalization problem is to determine the shielding distribution on C\ due to a charge +^ at Wq and a charge — J at i^o , where — pt = T(wo). Since we are considering only one singularity in the /)-plane, and ignoring the physical requirement of an equal singularity at the con- jugate complex point, we cannot apply the simple form of the inversion POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 361 theorem to Fa{w) directly. We could modify the theorem without difficulty but we may also solve the problem by using the well-known electrostatic method of images, f The complex potential for the required shielding dis- tribution is , 1 w — Wq 1 w — w WW = - log j- - - log Y y Wo d w* and the shielding charge distribution is obtained by evaluating the imaginary part of W\ If the contour C is symmetric with respect to the real frequency axis, symmetry considerations in the w-plsine will show that w = —wq; then the charge distribution may be written in the expUcit form ^.W=-tan [^(^.+ ,)_2ig2 3i,,J> where Wq = —A-\-iB and R^ = A^ -\- B^. This (integrated) charge distri- bution, when mapped back on the original ^-plane contour C, becomes the shielding distribution qx{s) sought. If the singularity were a zero instead of a pole, q\ would be given by the same expression with a factor — 1. The procedure for delay equalizing a group of singularities can be out- Hned as follows: (1) Find a conformal mapping of the outside of C on the outside of the unit circle. (2) Compute Qi=H qii i as a function of d. Here the sum runs over all the given singularities and qu is the distribution which equalizes the i-th singularity (computed from an expression like that for qi given above). (3) Since Qi puts some poles in the right half-plane, compute Q = Qi- Dsin d, choosing the constant D large enough to make all the poles of the distribution Q he in the left half-plane. The only effect of the distribution D sin d is to add flat delay. (4) Approximate Q by a, function with unit steps, say at ^i , ^2 , • • • , ^at . (5) Map the singularities found in (4) on the p-plane to obtain the equalizer singularities. Figures 23, 24, and 25 illustrate a delay equalizer design taken from actual practice. Figure 23a shows the p-plane locations of the singularities t L. Page, Introduction to Theoretical Physics, D. Van Nostrand an^ Co., New York, 1935, p. 404. 362 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 J REAL W X Xx X * -X 1 (- \l xf REAL p (a) p-PLANE (b) W- Fig. 23 — Delay equalizer singularities and assigned contour; (a) in ^-plane, (b) mapped on ^e^•plane. Fig. 24— Curve for integrated charge as function of 6 and its approximation by step functions. POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 363 (all poles) of a high-pass filter, f The contour C is shown surrounding the band of interest. There are really two contours, one surrounding a band of positive frequencies and another surrounding a band of negative frequencies. To obtain an exact solution for the charge distribution using two contours would be very troublesome. Fortunately the two contours are far enough 3.5 3.0 2.5 2.0 0.5 Z 2.870 FILTER AND EQUALIZER 1 y EQUALIZER ^ / ^ / V ^^ FILTER 1 2.860 \ \ ^^ \ FILTER AND EQUALIZER / \ \ "\ / V^ VA A/ -J 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 FREQUENCY IN MEGACYCLES PER SECOND Fig. 25 — Curves showing phase delay of filter, equalizer and their combination. apart so that the charges on one produce only small effects inside the other. The charge distribution on the upper contour was found by replacing the lower contour charges by a single large pair of positive and negative charges. The delay to be produced by the equalizer varies slowly across the band t The zeros (not shown) of the filter are on the imaginary axis below the pass band. They are ignored because they contribute no delay. 364 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 except near the low-frequency end. In view of the success of the condenser plate contour for producing fiat delay, it was felt that C should be chosen to be nearly rectangular. An actual rectangle could have been used for C, but the mapping to a circle involves unwieldy expressions containing elliptic functions. The contour shown was used instead because it is nearly rectangu- lar and because it has a simple mapping function • ^ in I 1 '7'7c 1-075 0.2 p = t 6.10 + 1.775w — — -— w ixr (here p is expressed directly in megacycles). This contour was obtained by plotting a few of the contours for different numerical values of the constants in the above mapping function. The w-plane images of the singularities and of the lower contour are shown in Fig. 23b. The charge Q as a function of d is shown in Fig. 24 together with the step function approximation. Figure 25 shows the delay produced by the filter and equalizer together. 19. Acknowledgements The author wishes to express his indebtedness to H. W. Bode, whose earlier potential analogue methods are included in this paper; to E. N. Gilbert, whose suggestions regarding potential theory were most helpful in simplifying the author's extension of the theory; and to S. A. Schelkunoff, M. C. Gray, and E. N. Gilbert, for their cooperation in the preparation of the manuscript. R-FERENCES 1. H. W. Bode, Wave Transmission Network, U. S. Patent No. 2,342,638, February 29 1944 2. W. Cauer, Das Poissonsche Integral und seine Anwendungen auf die Theorie der linearen Wechselstromschaltungen (Netzwerke), Elektrische Nachrichten Technik, 17, pp. 17-30, 1940. 3. R. F. Baum, Design of Broadband I.F. Amplifiers, Jour. Appl. Phys., 17, pp. 519-529 and 721-730, 1946. C. H. Dagnall and P. W. Rounds, Delay Equalization of Eight-Kilocycle Carrier Program Circuits, Bell Sys. Tech. Jour., 28, pp. 181-195, 1949. R. M. Fano, A Note on the Solution of Certain Approximation Problems in Network Synthesis, Franklin Inst. Jour., 249, pp. 189-205, 1950. W. W. Hansen, On Maximum Gain-Bandwidth Product in Amplifiers, Jour. Appl. Phys., 16, pp. 528-534, 1945. W. W Hansen and O. C. Lundstrom, Experimental Determination of Impedance Functions by the Use of an Electrolytic Tank, I.R.E. Proc, 33, pp. 528-534, 1945. W. H. Huggins, A Note on Frequency Transformations for Use with the Electrolytic Tank, I.R.E. Proc, 36, pp. 421-424, 1948. J. F. Klinkhamer, Empirical Determination of Wave-Filter Transfer Functions with Specified Properties, Philips Res. Reports, 3, pp. 60-80 and 378-400, 1948. Note that these represent only a small fraction of the papers published in the last few years, and they have been listed mainly because they consider problems closely related to those in the text. A complete bibliography would be too lengthy and would cover too wide a field. POTENTIAL ANALOGUE METHOD OF NETWORK SYNTHESIS 365 4. S. Darlington, Papers presented at meetings of the Basic Science Division of the A.I.E.E., January 1949 and January 1950. 5. S. Butterworth, On the theory of filter amplifiers, Experimental Wireless, 7, pp. 536- 541, 1930. For fuller information on the properties of the logarithmic potential the reader might find the following texts useful: O. D. Kellogg, Foundations of Potential Theory, JuUus Springer, Berlin, 1929; Chap- ter 12, The Logarithmic Potential. W. F. Osgood, Functions of a Complex Variable, Hafner Publishing Company, New York, 1948; Chapter 8, The Logarithmic Potential; and Chapter 9, Conformal Mapping of a Simply Connected Region. E. Weber, Electromagnetic Fields, Theory and Application — Volume I, Mapping of Fields, John Wiley and Sons, Inc., New York, 1950; Chapter 7, Two-Dimensional Analytic Solutions. A. G. \Vebster, Partial Differential Equations of Mathematical Physics, G. E. Stechert and Co., New York, 1927; Chapter 5, Methods of Green, Potentials, Boundary Problems. Zero Temperature Coefficient Quartz Crystals for Very High Temperatures By W. P. MASON {Manuscript Received Nov. 15, 1950) In order to determine the angles of cuts for low temperature coefficient crystals, the elastic constants of quartz have been evaluated in the temperature range from — 100°C to +200°C. This has been done by measuring a series of rotated Y-cut crystals in the thickness shear mode and a series of rotated X-cuts in the longi- tudinal length mode. From the measurements, low temperature coefficients AT, BT, CT, and DT type crystals can be determined which have their temperature of zero temperature coefficient at any prescribed temperature. Calculations are given for the properties of crystals to operate at 200°C. The characteristics of an AT type crystal have been investigated experimentally, and the measured results are in reasonable agreement with the calculations. It is shown that there is a maxi- mum temperature of 190°C for which an AT type crystal can have a zero temper- ature coefficient. I. Introduction Most quartz crystals used to control the frequency of oscillators or time measuring devices are used in places where the ambient temperature does not exceed 60° to 70°C. The crystals are usually adjusted in angle so that they have a zero temperature coefficient at a temperature of about 80°C and they are temperature controlled at this temperature. However, a class of uses occurs for which the ambient temperature may be considerably higher and for these uses ordinary AT and BT crystals, for example, are not satisfactory. This is evident from Figs. 1 and 2 which show the fre- quency variations for these crystals over a temperature range from — 1(X)°C to +200°C. For example, the flattest frequency temperature curve for the AT cut occurs at an angle of +35°18' rotation about the X axis from the Y cut. By going to +35°36' orientation about the X axis a minimum occurs at 100°C. For the BT cut shown by Fig. 2 the angle of -49°16' orienta- tion gives nearly a paraboHc shape centered at 20°C. By changing the orien- tation to -47°22' the parabola centers at 75°C. Hence if one wishes to raise the temperature for which the zero tempera- ture coefficient occurs he has to increase the rotation about X for the AT cut and decrease it for the BT cut. The amount needed for either orienta- tion can best be determined by evaluating the elastic constants as a func- tion of orientation and temperature, and that is the main purpose of this paper. The results are appHed to determining the best angles of orientation for the AT, BT, CT, and DT type crystals to obtain zero temperature coeffi- 366 ZERO TEMPERATUBE COEFFICIENT QUARTZ CRYSTALS 367 400 350 300 250 UJ < 200 I o Z 150 O 100 50 0 -50 -100 -150 -200 l4l M-t itii Jttt Tttr ^5/7 /- — --^ ^^■.^-J L / .-^ — ^^,--^1— — '"'^^ / / / y j^-""^ V O0_^ [1 + 35 X 10-(Ar)^ + 77X io~''(Ar)'+ •••] 5 - 2.503 X 10 r, ^^ vx 4rw— 9/A/n\2 /_4i°-2o/ = j [1 - 64 X 10 \ATy (18) -62 X 10"''(Ar)^+ •..] IV. Experimental Results Since the AT type crystal appeared to be more constant with tempera ture and to have a higher electromechanical coupHng factor than the BT type, some measurements were made for a number of crystals ranging from 36°26' to 36°45'. These were units made by A. W. Warner, all having dimensions of diameter 12.5 mm, thickness 0.166 mm. With a ratio of diameter to thickness of about 75 the dimensioning was not critical, and the correction for the length thickness ratio was smal). These had special solders and holders that will be described in a paper by A. W. Warner. These units were measured over a temperature range from 60°C to 250°C by T. G. Kinsley. The results for a crystal cut at +36°26' are shown by Fig. 3, 36°30' by Fig. 4, and 36°45' by Fig. 5. Figure 5 shows the fun- damental and third overtone frequency plotted as a function of temper- ature. The 36°30' crystal had a fundamental frequency constant of 1.660 X 10** — which agrees well with that given in equation (18) since a small allowance has to be made for the weight of the plating. However, the tempera- ture of zero coefficient is 182°C instead of the value of 200°C calculated and the curvature constants 02 and az are +73 X 10~^ and +254 X 10~^2. These deviations probably occur because of the fact that only three terms in the power series were included; whereas, to agree with experiment, further terms should be included. On the other hand, the change in orientation for a zero temperature coefficient at a given temperature is fairly closely pre- ZERO TEMPERATURE COEFFICIENT QUARTZ CRYSTALS 373 10,003 XIO-^ Q 10,002 I O ai to cr 10,001 \ \ 1 y to 111 O 10,000 u 2 >- ^ 9,999 lU \ \ 1 7 k / ^ Kv ; y O QC "- 9,996 \ K, / K / 9.997 X k Lfw \m 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 TEMPERATURE IN DEGREES CENTIGRADE Fig. 3 — Frequency temperature curve for a crystal cut at an angle of +36°26' rotation. 10,004 Q 2 O ^ 10,003 to cr OJ CL (/) 10,002 OJ _i o > u Z 10,001 o 2 LXJ g 10,000 LU 9,999 X 80 90 100 no 120 130 140 150 160 170 180 190 200 210 220 230 240 250 TEMPERATURE IN DEGREES CENTIGRADE Fig. 4 — Frequency temperature curve for a crystal cut at an angle of +36°30' rotation. dieted. If we plot the temperature for zero coefficients against angle of cut it is seen that a maximum temperature of 190° occurs at 36°26' and angles on either side of this have lower temperatures for zero coefficients. Hence this is the maximum temperature that can be reached by an AT type crys- tal. 374 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 V. Evaluation for the Remainder of the Elastic Constants over a Wide Temperature Range In order to evaluate the remainder of the elastic constants measure- ments were made of the frequencies of a series of X-cut longitudinal crystals over the same temperature range from — 100°C to +200°C.^ The longi- tudinal crystals measured had their lengths at -30°, 0°, -f 30° and +60° from the Y axis. For the four crystals measured the results are shown by I0,005j XIO^ k \ ^^. . 'v k / 1 N k A Y N N FUNDAMENTAL / .X N N, / r 3 RD HARMONIC 3 N ^ k ^ \y \ \ >s 5^^ W^ r y N k L_ y Y 10,000 ^>-^ >-o-<>-^ 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 TEMPERATURE IN DEGREES CENTIGRADE Fig. 5 — Frequency temperature curves for fundamental and third overtone for a crystal cut at 36°45' rotation. Table II. The analysis for fm = fbo" and the three constants ai , a^ and az are also shown. To correct for the temperature expansion coefficients, the increase along Ix is given by the last equation of (16) while / ± 30° and / ± 60° are / db 30° = .25/. 4- .75/x = 7o[l + 12.9 X \^\T - 50) -f- 5.42 X 10-8(r - 50)2 _ 18 X \^^\T - 50)' + / =t 60° = .75/, + .25/x = /o[l + 9.5 X \^\T - 50) -f- 3.68 X 10-9(r - 50)2 _ 16 X \0-^KT - 50)^ + Since the frequency of a long thin bar is given by the equation 1 1 „/ 1 (19) / - ^ . /—Tt 21 V^ ^, or 522 = ..2 ,2 p522 ^-'"»* P (20) introducing the length correction from (19) and the density correction from (7) one can correct for the effect of temperature expansion. » These measurements were made by T. G. Kinsley. ZERO TEMPERATURE COEFFICIENT QUARTZ CRYSTALS 375 S^ is s^« at r* XX I + II II 376 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 Applying these corrections to the frequency equations of Table II the resulting compliance constants become smo^x) = sn = 1.271 X 10r''[l + 16.5 X 10-^(T - 50°) + 58.5 X ICr^T - 50°)2 -i-SSX 10-'^(T - 50y + • • •] sm+zo^x) = 0.8159 X 10-i2[l + 96.4 X lQr'(T - 50) + 276.5 X ia-^(r - 50)2 ^ 219 A X l(y-'\T - 50)3 + . . .] sm-^ox) = 1.402 X 10-i2[l + 114.4 X 10-6(r - 50) ^^^^ + 178 X 10-9(r - 50)2 _ 91 6 X 10-i2(r - 50)3 + . . .] 5?2(+6o-x) = 0.8614 X 10-i2[l + 186.4 X 10-«(r - 50) + 302.2 X 10-9(r - 50)2 _^ 385 3 ^ 10-i2(r - 50)^ + • • •] The equation for the compliance constant 522 for an X-cut crystal at an angle 6 from the Y axis has been shown to be fB E 4/,| Bi'4/v rt E 3/,./i 522 = ^11 cos 6 + 533 sm 6 — 2^14 cos 0 sm 0 (22) + (25f3 + sfi) sin 0 cos ^ Solving for the constants in terms of the compliances for the four angles measured we find BE E ^22 (+30°) ~" -^22 (-30°) E _ E _i_ Oo^ ^11 = S22 (.0''X) ] Su — 1— ^ J -^33 — -^22(0°) -r -^^22 (+60°) 4^ 2 E /r, E , E \ 10 E 2 E /'o7^ — ^^22 (30°) — ^^22 (-30°); ^^13 "T '^44; = " ^ ^22(0°) " ^ ^22(60°) K^o) _,2Se ,26e + -Q-522(+30°) + -Q 522 (-30°) Hence adding the results we find 5fi = 1.271 X ia-^2[i + 16 5 X 10-«(r - 50°) + 58.5 X 10r\T - 50)2 + 33 x 10-i2(r - 50)^ + • • •] si, = 0.971 X 10-i2[l + 134.5 X 10-«(r - 50) + 144 X 10-9(r - 50)2 _j_ 570 x 10-^2(7^ _ 50)3 _|_ . . su = -0.4506 X 10-i2[l + 139.5 X 10-«(r - 50) + 40 X 10-9(r - 50)2 _ 54 X IQri^T - 50)3 + . . .] (25 fa + si,) = 1.785 X ia-i2[i + 300 X 10-«(r - 50) + 460 X 10-s(r - 50)2 _ 98 X 10-^2(2^ _ 50)3 + . . .] * See "Piezoelectric Crystals and Their Application to Ultrasonics," page 204, equation 10.26. (24) (26) ZERO TEMPERATURE COEFFICIENT QUARTZ CRYSTALS 377 All the compliance constants are now determined except S4a , Su and ^12 . From the relations for a crystal in the quartz class^ B E ^^4 ^ ~T~E i2 y ^*6 = 2(5fi — Su) = -^—i F2 (2^) C44C66 — Cu Cu ^66 — Cu the remaining constants can be obtained. Inserting the values of cu , ct% and cu from (12), we find Su = 1.986 X ia-^2[i + 201 X 10-«(r - 50°) + 200 X ia-^(r - 50)2 _ 26 x io-i2(r - 50)^ + • • •] sli = 2.89 X 10-i2[l - 138 X 10-«(r - 50°) - 18 X 10-»(r - 50)2 -f 3 X 10-i2(r - 50)^ + • • •] Su = -0.1005 X 10-i2[l - 678 X lOr^T - 50°) - 2110 X 10-9(r - 50)2 _^ 510 X 10-i2(r - 50)^ + • • •] Su = -0.174 X 10-i2[l - 1270 X 10-6(r - 50°) - 575 X io-9(r - 50)2 _ 215 x io-i2(r - soy + • • •] It is sometimes desirable to use the c values as a function of tempera- ture. The remaining values can be obtained from the relations valid for quartz^ r, E SS3 , Su r^ E _ SSS Su E _ SlZ E _ Sll + ^12 /rf^\ ZCii "I ^~ J ^^12 — -^ ', Cu — — ',Czz— \Zi ) a p a p a a where E / E i E \ rk B^ a E / E E \ rt E^ oi == S33 {Sii -\- Su) — 2su ; p = Su {sii — Su) — ^Su dz = 104.8 X 10+io[l - 165 X 10-6(r - 50) - 187 X 10-\T - 50)2 _ 410 x 10-i2(r - 50)^ + • • •] cfg = 9.6 X 10+io[l - 510 X 10-6(r - 50) - 2000 X 10-9(r - 50)2 + 600 X 10-i2(r - 50)^ H ] cn = 86.75 X 10+i°[l - 53.5 X 10-«(r - 50) - 75 X lOr'iT - 50)2 _ 15 x 10-i2(r - 50)^ + • • •] cu = 6.15 X 10i«[l - 3030 X 10-6(r - 50) - 1500 X 10-9(r - 50)2 _j_ 1910 X 10-i2(r -50)' + • • •] 5 See Piezoelectric Crystals and Their Application to Ultrasonics, page 207. (28) 378 THE BELL SYSTEM TECHNICAL JOUENAL, APRIL 1951 VI. Predicted Angles for CT and DT Face Shear Crystals The other two cuts of primary interest for frequency controlled oscillators are the CT and DT low frequency face shear modes. An exact solution for the frequency vibration of a face shear mode has not yet been obtained, but Hight and Willard^ •'' have pointed out an empirical relation that agrees with the measured frequencies over the entire range of angles of rotated Y cut crystals. This relation is for a square crystal 1.23 /~r^ f=-ri/-^ (29) where / is one edge dimension and ^^5 the shear elastic constant pertaining to the face shear mode. In terms of the orientation angle^ ^f5 = -^^4 cos d + ^fe sin 6 + 4^su sin 6 cos 6 (30) Introducing the values of su , sf% and su from equations (24) and (26) the frequency becomes fi X io-^« = 14.27 [(1.986 cos^ d + 2.89 sin^ 6 - 1.802 sin 6 cos 6) + (399 cos^ e - 398 sin^ d - 251.5 sin 6 cos 6) (31) X 10"'(r - 50) + (397 cos' ^ - 52 sin' 0 - 72 sin ^ cos 6) X 10~^(r - 50)' + (-52 cos' 6 + 8.7 sin' 0 + 98 sin $ cos 6) X 10~" (T - 50)' + • • • Since the formula is very approximate the small correction due to tem- perature expansions has been neglected. With this equation the indicated angles for zero temperature coefficient — which are obtained by setting the *A Simplified Circuit for Frequency Substandards Employing a New Type of Low Frequency Zero-Temperature- Coejficient Quartz Crystal, S. C. Hight and G. W. Willard, Proc. LR.E., Vol. 25, No. 5, pp. 549-563, May 1937. The factor 1.23 agrees better with experiment than the value 1 .25 given in the paper. ' Since this paper was written a much more nearly exact solution of a face shear mode vibration has been obtained by R. D. Mindlin and H. T. O'Neil. This solution is an ex- tension of the thickness shear vibration of a crystal published by Mindlin (Journal of Applied Physics, probably March issue 1951). For a square plate there are two solutions which are very close in freauency. For case A which corresponds to / of equation (29) ly- ing along the X direction the empirical factor F becomes F = 1.2718 - .03471g - .03727^2 where g ^ —^, and sn' and s^ are the elastic compliances corresponding to the rotated cuts. For the B case which corresponds to / lying along z' the same formula holds but g => t^ — -,. ZERO TEMPERATURE COEFFICIENT QUARTZ CRYSTALS 379 multiplier of {T — 50) equal to zero and solving for the rotation angles 6i and B% — are ei = +36°20' and 62 = -53°50' (32) as compared to the experimental values of +38°20' and —52°, which repre- sents a shift of about +2° orientation for both angles. At these calculated angles the frequencies are within about 1.5 per cent of the experimental values and the curvature constants agree approximately with the measured values. To obtain the angles for any other temperatures, for example 2(X)°C, we substitute T = 200 + AT (33) and obtain the expansion in powers of AT. For 200°C this results in fi X 10-^^ = 14^27 [2.055 cos' 6 + 2.829 sin' d - 1.840 sin 6 cos 6] + [514 cos' 6 - 413 sin' d - 266 sin 6 cos 6] X 10"'Ar (34) + [373 cos' ^ - 48 sin' ^ - 28 sin 6 cos 6] X 10"^(Ar)' + [-52 cos' d + 8.7 sin' ^ + 98 sin 6 cos 6] X 10""(Ar)') The zero temperature coefficient angles are obtained by setting the coeffi- cients of Ar equal to zero giving 514 cos2 d - 413 sin2 q _ 266 sin ^ cos (9 = 0 (35) Solving for 6 we find e = +39°50' and -56° (36) If we add 2° to each of these in order to correct for the difference between the formula and the measured results at 50°C, the most probable angles for zero coefficients at 200°C are 6 = +41°50' and -54° (37) At these angles the indicated frequencies and variations of frequencies with temperature should be e = 4r51'; / = ^-^^ ^ ^^' [1 - 63 X io-'(Ar)' - 8 X io-''(Ar)' + . • .] .= -54°; (^^) / = ^'^^ ^ ^^' [1 - 14 X lO-^(Ar)' + 8 X lo-^'(Ar)' + . . .] 380 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 While these results are probably not very exact on account of the lack of an exact solution for the frequency of a face shear plate, they indicate the angles and approximate variations with temperature for high temperature plates. So far no experimental results have been obtained for crystals of this type. Duality as a Guide in Transistor Circuit Design By R. L. WALLACE, JR. and G. RAISBECK {Manuscript Received Sept. 26, 1950) Because of a relationship which exists between the properties of a vacuum tube triode and those of a transistor, it is possible to start with a known vacuum tube circuit and to transform it into a completely different circuit suitable for use with transistors. The nature of this transformation is discussed and a number of examples are given. Introduction SINCE the invention of the transistor there has been a natural tendency to compare its properties with those of a vacuum tube triode. This comparison indicates that the two devices are different in many important respects. For example, the grounded cathode vacuum tube is essentially a voltage amplifying device with a high input impedance and a relatively low output impedance, while the groundeil base transistor is essentially a current ampHfying device with a low input impedance and a relatively high output impedance. Furthermore, high gain vacuum tubes tend to be unstable with open circuit terminations, while high gain transistors tend, on the other hand, to be unstable with short circuit terminations. The properties of the two devices are, in fact, so radically different that the development of the transistor has posed an entirely new set of circuit design problems. If the vacuum tubes in a known circuit are simply replaced by transistors (and appropriate changes are made in the supply voltages), it is usually found that the transistor is not used to best advantage and the circuit performance is not satisfactory. For this reason, circuit designers heretofore have exercised considerable ingenuity in devising new circuits which take into account the pecuHarities of the transistor and use them to best advantage. It turns out that some of these circuits bear Uttle resem- blance to vacuum tube circuits designed to perform the same function. Although there is a great difference between the electrical properties of transistors and vacuum tubes, there is a very simple approximate relation- ship between them. It is the purpose of this paper to show how it is possible, taking this relationship into account, to start with a known vacuum tube circuit and transform it into a completely different circuit suitable for use with transistors. Circuits derived in this way tend to take advantage of the pecuUarities of the transistor, and in a number of cases have shown excep- tionally good performance. 381 382 the bell system technical journal, april 1951 The Relation between Vacuum Tube and Transistor Properties It is the purpose of this section to show that the properties of a transistor are related to those of a vacuum tube triode through an interchange of current and voltage, and that transistor currents behave Hke vacuum tube voltages and vice versa. The discussion is aimed particularly at the large- signal properties of the two devices and is restricted to the frequency range in which static characteristics are sufficient to determine circuit perform- ance. Consider first the grid-cathode input terminals of a triode as compared to the emitter-base input terminals of a transistor. With respect to these terminals each device behaves as a diode rectifier the properties of which are relatively unaffected by biases appHed to the third electrode (plate or collector). The grid conducts when biased in the forward direction and fails to conduct when biased in the reverse direction. A similar statement can be made about the emitter. Furthermore, either device behaves as a low im- pedance when biased in the forward direction and as a relatively high im- pedance when biased in the reverse direction. The difference between the emitter circuit and the grid circuit comes about in the following way: The vacuuSi tube is most effective as an amplifier when the grid is biased in the reverse direction, while the transistor is most effective when the emitter is biased in the forward direction. With respect to these input terminals, then, the essential difference between the two de- vices amounts to the difference between "forward" and "reverse". But this, in turn, amounts to an interchange of current and voltage. Whatever quahtative statements can be made about emitter current and voltage can also be made about grid voltage and current, respectively. For example, the grid is normally given a moderate voltage bias at which the grid current is essentially zero, while the emitter is normally given a moderate current bias at which the emitter voltage is essentially zero. Furthermore, the principal non-h*nearity in the grid circuit occurs when the grid voltage is allowed to swing through zero with the result that grid cur- rent begins to rise, while the principal non-linearity in the emitter circuit occurs when the emitter current is allowed to swing through zero with the result that emitter voltage begins to increase. The comparison between the plate-cathode output circuit of the triode and the collector-base output circuit of the transistor is somewhat compli- cated by the effects of grid and emitter biases. Consider first the situation in which zero bias is applied to the input circuits {vg = 0 and ie = 0) . In this case, both the plate and the collector behave like diode rectifiers, conducting readily when biased in the forward direction and conducting relatively poorly when biased in the reverse direction. When input biases DUALITY AS GUIDE IN TRANSISTOR CIRCUIT DESIGN 383 are applied, however, the principal difference between the two devices be- comes apparent and turns out again to be associated with the difference between forward and reverse. This is because biases applied to the grid affect only the forward part of the plate circuit characteristic while biases apphed to the emitter affect only the reverse part of the collector circuit character- istic. Thus the grid and plate are normally biased in the reverse and forward directions, respectively, with the result that the vacuum tube input im- pedance is high and the output impedance is relatively low. The emitter and collector, on the other hand, are normally biased in the forward and reverse directions, respectively, with the result that the transistor input impedance is low and the output impedance is relatively high. The comparison of vacuum tube and transistor properties can be carried further with the help of Fig. 1 (a) which shows the plate circuit characteristics of a particular vacuum tube triode and Fig. 1 (b) which shows the collector circuit characteristics of a particular transistor. The axes in these two figures have been chosen to faciUtate comparison of transistor currents with vacuum tube voltages and vice versa. The result is that the two families look quite similar. It is seen that the quantities to be compared are Vp with —ic, ip with —Vc , — Vg with ie , and, though not shown, —ig with Ve . The consistent difference in sign between vacuum tube and transistor quantities holds only when the transistor is made from an iV-type semicon- ductor. If the transistor is made of P-type material there is no difference in sign between corresponding transistor and vacuum tube quantities. By referring to Fig. 1(a) it can be seen that to a first approximation the effect of applying a negative voltage bias to the grid is simply to shift the plate circuit characteristic to the right along the Vp axis. The number of volts shift caused by a change of one volt on the grid is called the voltage amplification factor, /x, of the triode. Similarly, it can be seen from Fig. 1 (b) that the principal effect of applying a positive current bias to the emitter is shnply to shift the collector ckcuit characteristic to the right along the — ic acis. The number of miUiamperes shift caused by a change in emitter current of one milHampere is called the current amplification factor, a, of the transistor. Thus, a of the transistor corresponds to fi of the vacuum tube. 1 The p-Germanium Transistor, W. G. Pfann and J. H. Scaff, Proc. I.R.E., 38, 1151. 384 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 It is interesting to note that the gross non-Hnearities in the vacuum tube plate circuit have their counterparts in the transistor collector circuit. For example, the counterpart of plate current cutoff is collector voltage cutoff. The relationship between vacuum tubes and transistors is not only quali- tative, but can be made quantitative as well provided a suitable vacuum tube is chosen for comparison with the transistor. The requirements are that the vacuum tube and transistor have similar dissipation ratings and that /z be equal to a. These conditions are roughly satisfied by the vacuum tube and transistor of Fig. 1(a) and Fig. 1(b). By comparing the axes in these two figures it may be seen that one milliampere in the transistor corresponds 132 0 10 20 MILLIAMPERES (d) (b) Fig. 1— The static characteristics of a transistor look like those of a vacuum tube triode provided transistor currents are compared with vacuum tube voltages and vice versa. to 6.6 volts in the vacuum tube and vice versa. It follows that, in this case, transistor currents are related to vacuum tube voltages through a "trans- formation resistance," r, given by 6.6 volts (1) f = (10) -3 amps = 6,600 ohms. Cmcurr Considerations The internal structure of a vacuum tube imposes a particular set of re- lationships between the vacuum tube currents and potentials. At low fre- quencies these relationships are given by the static characteristics which DUALITY AS GUIDE IN TRANSISTOR CIRCUIT DESIGN 385 show that over a fairly wide range of values the tube currents are roughly linear functions of the voltages. When the tube is connected into an external circuit, the circuit imposes a second set of algebraic relationships between vacuum tube currents and potentials and the performance of the circuit as a whole represents a simultaneous solution of these two sets of relationships. Now if the vacuum tube is replaced by a transistor and the external circuit is left unchanged, then the relationships internaUy imposed are markedly changed while the relationships imposed by the external circuit are left unaltered. Ordinarily this will lead to a completely different simultaneous solution for the two sets of conditions and hence to completely different circuit performance. If circuit performance (with respect to the terminals of the tube or transis- tor) is to be maintained after substituting a transistor for a vacuum tube then the external circuit must be modified. One might suppose, for example, that it should be possible to find a new external circuit such that the collec- tor voltage in the new circuit would behave exactly as did the plate voltage in the original circuit. To a certain extent this is possible, but this procedure meets with a serious difficulty. Although transistor voltages are fairly well behaved, roughly linear single-valued functions of transistor currents over fairly wide ranges of values, transistor currents are relatively more non- hnear, often double valued, functions of the voltages. This means at once that if circuit performance is to be maintained for large signals, non-linear elements will be needed in the external circuit. This approach seems very much less promising than another to which we now come. The new approach is to seek a transistor circuit in which every current behaves like a corresponding voltage in a known vacuum tube circuit and every voltage behaves like a corresponding current. This approach is rela- tively simple because, as has already been shown, half the problem is solved simply by exchanging transistor for vacuum tube. The remaining part of the problem is to find an external circuit which will impose the same rela- tion between transistor potentials and currents as the original circuit im- posed between vacuum tube currents and potentials. This amounts to say- ing that if the vacuum tube is to be replaced by a device in which the roles of currents and voltages are just interchanged then the external network should also be replaced by a new network which accomplishes this same interchange. Networks in which this sort of interchange is accompHshed are known as duals,^ one of the other. It has been shown in the literature that it is possible to find and to realize physically the duals of most practical circuits. The total number of circuit elements in a network is ordinarily preserved when the 2 Communication Networks, E. A. Guillemin, Vol. 2, pp. 246-254, John Wiley & Sons (1935) ; Network Analysis and Feedback Amplifier Design, H. W. Bode, p. 196, Van Nostrand, (1945). What Bode calls inverse we have called dual. 386 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 dual transformation is performed, each element being transformed into a new element which is its dual. The transformed elements are not, however, connected together in the same way as were the original ones. Elements in parallel are transformed into elements in series and vice versa. Nodes trans- form into loops and loops into nodes. There are cases when finding the dual of a network is not as straightfor- ward as the reader might infer from the above. Complications may arise when the network contains mutual inductance or non-Hnear elements, or if the network cannot be drawn on a flat surface without crossovers. Some of these questions are discussed by Bode.^ Duality Table 1 shows side by side a number of network elements and the duals of these elements related through the transformation resistance r. The table also shows the duals of a few simple networks. It is the purpose of this section to show by means of examples how these dual relationships are established. One network element is the dual of another provided the role of current in one is played by voltage in the other, and vice versa. Consider what this means in the case of a capacitance in which current and voltage are related by the equation (2) 6 = ^ u jC(a Interchanging the roles of current and voltage means replacing e in this equation by i'r and replacing i by e'/r. The value of r determines how many volts across the condenser are to correspond to an ampere through its dual. Making the indicated substitutions gives (3) i' = ^ ' jr'^Cif) This, however, is the kind of equation which relates the current through an inductance to the voltage across it. It is seen, therefore, that the dual of a capacitance C is an inductance of value given by (4) L' = r'^C. In the dual transformation of a network every capacitance in the original network will be transformed in this way into an inductance in the dual network. Also, if ec and ic represent the voltage across a capacitance and * Bode, loc. cit. DUALITY AS GUIDE IN TRANSISTOR CIRCUIT DESIGN 387 the current through it in the Kirchoff equations of the original network, these quantities will be replaced by U' , and Cl' -, respectively, in the Kirchoff equations of the dual network. The quantities II' , and Bl' , represent the current through an inductance of value L' given by (4) and the voltage across it. The argument just given can equally well be interpreted to mean that the dual of an inductance L is a capacitance C, the value of which is given by (5) C = L/r', so that every Bl and II in the Kirchoff equations of the original network are replaced by ic , and ec , respectively, in the Kirchoff equations of the dual network. The dual of a resistance R is found in the same way. The equation ap- plicable to a resistance is (6) e = Ri, which, with the substitution of ri' for e and e'/r for i, becomes (7) i' = e'l{rVR). Thus it is seen that a resistance R transforms into a resistance R! where (8) R! = r^lR. Also, Cr and Ir in the Kirchoff equations of the original network are replaced by iff' , and eR> , respectively, in the Kirchoff equations of the dual net- work. The dual of a temperature sensitive resistance which changes value with changes in average signal level can be found by exchanging the labels on the axes of an E-I plot of its characteristic. This shows that the dual of a resistance which has a positive temperature coefficient, and hence increases in resistance with increase in signal level, is a resistance with a negative temperature coefficient of resistance which decreases in resistance with increase in signal level. Similarly, the dual of a short-circuit-stable negative resistance is an open-circuit-stable negative resistance. The equations applicable to an ideal transformer of impedance ratio llo^are (9) ei — ae\ , and ii = ii/ot. Making the substitutions previously indicated leads to (10) ii — ail , and €2 = e-Ja. 388 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 Table I (ia) CONSTANT VOLTAGE SUPPLY (lb) CONSTANT CURRENT SUPPLY l'= E/r (2a) SERIES BATTERY AND RESISTANCE — l|l| — W\/ — E R (2b) CONSTANT CURRENT SUPPLY AND RESISTANCE IN PARALLEL l'=E/r, R'=r2/R Oa) SERIES BATTERY AND RESISTANCE -H|ih-vw— E R (3b) SERIES BATTERY AND RESISTANCE E' R' E' = (r/R)E, R'=r2/R (EQUIVALENT TO (2b), BY THEVENIN'S THEOREM) (4a) RESISTANCE (4b) RESISTANCE (Sa) POWER -SENSITIVE RESISTANCE WITH POSITIVE TEMPERATURE COEFFICIENT (5b) POWER -SENSITIVE RESISTANCE WITH NEGATIVE TEMPERATURE COEFFICIENT (6a) SHORT-CIRCUIT-STABLE NEGATIVE RESISTANCE (6b) OPEN -CIRCUIT -STABLE NEGATIVE RESISTANCE r E' r=E/r, E'=rl (7a) CAPACITANCE (7b) INDUCTANCE L' L'=r2c DUALITY AS GUIDE IN TRANSISTOR CIRCUIT DESIGN Table I — Continued 389 (8 6) IDEAL TRANSFORMER OF IMPEDANCE RATIO 1 : a2 : a2 (8b) IDEAL TRANSFORMER OF IMPEDANCE RATIO 3^. 1 (9a) IDEAL GYRATOR OF FORWARD TRANSFER IMPEDANCE R e, = -RL2 62 = RLi (9b) IDEAL GYRATOR OF FORWARD TRANSFER IMPEDANCE -P^/R 'LJ<3 e/= (r2/R)L2' e2'=-(r2/R)L/ (10 a) ANY TWO-TERMINAL NETWORK X (10b) THE SAME TWO -TERMINAL NET- WORK, X, PLUS AN IDEAL GYRATOR OF TRANSFER IMPEDANCE T I>CB i\]a) ANY THREE -TERMINAL NETWORK N (lib) THE SAME THREE -TERMINAL NET- WORK, N, PLUS TWO IDEAL GYRATORS -Jj^^^' (12 a) VACUUM TUBE TRIODE (12b) VACUUM TUBE TRIODE PLUS TWO GYRATORS (13a) SUITABLE VACUUM TUBE TRIODE (13 b) TRANSISTOR PLUS IDEAL PHASE REVERSING TRANSFORMER NOTE THAT (13b) AND (12 b) ARE EQUIVALENT (14a) ANY MID-SERIES TERMINATED CONSTANT -k FILTER SECTION OF DESIGN RESISTANCE R (14 b) THE SAME CONSTANT -k FILTER SECTION MID-SHUNT TERMINATED BUT WITH DESIGN RESISTANCE CHANGED TO r2/R T OJW^f- 390 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 This indicates that the dual of an ideal transformer of impedance ratio lla^ is another ideal transformer of impedance ratio ol^'A, It follows that the dual of a 1:1 ideal transformer is a 1:1 ideal transformer. The dual of a constant voltage supply E is, of course, a current supply which maintains a constant current equal to (11) rf E/r, and the dual of a constant current supply / is a supply of constant voltage equal to (12) £' = Ir. lo- ■VW- r; +eR2'- -AAAr R2 L2 ■o2 eL'feL C 1 + T ec' Ll'+Lc' 3 ei -ec'-eR,' = o e2 + ec'-eR2'=o (a) 'C' = e,/ (b) Fig. 2 — The dual of a network is found by transforming the Kirchoff equations. The procedure of substitution used in all the examples above can be used in a straightforward way to find the dual of a more complicated net- work, but, in view of what has already been said some labor can be saved by writing the Kirchoflf equations in the abbreviated notation used in Fig. 2. The equations on the left corresponding to the original network are then transformed into the equations of the dual network by making the following substitutions: ei = iv ii = ev Cr, = iR[ iRi = eR[ ih = Cc' , etc. From these transformed equations, shown on the right hand side of Fig. 2, the dual network shown above them can be drawn by inspection. DUALITY AS GUIDE IN TRANSISTOR CIRCUIT DESIGN 391 From the example given in this figure, it is seen that a ladder network is transformed into another ladder network with each series branch of the original network being transformed into a shunt branch in the dual network and vice versa. Note also that a series combination of L and C is trans- formed into a shunt combination of C and L'. The effect of a short circuit between terminals 1 and 2 in the original network (which makes ci = e^) is an open circuit at terminal 3 in the dual network (which makes ii = i-i). The Dual op an Ideal Vacuum Tube Triode In a previous section it was shown that transistor currents behave approxi- mately like vacuum tube voltages and vice versa. In view of what has been said about duality it might be assumed that, as three-terminal networks, the transistor and the vacuum tube triode are approximate duals. It is the purpose of this section to examine the relationships between the two devices in detail and to show that they fail to be duals one of the other principally because of a sign. What it amounts to is that signals transmitted through the dual of a vacuum tube suffer a phase reversal while, on the other hand, signals are transmitted through a transistor without change of phase. A convenient way of proceeding is to start with the 4-pole equations of an ideal vacuum tube triode and transform them, by the methods already presented, into the equations of the dual. These transformed equations will then be compared with the 4-pole equations of a transistor. The small signal behavior of a vacuum tube triode is represented by the equations, (13) where and These equations apply when the positive directions of current and voltage are as indicated in Fig. 3. The equations corresponding to the dual of the ideal vacuum tube triode are found by substituting in equations (13), U = ^i/ry ip = V2/rj Vg = rii , and Vp = ri2 . The quantities ii and v^ will then represent the current and voltage at the input terminals of the dual device and ^2 and V2 will represent the cur- ip = (OK+(OK, = gmVg + kpVp = kp{Vp + llVg), kp = gm/kp , 392 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 rent and voltage at the output terminals. Making these substitutions leads to Vl = (0)ti + (0)i2 , (14) V2 = r^gmii + r%i2 = r%(i2 + fJiii). It remains to be seen how the directions of current and voltage must be assigned in Fig. 3. If the directions of ^i and ii are arbitrarily assigned as indicated in the figure, then the directions of V2 and 12 can be found by an argument Uke that used in connection with the passive three- terminal network just discussed. The dual of making Vp = Vg by placing a short cir- cuit between plate and grid is making ii = ^2 by opening terminal 3 of the dual. This says that the positive direction of {2 is as shown in Fig. 3. Simi- larly, the dual of making ig = —ip by opening the cathode connection to the vacuum tube is making 2^1= —V2 by placing a short circuit between terminals 1 and 2 of the dual. This requires that positive values of Vi and V2 have opposite signs when measured with respect to terminal 3 and so fixes the positive direction of V2 as shown in Fig. 3. The 4-pole equations for a transistor^ are Ve = Tnie + rnic , (15) Vc = r2iie + r22ic = r22{ic + Oiie), where a = ^21/^22 . These equations are similar in form to equations (14) which correspond to the dual of an ideal vacuum tube triode. Comparing the two sets of equations shows that the following transistor and vacuum tube quantities correspond to each other; r^gm and r2i , r^kp and ^22 , and ju and a. Comparing the first of equations (14) with the first of equations (15) shows that the transistor quantities rn and rn should be zero if the transistor is to be an accurate dual of the vacuum tube triode. These quantities are small in present day transistors and there is hope that they may be made still smaller in the future. In the transistor of Fig. 1 (b) , for example, rn is approximately 200 ohms. This corresponds to a grid-to-cathode leakage resistance in the triode which can be computed from fg = r^/m . » Some Circuit Aspects of the Transistor, R. M. Ryder and R. J. Kircher, Bell Sys. Tech. Jl., 28, 367 Quly 1949). r DUALITY AS GUIDE IN TRANSISTOR CIRCUIT DESIGN 393 Since r = 6600 ohms for the transistor and vacuum tube of Fig. 1, Tq amounts to 218,000 ohms. This is large compared to r^ and would not seriously impair the operation of the tube for many purposes. What has been said indicates that transistor currents and voltages are fairly accurate duals of vacuum tube voltages and currents. As a three-termi- nal network, however, the transistor fails to be the dual of a vacuum tube because the values of u and Vc which behave as duals of v^ and i^ are measured with a convention of signs which is not consistent with Fig. 3. This can be seen by comparing the directions of i^ and vi in the dual of a vacuum tube (Fig. 3) with the convention of signs for the transistor indicated in Fig. 1 (b) . A transistor hke present day ones in all respects except for a reversal in sign of ic and Vc would be a fairly good dual for a vacuum tube triode. This discrepancy in sign means, of course, that the grounded base transistor fails to give the phase reversal which would be given by the dual of a vacuum tube. This does not mean that the duals of vacuum tube circuits cannot be i-1 DUAL OF i-a TRIODE + + Fig. 3 — The right-hand figure shows the convention of signs which must be used with the transformed equations (14). found and used to advantage with transistors. It simply means that if the circuits are to be strictly dual an ideal transformer or some other means must be used to supply the phase reversal. In finding the dual of a vacuum tube circuit there are several equally satisfactory ways of proceeding. Perhaps the simplest is to begin by treating the transistor as though it were a perfect dual of a vacuum tube triode. In this case, the transistor is substituted for the vacuum tube — emitter for grid, base for cathode, and collector for plate — and then the remaining part of the vacuum tube circuit is replaced by its dual. The resulting circuit fails to be a dual of the original only with respect to a phase reversal which can be corrected by inserting a phase reversing ideal transformer at the most convenient appropriate place. Another procedure, which is perhaps more straightforward but which may also require more work, takes care of the phase reversal automatically. The first step in this case is to write down the Kirchoff equations for the vacuum tube circuit and then transform them into a new set of equations 394 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 in the manner illustrated in a previous section (see Fig. 2). In doing this, replace ^pby -ic, ipby—Vey Vg by —ie , and • ighy—Ve. This gives a set of Kirchoff equations which apply to the dual circuit and it remains only to find, by inspection, a circuit which satisfies them. It will often be found that, in order to satisfy these equations, it is necessary to introduce a phase reversing transformer. Several examples of this method of procedure will be given in sections to follow. In the appendix a great many more examples of vacuum tube circuits and their transistor duals are shown. Gyrators and Duality Tellegen^ has shown that in principle it is possible to make a new kind of passive 4-pole circuit element to which he has given the name "ideal gy- rator". This device is characterized by the 4-pole equations ei — Ri2 and 62 = —Rii . Though such a device is not known to have been reaUzed in a practical physical form as yet, its properties are so closely related to duahty as to be worth mentioning here. The following interesting properties can readily be deduced from the equations above. First, signals are transmitted through the device in one direction without phase reversal, while signals transmitted in the other direction are reversed in phase. Second, if an impedance Z is connected across the output terminals of an ideal gyrator, the impedance seen at the input terminals is I^/Z. This means that the ideal gyrator has the property of transforming any two-terminal network into its dual. Also a three-termi- nal network can be converted into its dual by connecting one gyrator to the input terminals of the network and another to the output terminals. These gyrators must be so poled that no phase reversal is produced in either direc- tion by the action of the two together. This means that the dual of a vacuum tube triode can be obtained by using a triode plus two gyrators as shown in Table I and, of course, the dual of a transistor can be obtained by using a transistor plus two gyrators. Also, * The Gyrator, A New Electric Network Element, B.D.H. Tellegen, Phillips Research Reports, 1948, pp. 81-101. DUALITY AS GUIDE IN TRANSISTOR CIRCUIT DESIGN 395 since the gyrator gives a phase reversal or not, depending on the direction of transmission, a transistor plus two gyxators can be made the equivalent of a vacuum tube triode by pohng the gyrators in such a way as to take care of the phase reversal. Ideal gyrators are not yet available but passive circuit elements having very similar properties over a narrow frequency range are available and are used in certain vacuum tube circuits. A quarter-wave line or its lumped- constant equivalent (which amounts to a full section of low- or high-pass filter) has the property of impedance inversion at a single frequency. Instead of giving zero or 180° phase change as does the ideal gyrator discussed above, this single frequency gyrator can be designed to give either -|-90° or —90° phase change. In either case, the phase shift is independent of the + eci .'I/-.. 1-624 ' .i.e2 eu'^Li Ves: ki' /pi Cl-E, = 0 Ei + eL-ea-eR=o Vg2 - ep = 0 -Lci-Lc'-Ii =0 I, + Ic'- Ll,'- Ir'= 0 -i.e2-i-R= 0 eL= ec Lc'= Ll' Lpi + Ici + Lu + i-c = 0 -Vci + eu'H- ec'+ Bl' = o lg2 + i-R - Ici = 0 (a) -Ve2 + eR/-eu'= 0 Fig. 4 — A tuned amplifier stage and the transistor dual. (b) direction of transmission. This leads to the possibility of exchanging a transistor for a vacuum tube plus two quarter wave lines. An application of this sort will be discussed in a later section. The Dual or an Amplifier with Shunt Tuned Interstage Figure 4(a) shows a vacuum tube amplifier with the Kirchoff equations which apply to it. Figure 4(b) shows the transformed equations and a transis- tor circuit which satisfies them. The ideal transformer in this circuit has no effect on any aspect of the circuit performance except the phase of the output and, if this is not impor- tant, the transformer may be left out. The curved arrows represent constant current suppUes. All the element values in the transistor circuit may be 396 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 computed from the values in the vacuum tube circuit by means of the rela- tions of Table 1. Figure 5, (a) and (b), shows a different arrangement of power supplies in the vacuum tube circuit and the resulting more convenient arrangement of power suppUes in the transistor circuit. In this case, the ideal transformer has been omitted but in all other respects the circuits are duals. The apphcation of duality in this case has led to the use of a series tuned circuit in series with the load instead of the shunt tuned circuit in shunt with the load, which the vacuum tube circuit might otherwise have sug- gested. The series tuned circuit has the advantage when used with short- circuit unstable transistors of insuring stability outside the pass band. The Dual or a Push-pull Class B Amplifier Figure 6(a) shows the circuit of a push-pull amplifier and the Kirchoff equations which apply to it. Figure 6(b) shows the transformed equations (a) (b) Fig. 5 — An unconventional arrangement of power supplies in the vacuum tube circuit leads to a convenient arrangement for transistors. The phase reversing transformer which would make the transistor circuit strictly dual has been omitted. and the dual transistor circuit. In this case, not only the circuit configuration but also the choice of operating point is important. For class B operation the two tubes are given a high negative grid bias, so that in the absence of an input signal the two plate currents are nearly zero while the plate voltages are quite high. In the transistor case, the dual situation is that the emitters are given a high positive emitter current bias so that in the absence of an input signal the two collector voltages are nearly zero while the collector currents are quite high. During a positive half cycle of input voltage the upper vacuum tube plate circuit begins to conduct and the plate current of the upper tube goes through a positive half cycle while the plate current in the lower tube remains essentially at zero. During this half cycle the plate current of the upper tube is coupled through the output transformer to the load while the lower tube contributes nothing, behaving simply as an open circuit element in shunt with the load and with the upper tube. The cor- responding set of events in the transistor amplifier is that, in response to DUALITY AS GUmE IN TRANSISTOR CIRCUIT DESIGN 397 a positive half cycle of input current, the collector voltage of the upper tran- sistor goes through a negative half cycle while the collector voltage of the lower transistor remains essentially zero. All the collector voltage swing of the upper transistor is impressed directly on the load because, during this half cycle, the lower transistor serves as a short circuit element in series with the load and with the upper transistor. The next half cycle is, of course, like the first except that the lower tube and the lower transistor assume the active roles. It was this circuit which first showed the great advantage which can some- times be achieved through the use of duahty. Using two type A transistors in the circuit of Fig. 6(b), it has been possible to obtain 400 milHwatts of Lei \ Vei I Ve2 Vc, ! A VC2 \ k2 -Ui -l/ + 1/ = 0 -Le2 + l; + i; = 0 -ki -L2'- I2 = 0 -k2 + t3'- I2' = 0 -Ve, + Ve2- e/ = 0 -Vci + Vc2-f ea' = 0 (b) Fig. 6 — A class B amplifier and the transistor dual. audio output with a collector circuit efficiency of 60%. The same two tran- sistors which gave this result could not be made to deliver more than 25 milliwatts output when used as grounded base amplifiers in a conventional circuit like that of Fig. 6(a). The Dual of a Bridge Stabilized Oscillator Figure 7(a) shows the circuit of a bridge stabihzed oscillator due to Meacham,^ in which amplitude stabilization can be achieved through the action of a temperature sensitive resistance Rt which has a positive tem- 5 The Bridge-Stabilized Oscillator, L. A. Meacham, Proc. LR.E.26, 1938, p. 1278; Bell Sys. Tech. Jl. 17, 1938, p. 574; U. S. Pat. 2,303,485. 398 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 perature coefficient of resistance. At the resonant frequency of the tuned circuit Rt R. 1 + 1 where Rx is the equivalent resistance of the tuned circuit at resonance. The circuit values are chosen so that Rt is smaller than Rx and therefore the feedback is positive. As the ampUtude of oscillation builds up, the increas- ing signal level across Rt increases its temperature thereby increasing its + \ —1— \ + •■P i-e^ Ve V ^l-RT !! eRT < ;rt lrt -^p-^ -^P- Lrt + h i-c — ^— — UU(, -eRT + ;uuuuuvu 000 L i-L+i-c * ^WWK) O^MW" * ' -{ec' + eL') + ■ """^ vvv I Lc' Rt . Lg ' \{ — Ksmu ■ Vg f Vp - eRT = 0 -i-e- i-c- i-RT' = 0 2Vp - Cl - CRT = 0 -2Lc- Lc'-Lrt' = 0 eL= ec i-c'= Ll' i-p+ i-RT + i.L+i-c = 0 -Vc+eRT' + ec' + eL'=:o Ig + Lr T - «-L-Lc = 0 (a ) -Ve+eRT'- ec'-eL'=o (b) Fig. 7 — A bridge-stabilized oscillator and the transistor dual. resistance and bringing the bridge nearer to balance, so that the amount of positive feedback is reduced. This results in a stable amplitude of oscillation sufficient to make Rt slightly smaller than Rx . Figure 7(b) shows the transformed equations and the dual transistor oscil- lator. In this case, Rt' is a thermistor with a negative temperature coefficient of resistance. At the resonant frequency of the series tuned circuit 1 _ ^ ie Rx' 1 4- R.' where Rx' is the effective series resistance of the tuned circuit at resonance. The circuit values are so chosen that Rt' is greater than Rx' and therefore DUALITY AS GUmE IN TRANSISTOR CIRCUIT DESIGN 399 the feedback is positive. As the amplitude of oscillation increases, Rt' is heated so that its resistance decreases and brings the bridge more nearly into balance. This reduces the amount of positive feedback until a stable amplitude of oscillation is reached with Rt' only a little greater than Rx'. Meacham has shown that the stabihty of such an oscillator increases as the gain of the amphfier is increased. Since the vacuum tube amplifier of Fig. 7(a) can be made to give more gain than can be obtained from a single transistor, the transistor oscillator of Fig. 7(b) is not as stable as its vacuum tube dual. If increased stabihty is desired, it can be obtained by using a two-stage transistor amplifier instead of the single transistor shown. Circuits Using Vacuum Tubes and . Transistors Together Since the vacuum tube and the transistor are basically different kinds of circuit elements, it seems reasonable to suppose that there may be circuits in which both can be used together to advantage. Two examples of such circuits will be discussed. The first has to do with a very ingenious high efficiency linear amplifier designed by Mr. W. H. Doherty.^ This amplifier is particularly suited for use with ampHtude modulated radio frequency inputs. Figure 8 shows the basic features of one form of the Doherty amplifier. The networks iVi and iV2 are impedance inverting networks of the type already discussed and amount to ideal gyrators for frequencies near the carrier frequency. Tube Ti is biased nearly to cutoff and works, for small rf inputs, as a linear class B amplifier; while T2 is biased well below cutoff and is inactive except when the rf input is higher in level than the unmodu- lated carrier. Downward swings of modulation are amplified by Ti alone, which sees an effective load impedance just twice the value into which it could deliver maximum power. Under these conditions the peak voltage swing of Ti begins to approach the supply voltage just as the rf input reaches a value corresponding to the unmodulated carrier. For greater input signals Ti , if acting alone, would begin to distort. But as the input signal is increased above the value corresponding to the unmodulated carrier, T2 comes into action and contributes in two different ways to increasing the output signal Hnearly. First, T2 acts as a class C amplifier and delivers power to the load and second, through the action of the impedance inverting network N2 , T2 acts in such a way as to lower the effective load impedance seen by Ti . This makes it possible for Ti to deliver more power to the load without an increase in plate voltage swing. The result of all this, which is discussed in much greater detail in Doherty's papers, is a Hnear amplifier of unusually high efficiency. *A New High-Efficiency Power Amplifier for Modulated Waves, W. H. Doherty, Proc. I.R.E., 24, 1163 (September, 1936). 400 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 The part of the circuit of Fig. 8 shown inside the dotted box amounts to a vacuum tube plus two gyrators, which is just the dual of a vacuum tube. Apart from a phase shift of 180° this is equivalent to a transistor. This part of the circuit can therefore be replaced by a transistor plus a phase reversing transformer to obtain the basic transistor-vacuum-tube circuit of Fig. 9. This results in a considerable simplification because the impedance inverting networks are no longer needed. The operation of the circuit of Fig. 9 is exactly similar to that of Fig. 8 except that the transistor operates as the dual of Ti . This means that the transistor is given a large forward emitter bias so that collector voltage is Fig. 8 — The basic arrangement of a Doherty amplifier. almost cut off. Under these circumstances, it is capable of operation as a linear amplifier. The load resistance is just half that into which the transistor could deliver maximum power. The transistor acts alone to amplify down- ward swings of modulation {T2 being biased well below cutoff as before) but as the input signal exceeds that of the unmodulated carrier the collector current swing begins to approach the maximum value permitted by the (current) supply and T2 begins to contribute to the output in just 'the ways it did in the circuit of Fig. 8. First, it acts as a class C amplifier delivering power directly to the load and second, it behaves as a negative resistance bridged across the load and thereby increases the impedance into which the transistor works. This permits the transistor to deliver more power without increasing the collector current swing. Just as the basic Doherty circuit of Fig. 8 needs tank circuits to suppress I DUALITY AS GUIDE IN TRANSISTOR CIRCUIT DESIGN 401 carrier harmonics, so also does the circuit of Fig. 9. When these are added the circuit of Fig. 10 is obtained. Doherty shows that there are two basic circuit arrangements for obtain- ing the high efficiency hnear amphfier action which he describes. One of them has been discussed above. By starting with Doherty's other arrangement, Fig. 9 — The basic circuit of a Doherty-type amplifier using a transistor to replace a vac- uum tube and two impedance inverting networks. Fig. 10 — A Doherty-type amplifier in which low level signals are amplified by the tran- sistor alone. one arrives at the circuit of Fig. 11. In this case, it is the vacuum tube which operates class B and the transistor which helps to supply the peaks by class C operation. At low input levels the transistor behaves as a short circuit and the vacuum tube works into an impedance just twice the value into which it can deliver maximum power. As the input signal increases above the carrier level the transistor begins to operate, contributing in two ways 402 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 to increasing the power output. First, it delivers power directly to the load and, secondly, it behaves as a negative resistance in series with the load, thereby decreasing the impedance into which the vacuum tube works and permitting it to deliver more power without increasing its plate voltage swing. LOAD Fig. 11 — A Doherty-type amplifier in which low level signals are amplified by the vac uum tube alone. LOAD Fig. 12 — A high efficiency untuned amplifier in which small signals are amplified by the vacuum tubes alone. The Doherty amplifier is limited to narrow band operation only because the networks Ni and A^2 will behave as gyrators only over a narrow range of frequencies. Apart from a phase change of 180°, however, the transistor behaves as a vacuum tube plus two ideal gyrators and is therefore capable of acting as the dual of a vacuum tube over a wide band of frequencies. This DUALITY AS GUIDE IN TRANSISTOR CIRCUIT DESIGN 403 leads to the possibility of an entirely new, wide band, high efficiency ampli- fier which operates on the same principles as the Doherty circuit. Both the transistor part and the vacuum tube part of the amplifier must be made push-pull in order that both halves of the input wave be amplified equally. In the circuit of Fig. 12 the vacuum tubes are biased for class B operation, while the transistors are given a large forward emitter current bias so that they are operated well below collector voltage cutoff. For small input signals the transistors are inactive, serving simply as short circuit elements in series with the load. As the input signal reaches half the peak LOAD Fig. 13 — A high efficiency untuned amplifier in which small signals are amplified by the transistors alone. permissible value the vacuum tubes begin to distort because their voltage swings approach the supply voltage. At this point the transistors begin to operate in two separate ways, just as in the Doherty amplifier. First, they work as class C amplifiers delivering power directly to the load and second they behave as a negative resistance in series with the load thereby serving to reduce the impedance into which the vacuum tubes work. This permits the vacuum tubes to deliver more power without increasing their plate voltage swing. Just as there are two forms of the Doherty amplifier, there are also two forms of this wide band arrangement. In the second form shown in Fig. 13 the transistors are biased for class B operation (near collector voltage cutoff) while the vacuum tubes are biased well below cutoff. For small signals the transistors act alone as class B amphfiers and the vacuum tubes act simply 404 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 as open circuit elements in shunt with the load. As the instantaneous input signal reaches half the permissible peak value, the transistors begin to dis- tort because the collector current swing begins to approach the value of the (current) supply. At this point the vacuum tubes begin to operate in two separate ways to increase the power output. First they act as class C am- plifiers delivering power directly to the load and second, they behave as negative resistance elements in shunt with the load and thereby increase the impedance into which the transistors work. This permits the transistors to deliver more power without increased collector current swing. The circuits of Figs. 12 and 13 can both be adjusted to give reasonably Unear performance. Perhaps the most interesting aspect of these circuits is that the theoretical maximum efficiency (for sinusoidal signals) is 93%. This should be a matter of importance in applications where the greatest possible power output is desired from transistors and tubes of limited dis- sipation rating. It has been pointed out by Ryder and Kircher^ that a transistor with a just equal to unity behaves like a vacuum tube triode when operated with the emitter grounded. If transistors can be made to operate satisfactorily in this way with large signal swings then all the vacuum tubes in the circuits discussed in this section can be replaced by grounded-emitter transistors. General Comments It is obvious that not all useful transistor circuits can be found in the manner presented in this paper and, furthermore, not all of the circuits found through the application of duaUty are useful. One limitation of the method is imposed by the fact that present day tran- sistors correspond to rather low m vacuum tubes. On this account, vacuum tube circuits which require high /x tubes for satisfactory performance will lead to inferior transistor circuits. If further development of the transistor produces higher values of a, this limitation will be reduced. Another limitation of the method comes from the failure of the transistor to produce a phase reversal. Although this is not important in many cases, and in other cases in which it is important a transformer provides a satis factory solution, still the fact remains that transformers do not respond at^ d.c. and because of this fact some transistor dual circuits are useless. In spite of these limitations, the methods presented in this paper have led to a number of useful transistor circuits and may be expected to yield still more in the future. Acknowledgment The authors wish to express their gratitude for the keen interest in work shown by Mr. W. E. Kock and Mr. R. K. Potter under whose direction- » Ryder and Kircher, loc. cit. -.^^^i ^ DUALITY AS GUIDE IN TRANSISTOR CIRCUIT DESIGN 405 it has been carried out. We are indebted to Mr. B. McMillan and also to Messrs. Harold Barney, R. J. Kircher, L. A. Meacham, J. A. Morton, L. C. Peterson and R. M. Ryder for encouragement and helpful comments. APPENDIX The appendix is a brief account of some of the circuits which have been investigated with the aid of the methods described in the main text. The circuits shown do not exhaust all possibilities, and the specific configurations shown are not to be regarded as optimal choices. Figure 14 shows a one-stage resistance-capacitance coupled amplifier and its dual. In the input circuit of 14(a), C is a series element which passes alter- nating currents and blocks direct currents. The dual element, Z,, in the input circuit of 14(b) is a shunt element which is a short circuit to direct voltages, but not to alternating voltages. The resistance Ri is a shunt element which provides a path through the battery without creating a short circuit to ground for the alternating signal. Correspondingly, the resistance Ri pro- vides a path around the current supply, which otherwise would be an open circuit for the alternating signal. The passive elements in the input circuit are also capable of acting as a source of self-bias. Suppose, for example, that Ri be connected directly to ground with no battery interposed and that the emitter current supply be removed. The resulting vacuum tube circuit is famiUar. The usual explana- tion of its behavior is that when the grid is driven positive and draws grid current, the condenser C becomes charged, and that subsequently the con- denser discharges through the resistance Ri , supposed large enough to as- sure a long discharge time constant. In this way the condenser is kept charged so that grid current flows only a small portion of the time. The behavior of the dual circuit is exactly analogous, but is much harder to explain simply because words and expressions dual to those used above do not exist or are not in current use. For example, we speak of a condenser as ''charged" when there is a potential between the terminals. There is no corresponding term for an inductor with a current passing through it. The explanation, nevertheless, might be as follows: The emitter normally pre- sents a low impedance to positive input currents, and a high impedance to negative input currents. When the input current is negative, the high im- pedance of the emitter blocks the current and a current is therefore drawn through the inductor L, in an upward direction as the figure is drawn. Sub- sequently, when the input current becomes positive, the emitter presents a low impedance, and the current in the inductor is free to pass through Ri and the emitter. It is supposed that the inductance is large enough so that the decay time constant of the inductor through Ri and the emitter is large. Then the current through the inductor will be approximately constant over a short period and will be a bias current. This current will regulate itself 406 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 SO that the resultant emitter current is positive most of the time, becoming negative only long enough to keep the inductor "charged." The output circuit is easier to explain. The resistance R2 provides a path through the battery which is not a short circuit. The resistance R2 provides a path around the collector current supply which does not have infinite im- pedance to the signal. The loads Zl andZz, are the ultimate receivers of the amplified signal. The duality of the loads may be emphasized by pointing out that the condition corresponding to Zl = 00 is Zl = 0. If the circuits are analyzed with the aid of the equivalent circuits dis- cussed in the text, the voltage amphfication of the vacuum tube circuit will be found to be fp R2 Zl while the current amplification of the transistor circuit is found to be rm t. + R'. + Zl' These expressions are obviously duals. Transistor amphfiers like the one shown in Fig. 14 can be connected in cascade. Three examples are shown in Fig. 15 (b) and (c) and (d). Figure 15(b) is the most obvious connection, and 15(c) and 15(d) have provisions for correcting the relative phase inversion that occurs in the transistor cir- cuit. If the circuit equations for the three examples are written out, it will be discovered that only 15(c) and 15(d) are duals (in the sense defined in the text) of the vacuum tube circuit 15(a). The remaining example, 15(b), is the dual of a pecuHar looking circuit with one vacuum tube inverted. In the range where operation is nearly linear, the three cascaded amplifiers behave much alike; and 15(c) and 15(d) can be regarded as pedantic at- tempts to make the signs come out ''right." As soon as non-hnear operation is encountered, however, the differences between the circuits become pro- nounced. This will be clearer when multivibrators are considered. Figure 16 shows a variation of one of the circuits of Fig. 15 designed to operate on a single power supply. A circuit like this with four cascaded stages has been built and tested, and was found to work satisfactorily with selected matched transistors. The two extra resistors in each stage, Ri and R2 , are voltage dropping resistors, chosen to balance the voltage drops in the emitter and collector circuits respectively. Figure 17 shows a multivibrator, conveniently illustrated as a two-stage RC coupled amplifier with its output connected to its input. Below are shown three circuits, of which the first is almost a dual and the other two are duals DUALITY AS GUIDE IN TRANSISTOR CIRCUIT DESIGN 407 of the vacuum tube circuit. The first transistor circuit, 17(b), fails to be a dual in that besides having positive feedback around two stages, it has positive feedback in each stage separately. This is avoided in 17(c) by an isolatinsr (a) (b) Fig. 14 — Resistance — capacitance coupled amplifier and dual. Fig, 15 — Cascaded amplifier and duals. transformer. It has been shown nevertheless by practical tests that 17(b) acts as a multivibrator, and is perhaps even a better circuit than the others. It has the interesting characteristic that the two inductors are in parallel, and hence may be replaced by a single inductor. One explanation of the operation of a vacuum tube multivibrator is this. 408 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 Suppose one grid is at a large negative potential, cutting off that tube, and the other is at a positive potential or at zero potential. The potential of the R2 Fig. 16— Two-stage transistor amplifier using a single power supply. Fig. 17 — Multivibrator and duals. negative grid rises toward zero at a rate controlled by the grid resistor and the coupling condenser. When the grid potential rises above the cutoff DUALITY AS GUIDE IN TRANSISTOR CIRCUIT DESIGN 409 voltage, the plate potential falls, and the positive feedback accelerates the process so the first grid rises to a positive potential and the other grid falls to a large negative potential. The process is then repeated. The dual behavior of the transistor multivibrator is as follows: Suppose that the emitter current of one transistor is very large, and of the other about zero. The large emitter current passes through the emitter, an in- ductance, and a small resistor, and will decay at a rate controlled by the in- ductance and the effective resistance of the resistor and emitter. As it decays, no effect will result in the collector circuit until the emitter current falls below the collector voltage cutoff point, after which the collector current will decrease. The emitter current of the other transistor will increase^ as a consequence of the phase inversion built into the circuit, and the collector current of the second transistor will increase. As a consequence of positive feedback, the whole process will accelerate suddenly and proceed until the (a) (b) Fig. 18 — Cathode follower and dual. emitter current of the second transistor is large and that of the first is zero or negative. The process will then repeat. Figure 18 shows a simple cathode follower and its dual. It has been ex- plained in the text that, in circuits where the cathode current or the grid- to-plate voltage play an important part, the dual circuit will usually require a transformer. Alternatively it may be said that, in any circuit in which feedback in a single stage plays an important role, a transformer may be a necessity. In fact, we have found it impossible to avoid the use of a trans- former in the dual of the cathode follower. The transistor circuit shown will need another power supply for emitter bias, and a blocking condenser to prevent the bias current from flowing through one winding of the transformer. The power supply is required be- cause the transformer will not transmit d-c. signals, and the condenser is necessary because the d-c. impedance of a transformer winding is nearly zero. Extra blocking condensers will appear in association with transformers in many circuits, especially in cases where the transformer is being used as the dual of another transformer. A vacuum tube cathode follower ordinarily has a high input impedance 410 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 and a low output impedance, and has a voltage gain nearly equal to one. The dual circuit has a low input impedance and a high output impedance, and a current gain nearly equal to one. This comes about as follows: Suppose the collector circuit resistance and load are small. Then the collector is ap- proximately at ground potential. Let the input current increase. This tends to increase the voltage drop from base to collector, and therefore the base potential tends to rise. This rise is transmitted to the emitter by the trans- former, and therefore the emitter current rises. The rise in emitter current causes a drop in collector resistance, and counteracts the tendency for the collector-to-base voltage to rise. The result is that the input current passes through the collector circuit into the load without any corresponding rise in voltage between base and ground. This means that the input impedance is low. Of course, not all the input current passes to the load; some is passed to the emitter circuit. In a practical case tested, using a transistor whose ^h — I.-F:: — r"^^^^^ c^—E (a) (b) Fig. 19 — Plate detector and dual. base and emitter resistances were of the order of a few hundred ohms, with a load of 5000 ohms, the current gain was about .70 and the input impedance was about 40 ohms. Figures 19, 20, and 21 show several ampUtude modulation detectors and their duals. The purpose of all these circuits is to derive from an ampHtude modulated wave a wave proportional to the envelope of the given wave. Figure 19 shows a plate detector and its dual. The plate detector looks like a single-stage amplifier with a low-pass filter in its output circuit. It is biased approximately to plate current cutoff. As an amplifier it amplifies approximately the upper half of the input wave and does not pass the lower half. The filter smooths the succession of current pulses in the plate circuit and gives an output proportional to the average of the upper half of the input wave. If the input is a true ampUtude modulated wave, this is also proportional to the envelope. The dual circuit operates in the same way. The circuit looks like a one- stage amplifier with a low-pass filter in the collector circuit. It is biased to collector voltage cutoff. The negative part of the input signal is amplified, and the positive part is not. The collector voltage is a succession of pulses DUALITY AS GUIDE IN TRANSISTOR CIRCUIT DESIGN 411 of varying amplitudes. These are smoothed by the filter; and the output, as before, is proportional to the envelope of the input. It is important for the proper operation of these circuits that the filter in the plate detector have low input impedance outside of the pass band, and that the filter in the dual circuit have low input admittance outside of the pass band. The exact form of the filter is immaterial. Figure 20 shows a grid leak detector and its dual. The operation of the grid leak detector depends on the same principles as that of the grid leak bias circuit described before. The time constant of the bias circuit is chosen, however, so that the bias will be able to vary fast enough to follow the en- fa) (b) Fig. 20 — Grid leak detector and dual. A — ^. (a) (b) Fig. 21 — Infinite impedance detector and dual. velope of the input wave. The overall grid voltage or emitter current is then the input with a super-imposed wave proportional to the envelope of the input. These are amplified together, and the undesired high-frequency com- ponents are removed by a filter in the output circuit, leaving only the en- velope wave. The filter must have approximately the same quahties as in the previous case. Figure 21 shows an infinite impedance detector and its dual. This can be thought of as a cathode follower with a large capacitor across the cathode resistor. This capacitor charges through the comparatively low impedance of the tube when the signal is positive and reaches approximately the peak potential of the input wave. When the input voltage falls, the tube is cut off and the condenser must discharge through a comparatively high im- pedance. If the time constant of the discharge is properly chosen, the con- 412 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 denser will remain charged approximately to the instantaneous peak value of the input wave, which is the envelope of the input. The transistor circuit works in a similar way. When the input current is positive, the circuit be- haves like a cathode follower, and a current is sent through the inductor L which is approximately equal to the input current. When the input current falls, the emitter current rises, and the collector presents a low impedance. ■/TOT^— ^ RF I ! S J I AF RF I I I fHh- Zu' AF (a) (b) Fig. 22 — Plate modulator and dual. RFC Fig. 23— Constant current modulator and dual. The current through the inductor then decays slowly through the load and the low collector impedance. Each time the input signal has a positive peak, the effect is to draw a large current through the inductor, which persists dur- ing the rest of the cycle. The dual of the infinite impedance detector is not a very attractive circuit, because the transformer must act for the carrier frequency as well as for the envelope frequencies. Figures 22, 23, 24, 25, 26 and 27 show various amplitude modulator DUALITY AS GUIDE IN TRANSISTOR CIRCUIT DESIGN 413 circuits and their duals. These have as their object the production of a carrier frequency wave with a given envelope. Figure 22 shows a plate modulator and its dual. This circuit makes use of the fact that the output of a class C amplifier is proportional approximately to the plate supply voltage. In 22(a) the vacuum tube acts as a class C ampU- fier amplifying the carrier frequency wave, and the supply voltage is varied Fig. 24 — Modified constant current modulator and dual. U K (b) Fig. 25 — Grid modulator and dual. by adding to it the modulating voltage. The peak output voltage thus varies with the modulating voltage. The dual transistor circuit, 22(b), is also a class C amplifier, with its collector supply current varied by the addition of a modulating current. The output is proportional approximately to the total supply current, and hence varies with the modulating current. Figure 23(a) shows a particular embodiment of the plate modulator which is called a constant current modulator, because the total supply current to the two tubes in the circuit is (approximately) constant. It is easier to ex- 414 THE BELL SYSTEM TECHNICAL JOURNAL^ APRIL 1951 plain this circuit by saying that the output of class C amplifier is propor- tional to the supply current. Two tubes, one a sort of audio amplifier and one a class C amphfier, are connected in parallel to a single constant current power supply consisting of a battery in series with a large inductor. The Fig. 26— Cathode modulator and dual. ^§— viKHMy Fig. 27 — General balanced modulator and dual. class C amplifier can use only the current not used by the modulator tube, and hence its output varies inversely with the plate current of, and hence inversely with the grid voltage of, the modulator tube. The dual. Fig. 23(b), consists of a class C transistor amplifier in series with a class A modulator DUALITY AS GUIDE IN TRANSISTOR CIRCUIT DESIGN 415 transistor, connected to a source of constant voltage approximated here by a constant current supply in parallel with a large capacitor. The voltage available for the operation of the class C amplifier is the difference between the supply voltage and the collector voltage of the modulator transistor. Inasmuch as the output of the class C amplifier is proportional to its supply voltage, it is clear that the output will vary directly with the emitter current of the modulator transistor. Both the vacuum tube and transistor circuit of Fig. 23 suffer because the modulator element can never take all of the available power supply voltage or current, and hence 100% modulation cannot be attained. The circuits of Fig. 24 correct this defect with a transformer, which amphfies slightly the variations in current or voltage in the modulator element. In both circuits W2 > «i , and the total supply current or voltage is no longer constant, but it is nearly so. Figure 25 shows a grid modulator and its dual. Here the non-linearity of the transfer characteristics in the neighborhood of the cutoff point is made use of directly to produce modulation products. The tube is biased approxi- mately to plate current cutoff, and the transistor approximately to collector voltage cutoff. The desired modulation products are selected by a tuned circuit. Figure 26 shows a cathode modulator and its dual. These circuits combine some of the features of the grid modulator and of the plate modulator. Un- fortunately the phase relationships are such in the transistor circuit that a transformer is required, and this transformer must be able to pass modula- tion frequencies as well as carrier frequencies. The circuits of Fig. 25 and Fig. 26 can be operated as large-signal devices, using the gross non-linearities of the circuits to produce modulation products, or as small-signal devices, when they operate as 'square law' devices. They can, moreover, be combined to form various push-pull or balanced modula- tors. An example of such a circuit is shown in Fig. 27(a). This circuit has two inputs and two outputs. If it is operated as a square-law device the rela- tions between the input and output frequencies will be as follows: Inpul Output 2 1 2 2a a a a, 2a — b b, 2b, 2a a, a-fb, a-b b — 2a , 2b, a-fb, a-b a,b a, b a,b, 2a, 2b, a+b, a-b The same relations hold for the dual circuit, Fig. 27(b). The action of the dual circuit is analogous to that of the vacuum tube circuit. It is a two- transistor circuit operated at the same time as a push-pull circuit and as two transistors in series, in phase. At various points in the circuit certain com- 416 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 ponents of the signal are zero because of the symmetries of the circuit. Notice that the dual of two vacuum tubes in parallel is two transistors in series. Figure 28 shows a modulator which bears the same relation to the mod- ulator of Reise and Skene (U. S. Patent 2,226,258) that the amplifier of Fig. 11 of the test bears to the Doherty amplifier. The carrier wave is fed into the tube and the transistor in the same way that the signal is fed into the amplifier, and the modulating signal is fed into the grid and the emitter through the transformers AFi and AF2 . The effect of the modulating signal i«; to vary the biases of the active elements. Inasmuch as both elements are used as class 5 or C amplifiers, their outputs are dependent on their biases Fig. 28 — High efl&ciency modulator. (b) Fig. 29 — Hartley oscillator and dual. K the RF signal is large enough, and if the phases and turns ratios of the transformers are carefully chosen, the ampUtude of the output will be nearly proportional to the modulating signal. A similar modulator can be based on the circuit of Fig. 10. Figure 29 shows a Hartley oscillator and its dual. The configuration of elements in the Hartley oscillator may seem unfamiliar, but is chosen de- liberately to emphasize the point of view that the Hartley oscillator is an amplifier with feedback through a coupling network. The part of the circuit enclosed in dotted lines is the coupling network. The dual circuit is also an amplifier with a coupling network, but because of the fact that the vacuum DUALITY AS GUIDE IN TRANSISTOR CIRCUIT DESIGN 417 tube has an inherent phase reversal and the transistor has not, an extra transformer is needed in the coupHng network. It is conveniently placed as shown, where it can be combined with the inductor. The input circuits to the amplifiers have self bias circuits which have already been described. The Colpitts oscillator is similar to the Hartley oscillator. The difference lies in the coupling circuit. Figure 30 shows the coupling circuit for the Colpitts oscillator and its dual. The tuned-plate tuned-grid oscillator can be treated in exactly the same way. 0 — njw^ (a) (b) Fig. 30 — Colpitts coupling network and dual. ■|( — 050^^—0 c^(-^wr^ ■^7HH^(-^ ^ 1 Ca) (b) Fig. 31 — Transistor oscillator coupling networks. The coupling circuits used in successful vacuum tube oscillators are char- acterized by having a phase shift of 180°. This can be done with structures like low- or high-pass filter sections, by R-C networks, and in other ways. On the other hand, the coupling network required for a good transistor os- cillator must have zero (or 360°) phase shift. It is therefore probably most easily arrived at by designing a 180° phase shifting network and add- ing a phase inverting transformer. Two simple coupling networks which have zero phase shift are shown in Fig. 31. These are both band-pass struc- tures which lead to oscillation in the pass band. Of the two, the network of Fig. 31(b) gives a more rapid change of phase with frequency and hence leads to a more stable oscillator. In addition, this circuit has the potential ad- vantage of providing means for matching impedances. Some Design Features of the N-1 Carrier Telephone System By W. E. KAHL and L. PEDERSEN Introduction The economies which result from sharing the cost of line facilities among a number of channels, and the transmission advantages of carrier circuits (in the form of high speed transmission which minimizes delay and echo effects, low net loss and high quality), have combined to bring about a revolution in long distance telephony. Whereas fifteen years ago only 8% of the toll circuit mileage of the Bell System was furnished by carrier, today carrier circuits comprise about two-thirds of the total mileage. The mini- mum distance, however, for which carrier can economically replace voice frequency transmission has been limited by the cost of the carrier equip- ment, the cost of line treatment, the expense of installation and associated job engineering, and the maintenance effort required. As a result, the shorter toll circuits, relatively large in number though not in circuit mileage, have continued to operate at voice frequency. The newly developed Type N-1 Carrier Telephone System is aimed primarily at expanding the application for carrier into this field of short haul service. As explained elsewhere^, it is designed to obtain the advantages of carrier for toll and exchange cable circuits for lengths a small fraction of the previous economic minimum. Many system and circuit features contribute to this end. There are 12 channels per system with 8 kc spacing between carriers. The carrier and both sidebands are transmitted. AU of the pairs in a single cable can be used for Type N without special cable treatment. Repeaters are spaced 6 to 8 miles apart depending upon the gauge of the cable conductors. Power is fed over the cable pairs to two out of every three repeaters, which can be pole mounted. Different frequency bands on different pairs in the same cable are used for opposite directions of transmission, 44-140 kc in one direction, and 164-260 kc in the other. The frequency bands are interchanged and inverted at each repeater to avoid important types of crosstalk, and to provide automatic equalization of attenuation slope. Compandors, built into the channel terminals, raise the lower speech volumes prior to transmis- sion and restore them after reception, thereby minimizing the severity of crosstalk and noise problems on the line and in the terminals. An out-of- band signaling channel immediately above the speech band is provided by built-in equipment. * "The Type N-1 Carrier Telephone System: Objectives and Transmission Features," R. S. Caruthers, January 1951 issue of this Journal. 418 N-1 CARRIER TELEPHONE SYSTEM 419 Important as these new system and circuit techniques are, they could not in themselves accomplish the objectives of small manufacturing cost, mini- mum engineering by the customer, ease of installation, and substantial dimunition of maintenance effort. Contributing in large measure to the overall success of the Type N System are new and interdependent features in the components and equipment, which in combination represent a com- plete transformation from the past. Miniaturized components and improved assembly techniques yield large reductions in size and weight. Unitized construction with packaged sub-assemblies not only simplifies installation, but greatly facilitates the finding and correction of trouble, permitting shipment of defective units to a central point for overhauling and thereby making it possible to maintain the working equipment with plant personnel not highly trained in carrier techniques. A further contribution to ease of maintenance has been made in various instances by extension of the life of components in order to avoid the necessity for frequent replacement. These and other features of the Type N equipment are described in this paper, which discusses first the components and their characteristics, and then the design of the equipment assembly. Resistors, Capacitors, and Inductors The circuit arrangements of the N-1 System have been designed with adequate margins to permit generous use of the low cost, small capacitors, resistors and potentiometers in commercial manufacture. Deposited carbon resistors find application where high circuit precision is necessary, while vitreous enamel coated resistors are used where higher power dissipation is required. Capacitances of several microfarads or more must be compressed into a small volume for miniaturized equipment. Aluminum electrolytic capacitors, which have been used for this purpose, have limited life due to the suscepti- bility of aluminum to corrosion by common reagents and contaminants. In the Type N System, high capacity, long life tantalum electrolytic capa- citors of both polar and non-polar types find their first Bell System ap- plication^. These tantalum capacitors are considerably smaller than the aluminum type. Two types of tantalum capacitors are used. In the sintered type the anode is made by pressing powdered tantalum into a compact shape and then sintering in a vacuum furnace to weld the powder particles. This creates a porous mass in which a relatively large surface area is exposed for oxide fihn formation, and hence a large capacitance per unit volume of material is obtained. In the foil type, two foil electrodes are wound in the conventional manner into a cyUndrical unit with a paper separator. Size 2 "Tantalum Electrolytic Capacitors," M. Whitehead, Bell Laboratories Record, October 1950. 420 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 reduction is realized for this type since the high tensile strength of tantalum permits manufacture using very thin foil. From the measured stabihty of the tantalum oxide fihn, and from the known immunity of tantalum to at- tack by acid reagents, it is concluded that the life of a tantalum electrolytic capacitor will be several times that of the corresponding aluminum electro- lytic capacitor. Three capacitance ratings are in production for use in the lii ^M-}SW Fig. 1 — Tantalum capacitors. Upper: Sintered type, 4 mf/60 volt polar; Lower: Foil type, 1 mf/150 volt nonpolar. N-1 System: one of the sintered construction, 4 mf/60 volts polar; and two of the foil construction, 1 mf/150 volts polar and 1 mf/150 volts non-polar. Examples of these capacitors are illustrated in Fig. 1. The inductors employed in the Type N System are of several types. Two toroidal type inductors, each wound over a small low cost molybdenum permalloy dust core, are used in the voice frequency filters and in battery supply leads. Individually mounted duo-lateral wound inductors find ap- plication in interstage networks. Two duo-lateral type inductors wound on a common molded phenolic core tube are used in carrier frequency filters. N-1 CARRIER TELEPHONE SYSTEM 421 Adjustable magnetic cores are used with these latter inductors to facilitate precise tuning with associated capacitors. The mutual inductance inherent between inductors wound in this manner is desired in the case of the channel band filters. In the high and low pass carrier frequency filters, where the effect of mutual inductance is detrimental to filter performance, a small inexpensive inductor is added to annul this mutual. This inductor comprises Fig. 2 — Various types of inductors used in the N-1 carrier telephone system. a parallel pair duo-lateral winding on a solenoidal iron dust core. Figure 2 illustrates some of the inductors used in the system. Transformers In the transformer designs used in the system both miniaturization and low cost are attained through the use of few parts and common parts wher- ever possible, improved manufacturing techniques allowing the use of much finer wire than heretofore practical, and multiple-winding methods for all designs. For the voice and signaling circuit transformers, where there is no superimposed direct current flowing through the windings, the core struc- ture consists of interleaved "E" and "I" permalloy laminations. For the 422 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 case where superimposed direct current is flowing in the windings, the core structure is formed by a wrap-around assembly of several strips of permal- M MM B MS S fmSt f^m f^' ^x ^^ Fig. 3 — Voice, signaling and carrier frequency iia;,.-;v^inicis. loy tape and a stack-up of 'T' laminations. One of the signaUng frequency transformers is an adaptation of the type used in hearing aids which was modified to make it suitable for Bell System use. N-1 CARRIER TELEPHONE SYSTEM 423 The carrier frequency transformers also exemplify small size. They are alike in structure, employing acetate filled windings assembled over small toroidal molybdenum permalloy dust cores which are broken in half to accept the winding assembly and cemented together again. The winding and core assembly is supported from the terminals which are molded into the cover plate. This construction method further simpUfies fabrication by eliminating the need of intermediate lead wires from the winding assembly, the fine wire of the windings being connected directly to the transformer terminals. All transformers are housed in drawn aluminum cases and are equipped with threaded metal inserts in the covers for mounting. Construction fea- tures of the various transformers are shown in Fig. 3. Fig. 4 — Quartz crystal units used for carrier frequency oscillator control. Crystals The 12-channel carrier frequencies required for the system are supphed by quartz-crystal controlled oscillators covering the range of 168 kc to 256 kc in 8 kc steps. These crystals are -1-5° X cut quartz plates operated in a fundamental extensional mode, with gold electrodes plated on the major surfaces, wire mounted and hermetically sealed in metal holders with mounting leads. The crystal used to control the 304 kc carrier supply oscil- lator for the group modulator is a DT quartz crystal plate operating in the shear mode, otherwise similar to the crystals for the channel frequencies. The two designs are shown in Fig. 4. Varistors Nearly eight hundred small germanium varistors are used as circuit ele- ments in the two terminals of an N-1 system. Slightly more than half of this 424 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 number are used as single elements to perform such functions as vario- losser bias control, rectifier, channel demodulator, keyer for signaling fre- quency, voltage doubler in the signaUng circuit and current divider in the expandor circuit. The remainder are assembled into three groups of care- r-GFRMANnjM WAf=ER I i^'. 5 Oermanium varistors. Lower right: Germanium varistor unit with an exploded view directly above; Top: Magnified cross section of the same unit. The functional ele- ments are a wafer of germanium which is soldered to the fluted pin at the left and the "S" shaped tungsten wire in the pin at the right. The rectifying junction produced under the tungsten point contact with the specially prepared germanium surface is the seat of the non-linear resistance characteristic. Lower left: Vario-losser assembly. fully selected units, for use as the channel modulator, the compressor vario- losser and the expandor vario-losser respectively. The germanium varistor unit is shown at the lower right of Fig. 5. The compandor vario-losser varistors are of special interest because of the important function they perform and the way in which the desired close N-1 CARRIER TELEPHONE SYSTEM 425 limit non-linear characteristic is obtained. At the left of Fig. 5 is a view of the compressor vario-losser assembly and extending to the right the com- ponents from which it is constructed. Similar construction is used for the expandor and channel modulator units. The vario-losser units function by virtue of the fact that their a-c impedance can be varied and closely con- trolled by a d-c bias. Consequently, when made a part of a suitable network and controlled by a d-c bias proportional to the signal level, the compressor, which comprises four varistor elements, can be made to increase its attenua- tion as the signal increases; while in a different network, the expandor, which comprises six varistor elements, can be made to decrease its attenua- tion with increasing signal. The close degree to which the compressor and expandor characteristics must complement each other makes it necessary to use varistor elements that are very precisely controlled as to their a-c im- pedance at specific values of bias current. This is accompHshed by careful selection of elements which comprise only a fraction of the total distribution of characteristics produced and then grouping these selected units into as- semblies as illustrated. These selected groups must then pass transmission requirements which are directly related to the compandor performance. The channel modulator is also composed of selected germanium varistors but, unlike the vario-lossers, the modulators do not all have to be substan- tially alike. It is sufficient that the four elements comprising any one modu- lator be alike to control the carrier leak. One modulator may then differ considerably from another in impedance. Copper oxide instead of germanium varistors are used in the group modu- lators at terminals and repeaters because their lower impedance level and somewhat lower noise figure give better performance in these circuits. Thermistors A thermistor, which introduces a large change of resistance with tempera- ture, is used to regulate the gain of the repeaters and group amplifiers. The thermistor element is a tiny pellet of semi-conducting oxides which is equipped with lead wires, a glass coating and an insulated heater. This whole assemblage, which is less than a tenth of an inch in diameter, is covered with a bright gold coating and enclosed in an evacuated glass tube to reduce heat losses. A network consisting -of a thermistor disc and two wire wound resistors, and tailor-made on the basis of precision measure- ments on the individual thermistor and heater, is included in the assembly to serve as a contactless thermostat for the power sensitive thermistor pellet so that the resistance of the latter is wholly under the control of transmission currents. The thermostat network also serves to adjust the pellet to standard characteristics, thus avoiding impracticable close toler- ances on the basic dimensions and heat treatment processes during manu- 426 TECE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 facture. The complete thermistor illustrated in Fig. 6 has less than one- third the volume of the corresponding thermistor used in the earlier K2 carrier system and as a result of design refinements will operate on less transmission power. Fig. 6 — Thermistor assembly used for gain regulation of repeater and group amplifiers Filters and Equalizers Filter and equalizer assemblies required in any system usually are the largest apparatus items and they vary considerably in size due to the dif- ferences in the type and number of circuit components needed to provide the desired performance characteristics. Although smaller components shrink the dimensions of these assemblies correspondingly, they are still incompat- ible with the dimensions of other apparatus items. It was decided, after study of the different circuit configurations and circuit elements needed for the N-1 System, to divide up the more compUcated networks for as- N-1 CARRIER TELEPHONE SYSTEM 427 sembly into several units which could be connected together in the equip- ment assemblies. The more complicated filters and equahzers thus are com- prised of two or more such units. Except for the signaUng frequency filter the unit assemblies for all filters and equalizers in the system have the same housing and the same mounting facilities. This division of filters and equal- izers into combinations of externally identical units permits more efficient Fig. 7 — Filter units. Upper left: Voice frequency unit; Upper right: Carrier frequency Unit; Center: Common parts, voice and carrier frequency units; Lower: 3700-cycle signal frequency filter. use of space in equipment assemblies and is instrumental in lower manufac- turing costs by utilization of common assembly details. The unit assembly details consist of a drawn aluminum shield can equipped with mounting lugs and a cage type framework comprising two molded phenol end plates held together by four corner rods which also serve as four of the eight available terminals in the terminal side end plate. In the carrier frequency units, two duo-lateral type inductors wound on a common phenoHc core tube are held in place by means of keyed recesses in the end plates. A threaded insert in each of the end plates supports the magnetic 428 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 tuning slug associated with each inductor. In the voice frequency units, which use toroidal molybdenum permalloy core inductors, these same threaded inserts accept the machine screw which supports the inductors. The associated capacitors and resistors support themselves from their leads after connection to the unit terminals. Carrier and voice frequency units are illustrated in Fig. 7. Carrier Frequency Units There are seventeen designs of carrier frequency filters: twelve channel band filters (each comprising two identical units) for use in the terminal equipment, a high-pass input filter (two different units) and a low-pass group modulator output filter (two different units) for use in High-Low repeaters, a low-pass input filter (one unit) and a broadband group modu- lator output filter (three different units) for use in Low-High repeaters, and a low-pass group modulator filter (one unit) for use at low group trans- mitting terminals. The channel band filters are designed to utilize the mutual inductance between inductors, the bandwidth being a function of the coupling factor, and are schematically all alike. Channel separation by means of filters is required only at the receiving terminal. It was decided to do this separation only in the high frequency range. The use of one range required only 12 channel filter designs instead of 24, with resultant lower costs because of the doubhng of the demand for each design. The upper frequency range was chosen: (1) because less mutual inductance is required and, since this causes the inductors to be farther apart, better control of the mutual in- ductance value can be realized; and (2) because it reduced capacitance values and resultant cost. The designs are such that the corresponding inductor windings are identical for all twelve channels, while the distance between windings, which controls the coupling factor, and the associated capacitors are different for each channel. Modifications made on standard duo-lateral type winding machines have made it possible to eliminate any adjustment of the coupling factor, which is held to J% limits by dimen- sional control only. The high- and low-pass filters are of conventional configurations. The effect of mutual inductance in these circuits is to degrade performance by causing excessive distortion in passbands, displace attenuation peaks and limit otherwise realizable loss in the attenuating band. In order to utilize the same assembly methods as for the channel filters and to avoid the need for shielding schematically adjacent inductors, a small inductor is used to annul the unwanted mutual inductance. This inductor has two identical windings with nearly perfect coupling, so that the self inductance of each N-1 CARRIER TELEPHONE SYSTEM 429 winding and the parallel aiding inductance value are equal to the mutual inductance value to be annulled. If the loosely coupled windings of the main inductors are connected in series aiding, then interposing the windings of the annuling inductor in a series opposing fashion has the effect of adding nothing to the inductance of the main windings plus mutual but annuls the mutual in the equivalent T circuit. This is illustrated schematically in Fig. 8. X DESIRED SIMPLE LOW- PASS STRUCTURE La L X X (-M) IS DEGRADING EQUIVALENT ELEMENT LINKING INDEPENDENT CIRCUITS (La+M) (Lb + M) rmp — 1 — nm^ r^^r^— I M-~. (La+M)+(M-M) (Lb + M)+{M-M) (WP — -r — ^^^^^ L, d L2 Fig. 8 — Schematic illustrating the effect of introducing a mutual nulling inductor. Three designs of carrier frequency equahzers are used in the system. Two of these provide the means for equalizing the slope of one cable span, amount- ing to approximately 14 db. The equalization is divided between the trans- mitting terminal (pre-equaHzation) and the receiving terminal (post-equal- ization) in order to minimize the efifect of noise introduced along the cable. The third equalizer is designed to compensate for the accumulated small systematic distortions introduced by the cable spans and repeaters. This "deviation" equalizer is required only on the longer systems involving ap- proximately 10 or more repeaters. Each of these -three equalizers comprise 2 units similar in assembly to the carrier filters. 430 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 Voice Frequency Units Two designs of voice frequency low-pass filters (one unit each) are used in the transmitter modulator input and the receiver demodulator output in each channel. The modulator filter limits the range of voice frequencies Fig. 9 — (a) Operator inserting test filter in jig. Traces aj)pt'aring on tlie cathode ray tube are the characteristic of a reference filter and two reference discrimination levels. The lower trace represents transmission in the test path, which circuit has not j^et been completed, (b) Unadjusted filter characteristic appears on lower trace, (c) Adjustment completed, mid-band loss level being checked for limits, (d) Close-up of cathode ray tube which shows characteristic of filter under test coinciding with the characteristic of the reference filter. to be modulated and provides suppression against 3700 cycle voice fre- quency interference into the signaling circuit. The receiving low-pass filter supplements the suppression provided by the channel filters to prevent inter-channel crosstalk and has an attenuation peak at 3700 cycles to pre- vent the signal tone from interfering with the message circuit. The pass- N-1 CARRIER TELEPHONE SYSTEM 431 band characteristics of these filters are shaped to provide the equaHzation needed in the individual message channels. A narrow band filter centered at 3700 cycles selects the signal frequency at the receiving terminal and provides the suppression against all other frequencies needed to prevent false operation of the receiving signaling circuit. The design of this filter, which is also shown in Fig. 7, makes use of a cage type assembly similar to the other filter units but is somewhat smaller. Unit Adjustment and Inspection All carrier frequency filter and equalizer units are equipped with mag- netic slugs to facilitate accurate adjustment of critical circuit resonances. In the case of the carrier frequency high- and low-pass filter units and the carrier frequency equalizer units, adjustments are made at attenuation peak frequencies. After adjustment, transmission measurements made at these same frequencies only are suflicient to determine satisfactory performance. Adjustment and inspection of the channel filter units are accomplished by the use of a special test set which displays four traces on a cathode ray tube. One trace displays the transmission characteristic of the unit under test, the second trace displays the characteristic of an accurately adjusted reference filter unit and the two remaining traces display two reference discrimination levels. See Fig. 9. Blanking pulses are applied to the intensity grid of the cathode ray tube to blot out the traces at points corresponding to liz 4 kc from the mid-band frequency. The blotted out portion of the traces together with the discrimination level traces provide a coordinate system to establish bandwidth limits for inspection purposes. The magnetic slugs are adjusted so that the displayed characteristic of the filter unit under test is symmetrically located with respect to the displayed character- istic of the reference filter unit. If the adjusted characteristic of a filter unit passes through the coordinate established by the blanking pulses between the discrimination level traces it meets its requirements. The electrical performance of the voice frequency low-pass filters and the 3700 cycle signal band filter is determined by transmission measure- ments at critical frequencies using standard test equipment. Equipment Equipment design of N-1 Carrier terminals and repeaters has been directed particularly towards small size and weight, low manufacturing cost, sim- plicity of engineering and installation, and ease of maintenance. Size and weight have been minimized by arranging the miniaturized components compactly in die cast aluminum frames of a size and shape to fully utilize the rack space available in depth as well as in breadth and height. This may be called "cubic" construction as contrasting with the "planar" con- 432 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 struction of conventional panels. This also facilitates manufacture as does a new method of mounting components of the "pigtail" type in parallel thermoplastic strips and the division of the equipment into subassemblies convenient for shop handling and so composed of circuit elements that the same subassemblies can be used in more than one part of the system. Main- tenance is facilitated and service interruptions reduced to minimum length by arranging the units for interconnection by plugs and jacks so that a defective unit can readily be replaced by a spare and sent to a maintenance center equipped with adequate measuring equipment and manned by a technically trained and experienced personnel. Engineering and installation are faciUtated by packaging the equipment so that the maximum possible portion of the assembly and wiring work is performed in the shop, and by avoiding engineered options. The close packing of components in a relatively small space makes more serious the problems of wiring, shielding, heat dissipation, accessibility for inspection and maintenance, and major modifications. Unitized Construction This unit method of construction takes the form of conveniently sized plug-in assemblies. It makes efficient use of the full 10-inch depth available in the standard relay rack. The front of the unit carries the vacuum tubes adjusting potentiometers and test terminals which need to be accessible for routine system checking. Any space left over on the front panel is utilized by voice and carrier frequency transformers. Other components are com- pactly assembled inside the unit and are accessible only after the unit is removed from its frame mounting. The external connections of each unit terminate in a male connector which matches a female connector in the frame mounting. Both connector assemblies consist of a molded phenoHc rectangular block equipped with 20 gold plated contacts. These assemblies are mounted by means of shoulder screws to give them a slight floating action which relieves the strain on contacts and wiring when the units are plugged in. After the units are plugged in they are secured to the frame mounting by means of quick-acting fasteners. The plug-in method permits the testing of the units without expensive jack fields, and allows the removal of any unit in trouble and its replace- ment by a spare unit for immediate restoration of service. The defective unit can then be taken to a maintenance point where adequate tools and testing equipment are available for convenient repair work by experienced personnel. This is especially valuable in the N-1 system where a majority of the repeaters may be pole-mounted and many of the terminals located in unattended or partially attended offices. It will be valuable in other loca- tions by eliminating repair work from a ladder. For the handling of units N-1 CARRIER TELEPHONE SYSTEM 433 along the cable route or shipping of units to and from a maintenance center, small light-weight fibre carrying cases are available. To facilitate manufacture, the equipment units are subdivided into two or more subassemblies. The circuit is divided among these subassembUes in a way that is convenient for shop assembly and test. An additional ad- vantage, in stocking for maintenance, is that certain of these subassemblies are common to several equipment units, thus reducing the investment in spare units. When the subassemblies are separated, the apparatus and as- sociated wiring in each are readily accessible. Electrical connections between Fig. 10— Thermoplastic strips being positioned in assembly jig for pigtail components. The strips are precut to length from extruded "ribbons" and are stamped with equipment designations to identify the components. subassembUes are accompUshed by means of the same type of male and female connectors as are used between the complete unit and its frame mounting. For protection, particularly in handling, a slip-on can cover is provided for each equipment unit. Mounting or Components To meet the objective of low manufacturing costs, a simple and effective method of mounting the large number of pigtail components is essential. The method adopted arranges as many of these components as electrical requirements permit, on two parallel thermoplastic strips which in turn are mounted in the chassis. Sunple assembly jigs, an example of which is shown in Fig. 10, position the strips and components so that the terminal 434 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 leads rest on the edges of the strips. The application of a slight pressure by a heated shoe imbeds in one operation the terminal leads of all the compo- nents of the assembly into the plastic material. The machine used for this purpose is shown in Fig. 11. Simultaneously with this operation, the terminal leads extending over the edges of the strips are sheared off to a length suit- able to form terminals to which connections are made. If a component needs Fig. 11 — Operator preparing to feed assembly jig to machine where heated shoe im- beds terminal leads of components into the thermoplastic strips. Cuttings from sheared off terminal leads may be seen below machine. to be replaced this is readily done by applying heat to its leads with a solder- ing iron. To facilitate making the relatively large number of wiring connec- t'ons to the pigtail components as well as to terminals of other components, pistol wrapped connections are used in many cases rather than the wrapping by hand with a pair of pliers. The electrically operated wiring pistol illus- trated in Fig. 12 wraps the wire onto the terminal with high tension. The connections are then soldered. N-1 CARRIER TELEPHONE SYSTEM 435 Die Cast Chassis In order that components of varying types and sizes may be mounted with their terminals in good position for wiring, the chassis construction must provide for a variety of mounting surfaces in various planes. Such chassis cannot be fabricated economically even in large quantities, because Fig. 12— Operator using electrically operated wire wrapping pistol. All wires are precut to suitable length. of the multitude of operations required. They can, however, be designed for economical die casting. One of the eleven such castings used in the system is illustrated in Fig. 13. In addition to reduced costs, the die castings offer a number of other advantages. Die castings are uniform in dimensions, facihtating assembly as well as aiding the interchangeabiUty of the plug-in 436 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 Fig. 13 — Aluiniiiiiiii alloy (lie (asiiii.u l-.i ilic low <;r()ui) 1 raiisiiiil t in;; subassembly. On the front of the tasting may be seen tlie equipment designations. The large number of holes in the rear surface provide clearance for filter terminals as well as filter mounting holes. In the middle portion of the casting are a number of pockets used to hold miniature transformers. N-1 CARRIER TELEPHONE SYSTEM 437 subassemblies and equipment units. The surfaces are reasonably smooth as cast and the natural aluminum finish is rather pleasing in appearance, Fig. 14 — Commercial installation of N-1 carrier terminal equipment showing one com- plete terminal. At the bottom of the relay rack may be seen an experimental model of a blower and associated air hose connections. SO that no further finishing operations are necessary. Equipment designa- tions to identify components are incorporated in the die by the use of 438 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 raised characters in a recessed area, instead of being applied by stamping methods. The light weight of the aluminum die casting makes easier the handling of a plug-in unit, particularly when the maintenance man is working on a ladder. Terminal Equipment The terminal equipment as shown in Fig. 14 is designed for maximum flexibility and mounts in the relatively small rack space of 19 by 40 inches. Three such terminals can be mounted in a standard 11 -foot 6-inch relay rack. A complete terminal includes 12 channel units, a transmitting group unit and a receiving group unit. These units plug into a terminal mounting fabricated of aluminum in natural finish, which is secured to the relay rack. The terminal mounting, shown in Fig. 15, consists of two side members of channel section with metal shelves welded between them to support the equipment units. The twelve channel units are mounted five in each of the two rows and two in the third row; the remainder of the bottom row is used for the group units and for alarms and miscellaneous apparatus. The terminal framework and wiring are the same for a terminal transmitting the high group or one transmitting the low group. The fuses and alarm relays for the terminal, and fuses and resistors for the power supplied to an adjacent repeater, are located at the bottom of the terminal mounting. Provision is made for mounting a span adjustment pad when required. Both at the terminals and at the repeater points the receiving lines are built out by these span adjustment pads so that the electrical length of all lines is the same. The wiring between the connectors for the channel units and for the group units runs within the shelf structure out to each side of the bay and then extends up and down the mounting in the side members. Extra connectors are multipled with the group unit connectors to permit the replacement of these units without service interruption. All connectors are mounted so that the wiring and the soldered connections are readily inspected and maintained from the front of the relay rack, per- mitting back-to-back mounting or mounting against a wall. All external wiring is brought to terminal strips located at the bottom of the mounting. Channel Units Each channel unit contains the apparatus, including that required for signaling, associated with one channel. The units for channels 1 to 12 differ only in the receiving filter and in the crystal unit which determines the channel carrier frequency. The apparatus is mounted in three subassembly frameworks which are fastened together to form one unit, as shown in Fig. 16. The subassemblies, shown in Fig. 17, are (1) the compressor (voice-frequency transmitting) N-1 CARRIER TELEPHONE SYSTEM 439 Fig. 15 — N-1 carrier terminal mounting without any of the plug-in units. The shelf structures, including the fuse mounting at the bottom, are so arranged that they may be turned over to expose the wiring side of the connectors. 440 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 m^ y > te» Fig. 16 — Channel unil — front view. The unit is equipped with a perforated aluminum can cover. N-1 CARRIER TELEPHONE SYSTEM 441 subassembly; (2) the expander and signaling (voice frequency receiving) subassembly; and (3) the carrier frequency subassembly. Provision is made in the carrier frequency subassembly for automatic channel transmission regulation. Subassemblies (1) and (2) are identical for all channels. An exploded view of the expandor and signaling subassembly is shown in Fig. 18. Terminal Transmitting and Receiving Group Units The transmitting and receiving group units together contain the transmit- ting and receiving amplifiers; the group modulator, which is used in either the transmitting or receiving branch but not in both; the signaling oscil- lator; and the carrier alarm circuit. Provision is made for automatic group Fig. 17 — Channel unit subassemblies. Compressor at left; expandor and signaling at center; carrier at right. transmission regulation in the receiving circuit. There are four types of group units: one high group transmitting, HGT, and one low group receiv- ing, LGR, for a terminal which transmits the high group of frequencies and receives the low group; and one low group transmitting, LGT, and one high group receiving, HGR, for the reverse terminal. The group units are combinations of three of the following subassemblies as required: (1) high group transmitting, (2) low group transmitting, (3) high group receiving, (4) low group receiving and (5) oscillator. The oscil- lator subassembly supplies the group carrier frequency and the 3700 cycle signaling tone. The oscillator subassembly is plugged into a low group trans- mitting or a low group receiving subassembly and the combination equipped with a common can cover to form an LGT or an LGR unit. The addition of a cover to the high group transmitting or high group receiving subas- sembUes forms a complete HGT or HGR unit. 442 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 Terminal Temperature Control Equipment Due to the compactness of assembly achieved with the cubic method of mounting there remains very httle free space for natural or convective cool- ing, and excessive concentration of heat may be expected. For the N-1 carrier terminals it was found necessary in high temperature areas to pro- vide forced air cooling. Although the major power dissipation occurs in the vacuum tubes, which are mounted on the face of the units, consider- able heat from this source is conducted through to the inside of the units. 'Tt Fig. 18 — An exploded view of the expander and signaling subassembly ready lor Llic final assembly operation. This shows the extent to which prewiring of small assemblies is used. With a power input of approximately 400 watts per terminal serious damage to some of the apparatus might result if forced cooUng were not provided in those offices where summer temperatures are high. With forced cooling the maximum temperature rise is reduced to a limit well within the capabili- ties of the apparatus used. The temperature control equipment consists of a centrifugal blower driven by a iV HP 115 volt a-c motor which circulates air through ducts to the equipment. The motor and blower are mounted at the bottom of each relay rack with flexible connections to rectangular aluminum ducts extending up N-1 CARRIER TELEPHONE SYSTEM 443 along the faces of the terminal mounting framework uprights. Each duct has an aperture opposite each horizontal row of equipment units. A ther- mostat located in one of the terminal mountings starts the blower when cooling is required. Repeater Units Two types of carrier repeater equipment units are used in the N-1 system. They are identified by the designations HL (high-low) and LH (low-high). The HL repeater receives signals at high group frequencies from the line, translates them by modulation with a suitable carrier to low group fre- quencies, then amplifies and regulates them for transmission at the desired output level. The LH repeater functions similarly except it receives low group frequencies and transmits high group frequencies. Each repeater pro- vides for transmission in both directions and the two types are used alter- nately along the line. A repeater equipment unit is made up of three subassemblies. In the HL unit a right-hand high-to-low repeater and modulator subassembly for east-to-west transmission and a left-hand similar subassembly for west-to- east transmission are plugged into a common subassembly which supplies the carrier for group modulation and the voltage regulator, all under a common can cover. In the LH unit the right-hand and left-hand subassem- blies are similar to those in the HL unit except low-to-high instead of high- to-low. The common oscillator subassembly is identical in all repeaters. Repeater Mounting Arrangements Each repeater unit is plugged into a repeater mounting bracket which is a small die casting equipped with three multipled connectors, one into which the repeater is plugged and two for testing and in-service replacement of the repeater. A terminal strip for external wiring connections, and span adjustment pads, when required, are also mounted on this bracket. Four of these mounting brackets are fastened to a shelf structure arranged for relay rack mounting. With the four repeaters plugged in place, the entire assembly occupies a vertical space of approximately 14 inches. The four- repeater groups so constituted may be located in pole-mounted cabinets at non-power supply points or on relay racks with associated power distribu- tion panels at power supply stations. A total of twelve repeaters can be accommodated in a pole-mounted cabinet, as shown in Fig. 19, together with order wire equipment and a 52-pair cable terminal. The terminal is located at the top of the cabinet when the toll or exchange cable is aerial and at the bottom of the cabinet when the cable is buried. The cabinet is made of sheet steel with the out- side walls finished in white enamel to keep heat absorption to a minimum. 444 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 Fig. 19— Pole-mounted cabinet with 12 repeaters and cable terminal in position for aerial cable. N-1 CARRIER TELEPHONE SYSTEM 445 Thermal insulation and a thermostatically controlled vent damper limit the temperature range inside the cabinet to approximately 0°F to +150°F for an outside temperature range of — 30°F to +120°F. The temperature range within the cabinet would otherwise exceed that at which it is prac- ticable to operate apparatus components and insure good performance. This type of temperature control is necessary since power is not available for operating either a blower or a heater. At a power supply point, a power distribution panel is required for each four systems. This power distribution panel contains the power resistors, fuses and fuse alarm circuits for four local repeaters and four adjacent repeaters in each direction. Other equipment that may be furnished in such an office on a miscellaneous basis is the deviation equalizer panel and the artificial lines required to build out very short spans. The relay rack lay- outs may be arranged in a number of ways to suit the particular installa- tion since no shop wired bays are used. The installation effort is minor since very little wiring is involved. A typical 11-foot 6-inch relay rack lay- out at a power supply point will provide for 16 repeaters including some space allowance for miscellaneous equipment. Testing and Maintenance Features Potentiometer controls and test terminals are furnished in the various plug-in units for line-up and trouble localizing purposes. In the case of a channel unit, certain adjustments and tests may be made without removing the unit from its frame mounting while others can be made only following the removal of this unit. If removal is required, a multi-conductor test cord provides the means for reconnecting the removed unit to its connector in the frame mounting thereby providing access to test terminals and con- trols within the unit. Also at the terminal office, a portable group unit switching set permits substitution of an alternate transmitting or receiving group unit for the regular group unit without interrupting service. When the removal of a repeater is necessary, it is similarly accomplished without service interruption by the use of a portable repeater switching set. Both switching sets facilitate tube replacement. Two portable tube test sets have been designed for inservice testing of cathode activity of tubes in repeater and group units. An additional repeater test set is used in system line-up and maintenance adjustments. A portable maintenance center test set has been designed for use with N-1 carrier equipment. This set is capable of testing and adjusting all equipment units, and the two portable switching sets. The test set is es- sentially a device for interconnecting oscillators, measuring equipment and the units to be tested. Filters and attenuators are included for controlling test currents. 446 the bell system technical journal, april 1951 Power Supply The power supplies required for the N-1 system may be obtained from standard office signahng or telegraph power plants without additional filter- ing. The terminal equipment requires —48 volt and +130 volt supplies. Repeaters located at power supply points require +130 volt power only. For feeding pwwer over the line to distant repeaters +130 volt and —130 volt supplies are used in combination as a 260 volt source. Alarms and Order Wire Equipment Each system terminal makes provision for the following alarms which are connected to the standard office alarm system: a. Fuse alarms for all battery supplies. b. 3700 cycle signal oscillator failure alarm. c. Alarm which indicates failure to receive carrier at terminals. The equipment for these alarm circuits is assembled as part of the ter- minal mounting with all wiring accessible from the front of the relay rack. Similarly at the repeater point where power is locally supplied the associated power distribution panel is equipped with fuse alarm circuits for the battery supplies. No alarms are provided at or from non-power supply repeater points. Alarms from an unattended or partially attended repeater office can be extended to a fully attended office, when desired, over one pair of a quad in the cable which has its side circuit equipped with H88 or HI 72 loading. The other pair of this quad may be used as an order wire for system main- tenance. The simplex legs of the two pairs are used to transmit power from power supply points to the portable repeater switching set used at pole- mounted repeaters. The equipment arrangement for the order wire and alarm circuits makes use of the conventional panel method of mounting and provides for a variety of layouts to fit particular applications. Amplifiers are introduced into the order wire and alarm circuits at terminals and power supply repeater points as required. At pole mounted repeaters the order wire equipment consists only of a pair of binding posts for connecting a lineman^s test set. 1.03 IN. (O.D.) 0.06 LB Headpiece. — A panorama of loading coils 1904-1948. The Evolution of Inductive Loading for Bell System Telephone Facilities By THOMAS SHAW {Continued from January 1951 issue) PART III. LOADING FOR EXCHANGE AREA CABLES THIS portion of the present review is primarily concerned with non- phantom t3^e of loading on non-repeatered non-quadded cables, since the evolution of exchange area loading has been ahnost entirely in terms of these facilities. Phantom working has not been extensively practiced because in general it is not economical on exchange cables. In the occasional long cables where phantoming is economical, the phantom group loading makes use of loading apparatus developed for short-haul, two-wire type toll cable faciUties. The very wide range of impedance characteristics of the many different types of exchange cables (with and without loading, and as influenced by the terminal impedances provided by the many different kinds of subscriber loops and station sets) is such that telephone repeaters are necessarily Hm- ited to low gains when used at exchange area switching points. Moreover, it has not been generally feasible to use intermediate repeaters in the lines. Furthermore, the conventional two-wire type of telephone repeater used 447 448 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 in the toll plant is quite expensive in relation to the feasible gains in the exchange plant. Consequently, there has not been an extensive use of re- peaters in the exchange plant. Looking towards the future, however, the use of a low-cost telephone repeater of an entirely new design (Type El) is ex- pected to result in a much more extensive use of repeaters, and in conse- quence some considerable reduction in the demand for the heaviest weights of exchange area loading. (15) First Two Decades of Commercial Loading 15.1 General For about two decades after the estabUshment of the first standard cable loading systems (Table II, page 156), medium-weight loading was by far the most extensively used standard on exchange cables. However, a few of the longest exchange cables used heavy-weight loading. Also in some areas there was a moderate use of light-weight loading on short cables. In the period under discussion almost all of the exchange area loading was installed on 19 ga. cables in situations where, without loading, the circuit lengths and the transmission requirements would have forced the use of much more expensive 13 ga. or 16 ga. cables. Twenty-two gauge cable was available for subscriber cables and for short inter-office trunks. Nine- teen gauge non-loaded cable was used on short inter-office trunk cables, however, as it was then more economical than loaded 22 ga. cable, and had a greater supervision and signahng range. In the larger metropoHtan areas, loading was much more generally used on trunks to tandem-switching office and on connecting-trunks between local and toll offices, than on the direct inter-office trunks, because of the much more severe transmission limits imposed on the tandem and toll office trunks. In occasional instances, these requirements made it necessary to use loaded 16-ga. circuits. There was also a large use of loading on trunk cables between city tandem offices and suburban local offices. By avoiding the need for 13-ga. cable and by greatly reducing the need for 16-ga. cable in these important fields of use, the introduction of loading made possible very large savings in the first costs of additions to the rapidly expanding new plant, and in the subsequent annual charges. 15.2 Partial Loading In the course of the expansion of exchange area loading a practice of "partial loading" evolved. This is exemplified by the loading of a part of a trunk circuit when it exceeds by a moderate amount the length that would be satisfactory from the transmission standpoint without loading, instead INDUCTIVE LOADING FOR TELEPHONE FACILITIES 449 of applying loading to the entire length of the circuit. In effect the partially loaded circuit is a tandem combination of loaded and non-loaded circuits, with the loaded part preferably located near the center. The purpose is to reduce plant cost by restricting the use of loading in individual circuits to about the minimum amount that would be necessary to meet the trans- mission Umits set up as objectives in plant design. In these practices, cer- tain minimum limits regarding the number of loads per circuit were worked to on the basis of engineering experience, different limits being appUed in different operating areas. 15.3 Compressed Iron-Powder Core Loading Coils The first important change in loading coil standards for exchange area loading occurred during 1916, immediately following the successful develop- ment of the compressed annealed, powdered-iron core-materiaF described on pages 167-170. In general, the coils that used this new core-material were much better suited to the requirements of exchange facilities than to those of toll cables. The old standard 95-permeabiJity iron-wire core coils, Codes 506, 507, and 508, were superseded as standards for new plant by the new Nos. 573, 575, and 574 loading coils, respectively. The new coils had closely similar over-all dimensions to those of the superseded coils, and were sub- stantially equivalent, or slightly better, with respect to steady-state trans- mission properties. They were greatly superior with respect to their resistance to permanent or quasi-permanent magnetization by strong currents that might flow through their windings in consequence of accidental grounds on d-c signahng circuits, or from other external causes, including power-line crosses and lightning surges. For a period of several years, the loading practices with the new coils followed those which had evolved in the use of the older coils. (16) Development of Cheaper Cables for Exchange Areas and Standardization of New Loading Systems for Them 16.1 The New Cables During the early 1920's new, cheaper types of non-quadded cable began to be used extensively in the exchange area plant. These resulted from the continuing development work to reduce plant costs. By including design features that made them suitable from the crosstalk standpoint for the application of loading, the economies inherent in the use of loading sub- stantially augmented the large economies that directly resulted from the lower costs of the cables. These design improvements included the staggered pair-twist construction and other features previously appUed to the 0.066 450 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 mf/mi 19 and 16-gauge cables, Codes TB and TH, respectively, for which the early loading standards had been originally estabUshed. With respect to the use of loading the most important of the new cables, above referred to, were: (a) a 455-pair,(^) 19 ga. cable, Code BNB, having a mutual capacitance of about 0.085 mf/mi, and (b) a 909-pair,(^> 22 ga. cable. Code SA, having a mutual capacitance of about 0.083 mf/mi. Also there was a 1212-pair 24 ga. cable having a mutual capacitance of about 0.079 mf/mi. Fractional-size cables having these properties became avail- able subsequently. The 24 ga. cable did not become an important field for the economical use of loading until the late 1920's, following the develop- Table VII Loaded High- Capacitance Cables Type of (1) Cable Weight (2) of Loading (ohms) Theoretical Cut-off Frequency (cycles) Attenuation Loss at 800 cycles (db/mi) Nominal Impedance (ohms) 19BNB Medium-Heavy(2) Heavy Light-Medium<2) Medium (Non-Loaded) 2450 2050 2300 2025 0.31 0.29 0.45 0.41 (1.15) 1350 1600 980 1110 22SA Light-Medium Medium (Non-Loaded) 2320 2040 0.77 0.68 (1.63) 980 1120 ^'> In the tabulated data, the capacitance of 19BNB and 22SA cables are assumed to be 0.085 and 0.083 mf/mi, respectively, and their resistance 85 and 170 ohms per loop mile at 68° F, <2) The first word in the compound designations appHes to the coil inductance ("Medi- um" = .175 mh; and "Light" =0.135 mh). The second word in the compound desig- nation applies to the coil spacing ("Heavy" = 1.14 mi; and "Medium" = 1.66 mi). ment of the low-cost, compressed, permalloy-powder core loading coils de- scribed in Section 19. 16.2 New Loading Arrangements In order to avoid an objectionable degradation in transmission service, new loading systems were standardized during 1922 for use on the high- capacitance 19 ga. and 22 ga. cables, above mentioned. These involved the use of the standard medium loading coil (Code 574, inductance 175 mh) at "heavy" spacing, and of the standard Hght loading coil (Code 575, in- ductance 135 mh) at ''medium" loading spacing. Initially, these new load- ing systems were known as "medium-heavy" and "Ught-medium" loading. Co) The largest number of pairs previously available in 19 and 22 ga. cables were 303 and 606, respectively. INDUCTIVE LOADING FOR TELEPHONE FACILITIES 451 Their installed costs were about the same as those of standard heavy and medium loading, respectively. The special importance and significance of these new loading systems was that their use on the higher capacitance cables avoided a degradation in the loading cut-off standards and the ob- jectionable impairments in transmission inteUigibility that would otherwise have resulted. The use of lower inductances at standard spacing, in order to comply with the cut-off standards without raising costs, resulted in a reduction of nominal impedance which was desirable and an increase in the attenuation which was accepted as tolerable, under the circumstances. This decision on the new loading systems was largely influenced by certain fun- damental transmission-studies then under way which indicated that it would eventually be desirable to adopt much higher cut-off frequency standards, subsequently described. Table VII compares certain transmission properties of "medium-heavy" and "light-medium" loading on the high-capacitance cables with those which would have resulted from the use of standard medium and heavy loading. (17) First Increase in Minimum Cut-Off Frequency for Loaded Exchange Area Cables 17.1 General During 1924 there occurred the first major improvement in loading standards for exchange area cables, consisting of an increase in the minimum cut-off frequency from about 2300 cycles to about 2800 cycles per second. This decision implemented the conclusions reached in comprehensive fun- damental theoretical and experimental studies of exchange area transmis- sion that got well under way during the early 1920's. The improved loading systems initially involved the use of available types of 135 and 175 mh loading coils at spacings shorter than those previously used with these coils, and the use of new 88 mh loading coils much smaller in dimension and much lower in cost than the 135 and 175 mh loading coils. The new 88 mh loading inductance eventually became the most extensively used induc- tance value in exchange area loading. 17.2 New Technique for Computing Intelligibilily Indices for Complete Circuits In the theoretical aspects of the fundamental study, above' referred to, use was made of a new technique developed by Dr. Harvey Fletcher for computing the articulation index of complete telephone transmission sys- tems, taking into account the effects of attenuation loss and circuit distor- tion in the line, the subscriber loops and station sets, the effects of sidetone in the station sets, and allowing for the masking effects of line noise and 452 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 room noise/''^ The new technique was based on fundamental studies of speech and hearing, including a very extensive series of articulation tests on different combinations of lines and loops and telephone sets, in which the Hne portions were modified by electric wave filters to transmit various frequency-band widths, and distortionless attenuators] controlled the line loss. Different representative types of subscriber loops were included in the tests. The then standard deskset telephones were used (No. 337 transmitter. No. 144 receiver, and 46 induction coil) and also special telephone sets using experimental types of transmitters and receivers having ideal, fiat, fre- quency-response characteristics. In comparing complete systems having dif- ferent types of lines, but otherwise similar, the computed articulation- ratings agreed sufficiently closely with the ratings determined from tests to warrant substantial confidence in the experimental use of the computation technique in the exploratory loading development studies. 17.3 New Higher Cul-of Loading Systems The theoretical studies as appHed to an exchange plant using the stand- ard deskset telephones showed that a desirable improvement in the trans- mission intelligibihty of complete connections could be obtained by using the new higher cut-off loading systems which are described in general terms in Table VIII. As discussed later, large economies also resulted in the design of new plant, and in the rearrangement of old plant. The loading designations used in the table are in accordance with a simplified system of designations which was adopted in 1923. The letter-component is a symbol for the spacing, and the number signifies the inductance. Prior to the intro- duction of these new loading standards, medium loading-spacing (M) was about 8775 ft. It was changed to 9000 ft. to facilitate coordination with the other types of loading in the layout of the cable plant. The "D" spacing was an entirely new spacing. The decision to standardize the particular loading systems of Table VIII naturally involved extensive plant cost-transmission studies. These were directed to determining the maximum utilization of the new cheaper cables previously mentioned, and the most advantageous ultimate uses of the higher-grade, more expensive cables already in use. Practical considerations of economy dictated that the new series of loading standards should include systems which could use available loading coils and existing loading vaults in the important underground cable plant. These matters were also of great importance in the gradual rearrangement of the existing exchange area loading at a minimum expense to comply with the new cut-off standards. While the improvement in intelligibility was one of the factors influenc- <') Comprehensive information on Dr. Fletcher's researches is given in Reference (33). f INDUCTIVE LOADING FOR TELEPHONE FACILITIES 453 ing the design of the new loading systems, the engineering of the exchange cable plant continued for some time on the customary volume-efficiency basis, and the standards of over-all attenuation in the trunks were the same as before, in the use of the older loading systems. The improvement in intelligibiUty previously stressed was directly due to the abihty of the new loading systems to transmit efficiently a band of important high-frequency overtones which were suppressed by the old standard loading systems. The subscriber services directly benefited from the improved transmission quahty. Used in the foregoing manner, the new loading systems also yielded large economies in the first costs of new plant by extending the transmission range of the cheaper types of cables. In this respect, the M88 system was by far the most important of the new standards, since it made feasible the use of loaded 22 ga. cable for short trunks, in place of non-loaded 19 ga. Table VIII Improved Exchange Area Loading Standards Loading Designation Loading Sp>acing (feet) Coil Inductance (mh) Approximate Cut-off Frequency* High-Capacitance Cables (cycles) Low- Capacitance Cables (cycles) M88 H135 HI 75 D175 9000 6000 6000 4500 88 135 175 175 2900 2800 Not recommended 2900 3200 3200 2800 3200 * These particular figures take 0.083 mf/mi and 0.066 mf/mi as representative values for high-capacitance and low-capacitance cables, respectively. cable, and the aggregate length of the short trunks is a large fraction of the total exchange trunk mileage. The special economic importance of 22 ga. cable loading received recognition in the development of much cheaper loading coils which are described later on. The more expensive new H-spaced loading was advantageous on the longer cables, and in shorter cables when lower transmission equivalents were necessary. HI 75 loading was important because of its suitability for use on low-capacitance cables. The D175 system provided a field for the reuse of 175 mh loading coils that were displaced in the course of the plant rearrangements, previously mentioned. Also, it faciUtated the conversion of old Ml 75 facihties to meet the new cut-off standards, and with decreased attenuation. This conversion procedure involved the introduction of additional 175 mh loading coils, at or near the electrical centers of the old medium loading sections. Some typical performance characteristics of the new loading systems on 454 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 exchange area cables are given in Table IX. The tabulation, in general, is in the sequence of ascending costs. Although loaded 24 ga. cable is superior to non-loaded 22 ga. cable from the transmission standpoint, it was not sufficiently cheaper (when using iron-dust core loading coils) to warrant its general use. However, under some special circumstances involving large complements of the new coils, loaded 24 ga. cable could be proved in. In the design of the cable plant, the signaling characteristics of the facili- ties of course had to be taken into account along with the transmission characteristics. In some situations the total costs could be reduced by using Table IX Transmission Characteristics of Typical Exchange Area Trunks Cable Loading System Theoretical Cut-off Freq. (cycles) Nominal Impedance (ohms) Attenuation Conductor Gauge Capacitance (mf/mi) at 100 cycles (db/mi) 24 0.084 M88 2900 900 1.42 22 « 0.082 11 M88 H135 D175 2900 2800 2900 990 1300 1690 0.92 0.63 0.51 22 0.073 M88 3000 950 0.87 19 0.084 << M88 H135 D175 2900 2800 2800 860 1280 1680 0.49 0.34 0.28 19 « « 0.066 « M88 H135 H175 D175 3200 3200 2800 3200 950 1420 1640 1860 0.44 0.30 0.27 0.25 16 0.066 M88 3200 960 0.24 a more expensive grade of circuit that allows the use of less expensive sig- naling equipment. (18) Loading Coils for Higher Cut-Off Loading Systems 18.1 New Small-Size Coils for M88 Loading Preliminary design studies of cheaper and smaller loading coils for use on 22 ga. cables started well in advance of the decision to standardize M88 loading. It was realized that the maximum possible economies would result from a two-stage development plan, in which the first stage would consist of an improvised "stop-gap" design using available standard core-rings and simple modifications of existing standard loading coil cases, and the second step would be an entirely new design, having approximately optimum pro- INDUCTIVE LOADING FOR TELEPHONE FACILITIES 455 portions as regards transmission and cost features in the expected wide use on 22 ga. cables. For optimum economies in potting and installation, en- tirely new types of loading coil cases would be required for this design. In conformity with this plan, the temporary standard 88 mh loading coil. Code 601, became commercially available late in 1924, and its suc- cessor design. Code 602, approximately nine months later. The 601 coil used a 2-ring core of compressed, unannealed, powdered iron. The over-all coil dimensions were such that 200 coils could be potted in the largest size of exchange area loading coil case then standard, which had originally been developed for potting 98 coils of the 574 and 575 coil- size. A larger size of case which potted toll cable loading coils was modified to pot 300 No. 601 coils. During 1924 and 1925, while the production of the 602 coil was being built up to meet the large demand for H88 loading, over 80,000 No. 601 coils were manufactured. The 602 coil also used compressed, unannealed, powdered-iron cores, and it had much better proportions of axial length to diameter. Similar sizes of potting complements were standardized in the new cases. Coil F in the headpiece is a 602 coil. (Coil F in relation to Coil B shows the size difference for the contemporary standard coils designed for 22 ga. and 19 ga. cables, respectively.) Because of their smaller size, the 601 and 602 coils had a higher ratio of resistance to inductance than the older coils which had been developed for use on lower resistance cables. Making more efficient use of core material and copper, and using smaller- size, higher-speed winding machines, the 602 coil was substantially cheaper than the 601 coil, which in turn was considerably cheaper than the prior standard cable loading coils. In both instances, substantial economies in potting and installation costs also resulted. 18.2 Coils for HI 35 Loading Further consideration of the transmission economics of the new H135 loading led, about the middle of 1925, to a decision to develop a new 135 mh loading coil using the same core and the same types of loading coil cases as for the 602 coil. Under the code No. 603, this coil became available for commercial service during 1926. The 603 coil was intended for use on 22 ga. and 19 ga. cables, and yielded large economies during 1926-27 in these fields. The larger-size 575 coil was temporarily continued as a standard design, for use on long 19 and 16 ga. trunks where a better coil than the 603 coil could be justified. With this coil, the attentuation was about 0.03 db/mi better than that obtainable with the 603 coil. 456 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 18.3 Coils for H175 and D175 Loading Because of the small relative demand for new coils for these types of loading, and because the 574 coil was fairly satisfactory in transmission-cost relations for the relatively expensive types of facilities involved, the 574 coil was temporarily continued as standard for the 175 mh loading system. General: Looking backwards, the classification "temporary standard" for the 574 and 575 coils as used in the higher cut-off loading systems is ap- propriate, and would also be appropriate for the 602 and 603 coils, by vir- tue of the fact that aU of these coils were superseded as standard during 1927 by the new series of compressed, permalloy-powder core loading coils which are described below. A brief summary of some electrical and dimen- sional characteristics of the "iron-dust" core coils is given in Table X, prior to undertaking the discussion of the very much more important permalloy- Table X Iron Dust Core Loading Coils Used in Higher Cut-Off Loading Systems Coil Code No. Nominal Inductance (mh) Resistances— Ohms Approx. Over-all Dimensions — Inches d-c 1000 cycles Diam. Ax. Height 601 602 603 575 574 88 88 135 135 175 9.1 8.4 12.8 3.7 4.5 10.2 9.5 14.0 5.5 7.0 4.5 3.5 tt 4.5 1 1.12 (t 2.1 It core coil development. The resistance values include 0.5 ohm for the 22 ga stub cables for the loading coil cases in which the 601, 602, and 603 coils were potted, and 0.2 ohm for the 19 ga. stubs used with the older coils. (19) Compressed Permalloy-Powder Core Exchange Area Cable Loading Coils 19.1 General Since the general characteristics of the improved magnetic core-materiaP^ and the circumstances attending its development were briefly described on page 183, it is unnecessary to repeat this discussion as a part of the review of the evolution of exchange area loading. It is desirable, however, to call atten- tion to the fact that the exchange area loading coils were given priority over the toll cabl^ ''oils in the commercial exploitation of the greatly improved core-ma teri^^' for two important reasons. In the first place, the service re- quirements In exchange area cables were much less complex and much less severe than those in the long distance toll cables and, in consequence of the INDUCTIVE LOADING FOR TELEPHONE FACILITIES 457 smaller amount of development effort required, the large economies inherent in the use of the improved core-material could begin to be realized at a much earUer date. This was important because of the rapidly increasing demand for loading during the late 1920's. Secondly, by starting quantity production of the core material for use in the exchange area coils, the factory built up experience in the control of the many complicated new processes that were essential to the performance results which were particularly desirable in the toll cable coils. Also, knowing what could be expected from the commercial production of the core-material, the design engineers were in a better posi- tion to specify the most advantageous core-proportions in the final toll cable designs. The large demand for M88 loading, relative to that for the heavier weights of exchange area loading, resulted in the concentration of the early develop- ment work on smaller 88 mh loading coils. A comparison of the electrical and dimensional characteristics of the new^ permalloy-core coils is given in Table XI (page 460), following the general description of the new designs. 19.2 612 Coil for M88 Loading The new permalloy-core 612 coil became available for a trial installation late in 1926 and quantity production built up to a new high level for ex- change area coils during 1927. The size reduction made possible by the favorable permalloy character- istics of high permeability in combination with low losses was carried to a greater degree in the 612 coil than was feasible in the toll cable designs. It was somewhat less than one-fourth as large as the 602 coil in volume and weight. Coil G in the headpiece is a 612 coil. The careful cost-equihbrium study that was made to determine the com- mercial design requirements resulted in the 612 coil having a sHghtly smaller d-c resistance than the 602 coil. The resistance-frequency characteristics were sufficiently close to those of the 602 coil to warrant the acceptance of the new coil as an "equivalent" design, with respect to plant engineering. The development of the 612 coil involved new design and manufacturing problems beyond those encountered in the design and manufacture of the improved core-material. To make feasible the small size of the toroidal core, an entirely new type of winding machine suitable for high-speed wind- ing to an inner diameter of about 0.75 inch had to be made available. The use of small cores also made it desirable to have a better space-factor in the copper winding. This was achieved by using a composite (conductor) insulation of black enamel and single cotton, instead of the double serving of cotton employed in previous, much larger, designs. Subsequently this change was incorporated in the designs of all small loading coils. 458 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 The large size-reduction relative to the 602 coil resulted in substantial reductions in coil costs, notwithstanding the higher (per unit volume) cost of the improved core-material due to the more complicated processes and the high cost ratio of nickel to iron. The cost reduction in the coils was ac- companied by a large reduction in the potting and installation costs. When the coils were first standardized, the potting complements were similar to those for the 602 coils but the cases were much smaller. Later on, larger- f^ ■<■ a: Fig. 16 — Case size reduction resulting from coil size reduction. Cast iron cases con- taining 200 88-mh. coils. At left: No. 612 (permalloy core) coils; total weight potted coils, 725 lbs. At right: No. 602 (hard iron dust core) coils; total weight potted coils, 1750 lbs. size cases potting complements of 450, 600, and 9(X) coils were standardized. Using cases no larger than the previous maximum-size cases, potting com- plements ranging up to about 2000 coils could have been made available, if a demand for them should have arisen. Incidentally, the demand for the 900-coil cases was small. The extensively used complements in the range 300-600 coils proved to have a large value in relieving serious congestion in the underground loading-vaults in metropolitan areas, notably New York, INDUCTIVE LOADING FOR TELEPHONE FACILITIES 459 and in general made it feasible to provide smaller-sized loading vaults for new installations. It is important to note that the small size and reduced cost of potted 612 coils led to a general use of M88 loading on non-quadded 24 ga. cables, thus permitting additional cost-reductions in the cable plant. Such facilities were cheaper than non-loaded 22 ga. cables, and had a greater transmission range — subject in some instances to signahng restrictions. It is also of interest that the 612 coil was the first standard loading coil sufficiently small to be placeable within loading splice-sleeves. When only a few coils were required at a particular point, this method of installation permitted worthwhile economies as compared with the use of conventional types of loading coil cases and stub cables. The 612 coil remained standard for about 10 years, during which period more than a million of them were manufactured. It had a much greater economic impact on the fundamental design of the exchange area plant than any other individual loading coil, notwithstanding the fact that the present standard 88 mh loading coil, subsequently described, has already been used in much larger quantities. 1623 Coils for HI 35 Loading [624 Coils for H175 and D175 Loading During the development of the 603 (135 mh) iron-dust core coil described in subdivision 18.2, it was fully appreciated from the transmission cost equi- librium standpoint that a higher grade design would be warranted if it could be obtained at a moderate increase in cost. Since this would have meant a new coil-size intermediate between that of the 603 (and 602) coil and the much larger 575 coil, a decision was made to use the 602 core, thereby ob- taining quick savings. It was appreciated also that a less efficient loading coil than the 574 (175 mh) coil would be good enough for H175 and D175 loading, if it could be obtained with a sufficiently large cost-reduction. These objectives were carefully considered from the cost-equilibrium standpoint. It turned out that the use of a permalloy core of the same size as the iron-dust core of the 602 and 603 coils would come close to an ideal economic solution of the service requirements for the heavier weights of exchange area loading, and accordingly the use of this size of core and coil was decided upon. An important additional, immediate, economic advan- tage was that the new coils could be potted in the cases originally developed for the 602 and 603 coils, thus minimizing new potting developments. The demand for the heavier weights of loading could be met with smaller-sized complements than those frequently required for M88 loading, and conse- quently no new larger sizes of cases were necessary. 460 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 Compared with the 603 coil, the new 613 (135 mh) loading coil gave a material improvement in transmission, the value of which was large rela- tive to the small cost-increase involved. On the other hand, the 613 coil was nearly as good from the transmission standpoint as the much larger 575 coil and the cost per potted coil was about one-third lower. A substantially similar comparison applied between the new 614 (175 mh) coil and the old standard 574 coil. During the late 1920's the high demands for new faciUties and the plant rearrangements to meet the higher cut-off loading standards combined to require a somewhat larger total quantity of 613 and 614 than 612 coils. The importance of the higher inductance coils dropped substantially after 1930, especially that for the 175 mh loading. 19.4 618 (44 mh) and 619 {22 mh) Loading Coils These low-inductance coils, using the same core as the 612 coil and the same types of cases, became available during 1931, primarily for use in cor- recting spacing irregularities in loaded exchange area trunks. Table XI Compressed Permalloy-Powder Core Exchange Area Loading Coils Coil Code No. Nominal Inductance (mh) Resistances— Ohms Approx. Over-all Dimensions — Inches d-c 1000 cycles Diam. Ax. Height 612 618 619 613 614 615 88 44 22 135 175 250 8.5 4.9 2.5 5.5 8.0 12.0 9.3 5.2 2.7 6.8 9.7 14.0 2.0 « 3.5 « 0.75 a ii 1 .JO 19.5 Subscriber-Loop Loading During 1933 the practice of using the 618 (44 mh) coil at M or H-spacing got a good start on long subscriber loops. This new field for loading had been under study for some time, and has greatly increased in importance during the intervening years. In many instances, this practice makes it feasible to meet the transmission limits on long loops in available 19 or 22 ga. sub- scriber cables, when otherwise it would be necessary to use local battery telephone sets, or install more expensive cable plant, or use relatively ex- pensive telephone repeaters. Under some conditions, the 612 (88 mh) coil was also used for loading long loops. INDUCTIVE LOADING FOR TELEPHONE FACILITIES 461 19.6 Coil Data Some detailed data regarding the new coils above described are given in Table XI. The resistance data include 0.5 ohm for 22 ga. stub cables. The 615 coil was made available primarily for emergency replacement use in old plant using 250 mh loading. (20) Second Increase in Minimum Cut-Off Frequency For Loaded Exchange Cables 20.1 General During 1932 there became effective a second increase in the minimum cut-off frequency standards for loaded exchange trunks, which in terms of frequency ratio was about as large as the first change that was decided upon in 1924, the successive (minimum) standards being 2300, 2800, and 3500 cycles. The new cut-off frequency standard was implemented by the standardiza- tion of a graded series of higher-impedance, lower-attenuation loading systems described below. These made it possible to secure a substantial reduction in the over-all costs of the exchange area trunks by permitting a more extensive use of the cheaper types of cables, even though the cost of the loading per mile became greater in consequence of the closer coil spacing. The improved transmission characteristics, i.e., lower attenuation and reduced frequency-distortion, resulted from the use of standard coils at substantially closer spacings. The above mentioned change in the relations between cable costs and loading costs recognized a considerable departure from plant cost equilib- rium that came about during the late 1920's and early 1930's in consequence of the substantial reduction in loading costs that was realized by extensive use of the permalloy-core coils previously described. Moreover, the prospect of further savings was an encouraging factor in the adoption of the new standards. 20.2 The New Loading Systems The general characteristics of the new standard loading systems are given in Table XII. The letters H and B in the loading designations signify 6000 and 3000-ft. spacings. In the cable designations, ''high" and ''low" capacitance have the same significance as in Table VIII. Some typical attenuation data are given in Table XIII, for comparison with attenuation data given in Table IX. The attenuation comparison by itself, however, is not a completely adequate comparison since it ignores the distortion-reduction advantage of the wider frequency-band transmitted by 462 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 the improved loading. A brief general discussion of this particular advantage is given in subdivision 20.3. The field of use of the new loading systems on exchange area trunks in- volves a number of factors, the most important being the cable length and gauge, the subscriber-loop limits, and the transmission equivalent desired. The B spaced loading is required principally on long toll connecting trunks and tandem office facilities and has some use on the longest direct inter-office trunks. For plant simplicity and fiexibiUty reasons, both types of B spaced loading are seldom used extensively in the same exchange Table XII Improved Loading Systems Standardized in 1932 Loading Designation Approx. Cut-off Frequencies — Cycles Approx. Nominal Impedance — Ohms High Capacitance Cables Low Capacitance Cables High Capacitance Low Capacitance Cables H88 B88 B135 3500 4900 3900 3900 5500 4400 950 1350 1700 1100 1550 1900 Table XIII Attenuation Data— Loading Systems of Table XII Conductor Gauge Cable Capacitance (mf/mi) Attenuation at 1000 cycles— db/mi H88 Loading (612 Coil) B88 Loading (612 Coil) B135 Loading (613 Coil) 24 22 19 19 16 0.079 0.083 0.085 0.066 0.066 1.23 0.79 0.42 0.38 0.21 0.94 0.60 0.34 0.30 0.18 0.48 0.26 0.24 0.14 area. B135 loading is more likely to be used in large metropoUtan areas, and B88 loading in smaller multi-office areas. The H88 loading is used in all multi-office areas that have direct trunks long enough to require loading. In such use it supersedes the former standard M88 loading in new plant, and partly supersedes the former standard heav- ier-weight loading systems, H135 and H175. It was of great practical importance that the coil inductances used by the improved loading systems should be those of available standard coils and of extensively used former standard coils, so as to faciUtate the rearrange- ment and conversion of the old loaded plant to meet the new transmission standards. In this general connection, the exchange cable trunk plant must be more or less continuously fluid for several important reasons, including the following: (1) to accommodate the traffic growth along existing routes INDUCTIVE LOADING FOR TELEPHONE FACILITIES 463 and plant expansion in new routes, (2) to facilitate working to new trans- mission limits that occasionally become desirable in consequence of the introduction of improved subscriber sets, or for other reasons, and (3) to fit in with the installation of new central offices and faciUtate the occasional abandonment of old offices during changes from manual to dial operation, or for other reasons. In the plant rearrangements, old loaded circuits using former standard coil spacings or inductances can sometimes be reused to advantage, when engineered with suitable transmission distortion-penalties, as subsequently discussed. 20.3 Effective Transmission; Distortion Penalties The engineering transmission-cost studies that resulted in the standardi- zation of the improved loading systems described in Table XII were made during a period in which a new philosophy ^^^ of the design of complete telephone systems evolved. The basic feature of this philosophy was the acceptance of the rate of occurrence of repetitions requested by the users of a particular circuit in carrying on a regular telephone conversation as a measure of the grade of transmission-service performance of that circuit. This involved the preparation of an adequate new system^^ of transmission engineering data for use in the design of telephone systems, including the effects of all factors that influence the service performance. The new technique is of special interest in the present loading review because it made possible for the first time an accurate quantitative appraisal of the effect of the different widths of frequency band transmitted by differ- ent loading systems. This is done in terms of the effective transmission loss relative to that of the trunk in a convenient, working reference system. The speech distortion that results from a reduction of the effective transmission band width in a loaded trunk may be expressed as a loss which is equivalent in transmission-service performance to a definite increase in the distortion- less transmission loss. In comparing different types of loading, the differences in distortion penalties must be taken into account along with the attenuation differences. Also, when proving in the use of loading, the distortion penalty of the non- loaded trunk due to the unequal attenuation of frequencies in the speech band must be considered together with the 1000-cycle attenuation loss. For present purposes, in appraising the new loading systems under dis- cussion, it is sufficient to say that the distortion penalty ratings of exchange area trunks which use them are zero, or very close to zero, in the longest trunks likely to be required in working to the present or probable future ^■^ For comprehensive information on these matters reference should be made to an article (34) by W. H. Martin published in 1931, and an article (35) by Messrs. F. W. McKown and J. W. Emling published in 1933. 464 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 standards of transmission-service performance. On the other hand, the pen- alty ratings for trunks using the old standard types of loading having lower cut-off frequencies range from nearly 1 db to 4 db or more, depending pri- marily upon the theoretical cut-off frequency. From the foregoing, it can be understood that the distortion penalty in old cables having old types of low cut-off loading may be a substantial frac- tion of the total allowable effective transmission loss in the trunk. (21) Compressed Molybdenum-Permalloy Powder Core Exchange Area Loading Coils 21.1 The Improved Core MateriaP^ A brief general description of the new compressed molybdenum-permalloy powder core-material is given under this heading in Section 11.1. The low-inductance exchange area loading coils described below were given priority in the commercial exploitation of the improved core-material in message circuit loading. 21.2 622 (88 mh), 628 (44 mh), and 629 (22 mh) Loading Coils The preliminary development-activity was in terms of 88 mh loading, on account of the added importance of this loading which resulted from the adoption of the higher cut-off loading-standards, described in the preceding pages. The transmission engineering studies and the cost-equilibrium design studies resulted in a decision to reduce the coil size as much as possible, without degrading transmission performance. A size reduction of about 60%, relative to the 612 permalloy-core coil, proved to be feasible. The new coil. Code 622, was closely equivalent to the 612 coil. Actually it had somewhat better frequency-resistance character- istics, because of the superior eddy-current loss characteristics of the im- proved core-material. On the other hand it was not quite so good as the 612 coil with respect to susceptibiHty to magnetization by superposed d-c signaling currents. Coil H in the headpiece is a 622 coil (Coil G being its standard predecessor, the 612). The ability to make so small a molybdenum-permalloy core coil as the 622 coil, without degrading transmission, was principally due to the in- genuity of the factory engineers in devising an entirely new, high-speed, winding machine capable of winding a small toroidal core to a finished inside diameter of 0.5" — an achievement which seemed impossible a decade earlier when the 612 coil was developed. The use of an enamel-film insula- tion on the core ring, in place of the overlapping fabric-tape employed on larger and older designs, was a favorable factor in the more efficient utiliza- INDUCTIVE LOADING FOR TELEPHONE FACILITIES 465 tion of the core winding-space. Although the percentage cost-reduction was not large, the aggregate savings were large in consequence of the substantial amount of new loading required. The reductions in potting costs of the new smaller-size loading coil cases, and the savings in installation costs were important factors in the total savings. The new 44 mh and 22 mh loading coils. Code 628 and 629 respectively, used the cores designed for the 622 coil. They were substantially equivalent in transmission performance to the 618 and 619 coils. The new 628 (44 mh) coil became quite important in subscriber-loop loading. Over the years during which they remained standard, the average annual production was about one-fourth that of the 622 coil. Relatively very few 629 coils were used. 21.3 623 (135 mh), 624 {175 mh), and 625 {250 mh) Loading Coils The new 135 mh coil had about the same size and efficiency relations to the 613 coil, as those that existed between the new and old 88 mh loading coils (612 and 622). The entirely new size of core which was made available for it was also used in the relatively unimportant, new higher-inductance coils. The winding machine developed for the 612 coil was used in winding the coils under discussion. The over-all dimensions of the new coils were intermediate between those of Coils H and G in the headpiece, being closer to H than to G. The expected demand for the 623, 624, and 625 coils was not large enough to warrant the development of an entirely new series of loading coil cases especially for these coils. As these non-phantom coils were being developed concurrently with the molybdenum-permalloy core side circuit and phantom circuit coils for toll cables, i.e., the M-type loading units described in Section 11.2, arrangements were made for potting them in the new cases that were de- veloped for potting the loading units. However, different assembly arrange- ments and stub cables were required. Since the non-phantom coils were only about 20% smaller than the coil components of the loading units, this potting procedure was not unduly expensive for the non-phantom coils. The percentage savings resulting from the development of the 623, 624, and 625 coils was larger than that yielded by the 622, 628, and 629 coils but the aggregate savings were much smaller in consequence of the much lower demand for the higher-inductance coils. (22) Redesign of Exchange Area Loading Coils to Take Advantage OF Use of Formex Insulation on Winding Conductors 22.1 General During the late 1930's a greatly improved type of enamel insulation (developed by the General Electric Co.) known as "Formex" became com- 466 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 mercially available for use on small copper wires. Studies of its application to telephone apparatus indicated that further, worth-while size-reductions in loading coils could be achieved by virtue of the greatly superior space- factor of this insulation, relative to that of the combination of cotton and enamel insulation that had been used for more than a decade in small loading coils. Another advantageous possibility was the reduction of the coil resistance by employing a larger size of conductor to utiHze the winding space saved by the thinner conductor-insulation. Although the better space efficiency of the Formex conductor insulation was a contributory factor in the further size reduction of the smallest load- ing coils, the size-reduction achievement under discussion was mainly de- pendent upon the development and use of a new type of winding machine. The new non-phantom type coils that resulted from the redesign work are described below under appropriate headings. They all use compressed mo- lybdenum-permalloy powder cores. Additional information regarding them is given in an A.I.E.E. paper,^° previously referred to. In Table XIV (page 471) electrical and dimensional data are given on the individual coils, along with corresponding data on the designs which they superseded. 22.2 632 {88 mh), 638 (44 mh), and 639 {22 mh) Formex Insulated Coils The large current and expected future demand for the low-inductance exchange area coils, relative to that for all other types of loading coils, resulted in the concentration of the initial redesign efforts on these types of coils. In the redesign of the low-inductance coils, it was decided to reduce the coil size as far as possible without degrading transmission performance. An important secondary requirement was that the new design should not be more susceptible to magnetization by superposed signaUng currents than the current standard coils, previously described. Before these transmission requirements were finally set, the experimental design studies had shown that worth-while cost-reductions could probably be secured by using improved winding machines capable of winding the coils to a new size-limit of 0.35-inch finished inside diameter. In due course, the very difficult winding-machine design problem was solved by the factory engineers. The above stated transmission requirements made it necessary to use the same amount of core material (molybdenum-permalloy) as that used in the 622, 628, and 629 coils, previously described. The coil design problem was solved by a redesign of the core to obtain a shorter magnetic circuit having a larger cross-section, keeping the same volume. (The inside and outside diameters were reduced and the axial height increased.) This per- mitted about a 20% reduction in the over-all volume and weight of the wound coils, without appreciable degradation in transmission performance. INDUCTIVE LOADING FOR TELEPHONE FACILITIES 467 Altogether, this was a remarkable achievement of the apparatus develop- ment and factory engineers. The new coils had code designations 10 digits higher than those of the coils which they superseded, beginning on a quantity production basis dur- ing 1942. The very extensively used 632 coil became widely known as the ''wedding-ring" coil. It appears as Coil J in the headpiece. Fig. 17 — Case size reduction 100-coil complements 88 mh. coils. At left: Lead sleeve case containing No. 622, molybdenum-permalloy core, coils. At right: Welded steel case containing No. 632 coils having Formex insulated windings on molybdenum-permalloy To provide the most economical potting arrangements for the new coils an entirely new series of loading coil cases was developed. The economies that have resulted from these coil and case developments in the post-war period are large relative to the development cost, and are large in the aggregate, even though the savings per potted coil are small. The current demand for this series of coils greatly exceeds the aggregate demand for all other types of loading coils. At this point it is of interest to present Fig. 18, which illustrates the pro- 468 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 gressive size reduction in loading coil cases for exchange area loading which resulted from the coil size reduction, starting with the 602 coil (1925) and including the 612 coil (1927), the 622 coil (1937) and 632 coil (1942). These 88-mh loading coils are equivalent to one another in transmission perform- ance. Fig. 18 — Progressive case size reduction 1925-1942 200-coil complements — 88 mh. loading coils. Left to right: No. 602 (hard iron-wire core) coils in cast iron case; No. 612 (permalloy core) coils in "thick" steel cases, welded joints; No. 622 (molybdenum-per- malloy core) coils in "thick" steel cases; No. 632 (molybdenum-permalloy core) coils in tubular "thin" steel cases. 22.3 Special Loading Coil for Signal Corps Spiral-Four Cabled'' A digression from the main line of the story is appropriate and permis- sible at this jx)int, since the special coils used in loading the very important spiral-four cable carrier systems that were extensively used by the army during World War II were made possible by the development work that led to the standardization of the 632 coils, and by the development of the 60-permeability molybdenum-permalloy powder core-material, described in Section 11.1. These 6 mh "army" loading coils used 60-permeability cores INDUCTIVE LOADING FOR TELEPHONE FACILITIES 469 having the same dimensions as the 125-permeability cores of the 632 coils. The small over-all dimensions of the coils made it practical to mount them within the "connectors" that terminated each quarter mile length of spiral- four cable, without requiring the connectors to be appreciably larger than otherwise would have been necessary. Thus, in effect, the loading was built into the cables at the factory, thereby simplifying installation. Another re- markable feature of the loading was that it had a cut-off frequency of about 22 kc and provided satisfactory transmission for cable carrier systems using a frequency-band extending to 12 kc. One indication of the importance of the coil under discussion was that nearly two million of them were manu- factured for the United States Signal Corps before VJ day. 22.4 Impact of Strategic Material Scarcities on Loading Coil Design Before the redesign of other loading coils could be undertaken to take advantage of the space-saving possibilities inherent in the use of Formex- enamel insulation, a new design factor suddenly became controlHng. Nickel had become a strategic war material, and accordingly severe restrictions were placed upon its use, including all magnetic alloys in which nickel was a constituent. Molybdenum-permalloy was in this category. This made it necessary to redesign the toll cable phantom loading units, as mentioned in the description of the "SM" type loading units (Section 11.3), the high-inductance exchange area loading coils, and certain non- phantom type toll cable loading coils used principally for "order-wire" circuits in coaxial cables. As the new low-inductance exchange area coils (632, 638, 639), previously described, used only a very small amount of nickel (about 0.9 oz. per coil), no further worth-while reductions in the core size could be obtained with- out objectionable reactions on transmission, and without undertaking ex- tensive development work that would have interfered objectionably with much more important war jobs. Consequently, the new 632, 638, and 639 coils were continued as standard designs. Large quantities were used during the war, and very much larger quantities since VJ day. 22.5 643 {135 mh), 644 {175 mh), and 645 {250 mh) Exchange Area Loading Coils Since the standard 623, 624, and 625 coils, previously described, used about four times as much nickel in their cores as the 622 (and 632) loading coils, their redesign became an important factor in the new development program to conserve nickel. A relatively simple solution for this specific problem was worked out, namely to use Formex-insulated conductors on the cores developed for the 622 series of coils. This saved three-quarters of the nickel used in the 470 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 623 series of coils. By using the 622 core instead of the 632 core, a larger winding-space became available for the same savings in nickel, and a lower winding resistance was obtained. New loading coil cases were not required, since the redesigned coils could be potted in the cases developed for the 622 series of coils. The use of the much smaller cores necessarily resulted in resistance val- ues that were substantially higher than those of the 623 series of coils, notwithstanding the improved winding-space efficiency of the Formex- enamel conductor insulation. The increments in the d-c resistance , (relative to the 623-coil series) were a little over 60%. The effective resistances at 1 kc were approximately 50% greater. The attenuation impairments that resulted from the increases in resistance were in the general range 0.01 to 0.02 db/mi at 1000 cycles, depending upon the type of cable and weight of loading, and were considered to be tolerable for war-emergency designs. 22.6 641 (44 mh) and 642 [88 mh) Non-Phantom Toll Cable Coils These are briefly mentioned here because of their general similarity, ex- cept as regards inductance and resistance, to the 643, 644, and 645 exchange area coils described in the preceding paragraphs. They also make use of cores developed for the 622 coils and utihze Formex-insulated conductors. These coils are replacement "nickel-saving" designs for pre-war standard, "toll-grade" non-phantom type of cable loading coils, which were of about the same size as the side-circuit loading coils used in the M-type loading units. During the war the new coils had a moderate use as substitutes for SM-type loading units on toll cables, thereby saving additional amounts of nickel. The 641 (44 mh) coil has about the same resistance characteristics as the side circuits of the SM-type 44-25 mh phantom group loading units. A similar general relation exists between the 642 (88 mh) coil and the side- circuit of the SM-type 88-50 mh loading units. The present principal field of use for the 641 and 642 coils is on 4-wire type and 2-wire type "order-wire" circuits in coaxial cables for use in the operation and maintenance of coaxial cable systems. Some of these order- wire circuits are as long as or longer than the longest loaded commercial message circuits used prior to the general introduction of cable carrier sys- tems into the toll cable plant. The 643 coil also is occasionally used on short- haul order-wire circuits in coaxial cable systems. 22.7 651 (44 mh) Coil for Subscriber-Loop Loading This was a post-war development looking towards the reduction in cost of subscriber-loop loading. During the war, the design of a radically new type of automatic winding machine made it feasible to apply fine-wire, high-inductance windings on a INDUCTIVE LOADING FOR TELEPHONE FACILITIES 471 miniature toroidal core much smaller than the smallest loading coil core previously described. This eventually led to studies of the desirabiUty of using the miniature core in loading coils. The initial study showed definitely that this miniature core would not be good enough for loading coils. Larger cores, about one-half as large as the 632 coil core, were then considered. The transmission economic studies of this design showed it would not be suitable for general use in loading exchange area trunks, in consequence of the increased attenuation that would result. Table XIV Compressed Molybdenum-Permalloy Powder Core Loading Coils for non-quadded cables Nominal Inductance (mh) Approximate Approximate Coil Code No. Resistances— Ohms ^ 1 ' Over-all Dimensions — Inches d-c 1000 cycles Diameter Ax. Height 622 88 9.0 9.8 1.6 0.63 628 44 4.7 5.1 " (< 629 22 2.5 2.7 « (C 623 135 5.7 6.8 2.25 0.91 624 175 8.1 9.5 « « 625 250 11.9 14.0 (t « 632 88 9.0 9.8 1.25 0.63 .638 44 5.1 5.5 « u 639 22 2.6 2.8 « (( 641 44 3.5 4.1 1.60 0.63 642 88 5.9 7.4 « << 643 135 9.3 10.6 « u 644 175 13.0 14.7 « it 645 250 19.3 21.9 u li 651 44 7.5 8.1 1.06 0.43 (^) Resistance data include the resistance of 7| ft. of stub cable except for the 651 coil used only in loading splices and having low-resistance short leads. The standard 632 and 641 series of coils have 24 ga. stub cables with 0.8 ohm resistance. The superseded 622 and 623 series have 22 ga. stub cables with 0.5 ohm resistance, excepting the 622 coil when potted in lead- type cases or in its 450-coil case with 24 ga. stub cable. A proposed new 44 mh coil, using this core, was, however, found to be good enough for use as a partial substitute for the standard 638 coil in loading long subscriber loops under conditions mentioned below. This new ''miniature" loading coil is coded 651. It appears in the head- piece as Coil K. The very small size of this coil makes it especially suitable for potting in a plasticized-type "case" for installation in loading splices. These cases involve an assembly of coils on a common spindle. Under favorable con- ditions, by using one or more spindle units, loading complements ranging up 472 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 to a total of about 60, or more, coils may be installed at a single loading splice. It is expected that a considerable fraction of new installations of subscriber-loop loading may be in terms of splice installations of 651 coils. In occasional instances where large complements are required, and the cable-splicing conditions are not favorable for splice loading, the larger sized 638 coils will be used, potted in conventional types of loading coil cases. This plan avoids the need for developing entirely new, conventional design, cases for the 651 coil. Commercial production of the 651 coil and their new splice cases started during 1948. It is expected that the future savings in the cost of new plant (due to the cheaper coils, cases, and installation) will be large relative to the development cost. 22.8 Summary of Coil Data Table XIV gives a summary of electrical and dimensional data on the molybdenum-permalloy core message-circuit coils described in the preceding pages. Bibliography {Continued) 13. Buckner Speed and G. W. Elmen, "Magnetic Properties of Compressed Powdered Iron," Trans. A.I.E.E., Vol. XL, p. 596, 1921. 24. W. J. Shackelton and I. G. Barber, "Compressed Powdered Permalloy, Manufacture and Magnetic Properties," Trans. A.I.E.E. Vol. 47, p. 429, 1928. 26. V. E. Legg and F. J, Given, "Compressed Powdered Molybdenum — Permalloy for High-Quality Inductance Coil," Bell System Technical Journal, Vol. XIX, p. 385, 1940. 27. J. E. Ranges, "Loading The Spiral-4 for War," Bell Lab. Record, Oct. 1946. 30. S. G. Hale, A. L. Quinlan and J. E. Ranger, "Recent Improvements in Loading Ap- paratus for Telephone Cables," Trans. A.I.E.E., Vol. 67, 1948. 33. Harvey Fletcher, "Speech and Hearing," D. Van Nostrand Co., N.Y., 1929. 34. W. H. Martin, "Rating The Transmission Performance of Telephone Circuits," B.S.T.J., Vol. X, Jan. 1931. 35. F. W. McKown and J. W. Emling, "A System of Effective Transmission Data for Rating Telephone Circuits," B.S.T.J., Vol. XII, July 1933. (to be continued) Abstracts of Bell System Technical Papers Not Published in This Journal Deformation Potentials and Mobilities in Non-Polar Crystals * J. Bardeen^ and W. Shockley.i Bibliography. Phys. Rev., v. 80, pp. 72-80, Oct. 1, 1950. Abstract — The method of effective mass, extended to apply to gradual shifts in energy bands resulting from deformations of the crystal lattice, is used to estimate the interaction between electrons of thermal energy and the acoustical modes of vibration. The mobilities of electrons and holes are thus related to the shifts of the conduction and valence-bond (filled) bands, respectively, associated with dilations of longitudinal waves. The theory is checked by comparison of the sum of the shifts of the conduction and valence-bond bands, as derived from the mobilities, with the shift of the energy gap with dilation. The latter is obtained independently for silicon, germanium and tellurium from one or more of the following: (1) the change in intrinsic conductivity with pressure, (2) the change in resistance of an n-p junction with pressure, and (3) the variation of intrinsic concentration with temperature and the thermal expansion coefficient. Higher mobilities of electrons and holes in germanium as compared with siUcon are correlated with a smaller shift of energy gap with dilation. Lepeth Sheath for Telephone Cables. E. J. Larsen^ and R. B. Farrell.^ Elec. Engg., v. 69, pp. 1014-1017, Nov., 1950. Abstract — A new telephone cable sheath design has been developed by the Bell Telephone Laboratories in cooperation with Western Electric engineers. This sheath structure consists of a polyethylene jacket extruded on the cable core, over which a relatively thin lead sheath is applied. This design provides a high degree of protection against cable damage by lightning, and its adoption has resulted in a reduction in costs. Effects of Calendar Shifts in Series of Monthly Data. C. E. Armstrong.^ Am. Statistician, v. 4, pp. 20-21, Oct., 1950. Scattering of Electrons in Crystals in the Presence of Large Electric Fields. J. BardeenI and W. Shockley.i p^^^ ^^^ ^ ^ 80, pp. 69-71, Oct. 1, 1950. Abstract — By the calculation of transitions between states appropriate to electrons moving in a large uniform electric field superimposed on a periodic crystal field, it is shown the probabilities of scattering by lattice vibrations *'A reprint of this'article may be obtained on request to the editor of the B. S. T. J. i|B. T. L. 2W. E. Co. 3^A. T. & T. Co. 473 474 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 or imperfections are independent of the uniform field and are given by the usual expressions derived for zero field. This justifies the procedure of treat- ing acceleration by the field and scattering as independent processes. Conductivity Measurements at Microwave Frequencies * A. C. Beck^ and R. W. Dawson.J LR.E., Proc, v. 38, pp. 1181-1189, Oct., 1950. Abstract — Because of the skin effect, the surface condition of conductors becomes very important in determining attenuation at microwave fre- quencies. This has been investigated by measuring small wire samples at a frequency of about 9,000 megacycles. A sample of the wire to be measured is inserted in a metal tube to form the center conductor of an open-ended coaxial line. The ratio of the peak frequency to the half-power bandwidth of this coaxial-line resonator, measured with the aid of an oscillographic display of its amplitude-versus-frequency characteristic, gives its loaded Q. The amplitude characteristic of the frequency-modulated signal generator, on which a wavemeter marker appears, is viewed simultaneously and used as a reference. By correcting the result to obtain the unloaded Q of the center conductor alone, the effective conductivity of the sample is obtained. Results of measurements on a number of samples of different conductors having various surface conditions, treatments, and platings are given. These results are of value in the design of microwave components of all types where loss is a factor of importance. Propagation of UHF and SHF Waves Beyond the Horizon. K. Bullington.^ Letter to the editor. LR.E., Proc, v. 38, pp. 1221-1222, Oct., 1950. Simple Torsion Pendulum for Measuring Internal Friction. M. E. Fine.^ Jl. Metals, V. 188, sec. 1, p. 1322, Nov., 1950. Experiments on the Initiation of Electric Arcs* F. E. Haworth.^ Phys. Rev., V. 80, pp. 223-226, Oct. 15, 1950. Abstract — Arcs have been struck in vacuum between widely spaced elec- trodes by positive ion charging of an insulating film on the cathode, at sepa- rations from 0.5 to 5 mm and at potentials from 34 to 2000 volts. The arc current must be allowed to grow initially at the rate of at least 10^ amp./sec. for the arc to occur. These experiments constitute a test of one of the funda- mental steps postulated to account for the initiation of an arc between elec- trodes coming together at low voltages. Mobilities of Molecular and Atomic Rare Gas Ions in the Parent Gases: Helium, Neon, and Argon. J. A. Hornbeck.^ Letter to the editor. Phys. Rev., v. 80, pp. 297-298, Oct. 15, 1950. Bell Telephone Laboratories — A n Example of an Institute of Creative Tech- * A reprint of this article may be obtained on request to the editor of the B. S. T. J. »B.T.L. ARTICLES BY BELL SYSTEM AUTHORS 475 nology.* M. J. Kelly.^ Roy. Soc. Lond., Proc, A, v. 203, pp. 287-301, Oct. 10, 1950. Abstract — To keep pace with the evolution of its research laboratory and take advantage of the opportunities accruing from the adoption of the scientist and his methods, the engineering organization of industry has undergone major change. Its relatively simple operation, in the last century, of transforming the inventor's model into a design for manufacture, per- formed largely by empirical methods, has now expanded into many succes- sive interlaced operations. Each, as it has matured, employs more of the scientific method and of fundamental analysis in the solution of its problems. There has been so much emphasis on industrial research and mass-produc- tion methods in my country, that even our well-informed public is not sufficiently aware of the necessary and most important chain of events that lies between the initial step of basic research and the terminal operation of manufacture. In order to stress the continuity of procedures from research to engineering of product into manufacture and to emphasize their real unity, I speak of them as the single entity 'organized creative technology'. I am using the Bell Telephone Laboratories and its operations as an exemplifica- tion of this unity. Pseudo Closed Trajectories in the Family of Trajectories Defined by a System of Differential Equations. L. A. MacColl.^ Quart. Applied Math., v. 8, pp. 255-263, Oct., 1950. Abstract — ^This paper is concerned with certain simple closed curves, here called pseudo closed trajectories, which play an important part in deter- mining the topological properties of the family of trajectories (or char- acteristics) defined by a system of differential equations of the form Some of these curves are considered in a rather incidental way in the writings of Poincare. However, the full concept of pseudo closed trajectories does not seem to have been discussed explicitly heretofore. Teletype's Share in Bell System Operations. P. H. Miele.^ Bell Tel. Mag., V. 29, pp. 180-190, Autumn, 1950. Abstract — Western Electric makes equipment for transmission of the spoken word; Teletype, its subsidiary, makes equipment for transmission of the written word. * A reprint of this article may be obtained on request to the editor of the B. S. T, J. IB. T.L. 2W. E. Co. 476 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 Mechanism of Magnetization and Alnico V. E. A. Nesbitt^ and H. J. WiLLiAMS.i Letter to the editor. Phys. Rev., v. 80, pp. 112-113, Oct. 1, 1950. The P-Germanium Transistor.* W. G. PfannI and J. H. Scafe.i I.R.E. Proc, V. 38, pp. 1151-1154, Oct., 1950. Abstract — The transistor effect in p-type germanium is discussed and some properties are given for p-germanium transistors made in the laboratory. These exhibit higher cutoff frequency and somewhat lower current multipli- cation than their n-germanium counterparts. Under certain conditions a negative resistance "snap" effect is observed which is apparently peculiar to p-type germanium. Both types of transistor are governed by the same physical principles but they differ in the signs of the emitted carriers and of the bias voltages. Transistor as a Reversible Amplifier. W. G. Pfann.^ Letter to the editor. r.R.E., Proc, V. 38, p. 1222, Oct., 1950. Electronics. J. R. Pierce.^ Sci. Am., v. 183, pp. 30-39, Oct., 1950. Abstract — A general account of the means by which the smallest funda- mental particles are manipulated to accomplish many subtle tasks of our technological civilization. Millimeter Waves.* J. R. Pierce.^ Physics Today, v. 3, pp. 24-29, Nov., 1950. Abstract — Lying between the longest infrared rays and the shortest micro- waves of the electromagnetic radiation is the region of millimeter waves, which are difficult to produce and to measure and which have as yet found few applications. The millimeter wave range, a relatively undeveloped field for research, presents a challenge to theoreticians, experimentalists, and in- ventors alike. This article was prepared at the request and through the co- operative effort of the ONRD advisory committee on millimeter wave generation as a means for stimulating effort in this new field. Note on Stability of Electron Flow in the Presence of Positive Ions. J. R. Pierce.' Letter to the editor. .//. Applied Phys., v. 21, p. 1063, Oct., 1950. Communications Metallurgy.* E. E. Schumacher.' Delivered at annual autumn meeting of the Institute of Metals at Bournemouth, Sept. 18, 1950. Inst. Metals, Jl., v. 18, pp. 1-23, Sept., 1950. Abstract— The lecture describes the function of the metallurgical depart- ment in a communications system. The need for metallurgical research and development, the origin of metals problems, the requirements imposed on metal components, and the integration of metallurgical developments into an operating communications system are given emphasis. It is shown how * A reprint of this article may be obtained on request to the editor of the B. S. T. J. » B. T. L. ARTICLES BY BELL SYSTEM AUTHORS 477 the solutions to problems may derive from previous experience, from empiri- cal investigation, or from fundamental research. Illustrative examples are given to demonstrate the complementary roles of engineering and research in correlating the properties of metals with their structure, and their structure with their history of fabrication. Carrier Telephone on Rural Power Lines. J. L. Simon.'* Elec. Light & Power, v. 28, pp. 92, 137, Oct., 1950. Abstract — A pictorial and diagrammatic treatment of the problems in- volved in transmitting carrier telephone currents over existing rural power lines. Weathering Studies on Polyethylene.^ V. T. Wallder,^ W. J. Clark,^ J. B. De Coste,^ and J. B. Howard.^ References. Ind. & Engg. Chem., v. 42, pp. 2320-2325, Nov., 1950. Abstract — Polyethylene has been used for a number of years as a dielectric material but only recently has it been considered as a mechanical protection for wires and cables intended for direct exposure to the weather. Data are presented on the results of a 10-year program on the effects of weather on polyethylene. An accelerated test, which for the materials tested shows good correlation with natural aging, is described and used to evaluate the aging characteristics of compounds of polyethylene containing carbon black. Data are given showing effects on aging of different types of carbon blacks such as furnace and channel blacks, effects of carbon black concentration on aging, the necessity for efficient dispersion of the carbon black in the polyethylene, and the relation between aging and carbon-black particle size. Age resistance of polyethylene is shown to increase as the average molecular weight of the polymer is increased. These data indicate that channel grades of carbon black which have a particle diameter of about 25 m/i or less when well dispersed in an appropriate polyethylene at concentrations of 1 to 2% can produce compositions having a natural outdoor life expectancy suffi- ciently long to be considered for most outdoor applications in the wire and cable field. Why Standardize Thicknesses of Thin Flat Metals. I. V. Williams.^ Stand- ardization, V. 21, pp. 260-261, 272, Oct., 1950. Abstract — Before considering the methods of standardizing thicknesses of metals, let us first consider why there should be any demand or need for such standards. Some very strong arguments can be advanced in favor of such practice, and the benefits which are derived therefrom should favor pro- ducers, warehousemen, and consumers. * A reprint of this article may be obtained on request to the editor of the B. S. T. J. 1 B. T. L. * S. W. Bell 478 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 Test of 450-Megacycle Urban Area Transmission to a Mobile Receiver* A. J. AiKENS^ and L. Y. Lacy.i I.R.E., Proc, v. 38, pp. 1317-1319, Nov., 1950. Abstract — Measurements were made of mobile radio- telephone trans- mission at 450 Mc in New York City using frequency modulation. Compari- son was made with transmission at 150 Mc using identical speech modula- tion. Effective radiated powers were about equal. Direct comparison tests were made with the receivers installed in a moving automobile. The trans- mitter and the receiver used at 450 Mc were developed especially for the job. The receivers used at the two frequencies had substantially the same noise figures. The tests permitted estimates of the relative magnitudes of the shadow losses at the two frequencies and included measurements of r^ noise. Subjective tests of circuit merit comparing the two frequencies were made by a number of observers. Pressure Broadening of the Ammonia Inversion Line by Foreign Gases: Quadrupole-Induced Dipole Interactions* P. W. Anderson.^ Phys. Rev., V. 80, pp. 511-513, Nov. 15, 1950. Abstract — ^The broadening of the 3,3 line of the inversion spectrum of ammonia by foreign gases which are not expected to have dipole or quadru- pole moments has been measured accurately by Smith and Howard. This broadening is greater than that previously computed by the author using the interaction of the molecule's dipole moment with the induced dipole on the foreign gas atom. In this paper the broadening is explained quanti- tatively using the interaction of the induced dipole on the foreign gas atom with the quadrupole moment of ammonia. It is concluded that a model of the ammonia molecule using bond dipoles of the appropriate size to give the known dipole moment, or a model with point charges at the atoms, again adjusted to give the correct dipole moment, both give quadrupole moments which explain the broadening cross sections with good accuracy. Antenna Systems for Multichannel Mobile Telephony* W. C. Babcock^ and H. W. Nylund.^ LR.E., Proc, v. 38, pp. 1324-1329,. Nov., 1950. Abstract — This paper describes an arrangement whereby several antennas may be mounted on a single mast at the transmitting site of a multichannel system operating in the 152- 162-megacycle band. The antennas are so dis- posed as to minimize shadowing effect of the mounting structure, while keeping intertransmitter coupling to a tolerable minimum. Measurements of the electrical characteristics are presented for arrangements of 6 antennas mounted on a 62-foot steel mast. These measurements on a full-scale struc- * A reprint of this article may be obtained on request to the editor of the B. S. T. J. ARTICLES BY BELL SYSTEM AUTHORS 479 ture are supplemented by tests at a higher frequency on reduced-scale, sim- plified models. Wave Functions for Superconducting Electrons* ]. Bardeen.^ References. Phys. Rev., v. 80, pp. 567-574, Nov. 15, 1950. Abstract — The observed variation of the transition temperature of mercury with isotopic mass is evidence that the superconducting state arises from in- teraction of electrons with lattice vibrations. The interaction term which gives scattering of electrons at high temperatures contributes at low tem- peratures a term to the energy of the system of electrons plus normal modes. Frohlich has calculated the interaction energy at T = 0°K by second-order perturbation theory. The energy is calculated here by taking wave functions of superconducting electrons, which have energies near the Fermi surface, as linear combinations of Bloch functions whose coefficients are functions of coordinates of the normal modes. In an equivalent approximation, Frohlich's expression for the interaction energy is obtained. When the energy is calculated directly rather than by perturbation theory, modified expressions are obtained for the energy and distribution of electrons in the superconducting state. The criterion for superconductivity is h/r > ^^ IttkT, where r is the relaxation time for electrons at some high temperature T where tT is constant. It is shown that superconducting electrons have small effective mass. Clampers in Video Transmission* S. Doba, Jr.^ and J. W. Rieke.^ A. I. E.E., Trans., v. 69, pt. 1, pp. 477-487, 1950. Abstract — One of the major problems connected with the transmission of television signals is the exceptionally wide video band of frequencies in- volved. For the present black-and-white standards this amounts to about 4 megacycles. In the transmission of the television signal at video frequencies, that is, noncarrier transmission, the problem is further complicated because the lower limit of the frequency range extends literally to zero frequency. Calculation of Vowel Resonances, and an Electrical Vocal Tract.* H. K. DuNN.^ Bibliography. Acoustical Soc. Am., Jl., v. 22, pp. 740-753, Nov., 1950. Abstract — By treating the vocal tract as a series of cylindrical sections, or acoustic lines, it is possible to use transmission line theory in finding the resonances. With constants uniformly distributed along each section, res- onances appear as modes of vibration of the tract taken as a whole. Thus, the fundamental mode of the smaller cavity may be affected considerably by a higher mode of the larger; and in addition, higher resonances are found * A reprint of this article may be obtained on request to the editor of the B. S. T. J. 1 B. T. L. 480 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 without postulating additional cavities. This is an advantage over the lumped constant treatment, where it is necessary to postulate a different cavity for each resonance, and where the interaction terms in the equation do not include the higher modes of vibration. Under the distributed treat- ment, dimensions for each vowel may be taken from x-ray photographs of the vocal tract. The calculations then yield at least three resonances which lie in the frequency regions known for the vowel, from analyses of normal speech. Dependence of the different resonances upon the different cavities is discussed in some detail in the paper. An electrical circuit based on the transmission line analogy has been made to produce acceptable vowel sounds. This circuit is useful in con- firming the general theory and in research on the phonetic effects of articu- lator movements. The possibiUty of using such a circuit as a phonetic stand- ard for vowel sounds is discussed. Basic Theory Underlying Bell System Facilities Capacity Tables. A. L. Gracey.* A.LE.E., Trans., v. 69, pt. 1, pp. 238-243, 1950. Abstract — Discussion of the many considerations involved in the layout of a switching network adequate for present needs and flexible for future change is beyond the scope of the present paper. Rather, it deals with the specific problems of determining sizes of trunk groups and quantities of various components of dial central office equipment by the methods cur- rently used in the Bell System. Examples are given, with illustrative tables. Enough of the probability theory underlying the tables is given to bring out the assumptions made to fit or approximate the various service conditions. Binaural Localization and Masking.* W. E. Kock.^ Acoustical Soc. Am., JL, V. 22, pp. 801-804, Nov., 1950. Abstract — Binaural experiments are described which indicate that the ability of the brain to localize a desired sound and to suppress undesired sounds coming from other directions can be traced in part to the different times of arrival of a sound at the two ears. It is suggested that the brain inserts a time delay in one of the two nerve paths associated with the ears so as to be able to compare, and thus concentrate on, those sounds arriving at the ears with this particular time of arrival distance. The ability to perceive weak sounds binaurally in the presence of noise is shown to be a simple function of the direction of the desired sound and noise. An explanation is given for the effect reported by Koenig that front and rear confusion is avoided by head movements. * A reprint of this article may be obtained on request to the editor of the B. S. T. J. 1 B. T. L. ' A. T. & T. Co. ARTICLES BY BELL SYSTEM AUTHORS 481 Number 5 Crossbar Dial Telephone Switching System* F. A. Korn^ and James G. Ferguson.^ A.LE.E., Trans., v. 69, pt. 1, pp. 244-254, 1950. Abstract — The field of application of this new switching system is more extensive than that of any developed previously. The Number 5 system is capable of operating with all present local, tandem, and toll switching sys- tems of the Bell System and of the independent companies which connect with it. In addition, it can serve as a tandem or toll center switching office where this is advantageous. It can be readily equipped with features for operation as required at toll centers for nationwide operator toll dialing and also for automatic message accounting which permits subscriber dialing to be extended to considerable distances. Number 5 crossbar is designed for operation with as few as four digits in a subscriber number or it can complete calls which require as many as 11 digits, (dialed by operators) three for the national area code, three for the office code, four for the numericals and the last for the station letter of the called number on certain types of party line service. Carrier-Controlled Relay Servos * J. C. Lozier.^ Elec. Engg., v. 69, pp. 1052-1056, Dec, 1950. Abstract — A study of servo systems shows that, when properly designed, the carrier-controlled relay servo will perform as well as a servo system with proportional control. In this article the problem of designing a carrier- controlled relay servo system for remotely tuning the variable capacitors of a transmitter is analyzed. Quality Rating of Television Images * P. Mertz,^ A. D. Fowler,^ and H. N. Christopher.1 I.R.E., Proc, v. 38, pp. 1269-1283, Nov., 1950. Abstract — Two methods of evaluating impairments in television images are described. Both employ observers and, therefore, yield subjective evalua- tions. The first is an extension of Baldwin's in which observers vote a prefer- ence between pictures with different impairments; one of the pictures is optically projected somewhat out of focus and is used as a reference. In the second method, the impairment is rated by observers in terms of pre-worded comments which are numbered and form a rating scale. Both methods permit an evaluation in terms of liminal increments as computed from the distribu- tion of votes of the observers. These methods have been used to evaluate the impairing effects of echoes and noise in television pictures, and also to relate picture sharpness to other quality parameters. Fundamentals of the Automatic Telephone Message Accounting System* J. Meszar.i A.LE.E., Trans., v. 69, pt. 1, pp. 255-268, 1950. * A reprint of this article may be obtained on request to the editor of the B. S. T. J. » B. T. L. 482 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 Abstract — ^This paper discusses the economic background of the AMA sys- tem, explains its fundamental coding technique, describes its unique appara- tus elements, and presents the basic features of both the recording and processing machinery. Conduction Phenomena in Gases * J. P. Molnar.^ Elec. Engg., v. 69, pp. 1071-1076, Dec, 1950. Abstract — ^A review is made of the processes involved in the breakdown of a gas, in which a body of neutral gas particles that acts as an insulator is changed to one containing a great many charged particles that acts as a conductor. Factors which must be taken into account in discussing these mechanisms include the gas pressure and the nature of the applied field. Rooter for Video Signals.* B. M. Oliver.^ I.R.E., Proc, v. 38, pp. 1301- 1305, Nov., 1950. Abstract — This paper describes a device which takes the nth root of the instantaneous amplitude of a video signal. Its function is to linearize the over-all transfer characteristic, and thus to improve the picture quality in a television system using linear camera tubes and conventional cathode-ray viewing tubes. Tone Rendition in Television* B. M. Oliver.^ I.R.E., Proc, v. 3S, pp. 1288-1300, Nov., 1950. Abstract — This paper is a review of some of the brightness transfer char- acteristics which may be obtained in television using present-day apparatus and techniques. Several families of curves are presented which show the effects of varying one or more of the relevant factors, the remainder being held constant at reasonable values. New Electronic Telegraph Regenerative Receiver* B. Ostendorf, Jr.^ A.LE.E., Trans., v. 69, pt. 1, pp. 32-36, 1950. Abstract — An all-electronic device for removing distortion from start-stop teletypewriter signals is described. The circuit utilizes a sine wave oscillator for timing and binary counters for synchronization. It provides low output distortion, high tolerance to input distortion, hit-reduction, transmission of steady-space break signals, and regeneration of one element-length of stop time. It features quick change of speed and code, use of office battery power, and reduction of routine maintenance to one adjustment. Over a year's experience has been obtained with about 100 of these units. Toward the Specification of Speech.* R. K. Potter^ and J. C. Steinberg.^ References. Acoustical Soc. Am., Jl., v. 22, pp. 807-820, Nov., 1950. Abstract — This is an interim report on studies of the specification of speech * A reprint of this article may be obtained on request to the editor of the B. S. T. J. iB.T.L. ARTICLES BY BELL SYSTEM AUTHORS 483 sounds from acoustical measurements. Methods based upon analysis, syn- thesis, and vocal tract models are described. Included are the results of pre- liminary measurements on the vowel sounds of 25 speakers. Some of the problems in specifying the vowel sounds as indicated by these results are discussed. Protective Grounding of Electrical Installations on Customer's Premises. A. H. ScHiRMER.i A.I.E.E., Trans., v. 69, pt. 1, pp. 657-659, 1950. Abstract — The problem of electrical safety in rural areas is one of pro- viding adequate insulation on circuits and equipment, and effective ground- ing and bonding. Providing adequate insulation presents no particular prob- lems. However, there is some confusion as to what constitutes effective grounding and bonding. This paper briefly discusses the various factors which must be taken into account. The discussion is limited to a-c circuits. Six-System Urban Mobi'e Telephone Installation with 60-Kilocycle Spacing.* R. C. Shaw,^ p. V. DiMOCK,! W. Strack, Jr./ and W. C. Hunter.^ I.R.E., Proc, V. 38, pp. 1320-1323, Nov., 1950. Abstract — This paper describes a 6-system mobile radiotelephone installa- tion in Chicago, operating in the 152- 162 -megacycle band, and using 60-kc spacing of carrier frequencies, rather than the 120-kc spacing of previous practice. The measures required to achieve this frequency saving are de- scribed, including filters and special antenna arrangements at the land trans- mitter, "off-channel squelch" in the land receivers, connection of six land receivers to a common antenna, and other special co-ordinating means. Tone Rendition in Photography.* W. T. Wintringham.^ References. I.R.E., Proc, V. 38, pp. 1284-1287, Nov., 1950. Abstract — The photographic field is reviewed to find whether the tone rendition of a good picture can be predicted. The television engineer can find no solace in the fact that good photographs were made before measurements were made of the photographic media. He will be thwarted further when he learns that the best print is the result of experienced criticism of a work print. However, the experience of the photographer in obtaining pleasing results in spite of the limitations and distortions of the photographic proc- ess should be useful to the television engineer. Ferromagnetic Resonance in Nickel Ferrite.* W. A. Yager.^ J. K. Galt,^ F. R. Merrit,! and E. A. Wood.^ References. Phys. Rev., v. 80, pp. 744-748, Nov. 15, 1950. Abstract — ^The ferromagnetic resonance phenomenon in single crystals of NiO Fe203 has been studied at room temperature at 24,000 Mc/sec. Small * A reprint of this article may be obtained on request to the editor of the B. S. T. J. 1 B. T. L. 484 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 samples were used in order to avoid electromagnetic cavity- type resonances. The g-f actor observed is 2.19. The first-order magnetocrystalline anisotropy constant Ki was found so be —6.27 X lO'* ergs/cc. The absorption line was very narrow (half-widths less than 100 oersteds) and fit a resonance curve quite satisfactorily. Two Comments on the Limits of Validity of the P. R. Weiss Theory of Ferro- magnetism. P. W. Anderson.^ Letter to the editor. Phys. Rev., v. 80, pp. 922-923, Dec. 1, 1950. Television Picture Fidelity. M. W. Baldwin, Jr.^ Electronics, v. 24, pp. 106-107, Jan., 1950. Abstract — Consideration of the various factors involved in the physics of image formation on a television picture tube, and discussion of inherent limitations and attributes of the overall system and its production techniques. Changes in Conductivity of Germanium Induced hy Alpha-Particle Bombard- ment.* W. H. Brattain^ and G. L. Pearson.^ Phys. Rev., v. 80, pp. 846-850, Dec. 1, 1950. Abstract — ^The bombardment of n-type germanium by alpha-particles from polonium first removes the conducting electrons at the rate of 78 per alpha- particle. After the electrons are gone conducting holes are introduced at the initial rate of 8.6 per alpha-particle. Some of these holes disappear with time at room temperature after bombardment is stopped, leaving only two conducting holes per alpha-particle. This change takes place only to the depth of penetration of the particles, namely 1.9 X 10~^ cm. The distribution of holes with depth is not uniform. The concentration rises from an initial value to a maximum at 1.4 X 10~^ cm depth and then falls to zero. The maxi- mum is about 2.5 times the initial value and the integral under the curve is, of course, two holes per alpha-particle. Experimental Verification of Space Charge and Transit Time Reduction of Noise in Electron Beams.* C. C. Cutler^ and C. F. Quate.* Phys. Rev., v. 80, pp. 875-878, Dec. 1, 1950. Abstract — This paper describes a simple experiment which indicates some significant properties of the noise currents in a long electron stream, and veri- fies the applicability of the theory as worked out by Rack, Peterson, and Pierce to the noise properties of klystrons and traveling-wave tubes. An appendix shows that the observations are reasonably consistent with the theory. * A reprint of this article may he obtained on request to the editor of the B. S. T. J. 1 B. T. L. » A. T. & T. Co. ARTICLES BY BELL SYSTEM AUTHORS 485 Note on the Inertia and Damping Constant of Ferromagnetic Domain Bound- aries. C. KiTTEL.i Phys. Rev., v. 80, p. 918, Dec. 1, 1950. Reduction of SrO by Tungsten in Vacuum.* G. E. Moore,^ H. W. Allison,' and J. Morrison.' Bibliography. Jl. Chem. Phys., v. 18, pp. 1579-1586, Dec, 1950. Abstract — It is shown that in the temperature range 1150-1550°K, SrO is reduced by tungsten in vacuum. Both the rate of the reaction and its equilibrium constant can be calculated, giving values in substantial agree- ment with the experiments, which were performed under conditions such that both could be measured. The use of radioactive isotopes simplified the experimental work. Vaporization of Strontium Oxide.* G. E. Moore,' H. W. Allison,' and J. D. Struthers.' Bibliography. Jl. Chem. Phys., v. 18, pp. 1572-1579, Dec, 1950. Abstract — ^The vapor pressure of SrO was measured by studying the product evaporated from platinum filaments coated with SrO. Most of the experiments employed radiactive isotopes. The possibility of systematic error caused by chemical reduction of the oxide or by its thermal dissociation is discussed. A value of Xo, the heat evaporation at 0°K computed from the results, is used to evaluate precision and to derive a vapor-pressure equa- tion. Millimeter Waves.* J. R. Pierce.' Electronics, v. 24, pp. 66-69, Jan., 1951. Effect of Stress-Free Edges in Plane Shear of a Flat Body.* W. T. Read.' Jl. Applied Mech., v. 17, pp. 349-352, Dec, 1950. Abstract — This paper determines the tangential stiffness of a flat rectangu- lar body, or shear pad, with a uniform relative tangential displacement on the upper and lower surfaces. The state of stress differs from pure shear in that the edges are stress-free. The correction to the stiffness in pure shear is obtained as a function of Poisson's ratio and the length-to-thickness ratio. The paper also illustrates the power of energy methods in furnishing ac- curate approximations with a small amount of numerical work when only over-all quantities, such as stiffness, are investigated. By manipulating energy relations and using the Prager-Synge approximate method a few hours of slide-rule computation was sufficient to determine both upper and lower bounds for the stiffness. Growing Piezoelectric Crystals.* A. C. Walker.' Franklin Inst., J I., v. 250, pp. 481-524, Dec, 1950. Abstract — This paper is a summary of work carried out at the Bell Tele- * A reprint of this article may be obtained on request to the editor of the B. S. T, J. ^B. T. L. 486 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 phone Laboratories on the growing of large single crystals of three different piezoelectric materials: ammonium dihydrogen phosphate (ADP); ethylene- diamine tartrate (EDT); and quartz. Included are illustrations of some basic principles observed in the growing of these crystals, descriptions of improved apparatus for their growth, and pilot plant problems encountered in conjunction with the commercial production of ADP and EDT. Sttidies of the Propagation Velocity of a Ferromagnetic Domain Boundary * H. J. Williams,^ W. Shockley,^ and C. Kittel.^ References. Phys. Rev., V. 80, pp. 1090-1094, Dec, 15, 1950. Abstract — This paper discusses the results and interpretation of measure- ments of the propagation velocity of a ferromagnetic domain boundary in the single crystal of silicon iron with a simple domain structure employed previously by Williams and Shockley. The experiment is similar in prin- ciple to the Sixtus-Tonks experiment, with the important difference that in the present experiment the eddy current configuration is amenable to exact mathematical calculation, thereby enabling a quantitative comparison with observation. Experiments and analysis similar to those described in paragraphs III and V have been carried out by K. H. Stewart and were re- ported at the Grenoble Conference on Ferromagnetism and Antiferromag- netism as were the principal results of this article. However, it appears from Stewart's hysteresis loops unlikely that his specimen had as simple a domain structure as that encountered in our experiments. Progress in Development of Test Oscillators for Crystal Units* L. F. KoERNER.i I.R.E., Proc, v. 39, pp. 16-26, Jan., 1951. Abstract — Early crystal unit test oscillators as conceived some 20 years ago were principally duplicates of the actual equipment in which the crystal units were to be utilized, a practice which resulted in a large variety of test circuits and procedures for testing. It is now recognized that a knowledge of the equivalent electrical elements making up the crystal unit is essential to the circuit engineer, and that the older conception of frequency and ac- tivity, the latter being an attempt to express the quality of a crystal unit in terms of a particular oscillator circuit, do not define adequately its charac- teristics. The equivalent electrical circuit of the crystal unit contains essenti- ally a resistance, an inductance, and 2 capacitances, which together with frequency define the performance of the unit. Crystal units are available in the frequency range from about 1,000 cycles to over 100 Mc. Their re- sistance range may vary from less than 10 ohms to over 150,000 ohms, the inductance from a few millihenries to nearly 100,000 henries and the capaci- * A reprint of this article may be obtained on request to the editor of the B. S. T. J. iB.T. L. ARTICLES BY BELL SYSTEM AUTHORS 487 tances from about 0.001 /x/xf to 50 ju/xf. Modern test oscillators, with fre- quency and capacitance measuring apparatus as auxiliary equipment, will measure these quantities with accuracies sufficient to meet present needs. The transmission measuring circuit also is described and is proposed as the standard reference circuit for comparison with the test oscillators. Electro Spot Testing and Electrography* H. W. Hermance^ and H. V. Wadlow.^ Reprinted from A.S.T.M., Special Technical PMication No. 98, pp. 12-34, 1950. * A reprint of this article may be obtained on request to the editor of the B. S. T, J. » B. T. L. Contributors to This Issue Sidni:y Darlington, Harvard University, B.S. in Physics, 1928; Massa- chusetts Institute of Technology, B.S. in E.E., 1929; Columbia University, Ph.D. in Physics, 1940. Bell Telephone Laboratories, 1929-. Dr. Darlington has been engaged in research in applied mathematics, with emphasis on net- work theory. R. O. Grisdale, S.B., Harvard University, 1930. Bell Telephone Labora- tories, 1930-. In the Chemical, Physical Research, Electronic Apparatus Development, and Transmission Apparatus Development Departments, Mr. Grisdale has been concerned with the development of varistors, thermis- tors, ceramics, microphone carbon, carbon film resistors, wire coverings, and dielectric materials. A. H. Inglis, B.A., Yale University, 1914. Western Electric Company, Engineering Department, 1914-17. Signal Corps, A.E.F., 1917-19. American Telephone and Telegraph Company, Department of Development and Research, 1919-34; Bell Telephone Laboratories, 1934-. As Station In- strumentalities Engineer, Mr. Inglis has been concerned with both equip- ment and transmission matters of station apparatus. W. E. Kahl, Bell Telephone Laboratories, 1921-. Graduated in 1924 from the Student Assistants' Course given in the Laboratories. Prior to World War II Mr. Kahl was engaged in the development of filters, equalizers and other transmission networks used in various carrier systems, particu- larly those for the Type C and Type J Systems. During the war he was con- cerned with the development of airborne submarine detection equipment under-water mine detection equipment, and special networks for Naval Ordnance Laboratory projects. Immediately following the war he was active as apparatus engineer for the Type ''M" Power Line Carrier System and the N-1 Carrier System developments. Present activity is concerned with the development of special networks for military application. W. H. Martin, A.B., Johns Hopkins University, 1909; S.B., Massa- chusetts Institute of Technology, 1911. American Telephone and Telegraph Company, Engineering Department, 1911-19; Department of Development and Research, 1919-34. Bell Telephone Laboratories, 1934-. Now Vice 488 CONTRIBUTORS 489 President, Mr. Martin has been associated in various capacities with the work on telephone instruments and sets since 1918. He has participated also in the development and application of these and allied devices in the fields mentioned in the Conclusion section of his paper. W. P. Mason, B.S. in E.E., University of Kansas, 1921; M.A., Ph.D., Columbia, 1928. Bell Telephone Laboratories, 192 1-. Dr. Mason has been engaged principally in investigating the properties and applications of piezoelectric crystals and in the study of ultrasonics. L. Pedersen, graduate of Christiania Technical School, 1919. Western Electric International, 1919-20. Bell Telephone Laboratories, 1920-. Prior to World War II Mr. Pedersen was engaged chiefly in the development of d-c. telegraph equipment. During the war he was engaged in the design of the Spiral-Four carrier equipment and served with the U. S. Army in the European Theatre of Operation as a technical observer. Since the war his principal activities have been as equipment engineer for the N-1 and O Carrier telephone development. A. C. Pfister, B.M.E., Brooklyn Polytechnic Institute, 1939. Bell Tele- phone Laboratories, 1930-. In the Physical Research, Electronic Apparatus Development, and Transmission Apparatus Development Departments, Mr. Pfister has been engaged in research and development on microphone carbon and deposited carbon resistors. Gordon Raisbeck, Massachusetts Institute of Technology, 1941-43; teaching fellow, Stanford University, 1943-44; B.A. in pure mathematics, 1944; Radio Technical Officer, U. S. Navy, 1944-46; instructor in mathe- matics, M.I.T., 1946-47; Rhodes Scholar, New College, Oxford, 1947-48; instructor in mathematics, M.I.T., 1948-49; Ph.D. in pure mathematics, 1949. Bell Telephone Laboratories, 1949-. Mr. Raisbeck is in the Trans- mission Research Department and is engaged in the study of acoustics and acoustical devices. Thomas Shaw, S.B., Massachusetts Institute of Technology, 1905. American Telephone and Telegraph Company, Engineering Department, 1905-19; Department of Development and Research, 1919-33. Bell Tele- phone Laboratories, 1933-48. Mr. Shaw's active telephone career was mainly concerned with loading problems in telephone circuits, including the transmission and economic features of the loading apparatus. The article now being published was started shortly before his retirement in 1948. 490 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 W. L. TuFFNELL, B.S. in Electrical Engineering, University of Wisconsin, 1930. Bell Telephone Laboratories, 1922-27; 1930-. Until 1949 Mr. Tuffnell was chiefly concerned with the development of telephone instruments, and since then with the development of other station apparatus as Station Ap- paratus Development Engineer. W. VAN RoosBROECK, A.B., Columbia College, 1934; A.M., Columbia University, 1937. Bell Telephone Laboratories, 1937-. Mr. van Roosbroeck's work at the Laboratories was concerned during the war with carbon-film resistors and infra-red bolometers and, more recently, with the copper oxide rectifier. In 1948 he transferred to the Physical Research Department where he is now engaged in problems of solid-state physics. R. L. Wallace, Jr., B.A., The University of Texas, 1936; M.A., The University of Texas, 1939; graduate study at Harvard University, 1937-40. During the recent war Mr. Wallace was a special Research Associate at Harvard University, where he worked on military communications prob- lems. Since he came to work for the Bell Telephone Laboratories in 1946 he has been concerned with some problems in magnetic recording and with transistors. VOLUME XXX JULY X95X no. 3 THE BELL SYSTEM TECHNICAL JOURNAL DEVOTED TO THE SCIENTIFIC AND ENGINEERING ASPECTS OF ELECTRICAL COMMUNICATION Reduction of Skin Effect Losses by the Use of Laminated Conductors A.M. Clogston 491 Some Circuit Properties and Applications of n-p-n Tran- sistors R. L. Wallace, Jr. and W. J. Pietenpol 530 A Photographic Method for Displaying Sound Wave and Microwave Space Patterns W. E. Kock and F. K. Harvey 564 Some Basic Concepts of Translators and Identifiers Used in Telephone Switching Systems . . .H.H. Schneckloth 588 Waves in Electron Streams and Circuits J. R. Pierce 626 Interaxial Spacing and Dielectric Constant of Pairs in Multipaired Cables J-T. Maupin 652 iV-Terminal Switching Circuits E. N. Gilbert 668 Coaxial Impedance Standards R. A. Kempf 689 Instantaneous Compandors CO. Mallinckrodt 706 The Evolution of Inductive Loading for Bell System Tele- phone Facilities (Continued) Thomas Shaw 721 Abstracts of Bell System Technical Papers Not Published in This Journal 765 Contributors to This Issue 777 ^Oi Copyright, 1951 $1.50 per copy American Telephone and Telegraph Company p^^ Year THE BELL SYSTEM TECHNICAL JOURNAL Published quarterly by the American Telephone and Telegraph Company 195 Broadway, New York 7, N. Y, Leroy A. Wilson Carroll O. Bickelhaupt Donald R. Belcher President Secretary Treasurer EDITORIAL BOARD F. R. Kappel O. E. Buckley H. S. Osbome M. J. Kelly J. J. Pmiod A. B. Clark R. Bown D. A. Quarles F. J. Feely P. C. Jones, Editor SUBSCRIPTIONS Subscriptions are accepted at $1.50 per year. Single copies are 50 cents each. The foreign postage is 35 cents per year or 9 cents per copy. PRINTED IN U.S. A. The Bell System Technical Journal Vol. XXX July, igsi No. 3 Copyright, 1951, American Telephone and Telegraph Company Reduction of Skin Effect Losses by the Use of Laminated Conductors By A. M. CLOGSTON It has recently been discovered that it is possible to reduce skin effect losses in transmission lines by properly laminating the conductors and adjusting the velocity of transmission of the waves. The theory for such laminated transmission lines is presented in the case of planar systems for both infinitesimally thin laminae and laminae of finite thickness. A transmission line completely filled with laminated material is discussed. An analysis is given of the modes of trans- mission in a laminated line, and of the problem of terminating such a line. I. Introduction It has long been recognized that an electromagnetic wave propagating in the vicinity of an electrical conductor can penetrate only a limited distance into the interior of the material. This phenomenon is known as "skin effect'^ and is usually measured by a so-called "skin depth" 6. If 3; is measured from the surface of a conductor into its depth, the amplitude of the electro- magnetic wave and the accompanying current density decreases as f^ , provided the conductor is several times 5 in thickness, so that for 3; = 5 the ampUtude has fallen to 1/e = 0.367 times its value at the surface. The skin depth 5 is given by = J— (I-l) where g is the conductivity of the material, ^i is its permeabiHty and co is lir times the frequency/ under consideration. Throughout this paper ration- alized MKS units are used. From one point of view, skin effect serves a most useful purpose; for in- stance, in shielding electrical equipment or reducing crosstalk between com- munication circuits. On the other hand, the effect severely limits the high frequency performance of many types of electrical apparatus, including in particular the various kinds of transmission Hues. Surprisingly enough, it has been discovered that it is possible, within limits, to increase the distance to which an electromagnetic wave penetrates 491 492 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 into a conducting material. This is done essentially by fabricating the con- ductor of many insulated laminae or filaments of conducting material ar- ranged parallel to the direction of current flow. If the transverse dimensions of the laminae or filaments are small compared to the skin depth 5 at the frequency under consideration, and if the velocity of the electromagnetic wave along the conductor is close to a certain critical value, the wave will penetrate into the composite conductor a distance great enough to include a thickness of conducting material many skin depths deep. Physically speak- ing, the lateral change of the wave through the conducting regions is very nearly cancelled by the change through the insulating regions. In Fig. 1 there is shown a cross-section view of a coaxial cable with a Fig. 1 — Laminated transmission line. laminated center conductor. The center conductor is formed of a non-con- ducting core surrounded by alternate layers of a conductor of thickness W and conductivity a, and an insulator of thickness / and dielectric constant e. The center conductor is embedded in an insulator of dielectric constant ci which is in turn encased in the outer conductor. We will assume all the conductors and insulators to have the permeability fio of free space. We will associate with the inner laminated conductor an average dielectric constant^ for transverse electric fields given by (-?) (1-2) ' A similar average dielectric constant has been considered by Tokio Sakurai, Journal of Physical Society of Japan, Vol. 5, No. 6, pp. 394-398, Nov.-Dec. 1950. REDUCTION OF SKIN EFFECT LOSSES 493 It will be shown in the following sections that the electromagnetic wave and the accompanying currents will penetrate most deeply into the center con- ductor if the wave travels through the line with a velocity V = -^ (1-3) One way to make the wave assume this velocity is to let the dielectric con- stant ci have the value „ = . = ,(. + H) (1-4) If the depth of the stack of laminations D is small compared to the dis- tance between the stack and the outer conductor, and if the wave travels with the velocity given in equation (1-3), it will be shown that the wave decreases with distance into the center conductor as e~^'8y, where 6„, is given by 5„, = V3 (1 + t/W)i8/W)8; W « d (1-5) 1 . . Here 5 = / ^ is the skin depth appropriate to the material of the con- ducting laminae and the frequency / under consideration. Let us now also associate with the center conductor an average longitudinal conductivity given by ^ (1-6) W + / We will suppose for the present case that most of the attenuation of the transmission line results from the currents flowing in the inner conductor. It is easy to see that the attenuation of the line for very low frequencies will be A/dD where ^4 is a constant depending on the impedance of the line. As the frequency increases, 8w decreases, and when 6«, becomes several times smaller than D it will be shown that the attenuation becomes A/adu,. At still higher frequencies 8 will similarly become several times smaller than W, and the attenuation then becomes A /ad. From these considerations, a qualitative picture of the attenuation of the laminated line can be sketched as in Fig. 2. For comparison, we have also sketched in Fig. 2 the attenuation that would be obtained if the laminations in Fig. 1 were replaced with solid metal. At low frequencies, the attenuation of this line would clearly be A/aD. When the frequency becomes high enough for 5 to be several times smaller than D the attenuation will be shown to become A/a8. It will be observed how the attenuation of the unlaminated line remains 494 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 constant over a low range of frequencies and then rises at a rate propor- tional to the square root of the frequency. The laminated Une has a higher initial attenuation, but remains constant to higher frequencies. At high enough frequencies the attenuation of the laminated Hne rises at a rate di- rectly proportional to frequency for a while, and then eventually approaches the attenuation of the unlaminated line. The frequency at which the attenuation of the laminated Une begins to increase is greater than the corresponding frequency for the conventional line by a factor ^(0© SOLID CENTER CONDUCTOR ^=f 77-fytZo n 9*- o< cr QL 1 1 (TD LAMINATED CENTER CONDUCTOR V3 7T/Uo(rD^ 77-//o^WD FREQUENCY 77//o^W2 Fig. 2 — Comparison of conventional and laminated transmission lines. This is accomplished with an increase in initial attenuation by a factor which we will see later will be about 3/2 in a typical case. We might make a corresponding increase in the flat range of the conventional line by de- creasing <7 to a new value ai. In that case the attenuation would be increased by a factor ^(i)Q which may be very large since ( ^ ) ( ^ ) is just the number of laminations of conductor or dielectric used on the center conductor. REDUCTION OP SKIN EFFECT LOSSES 495 The flat range of the conventional Une might be alternatively increased to equal that of the laminated line by decreasing D to a, new value Di. In this case the attenuation would be increased by a factor l/^^(l)(w) just the square root of the factor achieved by changing — — - = lOiDy + Jy, ax dKy dEx dy dx = — io)Bi dDx , dDy dx dy (ii-i) (n-2) (II-3) (n-4) In these equations H, B, D, £, / and p all have their usual meanings. A positive time factor e*"' has been introduced. Y ■♦►x Fig. 3 — Rectangular coordinate system. Let us for the moment suppose that we are dealing with an anisotropic medium such that the following relations exist: Jx — Cx Eix 5 Jy — (Ty Ey Dx ^ €x Ex 5 Dy = €j/ Ey B, = ^ioHz (11-5) (II-6) (11-7) Here the a's are conductivities, the e's dielectric constants, and no is the permeability of free space. Suppose also now that the fields all vary with x according to a factor g-^^^. If k has a positive real part we will be dealing with a wave moving along the a;-axis in a positive direction, and a negative imaginary part will indicate that this wave is attenuated. Using the above relations, one can easily find the following equations: ioi^x + (Tx Ut3€y + (Ty Ex = [tWHO (Ty 1 ua€x H" ffx dy ik CoVo iy + k ]Hz dIL Ey^ . , tO)€y -j- (Ty H. (II-8) (11-9) (11-10) REDUCTION OF SKIN EFFECT LOSSES 497 Let us imagine that we have a semi-infinite volume of material arranged as shown in Fig. 4 where the 2-axis is pointing out of the paper. If Hzq is the value of Hi dit y = 0, it is clear from equation (16) that Hz must depend upon y according to H, = H^^e~ where a = ±|/: i03€y + (Ty [icO/Xo (Ty CO JUoCj/ + k ] (Il-U) (n-12) and the sign is chosen so that the real part of a is positive. We can now consider the case when the material under consideration is an ordinary conductor such as copper or silver. In this case we must let ► X (Tx = (Ty solid) and Fig. 4 — Orientation of solid conductor. = €y — e. Then a becomes (the subscript S stands for OLS = d= v ico/ioo" — coVoc + k'^ (11-13) Now, under any practical circumstances the propagation constant k will certainly not be more than a factor 100 larger than the propagation con- stant of free space k = \/co^/ioeo . This applies also to the factor \/co-)Uoc. CO/XoO" (T Consider then the ratio — = — . For the metal copper, for instance, C0€o w^oeo a = 5.80 X 10^ mhos/meter and the dielectric constant of free space €o = .885 X 10~^^ . If we consider frequencies as high as 10,000 megacylces the ratio is still as great as 10^ . Thus, the second two factors under the square root sign in equation (11-13) are entirely negligible and we have as = dc -s/ioiyLQC (11-14) 498 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 (1 + i) ^' Finally we have Real part (as) \'/ 2~ (11-15) (11-16) We can now turn our attention to the stack of laminations shown in Fig. 5. There are shown a series of conducting sheets of conductivity a and thickness PF, separated by a series of insulating sheets of thickness / and dielectric constant e. Suppose we let W and t approach zero while main- taining a constant ratio to obtain a homogeneous but anisotropic material ^x Fig. 5 — Orientation of laminated conductor. to which we can apply equation (11-12). In order to obtain €y , o-„ , ex and ax we can write 1 (Ty -f- icO€y W ■}- t\_ = < cosh TfW sinh r)W sinh rjW Ho ■ < > cosh rjW Eo (111-5) (III-6) (ni-7) For the dielectric laminae, equations (II-8) and (II-9) become d'H, df = (k^ — (a^ floe) He to)€ dy (III-8) (ni-9) Just as for the conducting lammae, let ^1 and £1 be the values of H^ and Ex at the lower surface of a dielectric lamination and let H2 and £2 be these values at the top surface. Then, if ^ = \/F — (jo"^ moc , one has H, > = < cosh ^i tooe twe sinh ^t sinh ^t \\ Hi > cosh ^t £1 (III-IO) From equations (III-7) and (III-IO), we can find the variation of H^ and Ex from the bottom surface of a conducting lamination designated as point zero, to the top surface of the adjacent dielectric lamination designated as point two. Thus, 502 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 £2/ 1^21 7^22/ \jEo where the T's are given below (III-ll) Til = cosh riW cosh ^t + ~l sinh 7]W sinh ^t (III-12) Tn = - sinh vW cosh ^/ + ^ cosh riW sinh ^t (III-13) T21 = 4- cosh riW sinh ^^ + - sinh ryP^ cosh ^t (III-14) 7^22 = A -sinh riW sinh ^t + cosh r/TF cosh ^t (III-15) It is easy to verify from the above that 2^11^22 - TuT2i = 1 (III-16) If we now designate the lower surface of each conducting lamination suc- cessively as points 0, 1, 2, 3,- • •, we can write down the following simul- taneous difiference equations Hn+i = TnHn + TuEn (III-17) En+l =^ TnHn + r22£n (III-18) The solutions of these difference equations are Hn = ^r + 5^"" (III-19) En = A ^-:-Il' r + 5 ^^^ " ^'' ^~" (III-20) i 12 ^12 where , = {':^^) + y/(?k±z.^y _ 1 (III-21) Let us now proceed to determine the skin depth to be associated with the stack of laminae in Fig. 5. Since we have assumed the stack to be very deep, A must be taken zero in equations (III- 19) and (III-20), and the fields vary into the stack according to a factor /3~" , so that Hn = FoT" (111-22) If we now define yn^iW + t)n (III-23) REDUCTION OF SKIN EFFECT LOSSES 503 one has = H^- "-«"<"'+'»■'» (III.24) where (the subscript w indicates a thickness W for the conducting laminae) {W + t) From equations (III-12) and (III-15) one has (III-25) (r^„) 1 /y A ("^-26^ = cosh T^PT cosh ^^ + \(~l ^-?--] sinh ryir sinh ^^ As a practical matter, only rarely will k^ be greater than ten times coVoc and € greater than 10 eo. Hence, ^ will be no larger than 10 \/coVo€o • Fur- thermore, we will see that / should not be very different in magnitude from /~T" Wj which must be smaller than A/ . Thus, we can be sure that ^t is y cojuoo- smaller than 100 a/ 2 — , a quantity which is, as before, much smaller than unity. Under these conditions, equation (III-26) becomes approximately (lR±I^) = coshvW + l^(^l + -^^)sinhr,W (III-27) \ 2 / 2 \ (T ^ tO)€ t]/ = cosh vW + -2 (^^ [ V + (^ ~ 7")] '^^ ''""^ "^^ (III-28) where we have again let P = wVoci as in equation (11-24). Let us set = ^[-^ + (^ + w)(^-t)] ("^-^°) Then, again neglecting — , we have for ««, (T <^v, = .ttA— cosh"' [cosh vW + PivW) sinh rjW] (III-31) W -f- t 504 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 w By definition, tjW = {1 + i) — - We can therefore write approximately, cos^,W^[l-l{^J]^i{^) (III-32) (rjW) sinh vWc^ -^^ (jj + i2 (^^ (III-33) Using expressions (III-32) and (III-33), equation (III-31) becomes cosh" ^ -- W + t Provided that (1 + 2P) ( — j « 1, equation (III-34) can be expanded in orders of magnitude. Thus, for W /dV 1-^ we find approximately "" (W + 0 V 5 / (111-36) • ( V- / + Vf^+j^ ± i V/TvF+TO where and g = 1 + 2P (III-38) The plus sign is to be used when g is positive and the minus sign when g is negative. Equations (III-36) for «,„ and (11-24) for ao are very similar. With a little manipulation we can rewrite equation (11-24) as -i/-(?)rT)V(?)'(?)"-('-?)") REDUCTION OF SKIN EFFECT LOSSES 505 Also equation (III-36) can be written Equation (III-39) is a very good approximation for a for a stack of infinitesimally thin laminae, but is inadequate for the discussion of situa- tions where the finite value of W/b is important. Equation (III-40) on the other hand is a good approximation to a when W/6 is appreciable, but the assumptions made in deriving (III-40) do not allow us to go cor- rectly to the limit W/b = 0. To estimate how small W must be before equation (III-40) fails, let us set ( — /j equal ^^ ( ~ ) ( "7 ) • We will also set €1 = e, since it is only then that these terms are important. In this case, W = - Jn - (III-41) (J \ Mo If we take e to be 5 times the dielectric constant €0 of free space, and take 0- = 5.8 X 10^ mhos/meter for copper, we obtain PT = 3.5 X 10~^ cm. Thus, for any practical purpose we can ignore the failure of equation (111-40) to have the proper limit for W jh = 0. By definition, the fields decrease into the stack according to e~'^v>^ . Let us define the distance at which the fields have decreased by X/e to be the effective skin depth 5^.. Then we have — = Real part (a,^) From equations (III-30) and (III-37) we find For €1 = e equations (III-43) and (III-42) give us finally 5.(€i = ^) = V3 (1 + 1^) (^) 5 (ni-44) 506 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 With the results obtained in Sections II and III, we can compare the curves of attenuation as a function of frequency for conventional and lam- inated lines. Let us consider a transmission line such as that shown in Fig. 1, where we may imagine the center conductor to be either laminated as shown or made of solid metal. Let us suppose, as in the introduction, that most of the power loss is in the center conductor and that the distance between the stack and outer conductor is large compared to the depth of the stack. Clearly, the attenuation of the line will be proportional to the power per unit area flowing into the center conductor for a given power flow in the line. If Ex is the transverse magnetic field and Ex is the longitudinal electric field, the power flow into the center conductor per unit area will be given by ^ I H, I . I £x I cos $ = i Real part {H,-Et) (III-45) where ^ is the phase angle between E^ and Ex and (*) indicates the con- jugate of a complex quantity. If C is the circumference of the center con- ductor, and Z is the characteristic impedance of the line, the attenuation of the line will be given by 7 = ^^^ L^ 1 2 Real part {E.-Et) (III-46) First, let us suppose that the inner conductor is solid and that the fre- quency is very low. In that case, the uniform current density in the metal will be Ez/D, and therefore Ex will be Ez/aD. Hence, for this case the attenuation will be ^'(^ ^"^") = 2-ctp ("^-^'^ In a similar manner, the attenuation of the line when the center con- ductor is laminated will be for very low frequencies 7 J/ small) = ^-^1^ (III-48) Next, let us consider the solid conductor again but for frequencies where 6 « D. Then we have from equations (II-9) and (11-15) Ex= - ^-t-* Ex (III-49) (TO Hence, -" = 2cL ("^-^°^ REDUCTION OF SKIN EFFECT LOSSES 507 Finally, we desire the attenuation y^v of the laminated line at elevated frequencies. Therefore we need the relation between Ex and H, at the first surface of the stack which, for definiteness, we can take to be a metal lamina. For a sufficiently deep stack, this ratio is the same at each successive cor- responding point. Referring to equations (III-7) and (III-IO) we wish to find i^ = § = t (III-51) By eliminating among these equations and using the same approximations made previously, we obtain 0 we have from equations (V-10) and (V-11) H.= Ei^ncos^e-^-^"^ (VII-6) n la £. = y^I:I>ncos^^-•'- (vii-7) where n = 1, 3, 5 • • • and kn is given by (V-8). Kt x = 0 the boundary conditions give ^+5+Zc„cos^=Z/)nCos^^ (VII-8) ^U-B)-J-Ec.(^)cos??^ r ., «... „ V 0 H. = Me'"'' cos !^^ + E ^n cos "^ e"^''"^ (VII-18) £„ = j^^-Me'"- cos g + Z iV„ cos ^ .-'"'] (VII-19) 524 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 with kn given by (V-8) and w = 1, 3, 5, • • • . At oc = 0, B+Zc.cos'^=M cos ^i+HN. cos '^ (Vn-20) -B - ;, 2^Cm[-^] cos"^ or Thus, we have for the transmitted power and for the incident power j/f"' The ratio of transmitted power to incident power is therefore (VII-21) Let us again let ei = e. By adding and subtracting we find _ 1 V C„ ^ cos ^ = 2 E iV« cos ^ (VII-22) tk m a a n 2d 2B + i Z C„ ^ cos t?^ = 2M cos ^ (VII-23) tk m a a 2d From (VII-23) it is clear that 2B = I- f 2M cos ^ dy (VII-24) 2-layer may be less than a thousandth of an inch thick. Static Characteristics A great deal of information about the low frequency performance of a transistor can be obtained from a set of static characteristics such as those shown in Fig. 4. Curves of this sort, are obtained simply by connecting suit- Fig. 2 — A beaded n-p-n transistor. EMITTER — *► /^ X -* — COLLECTOR Fig. 3 — The symbol for a p-type transistor on which the convention of signs for cur- rents and voltages is indicated, able current sources to the emitter and collector circuits of the transistor and measuring the resulting voltages. The currents are called positive when they flow into the emitter and collector as shown and the voltages are called positive when they have the signs shown in Fig. 3. Let us first examine these curves with an eye to finding out what kind of voltage and current supplies are needed to bias the transistor into the range in which it can amplify. To make this easy, that part of the characteristics which lies within the normal operating range has been shown as solid lines and that part of the characteristics corresponding to cutoff has been shown as dotted lines. PROPERTIES AND APPLICATIONS OF n-/>-« TRANSISTORS 533 Note from the upper set of curves that Ve is positive in the operating range. This means that the collector must be biased positive with respect to the 35 30 25 20 10 0 0.15 0.10 0.05 -0.05 -0.10 ■0.15 ■0.20 I.- 0 MA. r< -1.0 \ -1.5 -2.0 \ -2.5 \ -3.0 -3.5 -4.0 -4.5. -5.0, \ N N ' ti J Ie = 0 MA. -0.5 -1.5 -2.0 -3.01 -3.51 -4.0f "i -5.0/ 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Ic IN MILLIAMPERES Fig. 4 — Static characteristics of an n-p-n transistor. 5.0 base. For this particular transistor a bias voltage anywhere between about 0.1 volts and 35 volts is suitable. Note also that all the curves on this plot correspond to negative emitter currents. This means that the emitter must 534 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 be biased in such a way that current flows out of the emitter into a suitable current supply. Furthermore, the collector current corresponding to any given emitter current can be seen to be almost equal in magnitude to the emitter current. Since these two currents are opposite in sign, this means that most of the current which flows into the collector leaves by way of the emitter with the result that the current in the base circuit is very small. Suppose that the collector is held at a constant positive voltage as, for example, by connecting a battery between collector and base (with a trans- former winding in series, perhaps). Now if a negative current is forced into the emitter by a battery and resistance connected in series between emitter and base, the collector current can be controlled by varying the emitter current and will always be approximately equal in magnitude to the emitter current. Suitable collector currents for this particular transistor range from about 20 microamperes to about five milliamperes. The exact choice of collector current and voltage within the ranges men- tioned above will be dictated largely by the amount of power output re- quired. The more power output required, the more current and voltage will be needed from the power supply. Since the collector circuit efficiency can- not exceed the theoretical limit of 50% in Class A operation, the signal power output cannot exceed half the power supplied by the battery. This means, for example, that if the collector is worked at 20 volts and 2 milli- amperes the Class A power output cannot exceed 20 milliwatts. From the lower plot of Fig. 4 it is possible to obtain information about the bias voltage required for the emitter. Note, first, that the entire emitter voltage plot corresponds to a very small range of emitter voltages near zero and, furthermore, that the part of the characteristics corresponding to the operating range covers only a few thousandths of a volt. This means that if the collector voltage is held constant very small changes in emitter volt- age will produce fairly large changes in collector current, or if the collector current is held constant very small changes in emitter voltage will produce relatively enormous changes in collector voltage. This at once suggests the use of this transistor as a d-c. amplifier between a low impedance source and a high impedance load. In this application, voltage stepup of the order of 10,000 times is possible. The very great sensitivity of the collector circuit to emitter voltage sug- gests, however, that for a-c. ampHfiers one should use a current source as an emitter bias supply. This can be obtained from a battery and a large resistance in series. Furthermore, since the emitter voltage is always nearly zero, the emitter current can be calculated in advance by dividing the bat- tery voltage by the value of the series resistance (provided, of course, that PROPERTIES AND APPLICATIONS OF fl-p-fl TRANSISTORS 535 the supply voltage is large compared to the few hundredths of a volt drop across the emitter circuit). One can also draw some interesting conclusions from the static charac- teristics about the large signal operation of the transistor. If the load is resistive, the instantaneous operating point will swing up and down along a straight line such as the load line shown in the upper plot of Fig. 4. This par- ticular load line corresponds to an a-c. load resistance of 10,000 ohms. Suppose that the steady collector biases are 20 volts and 2 milliamperes so that the drain from the power supply is 40 milliwatts. Now consider the permissible swings of collector voltage and current. Since the collector char- acteristics are quite straight and evenly spaced over a wide range of cur- rent and voltage values, the output signal can swing nearly down to zero collector volts and nearly up to zero collector current without distortion. The limit on the lower end is imposed by the fact that the collector charac- teristics begin to be curved when Vc is less than about 0.1 volts; and the limit on the upper end is imposed by the fact that the collector current does not drop completely to zero when le drops to zero. The lower limit of collector current is, in this case, about 50 microamperes and, since this amount of current in 10,000 ohms corresponds to 0.5 volts, this means that the instan- taneous collector voltage is limited to swings between 39.5 volts and 0.1 volts. Starting from a quiescent value of 20 volts, the permissible positive swing is then 19.5 volts and the permissible negative swing is 19.9 volts. Reducing the quiescent voltage to 19.8 volts (and keeping the same load line) makes it possible to obtain a peak swing of 19.7 volts which corre- sponds to 19.45 milliwatts of signal delivered to the load. This gives a col- lector circuit efficiency of 48.5% out of a possible 50%. Some transistors take even less collector current when the emitter current is zero and hence permit even higher efficiencies. These computations of efficiency have all been based on the assumption of sinusoidal current applied to the emitter. It will be shown in a later sec- tion that the emitter resistance varies with emitter current, however, and this means that to realize high efficiency with low distortion it is necessary to drive the emitter from a high impedance source. Operation with Small Power Consumption For small signal applications the transistor represented by the charac- teristics of Fig. 4 can deliver useful gain at very much lower voltages and currents than those used in the example above. In order to show this, the characteristics of Fig. 5 have been plotted for a range of collector voltage extending up to only 2 volts and for a range of collector currents extending 536 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 2.0 1.8 — 1.6 — 1.4 1.2 1.0 0.8 0.6 0.2 Q. — < II V \ \ \ \ u \ o lO 1 o 8 1 O T t \ \ \ \ \ \ \ \ 1 \ \ \ /ZWATT \ \, s ^^ \ ^5; 3 ^ ^^**- "^ \ » 10 //WATl r ■■~-~ — - J .J V r~ 7 -/■ -J- r^ . ■=.'=.=.'^ 0.12 Ie=O^AMP 0.10 / / 0.08 1 1 1 0.06 i > ' 0.02 / -25 ,' >" 0 ,-50 -ao2 y-75 ' -100 -125 * -0.06 -150 '-175 -0.08 0 20 40 60 80 100 120 140 160 180 200 Ic IN MICROAMPERES Fig. 5 — Static characteristics showing behavior at very low applied voltages and currents. PROPERTIES AND APPLICATIONS OF fl-p-U TRANSISTORS 537 up to only 200 microamperes. It can be seen from the upper plot that the collector circuit characteristics are still quite usefully straight and evenly spaced in this micro-power range. In fact, for small signal operation it is sufficient to use a collector voltage only a httle in excess of 0.1 volts and a collector current a little in excess of 20 microamperes. This means that the power required to bias the collector into the operating range amounts to only a few microwatts. Contours are shown for 10, 50, and 100 microwatts of power supply. This ability of the transistor to work with extremely small power con- sumption is one of its most striking and perhaps most important features Fig. 6 — The low-frequency equivalent circuit of a transistor. When one considers that the total power consumption of a single transistor stage can be smaller by many thousands of times than the power required to heat the cathode in a vacuum tube, it is obvious that the advent of this device will make possible many new kinds of application. Variation of Transistor Properties with Operating Point Ryder and Kircher^ have shown that it is convenient to analyze the small signal properties of a transistor at low frequencies in terms of the equivalent circuit of Fig. 6 where re is called the emitter resistance, rt is called the base resistance, and r<. is called the collector resistance. The in- ternal generator, tmie , is the active part of the circuit and in this respect corresponds to the familiar fxCg of vacuum tube circuit theory. It is the purpose of this section to show what values these quantities have for a particular n-p-n transistor and to show how they vary with the applied biases. This will form a basis for the next section in which these quantities will be used to compute such things as the input and output impedances and the gains of various transistor connections. Ryder and Kircher have shown that these four r's can be obtained di- rectly from static characteristics such as those shown in Fig. 4 and Fig, 5. In the case of n-p-n transistors, however, the magnitudes of these quan- tities are such that it is difficult to obtain satisfactory accuracy in this way and it has been more convenient to measure the 4-pole r's by a-c. methods. 538 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 These measurements have shown that all of the r's are, to a first approxi- mation, independent of collector voltage so long as the collector voltage is above a few tenths of a volt and so long as the total dissipation is small enough to prevent appreciable heating of the transistor. In view of this fact it is perhaps sufficient to show how these quantities vary with emitter current for a moderate fixed value of collector voltage. Figures 7 and 8 show that Yc and r^ are very nearly equal and that they tend to decrease as /« increases. Theoretically Ym. and Yc should both be infinite. The fact that they reach values as low as 10 megohms in this case is a meas- 28 24 20 O 16 O UJ ? »2 TRANSISTOR NO. 1 Vc = 4.5 VOLTS ^ 1 \ \ ^^ . 0 -0.2 -0.4 -0.6 -0.8 -1.0 -1.2 -t.4 -1.6 -l.t le IN MILLIAMPERES ■2.0 Fig. 7 — The variation of collector resistance with emitter current at a fixed value of collector voltage. ure of the imperfection in technique of fabricating the transistor. Values as high as 60 megohms have been achieved in the laboratory. Figure 9 shows that Yh in this transistor is approximately 240 ohms and is independent of /« . Figure 10 shows that Ye decreases with increasing emitter current, ranging from about 500 ohms at 50 microamperes down to about 5 ohms at 5 milliamperes. Shockley'* has shown that r « should be given by fe = 9/. (1) where q is the charge on an electron, k is Boltzman's constant, T is the Kelvin temperature and /« is the emitter current. When the temperature PROPERTIES AND APPLICATIONS OF U-p-U TRANSISTORS 539 2^ 20 1 16 I O o ^'2 ^^ \ TRANSISTOR N0.1 Vc = 4.5 VOLTS K ^ ^ **""^ 0 -0.2 -0.4 -0.6 -0.8 -I.O -1.2 -1.4 -1.6 -1.8 -2.0 le IN MILLIAMPERES Fig. 8— Variation of r^ with emitter current at fixed collector voltage. 280 240 200 160 120 80 40 < o TRANSISTOR NO. 1 Vc = 4.5 VOLTS ■0.2 -0.4 -0.6 -0.8 -1.0 -1.2 -1,4 le IN MILLIAMPERES ■1.8 -2.0 Fig. 9 — Variation of base resistance with emitter current. Scatter of the data indicates that the measurements were not accurate. is about 80° F., this reduces to fe = 25.9 le (2) where /« is measured in milliamperes. Within experiment error, values of Ye computed from this relation agree perfectly with the measured curve shown in Fig. 10. 540 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 Figure 11 introduces a new quantity, a, the current amplification factor of the transistor. This quantity is defined by the equation Tm + n Tc + n (3) Since rm and Tc are both very large compared to rj, , a is approximately equal to the ratio of fm, to Tc . It will be shown in a later section that this quantity is important in determining some of the circuit properties of the transistor and that many of the circuit properties become more desirable as a ap- proaches unity. 800 700 600 500 400 300 200 n TRANSISTOR NO. 1 Vc = 4.5 VOLTS \ \ V "^ ^ ' j, 0 -0.2 -0,4 -0.6 -0.8 -1.0 -1.2 -1.4 -1.6 -1.8 -2.0 le IN MILLIAMPERES Fig. 10 — The emitter resistance is inversely proportional to emitter current. It can be seen from Fig. 1 1 that in this transistor a is approximately equal to 0.98 and that it increases slightly with increasing emitter current. The highest value of a so far achieved is 0.9965. Those units which have been made in the laboratory so far show consid- erable variation in some of the properties, but this is partly due to the fact that changes have been made deliberately to test one aspect or another of Shockley's theory. The data in table I are presented to indicate what properties have been achieved to date. The collector capacitance Cc will be discussed in a later section. General Considerations and Formulae It is a consequence of the fact that a is always less than unity in this structure that these transistors are unconditionally stable with all termina- PROPERTIES AND APPLICATIONS OF fl-p-fl TRANSISTORS 541 tions. This means that stabiUty considerations do not prevent working with matched terminations. Furthermore it is possible to obtain a variety of input and output impedances by connecting the transistor as a grounded- emitter, grounded-base, or grounded-collector stage. It is the purpose of this section to give some idea of the characteristics of these various stages and to show in each case at least one way of supplying the required biases and couplings to the stage. Ja 1.00 qT o y 0.96 o u. li 0.94 Q. < I- 0.92 Z lU cc § 0.90 O ( >^ '-- ? TRANSISTOR NO. 1 Vc = 4.5 VOLTS -0.2 -0.4 -0.6 -0.8 -1.0 -1.2 -1.4 le IN MILLIAMPERES -1.6 Fig. 11 — The current amplification factor, a, increases slightly with increasing emitter current. Note the expanded scale for a. Table I Constants for Various Transistors Measured at Ve = 4.5 v., /« = 1.0 ma. Transistor No. I II III IV v r« (ohms) 25.9 31.6 33.1 30.2 38.8 fb (ohms) 240 44 300 3070 180 fe (megohms) 13.4 • 0.626 1.11 1.21 2.00 fc - - fm (megohms) 0.288 0.00387 0.0168 0.00422 0.0439 a 0.9785 0.9936 0.9848 0.9965 0.9780 Co (/*Mf-) 7 7.7 18.9 27.9 21.2 It will be convenient to begin by writing down general relationships which will apply to all the possible connections. To this end let the transistor be represented by the box in Fig. 12. At low frequencies, the signal currents and voltages are related through the equations: Riiii + Rnii = Vi (4) If a generator of open circuit voltage v^ and internal resistance Rg is connected to the input terminals of the device as shown in Fig. 13, then Vi = V. iiRc (5) 542 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 and if a load of resistance Rl is connected to the output terminals V2 = — -Kl^*2 . The equations for the circuit of Fig. 13 are, therefore, {Rn + Rg)ii + Rui2 = v^ R2iii + (R22 + RL)i2 = 0 Solving for the voltage developed across the load (= —RlIx) gives Rl R21 V2 = (Rn + Rg){R22 + Rl) — R12R2 (6) (7) (8) Li 3-TERMINAL NETWORK J^ + REPRESENTING TRANSISTOR V, Fig. 12 — A three-terminal network representing either grounded emitter, grounded base, or grounded collector connection of a transistor. Note the convention of signs. 3-TERMINAL NETWORK REPRESENTING TRANSISTOR L2 Rl ^=-A/\An V2 Fig. 13 — The three-terminal network of Fig. 12 connected between a generator and a load. The power gain in the circuit is the power delivered to the load (vI/Rl) divided by the power available from the generator {i^g/4Rg). From equation (8), this gives G = 4i?oi?jr,i?21 [{Rn + Rg)(R22-h Rl) - R12R21V (9) The gain depends on Rg and Rl and will be maximum when these are chosen to match the input and output impedances of the transistor stage. But the input impedance depends on Rl and the output impedance de- pends on Rg in the following way: Input impedance = Ri = i^n — ^ ^^ '^L and Output impedance = Ro = R22 R22 + Rl Rn R21 Rn + Ro (10) (11) PROPERTIES AND APPLICATIONS OF fl-p-fl TRANSISTORS 543 If Ri = Rg and Ro = Rl then impedances are matched at the input and output terminals and the gain is a maximum. The conditions are: Matched input impedance = Rim = Rn Vl - Ri2R2i/RnRr2 , (12) Matched output impedance = Rom — R22 V 1 — Rl2R2\/ R11R22 ) (1^) Maximum available gain = ^•^•^' " R^2 [1 + \/T^=^2i?2l/i?lli?22l' ^^^^ The Grounded Base Stage In this and the following two sections we will put into equations (7) through (14) the appropriate 4-pole r's to obtain expressions for impedances and gains. As a numerical example we will substitute into the resulting equa- tions the measured values of these r's for Transistor No. I working at V ^ = 4.5v. and /c = 1 ma'. It must be understood that the numerical values may vary appreciably from transistor to transistor and that these numerical calculations are intended only for illustration and not as a basis for final circuit design. The numerical values to be used are Te = 25.9 ohms rb = 240 ohms re = 13.4 (10)« ohms (15) re- rm = 0.288 (10)« ohms a = 0.9785 In this section it will be shown that the grounded base connection is suitable for working between a low impedance source and a high impedance load. The input impedance may be of the order of a hundred ohms and the output impedance of the order of one or more megohms. In this connection the current amplification is always less than unity but the voltage amplifica- tion may be very large indeed. Power gains of the order of 40 to 50 db can be obtained between matched impedances, and appreciable gains can still be obtained if the load resistance is reduced to a few thousand ohms (be- cause the current gain is then almost equal to unity). In this case the gain of the stage is almost completely independent of those transistor properties 544 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 which tend to vary from unit to unit. This sort of stage does not produce a phase reversal. >2 hu) + V, (16) Fig. 14 — The grounded base connection of a transistor. For the grounded base stage shown in Fig. 14, Rii = re + n =" 266 ohms Rn = n = 240 ohms R-Li = rm-\- n = 13.1 (10)^ ohms R22 -= rc-{- n^ 13.4 (10)^ ohms a = — u + n = 0.9785 In this case if rt is neglected by comparison with r^ and fe , equation (8) leads to V2 = uRlVq (re + rft + Rg){\ + Rl/tc) - art (17) Since for these transistors — {=a) is always less than unity, the output r« voltage is in phase with the input voltage. Furthermore, if Rl is very high, the output voltage is enormous by comparison with the input voltage. For •example, ii Rg = 0 and Rl is infinite V2 = v. "re-\-n and for the numerical example this is V2 = 4.93 (10)* Vfl. (18) PROPERTIES AND APPLICATIONS OF n-p-fl TRANSISTORS 545 To achieve this step-up would require a load impedance very large com- pared to 13 megohms, but even with more modest values of load impedance the voltage step-up is large. If Rl is small compared to Tc , the second of equations (7) leads to (19) = —ii and the current delivered to the load is approximately equal to the current which the generator delivers to the transistor. From equations (10) and (11), the input and output impedances are R< = r. + r. - '•^1%+:^^ (20) i?, = r. + r. - ''t" Vi (21) Te -r n -{- Rg As the load impedance varies from zero to infinity, the input impedance varies from Ri = re-\-n\\- 'i^L+J}] for R^ = 0 ^u + n{l - a) ^^^^ = 31.1 ohm to R. = re + Tb = 266 ohms for Rl= ^. (23) When Rg = 0, the output impedance is Ro = U- -^ (fm - fe) (24) Te -f- n Te + n (25) = 1.56 (10)' ohms. As Rg increases to infinity Ro= rc-\-H= 13.4 (10)« ohms. (26) 546 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 From equations (12) and (13), the matched input and output impedances are approximately Rim = (re + n) \/l — an/ (re + n) = 91 ohms (27) (28) Rom = (fc + fb) Vl — arb/(re + ri) = 4.58(10)« ohms. With matched impedances, the maximum available gain is M.A.G. = ^^'"^ + ''^ [1 + Vl - an/ire + n)]-' , , ^e + n (29) = 2.7 (10)' or 44.3 db. The matched output impedance of this stage is inconveniently high but a useful amount of gain can be maintained if Rl is reduced to a more rea- \fr- Fig. 15 — One practical arrangement of a grounded base amplifier stage. sonable value. For example, if Rl = 200,000 and Ry = 25, equation (9) gives G = 5.3 (10)3 or 37.2 db. If stages of this sort are to be cascaded, a step-down transformer must be used to couple each collector to the following emitter. Otherwise, since the current amplification factor of the transistor is slightly less than unity, the gain per stage will also be slightly less than unity. One practical arrangement of a grounded base stage would be as shown in Fig. 15. The required value of R will be approximately li = ^' (30) where h is the desired collector current and Ebi is the voltage of the emitter- bias battery. For operating at /c = 1 ma, for example, £«i = 1.5 v and R = 1500 ohms would be suitable. PROPERTIES AND APPLICATIONS OF n-p-tl TRANSISTORS 547 The Grounded Emitter Stage For many applications the grounded emitter connection is more desirable than either of the other two. The power gains which can be obtained are high — of the order of 50 db — and the interstage coupling problem is sim- plified by the fact that the input impedance is somewhat higher than that of the grounded base stage while the output impedance is very much lower. The input impedance may be of the order of a few hundred ohms and the output impedance of the order of a few hundred thousand ohms. Both volt- age and current amplification are produced (with a phase reversal) and gains of the order of 30 db or more per stage can be obtained without the i^mLe Fig, 16 — The grounded emitter connection of a transistor and the equivalent circuit use of interstage coupling transformers. The input and output impedance- depend very critically on a and may vary appreciably from unit to unit For this connection, which is indicated schematically in Fig. 16, -^11 = Te -\- Tb = 266 ohms ^12 = Te = 25.9 ohms i?2i = Te- rm= -13.1 (10)« ohms R22 = re-\- Tc- rm = 0.288 (10)« ohms (31) Putting these values into equation (8) shows v^ is always opposite in sign compared with Vg , that is, that the grounded emitter stage produces a phase reversal as does the grounded cathode vacuum tube. If Rl is infinite and Rn = 0 V2 = r, Te — r„ = -4.93 (10)' V, 548 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 which is the same as for the grounded base stage. But if i?i, = 0 k = '?"""' ti (32) r^ + re — r^ 1 - « (33) = 45.5 ii. Thus it is seen that the grounded emitter amplifier can produce quite appreciable current amplification — particularly so when a approaches unity. The input impedance to the stage is Ri ==r.-hn+ ^-eCr^ " 'i p ♦ (34) re -{- fc - rm + Rl When Rl = 0 this reduces to R^ = n-\- Te (35) - rb+ Te 1 - « (36) = 1440 ohms. As Rl increases to infinity, the input impedance decreases to r« + n which, for the numerical example, is 266 ohms. The output impedance is Ro ^re+r.-r„.+ '^^" ~_[\ (37) re -{- n + Rg When Rg — 0, this gives Ro = r,- -^ {rm - rj (38) re + rb L re-\- rb A = 1.56 (10)' ohms As Rg increases to infinity, Ro decreases to Ro = re -\- re — rm = 0.288 (10)' ohms. (39) (40) PROPERTIES AND APPLICATIONS OF fl-p-fl TRANSISTORS 549 The matched input and output impedances are Rim = (re + rt) Vl + re(rm - u)l{r, -f n){u ^U- r^) (41) = 619 ohms and Rom = ir, + re - Trr) Vl + uir^ - re)/{r, + n){re + U - r^) (42) = 0.671 (10)6 ohms As a increases toward unity the matched input impedance increases and the matched output impedance decreases. They approach the limits I Rim = Vin + TcKre + n) (43) Rom = re V{n+rc)/{re-hH) (44) as a — ^ 1. I If fm in the transistor of our numerical examples could be increased to exactly the value of r^ (a = 1) then the matched impedances would be Rim = 59,700 ohms Rom= 5,800 ohms From this example, it is seen that the impedances vary rapidly with a as a approaches unity. With matched impedances, the maximum available gain from the grounded emitter stage is M.A.G. = v('+;)(^--?) +v''+^t:+'-?)] -2 (45) = 2.02 {lOy or 53 db When a is exactly unity this expression reduces to fc/re provided r^ and n are small compared with Tc . For values of a which are enough smaller than unity so that -' « 1 - a re the expression for maximum available gain reduces to the approximate expression M.A.G. = a(r„/r.) [,^(1 - „) 1' + j/i + (i - „) L»] ' (46) 550 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 From the above equations it can be seen that gain does not increase rapidly with a when a is sufficiently near unity. In the case of our numerical example, increasing a from 0.9785 to unity increases the gain by only 4.1 db. The gain of the stage is approximately proportional to Tc and inversely proportional to r^ and can therefore be increased by operating at higher emitter currents or by fabricating the transistor in such a way as to obtain higher values of tc . In the latter case it would be desirable also to increase a in order to keep the output impedance from becoming unreasonably high. It has been seen that, for the case of our numerical example, the matched output impedance is large compared to the input impedance (671,000 ohms compared to 619 ohms). This means that if the maximum available gain is to be obtained in cascaded stages, step-down interstage transformers must be used. But an appreciable amount of gain can be obtained without inter- stage impedance matching. This is because of the short-circuit current amplification previously mentioned which amounts approximately to 1 - a or 45.5 times in the case of our numerical example. For this transistor, then, the iterative gain per stage without impedance transformation would be 33.2 db. This gain increases very rapidly as a approaches unity, not only because the short-circuit current amplification increases, but also because the output impedance decreases and the input impedance increases so that a better interstage impedance match is obtained. From equations (41) and (42), it is seen that the matched input and output impedances are equal when fe — rm — fb or when 1-. re + n In this case the gain per stage would be approximately rc/fg . This says that if fm could be increased in the numerical example until a = 0.999821 the gain per stage (without impedance transformation) would be increased to 57.1 db. Values of a this near to unity have not even been approached in transistors made to date. This unrealistic example is included only to indi- cate one of the reasons for seeking to make a very near unity. Consider next one possible way of supplying biases to a grounded emitter PROPERTIES AND APPLICATIONS OF fl-p-fl TRANSISTORS 551 stage. Suppose that the collector is connected through a transformer winding to a fixed voltage supply as indicated in Fig. 17. Since Ve is always a very small fraction of a volt (see Fig. 4 and Fig. 5) the collector voltage will be approximately equal to the supply voltage. If no d-c. connection is supplied to the base, it will float at a potential above ground equal (in magnitude) to Ve — i.e., a very small fraction of a volt — and the collector current will be exactly equal to the emitter current. To find out approximately what this value of the current will be, consider the upper set of static characteristics in Fig. 5. Note that, when the emitter current is zero, the collector current is of the order of 20 microamperes (the exact value varies from 1 to 30 micro- amperes in transistors tested so far). The collector current is then of the order of 20 microamperes greater than the emitter current. If the emitter current is now increased by Ale , the collector current will increase by aAIe . That is, the increments of collector current will be slightly smaller than the incre- Fig. 17 — One practical arrangement of a grounded emitter stage. ments of emitter current and, as the emitter current is increased, the emitter and collector currents will become more nearly equal. If a were perfectly constant they would become exactly equal when /. = /c = ^-^ (47) 1 — a where Ico is the collector current which flows when the emitter current is zero. Equation (47), then, gives the value of emitter (and collector) current which will flow in a grounded emitter stage if no d-c. connection is made to the base. This current varies rapidly with a. For the transistor which has been considered numerically, this current would amount to about 465 micro- amperes which is certainly within the range of suitable values for the transistor. In certain low level applications, however, it might be desirable to work at a smaller current for the sake of decreasing battery power con- sumption. This requires that a small current be drawn out of the base. The required current is small because the collector current will decrease by 1/(1 — a) microamperes for each microampere drawn from the base. One method of obtaining this base current is to provide a resistive path between 552 THE BELL SYSTEM TECHNICAL JOXJRNAL, JULY 1951 base and ground as shown, for example, in Fig, 18. Since the base floats at a positive potential with respect to ground, this circuit produces a base current of the right sign to decrease the collector current. As the value of the series resistance is decreased to zero, the collector current decreases to Fig, 18 — Modification of Fig. 17 to obtain lower collector current. Fig. 19 — Modification of Fig. 17 to obtain higher collector current. Fig. 20^ A Iwo-stage grounded emitter amplifier which produces approximately 90 db power gain is shown on the right and a micro-power audio oscillator is shown on the left. a value corresponding to zero emitter voltage. A still further decrease in collector current can be obtained by inserting resistance between emitter and ground. In order to increase the collector current to values higher than that cor- responding to zero base current, a high resistance path between base and the positive supply voltage may be used as shown in Fig. 19. In this case the PROPERTIES AND APPLICATIONS OF fl-p-n TRANSISTORS 553 collector current will increase by 1/(1 — a) microamperes for each micror ampere which flows through the bias resistor. Since the current in the bias resistor will be approximately Eb/R, it is a simple matter to compute the required value of bias resistor once the desired collector current is known. Figure 20 shows a two-stage audio amplifier which gives approximately 90 db gain. The circuit is shown in Fig. 21. Fig. 21 — Circuit of the amplifier shown in Fig. 20. Fig. 22 — The grounded collector connection of a transistor and the equivalent circuit. The Grounded- Collector Stage Although the power gain obtainable from this connection is relatively low — of the order of 15 or 20 db — it has very interesting possibilities in producing very high input impedances or very low output impedances. If it is worked into a fairly high load impedance, the input impedance may be several megohms, or if it is worked from a source of moderately low impedance (a few thousand ohms), the output impedance may be of the order of 25 ohms or lower. For this type of stage, which is shown schematically in Fig. 22, i?ii = n-}- rc= ISA {lOy ohms Ri2 = Tc- Tm = 0.288 (10)6 ohms R21 = rc= 13.4 (10)6 ohms R22 = re-\- fc- fm = 0.288 (10)6 ohms (48) 554 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 If this stage is worked from a zero impedance generator into an infinite impedance load (49) and so, like a cathode follower, it gives an output voltage which is less than the input voltage, but in the same phase. K the stage is operated into a short circuit k = -ix — -^ (50) /•e + ^c — r^ 1 = — n -. 1 - « (51) = -46.5 ix which indicates that the stage can give an appreciable current gain. The input impedance is ^^-n+r.- /f ' -/"_[ (52) When Rl = 0, this reduces to Ri = n+ fe (53) - n-\- Te 1 - a = 1445 ohms. When Rl is infinite Ri = n-\- To = 13.4(10)« ohms. (54) (55) With respect to input impedance, the grounded collector stage is again seen to be like a cathode follower in that the input impedance is high when the load impedance is high. The output impedance is /?. = r. + r. - r„ - ^'^° ~ !"], (56) PROPERTIES AND APPLICATIONS OF fl-p-fl TRANSISTORS 555 For Rg = 0, this reduces to Ro=^u^-n^^ (57) (58) (59) - Te -{- n {i — a) = 31.1 ohms. For Kg infinite Ro=re-\-rc — fm = 0.288(10)« ohms. The matched input impedance is Ri« = (n + re) a/-^ + , ,,J:\, -i (60) = Vre[rt + r./(l - a)] = 139,000 ohms. The matched output impedance is (61) Rom — {re -{- fc — fm) A/ , f" 7 j v. " 1 T V n+ re {rb + re) (r^ + re - r„) = (!-«) Vrc[r6 + rj{\ - a)] = 2990 ohms. (62) (63) With matched impedance, the maximum available gain of the grounded collector stage is (r5 + re){re + fc - r^) M.A.G. = =— (64) L^ "^ T '^TTTc "^ (r6+ re)irl+ r, - rjj As a approaches unity, this approaches approximately M.A.G. = Te/^fe (65) but so long as re <3C re — r,„ , a good approximation is M.A.G. = 1/(1 - a) (66) = 46.5 or 16.7 db. 556 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 The considerations involved in supplying biases to a grounded collector stage are rather similar to those discussed already for the grounded emitter case. If the base is allowed to float, the collector current will be given ap- proximately by equation (47) as discussed for the grounded emitter case. A resistance between base and the negative side of the supply battery in Fig. 24 will serve to decrease the collector current while a resistance between base and ground will serve to increase it. In applications where it is deiired to make full use of the high input impedance which this stage can afford, it may be most desirable to let the base float as shown in Fig. 23. Fig. 23 — One practical arrangement of a grounded collector stage. Fig. 24 — Modification of Fig. 23 to obtain lower collector current. To raise collector current remove the resistance shown and connect a high resistance between base and ground. Frequency Response — General Remarks Shockley has shown that there are several different physical considera- tions which lead one to expect a high-frequency cutoff in the response of n-p-n transistors. The frequency at which cutoff occurs depends in a theoreti- cally understandable way on such things as the geometry of the transistor and the physical properties of the germanium from which it is made. If these factors could all be controlled and varied at will, it would be possible to design a transistor to have a specified cutoff frequency. One limitation comes about in the following way: In order to produce transistor action, the electrons which are injected into the p layer at the emitter junction must travel across this thin layer and arrive at the collector junction. They do this principally by a process of diffusion and require a finite (but small) amount of time to make the journey. If this time were I PROPERTIES AND APPLICATIONS OF W-/)-W TRANSISTORS 557 exactly the same for all electrons, the effect would be simply to delay the output signal with respect to the input and there would be no effect on fre- quency response. But there is a certain amount of dispersion in transit time which means that the electrons corresponding to a particlar part of the input signal wave do not all arrive simultaneously at the collector. When this difference in time of arrival amounts to an appreciable part of a cycle there is a tendency for some of the electrons to cancel the effect of others so that the frequency response begins to fall off. As the signal frequency increases beyond this point, the effect becomes more and more pronounced and the response continues to fall with increasing frequency. In terms of the equivalent circuit, this dispersion in transit time means that beyond a certain frequency, r^ (and hence a) begins to decrease with increasing frequency and so the transistor may be said to have a certain a-cutoff which we will call fca ■ Shockley has shown that fca is inversely proportional to the square of the />-layer thickness and hence increases rapidly as the p layer is made thinner. For n-p-n transistors now available, this cutoff should occur at fre- quencies between five and twenty megacycles. Another limitation on frequency response comes about from the fact that, at sufficiently high frequencies, the emitter junction fails to behave as a pure resistance and is, in effect, shunted by a capacitance. In terms of the equiva- lent circuit, this means that r^ is shunted by a capacitance. The effect which this has on frequency response can be reduced by re- ducing the impedance of the source from which the emitter is driven. But so far as the emitter junction is concerned, r^ is always in series with the source impedance and so it is the value of ri, which ultimately determines the emitter cutoff frequency. This capacitative reactance should begin to become appreciable with re- spect to emitter resistance at a frequency which may be of the same order as /ca . If Th is high, the emitter cutoff frequency /c<, will then be of the same order of magnitude as fca and will increase as r^ is decreased. A third cause for limited frequency response is the capacitance of the collector junction. The w-type germanium on one side of the junction be- haves as one plate of a parallel-plate condenser and the />-type germanium on the other side behaves as the other plate. Since the transition from n to p type germanium may be made in an exceedingly small fraction of an inch, the plates of the condenser are very closely spaced and the capacitance may be appreciable. Collector capacitance also depends on collector voltage, decreasing with increasing voltage. Theoretically, the capacitance should be in proportion to the negative one-third power of Vc . 558 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 15.0 10.0 9.0 8.0 7.0 \ TRANSISTOR NO. 1 Ic = 1.0 MILLIAMPERES \ \ \ ^ \ \ \ V \ V \ \ \ 6.0 in 5.0 !: o > 4.0 z 3.0 2.5 2.0 1.5 3 4 5 6 7 8 9 10 15 20 25 30 Cc IN MICRO-MICROFARADS Fig. 25 — Collector capacitance decreases as collector voltage is increased. ^A^ — r a. ■AM/ — (3^ Fig. 26 — The equivalent circuit of a transistor with collector capacitance shown. re Fig. 27 — The effect of collector capacitance is to change r,« and Tc to Vm and r'c See equations (67) and (68). Figure 25 shows measured values of Ce as a function of collector voltage. For rfasons which are not understood at present, these data show a de- parture from the usual inverse one- third power variation. At Vc = 4.5 volts PROPERTIES AND APPLICATIONS OF fl-p-n TRANSISTORS 559 the capacitance is seen to be approximately 7 micro-microfarads. In terms of the equivalent circuit, this capacitance is in shunt with the series combina- tion of fc and the generator, fmie , as shown in Fig. 26. This can be shown to be equivalent to the circuit of Fig. 27 in which Tc has been replaced by r/ = rc/(l + jCcTcOi) (67) and fm has been replaced by rL = rj{\ + jCcTcOj). (68) The effect of collector capacitance can be computed by substituting Tc and Ym for the values of r^ and Tc (implicitly contained) in equation (8). In the sections which follow, this will be done for each of the three transistor connections and the resulting collector cutoff frequencies jcc will be com- puted. It will be shown that at least for the transistor on which data are pre- sented collector capacitance tends to produce a cutoff frequency well below those to be expected from emitter cutoff or alpha cutoff. For this reason, only collector cutoff will be considered. Collector Cutoff in the Grounded Base Stage If the values of Tc and Tm from equations (67) and (68) are substituted for Tr. and Tm in equations (16) and the resulting values of the i?'s are sub- stituted into equation (8), the result is "''^"'^ ^ (re -\-H-\- R,)[\ -f k(l + icoC.r,)/rJ ^^^^ The cutoff frequency fc: is defined as the frequency at which the voltage across the load has dropped 3 db compared to its low-frequency value. This is the frequency at which the imaginary part of the denominator of (69) is equal to the real part. Solving for fee gives f =-^[1 + 1 I (70) i?L(re + r6+i?a). Substituting into this equation Cc = 7(lO)-i2 farad, numerical values of the r's from (16), and the values Rg = 91 and Rl = 4.58 (10)« ohms, cor- responding to maximum available gain gives /,, = 3390 cps. With these terminations, the low-frequency gain is 44.3 db. If Rg and Rl are reduced to 25 and 200,000 ohms, respectively, fee is raised to 23,500 cps and the gain is lowered to 37.2 db. A further reduction of Rl to 20,000 ohms increases /cc to 0.22 megacycles and reduces the gain to 27.8 db. This corre- 560 THE BELL SYSTEM TECHNICAL JOURNAL, JXJLY 1951 sponds to a gain-bandwidth product of 1.2(10)^ cps and shows that useful gain could be obtained at frequencies well above a megacycle, provided alpha and emitter cutoffs did not interfere. Collector Cutoff in the Grounded-Emitter Stage The procedure described in the last section leads, in this case, to "'^"'~'r.+ {n + R,){l-rJr.) ^^^^ + IreRL/rc + in + R,){re + i^JAcld + JTcCcCc) For the transistor of our numerical example, the imaginary term in the numerator is completely neghgible at frequencies below (10)^ cps. Neglecting it leads to r ^ J_ 1 + Rl/tc + [{n -f- Ra)/re][l - {rm - re - RL)/re\ ,^2) •^'^'^ 2irCe Rl + [{n + Ra)/re](re + Rl) In this case the values of Rg and 7^^ (619 ohms and 671,000 ohms respec- tively) which correspond to maximum available gain give fee = 3740 cps and M.A.G. = 53 db. Reducing R^ to 100,000 and increasing Rg to 1000 ohms gives fee = 11,120 cps G = 50 db. For Rg = 1000 ind Rl = 10,000, fee = 97,900 cps G = 41.3 db. and for Rg = R^ = 1000 ohms, fee = 943,000 cps G = 31.4 db. The gain-bandwidth product for this stage is 1.3(10)^ cps as compared to 1.2(10)* cps for the same transistor connected as a grounded base amplifier. It should be pointed out, however, that this stage is particularly sensitive to change in a and on this account alpha cutoff may influence the response at fairly low frequencies. For example, when the terminating resistances are both 1000 ohms, reducing a from 0.9785 to 0.900 reduces the gain from 31.4 db to 0.2 db. PROPERTIES AND APPLICATIONS OF H-p-H TRANSISTORS 561 Collector Cutoff in the Grounded Collector Stage In this case ''^"^ ^ k. + i?L+ (r.+ i?,)(l -rjr:)] ■ ^^^^ + (lAc)(r6 + Ra){re + Rl){\ + j^CcTc) and (74) For matched impedances (7?^ = 139,000 ohms and Rl = 2990 ohms), /cc = 320,000 cps G = 16.7 db. The cutoff frequency can be raised by decreasing either Rg or Rl . With Rg = 139,000 and R^ = 25 ohms fee =9.77 megacycles G= 1.8 db The gain-bandwidth product in this case is 1.5(10)^. Noise The data now available on noise are insufi&cient to give an adequate picture of the performance of n-p-n transistors in this respect. Such measure- ments as have been made, however, make it clear that these devices are very much quieter than early point-contact transistors reported on by Ryder and Kircher. Transistor noise seems still to decrease with increasing frequency at a rate of something like 11 db per decade. It also decreases as the thickness of the p layer is decreased. Of the order of half a dozen units of various dimensions have been meas- ured at 1000 cps and have shown noise figures as low as 8 db and as high as 25 db. The dependence of noise figure on operating point has been measured for only one transistor. As indicated in Fig. 28 and Fig. 29, these data show that the noise figure improves as Vc is reduced and that it may be roughly independent of collector current. These data were taken on a grounded emitter stage with impedance match at the input terminals. Noise figure for this connection varies shghtly with source impedance and has been found 562 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 to be a minimum when the source impedance is roughly equal to the input impedance of the stage. It must be emphasized that this functional dependence of noise figure on operating point and source impedance has been measured for only one transistor. Further measurements may show that these results are not typical. 20 CD 18 o UJ o Z 16 UJ a. Ic = 80>tZA -^ J, ^ / ^ y y- 8 10 12 Vc IN VOLTS 18 20 Fig. 28 — Noise figure increases with increasing collector voltage. 20 UJ (D U '8 UJ a ? 16 UJ tr. o 1^ ' progresses through the focal point the wave fronts become concave outward. Figure 7 shows a similar pattern but with the intensity of the signal increased. This procedure brings up the intensity of the weaker field and shows more clearly the minor lobe 570 THE BELL SYSTEM TECHNICAL JOtJRNAL, JULY 1951 Fig. 8 — A composite pattern of horn and lens which shows that the lens delays the wave fronts by approximately one wavelength. / = 9 KC. Fig. 9 — Flat phase fronts are obtained with a 30" diameter slant plate lens "illuminated" by the y aperture feed horn of Fig. 8 placed at the focus. / = 9 KC. SOUND WAVE AND MICROWAVE SPACE PAttERNS S7l Structure of the lens. The phase reversal at each successive minor Igibe is readily seen from the fact that the bright areas in the minor lobes line up with the dark areas of the adjacent lobes. The addition of phase makes it possible to obtain motion pictures of progressive wave motion. By taking successive movie ''stills", in which the phase front pattern is advanced one-eighth of a wavelength, a complete cycle is obtained. This series of eight pictures is then repeated until a rea- sonable length or loop of film is obtained. An example of the retarding effect caused by a delay lens is shown in Fig. 8. This wave pattern is a composite (two exposure) picture and was obtained in the following way: the left side of the photo was scanned with only the feed horn active (lens removed). The lens was then put in place and the probe continued to scan the area to the right. At the top of the photo, the circular wave fronts are seen to be continuous from the horn out, but in the shadow region behind the lens the wave fronts are retarded. One sees that the insertion of the lens has caused a delay equal to about one wavelength along the axis. This results in a curved wave front emerging from the lens and a consequent focusing action. An acoustic (or microwave) lens in which the delay elements are slanted guides similar in construction to a Venetian blind^ • "^ is shown in Fig. 9. The feed horn is the same as that in Fig. 8 and is set at the focus of this lens so as to produce fiat rather than converging phase fronts in the emerging wave. As the directional pattern of the feed horn would indicate (Fig. 8), the center portion of this lens is rather strongly "illuminated," but the result- ing energy concentration, in passing through the lens, is shifted upwards by the guiding action of the slanted plates. The resulting dissymmetry of the vertical amplitude distribution at the aperture of this lens (indicated by the increased thickness of the phase lines in the upper section of the photo- graph) is in a large part responsible for the unsymmetrical minor lobe struc- ture as reported. "^ The straightness of the phase lines, however, indicates that the lens has converted the circular wave fronts from the horn into the desired plane wave fronts. The undesirable concentration of energy at the center portion of the lens can be materially reduced by substituting, for the small feed horn of Fig. 8, a full conical horn shield having its throat at the focal point of the lens. The energy distribution entering the lens is then fairly uniform and the slant plates cause only a slight dissymmetry in the amplitude distribution of the emerging wave as shown in Fig. 10. The distribution of such a "shielded" lens in the horizontal plane, however, is even more uniform since it is not skewed by the slant plates in this plane (Fig. 11). *W. E. Kock, "Path Length Microwave Lenses," Proc. I.R.E., 37, 852 (1949). 572 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 Fig. 10 — The pattern of the slant plate lens of Fig. 9 when enclosed in a horn (vertical plane)./ = 9 KC. Fig. 11— The horizontal plane pattern of the horn and lens of Fig. 10. / = 9 KC. In some acoustic investigations it is desirable to have a source of plane waves of extended area. Figures 10 and 11 show that a shielded acoustic lens provides a simple way of achieving this result. The broad band nature of SOUND WAVE AND MICROWAVE SPACE PATTERNS 573 the slant plate lens ensures that plane wave fronts will be produced from 14 KC down to the lowest frequency contemplated for use, and almost any size can be employed since microwave lenses of 10 and 20 foot apertures^ have been built and found quite satisfactory. In the three preceding photographs, variations in the intensity of the emerging waves (variations in the thickness of the phase lines) can be ob- served. To show this effect more clearly and to indicate the symmetry of these amplitude variations, Fig. 11 was retaken with the phasing signal Fig. 12 — Removal of the phase signal in Fig. 11 shows more clearly the amplitude variations present in this horn-lens pattern./ = 9 KC. removed so as to obtain a pure amplitude pattern (Fig. 12). As mentioned in connection with Fig. 4, these patterns simply show the intensity varia- tions which are always present in the close-in or Fresnel field of any plane wave source having a finite cross-sectional extent. For a given wavelength and cross-sectional dimension, these variations can be calculated from diffraction theory and evaluated with the aid of Cornu's spiral. It is interest- ing to compare Fig. 12 with Fig. 13 which is a Schlieren photo of the sound field in front of an ultrasonic quartz radiator of 14 wavelengths aperture dimension.^ Although the aperture dimensions in wavelengths in the two cases are different and the actual wavelengths are quite different, there is a * W. E. Kock, "Metal Lens Antennas," Proc. I.R.E., 34, 828 (1946). ® K. Osterhammel, "Optische Untersuchung des Schallfeldes Kolbenformig schwingen- der Quarze," AkusHsche Zdts. 6, 82. (1941). 574 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 Fig. 13 — A Schlieren photograph of an ultrasonic quartz radiator shows the presence of amplitude variations similar to those of Fig. 12. (After Osterhammel.) Fig. 14 — Plane waves dififracted by a knife edge become cylindrical in the shadow region. / = 9 KC. remarkable similarity in the general appearance of the patterns. Immedi- ately along the axis of the radiators, one observes quite large amplitude SOUND WAVE AND MICROWAVE SPACE PATTERNS 575 fluctuations which become more rapid as the radiating source is approached; similar fluctuations are observed in front of large-area microwave antennas. Diffracted Waves Figure 14 shows the diffraction of waves over a straight edge. The sound waves in the upper half of the pattern are seen to progress with flat phase fronts, but in the shadow region of the f' wooden board circular wave fronts are evident, indicating that the edge is acting as a new Huyghens source. Figure 15 is a similar pattern showing diffraction around a wooden disk. Fig. 15 — The circular wave fronts in the shadow of a 10" diameter "opaque" disk combine to produce a lobe structure. The circular wave fronts emanating from the top and bottom edges are evident. Similar wave fronts are re-radiated from all around the circular edge of the disk and these combine to produce a concentration of energy along the axis corresponding to the "bright spot" of optics in the shadow of an opaque disk. Figure 16 is a repeat of 15 with the phase signal removed; this amplitude pattern shows the bright spot more clearly. Another diffraction effect of optics, the pattern produced by two small slits, can be duplicated by two non-directional sound sources separated several wavelengths and having equal amplitudes and phase. This produces the multi-lobed pattern of Fig. 17. Destructive intereference occurs in those directions for which the two sources are out of phase, and constructive inter- 576 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 Fig. 16 — Removal of the phase signal of Fig. 15 shows more clearly the major lobe of radiation in the shadow of a disc, the "bright spot" of optics./ = 9 KC. Fig. 17 — Radiation pattern of two equal sources of low directivity separated 3 wavelengths center to center. / == 9 KC. ference in whose directions for which the sources are in phase (such as straight ahead). The interference minima become filled in near the radiators be- SOUND WAVE AND MICROWAVE SPACE PATTERNS 577 cause the amplitudes of the two signals are unequal when their distances to the point of interference are unequal. Perfect cancellation can then not oc- cur. It is interesting to compare this photograph with the contour curves for this case as calculated from diffraction theory^ and shown in Fig. 18. Al- Fig. 18 — Calculated radiation pattern for two non-directional sources separated 3 wavelengths. (After Stenzel.) Fig. 19 — The pattern of Fig. 17 except that the sound sources have opposite phase. though the contour plot gives more quantitative information, the photograph allows one to grasp the qualitative effects more quickly. Figure 19 is similar ^ Heinrich Stenzel, "Leitfaden zur Berechnung von Schallvorgangen," (Julius Springer, BerUn, 1939), p. 59. 578 THE BELL SYSTEM TECHNICAL jOtJfeNAL, JULY 1951 to Fig, 17 except that the connections to one of the sound sources were reversed. With the two sources out of phase, cancellation now occurs straight ahead. The diffraction pattern of one wide slit would be similar to that of the 4 wavelength radiator of Fig. 4. To show the diffraction rings produced at the focal point of a lens, the sound field of a strip lens was scanned in a plane perpendicular to that of the previous photos. Figure 20 shows such a scan made in a plane passing through the focal point and perpendicular to the lens axis. The usual optical formulae Fig. 20— By scanning a plane perpendicular to the axis of radiation, the diffraction rings around the focal spot of the lens of Fig. 3 are portrayed. / = 9 KC. determine the size of the focal spot and the position of the surrounding diffraction rings. They are functions of the focal distance, the aperture, and the wavelength. In the previous lens patterns of Figs. 3 and 7, these diffrac- tion rings show up as minor lobes. For a perfectly symmetrical lens construc- tion, the rings would be more perfect, and the minor ''lobes" would in reality be cones of energy surrounding the major lobe. Diffusion of Sound The previous lenses have been of the convergent type for focusing or beaming energy. In the next pair of pictures is shown the effect of a diver- gent lens diffusing energy. The phase pattern of a 6" square aperture horn SOUND WAVE AND MICROWAVE SPACE PATTERNS 579 Fig. -The beam from the d" aperture horn loud speaker of Fig. 4 has fairly flat wave fronts and a narrow angular coverage. / = 9 KC. Fig. 22 — A diverging acoustic lens in the aperture of the horn in Fig. 21 converts the straight line waves into circular waves with their greater angular coverage./ = 9 KC. appears in Fig. 21. As in the pure amplitude pattern of this horn (Fig. 4), the directivity of this aperture is seen to be fairly high and the sound energy 580 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 is coUimated into a fairly sharp beam. High frequencies emanating from this horn would be projected through a rather small angular region and such a horn by itself would not be a very desirable general purpose loud speaker. Figure 22 shows the same horn with a slant plate divergent lens (described in reference 2) placed in front of its aperture. The transformation of the fiat phase Ironts into circular fronts and the wider angle of coverage can be readily seen. A frequency of 9 KC was used for these tests. When a large cone type loud speaker is operated at the higher frequencies it too becomes quite directive. Figure 23 is a radiation pattern of a 12-inch Fig. 23 — A large aperture loud speaker (12 inch) also becomes directive at high frequencies as evidenced by the flat wave fronts in the beam. / = 8.5 KC. loud speaker at 8.5 KC. The minor lobe formation is noticeable, indicating the presence of a central lobe surrounded by a region of low intensity. Microwaves and Sound The lenses employed in the preceding photographs were originally con- ceived and constructed for use at the very short radio wavelengths known as microwaves.^ The strip lens is, in fact, a small scale model of the type used in the antenna systems of the New York-Chicago microwave relay circuits of the Bell System for telephone and network television. A similar type of dual-purpose delay lens using disks instead of strips is shown in the 8 W. E. Kock, "MeUllic Delay Lenses," Bell Sys. Tech. Jour., 27, 58 (1948), SOUND WAVE AND MICROWAVE SPACE PATTERNS 581 next pair of pictures. In Fig. 24 the disks are arranged in an open construc- tion so that sound waves as well as microwaves will pass through. An acoustic amplitude pattern is shown taken at a frequency of 12 KC (X = 1.13"). In Fig. 25 the disks are copper foil and are supported on polystyrene foam which is transparent for radio waves but opaque for sound waves. The pat- tern now shows the intensity distribution of the microwave field being focused by the lens. The frequency was 9100 megacycles (X = 3.3 cm. or 1.3"). Fig. 24 — A sound field pattern of a disk array lens originally designed for 3 cm. radio waves./ = 12 KC. (X = 1.13"). To obtain this microwave picture, the loud speaker was replaced by a microwave radiator and the pickup microphone replaced by a tiny dipole and crystal detector. The microwaves are modulated with 120^^ pulses so that the same audio frequency amplifiers are used as before with sound waves. However, with this low frequency supplied to it, the neon lamp trace appears as a series of dots. In the next pair of pictures is shown a phase advance lens which likewise is effective only for microwaves. It uses parallel conducting plates in a wave- guide construction.^ Because the phase velocity is increased in passing through this medium, a concave lens is required for focusing (see Fig. 26). When the waveguide source (off to the left of Fig. 26) is brought in nearer so as to be at the focal point of the lens, the wavefronts straighten out and 582 THE. BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 Fig. 25 — An electromagnetic field pattern of a disk array lens in which the copper foil disks are mounted on polystyrene foam sheets./ = 9,100,000 KC (X = 1.3"). Fig. 26— A microwave field pattern of a waveguide type metal lens. Phase has been added, showing the curved wave fronts approaching and leaving the focal point./ = 9.1 KMC. the energy is collimated into a beam (Fig. 27). The reference signal for these phase patterns was obtained by the method illustrated in Fig. 28. A second- ary microwave source was employed which was fed from the main source SOUND WAVE AND MICROWAVE SPACE PATTERNS 583 Fig. 27 — When the waveguide feed of the lens of Fig. 26 is brought closer to the lens, a beam of flat wavefronts is produced./ = 9,1 KMC. 723 A-B KLYSTRON LENS FEED HORN REFERENCE FEED HORN WAVEGUIDE TYPE LENS Fig. 28 — The method of adding a constant-phase constant-amplitude microwave signal to the lens signals of Figs. 26 and 2? so as to portray the wave fronts. 584 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 and located on a line perpendicular to the scanning area and passing through its center. It was sufficiently far away to ensure that its wave front was ap- proximately plane, i.e., of uniform phase and amplitude, over the scanned area. The scanning microwave probe thus picked up a nearly constant phase, constant ampUtude signal from this secondary source in all positions of scan, and in addition sampled the variable intensity, variable phase microwave field coming from the lens. Microphone Patterns Using Transposition Techniques In the analysis of directional properties of acoustic or microwave radiators such as lenses, reciprocity can be employed, which is the property that equi- valent directional characteristics will be exhibited whether the transducer is used as a transmitter or receiver. Some electro-acoustic transducers are not reversible, however, and the directive properties of a carbon microphone, for example, cannot be easily ascertained unless some means is employed which measures its characteristics while it is receiving acoustic energy, i.e., in the microphone condition. In all of the preceding photographs the scan- ning device probed an actual sound field. In the analysis of a microphone, however, we are interested in its ability to pick up sound coming from vari- ous directions in space. We can therefore replace the sound source in the preceding photographs with the microphone under test, and replace the probe microphone with a scanning sound source. As the source scans the space in front of the microphone, the signal in the microphone will vary depending upon the abihty of the microphone to receive sounds from a partic- ular spot in the scanned area. If this microphone signal is used to control the brilliance of the lamp (still affixed to the scanner), the resulting photo will indicate the directional characteristics of the microphone by itself or in combination with a directional device such as a lens. As in the preceding photos, phase can be added by combining a constant amplitude signal with the microphone signal. The end result of all this is simply to interchange the connections of source and sink. Figure 29 shows a microphone pick-up pattern in which the strip lens has been placed in front of the microphone (not shown in the photo). Although this picture is now a representation of the microphone response for sound emanating from various points in the scanned space, it is seen to be nearly identical with the pattern of Fig. 7 which is an analysis of an actual sound field. This fact is simply a consequence of the principle of reciprocity. An interpretation which applies equally well to either of these two phase pictures is that the lines in each pattern are contours of equal phase length between the fixed and scanning transducers. With this transposition technique, however, we are now able to examine SOUND WAVE AND MICROWAVE SPACE PATTERNS 585 •oiMIIH Fig. 29 — A pattern taken with the microphone and loud speaker transposed. The sound source now scans and the pickup microphone is fixed (behind the lens). The phase signal is still employed indicating contours of equal phase "length" between the fixed and scanning transducers. The similarity to Fig. 7 can be observed. / = 9 KC. Fig. 30 — A pattern of a carbon telephone transmitter obtained by the transposition method of Fig. 29. The phase fronts are those which would be observed if the microphone were radiating sound./ = 4 KC (X = 3.4"). 586 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 the spatial response of a non-reversible transducer such as a carbon micro- phone. This is shown in Fig. 30 for an F-1 carbon telephone transmitter. It is also the directional characteristic the unit would have if it were capable of radiating. The addition of phase to a microphone directional pattern may seem superfluous but a knowledge of phase can often be useful. For example, in highly directional microphone arrays, the wave fronts in the close-in field Fig. 31 — A procedure for calibrating the photographic sound patterns. Part of the photo is scanned a second time with a constant signal on the lamp. Successive reductions of the signal (by 3 db steps in this case) produce the caUbration arcs. (A mask between the camera and the scanner prevents the calibration arcs from registering in the pat- tern area.) give information on the directional properties in the distant (far-field) region. Additional Details This concluding section will describe in more detail the scanning mecha- nism, the photographic procedure and methods for calibrating the photo- graph to provide a measure of the relative field intensities. The scanning arm rocks up and down over an angle of about 60°, making one stroke every two seconds. The vertical travel of the lamp in the course of a stroke is adjustable up to 40" while the horizontal travel is fixed at ys of an inch per stroke to provide a fine grain picture. The average picture is SOUND WAVE AND MICROWAVE SPACE PATTERNS 587 built up with about 300 lines or strokes corresponding to a 10-minute scan- ning time. However, pictures up to twice this length are occasionally taken. To make a picture (see Fig. 1) the loud speaker is turned on to provide a steady sound field. A filter in the microphone ampHfier is tuned to the signal frequency to reduce the interference from external noises. Absorbing blan- kets are sometimes desirable on nearly reflecting surfaces. The scanner is first moved manually to sample the sound level at various points so as to determine the proper gain settings and then placed in a starting position close to the acoustic lens whose pattern is to be taken. The room is darkened, the camera shutter opened, and the scanner started. Because the scanning process is relatively slow, the observer sees only the individual strokes of the flickering lamp. However, all the strokes are recorded on the camera film and form the desired pattern. When the scanning is completed, the shutter is closed and the room lights turned on. The film is then re-exposed for a few seconds to add the image of the acoustic lens. A dark background is provided so that the sound pattern will not be obliterated. The miniature glow lamps used for these pictures have been neon and argon types having no base resistances, e.g., the NE17, NE51, or AR4 and AR7. Neon seems to produce smoother gradations in intensity but argon is sometimes desirable because the film is blue sensitive. The lamps operate only over a voltage range from 70 to 120 volts, so that compression must be used in the amplifier circuit if the pattern is to show the maximum ampli- tude variations encountered which are of the order of 10 to 30 db. Many of the patterns were taken by just connecting the lamp to a high impedance circuit in the output of a power amplifier, the compression being obtained by the decreasing resistance characteristic of the lamp with applied voltage. In this as in any photographic process, the operator can control the effects pictured, intensifying or subduing images as desired by adjusting the film exposure and the circuit compression. When directivity is to be displayed and the major lobe is of main interest, the minor lobes may not even be exposed; when the phase fronts are desired in weak regions, the maximum range of the film and largest circuit compression may be used. When quantitative information is desired, the relative intensity of the sound field in the amplitude patterns can be ascertained by a calibration test performed before or after each run. This is illustrated in Fig. 31. A signal equal to the maximum signal the lamp receives during the scanning run is fed at constant level to the lamp while it is scanning the unused part of the photograph at the right. Successive reductions of the signal by a known amount of attenuation (3 db steps in this case) give a series of arcs of decreasing brightness. These can be compared to the various scanned portions of the photograph to get a measure of the amplitude. Some Basic Concepts of Translators and Identifiers Used in Telephone Switching Systems By H. H. SCHNECKLOTH {Manuscript Received April 26, 1951) The functions and typical designs of translators as applied to automatic tele- phone switching systems are first reviewed. The fundamental similarity of some existing translation schemes is noted and a discussion given of the factors which can be juggled to obtain economic application of such schemes. Identifiers and their uses are next described and some processes of identifica- tion are shown to have much in common with those of translation. Complications encountered in commercial application are discussed. Some needed improve- ments in general designs, possibly by new approaches, are indicated. Finally, the author points out the frequent occurrence of translation and identification processes in switching elements which are not labeled "translators" or "identifiers" and suggests that future improvements in translation and identifi- cation methods may consequently be useful in switching circuit networks in gen- eral. Introduction Those concerned with the technical details of automatic telephone switch" ing circuits usually regard a switching system as made up of a number of types of blocks or elements named in accordance with their main accom- plishment in the train of events in handhng a telephone call. Each of these elements is important as a useful cog in making the system work. Some of them, however, have an added distinction, if not a glamour, because their introduction to the switching world made possible funda- mental changes in switching technique or in the service which could be ofifered to subscribers. Two such elements are translators and identifiers. They will not be de- fined or explained until later, but a few words concerning their importance may be in order here. These elements were not used at all in early types of automatic switching systems. The invention of the translator in 1905, by Mr. E. C. Molina,^ and the philosophy that accompanied it are now generally credited with having laid the groundwork for the Bell System's adoption of systems of the common control type. In these, the paths necessary to reach a called number are not selected by the calling dial but by equipment which is common to many switching elements. The dial merely furnishes the customer's orders to the common equipment which, through the translation process, can set up a more suitable series of paths than is possible within the Umitations of direct dial control. » "Historic Firsts": Translation, p. 445 of Nov. 1948 Bell Laboratories Record. 588 TRANSLATORS AND IDENTIFIERS IN SWITCHING SYSTEMS 589 The advent of the process which made the dial an order-passing device rather than a direct-control device, of course changed the entire conception of what could be used in the way of automatic switches, how they were controlled and the number and arrangement of switching paths. But more important than the effect on technical methods in the equipment was the fact that the principle of translation reduced the limitations which sub- scriber numbering arrangements formerly had on the economy of giving subscribers direct access, by dialing, to large numbers of central offices in compUcated networks. First the benefit of this was in facilitating dial service in large metropolitan areas, later in making available suitable methods for diaUng of toll calls by subscribers. In other words, the translator was a practical means of pushing back the horizon for automatic telephone service. Systems based on the use of the translation principle are now found in many countries, and the Bell System's most modern crossbar arrangements depend on it more then ever. It is difficult to conceive of a nationwide auto- matic toll switching plan for a country as large as the United States without the use of translation. Identifiers are not so old as translators and have, so far, influenced the general design of switching systems in only a minor way. Their importance Ues in the fact that they were key elements in introducing to subscribers, both here and in Europe, a new kind of toll service. With this service, when- ever a subscriber dials a toll call, equipment in the central office auto- matically determines his own number and prints or otherwise makes a lecord of it along with other details of the call so that eventually he can receive a complete statement of toll calls which have been dialed and the detailed charges for each. Identifiers were essential in the first offices in which this service was pro- vided in order to determine the number of the calling party, and are neces- sary in plans now envisioned for giving this service in the large number of old-type offices still in service in the Bell System. Our newer type offices arranged for this service do not employ devices named "identifiers" as the identification function is spread over numerous elements. Nevertheless, the identification process is there and, named or not, it is found in many other situations. Translators and identifiers, while used for functions which seem offhand to be quite different, are often similar in so far as the general operation and problems of design are concerned and, in fact, have much in common with numerous circuit elements called by different names. Because of their funda- mental importance they have been the subject of much invention, directed toward use in specific conditions, the use of different types of apparatus, 590 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 improvements in reliability, increase in speed, and, most important of all, reduction in cost. Operable arrangements to meet all sorts of conditions of use can generally be selected from the present fund of knowledge but the choice in practice is much more limited than in theory. However, translators and identifiers, particularly those used on a large scale, can be varied in many ways to obtain maximum usefulness and to minimize the costs, not only of these devices themselves, but also of other parts of the associated system. In the following discussion a number of devices of these types will be illustrated to provide a general review of some of the methods available, and the factors encountered in practice in trying to obtain a proper balance between costs and usefulness will be examined. Translators What are Translators? The translators with which we are concerned in this discussion deal only with information in the form of electrically coded numbers. The "languages" carrying this information are the coding systems made up of the numbering bases and signalling methods. Unfortunately, the analogy between the switch- ing system translator and an interpreter of languages, implied by our use of the word ''translator," is not very consistent. The term ''translator," as used in this paper, means broadly a switching system element which, in response to an inquiry in the form of an input code, suppHes an answer in the form of an output code to the element presenting the input code or to some other element. Each code may represent one or more numbers. The translator may be a device which serves a number of other circuit elements in common, or it may be associated with a single such element or even built into it and unnamed. Now in practice we will find that in some applications translators are used so that the input codes and corresponding output codes represent the same numbers in different bases or with different signalling methods, that is, the same information in different languages. Here we have the nearest approach to our implied analogy. However, quite commonly, the switching translator is required to do things which would be decidedly out of order in the case of language translation, such as changing the information instead of the language or changing both at the same time. Some of the variations in switching translator applications which should be noted at this point are: (1) In practice, translators are arranged with a multiplicity of input and output possibilities. The inputs may be permanently associated with TRANSLATORS AND IDENTIFIERS IN SWITCHING SYSTEMS 591 corresponding outputs or the association may be changeable through movable jumpers or other means. Thus we have two major types of translators— ^^.reJ and changeable. (2) In most applications the input and output codes have no natural cor- respondence but require arbitrary translation determined by the designers of the system or those who operate it. Translation is of the systematic type where there is a definite relationship between the , input and output codes. The relationship may be purely mathematical I or may follow from some of the peculiarities of the switching system. (3) The input and output codes may be of the same numbering base with the same or a different number of places. Often the two codes are of different numbering systems and one or both may consist of mixed base numbers. As discussed later, many devices we do not call translators do in fact have a translating function, but they have been designed with a different point of view and have accordingly been given different but suitable functional names. However, the vagaries of telephone switching nomenclature have in some cases resulted in giving other names to elements clearly having the same functions as elements earlier or elsewhere called translators. The more important variants will be pointed out as we go along. One of these, the term ''code converter," seems more appropriate than the original term. Examples of Use It may now be in order to give a few examples of the kinds of uses made of translators in automatic switching systems. (1) Let us assume we have a common control system in a multi-office city. When a subscriber dials the digits of a local number which we call the "office code", indicating the central office unit in which the called subscriber is located, this number is received by the switching equipment of the originating office as a decimal number with three digits or less. The switching equipment, in extending the call to the central office indicated, may have to set up connections at numerous stages of switches, some in distant offices, which are not indicated by the dialed code. The switching operations which must be performed by the control equipment to reach the desired office are indeed represented by a numerical code, but it may be a number quite different from the dialed number and have no natural relation to it. For this purpose a translator is used to convert the dialed number to the required new code comprising the instructions for the switching oper- ations which must be performed. In British practice a translator used in this way is sometimes called a ''route table." Since the routing of calls corresponding to any particular office code 592 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 through the switching equipment may have to be changed from time to time, provision must be made in the translator so that the correspondence between dialed codes and switching codes can be changed economically when necessary by the operating personnel by making changes in the wiring of the translators or by other means. At present this is generally done by re-arranging jumpers. Here then we have an example of a translator of the changeable type with arbitrary correspondence between the input and output codes. This type of translation is used with almost all common control systems in the world. With some of these systems it is required because of the non- decimal nature of the switching arrangement. With other types, having decimal switches, it is not required but it is nevertheless used in order to make the trunking arrangements more flexible and efficient. Translators of this type are not large in some cases because of the small number of translations needed. A complete translator is sometimes perma- nently associated with each circuit element having need for translation service and the translator may be separately mounted or built into the associated circuit. In other cases one or more translators may be arranged for conamon use by numerous circuits requiring them. (2) In some switching systems, for instance the panel type, additional use is made of translation in the switching operations involving the further extension of a call after it has reached the desired central office. The nu- merical code, usually the thousands, hundreds, tens, and units digits dialed by the calling subscriber would, with some types of offices, directly serve to control the switching operation for the final selections; but in panel- type offices the terminations for the subscriber numbers, while arranged in an orderly manner, are not grouped on a decimal basis and a switching control code corresponding to the actual location of the called number must be determined. Here again a translator is used, but the input codes in this case have a definite relation to the output codes which is invariable; so the translator used is of the fixed type with systematic correspondence between the codes. This particular application followed from the first American invention relating to translators and marked an important step in the development of switching arrangements not requiring a direct correspondence between dialed numbers and switching operations. This appUcation is now found in many systems. When we examine the block diagrams of the switching arrangements for the panel and some other systems with this type of translation we do not find any block for this particular translator, as the systematic correspondence TRANSLATORS AND IDENTIFIERS IN SWITCHING SYSTEMS 593 between the input and output codes permitted the translating arrange- ment to be made a part of other equipment. (3) In our latest crossbar system the idea of not using the numerical digits of the called number as the switching control code has been carried still further. There are no terminals numbered as subscribers' telephone numbers. The switches obtain access to the called subscribers by con- necting to terminals for ''line equipment numbers". The line equipments correspond to subscribers' Hnes and are associated with subscribers' num- bers on an entirely arbitrary basis. The equipment numbers are not four- digit numbers but each is a series of five 1- or 2-digit numbers (a mixed base number) which indicate the locations of the equipments on the frames. Here again use is made of translation to convert the dialed decimal number to the non-decimal number forming the switching instructions the common equipment must have in order to reach a called subscriber. In this case, however, the simple, fixed, systematic type of translator used with the panel system cannot be employed, as the associations of the input and output codes are entirely arbitrary and may be changed from time to time to make changes in number assignments, and so the type of translator employed is of the changeable type with arbitrary correspondence. This type of translator, especially when used for large ofl&ces having 10,000 or more numbers (input codes) is decidedly a large scale affair and too costly for permanent association with each circuit unit making use of it. The translating equipment is, therefore, made common and is sectionalized in groups called number groups each handling several hundred numbers and operating independently. (4) In automatic equipments arranged for handling toll calls dialed by operators or subscribers, translation is an extremely important feature especially where the networks are as large and complicated as those of the Bell System. Our latest crossbar toll switching system has many important features and economic advantages made possible by the ingenious use of translation. In automatic toll switching practice a numerical code of three to six decimal digits is sent to the switching equipment in the originating toll office to indicate the particular geographical area in which the called num- ber is located. The area may be nearby or far away, trunking may involve only a few paths in series or a number of intermediate offices and many interswitch paths. The switching equipment must determine the necessary course of action from the 3- to 6-digit code which has been received, and this is done through the use of a translator. In the case of our newest toll crossbar office, the output code of the 594 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 translator actually consists of many different numbers in various bases, each indicating some different item of information required in order to complete the call. The information includes switching instructions for interswitch paths and intertoU routes of the preferred combination and also indicates where alternate combinations may be found if the preferred choices are busy or out of order. Because of the large number of possible codes, translators suitable for this application present special design problems. Typical Translators Before undertaking an analysis of the general concepts used in trans- lation, it may be well to review some of the typical translation methods which have been used in the field. In the following descriptions, details not necessary in illustrating the general method are omitted. Fixed Translators Figure 1 shows the principles of a fixed, systematic translation scheme employed in early panel and other systems for deriving from decimal numbers the switching instructions for controlling some of the non-decimal selections. This is one of the solutions for case (2) of the examples of use just men- tioned. The selection of a called subscriber's number by the terminating equipment in the called central office unit is governed by the last four decimal digits of the number, but the process required with the panel ar- rangement is in part non-decimal. The numbers are grouped in banks of 100, which means that, once switching has proceeded this far, the wanted number can be sehcted in the bank on a decimal basis as indicated directly by the tens and units digits of the number. Other groupings of final and preceding equipment involved are not decimal, so the preceding selections must be made on the basis of non-decimal switching control codes ob- ined by the common control equipment through the translation process. The switching code wanted in this case consists of three numbers for controlling selections called incoming brush (IB), incoming group (IG) and final brush (FB), and must be derived from the combination of the thousands and hundreds digits of the called subscriber's number as recorded on the register switches by the calling subscriber's dial. This can be done because the non-decimal arrangement of the switching equipment is orderly and there is, therefore, a systematic relationship between the input and output codes.2 It will be noted that the input code consists of a ground on one lead in ' Oscar Myers, Codes and Translations, A .I.E.E. Transactions, Vol. 68, 1949. Translators and identifiers in switching systems 5J5 each of four groups of leads from the "thousands" and ''hundreds" switches. This results in an output code of one marked lead in each of the three groups of non-decimal output code marking leads. The operation is simple. The IB code is determined directly from the pairing of consecutive terminals on the thousands register. The IG code is THOUSANDS ^o^ REGISTER HUNDREDS ° c/^ REGISTER lllllllil llllllllll Mill llllllllll INPUT CODES THOUSANDS o|-|c\i}fn|'*j>n|cD|t^|oo|cn| THOUSANDS o|-|fvi fo{^|'n|(o|f--}oo}o{ HUNDREDS in}«)|i^}oo|o>| HUNDREDS o| -| (\j| (o} •n| (d{ r- j ooj o} ^ilH ;-) EVEN -—TRANSLATOR 0|-JOJ(0^| IB FB OUTPUT CODES Fig. 1 — Fixed, systematic translator used in panel system for converting thousands and hundreds digits of called numbers to 3-part code for control of non-decimal selections. (Changes information) derived from a combination of the settings of the thousands and hundreds switches, which with the combining relay gives one of four possible code marks depending on whether the thousands number is even or odd and whether the hundreds number is in the first five or last five series. The FB code, one out of five, is derived from the hundreds switch by pairing the numbers in the first five series with those in the last five. 596. THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 The simplicity of this type of translator makes it economical to furnish one for each switching element (sender) requiring its use rather than pro- viding for use in common. In practice the translator is not even as discrete an element as shown here but is contained in and wired as part of each sender. It will be obvious that this form of translator may also be constructed with other types of apparatus. Figure 2 shows another form of fixed, systematic translator used as an element in changing the code for a number in a two-out-of-five system to a one-out-of-ten system. The operation is simply that a mark on two of the five input code leads will cause the operation of the two associated relays P^t _iHiH '.-' (0) jHi|i _dlll _Hi|H :-) w _di| Fig. 2 — Fixed, systematic translator for changing the coding for a single-digit decimal number from two out of five to one out of ten. (Changes "language") which will place a mark on one out of the ten output leads. This element is repeated for each place in the decimal number involved or the same ele- ment may be used, by the addition of suitable controls, for translating numerous digits on a sequential basis. Note that the two numbers repre- senting each input code add up to the number being translated, except that seven and four are assumed to add to zero. Figure 3 shows a systematic translator for changing the code for a number from the decimal to the centesimal system. Here the input code consists of a ground on one lead in each of the two input groups and the output code consists of a ground on one of the hundred output code marking leads. The operation of one of the "tens" relays by the grounded tens lead connects TRANSLATORS AND IDENTIFIERS IN SWITCHING SYSTEMS 597 the units leads to ten output code leads one of which will then be grounded. By adding suitable relays this translator can be expanded to a system in which the output code is a mark on one of a thousand or ten thousand leads. The arrangement of Fig. 3 occurs frequently as a selection device and when so used in the Bell System is now called a "relay tree".' It is often an element of other types of translators. TENS RELAY (1) GENERAL SYMBOL TENS i-; UK ^r TO TENS — > RELAYS (3)-(9) ::i TO > CONTACT MULTIPLE 8 OTHER LEADS TENS RELAY (2) ^; Hli^L 8 OTHER LEADS 7 OTHER TENS RELAYS TENS RELAY (0) 20 70 OTHER LEADS y> iUKi 8 OTHER LEADS 100 Fig. 3 — Fixed, systematic translator for changing a 2-digit decimal number to a cente s imal base. (Changes "language") A 100-point step-by-step switch can, of course, be used as the equivalent of the foregoing type of translator, and is frequently so used. In this case the input code is two sets of decimal pulses to drive the selector to the required point, and the output code is again a mark on one out of one hundred output code marking leads connected to the bank terminals.* Such a switch is also used in place of a relay tree as a selecting element in other types of translators. * S. H. Washburn, "Relay Trees" and Symmetric Circuits, A.I.E.E. Transactions, Vol. 68, 1949. * This is an elementary sample of a translator with sequential input and combinational output. 598 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 Changeable Translators The Western Electric Company's first full-automatic panel office made use of a rotary- type switch in order to obtain within the senders a trans- a. ^ -< TOl OF 15 — ^-M 2 FU(IO) < VG(7) >^ VF(IO) _S(I52 Fig. 6 — Number group translator for ^ 5 crossbar office. Ring Type Translator An example of a translator with still further simplification and improve- ment of the coding equipment is that shown in Fig. 7, which is also used in the ^ 5 Crossbar office, in this case for determining the directory number of a calling station when the equipment location number is known and it is desired to make a record of the caUing number for charging for the call. This is the reverse translation of the case covered by Fig. 6. As used in practice, the translator of Fig. 7 is limited to capacity for 1000 mixed base input codes, any of which may be translated to any of 40,000 directory number output codes in a 5-place decimal system. Here the relay selection tree, under control of the input code, causes the selection of a one-wire circuit to one out of 1000 equipment number terminals each of which has a cross-connection wire which serves directly as the coding element for translating the associated equipment number. This is 604 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 due to the fact that each jumper is threaded through a common array, of ring-type induction coils with one coil for each digit in each place of the output numbering scheme, that is, 44, as shown in Fig. 7. After the equipment number selection has been made, a surge of current is passed through the jumper. Since the jumper acts as a single turn primary for all the coils through which it is threaded, a high voltage is induced in ,^rGRP(20)x | \- TENS 2— \ o_ J5-2L z I ] o D O) 0-- 1 \ -1- ^1 if- o o -^ i- — J o o_ 2 s*- 10 1 o Z 1 O ^'^ UJ 1 H 1 ^9 /O)- 0 /\/ — — w_ -1 °,>^ - — J o z o_ 2! '^a*'' 1 in 1 Q 1 w 1 o^ Q_ " z 2> ^»- D 1 o 0 1 1 1 H 1 i/ " z w I 00 608 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 side to cause the auto selection of the coding tube for (A) number 1925 as follows: (1) Breakdown voltage is applied through the thousands register to the # 1 bus in the thousands group of the A side. This causes breakdown, or firing, at the thousands anode of all tubes that have one as the thousands A digit. In a fully equipped system this would be yo of all the tubes, or 1000. (2) ''Sustain" or ''hold" voltage (lower than breakdown voltage) is applied to the ^ 9 hundreds bus, followed by removal of the voltage from the thousands bus. This causes all previously fired tubes which have ^ 9 as the hundreds digit to be held ionized by the hundreds anode and the others dropped out, that is yo of the total tubes drop- ped out and yo or 100 held. (3) This drop-out process is continued through the tens and units steps so that first ten and finally only one tube (number 1925) is held by the units anode. Auto-selection of the code tube required is now complete and it remains only to read the coding of the B side. (4) Reading is accompHshed by applying "hold" or "sustain" voltage to all the bus bars on the B side. This causes anodes connected to this bus system to fire by transfer in only the one tube which is ionized. Thus all B anodes in tube 1925 will be fired and the resultant currents in the associated bus bars (one in each of the 4 "B" groups) are marks which can be read in the electronic reading circuit to register the B output number 5928. (5) The translator is dropped by removing all voltages, causing the selected tube to deionize, and the translator is ready for another job. All of this requires only the time of the various breakdown and transfer steps and intermediate deionizing times, totaling less than 100 microseconds. The advantages of possible cost reduction are obvious especially for large scale applications. The disadvantages, in the form here shown, are: (1) The possible hazards resulting from the fact that this is a single common unit with one-at-a-time operation. (2) The tractability for general use needs to be improved as it is neces- sary to change all the 4 or 5 required jumpers on one side of a coding element in order to make a translation change. (3) The special tubes need to be made in very large quantities in order to obtain the required low price. Further work now being done may resolve all these difficulties. This translator illustrates some of the variations the designer can consider TRANSLATORS AND IDENTIFIERS IN SWITCHING SYSTEMS 609 when dealing with a translation problem with a new approach, and also some which must be considered. These and other possible variations will be reviewed later. Slide Bar Translator This proposed device was the forerunner of one of the Bell System's most important projected translators and is worth examining for the new princi- ples.® In this case, as in the cross-reference system just described, one of the objectives was reduction in cost by eliminating the separate equipment for selecting the coding elements and combining the selecting equipment as far as possible with the coding equipment. A further purpose was to provide non-electrical coding elements with improved tractability for making changes. The construction of this device is shown in Fig. 9. The coding elements consist of thin slide bars shown in Fig. 9(a), each notched in accordance with the input code on one end and the output code on the other. These are stacked as shown in Fig. 9(d). The selecting equipment is a combination of code bars, Fig. 9(b), which work in combination with the wide and narrow notches of the slide bars, so that when a combination of select code bars is operated according to an input code all slide bars except the one carrying the input code are restrained from sliding when the common operating magnet is actuated. The one slide bar slides to the right, this representing the selection of the coding element. The reading code bars are now all operated and only the set corresponding to the output code of the displaced slide bar can operate fully. Contacts on the output code bars then mark the output code leads. Because this device is slow relative to relay or electronic translators owing to its mechanical elements, it has limited traffic capacity and would have to be duplicated many times in each office. Its advantage, however, lies in the fact that, when changes in translation are to be made, new coding elements (slide bars) can be prepared in advance and the changes made simply by substituting the new bars for the old, without changing cross connections. Card Translator While the slide bar translator is sometimes spoken of as a "card trans- lator" it is similar to but by no means the same as the card translator which the Bell System proposes to adopt for toll crossbar offices. « See U. S. Patent /j^ 2,361,246 issued to Mr. George K. Stibitz. 610 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 This card translator will not be illustrated at this time, but the following general notes are in order: The card translator is especially designed for toll application where a 3 to 6-digit decimal input must be translated to an output containing 30 INDIVIDUAL RESTORIIslG SPRING N W N N W W INDIVIDUAL COMMON OPERATING OPERATING N' N' W N' W SPR'NG ,.- BAR '^ SELECT END READING END / ill (INPUT) (OUTPUT) ^^...\^.. ^X.l.l (a (OUTPUT) ^ ' COMMON COMMON STOP ROD OPERATING (a) INDIVIDUAL SLIDEBAR OR CARD MAGNET _ \-^v^-^ INPUT CODE LEAD SELECT H-CODEBAR (COMMON) -dH CONTROL "-I \ ^READING CODEBAR ^ (COMMON) SrT-^';l \^ ) OUTPUT CODE LEAD (b) INPUT CODEBAR (ONE PER CODE ELEMENT) (C) OUTPUT CODEBAR (ONE PER CODE ELEMENT) (d) VIEW SHOWING TEN SLIDEBARS OR CARDS WITH FOUR SELECT CODEBARS AND THREE READING CODEBARS Fig. 9 — Slide bar translator. items of information with a very large number of possible combinations. The large number of possible outputs and the necessity of making changes quickly and frequently make the previously illustrated translators im- practicable. For such application the card translator is well suited. The TRANSLATORS AND IDENTIFIERS IN SWITCHING SYSTEMS 611 coding elements consist of steel cards, notched at the lower edge according to the input code. The output code is carried on the card in the form of small and large holes. The coding elements (cards) are selected, as in the sHde bar translator, by selecting code bars that will drop the required card. Reading is done by photo cells (actually photo-transistors) which detect the presence or absence of light through the tunnels formed by the holes in the stacked cards. Pre-translator for No. 5 Crossbar System This all-relay translator is used for obtaining one of three possible sets of switching instructions at a time when it is impractical to consult the more complete office code translator associated with the marker in this system. Provision is made for 576 possible input codes on a 3-place decimal basis each translatable to one of only three possible output codes each consisting of a mark on one of three output leads. Because of these restricted capabilities it will not be illustrated here,' but its general principles are worth noting because it is an example of how close tailoring to the requirements can effect economy. This translator is one of the few examples of changeable tianslators which do not follow the general principle used in the previously described translators of this type. That principle, it will be recalled, is that each input code causes the selection of an individual coding element which determines the output code and changes are made by causing the selection of different coding elements or by changing the output of the coding elements. In this pre-translator the input codes are teamed in groups of three, each of the group causing the selection of the same code point terminal. Hence only one third as many code point terminals are required as there are inputs. Each of these code point terminals is cross connected to one of 27 terminals, each of which represents a different permutation of each of the three possible outputs. At this terminal three possible answers are repre- sented, and three relays beyond this point select the correct answer, de- pending on whether or not the input code is the first, second or third of the group of three. Changes for any input code are made by changing the jumper affecting this code and its two associated codes to a new terminal representing the new permutation. This arrangement reduces the required number of relay contacts, cross connections and cross-connecting terminals as compared to the number required by more conventional all-relay translators. It would become im- ^ For a full description, see Pre-translation in No. 5 Crossbar, R. C. Avery, Bell Labora- tories Record, April 1950. 612 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 practical if only a few more output codes were required because of the great increase in the number of permutations. General Thoughts on Translators Broad Considerations in Choosing Translation System If a switching system designer were confronted with the problem of providing a large scale translator and he were given full latitude, there would be many factors he would have to consider and a wide variety of choices he could make in order to reach the most economical and useful design, even if he were uninventive and restricted to the combinations of the present art. Actually he would not have full latitude, for the translator design must always be coordinated with the design of other elements and often is subordinated or greatly limited by the importance of the more intricate or costly elements with which the translator must work. The best he can do is to arrange his design to help provide the most economical and serviceable system from an overall standpoint, and in this the translator design might not be ideal. What are some of the more important factors that the designer can juggle and what choices can be made within the known possibilities? Let us assume that the problem specifies, for some new type of common control ofl&ce, large scale translation between equipment and directory numbers in both directions. Then the following decisions are certainly important: (1) One-way or Two-way Operation? » This is determined by economic study if the available two-way translators are satisfactory. (2) Should translators be provided for each circuit requiring their use or should they be provided for access to circuits in common? This can be determined only be economic studies. (3) If the translation system is to be common, should it be based on the use of a single full-capacity translator or numerous smaller trans- lators involving more translator connecting devices? This involves economic studies and questions of the speed or traffic capacity of the translator and the question of relative service hazards in the two arrangements. (4) What type of translator shall be used? This involves economics, speed, reUability, types of apparatus available and tractability for making changes. TRANSLATORS AND IDENTIFIERS IN SWITCHING SYSTEMS 613 Detailed Considerations It has already been brought out that large scale changeable translators known to the present art follow the same basic concept and that there are, as a result, certain problems common to all of them. Let us examine Fig. 10 to see how some elements can be varied to change costs. This figure shows four general arrangements for coding, all working into the same output code marking lead bus-bar system. In practice all of the coding elements of the same translator would be of the same form and a large number would appear before the bus system or sections of the bus system. In the general arrangement covered here the coding elements are arranged in numerical order each permanently connected to its associated output bus bars. Types of systems having no output bus-bar multiple, such as the Dimond ring, slide bar or card translators are not illustrated, but covered in the discussion. Starting at the left with the input code leads, we have theoretically much choice as to the types of signaling (various combinational or sequen- tial t3rpes) and the system of numeration making up the input code. In spite of this freedom most translators in use employ decimal inputs with signaling generally on a code marking lead basis or sometimes on a decimal pulsing basis. Where code marking lead signaling is used the marks are almost always simple off-on marks and, for decimal notation, each place is represented by a 1 out of 10, 2 out of 5 or combinations of 4 group. The practical choice is limited by the fact that it has usually been uneconomical to change the coding system of the translator input to other than that existing at the output end of the relay or switch devices making use of the translator, as this would require a change of language by intermediate translation. If it were not for these limitations the number of input leads could be reduced by use of binary numeration for marking leads, or by signaUng over a single pair of wires with any of the other well known methods of signaling. However, the reduction of leads could, in any case, effect only minor savings as the leads are short. The largest savings possible would be in the reduction of the amount of translator selecting equipment required. The language of the translator input, of course, also affects the design of the coding element selector which could be any type of selecting equip- ment such as switches, relays, tubes or code-bar mechanisms or, in one proposal, self-selecting coding elements. Relay trees are frequently used and optimum designs for the common types of inputs are well estabUshed. For different types of inputs the design of such trees profits by mathematical analysis. 614 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 Now we come to the coding elements themselves. Because of the large number of these, optimum design is important. In the illustrations and in most applications the output codes are formed by the coding devices placing marks on the output code marking leads. The output language could be different, of course, and possibly with economy in the translator itself, but the philosophy of using code marking leads in the output end is the same as that just mentioned for the input system. CODE POINT SELECTOR OUTPUT CODE BUS BAR SYSTEM I I I I I I OUTPUT CODE MARKING LEADS OR BUS BARS Fig. 10 — Four general methods of output coding in changeable translators. The coding methods shown require a multiple of all or part of the output code leads before the coding elements, that is, a bus system. It is the prob- lem of the coding elements to mark the required buses in the various out- put groups without causing false marks on buses not involved by ''back-up" through the connecting network or at least keeping the back-up below levels providing adequate discrimination between wanted and unwanted signals. This back-up problem is solved in translators of the Dimond ring, slide TRANSLATORS AND IDENTIFIERS IN SWITCHING SYSTEMS 615 bar and card types by the fact that there is no bus-bar system, each output lead having only one connection on the translator. Each electrical bus-bar is replaced respectively by a coil, a code bar channel or a light tunnel. In systems using bus-bar output multiples the coding elements solve the coding and back-up problems in four general ways, as shown in Fig. 10, assuming that the output consists of four code groups: (1) By having an individual lead through the code-point selector and cross-connection field for each code group as shown in Fig. 10(a). Each lead is directly connected to the required bus. All are open in the selector except those involved in any individual translation, thus avoiding back-up. No apparatus other than the wiring is involved in the coding element. This saves apparatus, but the cost of the cross connections and the wiring apparatus in the coding element selector are higher than for the other cases because of the larger number of wires. (2) Figure 10(b) shows a one-wire arrangement with back-up prevented by a unilateral or non-Unear element in each lead to the bus-bars. (3) Figure 10(c) shows a one- wire arrangement which is connected to each of the four required output buses through a terminating and coding resistance network which reduces back-up through the unilateral ef- fect provided. (4) Figure 10(d), again one- wire through the selection and cross-connect field uses a relay to effect coding, back-up of course being prevented by the fact that the leads to all code buses are open at the relay contacts except those involved in a particular translation. Figure 8 operates on similar principles for avoiding back-up. Schemes (b), (c) and (d) reduce the wiring and the selector costs as com- pared to (a) through the use of only one wire but this is done at the ex- pense of the additional apparatus in the coding element. Figure 6 shows a compromise between (a) and (c) of Fig. 10. Different conditions for one-way translators may warrant a careful choice between one of the four general methods of coding shown in Fig. 10 and the methods involving no bus-bars mentioned above. In the case of the arrangements of Fig. 10 some cost changes can be ef- fected by juggling, in the design, with the coding elements and the bus-bar grouping. For instance, if the number base of the output were changed from deci- mal to binary, the number of output bus-bars would be reduced from 40 to 14, but the increased number of places in each output would require 14 leads from each coding element instead of the present four. This complica- tion of the coding elements would probably prove-out this change. 616 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 On the other hand, if the output number base were changed to centesimal the number of output bus-bars would be increased to 200 but the redtiction in the number of places would reduce the number of output leads from each coding element to two. This might be of possible economic advantage. If it were not permissible to end up with a centesimal output, it would be necessary to provide a secondary translator to change the output from a centesimal to the decimal or other system required, and this would reduce the economy of the centesimal output. What About New Concepts for Translators? There are in the "proposed" state numerous interesting variations of the basic translator principle which has been outlined. These have as ob- jectives lower system first costs and improved tractability for changes. The general concept for changeable translators of the non-systematic type which has been repeatedly stated above appears in so many forms in practice and in inventions and suggestions ranging through varieties of mechanical, electromechanical, electro-optical and electronic types that one might wonder: (1) Is it not possible to design a large scale changeable translator with a different basic concept? (2) If it is possible, what might be gained? We have noted, in the "pre-translator," a departure from the general concept of changeable translators, and there are others. However, they are all limited scale types apphcable to special conditions. A recently pubUshed article^ indicates a new hne of attack on the prob- lem of obtaining a changeable translator with greater speed and reliabihty so that it could be used to carry a greater load than now customary. Not enough details are given to indicate whether the electronic arrangements outlined depart from the basic concept of existing translators, but, if they do not, they at least present interesting variations. What could be gained by entirely new concepts for translators can not be answered in advance except in terms of what would be welcome. The present general designs give good performance and there is Uttle need for improvement in this respect. What is always welcome is lower costs, par- ticularly the cost of making changes. Identebters What is Meant by "Identifier" It was stated at the beginning of this paper that identifiers are relatively new in the switching art. This applies to identifiers which are sufficiently •T. H. Flowers, "Introduction to Electronic Automatic Telephone Exchanges- Register — Translators," Post Office Electrical Engineers^ Journal, January 1951. TRANSLATORS AND XDENTIFIERS IN SWITCHING SYSTEMS 617 limited in function or distinct as a switching unit to be so labeled. Un-named identifiers and identification processes have existed since the early days of the switching art. Only patent attorneys recognized these early arrange- ments and called them by their proper names. Let us confine ourselves, for the moment, to the type of device generally named as an identifier. This is a device for indicating in code form the designation of a line, station, trunk, frame or other unit to which the de- vice has a connection. The connection is generally electrical, but could con- ceivably be physical, optical or electro-magnetic. Examples of Use The term identifier first came into general prominence in connection with the introduction of "automatic ticketing" in the United States and Europe. These are systems used in connection with subscriber dialed toll calls for printing automatically a ticket carrying calling and called numbers and other details necessary to charge for the call. The identifier is the automatic device for determining the caUing number, a function ordinarily performed in manual service by the operator asking for the number. With the identi- fier it is also possible, on those calls requiring the service of an operator, to display the calling number automatically so that the operator's request can be avoided. Another example is found in Bell Crossbar Offices of the toll type in which it is necessary for certain equipment to determine the number of the frame on which a calling trunk is located. For this purpose, what is known as a "frame" identifier, is used. Of course, no arrangement for fully automatic completion of long haul toll calls can be successful without an automatic system for making a record of the details necessary to charge for the calls, including automatic identifica- tion of the calling number. Identification processes will, therefore, become more and more important. Typical Identifiers General Existing identifiers follow a number of basic concepts but many varia- tions of these fundamental notions are possible. A few examples illustrating the different concepts with some of their variations will be given. The task is simplified because some of these concepts have a strong resemblance to translator principles which have already been discussed. 618 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 Calling Number Identifiers — Searching Type Figure 11 shows an identifier used in the Bell System's first appUcation of automatic ticketing^ and with variations in similar applications else- where. The principle here is that the identifier, through the outgoing trunk to which the calling fine has been extended, applies a tone to the sleeve ter- minal of the calling line, utilizing the sleeve through all the switching stages. This tone finds its way through an equipment-to-directory number trans- lating jumper to one terminal common for each 1000 numbers, one com- mon for each 100 and one per number in each one hundred block. The numbers of the terminals with tones correspond to the various decimal digits of the caUing numbers. Relays connect tone detection equipment sequentially to the various thousands, hundreds, etc. terminals and each time the tone is found the corresponding digit is registered on relays in the identifier. These relays mark the output code leads. The variations in other identifiers of the searching type consist of the use of switches or tubes instead of relays, searching for special d-c. voltages instead of tone, and in transmitting the digits of the identified number back to the source of the identifying signal by pulses over the sleeve instead of transmitting them to code marking output leads. This type of identifier is obviously rather slow because of the sequence of operations and it is, therefore, necessary to provide a plurality of identi- fiers for each office. The different identifiers are prevented from interfering with each other by preference lock-out circuits, by discriminating signals such as different tones or by other special means. A ll-Eleclronic Calling Number Identifier This proposed identifier works much like a translator in that a coding element individual to each number is selected and this places marks on a decimal bus-bar output system. Referring to Fig. 12, it will be noted that there is a directory number field with a multi-anode tube of the type used in Fig. 8 for each number plus an RC filter to discriminate against surges. This identifier provides for party lines and for class of service indication requiring the two extra cross connections shown. The operation consists in the application by the control unit through the trunk and the switch sleeves to the line equipment sleeve terminal of a 10- millisecond pulse of +135 volts. This finds its way through the normal ' O. A. Friend, "Automatic Ticketing of Telephone Calls," Electrical Engineering, Vol. 63, Transactions, pp. 81-88, March 1944. TRANSLATORS AND IDENTIFIERS IN SWITCHING SYSTEMS 619 v^Nn«l ONIOQino 01 I sav3-i indino TT I I §^ Ql- CO bO C I P3 bO I- ill lN3l^dinD3 3Nn Oi \smJ [smJ -® — ®-^b,^qnnr^^:>»^"^K5^ z oi SLEEVE TRUNK CIRCUIT termination and coding element (one per number) 0 — 9 0 — 9 0 — 9 0 — 9 THOU HUNDS TENS UNITS (a) 40 CODE — >. MARKING LEADS BUS BAR SYSTEM O z Ox: COMMON EQUIPMENT IDENTIFICATION START TONE C— - LEAD Q-uj S? t- EQUIPMENT 03 HO UJ INTERMEDIATE NUMBER //"SWITCH STAGES-^N^ SLEEVE TERM. TRUNK CIRCUIT __ --1 i V- 1 ItHOU & HUNDS 1 rCODE SOURCE N / L _l i ItENS & UNITS j /code source ^^) ~ (b) CODING ELEMENT (one per NUMB COMMON RECEIVER Ox: O TU ---J 3 O OSCILLATORS AMPLIFIERS 0. 0- (c) THROUGH CONNECTING— >*->; RELAYS Fig. 13 — Identifiers with various arrangements of coding elements. COMMON RECEIVER TRANSLATORS AND IDENTIFIERS IN SWITCHING SYSTEMS 623 Here all the trunks in the same frame have one lead permanently con- nected to a coding element which produces a 3-frequency code. This lead is connected to common detection equipment when the frame identification is wanted and this registers the frequencies and converts them to an out- put on a code marking lead system. Identification by Reading Positions of Normal Selectors There are numerous patents and a few commercial systems involving identification of calling subscribers, calHng trunks, selected trunks, selected senders or registers, etc., in which the identification process consists in read- ing the position of the fine finder, switch or relay unit which has been op- erated to select the line, trunk or other unit involved. One of the oldest patents on calling number identification involves this principle.^2 The number of the switch group plus the number of the switch setting may in certain cases correspond directly to the wanted code. In other cases this indication must be translated, sometimes to a new arbitrary code and sometimes to obtain a code in a different numeration or signaling system. Two methods of reading the switch positions are used: (1) counting of the steps or checking and registering other action taken by the switch during the time the involved fine or other circuit is being selected, and (2) checking and registering the switch position after selection. One of the interesting applications of this method for calUng number identification where the fine finder group and position numbers indicate the calling number is illustrated in the article covered by footnote No. 2}^ Comments on Identifiers The identifiers we have discussed are divided into the following general types: (1) Searching types (2) Coding element types Type A — with transmission to common output Type B — With transmission to source over input lead (3) Switch position reading types The first two types depend on the use of a considerable amount of equip- ment comprising the identifier and a large number of leads, and the prob- lem of economy is generally solved by using one of the regular conductors of each connection (usually the sleeve) as part of the identification circuit. 12 Mr. W. W. Carpenter et al, U. S. Pat. 2,112,951. 1^ R. F, Stehlik, "La Louviere Automatic Network of the Belgian Telephone Sys- tem," The Automatic Electric Company Technical Journal, January 1951. 624 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 This procedure, in practice, requires that the identification equipment be arranged to discriminate against the surges directly introduced on these leads by other equipment connected to them and against crosstalk result- ing from capacitive or magnetic coupling to other leads. This is done in part by adjustment of impedances and by discriminators either at the coding elements or in the common circuits. The problem of feedback has been dis- cussed under Section II. There is no special technical difficulty in this but the economics is important. The third general type has no special problems due to large numbers of wires or coding elements or feedback or crosstalk. The economic considera- tions involve the additional equipment in numerous other switching ele- ments to read the switch positions and the fact that, if the switch position does not directly give the wanted number in the desired code form, resort must be made to additional translation. Future possibilities lie in new methods avoiding these various problems economically, probably methods with entirely new basic concepts. Conclusion General Remarks The similarity of the problem of identification to that of translation is obvious. In identification the general problem is to construct an output code for information on an item to which the identifier has a connection. In translation the problem is to construct an output code for information on an item for which the translator has a previously registered code to use as input information. Now, if we stretch the point, we could very well say that the identifier, because of its connection to the object being identified, also has an input code when a signal to start identification is applied to this connection, the input code simply being a mark on a one-out-of-X basis. What is probably of more importance than the similarity of identifiers and translators is the frequent occurrence in switching networks of elements that functionally or operationally or both are essentially translators or identifiers although they are not so named. The ordinary fine relay, responding to the subscriber when he starts a call, can be considered as a coding element in a translator in some simple dial systems, as it translates an input code consisting of a mark on one out of 100 leads to marks in a two-place decimal system used to direct the line finder to the line. In the case of the No. 5 crossbar system, the line relays and their associated group equipments, although not so named, can cer- tainly be considered as a identification system as the end result of their operation is the registration of the calling equipment number in a common TRANSLATORS AND IDENTIFIERS IN SWITCHING SYSTEMS 625 unit and in some patent literature the term "calling line identifier" is ac- tually used. In practice this number is later used as an input to a translator (Fig. 7) to obtain the calling directory number. Any relay not serving merely as a means to renew or register a signal acts as the coding element of a tians- lator or identifier. Finally it looks to the writer as if any of the units made up of numerous relays, or other devices, as used in common control systems, act like trans- lators with a vast number of possible input and output con^binations with the action resulting from the output codes often fed back as part of a new input code. There might then be considerable possibiHty that any fundamental im- provement in general switching network theory or in the theory of trans- lators and identifiers would be of mutual advantage. Acknowledgements The author wishes to express his appreciation to Messrs. O. A. Friend, O. Myers and R. Marino, of the Bell Telephone Laboratories, for their assistance in the work on this paper. Bibliography "Historic Firsts: Translation," p. 445 of Bell Laboratories Record, November 1948. E. B. Craft, L. F. Morehouse, H, P. Charlesworth, "The Machine Switching Telephone System, A I. E. E. Journal, April 1923. F. J. Scudder and J. N. Reynolds, "Crossbar Dial Telephone Switching System," A.I.E.E. Transactions, V. 58, 1939. Oscar Myers, "Codes and Translations," A .I.E.E. Transactions, Vol. 68, 1949. T. L. Dimond, "No. 5 Crossbar AMA Translator," Bell Laboratories Record, January 1951. 0. J. Morzenti, "Number Group Frame for No. 5 Crossbar," Bell Laboratories Record, July 1950. R. C. Avery, "Pre-Translation in No. 5 Crossbar," Bdl Laboratories Record, April 1950. J. A. Lawrence, "Contemporary Telephone Mechanization Abroad and Possible Future Trends," Post Office Telecommunications Journal, August 1950. T. H. Flowers, "Introduction to Electronic Automatic Telephone Exchanges: Register- Translators, The Post Office Electric il Engineers^ Journal, Jan. 1951. O. A. Friend, "Automatic Ticketing of Telephone Calls," AJ.E.E. Transactions, V. 63, 1944. William Hatton, "Automatic Ticketing of Long Distance Connections," Electrical Com- munication, V. 18, 1940. J. E. Ostline, "The Strowger Automatic Toll Ticketing System," Strowger Technical Journal, June 1940. R. F. Stehlik, "La Louviere Automatic Network of the Belgian Telephone System," The Automatic Electric Technical Journal, Jan. 1951. G. T. Baker, "Calling Line Identification in Automatic Telephone Exchanges," /. E. E. Journal, Vol. 94, Part III, No. 28. March 1947. R. Taylor and J. McGavin, "The A. T. & E. System of Calling Line Identification," The Strowger Journal, April, 1949. Waves in Electron Streams and Circuits By J. R. PIERCE (Manuscript Received Jan. 9, 1951) This paper reviews some of the assumptions made and some of the general problems involved in analyzing the behavior of electron streams coupled to cir- cuits. It explains why a wave approach is used. The propagation constant of the wave is obtained in terms of the properties of the electron stream and the im- pedance of the circuit. Some general properties of waves are discussed. The im- portance of fitting boundary conditions in the solution of an actual problem is discussed, and examples, including that of "backward-gaining" waves, are dis- cussed. Introduction Of recent years, a good deal of work has appeared concerning small linear perturbations of uniform clouds of electrons and ions.*^~^ A number of questions can be raised concerning the physical interpretations of such mathematical labors. First of all, for there to be a very direct physical interpretation, the unperturbed state must exist at some time or place and then be modified in the manner described by the perturbation. This condition is satisfied, for instance, in the case of an electron stream of moderate current shot into a long metal tube and confined by a longitudinal magnetic field. However, if the current is made large enough, the uniform flow becomes unstable^ • ^ and the method of perturbations can be used only to establish such instabiUty and not to determine what form the flow will assume. I feel some misgivings about drawing physical interpretations from perturbations of uniform d-c. plasmas and infinitely extending clouds of charge unless these unperturbed states can be shown to exist physically, or unless the results can be shown * A few late references only are given; others are quoted in those cited. ^ D. Bohm and E. P. Gross, Theory of Plasma Oscillations: A. Origin of Medium- Like Behavior, Phys. Rev., Vol. 75, pp. 1851-1864 (1949); B. Excitation and Damping of Oscillations, Phys. Rev., Vol. 75, pp. 1864-1876 (1949). Effects of Plasma Boundaries in Plasma Oscillations, Phys. Rev., Vol. 79, pp. 992-1001 (1950). 2 J. A. Roberts, "Wave Amplification by Interaction with a Stream of Electrons," Phys. Rev., Vol. 76, pp. 340-344 (1949). ' V. A. Bailey, "The Growth of Circularly Polarized Waves in the Sun's Atmosphere and Their Escape into Space," Phys. Rev., Vol. 78, pp. 428-443 (1950). * "Traveling Wave Tubes," J. R. Pierce, Van Nostrand, 1950. » A. V. Haeff, "Space-Charge Effects in Electron Beams," Proc. I.R.E., Vol. 27, pp. 586-602 (1939). * J. R. Pierce, "Limiting Stable Current in Electron Beams in the Presence of Ions," Jour. A pp. Phys., Vol. 15, pp. 721-726 (1944); and "Note on Stability of Electron Flow in the Presence of Positive Ions," JoUr. A pp. Phys., Vol. 21, p. 1063, Oct. 1950. 626 WAVES IN ELECTRON STREAMS AND CIRCUITS 627 to be approximations to those which would be obtained for more realistic but mathematically more refractory situations. Other misinterpretations have arisen through combining non-relativistic equations of motion with Maxwell's equations and then attaching signifi- cance to terms of the order {v/cYJ Finally, granting that all else is well, it is unsafe to draw conclusions from the examination of particular solutions of differential equations. In a very simple example, it is impossible to determine the gain of an amplifier tube which uses an electron stream simply by examining various "waves" which can travel on the stream. In solving a physical problem, one must not only solve the differential equation involved but he must satisfy the appropriate boundary conditions as well. In all, such confusion as there has been concerning waves in clouds of electrons and ions seems to have arisen not through lack of mathematical ambitiousness but rather through simple errors in physical interpretation. The following material concerns itself with some particular types of "waves" and with the importance and consequences of fitting boundary conditions. The work treats a very easy case, simplified and abstracted from a physically realizable system. The case was made so simple in order to avoid painful mathematics which might obscure the actual points to be made. The purpose is to explore this simple case thoroughly, avoiding basic misunderstandings. If it is objected that matters so simple should not be treated at such length, because no one could misunderstand them anyway, I can only reply that I did misunderstand some of the matters recounted herein. I. Why Are Waves Introduced? We will consider the case of a narrow or thin beam of electrons across which we can assume that the electric field is constant. f In our calculations we assume that all electrons in a given very small region have the same velocity, thus neglecting the thermal velocity distribution. J We assume that the flow is a smoothed-out jelly of charge, J with the charge per unit mass characteristic of electrons; thus, we neglect individual interactions between electrons, and consider only a sort of average effect. We will write the quantities involved in the following forms velocity = v -\- Uq 'L. R. Walker, "Note on Wave Amplification by Interaction with a Stream of Elec- trons," Phys. Rev., Vol. 76, pp. 1721-1722 (1949). t This is in itself a drastic abstraction. No attempt wiU be made to justify it here, beyond saying that it is useful in considering the problems that follow. X Other drastic approximations for which no justification will be given. 628 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 Here wo is a constant component and v is sl small fluctiiatin? or a-c. com- ponent charge density = p + Po where again po is the average or d-c. component, which will of course be negative, and p is the a-c. component convection current density i — lo Here /o is the average or a c. current density and, as the electrons are assumed to move in the +2 direction, the current density in the +2 direc- tion is taken as — /o . In other work I have used i and /o as current rather than as current density; I hope that this will cause no confusion. It is assumed that there is no average field. It is assumed that there is an a-c. field in the z direction only, and this is called E. We have two equations to work with. One is div -i- uq) e ^ _ = — _ /^ at m Here e/m, the charge-to-mass ratio of the electron, is taken as a positive quantity. The time derivative is that moving with an electron. We can in- stead take derivatives at a fixed point d{v + «o) d{v -\- Uq) . f . . div + uo) -r. = — -\- \v + Uq) dt dt dz which gives dv , dv dt + '^dz + ^+(. + «o)^ (1.1) dt dz . dv e -, -{- V— = --E dz m The terms on the second line are zero because dm/dt = 0, du^/dz = 0. Further, let us consider a series of solutions of (1.1) for fields in which E has the same form in time and space, but varies in magnitude. As E is made smaller and smaller, v will become smaller and smaller, and the term vdv/dz, which is a product of two a-c. quantities, will become relatively smaller WAVES IN ELECTRON STREAMS AND CIRCUITS 629 than the other two terms involving v. In our small signal theory we neglect the term vdv/dZj and write t: + «o - = — E (1.2) dt dz m We note, then, that this approximates the true equation for small values of E and v only. We have another equation ~{i-h)= -I-Ap + ih,) (1.3) dz dt This is the equation of continuity, or of conservation of charge. If we integrate it over a small distance As we obtain {i - Io)z+Az - {i - h)z = -Q^ [(P + Po)A2;l The quantity (p + po)Az is the charge per unit cross section in the distance Az. Thus, the right-hand side is the rate at which charge in the distance Az decreases. The quantity on the left is obviously the rate at which charge per unit cross section is flowing out of the space Az long. If we carry out the operations in (1.3) we obtain As dio/dz = 0, dpo/dt di dz n dio _ " dz dt dpo dt yj di _ dz dp dt (1.4) (1.5) We need to add that the convection current is given by i — Iq= (p + Po)(t' + Wo) i — lo = PqV -{- puo + poUo + pv The term pqUq is a constant term and is to be identified with — /o — /o = PqUq (1.6) The term pv is a product of a-c. quantities. Suppose we solve all our equa- tions neglecting pv. Then, the error caused by this approximation will be less as p and v are less, that is, at small signal levels. Thus, we write i = pMo + vpo (1.7) 630 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 We now have three approximate equations, which are good approxima- tions at small signal levels (1.2) (1.4) (1.7) We can eliminate p and v from these equations and obtain an equation re- lating i and E. To do this we solve (1.7) for v dv dt + Uo dv _ dz di _ dz i = -1e m dp dt puo + vpo 1 . Uo V = — I — — p Po Po differential:'^ dv _ 1 di Uo dp dt po dt Po dt use (1.4) dv _ 1 di Uo di dt po dt pa dz differentiate (1.2) with respect to /, dt \dtj dz \di) ~ m~di and substitute for dv/dt , obtaining d'i , ^ dH , 2 dH e dE ,, „, ;r7^ + 2Mo-— +Wo— = --Po— (1.8) dt^ dzdt dz^ m dt This is an equation relating i and its derivatives with E. It is a linear equa- tion; that is, i and its derivatives, and E appear to the first power only. This is because we have neglected non-linear terms, saying that at low levels they are small compared with the linear terms. Now, the electron flow interacts with surroundings of some sort, or, we shall say, with a circuit. Let us consider as an example of a circuit a trans- mission line with a distributed capacitance C per unit length and a dis- tributed inductance L per unit length, which will transmit a slow wave. Suppose that the electron stream flows along very close to the line. Then WAVES IN ELECTRON STREAMS AND CIRCUITS 631 if the current ai of the electron stream, where a is the area of electron flow, changes with distance, a current / will flow into the line per unit length as shown in Fig. 1.1 where di J = -(T dz If V is the voltage on the line and / is the current in the line we write ^ = -C — - - dz dt ^ dz — = -Z — dz dt (1.9) (1.10) (1.11) -Ir CURRENT DENSITY I^ .^_^TRKKK5M^yM5WO^JMM^ L PER UNIT LENGTH C PER UNIT LENGTH +Z Fig. 1.1 — A transmission line with an electron beam very close to it. We can eliminate / by differentiating dzdt d'i dzdt dzdt cH 1 d^V . .aV (1.12) dzdt L dz" dt^ We can further identify the field acting on the electrons as dz In (1.8), let us replace E by means of (1.13), and let us differentiate with respect to z and again with respect to /. We obtain (1.13) {^i\^o ^v^'»^a- ^^v^^^ (^\ = e d'V — Po m dz'df- 632 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 We can substitute for dH/dzdt from (1.12) and obtain dz^ dz^dt \ ml dz^df a^F aV (1.14) Thus, we have obtained a linear partial differential equation in F, z and /. So far, nothing has been said about waves or wavelike behavior. We might solve (1.14) for any boundary conditions on V and its derivatives that we chose, by any means, as by using a differential analyzer or a digital computer. There is, however, a well-established technique for dealing with linear partial differential equations with constant coefficients, such as (1.14) is. It is known that they have solutions of the form V = Ae^^^'e-i^' (1.15) As (1.14) is an entirely real equation, if (1.15) is a solution, the real part of (1.15) is also a solution, i.e.. Re {Ae^'^^e-^^') is a solution. Hence, we may regard the real part of the complex V as the true physical solution. If we substitute (1.15) into (1.14) we obtain ulp* - 2«ocoiS' + ( T - uILC - a-lA oiY \^ m / (1.16) + 2woICco'j8 - LCo)' = 0 Now (1.16) is an algebraic equation in w and jS. How are we to interpret it? Suppose we are interested in devices driven from sinusoidal generators, such as amplifiers.* This means that co is real, and that it is the radian fre- quency of the applied signal. We may then regard (1.16) as an equation in /3, and, as it is a fourth degree equation, there will in general be four roots. We may regard these as pertaining to four waves, whose voltages vary as Fi = Aie'^'''-^''^ V2 = A^e'^"''^''^ V, = A.e'^'"'-^''^ V, = A.e'^'"'-^''^ * We might, on the other hand, be interested in devices with an imposed spatial pat- tern, as in a magnetron oscillator. In this case we might assume /3 as a given, real quantity and solve for real or complex values of w. WAVES IN ELECTRON STREAMS AND CIRCUITS 633 Each of these four components is a solution of the diferential equation. The solution of an actual physical problem will be the sum of the four compo- nents, or, if we like, the real part of that sum, and the amplitude factors Ai — Ai, which are in general complex, will depend on the particular physical problem which is solved. What has been the purpose of this argument? First of all, it is intended to indicate how the waves get into the picture. The differential equations for a long beam of constant average velocity uq and charge density po were Unearized by neglecting terms in which the products of a-c. quantities ap- peared. By this means a linear partial differential equation with constant coefficients which relates i and E was found. This was combined with the linear partial differential equation for a uniform transmission-line circuit, and an overall partial differential equation for V was obtained, linear and with constant coefficients. Such an equation could be solved by any means, but it is known to have wave-type solutions, and the solution of the original physical problem must be a sum of all such solutions. In general, we will not expect so simple a relation between i and V or E as (1.12), that for a simple transmission line. Further, for broad electron streams the electronic behavior cannot be expressed so simply as it has been in (1.8). Nonetheless, we will find wave solutions in which all quantities vary with time and distance as as long as (1) the d-c. beam properties (the undisturbed electron flow) and the circuit properties do not vary with z. (2) the signal amplitude is low enough so that terms involving products of a-c. quantities can be neglected. When this is so, the solution of a physical problem can be expressed as the sum, or the real part of the sum, of such wave solutions, taken with the proper amplitudes.! n. The Component Waves Once we are convinced that the solution of our problem can be expressed as the sum of a number of waves which are solutions of a linear partial dif- ferential equation, it is simplest to use this fact directly in finding certain properties of the waves of which the solution is to be made up. Let us, for instance, let E in (1.8) contain the factor jut —j?z e e t An additional overall condition is that the electron flow has no velocity distribution. 634 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 In Other words, let E in (1.8) be one of the wave components of a solution. Then (1.8) becomes (— ca^ + 2«oco/3 — ul^^)i = — Jw — poJS m (2.1) Here c, the dielectric constant of vacuum, has been introduced for reasons which will become apparent later. It is further of interest to introduce other simple parameters. - - - = 0)^ (2.2) m € = /3p (2.3) = iSo (2.4) 6) The quantity cop is called the plasma frequency (a radian frequency), cop is positive because po is negative. jSo would be the phase constant of a wave travehng with the electron velocity. While /3p would be the phase constant of a wave traveling with a phase velocity equal to the electron velocity, and having a frequency cop , we may merely regard jSp as a convenient parameter which increases as the beam current is increased. In terms of /3p and j8o -■ - ~^' ^, O^) (2.5) (^0 - ^) This may seem a strange form in which to write the equation. It will perhaps seem less strange, however, if we recall that the current density / in a dielectric medium is given by / = icoeE Thus, we see that for real values of jS the electron convection current den- sity i is that which would correspond to a negative dielectric constant or a negative capacitance. Its magnitude depends on /3p , which is proportional to the d-c. beam current density; and the magnitude becomes very large when the phase velocity of the wave approaches the velocity of the elec- trons, that is when j8 approaches jSo . WAVES IN ELECTRON STREAMS AND CIRCUITS 635 Suppose we consider a beam of area o-. We can write the total electron convection current /« in the form le = (Ti = Y^ (2.6) We will call Yg the electronic admittance; it is measured in mho meters. Later we will deal with waves in which the electron stream transfers power to the circuit, and it is interesting to see under what conditions this can take place. Let the amplitude of the wave under consideration vary with distance as We may take the complex nature of the propagation constant into account by substituting in (2.7) This leads to -j^ = Qfl - j^i Y = -j<^^^^l (2.8) Ye = coe(r/3^[2ai(i3o - /Si) - jQgo - ^if] [(/3o - ^lY + al] The electron stream can transfer energy to the circuit only if the real part of Ye is negative (a negative conductance). For a wave which in- creases in the direction of electron flow (the +z direction), ai is positive and the electronic conductance wiU be negative if jSi > j^o ; that is, if the electron velocity is greater than the phase velocity of the wave.^ For a wave which decreases in the +z direction, the conductance will be negative if the electron velocity is smaller than the phase velocity of the wave. Let us now consider the interaction of our thin electron stream with the circuit. Here there is some possibility of confusion. In (1.12) the field caused by impressing a current on a circuit was calculated. This may be likened to the voltage along an impedance Z caused by an impressed current 7. 8 This is indicated by very elementary arguments (J. R. Pierce and L. M. Field, "Traveling Wave Tubes," Proc. I.R.E., Vol. 35, pp. 108-111, Feb. 1947). It is easy to forget, however, and was recently pointed out to me, to my consternation, by Dr. L. J. Chu. 636 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 Figure 2.1 will help to make this clear. Here the impressed current I flows to the right and back through the circuit of impedance Z. The voltage will increase to the right and hence the field will be directed to the left. In general, for an impressed current / we will write the field produced as £ = -Z(co, 3)1 (2.10) Here Z(co, jS) is a circuit impedance per unit length, which is usually a function of a> and j8. In terms of an admittance, the relation connecting impressed current and field is 7=-7(,i3)JE: (2.12) WAVES IN ELECTRON STREAMS AND CIRCUITS 637 Another way of putting this is to say r.+ F(o,,|3) = 0 From (2.13) and (2.7) we obUin j3 = j3o ± ft ./_m_a /3) (2.13) (2.14) ELECTRON STREAM ■RESONATORS Fig. 2.2 — An electron stream passing through a series of resonators, as in a multireson- ator klystron. Suppose, for instance, that the circuit admittance is capacitive and is equal to that for a longitudinal electric field in vacuum of area equal to the beam area a. Then F(w, j8) = jwe(T mho meter and we have two unattenuated waves /3 = /3o ± jSp We see that whenever (1) the circuit admittance is inductive or (2) the circuit admittance has a dissipative component, jS will be complex, and there will be increasing and decreasing waves. Either of these conditions can be achieved, for instance, by surrounding the electron stream by a suc- cession of essentially uncoupled resonators, tuned to be inductive, or with dissipation, as shown in Fig. 2.2. This is merely a continuous multi-resonator klystron. In a transmission-line type of circuit such as we have considered and such as is used in the traveUng-wave tube, for instance, the circuit admit- tance depends strongly on the phase constant /3, and in solving (2.14) for ^ we must take cognizance of this fact. We can, for instance, derive the circuit admittance from (1.12). We can use E = j^V 638 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 and rewrite (1.12) as Now, if the impressed current j8i , that is for waves with a phase velocity less than the natural phase velocity of the cucuit. This is easily explained. For small values of /3 the wavelength of the impressed current is long, so that current flows into and out of the circuit at widely separated points. Between such points the long section of series inductance has a higher impedance than the shunt capacitance to ground; the capacitive effect predominates and the circuit impedance is capacitive. However, for large values of (3 current flows into and out of the circuit at points close together. The short section of series inductance be- tween such points provides a path of lower impedance than that through the capacitances and ground; the inductive impedance predominates and the circuit is inductive. Thus, for fast waves (J3 small) the circuit is capaci- tive and for slow waves (jS large) the circuit is inductive. We can, then, immediately make one observation. For a lossless circuit, any increasing or decreasing wave must have a phase velocity less than the natural phase velocity of the circuit. We can make another observation as well; if the circuit has loss, F(co, /3) will have a real component, and from (2.14) all the waves must have an imaginary component of j8, that is, they must be increasing or decreasing. WAVES IN ELECTRON STREAMS AND CIRCUITS 639 K we like, we can combine (2.15) with (2.14). Doing this directly, we obtain (^ - PoY = o^^-rKM' (^f4^ (2.16) Unless the electron velocity is near the wave velocity 03o near to ^i) we will expect two sorts of solutions: one sort, for which /3 is near to /5o corresponding to "space-charge" waves; and the other, for which ^ is near to zb/?! , corresponding to "circuit" waves. If /3o is not near to j8i , we can easily obtain approximate values of jS for these two t3^es of wave. To obtain /3 for the space-charge waves we put j8 = /3o on the right- hand side of (2.16) and obtain ^ = ft ± ^, //f^ (2-17) If (2.17) gives a value of jS differing by a small fraction from jSo , then (2.17) is to be trusted. To obtain j8 for the forward circuit wave we put jS = /3i on the left of (2.16) and in the numerator on the right. This gives for the forward wave To obtain the backward wave, we put jS = jSi on the left of (2.16) and in the numerator on the right, and obtain Again, (2.18) and (2.19) are to be trusted as long as ^ as given by (2.18) differs by a small fraction only from j8i . We see that according to (2.19) the space-charge waves are unattenuated (real 0) for /3o < jSi , that is, for electrons traveling faster than the circuit phase velocity, while there are increasing and decreasing waves for jSo > i^i , that is, for electrons traveling more slowly than the circuit phase velocity. We see from (2.18) and (2.19) that the circuit waves are unattenuated (for lossless circuits), and travel a little more slowly than in the absence of electrons. Further, we see that (2.17) and (2.18) are not to be trusted when 0o is close to jSi , that is, when the electron velocity is near to the circuit phase velocity. As a simple example, let /3o = iSi (2.20) 640 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 It will turn out that j3 will be very nearly equal to j3o . Hence, ^ = ^0 + i5 - j^ = -iiSo + 6 (2.21) Then, from (2.16) we have i5 = ±i8, V'- oieaKMdo + j8) 5(-2i/3o + 6)" K we neglect 5 with respect to jSo in the sums inside the radical we obtain the equation 53 = -j^l^^oieaK (2.22) / /■ e(TKy'\-Vs/2 - j/2) 53 = mUaKy'Kj) We see that 5i represents an increasing wave slower than the natural phase velocity of the circuit, 82 represents a decreasing wave slower than the natural phase velocity of the circuit, and 83 represents an unattenuated wave faster than the natural phase velocity of the circuit. The 3 5's are illustrated in Fig. 2.3. If jSo ?^ i3i , and if /3i is complex (a lossy circuit) the equation for 8 is more complicated, but 8 can be obtained numerically. In addition to the three forward waves, that is, waves in the direction of electron motion, there is a backward wave. This is very much out of syn- chronism with the electron stream, and the backward wave is essentially the same as the wave in the absence of electron flow. WAVES IN ELECTRON STREAMS AND ClRCmTS 641 III. Fitting Boundary Conditions; Gain So far the discussion has been concerned with a differential equation and wave-type solutions of it. Let us now consider an overall problem. Suppose that we inject an unmodulated electron stream into a circuit of some finite length and apply a signal to the end of the circuit nearest the source of ele.nrons. Suppose that we adjust the output termination so that there is no backward wave.* How will the field strength vary along the circuit? To answer this question, we must find out what combination in phase and amplitude of the three forward waves corresponds to these conditions. In terms of solving differential equations, we must fit the boundary con- ditions. From Section I we have (1.2) or with which we couple In terms of these relations become dv dt , dv . e J)^ i -A (fio - /3,) -,MB 0 = ft + js \Uom/ > U)'- ?- (3.1) (2.5) (3.2) (3.3) These relations hold for each of the waves separately. Now, let us denote by El , Ezj Ez the fields of the three waves, and by E the actual field on the circuit. Then at the beginning of the circuit, where £ is £o , the applied field, the ampUtudes £io , £20 , £30 of £1 , £2 and £3 must satisfy £10 + £20 + £30 = £0 (3.4) * This is a very special case, requiring a unique impedance terminating the 4-z end of the output circuit. See Section V. 642 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 Also, at the beginning of the helix, a-c. velocity and the a-c. convection current must be zero. This means that • ^ + ^ + ^ = 0 (3.5) Ol 02 03 Eio E20 Ezo ^ . ,. -^ + -TT + -72- = 0 (3.6) Ol O2 O3 For the case we have considered, /Si = jSo , jSi real, 63 = 5ie+^'^^'^/^^ and our equations become £10 + JE20 + -E30 = -Eo iiio + -c,2o6 -r -C,30 = 0 iiio -h ii20 ^ + -c,30 = U We easily see that the solution is jEio = £20 = -E30 = 3 -Eo (3.7) If E is the field at a distance 2 along the helix E = \ Eoe-'^''ie''' + e''' + e'^') (3.8) In Fig. 3.1, 20 logi _E Eo is plotted vs CN, a factor proportional to distance. We see that initially the ampUtude does not change. This is necessarily so. The strength of the field can grow only through the electron stream giving energy to the circuit. The electron stream can give energy to the circuit only if it has an a-c. convection current. Initially the electron stream is unmodulated and hence it can give energy to the circuit only after it has traveled far enough to become modulated. In the case we have considered, the amplitudes of the three wave com- ponents of the field are initially equal. Now, £1 increases with distance, while £2 decreases with distance and £3 is unattenuated. Hence, if the tube is long enough, £2 and £3 will be negligible near the output of the tube; and the field at the output, a distance t from the input, will be very nearly E = lEoe-^^'^e'^^ WAVES IN ELECTRON STREAMS AND CIRCUITS 643 Under these circumstances the gain G in db will be very nearly 20.0 17.5 15.0 I [12.5 ? 7.5 5.0 2.5 G = 20 logi Eo 20 logio ie^'^'^^ db G = -9.54 + g ^ {^'^IceaKY'^t // / '/ / / / ASYMPTOTIC ^y EXPRESSION J^^ / / y / y 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 CN Fig. 3.1 — Signal level along the helix of a traveling- wave tube. lo^ -^ -^ ^ ^ ^ o— z=o Ejl .Jf- z=l Fig. 4.1 — A high-pass structure in which the phase velocity is in a direction opposite to that of power flow. IV. Backward Waves and Other Peculiar Waves It is important to notice that, for the usual travelmg-waVe tube, it is possible to express the overall gain in terms of the increasing wave alone only because of the relative ampHtudes of the three waves which make up the solution of the particular problem considered. That this is by no means a trivial point can be demonstrated by considering a case in which the circuit is a high-pass filter, as shown in Fig. 4.1. For such a circuit, the phase constant /3i is negative for a wave excited at the left end of the line which carries energy to the right. Such a wave will not interact with elec- 644 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 trons moving to the right. A wave excited at the right with power flow to the left has a positive value of /3 and will interact with electrons traveling to the right. Let us consider such an interaction. First, as to the 6's. We see that, for a wave which varies with distance as where jS is a positive number and has power flow to the left, the sign of V jl must be the opposite of what it would be if the power flowed to the right. This can be taken into account by reversing the sign of K in (2.19), and making 53 = +j^lfii(^eaK (4.1) where K is now taken as a positive number. We can then take Here 5i represents a wave whose amplitude increases to the left, that is, a wave which grows in the direction of energy flow. We might think that this would immediately imply a gain similar to that obtained for energy flow in the direction of electron motion, but this would be jumping at conclusions. Suppose we taken z = 0 at the left-hand or output end of the circuit. There the electron stream enters unmodulated. There also we will assume the circuit to be terminated so as to prevent reflection of power. At the right- hand or input end of the circuit power will be fed in, giving an impressed field E{. Suppose 61 , 82 and 63 are the appropriate 6's for this case. We see that our boundary conditions are e~'^'\Ei^'''^ 4- E^oe'"'^ + £30^"'*'^) = Ei Eio . £20 I £30 _ Q 61 62 ^3 ^10 E20 EzQ ^ di 02 dj WAVES IN ELECTRON STREAMS AND CIRCUITS 645 We have a relation between the 5*s 02 = die 63 = die From this we easily we see that a solution of the last two equations is Eio = E20 = E30 Accordingly, the first equation becomes Eioe-'^'\e'''^ -f- e^''^ + e^''^) = Ei J, Ete^^'^ (4.2) Let us now assume that the tube is very long. We easily see that in this case I e'''^ I » 1 e'''^ I So very nearly \e'''^\»\e'''^ Eie'^''^ Eio = E20 = E30 = — —7- (4.2) and the total field at the output end of the tube is E = E10 + £20 + £30 = SEce'^'^e-'"'^ (4.4)1 This, however, is much smaller than the field Ee at the input end of the tube. What is the physical picture? The electrons are injected into the circuit as an unmodulated stream. In order to fit the boundary conditions at this point, the three waves must have comparable magnitudes at the point of injection. If this is the output, then any wave which ''grows" from input toward output must be relatively very small at the input. If boundary conditions are fitted for other cases, as, for an electron speed not equal to the circuit phase velocity O^o 9^ jSi), it may be found that the output may be a little greater than the input under some circumstances; this represents a small gain achieved through a spatial interference of the three wave components. 646 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 A sure way of distinguishing conditions which will allow amplification from conditions which will not is through a solution of the differential equations together with a fitting of the boundary conditions. In the case of backward waves there are, however, considerations concerning the source of energy and its transfer to the circuit (or field) which are useful. Suppose that an unmodulated electron stream enters a microwave ampU- fier, travels for some distance through it, and emerges. If the electromag- netic output power of the amplifier is greater than the input power, the additional power must have come from the kinetic energy of the electron stream. The average electron must leave the amplifier with less energy of motion than it had on entering it. We can say a Uttle more. Let us call the total velocity of electrons, a-c. and d-c, u. Then we have, corresponding to (1.1) du , du e ^ — + u — = — - E ot dz m (4.5) ot dz m We will consider an amplifier in which the u and E at any z-position are truly periodic. Let us integrate over the period of a cycle, r, and divide by r 1 u+-~ u'dt= - E (4.6) t r oz J t T Jt As u will be the same at t and / + r, the first term on the left is zero, and we have ~u' = E (4.7) dz Here u^ and E are time averages. The field E is produced in a linear circuit by (1) the application of an a-c. signal, (2) by the presence of the electron stream. Certainly, the applied signal can produce no average field in a hnear circuit. Further, unless elec- trons are turned back, the average electron convection current is inde- pendent of r-f level. In a linear circuit the average field must be propor- tional to the average impressed current, so the average field E must be zero or independent of r-f level. Thus, the time average of u^ at a given point must be independent of r-f level.* This means that the electron stream cannot be slowed down bodily by * L. A. MacColl pointed this out to the writer. WAVES IN ELECTRON STRE.\MS AND CIRCUITS 647 the r-f field. Energy is extracted from the stream only by a bunching process in which in the emerging beam the charge density is higher when the veloc- ity is below average than it is when the velocity is above average. In other words, the kinetic energy averaged over electrons is reduced, even though the time average of u^ is not changed. This means that the emerging beam must be strongly bunched if much power is to be abstracted. In the conventional traveling-wave tube all is well. At the input the r-f field is small and the beam is imbunched. At the output the r-f field is high, and the beam is strongly bunched, having lost energy to the circuit. Imagine a tube using a backward wave, however. The electrons are in- jected unbunched at the output, where the signal level is high. They emerge at the input where the signal level is low. If the tube is to give high power, the stream must emerge strongly bunched. The disturbance in the electron stream cannot gradually increase as the field ampHtude increases. jx, JXt JX; jx, JX2 jx, JXj Fig. 4.2 — A ladder network. We have seen that one cannot draw conclusions about gain just by look- ing at the propagation constants of the waves. Waves are merely solutions of a differential equation connected with a physical system. To find the properties of the system one must examine, not various solutions of the dif- ferential equation, but the particular solution (which may be a combina- tion of simple solutions) which applies to the system in question. As a further example, we will examine another system whose differential equations yield "growing" solutions which turn out to be backward waves. Consider the ladder network of Fig. 4.2. This propagates an unattenuated wave if Xi and Xz have opposite signs, {Xi inductive and Xz capacitive, for instance). If, however, Xi and Xz are both capacitive or both inductive, then a wave excited in the circuit decays exponentially with distance. If we speak in terms of /3i , then ft = —jai where ai is a real number. 648 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 The characteristic impedance K is reactive, inductive if both impedances are inductive and capacitive if both impedances are capacitive. Let K = jX, where Xq is a real number. Then a positive value of Xq means inductive elements, and a negative value capacitive elements. The space-charge waves are given by (2.17) ^ = ^o±^p i/-^^^^o«igo (4.8) y al + ^l We see that ,the waves are unattenuated for negative, capacitive values of Xq , and are increasing and decreasing for positive, inductive values of Xq . It can be shown that the increasing space-charge waves can be used to obtain gain. The forward circuit waves are given by using K = jXq , /5i = —jai in (2.16), /3 = —jai on the left and in the numerator on the right and j8 = —ja in the denominator on the right. " = •■(■ + £?#■)■" As a = y/3, the variation with distance is as The backward wave is given by using /3 = -\-Joli on the left of (2.16) and in the numerator on the right If a differs little from ±ai , we can expand the square root in (4.6) and (4.7), separate real and imaginary parts, and write: Forward wave: " "'V^ 2(Bl + a\) (3l + air ) (4.10) Backward wave: "A'"^ 2(^S + a?) ^ (^S + a?)7 ^ ^ The circuit "waves" which were rapidly attenuated in the absence of electrons (/3p = 0) are a little more or less rapidly attenuated in the presence of electrons (more or less depending on whether Xq is positive or negative, and on the relative magnitudes of /3o and ai), and they now have a phase constant, that is, an imaginary component of the propagation constant. WAVES IN ELECTRON STREAMS AND CIRCUITS 649 The phase velocity may be either positive or negative, depending on the sign of Xo . This added feature gives the solution a more "wavelike" quality, but physically we have merely a slight perturbation of the disturbance natural to the non-propagating ladder network. In the absence of electrons, there is no real power flow in the modes of propagation of a purely reactive ladder network in which the shunt and series reactances have the same sign. Such a network can of course transmit power to a resistive load, but it transmits no power when terminated in its (reactive) characteristic impedance. In the presence of electrons, there is a small power flow in the circuit. We can easily evaluate this. If, in (1.11), we assume a variation of the quan- tities with time and distance as we obtain a JU3L Here coL stands for the series reactance, which we may call Xi wL = Xi A positive value of Xi means series inductance. For non-propagating lad- ders, Xi and the characteristic reactance Xq have the same sign. We then have ^ Xi The quantity —ja/Xi as evaluated in the presence of electrons will be the "hot" characteristic admittance. The complex power flow P is P= VI* So, in this case * ^ p = ^-L vv* Xi Now, the "backward" wave, for which a is given by (4.12), "increases" in the direction of electron flow. For it, the real part of the power Re F is given by coeo-jSpOiiXo Note that Xo and Xi must have the same sign. Thus, the power flow for the wave which "increases" in the direction of electron flow is always in the direction opposite to the electron flow. The circuit power does not flow in the direction of increasing amplitude for the wave which "grows" in the KeP/VV*= - ,T^;"\C^, (4.12) 650 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 direction of electron flow. We might have deduced this from the fact that the phase velocity for the wave is greater than the electron velocity (see (2.9)). While the wave which increases in the direction contrary to electron flow has its power flow in the direction of increasing amplitude, it is a back- ward wave and hence not suitable for producing gain. The disturbance on the non-propagating ladder is closely related to a passive or cut-off mode of a waveguide excited at a frequency less than the cutoff frequency for the mode in question. In this case, the analogue of the circuit power VI* is the integral of the Poynting vector over the guide cross section. When electrons flow through a waveguide these cut-off modes are perturbed much as indicated by (4.19) and (4.12). Because the per- turbed modes have a "wavelike" character in that the propagation con- stant is no longer purely real, and because the amplitude may increase in the direction of electromagnetic power flow, some workers have proposed to obtain gain from these "growing waves."^ V. Further Considerations Concerning Boundary Conditions How necessary is it to fit boundary conditions in order to deduce what will happen? The suspect waves we have examined so far might be rejected as increasing in a direction contrary to the direction of electron flow,* or as having electromagnetic power flow in a direction opposite to the direc- tion of growth. Can we find some method for separating waves useful in producing gain from waves which are not, without consideration, explicit or implicit, of boundary conditions? Let us consider the problem of fitting boundary conditions for a circuit plus an electron stream. Imagine that the end of the circuit near to the electron source ("near" end) is connected to a load impedance Z and that the end away from the electron source ("far" end) is driven by a voltage V. Let the wave which increases most rapidly in the direction of electron flow vary in amplitude as exp (az). Suppose that the length of the circuit is great, so that aL is a large number and exp (aL) is a very large number. At the near end the various wave components must be so related that i and V are zero and that the circuit voltage is ZI. At the near end, all four waves must be used to fit the boundary conditions at a given voltage level. Disallowing very special values of Z, we would expect that at the near end the four waves will have comparable amplitudes (the amplitudes are re- lated by linear simultaneous equations). Thus, at the far end of the circuit, the wave which increases most rapidly with distance should strongly pre- dominate. It seems that the most rapidly increasing wave is naturally con- nected with excitation of the circuit at the far end. •Though rejected only through considering boundary conditions. WAVES IN ELECTRON STREAMS AND CIRCUITS 651 On the other hand, assume that the far end of the circuit is terminated in some impedance Z. Consider the case in which the electron stream is velocity modulated at the source end and no exciting voltage is applied at the far end. We would expect that the required boundary conditions at the source end could be satisfied by using the waves excepting the one which increases most rapidly with distance. At the far end, to make F = /Z it is necessary to add a component of the wave which increases most rapidly with distance, a component of magnitude comparable to the sum of other com- ponents present at the jar end. However, this added component is so small at the near end that there it can be disregarded. Thus, the manifestation of large forward gain comes not from the mere presence of a wave which increases in the forward direction, but from special properties of the waves and/or the terminating impedances which can be determined with cer- tainty only by fitting boundary conditions. Are not these arguments at variance with the usual analyses of opera- tion of the traveling-wave tube? Suppose, for instance, that the helix is terminated in an arbitrary impedance at the input (near) end and that a voltage V is applied at the output (far) end. What wave will predominate? For a lossless helix, the true answer is that the increasing (forward) wave, not the unattenuated backward wave, will predominate. This can be avoided only by (1) choosing a particular (matched) value of source im- pedance or (2) making the helix lossy enough so that the backward wave "increases" more rapidly in the -|-z direction than any forward wave does. In tubes with a uniform loss along the helix, expedient (2) is adopted; when a center lossy section is used, both (1) and (2) are invoked, (1) in the output section and (2) in the center lossy section. It is dangerous to consider the solutions of the linear differential equa- tions of a physical system singly rather than in the combination which satisfies the boundary conditions. This sort of reasoning might lead one to believe that the problem of obtaining high voltages can be solved by find- ing a solution of Laplace's equation (say V = 1/r) for which the potential goes to infinity at some point. Cautions against neglecting the problem of boundary conditions apply equally well to problems of instability (increase of disturbances with time) as to problems of amplification. Thus, electron flow may be unstable when none of the waves grows with time for real values of ^. On the other hand, in criticizing the work of Bohm and Gross,^ R. Q. Twiss has shown^ that electron flow is not necessarily unstable merely because some of the waves grow exponentially with time for real values of /3. 5 R. Q. Twiss, "On the Theory of Plasma Oscillations" Services Electronics Research Laboratory, Extracts from Quarterly Report No. 20, Oct. 1950, pp. 14-28. Interaxial Spacing and Dielectric Constant of Pairs in Multipaired Cables By J. T. MAUPIN (Manuscript Received April 24, 1951) A major handicap in the evaluation of different designs and manufacturing processes, in respect to efficiency of space utilization inside the sheath of multi- pair telephone cable, has been the lack of a simple and accurate method of meas- uring the dielectric constant of such cable pairs. This paper describes a simple non-destructive method of determining both the interaxial spacing between conductors of a cable pair and the dielectric constant. An important by-product of the work is the demonstration of the fact that e = L X C is not a valid means of determining the dielectric constant of cable pairs. Introduction A cable pair consists of two individually-insulated conductors, of nomi- nally equal circular cross-section, which have been twisted together in a long helix and stranded into a cable core with similar pairs. It has not been pos- sible to analyze rigorously the electrical characteristics of such a circuit in terms of its rather complex physical configuration. For this reason, methods largely of an empirical nature have been used in the past to correlate physical and electrical characteristics of multipaired cables. The capacitance of any system of conductors immersed in a homogeneous medium is directly proportional to the dielectric constant of the medium. The dielectric of a cable pair is not homogeneous, but it can be described in terms of a homogeneous dielectric which would produce the same capaci- tance. In addition to the dielectric properties of the insulating medium, the capacitance of a cable pair is determined by the disposition of the paired conductors with respect to each other and with respect to the surrounding pairs or sheath. In particular, the interaxial separation between the wires of a pair has a critical effect on capacitance. The interaxial separation is determined by the abiUty of the insulation to resist deformation due to compressive forces encountered in cabling operations. Thus, the capacitance of a cable pair is largely dependent on the mechanical and dielectric properties of the con- ductor insulation, and a criterion of the relative efficiency of an insulation is the capacitance level, for a particular conductor gauge, resulting from a given cable space allowance or space-per-pair. Experience with paper ribbon and paper pulp insulated cables has shown that occasional wide deviations in capacitance can occur even though the space-per-pair allowance is substantially constant. The aforementioned em- 652 MEASUREMENTS IN MULTIPAIRED CABLES 653 pirical methods of capacitance-space analysis do not provide any insight as to whether these deviations are due to anomaUes in the mechanical prop- erties or in the dielectric properties of the insulation, or both. With respect to some electrical and physical characteristics, it is evident that there is a close analogy between the cable pair and an "ideal" balanced shielded pair consisting of two straight and parallel soUd cylindrical con- ductors enclosed in a cylindrical conducting shield, with the center line of the pair coinciding with the axis of the shield. A cross-section of such a circuit is shown in Fig. 1. The conductors are insulated from one another and from the shield by a homogeneous dielectric. Rigorous mathematical expressions for the capacitance and inductance of the ideal pair in terms of its dimensions and dielectric constant have been Cmu-fc — Ct2 + -g" Fig. 1 — A balanced, shielded pair. derived by the Mathematical Research Group of the Laboratories and others. Measured values of the capacitance and inductance of a given cable pair, when substituted into these expressions, determine a set of dimensions and a dielectric constant value which describe an ideal pair having the same capacitance and inductance as the cable pair. The extent to which these idealized values represent actual cable conditions depends on the accuracy of the assumed equivalence of the two structures. The purpose of this paper is to describe a few simple but direct experi- ments, the results of which demonstrate that these idealized parameters are closely representative of actual cable conditions in so far as interaxial spacing and dielectric constant are concerned. Thus emerges a simple technique, based on easy-to-make low-frequency measurements, for quantitative evalu- ation of these two important cable pair parameters. AppUcations of the 654 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 method to commercial designs of multipaired cable are included in what follows. ■ Low Frequency Inductance and Interaxial Spacing The self-inductance of a pair of straight parallel wires in free space or within any non-magnetic shield is a function only of the ratio of conductor diameter to the interaxial spacing if the frequency is so low that proximity, shielding, and skin effects are negligible. The formula is as follows: L = 1.482 log -^ + 0.1609 (mh/mi) (1) a S = interaxial spacing d = conductor diameter The first term gives the self inductance due to net external flux-linkage and the 0.1609 constant represents flux-linkage within the non-magnetic conductors. Some textbooks give the formula with {2S-d)/d as the argument of the logarithm. This form is not valid when d is not small compared to S, as is the case with cable pairs. The derivation of formula (1) in Russell's "Alternating Currents" shows that it is vaUd for any S, provided only that the current is uniformly distributed across the conductor cross-section. While it was believed that formula (1) was valid for cable pairs at, say, 1000 cps, it was desirable to estabUsh experimentally whether or not the twist in the pair, and magnetic coupling between pairs, affected the measured inductance at a frequency in this range. The effect of coupling between pairs is greatest when all of the cable pairs except the pair under test are shorted together at both ends of the cable, thus providing a large number of closed loops for any induced currents. In making laboratory inductance tests at 1000 cps on lengths of 19-gauge cable with 0.084 /xf/mi capacitance (Type CNB) it was found that opening or shorting the surrounding pairs did not affect the measured inductance. Also, grounding or floating the far end of the test pair made no difference. The tests were repeated with the same results on lengths ranging from 300' to 5000'. It should be noted that a correction term must be added to the measured 1000 cps inductance (L') to obtain the true distributed inductance (L) when the cable length is such that propagation effects become appreciable. When the correction term is included, the equation for L at 1000 cps becomes: L = V + l/3{R'yC Where L', R', and C are measured inductance, resistance, and mutual capacitance, respectively. MEASUREMENTS IN MULTIPAIRED CABLES 655 Expressed as a percentage of L per length, the correction term varies as the square of length. It is only 0.5% for 750' of CNB but is 20% for 5000' of the same type of cable. The single correction term given is not sufficiently accurate for lengths of CNB greater than about 5000'. The comparable Hmiting length for smaller gauges would be less; it is about 1000' for 26-gauge pairs. It is also necessary to allow for stranding takeup effects when converting from per length to per mile values. Stranding takeup is defined as the incre- ment in length of a given pair compared to the cable length, due to the helix introduced in the pair during the cabling operation. It depends upon the size of cable and stranding lay and is negligible for cables of 50 small gauge Table I Comparison of Measured 1000 CPS Inductance With That Calculated From the Theoretical Formula Spacing (5) d/2S Calculated L Measured L % Difference mh/mi mh/mi 13 Gauge Wire 75.6 106.2 145.1 0.474 0.337 0.247 0.641 0.860 1.060 0.641 0.856 1.063 0.00 -0.46 +0.28 19 Gauge Wire 38.8 69.0 0.464 0.261 0.656 1.027 0.656 1.021 0.00 -0.60 Theoretical Formula L = 1.482 log 2S/d + 0.160 9 (mh/mi) pairs or less but causes an increase of 2.7% in pair length over cable length for pairs in the outside layer of a full size CNB cable (2|" diameter over the paper wrapped core). Some short lengths of pair with wires parallel and approximately straight and with accurately known dimensions were made up in the laboratory. Inductance measurements at 1000 cps on these pairs agree very closely with inductances calculated from formula (1), for d/2S ratios from about 0.25, which is close to the nominal value for cable pairs, up to nearly 0.50, which is the highest possible value. These results are shown in Table I. The 19-gauge pair with a d/2S ratio of 0.261 was twisted fixed carriage style under constant tension. There was no measurable change in inductance for twist lengths as short as 2", compared with the straight, parallel condition. Measurement accuracy was aboutdzO.25%, 656 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 The foregoing results lead to the conclusion that the effective djlS ratio along the length of a cable pair can be determined from formula (1) using 1000 cps inductance, with an accuracy equal to that of the inductance tests. Since d is generally known or can be found with greater precision than the inductance, S can likewise be found with an accuracy dependent on the precision of the inductance tests. This conclusion appUes regardless of the type of conductor insulation. However, it should be noted that formula (1) would not be accurate if there happened to be magnetic materials in close proximity with the pair under test, such as, for instance, pairs surrounding a core of steel tape bound coaxials. The Dielectric Constant The dielectric of a cable pair consists of a non-homogeneous mixture of solid insulating material and air. The dielectric constant of a cable pair can be defined as the ratio of the actual mutual capacitance of the pair to the mutual capacitance which would result if the solid insulating material were removed leaving a 100% air dielectric in the otherwise undisturbed cable. The problem is, of course, to find out what the mutual capacitance would be with an air dielectric, or with any other homogeneous dielectric of known dielectric constant. Because of the complex configuration of the cable struc- ture it is not calculable. The shielded balanced pair (referred to herein as the "ideal" pair) structure and its components of mutual capacitance are illustrated in Fig. 1. Although the cable pair structure is different from that of the ideal pair, it has es- sentially the same components of mutual capacitance. The static shield for the cable pair is not solid and perfectly cyhndrical but consists of the other cable pairs or sheath which are immediately adjacent to the pair under consideration. The direct capacitances of the two wires to this ground or shield are very nearly equal. Rigorous mathematical formulas have been derived by Mrs. S. P. Mead of the Bell Telephone Laboratories for the mutual capacitance (Cmut) and the capacitance to ground (Co) of the ideal pair. These formulas are given in Appendix I. For discussion purposes they can be written as follows: Cmut = 7"^ ^ (2) ^\2S' d) MEASUREMENTS IN MULTIPAIRED CABLES 657 where e = dielectric constant and /„, and /j, are the functions defined in appendix I. Dividing equation (3) by equation (2): Ca/c^^,= r^'^J (4) \2S'dJ Thus, the Cg/Cmnt ratio is independent of the dielectric constant, being a function only of the dimensional ratios describing the ideal pair configura- tion. The ratio d/2S also appears in formula (1). Therefore, knowledge of L, Cgj and Cmut for an ideal pair is sufficient to find its dimensional ratios and dielectric constant, using the following procedure: 1. Equation (1) is solved for d/2S, 2. Knowing Cg/Cmnt and d/2S, equation (4) is solved implicitly for S/D. 3. Knowing Cmut, d/2S, and S/D, equation (2) is solved for e. Curve sheets to faciUtate the solution of equations (2) and (4) for the ap- plicable ranges of d/2S and S/D are shown in Figs. 2 and 3. When this same procedure is appUed to a cable pair using its measured 1000 cps L, Cg, and Cmut, the dielectric constant value obtained is truly representative of the pair in accordance with our definition of dielectric constant, only if the ideal and actual structures are equivalent. An absence of rigor in this method would be expected due to differences in configuration, and non-homogeneity in the cable dielectric. The magnitude of the error in the dielectric constant of a cable pair, when determined by this method, was evaluated by comparison of tests on a cable having a known, homogeneous dielectric with tests on an identical cable structure having a non-homogeneous dielectric but a known dielectric constant. These tests were made on a short length of cable containing twenty-two 19-gauge pairs. The conductors were insulated with solid polyethylene. The core wrap was polyethylene tape under an alpeth* sheath. A low molecular weight polyethylene compound known as DXL-1 has the same dielectric constant as solid polyethylene (2.26). The compound is in a semi-solid state at room temperature and flows easily at 150° Fahrenheit. By filling the interstitial air space in the cable with DXL-1, a cable having a homogeneous dielectric with a dielectric constant of 2.26 is obtained. The dielectric con- stant of the cable structure before filling with DXL-1 is found from the ratio of mutual capacitance before and after filling, and a check on the accuracy of the ideal pair formulas as applied to cable pairs is available. * Bdl Laboratories Record, November 1948. 658 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 These objectives were not realized with the hoped-for finesse, because of difficulty encountered in filling the interstitial air space with DXL-1. Both vacuum and pressure injection methods were tried, and the best that was Cmut W^D y 1.40 y y y y y y y y y y y y y / y y / A 1.30 '4\ y y / y y y < A r\y y y y <. / 1.25 y y y .C / y / y /, / y y / 'r y y y / / / 1.20 y y / y y y / f y / y / / / y y y / / y ^y y / 1.15 r y y r" / y y V /^ / / y / y y / / 1.10 / y / / / / / / / y / y / 1.05 / / y / / / / y y 1.00 / y / / / 0.95 / 0.32 0.34 0.38 0.40 0.42 S/D 0.44 0.46 Fig. 2— Cg/Cn,ut as a function of d/2S. S/D. Obtained was a cable with from 85 to 90% of the interstitial space filled with DXL-1, or about 9?> to 95% of the total dielectric space filled with poly- ethylene. These percentages are based on the measured increase in cable weight as a result of filling with DXL-1, and the air volume before filling cal- culated from nominal insulated conductor and core diameters. Evidently MEASUREMENTS IN MULTIPAIRED CABLES 659 the cable did not fill completely, because small bubbles of either air or ethylene gas formed during the injection process and would not "wash out" by continued flow. While these results are short of the objective, they are close enough to be useful. 22 21 20 19 18 17 16 15 \ e = : DIELECTRIC CONSTANT UNITY FOR air) ^ \ Cmut = MUTUAL PAIR CAPACITANCE IN AtF PER MILE ^^ ^ s. ^: v^ $: s^ ^ V <^ ^^ S/D = ^.34 \ s.\ ^ ^ s^ 0.36 ■ \ X \^ Vs ^ 0.38 \ ^ n:: SN ^ 0.40 \ ^ s^ P^ ^ 0.42 V \^ ^ ^ ^ ^.44 \ X x" \S ^ ^.46 N s> ;>: :S: X ^ sN ::^ $^ :n S <: <> ^ ^ ^^ V V < <: ^ ^ $^ \, \ S s $^ ^ \ s^ ^ ^ \ < <: \ 0.18 0.20 0.22 0.24 0.26 0.28 0.30 d/2S Fig. 3 — e/Cmut as a function of d/2S, SD. 0.32 0.34 The remaining air in the cable, occupying interstitial space, should not reduce the dielectric constant below that of polyethylene (2.26) in propor- tion to the percentage of air volume. This is because the electric field is weaker in the interstitial space than in the space immediately surrounding the conductors. The dielectric constant of the experimental cable should, therefore, be somewhere between 2.26 and 1 + (93% of 1.26) = 2.17. 660 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 Table II shows the results of application of the ideal pair formulas to 1000 cps inductance and capacitance measurements on the experimental cable both before and after injection ctf DXL-1 compound. The dielectric constant so obtained for the cable pairs after injection of DXL-1 is 2.20. This figure is within the limits set forth previously, and it seems probable that it is ac- curate to =bl%, although there is evidently no way to make an independent check. If we accept 2.20 for the dielectric constant of the cable after filling with DXL-1, the dielectric constant for the unfilled or normal condition can be evaluated. Since only the dielectric was altered in filling the cable, the dielectric constant before filling is given by: . - 2 20 y 00881 _ ... €.ut - 2.20 X ^j^ - 1.81, Where: 0.0881 /zf/mi. = Cmut before filling. 0.1070 Mf/mi. = Cmut after filling. Table II shows, however, that apphcation of the ideal pair formulas gives 1.88 for the normal dielectric constant. This figure is 4% higher than the correct 1.81 value. Examining the changes in mutual capacitance and capacitance to ground which occurred when the cable was filled with DXL-1, it is seen that Cg increased by 27.9% whereas Cmut increased by only 21.4%. The direct capacitance between wires of a pair, Cu, increased by only 12.5%. Since Cn is a component of Cmut but not of Cg, this ac- counts for the lower increase in Cmut as compared with Cg. The amount of air in the cable after filling is so small that it can be assumed that the dielectric is substantially homogeneous. Had the dielectric been homo- geneous before fiUing, the percentage changes in Cg, Cmut, and Cu would all have been equal. Thus it is evident that in the normal condition there is a dielectric constant (eg) applicable for Cg which is different from €mut. We find that Cj, is: e =220X^:5??^ = 172 Where 0.0983 juf/mi. = Cg before filling. 0.1256 /xf/mi. = Cg after filling. For a given set of capacitance and inductance data, there is, of course, only one value of dielectric constant which will satisfy the ideal pair for- mulas. This value will not be truly representative of actual cable condi- tions if non-homogeneity exists. Non-homogeneity, as evidenced by the experimentally determined inequality in tg and €mut, accounts for the 4% MEASUREMENTS IN MULTIP AIRED CABLES 661 OOO 1 «» OO CM *-tes ^ ;3 Tl^VO ■rH*d > CS«N H U) l-~ vO ^ a u 1 Q Q 1 OO tH M H Q t^ H ■~-- cOrH <: O) )-) do !=> _ C/3 »5 a OO ^3 , 1 >< T^^ w a> OOOO ^ CS . On OS P^ kq do fN CN w 3 lOlO o S T— 1 t-^ t> o y-i 1—1 < ~^ q o •.-1 i-H d\ , 1 B3 ■g i^ o < a. O OtO dd«s o 6 1-1 5; 1 H i-q ■| -rHO 00 r- § 5 §2^ a o ^^?3 i "g S3^ c55 0\ (M 1 <=^°^ H en • • • 1 ;z; o U o a a Q Q "o O (3 •^ o injec njecti rease. JU— o |Sfi 0. PC < ^ ;l 662 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 error in the 1.88 figure. This follows from the fact that if the Cg/C mut ratio obtained in the filled or homogeneous condition is used in the determination of the normal dielectric constant, then the correct 1.81 figure is obtained. Of course, these statements regarding the accuracy of the normal dielectric constant are predicated on the absolute accuracy of the 2.20 figure for the dielectric constant of the filled cable. However, as pointed out previ- ously, there is but little room for uncertainty in this connection. To summarize, it appears that the principal error involved in the use of ideal pair formulas to determine the dielectric constant of cable pairs is due to non-homogeneity of the dielectric. For polyethylene insulated 19-gauge pairs the error is about 4-4%. The magnitude of error expected for paper and pulp insulated pairs is less, as is explained below. a. Effective Diameter of Shield It has been shown that solution of equation (1) provides a value for S which does in fact equal the average interaxial spacing between wires of a cable pair. In the process of finding € using the ideal pair formulas, a value for S/D is found from which a value for D can be determined. The relation between the D value and the physical configuration of the cable pair struc- ture is not precise. It is necessary to consider that D represents an effective diameter of shield; it is the diameter of the cylindrical shield of an ideal pair structure having the same d/2S and Q/Cmut ratios and the same d as the cable pair. The value of effective D is larger if the dielectric is non-homogeneous, as shown by comparing the figures for D in Table II obtained before and after filling with DXL-1. The D value obtained under homogeneous conditions is more representative of the average physical placement of conductors com- prising the shield. b. Paper Ribbon and Paper Pulp Insulated Cable The distribution of solid insulating material in paper ribbon or pulp in- sulated cable is different from that in polyethylene insulated cable. Whereas in the latter there is a solid sheath of insulation around the conductor with air occupying interstitial space only, the paper ribbon or pulp insulated cable has some air dispersed among the insulating material in all portions of the dielectric space. "Interstitial space" is not well defined since the paper insulation tends to deform during cabling operations. This sort of dielectric would seem to be more homogeneous than that of the polyethylene insulated cable. A method for approximating the ep/e,„ut ratio in terms of power factor measurements on the balanced and grounded circuits is discussed in Ap- MEASUREMENTS IN MULTIPAIRED CABLES 663 pendix II. e^/emut ratios obtained for three pulp insulated cables do not differ from unity by more than d=2%. These results, although not con- clusive, tend to substantiate the above qualitative comparisons. It is be- lieved, therefore, that e values obtained for paper ribbon or pulp insulated cables are probably accurate to about 1 or 2%. Table III shows results of the use of the methods herein described to obtain the average S, e and effective D for examples of some cable designs now in use or under experimental investigation. These data are included pri- marily to illustrate the method for a variety of cases, and are not compre- hensive enough to serve as the basis for a study of the various cable designs and insulations. c. Dielectric Constant from L X C at High Freqttencies For the ideal pair structure the mutual capacitance and inductance are inversely related when the frequency is so high that current does not pene- trate either conductors or shield. The relation between inductance and capacitance, in practical units, is then: €= 34.70 CL«, (5) Loo = limiting value approached by inductance as the fre- quency increases indefinitely — mh/mi. C = capacitance — /zf/mi. It is known that Loo of individually shielded pairs, that is, pairs having metallic tape shields applied with an overlapped longitudinal or helical seam, can be accurately approximated from a series of inductance tests using the relation: Lf = L^ + ^y (6) Where Lf = distributed inductance at frequency F. M = a constant F = frequency The tests are usually made in the range from 2 to 5 mc. Application of formulas (5) and (6) to individually shielded pairs is known to be an ac- curate technique for evaluating the dielectric constant of non-homogeneous combinations of air and solid materials and has been in use for many years. This same method has sometimes been used with cable pairs. However, for the filled cable having a dielectric constant of about 2.20, these techniques gave a dielectric constant value of 2.58, which is about 17% too high. The reason for this large discrepancy is apparent when it is considered that the inverse relationship of L and C obtains only when the static and magnetic 664 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 So « r-, E5g «> lO io Jo lO 00 .£5 re go O »0 lO »— 1 t^ CS tH T-( ^-H T-H § vo r>- to »o vo CO fOfOCO ro 1 t^ CN On OO '— 1 iou-)a\Oo ^-1 tH O '-H •<— 1 "a en ooio Ofot^ Ir-- to »0 -"^ VO fOcOOrfiiO CS CO CO CO CM S<6d>d>S !3 CD a »o CO < i i 6 OOsOOOvO ■^' d d d ■-h' 1 VO Os O OMO i O O '— • CO »-i T-H fN ,-( t^ ro ddddd ■1 1 1 1 .s ^^ aa| .-2.-2 ^ ^ >^ «_ «_ Ui ^^ "nj ocs i OjOvOjC^ON 8^8 8 go -§ ^'i OJ w O ^ 4>.S O e<3 ^ 111' 111 III ^D IZi .t3 Oi ^ M i ^ ^ o >'0-'^co ?^ C ^ fe.lg I ^-5 o § en C! «^ j3 a Si 3 q3 H-a o It (U OjQ « M O S3 ^, -O MEASUREilENTS IN MULTIPAIRED CABLES 665 fields are completely terminated on the same shielding surface. The shield around a cable pair resembles a Faraday "cage" of wires which is inherently transparent to the magnetic field at low frequencies. Furthermore, at the highest frequency investigated (about 5 mc), the magnetic shielding of a cable pair by the adjacent surrounding conductors is still much less effec- tive than the essentially perfect static shielding. Thus, it is concluded that the L X C method should not be used for cable pairs when good accuracy is desired. Acknowledgments The writer wishes to acknowledge the valued assistance of his associates in this work, which was directed by Mr. O. S. Markuson. APPENDIX I The following formulas were developed by Mrs. S. P. Mead: I. Formula for the mutual capacitance of a balanced shielded pair: 0.01944 € ^mut — /l 1 ^\ Cmut is in fii/mi. u = d/2S V = S/D d = conductor diameter 5 = interaxial separation D = inside diameter of shield € = dielectric constant (unity for air) 8i2 is a complicated function of u and v. It increases for larger values of u and/or smaller values of v. The term 0.1086 5i2 amounts to from J% to about 7% over the ranges of u and v values plotted in Fig. 3. n. Formula for the capacitance to ground of a balanced shielded pair: _ 0.03889 € ^' ~ , /[3 - Vl + 4^2] [1 _ y\i -I- ^u^)]\ -I- 0.4343A1 log Suv" ') Cg is in /zf/mi. e, u and v are defined in section I. Ai is also a compUcated function of u and v. The term 0.4343 Ai amounts to from less than J% to about 3% over the ranges of u and v plotted in Fig. 2. It increases for larger values of u and/or larger values of v. 666 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 APPENDIX II It has been shown that if there is a dielectric constant for capacitance to ground (e^) which is different from €mut, then values of €mut as found from the ideal pair formulas will be in error. This appendix describes results of an attempt to evaluate the e^nut/^g ratio for paper ribbon and pulp insulated cable using a method suggested by Mr. M. C. Biskeborn. It was reasoned that whatever non-homogeneity exists in the cable dielectric would be caused by variations in the insulation density in various portions of the dielectric space. Compressive forces encountered in twisting and stranding the pairs tend to make the density for the space between wires of a pair high as com- pared with an average density for the total dielectric space. Since (e — 1) and the power factor, or simply G/C, go to zero approximately in direct Table A Evaluation of eg/emut for Pulp Insulated Cable AWG Description Cable Averages 1000 cps A = Gmut Cmut Cable Averages 1000 cps B = Cg F = B/A Power Factor Ratio «g Cmut /if/mi Gmut /timhos/mi. 2.00 1.12 1.09 Cg /if /mi. Gg Mnahos/mi. emut 19 19 22 51 Prs. Pulp 51 Prs. Pulp 51 Prs. Pulp 0.0858 0.0811 0.0773 23.3 13.8 14.1 0.0850 0.0810 0.0779 1.86 1.19 1.08 21.9 14.7 13.9 0.94 1.065 0.985 0.980 1.022 0.995 proportion to the amount of soUd dielectric material, the following equation may be used to find an approximate value for eg/emut: €g — 1 Power Factor of Grounded Circuit €mut ~ 1 Power Factor of Balanced Circuit in ~ r — 7r — ~ ^ (power factor ratio) €mut -1 tjmut/v-'mut Dividing by €mut and rearranging: €mut = F + \ Cmut / Substituting 1.50 for Cmut on the right hand side introduces but small error in the eventual result since F is known to be closely equal to unity and permits solution for €(,/€mut as follows: = 1 Cmut C-i-O MEASUREMENTS IN MULTIPAIRED CABLES 667 This relation was used to evaluate €o/€mut for 3 pulp insulated cables for which the necessary data were available. The results are shown in Table A. None of the 3 cables has a Cg/emut ratio different from unity by more than 2%. The average for the 3 cables is 1.0 and it is felt that the ±2% deviation could be due to inaccuracies inherent to conductance measurements. These data represent the only attempt to quantitatively evaluate non-homogeneity in pulp or paper insulated cable dielectrics and, while not by any means conclusive, they tend to substantiate the belief that the effects of any such non-homogeneity on the ej,/€mut ratio is small. A^-Terminal Switching Circuits By E. N. GILBERT (Manuscript Received Feb. 14, 1951) The circuits considered have N accessible terminals and are operated by gangs of selector switches. Synthesis of any iV-terminal switching function is accomplished. The synthesis method is proved to be economical in the sense that the switching functions which can be synthesized by any other method using much fewer contacts comprise a vanishingly small fraction of the total of all possible switching functions. Introduction In a recent issue of The Bell System Technical JoumaP, C. E. Shannon discussed the synthesis of two-terminal relay contact networks. Some of his results will be generalized in this paper to A^-terminal networks which use selector switches with any number of positions instead of the two of a relay. The kind of circuit which will be considered may be visualized as a black box with N accessible terminals and with M shafts extending from it. Each shaft operates a selector switch (which will usually consist of several simple selector switches ganged together) inside the box. The rotors and con- tacts inside the box are connected electrically to one another and to the N terminals so that each way of setting the M shafts determines a pattern of interconnection of the N terminals. We do not permit the black box to contain relay magnets or other devices which would allow the circuit to operate sequentially. Because of this re- striction our results apply only to the simplest kind of switching circuit in which the state of the N terminals depends only on the present state of the M shafts, and not on the past history of the shafts. We may then use the term N -terminal switching function to mean a rule which assigns to each way of setting the M shafts a state of the terminals. We are concerned with the problem of synthesis: given an TV-terminal switching function/, to find a switching circuit for which the states of the shafts and terminals correspond in the way indicated by /. Let />i , • • • , />Af be the numbers of positions which the M shafts can assume. Then there are Pi " • pM different states of the shafts and the shafts have a memory^ » C. E. Shannon, B.S.TJ., 28, pp. 59-98 (1949). « C. E. Shannon, B.S.TJ., 29, pp. 343-349 (1950). 668 iV-TERMINAL SWITCHING CIRCUITS 669 M ^ = Z log pi t=l bits (in this paper "log" stands for "logarithm to base 2"). The results to follow include an estimate of the minimum number of contacts needed for almost all iV-terminal switching functions and a network synthesis method which uses a number of contacts of the same order of magnitude as the minimum number. The number of contacts needed for almost all iV- terminal N log N l" switching functions is about „ . , — whenZf andiV are large. The words ±? + log iV "almost all" are used here in the sense that the fraction of switching func- tions which can be synthesized using fewer contacts than the given number tends to zero as R and/or N increases. The number of contacts used by the synthesis method is about — — — where P is the number of positions on the largest switch. The factor P can be reduced in most cases. The analogous ex- pressions found in Shannon's paper are — and where n is the number of n n switching variables. One of the most surprising facts about switching functions is that, if H is moderately large, almost none of them can be synthesized without using fantastically many contacts. This is already true of Shannon's two-terminal networks, and for iV-terminal networks the situation is even worse. The reader may first turn to page 685 where a numerical example illustrating this phenomenon is given. These paradoxical results are explained by noting that switching functions in general are much different from the usual kinds of switching functions which have practical applications. One concludes that the invention of better methods for synthesizing any imaginable function whatsoever will be of little help in practice. Almost all these functions are impossible to build (because of contact cost) and would be of no use if built. Instead one must try to isolate classes of useful switching functions which are easy to build. Part I: Two-Terminal Networks Selector Switches A typical selector switch is shown in Fig. 1. It consists of a number of rotors turned by a shaft which can be set in any one of p positions. In each position of the shaft, certain of the rotors touch contacts, thereby closing those branches in the network containing the touched contacts. However, the only kinds of switches to be considered here are those with the property 670 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 that, if a contact is touched by a rotor when the shaft is in position number j, then this contact remains untouched for all other positions of the shaft. Networks built from two-position switches are analyzed with the aid of Boolean Algebra. It is possible to construct an algebra which is appropriate for selector switch circuits. A detailed account of this algebra has been given by H. Piesch.^ The state of a switch with p positions can be associated with a switching variable x which ranges over the values 1, 2, • • • , />. Then "a; = ^" means the same as ''the switch is in its k^^ position." The state of a two- terminal network, using M switches with pi j - • - , and pM positions, is a hindrance function f{xi , • • • , Xm) of the M switching variables Xi , • • - , Xm with Xi -^. SHAFT Fig. 1 — Selector switch. ranging from 1 to pi . As usual / = 1 means the circuit is open and / = 0 means the circuit is closed. Then/(ii;i , • • • , Xm) + g{xi , • • • , Xm) is the func- tion representing the series connection of two networks whose functions are f and g while f{xi , • • • , Xm) g{xi , • • • , Xm) represents the networks/ and g in parallel. The circuit which consists of just a rotor which touches a contact in its i^ position has hindrance function fl if X7^ i Ciix) = \ [0 \i X = i »H. Piesch, Archivfiir ELectrotechnik, 33, pp. 674, 686 and pp. 733-746 (1939). TV-TERMINAL SWITCHING CIRCUITS 671 There is no simple identity which corresponds to the Boolean Algebra expansion by sums. An identity analogous to the Boolean Algebra expansion about xi by products is (1) »=1 where the range of xi is from 1 to p. To prove (1) we need only observe that in the product all the terms for which i 9^ Xi have the value 1. The remain- ing term, for which i = Xi , has the value /(xi , • • • , Xm)- The switching interpretation of (1) is illustrated in Fig. 2. By repeated use of (1) it follows that any function f{xi , • • • , Xm) can be written as an expression involving ■rO,X2,-,XM) / / ei(x,)^ r f(2,X2,-,XM) / ep(x,) Q - \ ■r(p,x2,-,XM) Fig. 2 — Expansion oijixx , . . . , xm) about x\ . parentheses, addition signs, multipUcation signs, the ^ife), and nothing else. Such expressions may be regarded as Boolean functions with the eiix^ as variables; they may be rearranged and factored according to the usual rules of Boolean Algebra. However, one should keep in mind that the ei{x^ are subject to the constraints that a selector switch can be in only one position at any given time. The effect of these constraints is to add a cancellation law 6/.fe) + ^tfe) = 1 \i ]i7^ i. The inverse ei{xj) of the Boolean variable ei{xj) is the Boolean function ei{xj) = 1 when ei{Xj) = 0 0 when ei{xj) = 1 . 672 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 Regarded as a hindrance function of the switching variable Xj , 0 when Xj 9^ i Then by (1), e'iixj) = II when Xj = i e'iixj) = n ^h{xj). If the switch xj has pj positions, it takes pj — 1 contacts to build a circuit with hindrance function ei{xj). Synthesis Suppose that M shafts, governed by switching variables Xi y - -- , Xm y are given, together with a two-terminal hindrance function /(xi , • • • , Xm)- The synthesis problem is to design a network with hindrance function f{xi , • • • , Xm)) adding suitable rotors and contacts to form selector switches from the given shafts. One solution can be found immediately: (i) As described above, express the hindrance function f{xi , • • • , Xm) as a Boolean function ^(^1 , • • • , ^r) of Boolean variables ^1 , • • • , ^b (which are the ei{xj) with new labels). Here R = pi + p2 -\r " ' -\- pM - (ii) Any of the well known methods of synthesizing relay networks can be used to design a network operated by the Boolean variables ^1 , • • • , ^r and with hindrance function ^fe , • • • , ^r). (iii) In the network found in (ii) replace each contact ^a by the appropri- ate ei(xj) and each back contact ^a by the appropriate circuit ei{xj). The solution found in (iii) will ordinarily use up a number of contacts which is unnecessarily large by many orders of magnitude. From Shannon's theorems on relay networks we know that the probabiUty is high, that as many as 2" contacts will be needed in step (ii). The final circuit (iii) will have even more contacts if some circuits ei{xj) are used. The synthesis process which follows replaces the exponent i? = X^^i pi in the estimate of the number of contacts by the smaller number ^JLi log pi . The reader may recognize the process as essentially the same as the one given by Shannon for two-terminal relay networks. The network will again take the form of a tree connected to a circuit which produces all functions of the switching variables which govern it. iV-TERMINAL SWITCHING CIRCUITS 673 If one expands f{xx , • • • , Xm) about Xi , • • • ,Xk one finds / = II krfe) + ^5(^2) + • • • + e,{xk) (2) 4-/(r, 5, ••• ,z, Xifc+i, ••• jOtTAf)] where the muhiple product is taken over the entire range of the variables ^*i , • • • , ock . The different functions er{xi) + esix^) + • • • + ezipck) can all be realized with one tree circuit as shown in Fig. 3. If the expansion had been performed about all the variables X\y • • • ^Xm ^ identity (2) would e,(Xi) + ei(X2)- e,(x,) + ei(X2)- .+ei(Xk) •+e2(XK) eptC^O + ep2(X2H...+ep^(Xk') Fig. 3— Tree. show that the desired function / could be synthesized by connecting one terminal to the input lead of a tree and the other terminal to certain of the tree's output leads. The number of contacts used would have been about 2^"*"^ . The method which follows uses still fewer contacts. The network which we use to synthesize the function/ is shown in Fig. 4. It consists of the tree of Fig. 3 with its output leads connected to the input leads of a network on the right which is designed so that the hindrances from its input leads to its output lead are the functions /(r, 5, • • • , z, Xk+i , 674 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 • • • , ocm)' For given values ro , ^o , • • • , Zo of the switching variables ^1 , • • • , ^jt of the tree, there is only one closed path through the tree ; this path ends at the output lead labelled groW + • • • + ^«ofe)- The hindrance from this point to the output lead of the right-hand net- work is the hindrance of the network of Fig. 4. This hindrance is just /(ro , ^0 , • • • , 2o , Xk+i , • • • , Xm) (note that the connections to the dis- junctive tree do not cause any interconnections among the other leads of the right hand network), which proves that the network has the required hindrance. By proper choice of the number k of switches in the tree we will obtain an economical design. Network to Produce All Functions To produce all of /(r, ^, • • • , z, Xk+i , • • which produces every function of (xk+i , Xm) it suffices to build a circuit • , Xm)' Let these variables be ei(Xi)+...+ei{Xk) ei(x,)+...+e2(XK) TREE ep,(x,)+...+ep^(xk) Fig. 4 — Network for/(a;i f(i,...,i,Xk+i,---,XM) f{1,.--,2,Xk+i,---,XM) NETWORK Xm)- relabelled yi , • • • , yL and have ranges pi , Pi, " ' , pLhe called P. Theorem I. A network which produces every function of {yi , be built with a number xj/l of contacts satisfying , pL . Let the largest of , Jl) can (3) rpL < P2' The proof is by induction on L. Suppose that a network to produce every function of (3/1 , • • • , yy_i) has been built with ^y_i contacts and try to build one for every function oi {yi , • • • , yy). The number of functions which the network must produce is 2^*"^' , for there are p\ " • pj different ways of setting the switches and two choices (0 or 1) for the value of the function for each state of the switches. Of these functions, the ^j_i network itself provides 2^' '''"' functions with no additional contacts (these are the func- tions independent of yy). Any one of the remaining (2 ''*'^' — 2^^'"^'^^) func- iV-TERMINAL SWITCHING CIRCUITS 675 tions / can be obtained by connecting to the functions f{yi , • • • , jj-i ,1), • • • Jiyi , • • • , Ji-i , py) through eiiyi), • • • , e^^iyi) as shown in Fig. 5. In this way a new network is found which produces all functions of the j vari- ables and uses ypj contacts where (4) y^i - ^y_i < p(2^^---^' - 2^'-"^-'). If we now assume that formula (3) holds for ^y_i we obtain Thus the theorem will follow by induction when we prove (3) for the case L = 1. Since ^o = 0 (no contacts are needed to synthesize the two functions 0 and 1) the inequality (4) reduces, when L = 1, to ^1 < P(2^^ - 2) and the theorem is proved. Fig. 5 — Network to produce all functions of (yi , . . . , yy) . The induction process we have just described will use up the smallest number of contacts when the large switches are used up first and the small switches last. If, in the process, pj > pj+i , then the number of contacts which would have been saved by making switch yy+i precede switch yj is found to be (pj - Pj+i)2 P1---PJ. X2''' - 1)(2 P/+1 1). By adding switches in order of decreasing size in the induction process, the factor P in (3) can be reduced to nearly pi. , the smallest of the L ranges. This refinement is unnecessary for the theory which follows. 676 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 The Tree The number of contacts used in the tree of Fig. 3 is A ••• ^.(l + i+ — L- + ••• + -— L—). \ pk pk-1 pk pk " • pll It can be shown that the most economical way to build the tree is to put the small switches at the narrow end of the tree. If the smallest number of positions of any of the switches in the tree is p\ then the number of contacts in the tree is less than Upper Bound Having counted the number of contacts which are used in the tree and in the network which produces all functions in Fig. 4, it only remains to decide how many of the given switches X\^ • • • , ^Cm are to be put in each of these two parts. Theorem II. Let P be the largest of the numbers pi ^ • • • , pM of values which the variables Xi , • • • j Xm can assume. Then any switching function of (xi , • • • , Xm) can be synthesized using no more than contacts when H > 4 bits. To prove the theorem we consider two cases according as P is greater or less than F - 2 log H. Case 1: (P >' H - 2\ogH) In this case we use the synthesis process described above, putting all the switches into the tree and none in the network which produces all functions. The number of contacts used is less than 2-2^ and the theorem follows because P>H-2\ogH, Case 2: {P < H - 2\ogH) In this case we use the synthesis process described above, putting into the right-hand network a collection 5 of switches so chosen that YLs pi comes as close as possible to -^ — 2 log ^ without actually exceeding it. Then if 11^= {H - 2 log H)F, iV-TERMINAL SWITCHING CIRCXriTS 677 we have F < 1. Also, F 9^ 0 since any pi satisfies Pi 1/P. For if 0 < F < 1/P, adding another switch to the collection S will increase XI^ pi without making it exceed F - 2 log H. Using (3) and (5), the number of contacts in the network is less than ^ {H - 2 log H)F -\H'^H-2 log H/ ' Since P < H -2\ogH, W H H - 2logH and the theorem is proved. Only a small fraction of the functions will use up this many contacts. In any particular case, the number of contacts used will be about (hi) H - 2 log H and, if many different sizes of switches are used in the network, one should be able to make 1/F much closer to 1 than P. Even when all the switches are the same size, one expects in about half the cases. Part II: TV-Terminal Networks Synthesis Let the accessible terminals be labelled 1, 2, • • • , N.To each pair i, j of terminals of an iV- terminal network there corresponds a hindrance function Bij{xi , • • • , Xm) which tells whether or not there is a closed path between i and j. The Bij satisfies a consistency requirement (7) "Bia + Bab+ '-' +Bde+Bej=0 impUcs Bij = 0". The number of consistency requirements (7) is ^ N\ ^eNl h2{N - r)\^ 2 ' 678 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 However, one can show that all the requirements (7) hold if and only if the N(N - 1){N - 2) requirements ''Bia + Baj = 0 implies Bij = 0" hold. N(N — 1) Conversely, any set of hindrance functions which satisfy (7) determine a realizable iV-terminal network. One way of synthesizing the network is just to connect, between each pair i,j of terminals, a two-terminal network with hindrance function Bij . It follows from theorem II that Theorem III. Any N -terminal switching function of switches with P or fewer positions can be synthesized with no more than ^(^-^K^ + 2-)f^ 2 1og^ contacts when H > 4 bits. The network can also be synthesized using N trees, each of which pro- duces all of the possible functions Crixi) -{■ es{x2) + • • • + e^ixM)- Each terminal is connected to the input lead of one of the trees; and the output leads, to which the terminals are connected in any given state (xi , • • • , Xm), are interconnected in the way one wants the terminals to be interconnected in that state. The number of contacts used in this type of synthesis is less than The synthesis using two-terminal networks ordinarily requires fewer con- tacts than the one using trees as long as H-2\ogH>^{N-l){P-\-i) An example illustrating the design of a typical three-terminal network is given in the appendix. Number of Functions Every A^-terminal switching function determines a realizable matrix of hindrance functions Bij{xi , • • • , Xm)- It is important to know the number of different switching functions oi {xi , • • • , Xm)- A state of the N terminals is determined by specifying the groups of terminals which are connected together. The number (t)(N) of such states is the number of ways that N different objects can be distributed into 1, 2, • • • , or .V parcels when the parcels are indistinguishable from one another and no parcel is left empty. TV^-TERMINAL SWITCHING CIRCUITS 679 A switching function represents one of these 0(iV) different states for each of the l" different switch settings. Hence the number of switching functions is Although there is no simple formula for 0(iV), a generating function for 0(A^) is well known :^ (8) ^..-1^ |^0W^n_- A recursion formula which can be used to calculate 0(7V) is (9) 0(iv + i) = i:c^..<^w. A;=0 When N is large <^(iV") can be estimated with the help of the upper and lower bounds to be derived. These bounds will be of use to us later mainly because they show that, for large iV, log <^(iV") is approximately iV" log TV. Theorem IV . (10) *(^) ^ -e ^\ gAT/logeJV L'"^' i^l Proof. The maximum value of | e^* ^ | on the circle | z | = r is e***^ ^ . Using (8) and Cauchy's inequaUty for the iV*^ coefl&cient in a power series, (11) {N) < N\e''-' for all r > 0. The best estimate of 4>{N) will be obtained by minimizing (11) on r. To do this one sets r = ro where roe' = N. The simpler result (10) is obtained from (11) by setting Theorem V. (12) TT — *^^^^ f^^ ^^^ integers A. Proof. Let Q{Nj A) he the number of ways that N different objects can be distributed into 1,2, • • • , or ^ indistinguishable parcels. Then Q{N, A) A ! 4 W. A. Whitworth, Choice and Chance, p. 88, Cambridge, Bell, 1901. 680 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 must be greater than the number of ways N different objects can be placed in A different boxes (labelled 1, • • • ^ A); i.e. A"" {N)A\. To obtain the best lower bound from (12) one may maximize on A. The best value of A to use is one which comes close to satisfying N-l (' - r - ^ For large N the solution is approximately A= ^ logeN To perform the minimization in theorem IV more carefully one would solve Aq loge ^0 = N for Aq . This is the minimizing equation given in theorem IV with To = loge ^c . It is also very nearly the minimizing equation given in theorem V. Then our proofs of thegrems IV and V show that iN Aq—I Aol - -^ ^ - -(loge^o)^* For large N these bounds differ by a factor of about gTT N e Vloge TV More accurate information about the behavior of 0(iV) for large N is provided by an asymptotic series found by L. F. Epstein.^ The first term in his series is {N)- d'-e^-' Vloge a where a is found by solving a loge (a + 1) = iV. Figure 6 is a graph of <^(A^) vs. N using a log log scale for {N). The points are exact values and the curves show the upper and lower bounds. » L. F. Epstein, J.M.P., 18, 3, pp. 153-173 (1939). A^'-TERMINAL SWITCHING CIRCUITS 681 Number of Graphs Let G(iV, K) be the number of topologically distinct linear graphs which can be drawn interconnecting the iV-terminals and using K branches. G{N, K) counts all graphs including graphs with dangling branches and disconnected pieces. It also counts graphs in which any or all of the N- terminals are connected to no branches. Figures 7a, b, c, d, e show some topologically distinct graphs which would be counted in finding G(3, 10). 8 - / - / - / 2 ,0100 - / / / / - / - / - A - / / lO'O // / - // - // 6 - UPPER BOUND""- y ^^ LOWER BOUND - / / Y 10' 1 ^ 1 _L 1 \ 1 j_ 1 1 1 4 6 8 10 20 40 60 80100 200 NUMBER OF TERMINALS, N Fig. 6 — Number of possible states of iV terminals. 400 600 1000 Graph 7f is topologically identical with graph 7b and so is not to be counted again. The first step toward finding a lower bound on the number of con- tacts which almost all switching functions require is to find an upper bound onG(i\^, i^). Theorem VI. G(N, K) < l^'-^^iN + 2K)^ . 682 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 Proof. Every linear graph can be constructed by the following process. Let the branches be numbered 1, 2, • • • , i^ and let the end points of the k^^ branch be called Ak and Bk . There are iT — 1 places where partition marks can be inserted in the sequence Ai, • • • , Ak and hence there are 2^"^ ways of partitioning the ^^'s into groups of the form Gi = Ui, ^2, ••• , Aa) G2 = {Aa+1 y '" yAb) Gz = (Ab+i y "' ,Ac) (a) (b) (c) i> (d) 30 (f) Fig. 7 — Examples of graphs. There are 2 ways of selecting some of the terminals 1,2 • • • , N. Suppose that m of the terminals have been selected; then pick one of the partitions of the AkS which has m or more groups Gi , • • • , Gm+« . Connect all the end points in Gi to the first selected terminal, all the end points in G2 to the second selected terminal, etc. Next connect the terminals in Gm+i , * • • , Gm+f together to form 5 nodes. The number of ways of performing all these operations is less than iV-TERMlNAL SWITCHING CIRCUITS 683 Connect Bi to one of the A^-terminals or to one of the nodes just made or else use Bi to make a new node. Connect B2 to one of the terminals or nodes or else use B2 to make a new node, etc. The number of ways of con- necting Biy • • • y Bk is less than {N-^K+ 1){N -i-K+l) '•' {N+2K)<{N+ 2Kf , which proves the theorem. Since most graphs can be constructed in many different ways by this process, theorem VI gives a very poor estimate of G(iV, K). In the applica- tion which we will make of G{Nj K) it is enough to know that log G{N, K) behaves something like K log K. To prove that K log K cannot be replaced by anything much smaller we now give a lower bound for G{Nj K). Theorem VII. Proof. G{Nf K) is larger than the number of graphs which can be drawn without specifying certain nodes as terminals 1,2, • • • , iV. Of these graphs let us count only those which have the property that no cycle in the graph has an odd number of branches. Another characterization of these graphs is that their nodes can be divided into two classes A and B such that no branch joins two nodes of the same class. To construct such graphs we first number the branches 1,2, • • • ^ K and give them an orientation (say by putting an arrow head at one end of each branch). The front ends of the branches can be grouped together into nodes in 4>{K) ways. Then the tail ends of the branches are grouped together in one of <1>{K) ways. In this way a total of {{K)y different graphs can be drawn, in which the branches are numbered and oriented. If we now ignore the numbers on the branches we still have at least — /^ distinct graphs with oriented branches. If the orientation is ignored, the number of topo- logically different graphs which remain is greater than Lower Bound We have seen that any switching function can be realized with no more than about N^P2^ H - 2 log H 684 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 contacts. To show that this number cannot be improved very much we will now show that almost all switching functions require a number of contacts of this order of magnitude. Theorem VIII. Let any €> 0 be given. The fraction of switching functions which can he synthesized using less than (13) (1-e) 2^^^^^^^) H+\og\og4>{N) contacts approaches zero uniformly as the number M of switches becomes large. ^ Proof. The number of switching functions which can be constructed with K contacts or less is certainly smaller than the number of ways the K branches of the G{N, K) graphs can be replaced by contacts er{x^) or open circuits; i.e. smaller than G{N, K) / M \1 By theorem VI the fraction F{K) of the {(l){N)Y switching functions which can be built using K contacts or less satisfies (M \K E A + ij i't'Wr"' 2N+k( logi5:+2+log 2 Pi+^ )-2^ log « where we have used • log2 (N + 2K) < loga 2K + ^ log, e --). Since --^_—^ — — °— -_^* approaches zero as the number of switches M gets large, it follows that for sufficiently large M and any N • The word uniformly is used to indicate that the fraction in question can be made smaller than any given number 6 > 0 by making M larger than a certain number M{S) which depends on S but not on N. iV-TERMINAL SWITCHING CIRCUITS 685 (14) log (2^ + 1) + 2 . ^+ log log (/,0V) ^ 2' Then (15) FW < 2"(<^(iV))-'^''-' which approaches zero uniformly as M increases. For most of the switching functions of practical interest H is much bigger than log log 0(iV). In these cases the number E -1 log // is larger than (13) by a factor of about NP/\og N. In the case of two-ter- minal relay circuits the corresponding factor found by Shannon was only 8. It is not clear whether this difference indicates that there is a wider range of complexity for iV-terminal networks than for two-terminal networks or that our methods for obtaining upper and lower bounds lose some of their effectiveness as N increases. Nevertheless, (13) is surprisingly large, as we shall see in the example which follows. Example. Consider a telephone central office with 10,000 lines. If the office must be able to connect the lines together in pairs in any arrangement and to remember which line of a pair originated the call, a count of the number of different states which must be produced reveals that the office needs a memory of at least H = 64,000 bits, which can be supplied using 19,200 switches with 10 positions each. The number of other switching func- tions that one might ask these 19,200 switches to perform is .^(10,000)^"-°" = (io»'»«»)'«""° = 10'»"'"° approx. To apply theorem VIII to these other functions we first note that (14) will be satisfied as long as we pick e greater than .006. Then, substituting in (13) and (15) we discover that the chance that one of these switching func- tions chosen at random can be synthesized with less than about ^ rvl9 ,000 , , 10 contacts is less than some number of the order of 1019,200 If the same calculation is repeated for a 10,000-line office which is capable 686 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 of handling only 1,250 calls at one time we find H = 22,000 bits, 6,666 .015 or larger # switches = 6,666 ^ functions = 10 # contacts = 10^-*^^ or more for all but a fraction 10 ^°^'^ * of the functions. Although these numbers of contacts appear incredible at first sight, there is no reason to expect the number of contacts for almost all switching func- tions to be a good indication of the number of contacts needed for the switching functions of practical use. This phenomenon has been discussed in detail by Shannon for the case of two- terminal networks. For iV- terminal networks there are at least two other factors which may be mentioned. Almost all switching functions can assume states which are not typical of the functions encountered in practice. For example, it can be shown that of the {N) possible ways of distributing N different things into parcels, al- most all of them use a number of parcels which is near iV/log^ N, Thus, in a typical state of a typical switching function the terminals are connected together in groups which average about logeiV terminals per group in size. Telephone switching equipment ordinarily connects terminals together in pairs or in small groups. A big difference between the design of two-terminal networks and of A'- terminal networks is that, in the former case, one wants to obtain one specific switching function while, in the latter case, one is usually satisfied with a network which can produce certain desired states. There are many switching functions which all produce the same states but for different settings of the switches. For example, if the 2* desired states are all dif- ferent, the designer will be content with any one of (2^) ! different switch- ing functions. We believe that it actually would require something like jQ6,67i contacts to build a central ofl&ce if the designer first listed all the desired states at random 5i , ^2 , • • • , S^h and then required the oflSce to be in state ^i for switch setting (1, 1, • • • ,1). in ^2 for the switch setting (1,1, ... ,2), etc. Number of Selector Switch Rotors Since our estimate (13) of the number of contacts is the same whether the memory H is stored in two-position switches or in larger selector switches, one might hope that the selector switch circuits could be built using fewer rotors than the corresponding two-position switch circuits. We believe that this is not true. A typical node in one of the graphs constructed by the process of theorem VI has only about three or four branches connected to i\r-TERMlNAL SWITCHING CIRCUITS 687 it. This is so regardless of how large K is. If the rotor of a selector switch is connected to such a node, the chance is great that none of the other branches at the node are operated by this same switching variable. Hence we suspect that a typical switching network requires almost as mnay rotors as contacts. Acknowledgment The author has discussed this switching problem with B. D. Holbrook, A. W. Horton, J. Riordan, and C. E. Shannon and has received valuable com- ments and ideas from them. He is also indebted to A. E. Joel and W. Keister for their suggestions for improving the readability of the manuscript. Table I X y z Kx, y. z) /m /» /« 0 0 1 (12) (3) 0 1 1 0 0 2 (123) 0 0 0 0 0 3 (1) (2) (3) 1 1 1 0 0 4 (13) (2) 1 0 1 0 1 1 (13) (2) 1 0 1 0 1 2 (1) (23) 1 1 0 0 1 3 (123) 0 0 0 0 1 4 (1) (23) 1 1 0 0 1 (1) (23) 1 1 0 0 2 (13) (2) 1 0 1 0 3 (1) (2) (3) 1 1 1 0 4 (12) (3) 0 1 1 1 1 (123) 0 0 0 1 2 (123) 0 0 0 1 3 (1) (23) 1 1 0 1 4 (1) (2) (3) 1 1 1 APPENDIX To illustrate how the network synthesis method operates in a typical case consider a three-terminal network using three switches x, y, z. Switches X and y have two positions 0 and 1, and z has four positions 1, 2, 3, 4. A three- terminal switching function fix, y, z) is defined by means of the first four columns of Table I. The sixteen entries in column four represent the states of the terminals which the network must produce for the correspond- ing switch settings given in the columns labelled x^ y, z. In column four, parentheses are used to group terminals which are connected together; for example /(I, 0, 4) is the state in which terminals 1 and 2 are connected together and 3 is left free. A network with switching function f{xj y, z) will be designed by connect- ing two- terminal networks between the pairs of terminals 1, 2; 2, 3; and 1,3. The hindrance functions of these three two-terminal networks will be called 688 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 /i2, /23, and /i3 . We determine them, as shown in the last three columns of Table I, by setting /»y = 0 whenever terminals i snxd j are to be connected and fij = 1 otherwise. Our methods of two-terminal network synthesis will produce the fij networks. Our criterion (P > H — log H) for deciding which of the two synthesis methods to use (case 1 or case 2 of theorem II) is not the best rule when H is as small as it is in this example. By actually trying the different ways of apportioning switches with 2, 2, and 4 positions between a tree and a net- work to produce all functions, one finds that the most economical way is to Fig. 8 — Network with the 3-terminal switching function f{x, y, z) of Table I. put a two-position switch, say x^ into a network which provides all functions of X (0, 1, ac, and ic'), and the other switches into a tree. When this pro- cedure is adopted we next express /,j in the form of identity (2). For example fu = ly + e2iz)][y -h ei(z) + x][y + e^iz) + x][y + ^2(2) + x][y + ^1(2)]. The synthesis method described in the text then leads directly to a net- work for fu which is shown joining terminals 1 and 3 in Fig. 8. The net- work for /12 which is shown in Fig. 8 was obtained by the same process. For the sake of illustration the f2z network was found using a tree only. Coaxial Impedance Standards By R. A. KEMPF {Manuscript Received Mar. 7, 1951) The calibrations of bridge networks used in developmental tests on coaxial cable are obtained by comparison of the networks with calculable standards of impedance consisting of a group of short-length precision copper coaxial lines. The standards are calculable by reason of the availability of precise formulae relating the distributed primary constants to the measurable physical constants and dimensions of the coaxials. This paper outUnes the constructional problems and design features of a group of such standards of impedance which provide a range of values over a broad band of frequencies. Introduction The "mile of standard cable" was for a long time the basis for rating the transmission qualities of telephonic apparatus and networks.^* ^ The title of this paper suggests that a return to the old standard has been accom- pUshed. This is true in a restricted sense, but with important differences. The standards here described consist of varying lengths of a rigid coaxial transmission line structure. Their sole function is to supply primary refer- ences of resistance, inductance, capacitance and conductance which are numerically comparable to typical unknowns encountered in laboratory cable measurements. Unlike the mile of standard cable, the rigid coaxial is simple structurally, its physical constants and dimensions may be deter- mined accurately, and precise formulae are available for translating these properties into electrical constants at any frequency. It is thus an excellent means for the objective — calculable radio-frequency laboratory standards of R, L, G, and C of the restricted numerical range needed to calibrate the bridge networks used in measurements on the short lengths of cable avail- able to the cable development engineer. Because developmental cables are not usually available in the longer lengths on which the secondary constants of attenuation, phase, and char- acteristic impedance may be measured directly, laboratory measurements on a cable sample are usually confined to determination of the four dis- tributed primary parameters or constants. From these the secondary con- stants may then be calculated. Measurement of the distributed primary constants of a given line struc- ture is an indirect process, except under limited or restricted circumstances. 1 R. V. L. Hartley, "The Transmission Unit," Electrical Communication, Vol. /, No. 1, July, 1924. 2 W. L. Everitt, Communication Engineering, pp. 101-2. 689 690 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 This is because (1) an impedance bridge can do no more than measure the unknown impedance which may be placed across its terminals; and (2) the line structure can be measured only by making bridge readings at its input or output terminals, from which points the true distributed series properties of the line appear to be altered by the shunt properties, and vice-versa. Statement (2) applies to all observations at the end of a section of trans- mission line, except when the line is very short electrically. Assuming that accurate bridge measurements of the impedance at the terminals of a line are available, standard transmission formulae may be used to calculate rigorously the distributed primary constants. Uncertainty as to the accuracy of impedance bridge measurements led to the develop- Table I Dimensions and Physical Properties which Determine The Primary Electrical Constants of Any Coaxial Transmission Line Distributed Primary Electrical Constants Determining Physically Measurable Quantities Series Constants, R and L Center Conductor Outer Conductor P,d,F P, ID, t, F Shunt Constants, G and C Capacitance Conductance d, ID, e d, ID, F„ e, F R, L, G, and C are distributed resistance, inductance, conductance and capacitance, respectively, at any frequency, F. p is the dc volume resistivity of the copper conductors which have diameters ID and d, and wall thickness t. c and Fp are the composite dielectric constant and power factor respectively, assumed independent of frequency. ment of coaxial impedance standards as a means of checking the accuracy of test apparatus. As this work progressed, and the merit of the standards was more fully appreciated, it came about that the bridges were not merely checked against the coaxial standards, but instead the bridge calibrations were derived from the coaxial standards. Input Impedance of a Coaxial The distributed primary constants of any coaxial with a uniform structure may be precisely computed in terms of dimensions and physical constants using formulae which have been developed by SchelkunofP and others. Table I indicates the physically measurable quantities used to compute the respective distributed electrical constants, R, L, G, and C. ' S. A. SchelkunoflF, "Electromagnetic Theory of Coaxial Transmission Lines and Cylindrical Shields," B.S.TJ., Oct. 1934. COAXIAL IMPEDANCE STANDARDS 691 It is the open (Zop) and short circuit (Zah) input impedances which are of utiHty for bridge calibration work, however, and except for lines much less than quarter wave in length, Zop and Zsh must be computed from the dis- tributed constants using the transmission line equations. The propagation constant and characteristic impedance may be computed from the distributed constants by means of the equations: 7 = V(R + joiLYJG + >C), and (1) = 4/^44^, (2) G +joiC' where the numerical values of the distributed constants are, of course, de- pendent on the appropriate quantities as in Table I and the length of the Hne. Further, for any coaxial line terminated in an open circuit or a short circuit, respectively: J_=G'+icoC' = ^, and (3) Z,h = R' + J03L' = Zo tanh 7 (4) Equations (3) and (4) rigorously relate the input impedances for open and short circuited far-end conditions to 7 and Zo in (1) and (2), and thus back to the physically measurable quantities of the coaxial structure. Precise values of the apparent distributed primary constants R', L', G' and C are the final objective, as these quantities comprise the standards. As is shown, they are computed from basic data on the dielectric of the co- axials and on a single metal comprising the conductors of the coaxials. It is of interest to note that, because of the mutual effects of the dis- tributed constants on each other, the conductance component of the input admittance of a coaxial line becomes increasingly a function of the dimen- sions and resistance of the conductors of the line, as frequency is increased. Thus calculable standards of conductance are obtained which are essentially independent of losses in the insulating material used to support the center conductor. Coaxial Standards for Laboratory Use General Description Although short-length coaxials have been used by the Laboratories for some years as impedance standards for cable measurements, refinements in measurement techniques have made it desirable to construct a new set of standards with very uniform components and improved structural qualities. 692 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 It is with the new set of impedance standards that this paper is chiefly concerned. The new standards have been constructed in lengths varying from six inches to thirteen feet in increments of length so that, at a given frequency and far-end condition, eighteen standard impedances are available. The completed standards have been, provided with a permanent storage cabinet, Fig. 1, located in an air-conditioned cable development laboratory adjacent to measurement facilities. The special tools developed for con- struction, assembly, and use of the standards are also stored in the cabinet together with spare materials for maintenance. Each standard consists of a seamless hard drawn copper tube f I. D. as outer conductor and a straight hard drawn copper wire, nominally No. 10 A.W.G., as center conductor. The insulation is expanded polystyrene in the form of spaced cyhnders. An aluminum tube is used over the copper tube for mechanical protection but is insulated from it. Stainless steel fittings are provided at each end to exclude dust, to facilitate connection for cir- culation of dry air, and to provide the short-circuit necessary for Zsh meas- urements. The properties, selection, and preparation of the three compo- nents— v/ire, tubing, and insulation and the provision of a repeatable method for short circuiting the coaxials are the basic problems in construction, and are discussed in the following paragraphs. Physical Constants The measured physical constants of the copper wire and tubing which are of interest in this appHcation are given in Table II, and those of the expanded polystyrene insulation in Table III. Wherever practicable the absolute accuracies of the measuring instruments were checked against secondary standards of weights and measures, periodically referred to the U. S. Bureau of Standards laboratory for calibration. Dimensions The I. D. dimension quoted in Table II is the average of a number of tests on end samples of tubing and was obtained from dimensional and weight relationships as expressed by the equation: -/■>•-:-?• (5) where V is the volume of copper in the sample as measured by the displace- ment technique. Do is the measured O. D. of the sample and C is its length. The I. D. was also determined by direct measurements of O. D. and wall thickness, and agreement obtained with the figure quoted for the above COAXIAL IMPEDANCE STANDARDS 693 ^^^ 694 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 method. Variations of weight and dimensions along individual lengths of either wire or tubing are not significant as determined by checks at intervals on a number of the lengths. The measurements of d-c. resistance needed to determine the resistivity of the copper conductors are subject to limitations of knowledge of tempera- ture, particularly where the samples must be measured in long straight lengths. The laboratory setup used to obtain the data consisted of a long trough through which oil was circulated over the immersed samples. A feature was the use of a 200 gal. tank of water in thermal contact with the oil circuit to maintain it at a constant, or very slowly changing temperature. Table II Measured Average Physical Constants of Copper Tubing and Wire for Coaxial Impedance Standards Density (gm/cc) Outside Diameter (inches) Inside Diameter (inches) Wall Thickness (inches) Volume Resistivity (microhm cm) Mass Conductivity (per cent of lACS) Temperature Coefficient of Resistance, 20°C. Wire Tubing 8.89 8.938 0.10042 0.50016 0.37137 — 0.06439 1 . 7480 1.7209 98.76 99.76 0.003886 0.003938 Table III Measured Average Physical Constants of Expanded Polystyrene Insulating Cylinders for Coaxial Standards Volume Expansion Ratio. Weight (gm/disc) Length (inches) Density (gm/cc) Dielectric Constant 41 0.1789 0.396 0.0257 1.033 A Kelvin double bridge used for the tests was operated in accordance with minimum-error principles.'* Components-Wire The center conductor of each coaxial must be drawn staright so that only light spaced support need be used to keep it in axial alignment with the tube. Since available commercial wire drawing machines normally depend on a driven small-diameter capstan to pull the wire through the final re- ducing die, it was necessary to draw the wire in the laboratory so that straight-out drawing could be achieved. Commercial machines were, how- ever, used to reduce the supply from f" rod to 0.110" dia. wire without * Electrical Measurements, Laws, McGraw-Hill, 1917. COAXIAL IMPEDANCE STANDARDS 695 intermediate annealing. The laboratory operation consisted of drawing the 0.110" stock straight out through a 0.1004" I. D. diamond die pre-selected as to circularity and finish of the bore. The copper which was used is known in the trade as "electrolytic tough pitch" chemically composed of 99.95 per cent copper, 0.02 per cent oxygen and 0.03 per cent divided between six other minor contaminants. There has always been some concern as to the possibility that a wire drawn from annealed stock might well have a thin full hard shell over a relatively annealed core. The d-c. resistivity measurements would then de- termine a weighted average resistivity, instead of the surface resistivity needed for calculations. To settle this point, tests were made on full-hard wire, semi-hard wire as used in commercial coaxials, fully annealed wire, and on annealed wire plated with a 0.2 mil layer of silver. The tests con- sisted of (a) comparing the a-c. resistance of the wires by precise methods at 1 mc where transmission is at a skin depth of 2 mils, and (b) microscopic study of grain structure of polished-etched cross sections of the samples at magnifications to 2000 diameters. The conclusion from both studies was that no thin skin exists. The wire is therefore treated as homogeneous throughout its cross section in computation of d-c. resistivity and in com- putation of a-c. resistance. Copper Tubing The effects on the resistance of a coaxial traceable to the physical con- stants of the outer conductor are scaled down about 5 : 1 so that the require- ments on the tubing are not so severe as on the wire. However, stock cop- per tubing from a distributor's warehouse cannot normally be used. Such tubing may have unacceptable inside surface roughness, ellipticity of bore, and a high and variable resistivity. Roughness and ellipticity are the result of worn plug dies frequently used in the drawing of commercially acceptable tubing, or omission of the plug die in drawing the tubing to final diameter. Most stock tubing contains phosphorous and, even though the percentage of phosphorous may be very small, the effect in increasing the resistivity is marked. The full-hard tubing used in the coaxial standards here described was procured directly from a mill, and was largely drawn in consecutive lengths from a single casting of oxygen-free electrolytic copper using selected dies. Insulation Expanded polystyrene is the dielectric material used in the standards and its applicable properties are shown in Table III. In solid form it has a dielectric constant, e', about 3% greater than that of air and, when used 696 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 to insulate the coaxial standards in the form of spaced cylinders, the com- posite dielectric constant is increased only about 0.4% over theoretical for air. Errors in determining the constant of the expanded material are thus scaled down by a factor of nearly 10: 1 in their effect on the composite con- stant. The figure quoted for dielectric constant in Table III was obtained by adding incremental amounts of dielectric to a 12" length of standard coaxial and plotting the measured capacitance as increments above the computed capacitance for air dielectric, as in Fig. 2. The distributed conductance, G, is derived from the power factor of the dielectric which, in the case of any reasonably good material, is so small 2 < y / i a. 0.4 o ■2. n / / / o 2 0.3 z 1- z UJ |o.2 o Z y / y / / / > / UJ o z < 0.1 o < o 0 /" / / / / 0 (AIR) 0.2 0.3 0.4 INSULATION IN GRAMS 0.5 0.6 Fig. 2 — Data for determination of dielectric constant of expanded polystyrene. that experimental determination is subject to large error. The apparent conductance G' from (4) is the value at the input terminals of the coaxial. An important feature of the standards is that G' becomes independent of G at high frequencies and, therefore, it is desirable to reduce G (representa- tive of the loss in the dielectric) to as small a value as possible in order that G' may become independent at the lowest possible frequency. This is ac- complished by the use of expanded polystyrene as the dielectric of the stand- ards. Polystyrene is of such molecular structure that it is not hygroscopic. However, under certain conditions, water vapor may condense in cells of the expanded material in sufficient amount to increase the dielectric con- COAXIAL IMPEDANCE STANDARDS 697 stant and the conductance losses. For this reason all insulating cyUnders have been pierced longitudinally so that low pressure dry air may be cir- culated through the assembled coaxials when they are in use. The cylinders were cut with a high-speed fly cutter, and the center hole drilled in the same operation. It was determined by sensitive electrical tests that centering precision in the assembled coaxials was equivalent to that obtained in coaxials with lathe turned diics of solid materials. Cylinder spacing of 3'' on centers was determined as about the maximum permissible to prevent detectable sag in the center wire between points of support. There is no specific strength requirement on the cylinders except that they must support the weight of the straight drawn wire. However, a single polyethylene disc is used at the test end to resist radial thrusts which may occur in making test connections. -^— — *^M Fig. 3 — Partially assembled coaxial standard. Assembly Features It is necessary to have mechanical protection for the copper tubes of the standards, and this is provided for each by an aluminum tube slipped over the copper tube, with insulation consisting of a helical wrap of 0.0015 x |" paper ribbon first applied to the copper tube. The aluminum tube is locked on the copper tube by short lengths of fibre tubing wedged between at each end. The wedging action occurs when the end fittings are screwed to the aluminum tube. Figure 3 is a photograph of a partially assembled standard to illustrate further the construction. The presence of the aluminum tube may be disregarded in so far as its electrical effects are concerned because of the self-shielding qualities of the copper tube. End Effects Experimental data indicate that if a coaxial tube is longer than its center conductor and the wire is then lengthened incrementally until it is as long as the tube, the capacitance of the coaxial remains directly proportional to 698 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 the length of the wire to better than 0.01 ju^f- The 'bringing effect" at an open-end of a coaxial is considered negligible. The individual center wires of the standards have been cut 0.500" longer than the tubes and the extra length utilized at the test end for connection to the test equipment. In computing the impedances, the length of the tube has been used. The 0.500" center wire projection is considered as part of the test-equipment leads and is separately accountable. Disc Short Circuiting of Coaxial Standards A shortcoming of coaxial standards previously developed has been in the use of solder to attach a short circuiting disc at the far end when using the length to provide calculable series impedance (Zgh). The use of a disc is the best means to short-circuit the inner and outer conductors with a minimum and calculable terminal impedance, and the accomphshment of this objec- tive by repeatable mechanical means is an important feature of the new standards. A very thin disc pressed against the end of a coaxial is effectively con- tacted along two concentric rings representing the peripheral edges of wire and tube of diameters d and D respectively. The d-c. resistance of the metallic area between the rings in terms of its resistance, r, in ohms per square is: D/2 = J^f-^ (6) (6) reduces to : R d/2 i? = ^lnD/d. (7) Figure 4 shows a cress-section of the short-circuiting device developed for the standards. Figure 3 includes a view of the assembled device. It con- sists of a stainless steel housing carrying a trapped silver disc and other parts to effect a repeatable, minimum-impedance short circuit when the housing is screwed to the end fitting of the coaxial. The operation is as follows: (a) When the housing is screwed on the end fitting, the disc is forced against the end of the copper tube, with pressure equalized by and derived from the rubber grommet. (b) Assuming the housing is always screwed on the end fitting as far as it will go, the total pressure on the disc is regulated on initial as- sembly by contTol of the amount of projection of the tube beyond the end fitting. COAXIAL IMPEDANCE STANDARDS 699 (c) The center wire is drilled and tapped to a depth of xV at one end to accept the 0-80 screw carried by the stud. After the disc is tightly pressed against the tube as in (a), the center wire screw stud is turned until the center of the disc is drawn tightly against the end of the center conductor. The stud projects from the end of the housing and is milled at its end to accept a torque wrench. The wrench provides the means for development of repeatable pressure of the end of the wire against the center of the disc. Experimental data on the relative pressure versus d-c. resistance char- acteristics are illustrated by the curves of Fig. 5. Disc pressure on the cen- ter wire is controlling as would be expected. The total d-c. resistance in- RUBBER ' PRESSURE GROMMET 0-80 SCREW (TO ENGAGE CENTER WIRE) -HOUSING Fig. 4 — Assembly detail, end-shorting device. troduced by the short circuit is of the order of 0.1 milliohm, which includes the contact resistance. On the basis of experimental observation the resist- ance at radio frequencies appears to be more stable because the area of contact becomes of less importance as frequency is increased. The inductance introduced by the disc is negligible for all lengths and frequencies. The a-c. resistance of the disc is equal to its d-c. resistance up to about 1 mc where complete wave penetration ceases and skin effect becomes apparent. Above 2 mc the disc resistance increases as the square root of frequency. Connection — Test End A connector currently in use at the test end of the outer conductor is shown in position in the photograph, Fig. 3. The projection normal to the 700 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 axis of the assembly is used for clamp- type connection. A guillotine clamp for short-circuiting the input of the coaxial, as required in substitution type measurements, is placed across the center wire and the projection parallel to the axis of the assembly. The center conductor of each coaxial extends 0.500" beyond the tube, and is thus available for clamp type connections. Soldered connections are thus completely eliminated in the use of the stand- ards. Eccenlrkity Concentricity of the axes of wire and tube is assumed in most pubHshed formulae which relate the dimensions of a coaxial structure to its electrical 0.130 0.125 t 0.120 -3 5^0.110 S^ 0.105 <> •^"^ 0.100 0.095 0.090 / / CENTER WIRE COMPONENT ADJUSTED BY TIGHTENING^ STUD ON CENTER WIRE J /' > / / OUTER CONDUCTOR component /adjusted by rotatingA V THE HOUSING ) 1 1/ ^^ A — ■ X 0 10 2 BOTH STUD AND HOUSING TIGHTENED 40 50 60 70 80 90 100 CIRCULAR DEGREES FROM CLOSURE 120 130 140 Fig. 5 — Measured d-c resistance introduced by end shorting device as a function of adjustment. constants. Consistent departures from concentricity, i.e. eccentricity, are subject to analysis as regards effects on the electrical constants. In the case of the standard coaxials, the use of straight, hard-drawn wire and tubing combined with close-spaced support of the wire are all factors which reduce eccentricity. However, it is obviously desirable to check the degree of resid- ual eccentricity of the assembled coaxials point by point along each length. A method developed to do this makes use of Biot and Savart's law.^ The external field, at any point P, of a long circular wire or tube carrying a current I is given by r * W. R. Smythe, Static and Dynamic Electricity, p. 272. (8) COAXIAL IMPEDANCE STANDARDS 701 where r is the distance from the axis of the wire or tube to point P. This assumes that the current density on any concentric circle is uniform. If the wire and tube are carrying the same current I but in opposite di- rections and if the axes of the wire and tube coincide, there will be no mag- netic field at any external point. Therefore an alternating current in the conductors will not induce a voltage in a pick-up coil placed external to the coaxial. If, however, the two axes do not coincide a voltage will be induced in the pick-up coil and will be a maximum when the pick-up coil is in the 1.6 1.4 1.2 -J 1.0 O > 0.4 _...,., / / / / INDICATED FIELD yCALIBRATION f^— ' POINT 1 / / 1 1 y / I / / 51 / / / / 11 1 / / 1 1 A \ i 1 j 1 1 1 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 DEPARTURE FROM CONCENTRICITY IN MILS 6.0 6.5 7.0 Fig. 6— Typical calibration curve in measurements of eccentricity of coaxial standards. plane of the two axes. The magnitude of this maximum voltage will be proportional to the distance between the two axes if the measuring distance is large compared to this separation distance. In practical use, the maximum field at P was measured in terms of volts relative to a known eccentricity obtained by insulating a coaxial with discs of the known eccentricity. Advantage was taken of the linear relationship of eccentricity and detectable field so that, with the distance to the tube maintained constant, the calibration curve of Fig. 6 was used to evaluate all standard coaxials after final assembly. The sensitivity was such that the 702 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 effect of an 0.08 mil known deviation in diameter of the wire was detectable in coaxials with otherwise perfect symmetry. Such deviations in symmetry as were observed developed primarily from variations in wire diameter as already stated, and from deviations in wall thickness of the copper tubing. 1.0 03 0.6 0.4 S 0.2 0,1 o I 0.08 S 0.06 ^ 0.04 0.01 0.02 0.04 0.06 0.1 0.2 0.4 0.6 1.0 2 4 6 8 10 20 FREQUENCY IN MEGACYCLES PER SECOND 40 Fig. 7— Distributed resistance, R, and R' component of Z^h of 7.0 ft. length, coaxial impedance standard. X Oo a. " o 70 0.65 UJ ^O o 2 0.50 0.1 0.3 0.4 0.6 0.8 1 2 3 4 6 8 10 FREQUENCY IN MEGACYCLES PER SECOND Fig. 8— Distributed inductance, L, and L' component of Zsh of 7.0 ft. length, coaxial impedance standard. Numerical Valines of Standard Impedances Graphical Example As an example, values for the apparent series and shunt primary con- stants R', L', G' and C for a length of 7.0 feet are presented graphically in Figs. 7-10. For comparison, the distributed primary constants have also COAXIAL IMPEDANCE STANDARDS 703 4 2 1.0 0.8 0.6 0.4 0) o I o a: u 0.2 0.1 0.08 5 0.06 z 0.04 UJ U z u Q Z 0.02 0.01 0.008 0.006 u u 0.004 0.002 0.001 0.0008 0.0006 0.0004 0.0002 [1 1 iiii/| nil L ^ :: ?:: :: - S :: t------ ± :? :^-=^^-- r 7^ } J .__:;.?_::: 1 ^ ■ ;;^7::; :;; t/ / / — / 0.0001 0.1 0.2 0.4 0.8 1 2 4 6 8 10 20 40 60 100 FREQUENCY IN MEGACYCLES PER SECOND Fig. 9 — Distributed conductance, G, and G' component of Zop of 7.0 ft. length, coaxial impedance standard. 130 _Q 120 ^< CC UK ou. 110 70 ered references, see list at end of paper. 706 INSTANTANEOUS COMPANDORS 707 exposure. Stronger signals are amplified less highly. Loss, therefore, is re- moved from the expandor as the signal increases and the noise increases correspondingly. When the signals are conventional speech signals, loss is removed from the expandor as the speech volume increases and consequently the noise volume increases correspondingly. An instantaneous compandor has the important advantage that level adjustments are frequent, for example, in a pulse-modulation system at the rate of about 8000 times per second for a message channel whose bandwidth approaches 4000 cycles. Consequently, the increased noise will be continuously masked by increased speech sound. During all silent periods, unwanted noise and interference receive maximum noise suppression in the expandor. For an ordinary message channel these advantages are substantial. Viewed broadly, an instantaneous compandor provides a read)' means for making the noise susceptibility a function of the magnitude of the signal. If the noise susceptibility is made less than that of a linear system in one portion of the range, then it must be greater than that of a linear system in some other portion of the range. Whether an over-all improvement results depends entirely upon the nature of the signal. For example, in certain tjrpes of picture transmission systems a given value of noise produces about as much harm whether the signal be weak or strong. In this instance no benefit would accrue from making the noise susceptibility a function of signal Strength. An important consideration, therefore, is the evaluation of the noise ad- vantage due to instantaneous companding. The theoretical treatment will give relationships for signal-to-noise ratio and noise susceptibility. Applica- tion of the theory to a particular example including a numerical evaluation of the noise advantage will be deferred to the last section. Method of Analysis The analysis is based upon deductions'^ related to the sampling principle and is illustrated by Fig. 1 which shows a schematic of one channel of a multi- channel time-division system. The incoming signal (Fig. 1) is filtered by a low-pass filter designated Fy. At the output of Fi the signal should be regarded as an arbitrary signal oc- cupying the band of all frequencies slightly less than B. Brief samples of the signal are taken uniformly at the rate of 2B samples per second. In this manner the signal is converted into a series of PAM (pulse amplitude modu- lated) pulses as indicated in Fig. 2. There is a unique relationship'^ between signals and samples (PAM pulses) ; if we are given the signal wave we can 708 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 determine the samples; if we are given the samples we can determine the signal wave. In Fig. 1, if we ignore the compressor, the samples are immediately fil- tered by another low-pass filter designated F2 which temporarily will be assumed to be similar to Fx. If F2 attenuates all frequencies higher than B and if each filter includes accurate in-band equalization including cor- rection for phase distortion, then the wave at the output of F2 except for delay will be an attenuated replica^^ of the wave at the output of Fx. TRANSMITTING TERMINAL TRANSMITTING RECEIVING TERMINAL TRANSMITTING MEDIUM INPUT SIGNAL CHANNEL 1 \ COMPRESSOR LOW- PASS FILTER TO OTHER CHANNELS i LOW- PASS FILTER EIHIKl^ LOW- PASS FILTER EXPANDOR CHANNEL 1 QujpuT 'EH LOW- PASS FILTER \=:z\ TO y OTHER CHANNELS SEQUENTIAL SAMPLER SAMPLER & SEQUENTIAL DISTRIBUTOR Fig. 1 — Block schematic of multi-channel PAM system. -~-^^ ^ ^h^ .^SIGNAL -^ N. HJ^ V \ / ■^v ^^ TIME— ^ ^--l ^^'' Fig. 2— PAM pulses. If the cut-off frequency of Fi is raised sufficiently, then in the output of this filter one finds PAM pulses clearly separated in time. These pulses are samples, on an enlarged scale, of the signal that would have existed had the cut-off frequency been in the neighborhood of B. If now the compressor (Fig. 1) is taken into account, then the PAM pulses at the output of the sequential sampler will be impressed upon the input of the compressor. The general form of a compressor characteristic is indi- cated in Fig. 3. The compressor is essentially instantaneous if its bandwidth is wide enough so that it can effect the required change in the magnitude of each pulse without increasing its duration. It is also significant to note that, theoretically, no more bandwidth^^ js needed to transmit the samples INSTANTANEOUS COMPANDORS 709 after they have been compressed than before. Clearly, if the samples are compressed in accordance with an arbitrary but known law, and if the re- ceiver expands them by an exactly inverse operation, the wanted informa- tion can be recovered. Pulses from the sending end are fed to the transmitting medium (Fig. 1) and conveyed to the receiving terminal. This might be done by any of a number of different ways and the details of this portion of the system are not important to this discussion. What is important is that the analysis will assume that the signal at the input to the receiving end, except for noise accumulated along the way, is an exact but delayed copy of the signal leav- ing the transmitting end. The low-pass filter ¥{ (Fig. 1) is similar to Fi and has been inserted to reject unwanted high-frequency noise. + V, + ^^ UJ o > 0 1- Q- 3 O Y\ UJ Q. Z /] El y E, _ _ ^ INPUT VOLTAGE COMPRESSOR OUTPUT VOLTAGE EXPANDOR Fig. 3 — Instantaneous compandor. The filtered PAM pulses go to the input of an instantaneous wide-band expandor whose characteristic is the inverse of that of the compressor. By interchanging the designations "input" and "output" on the compressor characteristic (Fig. 3) the characteristic becomes that of an expandor. The combination of compressor and expandor makes the over-all system linear as illustrated by the dotted lines in Fig. 3. The pulses from the expandor go to the sampler which is accurately synchronized® . 7 , lo . n^ Channel 1 pulses from the sampler go to F3, a low-pass filter similar to Fi, and produce in the output of Fz a copy of the original signaP together with noise accumulated for the most part in the transmission medium. Signal-to-Noise Ratio To understand how the compandor afTects the signal-to-noise ratio of the system, consider a single operation at the receiver. The magnitude of a 710 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 particular pulse may be represented as Fi + ?^i, where Vi corresponds to the signal voltage and vi to the noise voltage This pulse is impressed upon the input of a wide-band expandor (Fig. 4) and produces a new pulse at the output of the expandor. It will be assumed throughout that the maximum values of expandoi input and output voltages are equal, and for convenience will be taken as unity. The solid curve is the positive portion of an assumed expandor characteristic. Since Vi represents the magnitude that the input pulse would have if the noise voltage were zero, Ei repiesents the corre- sponding magnitude of the output pulse. When the effect of noise is taken into account, the magnitude of the output pulse is £i + A£i. This goes by way of the sampler and distributor to the input of Fz. 1 ^7 // / / • / • / • / / / • / z' / ^/ 1 lU / / o / / < ^ / H • / _1 • / o / / > • / 1- O / / / y / y / ^^ Ei+AEi / ^/^ E, / ^ / _ — o • ^— ***^ V, V,+v, INPUT VOLTAGE Fig. 4 — Instantaneous expandor. From the sampUng principle one deduces^'^ that each pulse which appears at the input to Fa is directly proportional to the signal which occurs A/ seconds later at the output, where A/ is the delay in Fz. This delay will be neglected. Thus, in response to Ei + A£i at the input, the value of the voltage at the output of Fz is k{Ex + AjEi) where k depends upon the design details of the system. Represent instantaneous signal and noise voltages at the output of Fz by S\ and iVi. Then, S, = kE, (1) and (2) INSTANTANEOUS COMPANDORS 711 AEi It is apparent (Fig. 4) that — is a function of the slope of the expandor characteristic. Represented by Ji, this ratio is an important quantity and will be referred to as the "noise susceptibility of the system." Dividing (1) by (2) and dropping subscripts, ~ = - (3) N vs where S/N is the ratio of instantaneous signal to instantaneous noise at the output of Fz and — the corresponding ratio without a compandor. Noise Susceptibility If it is assumed that the maximum signal is large compared to the noise, then Because the characteristic of the expandor is nonlinear, the noise sus- ceptibility, ^, varies as a function of signal input. When 5 is unity the noise susceptibiUty equals that of a linear system. The object of instantaneous companding is to make 5 a predetermined function of the magnitude of the signal. However, the predetermined choice is not entirely arbitrary. To avoid ambiguous signals at the receiver, as the input to the compressor varies con- tinuously from zero to unity, the input-output characteristic must be single valued. One notes that if ^ is averaged with respect to the expandor input voltage, the average value is unity regardless of the shape of the characteristic. Simi- 1 larly, if - is averaged with respect to expandor output voltage, the value obtained is always unity. Important Difference Between Syllabic and Instantaneous Types of Compandors At this point it seems advisable to emphasize an important difference between syllabic and instantaneous types of compandors. Signals com- pressed on a syllabic basis can be transmitted in a band not significantly different from that occupied by the original signal. Moreover, the require- ments on the phase and attentuation-frequency characteristics of the path between compressor and expandor are about the same as if the signal were not compressed. Accordingly, syllabic compandors can and have been applied to a wide variety of existing types of systems. 712 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 This is not true of the instantaneous compandor. While instantaneous com- panding theoretically does not require an increase in bandwidth ^^ between compressor and expandor, additional transmission requirements^' which this path must satisfy usually would be regarded as very severe when this band is no more than the bandwidth of the signal entering the compressor.* This means, for example, that for practical reasons instantaneous com- pandors cannot be applied to existing types of single-sideband carrier tele- phone systems. On the other hand, if a pulse modulation or other type of multi-channel time-division system is capable of operating without com- pandors, the addition of instantaneous compandors will not alter matters. Of course, the net over-all transmission will change more than one db for each db change in the propagation from compressor output to expandor input, but this is true for either type of compandor and depends essentially upon the properties of the expandor. Application of Theory The theory will be used to evaluate the noise advantage of an instantane- ous compandor in the PAM system shown in Fig. 1 when the signal is speech. The result is applicable^" to other types of multi-channel pulse-modulation systems. Choice of Expandor Characteristic The first step is to select a suitable characteristic. If the characteristic of the compandor is logarithmic, the signal-to-noise ratio at the output of the system will be independent of speech volume. It appears reasonable for talkeis of different volume to be treated alike and so a logarithmic char- acteristic will be chosen. Results of experimental observations on this type of characteristic will be discussed in a later paragraph. A logarithmic compandor is one in which the output voltage of the com- pressor is a logarithmic function of its input voltage. Conversely, the output voltage of the expandor is an exponential function of its input voltage. This relationship may be written: rL = ae where a and b are arbitrary constants, E is the expandor output voltage, and V the expandor input voltage. * This implies suitable instrumentation which, for convenience, may utilize sampling. If a signal be compressed by an instantaneous compressor, the bandwidth occupied by the compressed signal obviously will be considerably increased. However, the information content of the compressed signal is no more than before and accordingly may be repre- sented by another appropriate information signal whose frequency range is restricted to the bandwidth of the signal entering the compressor. INSTANTANEOUS COMPANDORS 713 It is apparent that the characteristic cannot follow the exponential law at low values of input voltage, because, if the relationship is exponential, E is not zero when V is zero. This difficulty is avoided by using a characteristic which is linear for input voltages below a given value and exponential for input voltages above this value. A characteristic of this type is illustrated in Fig. 5. The point at which the characteristic changes from a linear to an DO Q.-I DID O 0 EXPONENTIAL PORTION ^ ^ 10 20 ^ ^ ^ 30 ^x^ TRANSITION poiNT\ ^y ^ 40 X^r .^ SO 1 0.1 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.020 0.012 mO < 0.004 LINEAR PORTION r y .--^ y TRANSITION -^v POINT ^^^ ^•- ** t'^ ^ ■^ 0.05 0.10 0.15 INPUT VOLTAGE 0.20 0.25 Fig. 5 — Expander characteristic. exponential relationship is referred to as the '^ transition point." The transi- tion from one function to the other occurs smoothly and the first derivative of the output with respect to the input is continuous at the transition point. Logarithmic Compandor Since the characteristic of the compandor is an odd function, all formulas will be limited to the positive portion. The exponential portion of the ex- pandor characteristic is given by (V-l)IVt (5) 714 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 provided E = 1 when F = 1 and provided — - = — ' at the transition point dV V t where the expandor voltages are designated Vt and Et. From (5) we write E, = ,<^-^>/^'. (6) Let "expansion ratio" be defined by the ratio of Em/Et to Vm/Vt where Em and Vm are the maximum values of the expandor output and input voltages. Recall that Em = Vm = lySet K equal to the expansion ratio and write K = J'. (7) The expansion ratio may be represented as a function of Vt by replacing Et in (7) by its value in (6), viz., K=Vte''- '''''''*, (8) Expressed in decibels, i^(in db) = 20 logio iVte^'-'''^"''). (9) When the value of K given by (9) refers to the compressor, it is called "compression ratio." This follows from the identical (Fig. 3) compressor and expandor characteristics after input and output designations are inter- changed. The manner in which K and Et are related to Vt is given by (8) and (6) respectively. These relationships are plotted in Fig. 6. Clearly, if any one of the three parameters is fixed, the entire expandor characteristic is known. Signal-to-Noise Ratio Let 5i represent the noise susceptibility of the system during intervals when the magnitude of the signal voltage is within the exponential range of the expandor. By differentiating (5) with respect to V and using (4) we get ,, = 1 e'-"'"' (10) Vt which relates noise susceptibility to expandor input voltage, V, which in turn equals the compressed signal voltage. To express ^2 as a function of the normal signal voltage, apply (5) to (10), viz., ^: = f . (11) Vi INSTANTANEOUS COMPANDORS 715 Noise susceptibility, therefore, is directly proportional to the magnitude of the signal voltage. When ^ in (3) is replaced by the right-hand side of (11) we get 5 N Vt V (12) 20 25 30 EXPANSION RATIO, K, IN DECIBELS Fig. 6 — Expander parameters. This shows that the ratio of instantaneous signal to instantaneous noise voltages at the output of the system is independent of the magnitude of the signal for voltages within the exponential range of the expandor. Noise in the transmission medium is assumed to be fluctuation noise of uniform power density. It is convenient to replace v in (12) with the rms value of the noise voltage at the input to the expandor.^^ Designate this 716 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 voltage 7v, replace N by Nr, and (12) becomes — = ^' Nr I %r (13) The physical significance of this ratio may be explained as follows. The voltage which appears at the output of the system after the occurrence of a PAM pulse may be represented as the sum of a noise voltage and a signal voltage. Suppose that a very large number of measurements were made of the noise voltage which occurs along with a preassigned value of signal voltage. If the magnitude of the signal voltage is within the exponential range of the expandor, then the ratio of signal voltage to the rms value 15 3 UJ =)H -15 (0< «0CC-20 O z -30 / / LINE AR SY STEM / / / / / — / -25 70 65 60 55 50 45 40 35 30 25 20 15 10 5 EXPANDOR OUTPUT VOLTAGE, E, IN DECIBELS BELOW 1 VOLT MAXIMUM Fig. 7 — Noise susceptibility. of observed noise voltages would equal SjlSIr in (13). The same value of SjNr would be obtained if the measurements just described were repeated for any other preassigned magnitude of signal voltage within the exponential range of the expandor. When the voltages impressed upon the input of the expandor are within the linear range of the characteristic, the noise susceptibility, designated 53, 17 is equal to -^ . From (7) we write ^. = i (14) This shows that, within the linear range of the compandor, noise suscepti- bility is inversely proportional to expansion ratio. INSTANTANEOUS COMPANDORS 717 Figure 7 illustrates the relationship between noise susceptibility and signal voltage. Noise susceptibility (Fig. 7) is expressed in db relative to that of a linear system. Value of S/Nr To evaluate the noise advantage which results from the use of an instan- taneous compandor, it is necessary to know what requirement to place on S/Nr. This ratio refers to noise at the output of the system during intervals when the signal magnitude is within the exponential range of the expandor. During these intervals the noise susceptibility of the system is propor- tional to the signal magnitude, so that the character of the noise is entirely different from that encountered in a linear system. People listening to speech transmitted through a system equipped with an instantaneous compandor have mistaken this type of noise for the distortion produced by an over- loaded amplifier. Accordingly, experiments were made to determine how small S/Nr could be in a telephone channel whose frequency range was 200 to 3500 cycles. A test circuit was devised which simulated the noise performance of a system equipped with a logarithmic compandor, and arrangements were provided so that the signal-to-noise ratio S/Nr could be adjusted over a wide range of values. The test procedure was to allow an observer to listen, during two consecutive intervals of time, to speech from the output of a Unear system and from the compandor system. Conditions were arranged so that the noise at the outputs of the two systems was the same when the signal voltages were within the linear range of the compandor. The sequence in which the two conditions were presented to the observers was changed in a random manner, so that there was no way of identifying the compandor system except for the effect of the enhanced noise susceptibiUty during intervals when the signal magnitude was within the exponential range of the expandor characteristic. Twenty- two observers participated in these tests and different speech volumes were used covering a range of 26 db. Experimental results showed that the compandor system could be readily identified when S/Nr was 16 db or smaller, whereas the difference between the two systems was difficult to detect when S/Nr was 24 db or greater. An acceptable value of S/Nr for a typical telephone system is therefore some- where between these two limits. A value of 22 db* was selected as a con- servative estimate. To confirm this, several people experienced in rating the quality of telephone systems were asked to listen to the output of the test circuit with S/Nr adjusted to 22 db. The consensus was that the quaUty was satisfactory. * This value is in agreement with the one used by C. B. Feldman and W. R. Bennett in studies of bandwidth and transmission performance, reported in reference 10. 718 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 Another point brought out by these tests was that the difficulty or ease with which the difference between the two systems could be detected was substantially independent of speech volume. Noise Ad.antage The value of S/Nr given above may be used to evaluate the noise ad- vantage. Basically the problem is to find the permissible db increase in noise at the output of the transmission medium when the PAM system of Fig. 1 is equipped with an instantaneous compandor instead of linear net- works having characteristics indicated by the dotted line in Fig. 4. For the comparison to be valid, the noise at the output of the system during intervals when the signal voltage is zero must be the same for the two conditions, and when the compandor is used S/Nr must equal 22 db. Recall that Vr represents the rms value of the noise voltage at the output of the transmitting medium when the instantaneous compandor is used, and let Vr represent the corresponding value when the linear networks are used. The noise susceptibility of the linear system is unity. Therefore, the noise at the output of the system during intervals when the signal voltage is zero will be the same for the two conditions provided Vr = Vr Sz. When S3 is replaced by its value in (14) we require that r, = |. (15) The equation which specifies that S/Nr equals 22 db is Vt 12.59 = — (16) obtained by replacing S/Nr in (13) with the voltage ratio corresponding to 22 db. As shown by the lower curve of Fig. 6, Vt is a function of the ex- pansion ratio, K. The quality of the two systems will be the same provided (15) and (16) are satisfied simultaneously. Values of Vr, Vr, and K which simultaneously satisfy (15) and (16) are plotted in Fig. 8. Larger values of K would yield values of S/Nr smaller than the specified value of 12.59 db. Smaller values of K correspond to less noise improvement and make S/Nr larger than assumed necessary. The use of these curves will be illustrated by the following example. It will be assumed that the rms value of the noise voltage at the output of a typical telephone channel is approximately 56 db below the hghest signal voltage which the system is called upon to transmit. In the PAM system of Fig. 1 one volt was arbitrarily taken as the peak signal voltage at the output of the transmitting medium so that Vr is 56 db below one volt. From the upper INSTANTANEOUS COMPANDORS 719 curve of Fig. 8, it is apparent that the noise at the output of the transmission medium, iv, can be 35.8 db below one volt, and the corresponding value of K is 20.2 db. The noise advantage of the compandor equals K, and is about 20 db. Figure 6 shows that, in a 20 db expandor, Vt is 13.8 db below one volt. The noise voltages at the expandor input are well within the linear range of its characteristic. Otherwise (15) would not be valid. •40 Li 45 ^ 3 55 UJ CO !3 60 UJ CD z >" 70 75 _^ -^ ^ y^ ^ ^ ^^ ^ / y EXPANSION RATIO, K, IN DECIBELS RELATIVE TO UNITY yi O U» O en O ^;t?rs; o a m kJ > C «3 CJ C ,i_) c OJ P o o _rt t/. ■ — 1 c ^ o _aj E ra . tfi .ti -^ c c3 =3 rt QJ bO^ C ■ — ' ^ • — cc X) -^ QJ c^ ^ XI ^ o en QJ O 3 U2 ^ p <: .. jn tn ^ 'o *s c (LI 3 4_> O to ^il ^' W3 c C3 ^■g a 13 c '> 'S a^ c o .S o i 724 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 aerial cable jobs. Certain differences also were necessary in the mounting details. These various differences were recognized in the case code designa- tions. Beginning in the early 1930's, sections of lead sleeving with soldered lead (and later on, brass) tops and bottoms came into general use for small load- ing complements. To add mechanical support to the inherently weak, cylin- drical lead sleeve, the larger-size lead cases were equipped with inner-lining steel tubes when used on cables maintained under gas pressure. The lead cases^"^ are less expensive than rectangular-shaped welded-steel designs of equivalent potting capacity, and are suitable for use on underground and on aerial cables. On the lead cases used in buried cable projects, and on their W Fig. 21 — Si)lice loading cases for exchange area loading. 88 mh coils potted in cardboard containers, and equipped with fabric tapes for fastening to cable core at splice. At left: 622 coil. At right: 632 coil. stub cable sheaths, a special finish reinforced with armor provided protec- tion against injury by rodents. Corresponding protection was also provided on the sheaths of stub cables of cast iron and welded steel cases intended for use on buried cables. Another general change in the design of loading coil cases started about 1940 with the introduction of cylindrical, J-inch steel-tubing in place of thick steel-plate rectangular designs. ^^^ While initially this was a steel conserva- tion measure, it was found to be very advantageous with respect to manu- facturing techniques and economy. This development will eventually reduce the use of the previously mentioned lead-sleeve designs. The basic problem of securing the most economical designs for different potting complements and different installation conditions has included the provision of special case designs for placement in cable splices, which do not <"^ Some lead sleeve cases for exchange area loading are shown in Fig. 17 (page 467). ^"^ Some of these cylindrical thin steel cases are shown in Fig. 18 (page 468) and in the in- stallation photographs Figs 26, 27, 28 A and 28B (pages 728, 729, 730 and 731 , respectively). INDUCTIVE LOADING FOR TELEPHONE FACILITIES 725 C! O a in y 03 5 !> tn ■5^ ex O c« c« eg ^ o o ."I^ U ^ o I bb 726 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 19vSl require stub cables, for office rack-installations, for submarine cables, and for buried, insulated wire. The splice-loading designs include individual cardboard containers for small exchange area (Fig. 21) and toll cable coils (Fig. 20), and baked varnish impregnated spindle-assemblies of coils for coaxial cable order-wire circuits, and for small exchange area cables (Fig. 22) . Case Sizes and Shapes Where involved, the case size and shape limitations have generally been imposed by underground cable installation conditions. The circular tops of Fig. 23 — Office type loading coil case for installation on office mounting plates. Designed for potting molybdenum-permalloy core program circuit loading coils. the cast iron cases and the rectangular tops of the welded steel cases had to be small enough to permit lowering the cases through the circular manhole openings in the loading manholes and loading vaults. In the early applica- tions of loading, 26 and 27-inch manhole openings were very common; later on, 30-inch openings became standard for loading manholes. In recent years, in redesigning the large, thick-steel cases that required 30-inch manhole openings for their installation, the superseding thin-steel designs were pro portioned to permit installation in line manholes having 27-inch openings. The case bodies of the cast iron cases were approximately circular in cross- section with scallop-shaped contours corresponding to the compartments in which the coil spindle-assemblies were mounted. These ranged from 3 to 7 in number. In the rectangular cross-section, welded steel designs, there INDUCTIVE LOADING FOR TELEPHONE FACILITIES 727 I'ig. 24 — Installation of submarine cable loading. An early type of cast iron case ready for lowering into water. 'Fig. 25 — Moulded rubber loading coil case for buried wire loading installations. Views of piece parts, partial assembly, and potted coil ready for installation. 728 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 0) o) rt O cj <-* - '5 ^^ ^ ^ u, t« « «J c3 t« .-^ +-> ra K^ rt 3 2.2 1-^^ C CI-''-* -. rt ^ c« >-i o3 o ^ o '^ '^ — c£.>^ 535 5 .OH »- -'p oJl ■ti . (U -5 So (L> "rt JS uj J3 9- C J- 3 •2^ 2 o ^-^^ :3 ^1^ j3 e" o <" S°J u ^ ^ .- (U 3 o D-43 "^ O *J u w rt fO INDUCTIVE LOADING FOR TELEPHONE FACILITIES 729 usually was design flexibility in proportioning the case heights and the cross-section dimensions to be approximately optimum for most efficient Fig. 27— Exchange area loading installation in side street auxiliary loading vault. In congested areas, space limitations frequently require the installation of underground cable loading coils in an auxiliary loading vault located in a side street near its intersec- tion with the street under which the main cable conduit system is laid. Extensions of the case stub cables carry the coil terminal leads to the main cable splices. At time of photo- graph, a total of 18 cases containing a total of 7283 coils were installed in this auxiliary vault. Six cases had 303 or 304 coils, and 12 cases had 455 or 456 coils. The 18 cases in- clude 2 cast iron cases, 5 rectangular welded steel cases, and 1 1 tubular, thin steel cases. The individual coil codes are Nos. 612, 632 and 643; 92% have 88 mh inductance, the remainder being 135 mh coils. 27% have permalloy cores; the remaining 73% have molyb- denum-permalloy cores and formex insulated windings. This figure shows the far end of the loading vault where 14 cases are placed. Several tubular steel cases are hidden by larger cases in foreground. use of the available mounting and splicing-space in the loading manholes, subject of course to the manhole-opening Umitations previously mentioned. 730 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 ^ -Wit ^ 5L»> i V ■^^tf ^«^> -^ ** Fig. 28A — Another auxiliary vault installation of exchange area loading. One end of vault. At time of photograph, 33 cases containing a total of 11,241 coils were installed in this vault. A majority of the cases appear both in this view and in the view of Fig. 28B. 25 cases have 303, 304 or 305-coil complements, each of the other 8 cases have 455 or 456 coils. The total complement comprises 2 cast iron cases, 17 rectangular welded steel cases, and 14 tubular thin steel cases. The individual coil codes are 612, 613, 614, 622, 623, and 643. The coil inductances are: 88 mh, 70%; 135, 27% and 175 mh, 2.7%. 35% of coils have permalloy cores; the others have molybdenum-permalloy cores. 57% of coils have formex insulated windings. Many of the individual designs were relatively tall, with cross sections re- quiring small amounts of floor space. The recent trend in case design (1948, INDUCTIVE LOADING FOR TELEPHONE FACILITIES 731 1949) revolves about two requirements: (1) the cases shall be capable of being installed in manholes having 27-inch openings, and (2) the vertical Fig. 28B— Other end of vault in Fig. 28A. dimensions shall be as short as possible while meeting requirement (1). The primary purpose of these changes is to reduce the cost of manhole construc- tion in new conduits. The submarine cable loading cases previously mentioned are cylindrical 732 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 in shape, designed and installed so that the axis of the cylinder is in line with the axis of the submarine cable. A stub cable extends from each end, one having the IN leads to the coils, and the other the OUT leads. (Refer to Fig. 24, page 727.) Potting Complement Sizes Usually, the initial traffic requirements and estimated rate of traffic growth are the most important factors in determining the potting complement sizes for particular projects. Frequently the initial loading complement is greater than subsequent complements. In some situations, two or more cases may be installed at the same time, because of the case-design size limitations. Non-Phantom Coils: In the early loading applications of non-phantom coils, the most common potting complements were of the order of about 50 coils. The maximum complements prior to the development of inexpensive loading for 22 ga. exchange cables ranged up to 98 coils. Complements of 200 and 300 coils became quite common with the Nos. 601 and 602 coils. With the introduction of the No. 612 (permalloy-core) coils, complements of 450 and 600 coils became common, and occasionally a 900-coil complement was used. The maximum complements of the much smaller molybdenum- permalloy core coils have been held to about 450 coils. The foregoing is an interesting manifestation of the stubborn limits upon case-design cost-reduc- tion that come into play as the coils become smaller and smaller. The labor- cost component is dominant and little saving in materials can be achieved. In consequence, it is frequently preferable to use two medium-size comple- ments, rather than one over-size complement having the same total number of coils, especially if the second complement can be deferred for some time. Side and Phantom Coils: In the early applications of loading to quadded 19 and 16 ga. toll cables, the side circuit coils and the phantom coils were some times potted in separate cases. In such applications, the side circuit coil complements ranged up to 98 coils, and the phantom coil complements ranged up to 48 coils, but the average-size complements were substantially smaller. Soon it became the common practice to pot associated side circuit and phantom circuit coils together in the same case, and in such instances loading complements for 24 cable quads were common. To help meet the increasing demand for toll cable loading in the early 1920's, maximum com- plements for loading 36 cable quads became available. When the phantom coils were reduced to side circuit coil-size (1923), the maximum potting com- plement was increased to 45 loading units. The large coil-size reduction that resulted from the use of compressed permalloy-powder cores made practicable during the late 1920's and early 1930's a further, very substan- tial, increase in the range of standard potting complements covering up to INDUCTIVE LOADING FOR TELEPHONE FACILITIES 733 84 phantom loading units of the P-type, and up to 108 loading units of the PB-type. These very large loading complements had an interesting economic significance. At the time they became available the demand for additional toll cable facilities was increasing by leaps and bounds, and it was not un- common for standard-size and over-size cables to be fully loaded at the time of the installation of the cables. In this connection, full loading for a 50% over-size, quadded, composite 19 and 16 ga. cable could be provided with two of the maximum-size potting complements of phantom loading units. This contrasts with fairly common experience in early installations of full- size cables, where four, five or six cases were used to provide complete loading. The further size-reductions in toll cable loading coils that were achieved with the standardization of the M-type phantom loading units and later with the MF-type units occurred during a period of greatly reduced demand for toll cable loading, influenced by the exploitation of carrier systems on conductors from which loading was removed and on new non-loaded cables. The maximum potting complements were accordingly held to 80-unit and 48-unit sizes for the M-type and MF-type loading units, respectively. Assembly Methods and Stub Cables General: From the beginning of commercial manufacture, multi-coil com- plements of cable loading were coaxially assembled on spindles which were held infixed positions in the cases. Preceding this operation, the accumulated moisture was expelled from the coil windings and the coils were dipped in a moisture-resisting compound. In the multi-spindle cases, the different spindle-assemblies were mounted in separate compartments of the cases, with the compartment partitions providing shielding to control crosstalk among the spindle-assemblies. On the individual spindle-assemblies, cross- talk was controlled by using steel washers between adjacent coils and mount- ing the coils so that their small, external, magnetic fields would be substan- tially non-interfering. The winding ends of the coils were connected to textile- insulated twisted-pair leads in spindle unit-cables, treated with wax for moisture protection. After the spindle-assemblies had been fixed in position in the case compart- ments, the spindle unit-cables were formed by hand into a stub cable core over which a somewhat loose-fitting lead sheath was drawn. A color code on the conductor insulation provided identification for "wire" and "mate" conductors, and for IN and OUT coil terminals. The final assembly operations included filling the case compartments with a viscous rosin-oil compound, and a top layer of asphalt compound; and the stub cable sheath was soldered to a nipple in the case cover. At various stages in the assembly 734 THE BELL SYSTEM TECHNICAL JOXJRNAL, JULY 1951 operations, suitable inspection tests were made to assure satisfactory con- formation to specification requirements. After the final inspection tests, the outer end of the stub cable sheath was sealed to prevent entry of moisture. When phantom loading started, the phantom coils were much larger than the side circuit coils. To conserve potting space in cases containing both types of coils, the individual spindle-assemblies consisted of only one type of coil. The phantom unit cross-connections between the phantom coils and their associated pairs of side circuit coils were made at the top of the case between quadded spindle unit-cables containing the OUT terminal leads of the phantom coils and the IN terminal leads of the side circuit coils. The quadded IN terminal leads of the phantom coils and the OUT terminal leads of the side circuit coils constituted the main line terminals of the complete loading units. In general, all of the stub cable leads to the IN and OUT terminals of non-phantom type coils, and to the main line terminals of phantom unit combinations of side circuit and phantom circuit loading coils, were con- tained in a single stub cable sheath. Necessary exceptions to this practice occurred, however, in the submarine cable loading coil cases (which had two stub cables extending from opposite ends) and in the underground and aerial cable cases containing very large complements of P-B type loading units. The first important change from the original potting practices followed soon after the introduction of phantom group loading. The original wax- dipped textile-insulated stub cables were found to be seriously objectionable sources of phantom- to-side and side- to-side crosstalk. To reduce crosstalk, and also to improve transmission, the practice started of using strip-paper insulated quadded conductors in a machine-stranded stub cable. This re- quired a splice to be made inside the case, at the top, between the paper- insulated stub and the textile-insulated spindle unit-cables. Apparatus Group-SegregaHon,Four-Wire Circuits: Several years later, when the development work on long-distance four-wire repeatered circuits got well under way, the assembly arrangements in the loading coil pots and the stub cable designs were changed to provide crosstalk segregation between the groups of coils used on the opposite-direction branches of the four-wire circuits. The segregation arrangements in the stub cables included shielding between the gioups of terminal quads associated with the opposite-direction circuit groups. These loading coil case and stub segregation -arrangements were details of a fundamental plan for complete group-segregation between the opposite-direction branches of four-wire transmission systems (including the main cables themselves and the repeater office circuits) in order to con- trol the intergroup near-end crosstalk coupling and prevent it from being a serious factor in the over-all crosstalk. (The relatively high amplification INDUCTIVE LOADING FOR TELEPHONE FACILITIES 735 in the four-wire repeaters made very desirable the rigorous control of this type of crosstalk coupling.) Initially, the loading apparatus and associated stub cable quads intended for use on two-wire repeatered circuits were seg- regated in the coil cases from the two opposite-direction groups of four-wire circuit apparatus. Later on, this apparatus segregation between two-wire circuit coils and four-wire circuit coils was discontinued. In mixtures of the two types of coils, the two-wire circuit apparatus was divided into approximately equal groups, each of which was combined with one of the four-wire opposite-direction groups. In order to simplify potting practices, the two-group segregation plan became the standard plan for all toll cable loading cases and was used in loading complements containing mixtures of two-wire circuit and four-wire c'rcuit loading apparatus, and for complements consisting wholly of two-wire circuit coils, or of four-wire circuit coils. In the most recent (1948-1949) general redesign of toll cable cases and stub cables, the segregation arrangements just described have been simpli- fied, largely because of the present very small demand for additional H44-25 four-wire circuits. Group segregation of the apparatus within the cases is used only when four-wire H44-25 loading is involved. The use of shielding and of group-segregdtion arrangements in the stub cables has been discon- tinued. In complements of units for H44-25 loading, one of the opposite- direction groups is connected to a group of terminal quads having contigu- ous "quad counts" at the low end of the quad counting scheme described on page 737, and the other group is connected to the quads having "quad counts" at the high end of the quad counting scheme. When two-wire circuit coils are included in a loading complement containing four-wire circuit coils, the terminal quads of the two-wire coils use terminal quads having "quad counts" intermediate between those of the two opposite-direction groups of four- wire coils. Phantom Coil Size-Reduction: The next important potting-practice change resulted from the size-reduction of the phantom coils to side circuit coil- size. From then on, the phantom coils were mounted on the same spindles as the side circuit coils, with each phantom coil immediately adjacent to its associated pair of side circuit coils. This permitted a more efficient use of potting space and made unnecessary the use of spindle-unit cabling for the cross connections between the coil components of the phantom loading units. The miniature inductance coils used in the loading-unit crosstalk adjust- ments were mounted on a frame located at the top of the coil spindle-assem- blies and were connected in the circuit at the splices made between the stub cable and the spindle unit-cables leading to the coil line terminals. Assembly Redesign, Exchange Area Coils: The first major change in the 736 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 assembly and case-wiring arrangements for non-phantom exchange area coils was made during the middle 1920's in solving difficult problems that arose in the design of cases for 200-coil, 300-coil, and larger complements of the new small-size loading coils. The spindle-assemblies of coils were fas- tened to a skeleton frame to which the case pot-cover and the machine- stranded textile-insulated stub cable were attached. The part of the stub cable that extended within the case was subdivided into unit cables which were associated with the individual spindle-assemblies, to which the coil leads were connected, thus eliminating the intermediate spindle cables. After these connections had been made, the complete coil-assembly, with stub cable, was lowered into the coil casing. The case cover was then fastened to the coil casing, and the case filling-compound was poured through a small temporary opening in the cover. Assembly and Cabling Changes; Beginning of Use of Loading Units in Individual Shielding Containers: Some of the improved assembly-arrange- ments, above described, were made available for phantom loading units soon after the permalloy-core toll cable coils became available, along with the standardization of the P-B type loading units. Certain differences were necessary, however, in order to permit the assembly of the 3-coil loading units in individual, cylindrical, shielding containers, having one end open. The associated three coils of a unit were mounted on a short hollow dowel, at one end of which was mounted a frame supporting terminal posts for all of the line terminals of the individual coils and the crosstalk adjustment- elements (small inductances and resistances, preselected to meet crosstalk requirements). The cross-connections between the phantom and side cir- cuit coils were made between appropriate terminal posts, and the loading unit main-line terminals were connected to the stub cable conductors at this point, after the crosstalk adjustment-elements were connected in the cir- cuit. The individual loading units in their shielding containers were fastened to a vertical frame by bolts extending through the hollow spindles. This frame was attached to the case cover. The stub cable was a machine- stranded, single piece of paper-insulated cable having the part below the case cover separated into unit cables for the connections to horizontal rows of loading units. The loading unit and potting assembly methods are illustrated in Figs. 10 and 11 (pages 186 and 188, respectively). Generally similar arrangements were used with the M-type and SM-type loading units. With the standardi- zation of the MF-type loading units, the adoption of cylindrical steel case bodies resulted in some potting assembly changes which are illustrated in Figs. 12, 13, and 14 (pages 192, 193 and 194, respectively). In the medium and large size potting complements, the individual loading units are mounted INDUCTIVE LOADING FOR TELEPHONE FACILITIES 737 near the outer periphery of circular mounting plates, and the inner end of the stub cable extends through a circular opening at the center of these plates, (Fig. 13). In the very small complements, the MF units are stacked one above the other as shown in Fig. 14. The concentric layer-type stub cables, used with new cases potting P-B type loading units and subsequently with the M-type, SM-type, and MF- type loading units, had an improved color-code for the conductors of the terminal quads which provided a counting-scheme type of identification for each of the individual loading units potted in a given case. To facilitate this full-scale identification of the individual units, it was necessary to have a precise wiring coordination between the positions of the individual units on the case assembly frames and the positions of their terminal quads in the stub cable (which were identifiable in terms of the quad-count color- code). This permitted the necessary coordination of the coil-grouping arrangements which were desirable for crosstalk reasons in complements of four-wire circuit loading (as previously discussed) with the group segregation and shielding arrangements of the associated stub cable terminal quads. A simplifying factor was the use of adjacent quads for the IN and OUT terminals of same loading unit. The improved stub designs greatly simplified the manufacturing problems involved in providing, (a) full flexibility as regards loading complement sizes, and (b) full flexibility for desirable combinations of different types of loading units. (a) Using a relatively small number of case sizes, provision was made for obtaining any total-complement size, ranging from one up to the maximum- complement size, in steps of one loading unit. A different size of stub cable was used for each different size of case. When less than a full complement was desired in a particular size of case, the unused terminal quads were left open at the inner end of the stub cable and were tagged at the outer end. In terms of "quad counts" these non-used quads had contiguous numbers at the ''high" end of the quad counting-scheme, and were readily identified by means of the quad-count color-code and the tags previously mentioned. (A name-plate on each case recorded the number and the code types of loading units potted in the case.) In the prior art, different stub cables had been provided for fitting the different partial and full potting-complements in particular sizes of cases. (b) For several years prior to the standardization of the improved as- sembly and stub design it had been a common practice to use mixed potting complements of different types of loading units, in order to realize the maximum potting and installation economies inherent in the use of larger- size loading complements made practicable by size-reduction of the loading 738 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 coils. These mixtures usually comprised combinations of coils for four-wire long-haul circuits with one or two types of coils for short-haul or medium- haul two-wire circuits. When this practice of mixed potting complements started, it was customary to use different stub cables for each different potting-mixture, even when the same total number of loading units were involved. In these stub cables, each of the different types of loading units had its own individual color-code identification. In the new set-up, the rela- tively simple color-code counting-scheme provided full flexibility for all desirable combinations of different types of loading units. Loading units of a given type made use of terminal quads having con- tiguous numbers in the quad counting-scheme. In mixtures involving two types of loading units, for example PIB and PUB units, the units having the lower-number component in their code-designation used the low-numbered terminal quads, and the units having the higher code-number used the high- numbered terminal quads. In mixtures involving three different types of loading units, the units having the intermediate code-number in their code designation used a contiguous group of terminals which were intermediate in position between the low-numbered quads and the high-numbered quads which were respectively associated with the loading units having the lowest and the highest code numbers. These procedures were followed in each of the two segregated groups of opposite-direction loading units previously mentioned. Quadded Stub Cables for Non-Phantom Coils: During the 1930's, the practice of using quadded stub cables for cases potting non-phantom type exchange area and program circuit loading coils was started. One pair of each terminal quad was connected to the IN terminals of a coil, and the associated pair was connected to the OUT terminals of the same coil. Previously, the IN and OUT terminals had been grouped in different unit cables. The close association of IN and OUT terminals in the new quadded stub cables reduced the factory testing-time, and simplified the preparatory phases of the field splicing of the stub cables to the main cables. Other subsequent improvements included the use of paper-pulp insulation on the stub cable conductors, in place of textile insulation. By this time it had become a common practice to terminate the coil windings on terminal clips mounted in close proximity to the coils. The inner ends of the stub cable conductors were soldered directly to these clips. Stub Cable Conductor Sizes: Since the case stub cables are extensions of the main cables, transmission considerations have generally led to the use of about the same sizes of conductors. However, notable exceptions to this rule have been accepted in situations where conformation to the rule would have made the stub cable unduly expensive, or unduly large and difficult to INDUCTIVE LOADING FOR TELEPHONE FACILITIES 739 handle at the factory or during installation. The stub cable conductor sizes have ranged from 13-gauge in the cases containing coils designed for com- posite coarse-gauge toll cables to 24-gauge in the standard cases for the coils used principally on 22 and 24-gauge non-quadded exchange cables. For Fig. 29 — Buried coaxial cable installation of voice-frequency loading on outer layer quads. View of installation after completion of the splicing work, and prior to filling in the excavation. The loading coils are potted in two tubular, thin steel, cases. Each of black boxes near center covers a cable splice, and furnishes protection against mechani- cal injury. At each splice, connections are made to the stub cable conductors of a single loading coil case. Splicing difficulties prevent all of the connections from being concen- trated at a single cable splice. several decades, 19-gauge stub cables were used for the toll cable loading cases. The most recent case designs are using 22-gauge conductors. Dielectric Strength From the beginning of the use of cable loading, a fundamental design requirement has been that the insulation of the loading coils and of the 740 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 associated stub cable and pot wiring should have a dielectric breakdown- strength as high as that of the cables for which the loading was intended, and preferably somewhat higher, to assure that the loading apparatus would not be dielectrically weak points in the loaded cable systems. When dielectric-strength improvements in toll cable design started during the late 1930's in order to reduce damage by lightning, especially on buried and aerial cables, equivalent improvements were also made in the loading apparatus. These cable and apparatus improvements were primarily con- cerned with raising the dielectric strength of the insulation between core and sheath. During recent years, the extensive installation of buried toll cables in areas where the ground resistance is high has led to the use of cables having very much higher dielectric strength (wire to ground) than those used during the 1930's. The development of the copper-jacketed toll cable having a thermoplastic protective covering between the lead sheath and the jacket, which was capable of withstanding a dielectric-strength test of 10,000 volts d-c, between the sheath and the jacket, made it necessary to apply an equivalent insulation to the exterior of the buried loading coil cases. The more recent development of the "Lepeth" sheathed toll cable has made it possible to approach a dielectric breakdown-strength of the order of 25,000 volts d-c between cable core and sheath. This is achieved by extruding a sheath of polyethylene of suitable thickness over the cable core, and over this a thin lead sheath. Loading coil cases were redesigned to match this construction^ using an inner lining of thermoplastic insulation to provide equivalent insulation between the coils and the case. The stub cables have dielectric design-features corresponding with those of the Lepeth toll cable. Potting Costs The potting cost per coil, or loading unit, varies considerably with the potting complement-size, and is a maximum in small complements. These general relations apply for all types of coils. In the early designs, the average potting cost per coil was much smaller than the coil costs. Over the years, the'case cost-reduction that has resulted from coil size-reductions, increased complement-size, and other design changes, has been smaller on a percentage basis so that in the present designs the average per coil potting costs are somewhat greater than those of the coils. Notwithstanding the changes in cost relations just mentioned, the direct and indirect savings that have resulted from the potting development work constitute a substantial fraction of the aggregate plant cost-reduction which has been achieved by the use of coil loading. INDUCTIVE LOADING FOR TELEPHONE FACILITIES 741 PART V: LOADING FOR INCIDENTAL CABLES IN OPEN- WIRE LINES Introduction From the earliest days of telephony, when it became necessary to use pieces of cable in long-distance lines to provide toll entrance facilities at toll centers or for other purposes at intermediate points, such cables have had more or less objectionable effects on the. over-all transmission-system per- formance. These impairments resulted from the much greater transmission loss per unit length in the inserted cable, and from reflection effects occurring at the cable junctions with the open-wire — these being due to the large differences between the cable and open-wire impedances. Prior to the advent of loading, the losses in incidental cables could be reduced to low unit-length values only by using expensive coarse-gauge cables. Cable loading became available just in time to head off the instal- lation of some very expensive coarse-gauge cables that had been proposed for unusually long entrance facilities in the New York and Boston areas. The use of loading on the open wires greatly increased the economic importance of attenuation reduction in the incidental cables occurring in such Unes. By substantially raising the line impedance, loading also increased the magni- tude of the reflection losses at junctions with non-loaded cables. Starfdard "heavy" loading (Table II, page 156) came into general use on long entrance cables in the loaded lines. While this loading did not have a sufficiently high impedance to match that of the loaded line, it was close enough to reduce the junction reflection losses to acceptable values. A special light-weight loading found some use on incidental cables in non-loaded lines. When satisfactory types of telephone repeaters became available for ex- tensive use on loaded open wires, the cable junction impedance-irregulari- ties, and other irregularities, had to be reduced to very small values so as to avoid repeater circuit unbalances that would objectionably restrict the repeater gains. These severe requirements put a high premium upon the use of an improved type of cable loading having impedance characteristics that matched closely those of the associated open-wire circuits. This "extra- high" impedance loading also had very satisfactory attenuation properties. Subsequently, when the exploitation of the vacuum-tube repeater started on non-loaded open-wire lines it became necessary to use a new, low-im- pedance type of impedance-matching loading on their associated incidental cables. Because of the low impedance, the attenuation reduction was con- siderably less than that provided by the extra-high impedance loading just 742 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 mentioned. This, however, was not a serious limitation in the non-loaded repeater circuits. After open-wire loading became obsolete, further improve- ments in telephone repeaters and in transmission standards led to progressive improvements and refinements in the loading used on cables in non-loaded lines. Beginning around 1920, the rapidly increasing use of open-wire telephone and telegraph carrier systems made it necessary to use in the associated incidental cables improved loading systems that provided good impedance- matching and attenuation-reduction properties over the complete voice and carrier-frequency bands used by the carrier transmission systems. The use of several different carrier telephone systems employing materially different frequency-band widths made it economically desirable in due course to use several different types of loading to provide the necessary transmission bandwidth through the incidental cables. The various types of cable loading mentioned above are separately con- sidered under suitable headings in the following pages. The two principal subdivisions of Part V are devoted to voice-frequency loading and to carrier loading, respectively. A third subdivision briefly describes a special type of voice-frequency phantom loading which is used in coordinated phantom- group combinations with side-circuit carrier loading systems that provide 10-kc and 30-kc transmission bands. The importance of the incidental cable loading described in Part V of this article is due to its substantial, beneficial contributions to the transmission service-performance of the relatively expensive open-wire facilities, rather than from the amount of loading so employed. This is quite small relative to that used in voice-frequency toll cables and exchange cables. (V-A) Voice-Frequency Impedance-Matching Loading Since the most important early uses of the vacuum-tube repeaters on open-wire facilities were on loaded lines, the first new impedance-matching loading system was developed for this particular use. As noted later, this had an important effect on the loading system subsequently developed for use on cables in non-loaded lines. Loading for Cables in Loaded Open-Wire Lines The new phantom-group loading for this use was designed to have closely the same values of nominal impedance and theoretical cut-off frequency as those of the loaded lines. The cable coil inductances had to be a little higher than the open-wire coil inductances, in consequence of the smaller amount of distributed inductance in the cable. A standard cable coil-spacing of about rNDUCTIVE LOADING FOR TELEPHONE FACILITIES 743 5575 ft. (0.062 mf/mi cable) was adopted so as to have loading section capacitances close to those of the open-wire loading sections. This cable loading system originally known as "extra-heavy" loading, and later desig- nated E248-154, was used on coarse-gauge cable conductors and had a slightly lower attenuation loss than that of the then standard ''heavy" loading for coarse-gauge toll cables. (In the loading designation, E is the symbol for 5575-ft. spacing.) The loading coils used 65-permeability iron-wire cores with two short, series air-gaps, to secure good magnetic stability. The long obsolescence of open-wire loading makes further description of the E248-154 cable loading unimportant. Loading for Cables in Non-Loaded Open-Wire Lines When open-wire repeaters first came into general use, it was a common situation for entrance and intermediate cables to have one group of circuits associated with loaded open-wire pairs, and another group connected to non-loaded pairs. In such situations, it was obviously very desirable that the different types of cable loading associated with the loaded and the non- loaded lines should be installed at the same cable loading points. Early Standard Loading Systems E28-16 Loading: It was found that a satisfactory, low-impedance type of impedance-matching loading could be obtained by using 28 mh side circuit coils and 16 mh phantom coils at the spacing used for E248-154 loading. Some quantitative data regarding this low-impedance loading, designated E28-16, are included in Table XV (page 746) along with corresponding data on other voice-frequency loading systems subsequently standardized for cables in non-loaded lines. M44-25 Loading: In many situations where the impedance-matching requirements were not so severe, and where loaded open-wire hnes were not involved in the incidental cables along with the non-loaded lines, a some- what cheaper type of low-impedance loading using a longer coil-spacing was utilized. Data regarding this loading, designated M44-25, are included in Table XV. (It is of interest that this type of loading had been used on a small scale prior to the extensive utilization of telephone repeaters.) From Table XV it will be noted that the two loading systems had the same nominal impedance and that the better system, E28-16, had much higher cut-off frequencies. A brief digression regarding the important part which the cut-off frequency plays in the impedance-matching problem in the upper speech-frequency band is appropriate at this piont. 744 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 Importance of Cut-Off Frequency Basically, the general impedance-matching problem under discussion is complicated by the fact that the non-loaded line is a "smooth," i.e., a uniform, line, whereas the loaded cable is a "lumpy" line. On the one hand, the sending-end impedance of the non-loaded line is substantially a constant resistance with negligible reactance over the frequency range above about 1 kc. On the other hand, the high-frequency impedance of the loaded cable may vary substantially in its resistance and reactance components with rising frequency, depending upon the type of loading termination employed. "Half-coil" and "mid-section" terminations have the important advantage of substantially negligible reactance, for which reason one or the other of them was used in the early applications of impedance-matching loading. ^"^^ With these particular loading terminations, the resistance component of the loaded cable impedance changes with rising frequency, at a rapidly ac- celerating rate as the cut-off frequency is approached. The reference im- pedance in these changes is the nominal impedance of the loaded cable, which for optimum impedance-matching should be equal to that of the non- loaded line. (Numerically, the nominal impedance in ohms is equal to the square root of the ratio of the total circuit inductance, in henrys, to the total mutual capacitance, in farads, per unit length.) The resistance changes with rising frequency go up when mid-section termination is used, and drop down when half-coil termination is used. The important practical significance of the foregoing is that the high- frequency impedance irregularities at the open-wire cable junction become progressively smaller as the loading cut-off frequency is raised (provided that the nominal impedances of the line and cable are closely alike). With the simple types of loading terminations above described, the requirements for good impedance-matching make it desirable to have much higher cut-off frequencies than those which are necessary from the standpoint of attenu- ation-frequency distortion in entrance and intermediate cables. E28-16 Loading The discontinuance of the manufacture of open-wire loading coils about 1924, and the decreasing importance of open-wire loading, made it desirable to discontinue the use of the E-spaced loading solely for entrance and inter- mediate cables. Plant simplicity and flexibility requirements made it de- sirable to use H-spaced loading to permit coordination with the loading <^^ Half-coil termination involves the use of coils having one-half of the regular "full- coil" inductance at the end of the cahle, followed in regular periodic sequence by "full" loading sections and "full" loading coils. In "mid-section" termination, the first full- coil is located one-half of a full loading section away from the end of the cable. INDUCTIVE LOADING FOR TELEPHONE FACILITIES 745 used on toll cable circuits along the same routes. Studies of these coordination possibilities resulted in the standardization of H28-16 entrance cable loading during 1927. Referring to Table XV, it will be seen that the change from 5575-ft. spacing to 6000-ft. spacing, using the same loading inductance values, resulted in a small drop (about 4%) in nominal impedance and theoretical cut-off frequency. A contemporary allied development made available new types of balancing networks which simulated the iterative impedances of the H28-16 loaded cables. The use of these new networks with repeaters at the office ends of long H28-16 loaded cables gave considerably better repeater balances than those obtained with open-wire balancing net- works at the office ends of long E28-16 loaded cables. Up to this time, balancing networks which simulated the impedances of the associated open- wire lines had been used with the open-wire repeaters. This early practice was continued on open-wire lines having short entrance cables with H28-16 loading. H31-18 Loading General: It was known prior to the standardization of H28-16 loading that the 28-16 mh loading inductances were not optimum from the impedance- matching standpoint for use at 60(X)-ft. spacing. However, it was appreciated that the concurrent development work on the compressed permalloy-powder core-material previously described (Section 9.1) was approaching completion and that a general size-reduction redesign of all toll cable and toll entrance loading coils would soon be undertaken. These considerations made it un- desirable to develop for the H-spaced 28-18 loading new iron-dust core loading coils which would in all probability be superseded in a short time by permalloy-core coils. Thus it happened that the development work for the improved H31-18 loading system was coordinated with that on smaller-size, permalloy-core, loading coils having the necessary new inductance values for use in that system. The H31-18 loading was designed to have a slightly higher nominal impedance than E28-16 loading, to make it more suitable for use on inci- dental cables in 104-mil open-wire lines, which were expected to be its principal field of use, since the more expensive, larger conductors (128 and 165-mil) were destined for use principally on a carrier basis and would require carrier loading on their incidental cables. Improved Loading Terminations: It was also considered desirable to pro- vide better impedance-matching characteristics at high voice-frequencies to assist in obtaining more satisfactory repeater operation on long-haul, multi- repeater, voice-frequency circuits which were becoming more common and more important in the rapid expansion of the open-wire plant. This require- 746 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 ment was met by providing improved loading terminations, which kept the resistance component of the cable impedance fairly close to the nominal impedance over the upper part of the frequency-band transmitted by the voice-frequency repeaters, and which also had satisfactory low reactance. Two different but equally satisfactory terminations^^ were developed, to provide flexibility and economy in the loading layouts. One of these was theoretically based on the mid-section termination previously described. This half-section termination was extended to about an 0.83-fractional section, followed at the open-wire junction by a terminal loading unit having inductance values about .36 of the full-weight loading inductances used in the loading designations. The other new loading termination was theo- Table XV Voice-Frequency Loading for Incidental Cables in Non-Loaded Open-Wire Lines Loading Designations Coil Spacing (ft.) Type of Circuit Nominal Impedance (ohms) Theoretical Cut-off Frequency (cycles) E28-16 5575 Side Phantom 650 400 7250 7650 M44-25 8750 Side Phantom 650 400 4600 4900 H28-16 6000 Side Phantom 630 380 7000 7400 mi^i8 6000 Side Phantom 666 403 6700 7000 Note: The full-coil inductances in millihenrys are given in the loading designations. The first number applies to the side circuits and the second number to the phantom circuit. retically based on the mid-coil termination previously described. It used 0.86-fractional coils instead of half coils, and had a 0.36-fractional loading section adjacent to the open-wire side. These new loading terminations were known as ''Fractional coil" or "Fractional section" terminations, depending on whether the fractional coil or the fractional section was the terminal element closest to the open-wire line. At the office ends of loaded entrance cables a mid-section loading termination was frequently used, and the re- peater balancing network-circuits were adjusted to correspond with this situation in the line. The H31-18 loading system was standardized in 1928 and is still the standard voice-frequency loading system for incidental cables in open-wire circuits which are not arranged or used for carrier operation. Loading Systems Data: General transmission data regarding the loading systems briefly described above are given in Table XV. INDUCTIVE LOADING FOR TELEPHONE FACILITIES 747 Attenuation Data: The relatively low cable impedances which are necessary for good impedance-matching limit the attenuation-loss reduction to smaller values than those obtained with the higher impedance loading systems used on toll cable facilities. The theoretical 1000-cycle attenuation values for H31-18 loading (on a db/mi basis) are 0.56, 0.30, and 0.16, respectively, for 19 ga., 16 ga., and 13 ga. cables. The phantom circuit attenuation is nearly 20% lower, being about 0.47, 0.24, and 0.13 db/mi. The attenuation losses in the other loading systems of Table XV are close to those for H3 1-1 8 loading. This follows from the fact that their im- pedances are nearly the same in magnitude. Lffw-Frequency Impedance Matching Before ending the discussion of transmission system characteristics, it is important to note that the attainment of optimum impedance-matches at low voice-frequencies, with the types of loading under discussion, involves the use of the so-called ''optimum" cable conductor sizes. This follows from the fact that at these low frequencies the circuit resistances are important factors in determining the open wire and cable impedances. The optimum conductor combinations are 13 ga. cable for use in association with 165-mil open-wire lines, 16 ga. cable with 128-mil lines, and 19 ga. cable with 104-mil lines. Allowing for the loading coil resistances, these combinations of cable and open-wire conductor-sizes closely conform to the fundamental theoretical requirement that the unit-length ratio of series resistance (ohms) to shunt capacitance (farads) to total Hnear inductance (henrys) in the loaded cables should be close to the corresponding linear ratio in the associated non-loaded lines. Loading Coils and Cases for Incidental Cables In their general design features, excepting inductance and effective resistance, the voice-frequency loading coils for incidental cables corre- sponded with those currently used in toll cable circuits. When the toll cable coils were redesigned to take advantage of new core-materials, or in other important features, the entrance cable coils were included in the general redesign work. The first loading units developed for H3 1-1 8 loading were coded in the "P" series. The code designation P4 applied to the "full-weight" loading unit. The fractional-weight loading units developed for use in the "fractional section" and the "fractional coil" loading termination were coded P5 and P6, respectively. These numerical code components have been retained in the code designations of all standard replacement designs, namely the PB, M, SM, and MF series of loading units. The potting practices used with the entrance cable coils were generally 748 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 similar to those used with similar-sized toll cable coils. The potting com- plements for incidental cables, however, were small relative to the com- plements most generally used in the toll cables. Occasionally, in situations where toll entrance facilities and long-distance cable facilities shared the same cable for a short distance, the potting complements would include both types of loading. The color code used on the coil terminal quads in the stub cables of the loading coil cases facilitated identification of the different types of loading in the cable splicing-operations. (V-B) Carrier Loading for Incidental Cables in Open-Wire Carrier Systems Historical The first open-wire carrier telephone system was installed late in 1918, and in the early 1920's general commercial use began to expand rapidly. A comprehensive account of the pioneering development work is given in a 1921 A.LE.E. paper^^ by E. H. Colpitts and O. B. Blackwell. Experimental types of carrier loading were made available for use on incidental cables in the open-wire lines on which the first carrier systems were installed. In general, these early carrier loading installations were engineered to specific job requirements. C4.1 and C4.8 Loading: From this experience there evolved a quasi- standard loading treatment which served the current service needs, pending completion of the development of the first standard carrier loading systems, C4.1 and C4.8, late in 1923. These were designed to provide good impedance- matching up to a top frequency of about 30 kc. During the intervening years this loading has remained standard for incidental cables in carrier systems using this frequency-band, even though important changes have been made in the carrier systems themselves, notably the first Type C carrier systems^^ during the middle 1920's, and the improved Type C systems^^ during the late 1930's. B15 Loading: During the late 1920's a lower cut-off carrier loading system designated B15 was designed especially for use with carrier facilities operat- ing below a top frequency of about 10 kc. This loading served a double purpose. It was suitable for use with the old standard Type B carrier telegraph system'^ and with the new standard, single-channel, Type D carrier telephone system.^^ (In many of its early applications the Type B telegraph system used the frequency space between the voice circuit and the carrier telephone channels.) The B15 loading system is still in good standing. When an improved single-channel telephone system, Type H^^ was developed during the late 1930's, its frequency allocation was chosen so that it could use "spare" B15 circuits which had become available on a substantial mileage of incidental cables. INDUCTIVE LOADING FOR TELEPHONE FACILITIES 749 A 2. 7 and 3.0 Loading: During the late 1920's the rapid expansion of carrier working led to extensive studies of the practicability of obtaining a larger number of telephone channels in long-haul carrier systems. These studies indicated a good prospect of using a wider frequency-band extending up to a top frequency of about 50 kc. In order to secure a much better con- trol of intersystem crosstalk over the wider frequency-band, plans were made for spacing the wires of individual pairs much closer together, and for spacing adjacent pairs at greater distances apart. Also, improved trans- position systems were designed for these new open-wire arrangements. In the period of interest, the open-wire plant was expanding very rapidly, and as a part of this expansion several entirely new pole lines were required for important long-haul service. These Unes incorporated the improved con- struction features above mentioned. Even though the proposed new broader- band carrier systems were still in the "discussion stage" of development, it seemed desirable that a new type of broader-band loading should be installed on the incidental cables in the new pole lines, in order to avoid the larger expense of eventually replacing the 30-kc Type C loading, if it should be used initially. These considerations resulted in the rush development of the Types A2.7 and A3 carrier loading systems specifically to meet the im- pedance-matching requirements over the proposed 50-kc band. This loading was duly installed according to plan, but fate decreed that it should never be used for its originally intended purpose. Type C carrier telephone systems were immediately installed on the new lines, in the expectation of removal when broader-band systems became available, and the Type A loading was actually used only for 30-kc transmission. The explanation for this turn of events was that before the final develop- ment requirements could be established for the proposed new 4 or 5-channel systems, some entirely new factors^''^ entered the continuing studies and eventually resulted in a decision to develop a 12-channel system.**^ This was designed for placement above a Type C system on the same open-wire pair, making a total of 15 carrier channels above the voice-frequency circuit. The new broad-band carrier telephone system was coded in the "J" series. Its top working-frequency was about 143 kc. Type J Loading: In due course, the development of new carrier loading was coordinated with the work on the new carrier telephone system. Three loading systems, designated J-0.72, J-0.85, and J-0.94, became available during 1937-1938 and are still in good standing, although they are not extensively used. In the following pages, the general transmission characteristics of the Type C, B, and J loading systems are described, and some general informa- (^^^ Including high-gain, high-stability, negative-feedback repeaters, and crystal filters. 750 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 tion is given regarding the loading apparatus and the building-out apparatus. The Type A systems are not included. Loading Systems Characteristics General: A summary of loading systems characteristics is given in Table XVI, below. Attenuation data are given in Table XVII. Compensated Loading Terminations: These loading systems are commonly known as compensated loading by virtue of their use of compensated loading terminations^^ to provide the desired impedance-matching characteristics at about the minimum cost. Over the working carrier-band the impedances of these compensated circuits closely approximate the non-reactive, flat, fre- quency-resistance characteristic of their "corresponding smooth lines"; that Table XVI Carrier Loading for Incidental Cables in Open-Wire Carrier Telephone Systems Loading Designa- tion Approx. Top Working Freq. (kc.) Theoretical Cut-off Freq. (kc.) Nominal Impedance (ohms) Theoretical Total Loading Section Capacitance (mmf.) 12100 12100 36850 3027 3105 3105 Theoretical Coil Spacing (ft.) Representa- tive Coil Spacing (ft.)^ Full-Ccil Inductance (mh.) C4.1 C4.8 B15 J-0.72 J-0.85 J-0.94 30 30 10 142 142 142 45 41.5 13.5 208 190 181 590 640 640 542 575 600 929* 929* 3000* 633t 648t 648t 740 740 2800 500 500 500 4.09 4.78 14.7 0.72 0.85 0.94 Notes: * In ordinary quadded cable having 0.062 mf/mi side circuit capacitance, t In special 16 ga. disc insulated cable having 0.025 mf/mi capacitance. is to say, the "lumpiness-of -loading" effects on the loaded cable impedance are reduced to tolerable low values over a predetermined frequency-band. By also having the nominal impedance of the loaded cable close to that of the associated open-wire line, satisfactory impedance-matches are obtained up to a much higher fraction of the loading cut-off than is possible with the more simple loading terminations used with the voice-frequency loading. In some carrier loading designs, this impedance-matching band extends up to about 0.75 of the cut-ofif frequency, or a Uttle higher. An extension to still higher frequencies, relative to the cut-off frequency, would tend to result in objectionable *4umpiness-of-loading" attenuation impairments. The com- pensated loading terminations achieve substantial economies in the loading costs by permitting the use of much lower cut-off frequencies than would otherwise be feasible, thus allowing the full-weight coils to be spaced at much longer intervals. INDUCTIVE LOADING FOR TELEPHONE FACILITIES 751 Additional information regarding the loading terminations is given in the description of the terminal loading units which are used in these terminations. Control of Impedance Irregularities; Loading Layouts: The carrier loading systems are engineered and installed to meet unusually severe limits on impedance irregularity among the individual loading sections and at the terminals. In installations involving more than one carrier system, it is especially desirable to restrict the individual impedance irregularities in order to control intersystem reflection crosstalk. The significance of this is under- standable when one appreciates that usually the dominating reason for using carrier loading on the incidental cable is to avoid the objectionable reflection crosstalk that would result from the impedance irregularities caused by non- loaded cables. An additional important reason for the control of impedance irregularities is to avoid large humps in the insertion loss-frequency charac- Table XVII Carrier Loading Attenuation Data Loading Designation Cable Cable Attenuation — db/mi Conductor Gauge Capacitance (mf/mi) Ikc 10 kc 30 kc soke 140 kc C4.1 13 0.062 0.28 0.39 0.92 16 0.062 0.42 0.52 1.04 C4.8 16 0.062 0.40 0.50 1.14 19 0.062 0.67 0.78 1.37 — — B15 16 0.062 0.35 0.54 — — — 19 0.062 0.62 0.80 — — — J-0.85 16 0.025 0.41 0.51 0.64 0.93 1.36 teristics which might cause objectionable frequency-distortion within the individual channels. The procedure for controlling impedance irregularities in the loaded incidental cables involves the adjustment of the total capacitances of the individual loading sections to values close to the theoretical design values by means of adjustable building-out condensers. Ordinarily, a precision limit of about ±1% is involved. To make these limits economically practicable, precision types of capacitance measuring-instruments have been made available, along with low cost building-out devices capable of simple pre- cision adjustments. The theoretical total loading capacitances for the different carrier loading systems are given in Table XVI, along with theoretical values of coil spacing in terms of the "nominal capacitance" of the usual type of cable involved. The actual geographical coil-spacing is usually well below this theoretical spacing because of the unavoidable capacitance deviations that occur in commercial paper-insulated cables. The loading layout procedure is such 752 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 that the highest-capacitance cable pairs in the individual loading sections will not have too much capacitance. When the loading is installed, the capacitances of the various pairs in the individual loading sections are meas- ured, as also are the mutual capacitances of the loading coils and their associated stub cables, and then enough shunt capacitance is added to obtain the desired theoretical total capacitance, per loading section. In many installations, especially in underground cables, the theoretically best loading points for the carrier loading coils (after engineering allowances have been made for cable-capacitance deviations) frequently occur at points where it would be unduly expensive to install the loading. In such instances, shortened spacings are used, and the building-out adjustments are increased to correct for the geographical spacing-deficiency along with the cable- capacitance deviations. For reasons above mentioned, the individual coil-spacings may vary con- siderably in the same project, and the average coil-spacing may be quite different on different projects involving the same type of loading. The "representative coil-spacings" given in Table XVI are representative job averages. As with the voice-frequency loading, the choice of cable conductor-gauge is important in the impedance-matching performance of the C4.1, C4.8, and B15 loaded cables at low voice-frequencies. The optimum resistance rela- tions between the cable conductors and the open-wire conductors are the same as in voice-frequency loading. In the use of the Type J loading as practiced on short cables, this resistance-ratio question is unimportant because such loaded cables are substantially '^ transparent" at voice fre- quencies. The loading terminations are unimportant factors in voice-frequency impedance-matching. This follows from the fact that the voice frequencies are low relative to the loading cut-off, for which reason the carrier loaded circuits act as electrically smooth lines in this range. Type C Loading: These loading systems were designed for use on cable pairs connected to 12-inch spaced open-wire pairs. The impedances of the open-wire pairs vary substantially with the conductor size and because of this a single cable-loading system would not be satisfactory as regards carrier-frequency impedance-matching for all types of open-wire. The C4.1 system is used on cable pairs connected to 165-mil open-wire pairs. The C4.8 is a compromise system for use on cables connected to the less important and less expensive 128-mil and 104-mil open-wire pairs. It is of interest that the theoretical coil-spacing for Type C loading is one-sixth of that of the E-spacing described in the discussion of voice- frequency impedance-matching loading. INDUCTIVE LOADING FOR TELEPHONE FACILITIES 753 Considerable Type C loading has been used on cables associated with open-wire pairs which have their conductors spaced 8 inches apart. The closer wire-spacing reduced the open-wire impedances below the values for which the carrier loading was originally designed. To obtain better im- pedance-matches when used with these lower-impedance lines, the Type C carrier loading was "modified" to have lower impedances by systematically building-out each loading section to have a higher total loading-section capacitance. This procedure also reduced the loading cut-off by an amount proportional to the impedance reduction, which effect limited the allowable impedance reduction. The "standard" modification of C4.1 loading dropped the nominal impedance to 558 ohms, and the cut-off to 42.5 kc. The ''modifi- cation" of C4.8 loading dropped the nominal impedance to 625 ohms, and the cut-off frequency to 40.5 kc. The standard Type C loading apparatus was used in these installations. B15 Loading: The single-channel open-wire carrier system with which this type of incidental cable loading is associated is a short-haul transmission system, principally used on 104-mil open-wire pairs. Since the impedance- matching requirements are much more lenient than those for loaded cables in the multi-channel systems a single weight of loading is sufficient. The cable-capacitance deviations tend to be considerably smaller than with Type C loading, because of "random" splicing at a considerably larger number of intermediate cable splices within the individual loading sections. In consequence, the average amount of capacitance building-out is much smaller (on a percentage basis). Type J Loading: Because of the higher frequencies involved in the Type J carrier systems the impedance-matching requirements are even more severe than those for the Type C systems. For this reason, a series of three Type J loading systems were made available, as noted in Table XVI. To make carrier loading economically feasible for 140-kc transmission it was necessary to develop an entirely new type of low-capacitance cable for use with the loading. The new cable makes use of shielded, "spiral-four" units of 16 ga. conductors. The conductors are supported by means of insulating discs at the corners of a square, and the diagonally opposite conductors are associated as working pairs. The spacing between these wires and between them and the quad shields is such as to obtain a mutual capaci- tance very close to 0.025 mf/mi in the individual carrier pairs. The structural relations between the associated pairs of the individual units are such as to minimize crosstalk coupling. The over-all dimensions of the shielded units are such that not more than 7 or 8 units can be provided in a single cable without using an over-size sheath. In consequence the cable cost per carrier pair is high. 754 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 The low-capacitance construction, above described, also results in a much higher ratio of distributed inductance to distributed capacitance than that of paper insulated cables. This makes it necessary to build out the series inductance in a proper ratio to shunt capacitance, when geographical spacing- deviations require the use of corrective building-out adjustments. These capacitance-inductance adjustment devices are considerably more expensive than the relatively simple condensers used in the adjustments on Type C and B loaded circuits. Closer coil-spacing also makes the Type J loading more expensive. All in all, the total cost of the Type J loaded cable pairs is very high relative to that of the Type C loading. Furthermore, the attenu- ation-reduction feature of the loading, although it is substantial in magnitude per unit length, does not have a large economic value in reducing the number and cost of repeaters required in a complete carrier system. These con- siderations have limited the use of Type J loading to short cables, seldom more than 0.5 mile long. In entrance-cable installations of greater length it is common practice to use line filters at the outer end of the cable to separate the ''J" frequencies from the lower frequencies. The "J" frequencies are then transmitted to the office over non-loaded pairs terminated at each end in impedance modifying transformers. Separate cable pairs having Type C loading transmit the "C" carrier channels and the voice frequencies. In such installations a special type of adjustable loading is used on the short ''lead-in" cables from the bare open wire to the line filters, when they are installed in "filter huts" at the outer end of the cable. At the filter hut, this loading uses a continuously variable air-core inductance coil of the solenoidal, inductometer type, with which adjustable condensers are associ- ated, one on each side of the coil. This provides a variable impedance loading which is adjustable for a predetermined range of impedances and for a pre- determined range of lengths of lead-in cable. Long lead-in cables also require a (non-adjustable) loading unit at their open-wire end. The adjustments for optimum impedance-matching are made in terms of return-losses measured at the open-wire end of the lead-in cable. Carrier Loading Apparatus General: The initial, experimental designs used large-size, toroidal-shaped, non-magnetic cores, and finely stranded copper conductors. These coils were nearly as large as the biggest coil shown in the headpiece, (page 149). Their construction made it possible to secure lower effective resistances at the high carrier-frequencies than could be obtained for the same total cost using the best magnetic materials then available. An additional advantage was that their non-magnetic cores could not cause non-linear distortion. This particu- INDUCTIVE LOADING FOR TELEPHONE FACILITIES 755 lar advantage assumed critical importance in later years when it became necessary to work to stringent over-all limits of non-linear distortion in the long-haul carrier facilities. As an example of the importance of controlling non-linear distortion, it became necessary during the late 1920's to mount the carrier loading coils in individual, shielding containers in order to prevent the small leakage fields of the toroidal air-core coils from penetrating nearby magnetic parts of the loading coil cases, thereby causing objectionable inter- channel modulation interference. The satisfactory control of non-linear distortion has made it necessary to continue the use of non-magnetic cores in the carrier loading coils, notwith- standing the large improvements that have been made in magnetic core- materials during the last three decades. These improvements would make it possible to use much smaller coils without objectionably degrading the steady-state transmission performance. However, the hysteresis character- istics of the best available magnetic materials are such that if these materials should be employed it would be necessary to use coils larger and more ex- pensive than the non-magnetic core coils, in order to meet present-day se- vere limits on allowable intermodulation interference in the Type C tele- phone systems. Types C and B Loading Ftdl Coils: These loading systems use the same general types of full- weight loading coils and terminal loading units, except as regards their electrical parameters. The over-all dimensions of the full- weight coils are about 6f inches in diameter and 2\ inches axial height. The shielding con- tainer has an over-all diameter of about 7J inches and an axial height of 3j inches. Terminal Loading Units: The terminal loading units which provide the compensated loading terminations, previously mentioned, include a 0.82 fractional-weight series loading coil. This is shunted on the open-wire side (or office side) by a two-element network consisting of a condenser in series with an inductance coil, and located between the two haK-windings of the coil. The complete terminal network may be regarded as an extension of half-coil termination. The portion beyond the half -coil point in the series (fractional) coil functions as an impedance corrective-network to produce the approximate ** corresponding smooth line" impedance, previously de- scribed. The correct electrical proportioning of the elements of this corrective network is very important. The series loading coil is much smaller than the regular full-weight loading coil. Its size and those of the other network- elements are such as to allow the assembly of the complete terminal loading unit in the same size of shielding container as that i^sed for the full- weight 756 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 loading coils. The standard potting complements range up to 16 coils oi" terminal units. The loading units are installed at the ends of full-length Fig. 30 — Various stages in the assembly of toroidal type carrier loading coils. Several coils mounted in their shielding containers are piled on a bench at right center. On the bench at left center, an assembly of coils is being connected to the stub cable conductors. In diagonal center, a completely assembled and cabled complement of 16 coils is ready for placement in a tall, rectangular shaped, cast iron case. terminal loading sections. When short cables have only one loading section, terminal loading units are used at each end. Building-Out Condensers: As previously indicated, building-out capaci- tance adjustments are extensively required in the control of local impedance irregularities, especially in the installations of the Type C loading. INDUCTIVE LOADING FOR TELEPHONE FACU.ITIES 757 In the office adjustments of the capacitance of the terminal loading sections, multi-unit paper-insulated condensers are employed. These con- densers consist of ten different unit-condensers having six different nominal capacitance values, the ratio between the highest and lowest being of the order of about 30 to 1. Parallel combinations of the individual units are Fig. 31 — Multi-unit, paper insulated building-out condenser for use in offices. Upper views show can cover for terminals of individual condensers removed to permit parallel cross connections, to obtain desired total capacitance. Lower view shows the complete assembly. The main terminals of the parallel connection of unit condensers appear at the left end in close proximity to the studs which are used in fastening the condenser case to the office mounting plates. selected by measurement to provide the total required building-out capaci- tance, with the required precision. The intermediate and open-wire terminal loading sections make use of small wire-wound and small mica condensers in the capacitance building-out adjustments. These are usually installed at a cable loading point, placed within the sleeve of the loading splice. The wire-wound condensers consist of parallel, insulated conductors wound in layer formation around small ceramic spools, and impregnated with moisture-resisting compound. Their 758 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 capacitances are continuously adjustable, by unwinding the outer end of the bifilar winding, and trimming off the excess length. The nominal capacitance Fig. 32 — Building-out condensers designed for installation within carrier loading splice sleeves. Upper view: Continuously adjustable, wire-wound condenser. Lower view: Non-adjustable, mica insulated condenser in small canvas bag. The upper part of each view shows the containers in which the condensers are placed, to protect them from moisture penetration and physical injury during the period intervening between manu- facture and installation. values, prior to adjustment, range from 500 mmf to 3000 mmf . In occasional instances where the total required capacitance cannot be provided by the highest-capacitance wire-wound condenser, a non-adjustable mica condenser INDUCTIVE LOADING FOR TELEPHONE FACILITIES 759 is used in pamllel with a wire-wound condenser. In such combinations, the precision capacitance-adjustments are made with the wire-wound condenser. The nominal capacitances of the mica condensers range from 500 mmf to 4500 mmf. Prior to the development of these small splice-installation types of build- ing-out condensers (during the late 1930's), building-out stub cables were extensively used in the loading-section capacitance adjustments. Several pairs in these stubs were connected in parallel for use with an individual main cable pair. By varying the number of parallel pairs, and the length of J) Fig. 33 — Solenoidal type non-magnetic core loading coil used for type J carrier loading. At right: Internal coil structure and supports; At left: Copper shielding-container, with coil inside. This view shows the terminal strip on which the coil terminal clips are mounted, and also one of the brackets used in fastening the coil in position in the loading coil cases. the stub cable, the necessary wide range of building-out capacitance was obtained with the required degree of precision. Type J Loading Full-Weight Loading Coils: The full-weight loading coils are small sole- noidal-type, air-core coils having a layer- type winding with a very finely stranded conductor, for control of coil resistance at the high ''J" frequencies. The outside diameter and axial length are 2f inches and 0.5 inch, respec- tively. To contain the external magnetic field, and control modulation effects and intercoil crosstalk that would otherwise result, a relatively large shielding container is required. Its over-all diameter is about 5f inches and its axial 760 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 length about 5} inches. The container dimensions are such that the small energy losses in the container-material have unobjectionable reactions upon the frequency-resistance and inductance characteristics of the coils. A comparison of the effective resistance characteristics of representative toroidal and solenoidal types of carrier loading coils is of interest at this point. Referring to table XVIII, the more favorable resistance values of the solenoidal coils at 30 kc. and above are due to greater refinements in the stranding of the copper conductors. The relatively small coil size, however, penalizes the low-frequency resistance; this is tolerable in the Type J systems because of the relative unimportance of the voice-frequency circuit. Terminal Loading Units: For engineering flexibility in the loading layouts, and to minimize the cost of building out the terminal loading sections, two different, equally satisfactory, types of compensated loading terminations'*' are provided for use with Type J carrier loading systems. One of these is electrically analogous to that used with the 30-kc. and 10-kc. loading sys- tems, and is theoretically based on the half-coil termination previously described. Lower inductance and capacitance elements are used because of the much wider carrier frequency-band. The alternative type of loading termination is theoretically based on half-section termination. It involves an extension of the terminal loading section from half-section to about 0.8 full- section and the use of a terminal loading unit which employs a fractional weight loading coil (approx. 0.32 full-coil inductance) in series with the cable, and which has equal-capacitance condensers connected in parallel across each of the two line windings of the fractional coil. Table XVIII Effective Resistance Data — Representative Carrier Loading Coils Type of Coil Nominal Inductance (mh) Resistance in ohms per Millihenry at Specified Frequencies in Kilocycles 1 10 30 80 140 Toroidal 4.83 14.75 0.85 0.48 0.45 0.95 0.58 0.76 0.95 1.35 1.1 1.3 Toroidal Solenoidal 2.0 At the junctions of cable and open wire, the cases which pot the shielded terminal units in pairs are mounted on crossarm fixtures in close proximity to the bare open wire. In office installations, the loading unit assemblies are mounted on individual panels for installation on an equipment bay in close proximity to the associated Type J system line filters. Building-Out Units: The building-out apparatus used in conjunction with INDUCTIVE LOADING FOR TELEPHONE PAClLITIEg 761 Type J loading is radically different from that used with the Types C and B loading, primarily because it is usually desirable to include series inductance along with shunt capacitance, in proper proportions, because of the relatively high ratio of distributed inductance to distributed capacitance in the disc- Fig. 34 — Building-out units used in electrical adjustments of type J carrier loading sections. Upper View: Continuously-adjustable wire wound unit. Prior to adjustment it has a distributed shunt capacitance of about 275 mmf, and a series inductance of about 16.5 microhenrys; Lower View: Single section non-adjustable artificial line, providing a shunt capacitance of about 250 mmf (single condenser) and a total series inductance of about 15 microhenry (2-coils). This particular unit simulates a length of about 53 ft. of disc-insulated cable pair. Other (multi-section) artificial line units simulate longer lengths of cable pair. insulated cable with which the loading is used (about 1.4 m.h. inductance and 0.025-mf capacitance, per mile). Two types of building-out units are required, (1) a continuously adjust- able, wire-wound unit which is used for making precision adjustments, and 762 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 (25r i graded series of non-adjustable artificial lines using lumped shunt condensers and lumped series inductances, these ''lumps" being electrically smaU enough to avoid objectionable "lumpiness" effects. The required building-out units are connected in tandem with the loaded cable pair under adjustment. The adjustable unit consists of a single-layer, bifilar winding on a non- magnetic spool about 4 inches long and f inch in diameter. The wiring of the unit to its two pairs of Une terAiinals is such as to provide a series in- ductive-aiding connection of its fine windings when the unit is serially inserted in the cable pair according to plan. The diameter of the spool is chosen to provide the desired ratio of inductance to capacitance per bifilar turn, taking into account the increase of capacitance of the winding which is caused by a wax-dipping process. The inductance coils used in the non-adjustable units are very small air- core solenoids. Their inductances are adjusted (in manufacture) to have the correct electrical relations with the associated very small, mica-type, shunt condensers. The complete building-out adjustment for an individual loading section usually involves the use of one or more artificial-line units in tandem with an adjustable unit. The adjustments are made in terms of capacitance measurements, since this procedure automatically provides the required series inductance. Capacitance measurements of the cable pair to be ad- justed and of preselected non-adjustable units precede the precision adjust- ment of the wire-wound unit. This latter is accomplished by removing an integral number of bifilar turns from the winding, to meet the capacitance requirements, after which the shortened winding is reconnected to its main line terminals. Housing of Building-Out Units: For flexibility in installation, the different electrical sizes of building-out units are "potted" in individual containers of the sam3 size. These are much too large for installation in the loading splice-sleeves. Accordingly, in the cable- type cases for full-weight loading coils, and in the open-wire terminal pole cases for terminal loading units, space is provided in compartments with removable covers for the installation of the cable building-out units. The connections to the main cable circuit are made to terminal strips mounted in these compartments. Thus the installation of the building-out units can be made after the loading coils and loading units have been spliced to the disc-insulated incidental cables. The terminal loading units used at office ends of loaded entrance cables also include space and wiring provision for the installation of building-out units which may be required on the cable side of the terminal loading unit. INDUCTIVE LOADING FOR TELEPHONE FACILITIES 763 (V-C) Voice Frequency Phantom Loading for Combination with Side Circuit Carrier Loading Voice-frequency, impedance-matching, phantom circuit loading is avail- able for use in coordinated combinations with C4.1, C4.8, and B15 carrier loading in situations where the need for improving the phantom circuit transmission in an incidental cable warrants the use of loading. This brings up a factor not previously mentioned, namely, that the early applications of carrier telephone systems made use of the side circuits of open-wire phantom groups. This is still the general situation, especially with the short-haul, single-channel systems. On the other hand, a substantial fraction of the Type C systems installed since the late 1920's, including those that now work in the frequency-band below a Type J system, uses open-wire pairs that are not arranged for phantom working. The phantom loading under consideration is limited to voice-frequency operation because of the serious technical difficulties and high costs that would be involved in the satisfactory operation of carrier systems simul- taneously on open-wire side circuits and their associated phantoms, and through the incidental cables. The phantom group full- weight loading units and terminal loading units, which provide the phantom circuit loading, also include carrier loading apparatus for the associated side circuits; i.e., the phantom loading appara- tus is not separately available. Thus, when phantom loading is required, it is necessary to engineer and install the loading on a carefully coordinated phantom-group basis. The "full-coil" inductance of the phantom loading used in association with 30- kc. side circuit loading is 12.8 mh. and the full loading-section capacitance corresponds to that of "E" spacing. Thus its loading designation is El 2.8, and the complete phantom-group loading designations become CE4.1-12.8 and CE4.8-12.8. The corresponding phantom circuit loading for use in association with B15 side circuit loading is designated H15, and the phantom group loading is designated BH15-15. There must be an integral number of side circuit carrier loading sections in each voice-frequency phantom loading section. This ratio is 2 to 1 with BH loading. With CE loading, it may be 7 or 8 or 9, to 1, depending upon the average amount of building-out in the side circuits. This numerical variability with CE loading results from the fact that the condensers which are used primarily for building out the (carrier) side circuits add negligible capacitance to the phantom. An adjustable four-wire type of condenser is available for capacitance building-out adjustments of the phantom circuit. Depending upon the amount of capacitance building-out used in the carrier 764 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 side circuits, the average geographical spacing for the full-weight phantom loading units ranges from about one mile to nearly 6000 feet. The voice-frequency attenuation in the loaded phantom circuits is ap- preciably lower than that in the associated side circuits. The small trans- mission impairments which the phantom loading apparatus introduces into the associated carrier side circuits are negligible. The voice-frequency impedance-matches between the loaded cable phantoms and the (non- loaded) open-wire phantoms are nearly as good as those obtained with voice- frequency phantom group loading. An interesting feature of the phantom loading under discussion is that it uses a 2-coil scheme, with similar phantom coils in each side circuit at each phantom loading point. This scheme is one of several covered by the basic phantom loading patent {U. S. No. 980,921; Jan 10, 1911) but was not used commercially in the Bell System until the late 1920's when very severe side-to-side crosstalk limits became necessary in phantom-group carrier installations for the control of high-frequency intersystem crosstalk. This control was strengthened by shielding the two associated phantom loading coils from one another. Bibliography {Continued) 6. B. Gherardi, "Commercial Loading of Telephone Circuits in the Bell System," Trans. A.I.E.E., Vol. XXX, p. 1743, 1911. 8. Thomas Shaw and William Fondiller, "Development and Application of Loading for Telephone Circuits," Trans. A.I.E.E., Vol. XLV; Published in The Bell System Technical Journal, Vol. V, pp. 221-281, April 1926. 12. R. S. Hoyt, "Impedance of Loaded Lines and Design of Simulating and Compensating Networks," B.S.T.J., July 1924. 26. V. E. Legg and F. J. Given, "Compressed Powdered Molybdenum-Permalloy for High-QuaUty Inductance Coils," B.S.T.J., Vol. XIX, p. 385, 1940. 30. S. G. Hale, A. L. Quinlan and J. E. Ranges, "Recent Improvements in Loading Ap- paratus for Telephone Cables," Trans. A.I.E.E., Vol. 67, 1948. 36. E. H. Colpitts and O. B. Blackwell, "Carrier Current Telephony and Telegraphy," Trans. A.I.E.E., Vol. XL, p. 205, 1921. 37. H. A. Affel, C. S. Demarest and C. W. Green, "Carrier Systems on Long Distance Lines," Trans. A.I.E.E., Vol. 48, 1928; B.S.T.J., Vol. VII, July 1928. 38. J. T. O'Leary, E. C. Blessing and J. W. Beyer, "A New Three-Channel Carrier Tele- phone System," B.S.T.J., Vol. XVIII, Jan. 1939. 39. H. S. Black, M. L. Almquist and L. M. Ilgenfritz, "Carrier Telephone System for Short Toll Circuits," Trans. A.I.E.E., Vol. 48, 1929. 40. H. J. Fisher, M. L. Almquist and R. H. Mills, "A New Single Channel Carrier Tele- phone System," Trans. A I E.E., Jan. 1938; B.S.T.J., Jan. 1938. 41. B. W. Kendall and H. A. AfTel, "A Twelve Channel Carrier Telephone System for Open-Wire Lines," B.S.T.J., Vol. XVIII, Jan. 1939. {to be concluded) Abstracts of Bell System Technical Papers Not Published in This Journal Possible and Probable Future Developments in Communication* O. E. Buckley^ Franklin Inst. JL, v. 251, pp. 58-64, Jan., 1951. Electrochemical Industry. R. M. Burns^ Bibliography. Ind. & Engg. Chem., V. 43, pp. 301-304, Feb., 1951. Cracking of Stressed Polyethylene; Efect of Chemical Environment.* J. B. De Coste\ F. S. Malm^, and V. T. Wallder^. Ind. & Engg. Chem., v. 43, pp. 117-121, Jan., 1951. Abstract — In a number of applications for polyethylene, particularly cable sheaths and cosmetic containers, it has been found that under certain conditions failure of the polyethylene results in a cracking of the plastic. Considerable information is available to show that in an unstressed condi- tion polyethylene is highly resistant to a wide variety of chemical environ- ments such as alcohols, soaps, and fatty oils. However, when polyethylene is exposed to these environments under polyaxial stress it fails by cracking. The work described in this paper was undertaken to determine the factors involved in polyethylene cracking. A qualitative laboratory test was de- veloped to evaluate this property and the effect of a variety of organic and nonorganic materials was studied. It was found that the higher the molec- ular weight of a polyethylene the more resistant it becomes to cracking, that the degree of crystallinity affects its readiness to crack, and that the addition of polyisobutylene or Butyl rubber improves crack resistance. This paper shows that useful end products, which are resistant to crack- ing, can be made from polyethylene. Atomic Relationships in the Cubic Twinned State.* W. C. Ellis^ and R. G. Treuting^ References. Jl. Metals, v. 191, pp. 53-55, Jan., 1951. Abstract — The twinned state is characterized by a lattice of coincidence sites. Imperfections are required at stable lateral twin interfaces. Twinned regions can occur with relative ease in the diamond cubic structure. Transitions in Chromium.* M. E. Fine^, E. S. Greiner^ and W. C. Ellis^ References. Jl. Metals, v. 191, pp. 56-58, Jan., 1951. ABSTR.A.CT — Discontinuous changes of Young's modulus, internal friction, coefficient of expansion, electrical resistivity, and thermoelectric power are evidence for a transition in chromium near 37° C. Although the X-ray * A reprint of this article may be obtained on request. 1 B. T. L. 765 766 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 diffraction pattern gives no due, a difference between the thermal expan- sivity and the temperature dependence of the lattice parameter suggests a crystallographic change. Young's modulus data disclosed another transition near — 152° C. How to Measure Apparatus Noise. C. H. G. Gray^ Standardization^ V. 22, pp. 55-56, Feb., 1951. Fluorocarbon Hermetic Seal Design. A. B. Haines^ Elec. Mfg., v. 47, pp. 113-115, Jan., 1951. Abstract — ^Terminal seals using molded trifluorochloroethylene resin solves sealing problem in design of miniaturized 400-cycle high-operating- temperature power transformers. Dynamic Shear Properties of Rubberlike Polymers.'*' I. L. Hopkins^ Refer- ences. A.S.M.E., Trans., v. 73, pp. 195-203; disc. pp. 203-204, Feb., 1951. Abstract — A simple apparatus for determining the dynamic properties of elastomers in shear at audio frequencies is appraised. Typical values of shear modulus and viscosity for several elastomers are given, both at room conditions and at 150 F. The frequencies of test range from 100 to 5250 cy- cles per second, the shear moduli from 0.5 X 10^ to 480 X 10^ dynes per sq cm and the viscosities from 20 to 75,000 poises. Production-Line Frequency Measurements. G. J. Kent^. Electronics, v. 24, pp. 97-99, Feb., 1951. Abstract — Simplified equipment allows relatively inexperienced per- sonnel to make extremely accurate measurements of frequencies up to 10 mc. Entire system is standardized against WWV by simple adjustments while frequency measurement is being made. Progress in Development of Test Oscillators for Crystal Units.* L. F. KoERNERi. I.R.E., Proc, v. 39, pp. 16-26, Jan., 1951. Abstract — Early crystal unit test oscillators as conceived some 20 years ago were principally duplicates of the actual equipment in which the crystal units were to be utilized, a practice which resulted in a large variety of test circuits and procedures for testing. It is now recognized that a knowledge of the equivalent electrical elements making up the crystal unit is essential to the circuit engineer, and that the older conception of frequency and ac- tivity, the latter being an attempt to express the quaUty of a crystal unit in terms of a particular oscillator circuit, do not define adequately its char- acteristics. The equivalent electrical circuit of the crystal unit contains essentially a resistance, an inductance, and 2 capacitances, which together * A reprint of this article may be obtained on request. 1 B. T. L. »W.E.Co. ABSTRACTS OF TECHNICAL ARTICLES 767 with frequency define the performance of the unit. Crystal units are available in the frequency range from about 1,000 cycles to over 100 Mc. Their resist- ance range may vary from less than 10 ohms to over 150,000 ohms, the inductance from a few millihenries to nearly 100,000 henries and the capaci- tances from about 0.001 uuf to 50 uuf. Modern test oscillators, with fre- quency and capacitance measuring apparatus as auxiliary equipment, will measure these quantities with accuracies sufficient to meet present needs. The transmission measuring circuit also is described and is proposed as the standard reference circuit for comparison with the test oscillators. Local Wire Television Networks* C. N. Nebel^ Elec. Engg., v. 70, pp. 130-135, Feb., 1951. Abstract — A new local video distribution system has been developed which provides equalization and amplification of signals transmitted over links between television studios, transmitters, coaxial cables, and micro- wave networks. The equipment consists of a transmitting terminal, an inter- mediate repeater with cable equalizers, and a receiving terminal. Effect of Heat Treatment on the Electrical Properties of Germanium* H. C. TheuererI and J. H. Scaff^ //. Metals, v. 191, pp. 59-63, Jan., 1951. Abstract — Germanium may be reversibly converted from n to p type by heat treatment. Data for the conversion and the associated changes in re- sistivity are given and the results are interpreted in terms of changes in the donor-acceptor balance. Aging of Black Neoprene Jackets* G. N. Vacca^ R. H. Erickson^, and C. V. LuNDBERG^ References. Ind. & Engg. Chem., v. 43, pp. 443-446, Feb., 1951. Abstract — Considerable loss in elongation of black neoprene jackets re- moved from wires which had been in outdoor service for comparatively short periods of time raised the question of the life expectancy of such cover- ings. Information available did not permit estimation of service life and a program of testing was undertaken to provide this information. Accelerated aging tests corroborated by later field tests indicated that early loss of considerable elongation is not indicative of early failure in service as loss of elongation levels off and changes much more slowly on continued exposure. Accelerated aging in air at temperatures up to 100° C. gave results most comparable with outdoor aging as regards loss of elongation. As a result of this work, it can be predicted with a good degree of reliability that a black neoprene jacket will remain serviceable for periods of the order of 20 years. * A reprint of this article may be obtained on request. 1 B. T. L. 768 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 Choice of Gauge in London's Approach to the Theory of Superconductivity, J. Bardeen^ Letter to the editor. Phys. Rev., v. 81, pp. 469-470, Feb. 1, 1951. Ferromagnetism. R. M. Bozorth^ N. F., Van Nostrand, 1951. 968 p. (Bell Telephone Laboratories Series). Community Dial Office Equipment* A. Burkett^ Elec. Engg., v. 70, pp. 231-234, Mar., 1951. Abstract — Equipment for community dial offices which serve small or sparsely settled communities is described in this article. The discussion covers service features, equipment features, and maintenance facilities. Operational Study of a Highway Mobile Telephone System* L. A. Dorff^ Elec. Engg., v. 70, pp. 236-241, Mar., 1951. Abstract — The problem of interference of nearby stations was one of the greatest problems which had to be overcome to permit the satisfactory use of mobile telephone service. This article tells of a study made of the interference encountered on one highway mobile telephone system and the measures made to counteract it. A Precision Decade Oscillator for 20 Cycles to 200 Kilocycles. C. M. Edwards^. I.R.E., Proc, v. 39, pp. 277-278, Mar., 1951. The Control Chart as a Tool for Analyzing Experimental Data.* E. B. Ferrell'. I.R.E., Proc, v. 39, pp. 132-137, Feb., 1951. Abstract — The statistical methods that have been developed for use in quality control are a powerful tool in the interpretation of laboratory ex- periments where only a small amount of data is available. An understanding of these methods also permits more logical planning of experiments and improves what we might call "the efficiency of experimentation." One of the simplest and most broadly useful of these tools is the control chart. It is easy to understand and use and in many cases can take the place of more labori- ous and complicated methods of analysis. Crystalline Magnetic Anisotropy in Zinc Manganese Ferrite. J. K. Galt^, W. A. Yager^, J. P. Remeika^ and F. R. Merritt^ Letter to the editor. References. Phys. Rev., v. 81, p. 470, Feb. 1, 1951. A Submarine Telephone Cable With Submerged Repeaters.* J. J. Gilbert^. Elec. Engg., v. 70, pp. 248-253, Mar., 1951. Abstract — Repeaters designed for long life are incorporated in the cable structure and are laid as part of the cable of the recently installed Key West-Havana submarine telephone cable system. To eliminate the need for servicing the repeaters, the components were designed so that parts would not have to be replaced for 20 years or more. * A reprint of this article may be obtained on request. » B. T. L. «W.E.Co. ABSTRACTS OF TECHNICAL ARTICLES 769 Measurement of Hole Diffusion in N-Type Germanium. F. S. Goucher^ Letter to the editor. Phys. Rev., v. 81, p. 475, Feb. 1, 1951. Theory and Experiment for a Germanium P-N Junction. F. S. Goucher^, G. L. Pearson', M. Sparks^ G. K. Teal', and W. Shockley'. Letter to the editor. References. Phys. Rev., v. 81, pp. 637-638, Feb. 15, 1951. Gain of Electromagnetic Horns.* W. C. Jakes, Jr.^ I.R.E., Proc, v. 39, 160-162, Feb., 1951. Abstract — An experimental investigation of the gain of pyramidal elec- tromagnetic horns is described. For the horns tested it was found that (1) the "edge effects" are less than 0.2 db so that the gain of the horns may be computed to that accuracy from their physical dimensions and Schelkunoff's curves; and (2) for the transmission of power between two horns the ordinary transmission formula is valid, provided that the separation distance between the horns is measured between the proper reference points on the horns, rather than between their apertures. A Pulse Method of Determining the Energy Distribution of Secondary Elec- trons from Insulators.* K. G. McKay^ References. Jl. Applied Phys., v. 22, pp. 89-94, Jan., 1951. Abstract — A novel method is described of determining the energy dis- trubution of emitted secondaries from an insulator. This is based on an analysis of the transient resulting from pulse bombardment. The analysis is simplest when leakage through the target is negligible, but the effect of leakage is also treated. Space charge limitation of the emitted current is assumed to be negligible. Some General Properties of Magnetic Amplifiers.* J. M. Manley'. Refer- ences. I.R.E., Proc, V. 39, pp. 242-251, Mar., 1951. Abstract — The magnetic amplifier is discussed in general terms as a carrier system in which there is a modulation gain and a small demodulation loss. Relations are given which show how a magnetic modulator may exhibit a gain. Some results of calculation and measurement on the type of circuit in which the modulator output consists of the even harmonics of the carrier source for dc signal input are given. It is shown that the ratio of dc gain to response rise time is a constant depending only on the carrier frequency, the losses in the nonlinear core, and its nonlinearity. The conditions for self- oscillation at the carrier even harmonics are also given. Influence of Rotatory Inertia and Shear on Flexural Motions of Isotropic, Elastic Plates. R. D. Mindlin^ References. Jl. Applied Mech., v. 18, pp. 31-38, Mar., 1951. * A reprint of this article may be obtained on request. » B. T. L. 770 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 Abstract — A two-dimensional theory of flexural motions of isotropic, elastic plates is deduced from the three-dimensional equations of elasticity. The theory includes the effects of rotatory inertia and shear in the same manner as Timoshenko's one-dimensional theory of bars. Velocities of straight-crested waves are computed and found to agree with those obtained from the three-dimensional theory. A uniqueness theorem reveals that three edge conditions are required. Growth of Germanium Single Crystals Containing P-N Junctions. G. K. Teal\ M. Sparks^ and E. Buehler^ Letter to the editor. Phys. Rev., V. 81, p. 637, Feb. 15, 1951. A Mechanical Determination of Biaxial Residual Stress in Sheet Materials.* R. G. Treuting^ and W. T. Read, Jr.' References. J I. Applied Phys., V. 22, pp. 130-134, Feb., 1951. Abstract — A method is given for determining the residual stress in a sheet material by removing successive uniform layers of material from the surface of a test specimen and measuring the resulting curvature. From the condition of equilibrium of a free specimen, a stress vs curvature relation is derived which holds over the depth to which material has been removed. The method applies when the stress is constant in the plane of the specimen and varies through the thickness. An experimental technique is described which is believed to satisfy the essential requirement that the removal of surface layers should not affect the stress in the remaining material, and a practical example is given. Improved Methods for Measuring Ultrasonic Velocity.* G. W. Willard^ References. Acoustical Soc. Am., Jl., v. 23, pp. 83-93, Jan., 1951. Abstract — Some improved sound wave interference methods for measur- ing the lo gitudinal and transverse ultrasonic velocity in opaque as well as transparent solids may be simply carried out by using the ultrasonic light- diffraction system (as arranged for making sound beams visible on a screen). The sonic unit of the system is arranged to produce two individual traveling- wave sound beams, by use of two generators or by splitting a single beam. Three simple arrangements are described in detail. In Case A one beam travels entirely in a reference liquid, while the other beam travels a parallel path in an immersed transparent test specimen. In Case B one beam travels entirely in a reference liquid, while the other beam travels an adjacent course through an immersed, transparent or opaque test prism, and on into the liquid at an angle to the first beam. In Case C the two beams are generated at the equal edge faces of a transparent or opaque isosceles test prism (only * A reprint of this article may be obtained on request. ' B. T. L. ABSTRACTS OF TECHNICAL ARTICLES 771 the base edge face contacting the liquid). The two beams traverse the prism to the base, where they are refracted into the test liquid as confluent beams. In Cases A and B, simulated interference (by optical integration), and in Case C true interference, each give a light and dark band interference pattern on the screen, whose band spacing is used in calculating the velocity of sound in the test solid. The other required factors are the optical image magnification, the frequency of the sound, the angular disposition of the one or more acoustic surfaces of the test solid relative to the incident sound beams, and in Cases A and B the velocity of sound in the reference medium. Other variations of arrangement are suggested. Advantages of the improved methods are simple preparation of test speci- men, directness and simplicity of measurement and calculation, good ac- curacy, low sonic power requirements. A table of measured velocities (and attenuations) in two metals and in numerous plastics and polymers show the wide range of materials that may be measured by the new interference methods. Ferromagnetic Resonance in Various Ferrites. W. E. Yager\ F. R. Merritt\ and C. Guillaud^ Letter to the editor. Phys. Rev., v. 81, pp. 477-478, Feb. 1, 1951. The Study of Size and Shape by Means of Stereoscopic Electron Micrography * C. J. Calbick^ Photo grammetric Engineering, v. 16, pp. 695-711, Dec, 1950. Electrical Excitation of Nerves in the Skin at Audiofrequencies * A. B. Anderson^ and W. A. Munson^ References. Acoustical Soc. Am., JL, v. 23, pp. 155-159, Mar., 1951. Abstract — ^This is a report of results obtained in preliminary tests of perception of signals applied directly to the skin in the form of electrical po- tentials. The lowest signal level that could be felt and the highest level that could be applied without extreme discomfort to the observers were deter- mined for sine wave potentials ranging from 100 to 10,000 cps. The differ- ence between the lowest and highest levels was about 25 db over this frequency range. Difference limen measurements for intensity and frequency showed that intensity discrimination is not greatly different from what it is for hearing but the ear is vastly superior in the matter of frequency discrimination. Field Variation of Superconducting Penetration Depth. J. Bardeen^ Letter to the editor. References. Phys. Rev., v. 81, pp. 1070-1071, Mar. 15, 1951. Determination of the Efects of Dissipation in the Cochlear Partition by * A reprint of this article may be obtained on request. 1 B. T. L. 772 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 Means of a Network Representing the Basilar Membrane* B. P. Bogert^ Acoustical Soc. Am., JL, v. 23, pp. 151-154, Mar., 1951. Abstract — Results are given of measurements made on a 175-section net- work representing the basilar membrane, which was modified to include the effects of dissipation in the cochlear partition. The results show that the dynamical theory of the cochlea, when dissipation is considered, is in good agreement with experimental evidence. A Professional Magnetic-Recording System for Use With 35-, 17^- and 16-Mm Films. G. R. Crane^, J. G. FrayneS and E. W. Templin^ S.M.P.E., JL, V. 56, pp. 295-309, Mar., 1951. Abstract — This paper describes a portable magnetic-recording system for producing high-quality sound tract in synchronism with pictures. The system has been designed to enable magnetic recording to conform with standard motion picture studio operating practices. A number of features such as high-speed rewind, interlocked-switching facilities, one basic type of amplifier and the use of miniature tubes throughout have been incorporated in the system. Additional Continuous Sampling Inspection Plans.* H. F. Dodge^ and M. N. TorreyK Ind. Quality Control, v. 7, pp. 7-12, Mar., 1951. The Mobility and Life of Injected Holes and Electrons in Germanium.* J. R. Haynes^ and W. Shockley^ Bibliography. Phys. Rev., v. 81, pp. 835-843, Mar. 1, 1951. Abstract — The mobilities of holes injected into n-type germanium and of electrons injected into p-type germanium have been determined by measuring transit times between emitter and collector in single crystal rods. Strong electric fields in addition to those due to injected current were em- ployed so that spreading effects due to diffusions were reduced. The mobili- ties at 300°K are 1700 cmV volt-sec for holes and 3600 cmV volt-sec for electrons with an error of probably less than five percent. The value for electrons is about 20 percent higher than the best estimates obtained from the conventional interpretation of the Hall effect and the difference may be due to curved energy band surfaces in the Brillouin zone. Studies of rates of decay indicate that recombination of holes and electrons takes place largely on the surface of small samples with constants varying from 10^ to > 10^ cm/sec for special treatments. On the Theory of Spin Waves in Ferromagnetic Media.* C. Herring^ and C. Kittel^. Bibliography. Phys. Rev., v. 81, pp. 869-880, Mar. 1, 1951. Abstract — The theory of spin waves, leading to the Bloch T^ law for the * A reprint of this article may be obtained on request. ' B. T. L. * Westrex Corp. ABSTRACTS OF TECHNICAL ARTICLES 773 temperature variation of saturation magnetization, is discussed for ferro- magnetic insulators and metals, with emphasis on its relation to the theory of the energy of the Bloch interdomain wall. The analysis indicates that spin-wave theory is of more general validity than the Heitler-London-Heisen- berg model from which it was originally derived. Many properties of spin waves of long wavelength can be derived without specialized assumptions, by a field-theoretical treatment of the ferromagnetic material as a continuous medium in which the densities of the three components of spin are regarded as amplitudes of a quantized vector field. As applications, the effects of anisotropy energy and magnetic forces are calculated; and it is shown that the Holstein-Primakoff result for the field dependence of the saturation magnetization can be derived in an elementary manner. An examination of the conditions for vahdity of the field theory indicates that it should be valid for insulators, and probably also for metals, independently of any simplifying assumptions. The connection with the itinerant electron model of a metal is discussed; it appears that this model is incomplete in that it omits certain spin wave states which can be proved to exist, and that when these are included, it will yield both a magnetization reversal proportional to T^ and a specific heat proportional to T. Incidental results include some insight into the relation between the exchange and Ising models for a two- dimensional lattice, an upper limit to the effective exchange integral, and a treatment of spin waves in rhombic lattices. Edticational Patterns in U. S. and England* M. J. Kelly^ J I. Engg. Education, v. 41, pp. 358-361, Mar., 1951. A Barium Titanate Transducer Capable of Large Motion at an Ultrasonic Frequency* W. P. Mason' and R. F. Wick^ Acoustical Soc. Am., JL, v. 23, pp. 209-214, Mar., 1951. Abstract — By using a barium titanate cylinder poled radially a length- wise motion can be excited in the cylinder whose resonant frequency is con- trolled by the length of the cylinder. By using a 4 percent lead titanate-barium titanate combination, stresses up to 1000 pounds per square inch of cross- sectional dimension and motions up to 50 parts in 10® times the length of the cylinder are available for static or slowly varying voltages of 15,000 volts per centimeter along the radial dimension. When such a cylinder is driven at its resonant frequency, the maximum strain appears to be limited to 10~^ by heating considerations if no coohng is used. For a cylinder 12 centi- meters long, which resonates at 18 kilocycles, this corresponds to a displace- ment on each end of 3.9 X 10"'* cm, a particle velocity of 44 cm/sec and an acceleration of 5 X 10* cm/sec/sec. All of these quantities can be en- * A reprint of this article may be obtained on request. 1 B. T. L. 774 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 hanced by a factor of 10 by soldering a solid brass ''horn," tapered exponen- tial, to the end of the barium titanate cylinder. If the large end of the horn, which is soldered to the cylinder, is 10 times the diameter of the small end, the horn acts as a transformer to increase the particle motion by a factor of 10. Hence, a 1.5-mil motion is possible with this combination at 18 kilo- cycles. This structure has been made the basis of several instruments used for testing wear, for measuring magnetic flux, for testing adhesion of films, and for boring odd-shaped holes. A feedback amplifier system with a diode limiting element is used to keep the amplitude constant. Transmission-Line Equivalent of Electronic Traveling-Wave Systems * W. E. Mathews^ References. Jl. Applied Phys., v. 22, pp. 310-316, Mar., 1951. Abstract — It is well known that the small-signal behavior of long elec- tron beams may be analyzed in terms of propagating space-charge waves suggesting an equivalence between such beams and longitudinally moving transmission lines. This in turn suggests the analysis of such electronic devices as the traveling-wave amplifier, double-stream or electron-wave amplifier, and multicavity magnetron, in terms of coupled distributed- parameter transmission lines moving relative to each other. It is shown that this approach is equivalent to a rigorous field-theory analysis in certain cases of particular interest, and the procedure for calculating the significant distributed parameters is indicated. Final results for the idealized helix and thin cylindrical electron beam are presented. Electronic Music for Four. L. A. Meacham^ Electronics, v. 24, pp. 76-79, Feb., 1951. Thickness-Shear and Flexural Vibrations of Crystal Plates. R. D. Mindlin^ References. Jl. Applied Phys., v. 22, pp. 316-323, Mar., 1951. Abstract — ^The theory of flexural motions of elastic plates, including the effects of rotatory inertia and shear, is extended to crystal plates. The equations are solved approximately for the case of rectangular plates excited by thickness-shear deformation parallel to one edge. Results of computations of resonant frequencies of rectangular, AT-cut, quartz plates are shown and compared with experimental data. Simple algebraic formulas are obtained relating frequency, dimensions, and crystal properties for resonances of special interest in design. Television Transmission in Local Telephone Exchange Areas. L. W. Morrison^. S.M.P.E., JL, v. 56, pp. 280-294, Mar., 1951. Abstract — The functions of a video transmission system in a local ex- change area in providing mobility for the pickup camera and interconnection * A reprint of this article may be obtained on request. > B. T. L. ABSTRACTS OF TECHNICAL ARTICLES 775 with the intercity networks are discussed; and an analysis of some of the tele- vision transmission problems is presented. A description is given of the physi- cal and electrical characteristics of the various types of cable facilities, the video amplifiers, and equalizers now employed; and an example of the television transmission performance obtained is included. Significance of Composition of Contact Point in Rectifying Junctions on Germanium. W. G. Pfann^ Letter to the editor. References. Phys. Rev., V. 81, p. 882, Mar. 1, 1951. The Characteristics and Some Applications of Varistors* F. R. Stansel^ Bibliography. I.R.E., Proc, v. 39, pp. 342-358, Apr., 1951. Abstract — Varistors, circuit elements whose resistance is a function of the voltage applied, represent one important commercial application of semiconductors. They may be divided into two classifications: nonsymmetri- cal and symmetrical varistors. The first classification includes both metaUic rectifiers such as copper oxide, selenium, and copper sulfide, and point contact rectifiers such as silicon and germanium. The only commercial varis- tor of the symmetrical class is the silicon carbide varistor, although a sym- metrical characteristic may be obtained by connecting two nonsymmetrical varistors in parallel with proper polarity. Each varistor has its volt-ampere characteristic and at each point on this characteristic two different values of resistance may be defined, namely the dc resistance, defined as the ratio of voltage to current, and the dynamic or ac resistance, defined as the ratio of dE to dl. The former is important in problems dealing with steady-state dc or large-signal applications, while the latter is important when dealing with small applied signals. Because of the state of the art, varistors as manufactured commercially are less uniform than many other circuit elements and required uniformity is often obtained by special selection. Economical use of these elements therefore requires the circuit engineer to recognize clearly which of the several properties are important in his application and to specify special selection for only those properties and to the extent necessary for his ap- plication. Other properties of varistors which may be of importance are capacitance, maximum inverse voltage, effect of temperature and frequency on any of the other characteristics, long and short time stability, and noise. Of the many applications of varistors three are discussed which illustrate how different properties may be determining factors in different applications. In power rectifiers the limiting factors are those which may physically damage the unit, energy dissipated within the varistor, and inverse voltage * A reprint of this article may be obtained on request. 1 B. T. L. 776 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 across the varistor. As a result such items as ventilation, duty cycle, and the like, are important. In bridge- and ring- (lattice) type modulators the problem of protecting the varistor against physical breakdown is seldom present, but the limiting factor is the extraneous modulation products introduced into the circuit. It is therefore necessary to make detailed analy- ses of the spectrum of the sum and difference products involved. In the com- pandor (compressor plus expandor), operating economies are obtained by a device which is dependent on the uniformity of the dynamic characteristic of the varistor in its forward direction. A selected bibliography is included. Japan's Recovery and Telephone Service. H. F. Van Zandt^. Telephony, v. 140, pp. 15-17, 46, Mar. 24, 1951. Growing Quartz Crystals for Military Needs. A. C. Walker^ Electronics, V. 24, pp. 96-99, Apr., 1951. Abstract — Perfected technique gives large, perfect crystals in quantities that mean eventual independence of Brazilian sources. Quartz scrap, alkaline solution and seed plates are sealed into steel bomb by welding, then heated to 400 C to develop 15,000 psi for optimum growth. Relation between Lattice Vibration and London Theories of Superconduc- tivity."^ J. Bardeen^. References. Phys. Rev., v. 81, pp. 829-834, Mar. 1, 1951. Abstract — A gas of noninteracting electrons of small effective mass, meff, has a large diamagnetic susceptibility. It is shown that the London phenomenological equations of superconductivity follow as a limiting case when nieff is so small that the Landau-Peierls theory yields a susceptibility < — Jtt. Justification is given for the use of an effective mass, ms '^ 10~"* m, for superconducting electrons in the lattice-vibration theory of supercon- ductivity. This value is sufficiently small to show that the theory gives the London equations and, as a consequence, the typical superconducting proper- ties. The concentration of superconducting electrons, Us , is smaller than the total electron concentration, n, by about the same ratio as the effective masses, so that mjw^ ^^ ^/^, and thus the penetration depth is of the same order as that given by the usual London expression. * A reprint of this article may be obtained on request. ' B. T. L. ' Southwestern Bell Telephone Company Contributors to This Issue A. M. Clogston, Massachusetts Institute of Technology, B.S. in Physics, 1938; Ph.D., 1941; from 1941-46 he worked on magnetrons in the Radiation Laboratory at M.I.T. Bell Telephone Laboratories, 1946-. Dr. Clogston is now doing research principally on electron tubes. E. N. Gilbert, B.S. in Physics, Queens College, 1943; Massachusetts Institute of Technology Radiation Laboratory, 1944-46; Ph.D. in Mathe- matics, M.I.T., 1948. Bell Telephone Laboratories, 1948-. Dr. Gilbert has been concerned with mathematical problems of switching and communica- tion theory. F. K. Harvey, B.E.E., New York University, 1939. Bell Telephone Lab- oratories, 1929-. In the Physical Research and Transmission Research Departments, Mr. Harvey has been chiefly concerned with the investigation and measurement of acoustical devices. R. A. Kempf, B.S. in Electrical Engineering, University of Illinois, 1937. Bell Telephone Laboratories, 1937-. Mr. Kempf is in the Outside Plant Development Department and has been with the Toll Cable group located at Point Breeze, Baltimore, Maryland since coming with the Laboratories, except for the period from 1941-45 when he was on active duty in the U. S. Navy. Winston E. Kock, B.E., University of Cincinnati, 1932; M.S., 1933; Ph.D., University of Berlin, 1934. Institute for Advanced Study, Princeton, New Jersey, 1935-36. Director of Electronic Research, Baldwin Piano Company, Cincinnati, Ohio, 1936-42. Bell Telephone Laboratories, Research Department, 1942- . Dr. Kock was engaged in radar antenna work in the Radio Research Department during the war. He is now engaged in micro- wave and acoustic research. C. O. Mallinckrodt, Washington University, B.S. in E.E., 1930. Bell Telephone Laboratories, 1930- April 1951. Mr. Mallinckrodt engaged in the development of carrier telephone repeaters and transmission regulators. During the war he worked on pulse modulation telephone systems which led to the development of the theory of instantaneous compandors. 777 778 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 J. T. Maupin, B.S. in E.E., University of Kentucky, 1947. U. S. Air Force, 1943-46. Bell Telephone Laboratories, 1947-. Except for one year in the School for Communication Development Training, Mr. Maupin has been engaged in research and development work on telephone cables. J. R. Pierce, B.S. in Electrical Engineering, California Institute of Tech- nology, 1933; Ph.D., 1936. Bell Telephone Laboratories, 1936-. Dr. Pierce has been engaged in the study of vacuum tubes. William J. Pietenpol, University of Colorado, B.S. in Electrical Engi- neering, 1943; Radio Corporation of America, Lancaster, Pennsylvania, 1943^6. Ohio State University, 1946-49; Ph.D., 1949. Bell Telephone Laboratories, 1950-. Dr. Pietenpol is engaged in Transistor development. H. H. Schneckloth, B.S. in Electrical Engineering, University of Minne- sota, 1925. Western Electric Company, 1917-18; Northwestern Bell Tele- phone Company, 1918-29; American Telephone and Telegraph Company, Department of Development and Research, 1929-34; Bell Telephone Labo- ratories, 1934-. Mr. Schneckloth 's work was in the manufacturing, mainten- ance, and equipment engineering phases of telephone switching prior to 1929. Since then he has been engaged in switching systems engineering and planning work. Thomas Shaw, S.B., Massachusetts Institute of Technology, 1905. Ameri- can Telephone and Telegraph Company, Engineering Department, 1905-19; Department of Development and Research, 1919-33. Bell Telephone Labora- tories, 1933-48. Mr. Shaw's active telephone career was mainly concerned with loading problems in telephone circuits, including the transmission and economic features of the loading apparatus. The article now being published was started shortly before his retirement in 1948. Robert Lee Wallace, Jr., University of Texas, B.A. in Physics and Mathematics, 1936; M.A., 1939; Harvard University, 1939-45; Special Research Associate in the field of military communications, 1941-45. Bell Telephone Laboratories, 1946-. Mr. Wallace has been concerned with problems in magnetic recordings and with Transistors. HE BELL S Y S T E i\l / meat ourna \ O T E D TO THE SCIENTIFIC ^^^ AND ENGINEERING PECTS OF ELECTRICAL COMMUNICATION LUME XXX OCTOBER 1951 NUMBER 4 PART ] C. J. DAVISSON BELL SYSTEM RESEARCH PHYSICIST 1917-1946 NOBEL LAUREATE 1937 AET. 70 • OCTOBER 2 2,1951 COPYRinHT lOSl AMF.Rfr.AN TF.T.F.PTiniV P. A IV n TF.I.F.riR A PR rOMPAlVY THE BELL SYSTEM TECHNICAL JOURNAL PUBLISHED QUARTERLY BY THE AMERICAN TELEPHONE AND TELEGRAPH COMPANY 195 BROADWAY, NEW YORK 7, N. Y. CLEO F. CRAIG, President CARROLL O. BICKELHAUPT, Secretary DONALD R. BELCHER, Treasurer EDITORIAL BOARD F. R. KAPPEL O. E. BUCKLEY H.S.OSBORNE M.J.KELLY J. J. PILLIOD A. B. CLARK R. BOWN D. A. QUARLES F. J. FE E LY P. C. JONES, Editor M. E. STRIEBY, Managing Editor SUBSCRIPTIONS Subscriptions are accepted at $1.50 per year. Single copies are 50 cents each. The foreign postage is 35 cents per year or 9 cents per copy. THE BELL SYSTEM TECHNICAL JOURNAL \ O L U M E XXX OCTOBER 19 N U M B K R 4 P A H T 1 THIS ISSUE OF THE JOURNAL CELEBRATES THE SEVENTIETH BIRTHDAY OF CLINTON JOSEPH D A V I S S O N IT IS CONTRIBUTED BY SOME OF HIS MANY FRIENDS AND FORMER ASSOCIATES IN THE BELL TELEPHONE LABOBATORIES AS A TOKEN OF THEIR AFFECTION AND OF THEIR RECOGNITION OF THE VALUE OF HIS MANY CONTRIBUTIONS IN THE FIELD OF PHYSICAL RESEARCH C. J. DAVISSON From a portrait by H. E. Ives of about 1938 The Bell System Technical Journal Vol. XXX October, igsi No. 4 Copyright, 1951, American Telephone and Telegraph Company Dr. C. J. Davisson By M. J. KELLY DR. DAVISSON, affectionately known to his large circle of friends as "Davy," joined the research section of the Engineering Department of the Western Electric Company in March, 1917 to participate in its World War I programs. He came on leave of absence from Carnegie Insti- tute of Technology with the intention of returning to his academic post at the close of the war, but remained with its engineering organization, later to become Bell Telephone Laboratories, until 1946, when he retired at the age of sixty-five. He then accepted a research professorship in the Depart- ment of Physics at the University of Virginia. \\'hen I joined Western's Engineering Department at the beginning of 1918, I had the good fortune to be assigned an office with Davisson. This was the beginning of a lifelong intimate friendship and an uninterrupted and close professional association terminated by his retirement. Beginning in 1912 the Western Electric Company under the able leader- ship of Dr. H. D. Arnold pioneered in the development of the thermionic high-vacuum tube for communications applications. Although such devices already had important application as voice-frequency amplifiers in long- distance circuits at the time of our entrance into World War I, tubes were really not yet out of the laboratory, and the relatively few that were re- quired for extending and maintaining service were made in the laboratories of the Engineering Department. Research and development programs di- rected to military applications of these new devices brought about a large expansion in the work of the laboratories. Davisson and I were assigned to the development of tubes for military use. Important applications resulted from this work, and thermionic high- vacuum tubes had to be produced in what was for that time astronomical quantities. The science, technology, and art essential to such quantity pro- duction did not exist, and had to be created concurrently with a most rapid 779 780 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 build-up in production. All of the tubes employed an oxide-coated cathode, which was later to become the universal standard the world over for low- power thermionic vacuum tubes. Davisson early took a position of leadership in problems of fundamental physics relating to the emitter and high-vacuum techniques. We were forced to move so rapidly that much of the work was necessarily empirical. Even in this atmosphere of empiricism Davisson's work was unusually funda- mental and analytical. Increasingly all of us went to him to discuss funda- mental problems that were in urgent need of an answer. He was always available and displayed a friendly interest; we rarely left him without bene- fit from the discussion. Frequently he would continue his study of the problem and come later to give the benefit of his more mature consider- ation. During this period of intensive work performed in an atmosphere of urgency, Davisson displayed the characteristics that were important in determining the pattern of his work through the years and the nature of his contributions to our laboratories and to science. His inner driving force was always seeking complete and exact knowledge of the physical phe- nomena under study. Thoroughness was an outstanding characteristic. The rapid tempo of the work with the necessity of accepting partial answers and following one's nose in an empirical fashion were foreign to his way of doing things. As a war necessity he yielded to it, and performed as a good soldier. His interests were almost wholly scientific, but the needs of the situation forced upon him somewhat of an engineering role for which he had little appetite. As an adviser and consultant, he was unusually effec- tive. In this he has few equals among scientists of my acquaintance. I be- lieve that his success here is due to the high level of his interest in solving problems, to his broad area of curiosity about physical phenomena, and to his warm, friendly, and unselfish interest in the scientific aspects of the work of his associates. Industry's scientific and technologic support of the war effort led to a rapid expansion of industrial laboratories in the postwar period. Our lab- oratories had expanded during the war period, and this was continued at a rapid rate throughout the following decade. The scientists who had come to the Laboratories during the war and the years immediately preceding it, with few exceptions moved out of the laboratory and assumed places of management and leadership in the research and development sections of the Laboratories' organization. At that early period in the life of industrial laboratories, the major emphasis was on applied research and development; there was very little research of a pure scientific nature. Davisson was one of the few who did not gravitate to positions of man- DR. C. J. DAVISSON 781 agement and leadership. His compelling interest in scientific research led Dr. Arnold to make a place in it for him, very rare in industrial laboratories of the time. A pattern of work of his own choosing gradually evolved, and he worked within it throughout his career. One or two young physicists and a few laboratory technicians made up the team that worked on his research problems. The young physicists and technicians did most of the work in the laboratory, although Davisson would frequently be found in the laboratory making observations in association with his co-workers. He took a leading part in planning the experiments and in designing the appa- ratus. His thoroughness and absorbing interest in detail were especially rewarding in this area for his experiments were always well conceived and their instrumentation w^as beautiful. The maximum of reliability, long life (measured in years) and the highest electron-emitting efficiency from the cathode were early recognized as im- portant to the full utilization of the thermionic high-vacuum tube in tele- communications. For several years after the close of the war, Davisson's researches were directed at a complete understanding of the emission phe- nomena of oxide-coated cathodes. This emitter is an unusually complex system. Chemical, metallurgical, and physical problems of great complexity are interleaved. Over the years, our laboratories have made great progress in reliability, long life, and high electron-emitting efficiency of thermionic vacuum tubes for telecommunication uses. The benefits of this work to the telephone user have been large, and annual savings to the Bell System of many millions of dollars have resulted. Davisson's researches during the five years following the close of the war. and his continuing advice to others through a longer period were significant in the advances that our labora- tories have made. As multigrid structures came into use and the tubes came to be used in circuits of ever increasing complexity, unwanted secondary electron emis- sion from the grid structures became a major problem. The presence of this emission and its variation in amount from tube to tube brought about mal- functioning and unreliability. If it were to be controlled, its complete under- standing was essential. A basic study of secondary emission was Davisson's next area of research. In these studies he came upon patterns of emission from the surface of single crystals of nickel that aroused his curiosity. His examination of these patterns led to his discovery of electron diffraction and the w^ave properties of electrons. In recognition of this masterful re- search with its important and highly significant results, he was awarded the Nobel Prize in 1937. After the discovery of electron diffraction, Dr. L. H. Germer, who had worked with Davisson on the secondary emission researches, took the prob- 782 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 lem of applying electron diffraction to the study of the structure of thin surface films. He was the pioneer in utilizing electron diffraction in studies of surface structure, and made a large contribution to the science and tech- nology of this new and important analysis technique. While Germer, grad- uating from his place as an aide to Davisson, worked independently on this problem, he benefited from frequent discussions with Davisson. After Germer had perfected an electron diffraction spectrometer, he operated it for a num- ber of years as an analytical aid to many of the research and development projects of the Laboratories. The interpretation of the patterns and the determination of the crystalline structure of surface films were complex problems. During the period that Germer was developing techniques and getting order into the analysis of the patterns, Davisson of ten joined him in puzzling out the crystal structure revealed in photographs of the diffrac- tion patterns of many different kinds of surfaces. As a logical consequence of Davisson's interest in electron diffraction, he next concerned himself with a variety of problems in electron optics. He was one of the first to develop analytical procedures in the design of struc- tures for sharply focusing electron beams. For many years, beginning in the early 1930's, Davisson gave much attention to the analytical side of electron optics and designed and constructed many structures for electron focusing. Prior to his work much of the vacuum-tube development work in our lab- oratories, as elsewhere where electron focusing was required, was largely empirical. Unfortunately he did not publish much of the fine work that he did, although he reported on portions of it to scientific and technical groups. However, the effect of his work and his ever increasing knowledge of elec- tron optics on the programs and men of our laboratories concerned with electron dynamics was large. Dr. J. B. Fisk, Dr. J. R. Pierce, Dr. L. A. MacCoU, Dr. Frank Gray and others of our laboratory obtained guidance and inspiration from Davisson, the consultant and adviser. His work in electron optics came at a fortunate time in relation to our laboratories' studies of the transmission of television signals over coaxial conductor systems. Although it was possible to measure the amount and characteristics of the electrical distortion of signal currents, there were not available cathode ray tubes precise enough in their design for evaluating the degradation in the picture's quality resulting from the passage of the signal through the coaxial system. He undertook the development of a cathode-ray tube for this test purpose employing the principles of electron optics that he had worked out. In doing this he made one of his few excur- sions into technology. There resulted from his work a cathode-ray tube of great precision. By virtue of the fundamental design of the beam and de- flecting system, the tube provided an extremely small rectangular spot on DR. C. J. DAVISSON 783 the flourescent screen that remained in sharp focus over the entire screen area and had a much improved response characteristic. He took unusual pride in this project, and played a leading part in the design of every ele- ment of the complicated structure. The tube proved to be a useful tool in the evaluation of picture impairment resulting from different types of signal distortion. Our laboratories steadily increased their participation in research and development activities for the military beginning in 1938. This effort ex- panded with terrific speed at the beginning of World War II, and soon became our major activity, continuing until the close of hostilities. Davis- son was most anxious to contribute in any way that he could in our mili- tary work. While continuing his researches, he gave attention to the new and important multicavity magnetron that was receiving increasing atten- tion. His background in electron optics made him invaluable as a consultant to Fisk, who led our magnetron work. As in World War I, speed was again the driving force in our programs, and substantially all of our research people turned to development. By keeping aloof from the rapidly moving develop- ment stream, he was able to give unhurried consideration to many of the basic electron dynamics problems of the magnetron. When Dr. J. C. Slater joined us in 1943 to participate with Fisk in the basic magnetron problems, Davisson turned his attention to problems of crystal physics in relation to our programs on quartz crystal plates as cir- cuit elements. Our laboratories were the focal point of a large national effort for the development, design, and production of quartz crystal plates for a multitude of electronic circuit applications. Drs. W. P. Mason, W. L. Bond, G. W. Willard, and Armstrong- Wood were the basic science team working on a multitude of problems that arose with the tremendous expansion of quartz plate production and use. Davisson spent the major portion of his time from 1943 until his retire- ment in 1946 on a variety of crystal physics problems. He brought a fresh viewpoint into the crystal physics area. Through consultation, analyses, and experiments, he was of material assistance to our crystal physics group in the large contribution they made to the application of quartz plates to electronic systems for the military. Davisson exerted a constructive influence on programs and men in the research and development areas of our laboratories throughout the thirty years of his active service. His door was open to all, and through his con- structive interest in the problems presented, he developed large and con- tinuing consulting contacts. This was not an assigned task but rather one that was personal to him, and its amount and continuance through the years were expressions of a facet of his personality. His contribution to the 784 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 adjustment of the young men to their change in environment from the university to industry as they came to our laboratories was considerable. It became a habit of the research directors to place with him for a year or so junior scientists on their entrance into our laboratories. Dr. J. A. Becker and Dr. William Shockley are typical of the men who were introduced into the Laboratories through a period of association with him. We have always welcomed young scientists from the graduate schools of our universities for summer work. This gives them a view of the operation of an industrial laboratory, and is an aid to us in the selection of young research men from the schools. Several of them were assigned to work with Davisson. Some have since had distinguished careers in science. Drs. Lee A. DuBridge, Merle Tuve, and Philip Morse are among the graduate students who worked with Davisson during their summer employment with us. It was fortunate that Davisson, who had come to stay for the duration of the war, elected to stay with the laboratories to work as a scientist in areas of physics important to our programs rather than return to university life. He established a pattern of fundamental research that has continued and enlarged in scope as our laboratories have evolved and reached matur- ity. Across the forefronts of the physics, mathematics, and chemistry, which are basic to telecommunication technology, we now have many scientists whose programs are directed, as was Davisson's, only at expanding funda- mental knowledge, and who do not divert their energies even to the funda- mental development phases of our technology. It is a tribute to Davisson's overpowering interest in science, and to his steadfastness in the pursuit of knowledge through the scientific method of experiment and analysis that during the pioneering and rapid expansion years of our laboratories, when development demanded the attention of most of our scientists, he gave almost undivided attention to the scientific aspects of our work. Through- out his career he has remained a scientist and has maintained a working knowledge at the forefront of a wide area of physics. Throughout his thirty years at the Laboratories, Davisson's circle of friends among scientists steadily grew, not only within his own country but extending to Europe and the Orient. His capacity for friendships is large, and each of us at the Laboratories in daily contact with him has enjoyed a close friendship of exceptional warmth. The integrity and quality of his work are universally appreciated. He is held in high regard, not only for it but also because of his fine personal qualities. He is shy and modest. Be- cause of this, it requires an association of some duration to know Davisson the man. He has a keen sense of humor, which flashes upon you in most un- expected ways. Unusually slight in stature with a fragile physical frame, his weight never exceeded 115 pounds, and for many years it hovered DR. C. J. DAVISSON 785 around 100. While his health has been good, his store of energy has been limited, and it has been necessary for him to husband it carefully. Davisson's modesty causes him to undervalue the importance and scope of his contributions. This characteristic, the low level of his energy, and the high standard he has always set for his work have combined to limit the amount of his publication. His influence on science and technology gen- erally has, therefore, not been at so high a level as it has attained within the Laboratories, where his personal contact with individuals and their work has been more effective than publication. In recognition of his constructive influence on the evolution of the basic science programs of our laboratories and his contribution of important new knowledge in the areas of thermionic emission, secondary electron emission, electron diffraction, and electron optics, the editors and the editorial board of The Bell System Technical Journal have invited members of our staff whose work and careers have benefited through association with Davisson to contribute papers to this issue of the Journal in celebration of his seven- tieth birthday. The Scientific Work of C. J. Davisson By KARL K. DARROW THE very first piece of work which is published by a physicist who is destined to be great is not often outstanding; but sometimes it has curious affinities, accidental rather than causal, with aspects of the work that was to come thereafter. In the first paper pubHshed by C. J. Davisson, we find him working with electrons, concentrating them into a beam by the agency of a magnetic field, directing them against a metal target, and looking to see whether rays proceed from the target. True, the electrons came from a radioactive substance, and therefore were much faster than those of his later experiments. True also, he did not actually focus the electron-beam. True also, the rays for which he was looking were X-rays, and in these he took no further interest. Yet in nearly all of his subsequent researches he was to use some of the principles of electron-focussing or elec- tron-microscopy; in many, he was to look for things that were emitted by the target on which his electrons fell. This maiden papei was presented be- fore the American Physical Society at its meeting in Washington in April 1909; the printed version may be found in the Physical Review, page 469 of volume 28 of the year 1909. It was signed from Princeton University, whither Davisson had gone as a graduate student. Another characteristic of Davisson's work in his later years was his fre- quent study and use of thermionics. Already in 1911 we find him working in this field — but it was thermionics with a difference. The word "thermi- onics" now signifies, nearly always, the emission of electrons from hot metals; but at first it included also the emission of positive ions from hot metals and hot salts. Though neither useless nor uninteresting, the emission of positive ions is now rated far below the effect to which we now confine the name of thermionics: emission of electrons from hot metals is one of the fundamental phenomena of Nature, and its uses are inimitable. It may be plausibly conjectured that in 1911 the difference in the importance of the two phenomena — emission of positive ions and emission of electrons — was far less evident than it is now. Davisson, working under the British physicist O. W. Richardson who was then professor at Princeton, estab- lished that the positive ions emitted from heated salts of the alkali metals are once-ionized atoms of these metals — that is to say, atoms lacking a single electron. He also showed that if gas is present in the tube, it may enhance the number of the ions but does not change their character. This 786 THE SCIENTIFIC WORK OF C. J. DAVISSON 787 work was presented before the April meeting of the American Physical Society in 1911. Abstracts of the papers which he there gave orally may be found in Physical Review, but the publications in full appeared (in 1912) in Philosophical Magazine. Davisson's choice of a British journal was advised by his transplanted teacher, but it must be realized that in 1912 the Physical Review had by no means ascended to the rank that it holds today. With this work came to their end the contributions of his student years, and next we find him publishing as an independent investigator. From Davisson's years (1912-17) at the Carnegie Institute of Tech- nology there is a paper embodying an attempt to calculate the optical dis- persion of molecular hydrogen and of helium from Bohr's earliest atom- model. It shows him possessed of no mean mathematical technique, but is based — as the date by itself would make evident — on too primitive a form of quantum-theory. In June 1917, in the midst of World War I, Davisson came for what he thought would be a temporary job at the institution then known as the Research Laboratories of the American Telephone and Telegraph Company and the Western Electric Company, thereafter — from 1925 — as Bell Tele- phone Laboratories. Not for a year and a half was he able to devote him- self to work untrammeled by the exigencies of war. So far as publication is concerned, his second period began in 1920, when he presented two papers before the American Physical Society: one at the New York meeting in February, one at the \\'ashington meeting in April. In the former of these his name is linked with that of L. H. Germer, a name associated with his in the great discovery of electron waves; in the latter it is linked with that of the late H. A. Pidgeon. These two papers are represented only by brief abstracts; and this is the more regrettable, as they form the only contributions published under Davisson's name to the dawning science of the oxide-coated cathode. In the former, he estabHshed that the remarkably high electron-emission of oxide-coated metals — as contrasted with bare metals — is not due, as had been elsew^here suggested, to the impacts of positive ions from the gas of the tube against the coatings: it is true thermionic emission. In the latter, he studied the rise and eventual fall of the thermionic emission as more and more oxide is laid down upon the metal surface, and concluded that the emission occurs when a definite number of oxide molecules is assembled into a patch of definite size on the surface: the number of patches of just the right size first rises, then declines as the deposition continues. According to colleagues of his, these two papers fall short by far of indicating the ex- tent of his contributions to this field; and one of them has said that Davis- son was excessively scrupulous about putting his work into print, being 788 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 unwilling to publish his observations until he felt sure that he understood all that was taking place. It is in an article by another — the late H. D. Arnold, first to hold the post of Director of Research in Bell Telephone Laboratories and its antecedent organization — that we find a description of Davisson's ''power-emission chart," now standard in the art. In Arnold's words: "Dr. Davisson has devised a form of coordinate-paper in which the coordinates are power supplied to the filament (abscissae) and thermionic emission (ordinates). The coordinate lines are so disposed and numbered that if the emission from a filament satisfies Richardson's relation, and the thermal radiation satisfies the Stefan-Boltzmann relation, then points on the chart coordinating power and emission for such a filament will fall on a straight line." In a paper presented at a meeting toward the end of 1920 (it was a joint paper of himself and J. R. Weeks) Davisson gives the theory of the emis- sion of light from metals, deduces a deviation from Lambert's law and verifies this by experiment. A connection between this and the study of thermionics may be inferred from the words which I quoted earlier from Arnold's description of Davisson's power-emission chart. This work was published in full, some three years later, in the Journal of the Optical Society of America. We turn now to Davisson's investigations of thermionic emission from metals. Those whose memories go back far enough will recall that two laws have been proposed for the dependence of thermionic emission on temperature. Both were propounded by O. W. Richardson, and each, somewhat confus- ingly, has at times been called ''Richardson's law." The earlier prescribed that the thermionic current i should vary as r^exp(— ^/T), T standing for the absolute temperature; the later prescribes that t should vary as T^tx\i{—b/T). The former is derived from the assumption that the velocities and energies of the electrons inside the metal are distributed according to the classical Maxwell-Boltzmann law. The latter follows from the assump- tion that these velocities and energies are distributed according to the quantum-theory or Fermi-Dirac law: it was, however, derived from thermo- dynamic arguments some thirteen years before the Fermi-Dirac theory was developed, and the experiments about to be related were performed during this thirteen-year period. In the interpretation of either law, b is correlated with the work of egress which an electron must do (at the expense of its kinetic energy) in order to go from the inside to the outside of the metal. I will leave to a later page the phrasing of this correlation, and say for the moment that h multiplied by Boltzmann's constant k represents what used to be called and is still some- THE SCIENTIFIC WORK OF C. J. DAVISSON 789 times called the '^thermionic work-function" of the metal. If a given set of data is fitted first by the T'^ law and then by the 7^ law, different values of b and therefore different values of the thermionic work-function are ob- tained. Which is right? This question can be answered if the thermionic work-function can be measured with adequate accuracy by some other method. Such a method exists: it is called the ''calorimetric" method. Suppose an incandescent wire surrounded by a cylindrical electrode. If the latter is negative with respect to the former, the emitted electrons will return to the wire, and there will be no net thermal effect due to the emission. If, however, the cylinder is positive with respect to the wire, the electrons will be drawn to it, and the wire will fall in temperature: this is the ''cooling-effect" due to the emis- sion. The resistance of the wire will decrease, and if the current into the wire is held constant, the voltage between its terminals will be lessened. The experiment may sound easy, and so it might be if all of the current flowed within the wire from end to end; but the bleeding of electrons through the entire surface makes the current vary from point to point along the wire, and complicates the test enormously. Others elsewhere had tackled this difficult problem of experimentation; but Davisson and Germer found a better way to handle it, and their results for tungsten were presented at a meeting at the end of 1921 and published fully the following year. From their data they calculated the thermionic work-function of the metal, which when thus determined we may denote by e(f). It agreed with the value of kb obtained from the newer form of "Richardson's law," disagreed with the other. Thus Davisson was in the position of having confirmed the Fermi- Dirac distribution-law before it had been stated! It remains to be said that, years later, Davisson and Germer repeated this experiment upon an oxide-coated platinum wire. Here they came upon a complication from which clean metal surfaces are fortunately exempt. The character of the oxide-coated wire changed with the temperature; and, since the measurement of the "constant" b requires a variation of the tem- perature, its value did not provide a reliable measure of the work at any single temperature, whereas the "calorimetric" measurement did. Now at last we are ready to attend to the early stages of the studies which were destined to lead to the discovery of electron-waves. These were studies of what I shall call the "polycrystalline scattering patterns" of metals: the name is descriptive rather than short. A beam of electrons is projected against a metal target which is in the condition, normal for a metal, of being a complex of tiny crystals oriented in all directions. Some of these electrons swing around and come back out of the metal with un- diminished energy: these are the electrons that are "elastically scattered," f 790 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 (Davisson records that elastic scattering had previously been observed only with electrons having initially an energy of 12 electron-volts or less). A collector is posted at a place where it collects such electrons as are scattered in a direction making some chosen angle 6 with the direction exactly oppo- site to that of the original or "primary" beam. There may be inelastically- scattered or secondary electrons which travel toward the collector: its potential is so adjusted as to prevent the access of these. The collector is moved from place to place so as to occupy successively positions corresponding to many values of the angle d. It is always in the same plane passing through the primary beam, and so the curve of number- of-scattered-electrons (per unit solid angle) plotted against 0 is a cross- section of a three-dimensional scattering pattern; but, for obvious reasons of symmetry, the three-dimensional pattern is just the two-dimensional pattern rotated around the axis which is provided by the primary beam. This two-dimensional pattern is what I have called the polycrystalline scattering-pattern. It is a curve plotted, in polar coordinates or in Cartesian, against B over a range of this angle which extends from —90° to +90°; but the part of the curve which runs from 6 = —90° to 0=0° is the mirror-image of the other part, and either by itself suffices. The curve can- not be plotted in the immediate vicinity of ^ = 0°, because the source of the electrons gets in the way. The first published report of such an experiment is to be found, under the names of Davisson and C. H. Kunsman, in Science of November 1921; in that same November Davisson presented the work before the American Physical Society. The metal was nickel, and the pattern had two most remarkable features. These were sharp and prominent peaks; one inferred from the trend of the curve in the neighborhood of ^ = 0"^ and presumably pointing in exactly that direction, consisting therefore of electrons which had been turned clear around through 180 degrees; the other pointing in a direction which depended on the speed of the electrons, and for 200-volt electrons was at 70°. Any physicist who hears of experiments on scattering is likely to think of the scattering-experiments performed by Rutherford now more than forty years ago, which established the nuclear atom-model. These were measurements of the scattering-pattern of alpha-particles, and this does not look in the least like the curve observed by Davisson and Kunsman: it shows no peaks at all. Alpha-particles, however, are seven thousand times as massive as electrons: they are deflected in the nuclear fields, and so great is the momentum of an alpha-particle that it does not suffer any perceptible deflection unless and until it gets so close to a nucleus that there are no electrons at all between the nucleus and itself. But with so light a particle \ THE SCIENTIFIC WORK OF C. J. DAVISSON 791 as an electron, and especially with an electron moving as slowly as Davis- son's, the deflection commences when the flying electron is still in the outer regions of the atom which it is penetrating. The deflection of the individual electron and the scattering-pattern of the totality of the atoms are, there- fore, conditioned not only by the nuclear field but by the fields of all the electrons surrounding the nucleus. How shall one calculate the effect of all these? This is a very considerable mathematical problem, and Davisson simpli- fied it to the utmost by converting the atomic electrons into spherical shells of continuous negative charge centered at the nucleus. The simplest con- ceivable case — not to be identified with that of nickel — is that of a nucleus surrounded by a single spherical shell having a total negative charge equal in magnitude to the positive charge of the nucleus itself. Within the shell the field is the pure nuclear field, the same as though the shell were not there at all; outside of the shell there is no field at all. This is what Davis- son called a ''limited field." Calculation showed that the scattering-pattern of such a system would have a peak in the direction d = 0°, so long as the speed of the electrons did not exceed a certain ceiling- value ! And there was more: "the main features of the scattering-patterns (Davisson said "distri- bution-curves") for nickel, including the lateral maximum of variable posi- tion, are to be expected if the nickel atom has its electrons arranged in two shells." Nickel in fact is too complicated an atom to be represented, even in the most daring allowable approximation, as a nucleus surrounded by a single shell; two shells indeed seem insufficient, but the fact that a two-shell theory leads in the right direction is a significant one. Magnesium might reason- bly be approximated by a single-shell model; Davisson experimented on this metal, and published (in 1923) scattering-patterns which lent themselves well to his interpretation. He measured scattering-patterns of platinum also, and these as to be expected are much more wrinkled with peaks and valleys; the task of making calculations for the platinum atom with its 78 electrons was too great. Nickel continued to be Davisson*s favorite metal, and four years later (1925) his study of its polycrystalline scattering-pattern was still in prog- ress. In April of that year occurred an accident, of which I quote his own description from Physical Review of December 1927. "During the course of his work a liquid-air bottle exploded at a time when the target was at a high temperature; the experimental tube was broken, and the target heavily oxidized by the in-rushing air. The oxide was eventually reduced and a layer of the target removed by vaporization, but only after prolonged heat- ing at various high temperatures in hydrogen and in vacuum. When the 792 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 experiments were continued it was found that the distribution-in-angle of the scattered electrons had been completely changed. . . . This marked alteration in the scattering-pattern was traced to a re-crystallization of the target that occurred during the prolonged heating. Before the accident and in previous experiments we had been bombarding many small crystals, but in the tests subsequent to the accident we were bombarding only a few large ones. The actual number was of the order of ten." I do not know whether Davisson ever cried out 0 felix culpa! in the lan- guage of the liturgy; but well he might have. The exploding liquid-air bottle blew open the gate to the discovery of electron-waves. Fatal conse- quences were not wanting: the accident killed the flourishing study of polycrystalline scattering-patterns, and countless interesting curves for many metals are still awaiting their discoverers. This may illustrate a differ- ence between the industrial and the academic career. Had Davisson been a professor with a horde of graduate students besieging him for thesis sub- jects, the files of Physical Review might exhibit dozens of papers on the scattering-patterns of as many different metals, obtained by the students while the master was forging ahead in new fields. Now that we are on the verge of the achievement which invested Davis- son with universal fame and its correlate the Nobel Prize, I can tell its history in words which I wrote down while at my request he related the story. This happened on the twenty-fifth of January, 1937: 1 have the sheet of paper which he signed after reading it over, as also did our colleague L. A. MacCoU who was present to hear the tale. This is authentic history such as all too often we lack for other discoveries of comparable moment. Listen now to Davisson himself relating, even though in the third person, the story of the achievement. ''The attention of C. J. Davisson was drawn to W. Elsasser's note of 1925, which he did not think much of because he did not believe that Elsasser's theory of his (Davisson's) prior results was valid. This note had no influence on the course of the experiments. What really started the dis- covery was the well-known accident with the polycrystalline mass, which suggested that single crystals would exhibit interesting effects. When the decision was made to experiment with the single crystal, it was anticipated that 'transparent directions' of the lattice would be discovered. In 1926 Davisson had the good fortune to visit England and attend the meeting of the British Association for the Advancement of Science at Oxford. He took with him some curves relating to the single crystal, and they were surpris- ingly feeble (surprising how rarely beams had been detected!). He showed them to Born, to Hartree and probably to Blackett; Born called in another Continental physicist (possibly Franck) to view them, and there was much THE SCIENTIFIC WORK OF C. J. DAVISSON 793 discussion of them. On the whole of the westward transatlantic voyage Davisson spent his time trying to understand Schroedinger's papers, as he then had an inkling (probably derived from the Oxford discussions) that the explanation might reside in them. In the autumn of 1926, Davisson calculated where some of the beams ought to be, looked for them and did not find them. He then laid out a program of thorough search, and on 6 January 1927 got strong beams due to the line-gratings of the surface atoms, as he showed by calculation in the same month." Now I will supplement this succinct history by explanations. The first name to be mentioned in the explanations must be one which does not appear in the quotation: that of Louis de Broglie. Louis de Broglie of Paris had suggested that electrons of definite momen- tum— let me denote it by p — are associated with waves of wavelength X equal to h/p, h standing for Planck's constant. This suggestion he made in an attempt to interpret the atom-model of Bohr, a topic which is irrelevant to this article. Irrelevant also is the fact that Louis de Broglie's suggestion led Schroedinger to the discovery of "wave-mechanics," but I mention it here because Schroedinger's name appears in the quotation. Highly relevant is the inference that the ''de Broglie waves," as they soon came to be called, might be difi'racted by the lattices of crystals, and that the electrons of an electron-beam directed against a crystal might follow the waves into char- acteristic diffraction-beams such as X-rays exhibit. This inference was drawn by a young German physicist Walther Elsasser by name, then a student at Goettingen. It was one of the great ideas of modern physics; and, in recording that its expression in Elsasser 's letter was not what guided Davisson to its verification, I have no wush to weaken or decry the credit that justly belongs to Elsasser for having been the first to conceive it. Dr. Elsasser has authorized me to publish that he submitted his idea to Einstein, and that Einstein said ''Young man, you are sitting on a gold-mine." The letter which I have mentioned appeared in 1925 in the German periodical Die N aturwissenschaften. As evidence for his idea Elsasser there adduced the polycrystalline scattering-patterns, in particular those for platinum, that had been published by Davisson and Kunsman. But Davisson as we have seen did not accept this explanation of the patterns; and never since, so far as Elsasser or I are aware, has anyone derived or even tried to derive the polycrystalline scattering-patterns from the wave- theory of electrons. This must be listed as a forgotten, I hone onlv a tem- porarily forgotten, problem of theoretical physics. Essential to the application of Elsasser's idea is the fact that the wave- lengths of the waves associated with electrons of convenient speeds are of the right order of magnitude to experience observable diffraction from a 794 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 crystal lattice. It is easy to remember that 150- volt electrons have a wave- length of one Angstrom unit, while the spacings between atoms in a solid are of the order of several Angstroms. This fact of course did not escape Elsasser, and it figures in his letter. From the quotation it is clear that the earliest patterns obtained from the complex of large crystals were obscure, and the definitive proof of Elsasser 's theory was obtained only when Davisson instituted his "program of thor- ough search" and simultaneously in England G. P. Thomson instituted his own. Two other items in the quotation require to be explained. The hypothesis of "transparent directions" I will consider to be explained by its name. Were it correct, the directions of the beams would be independent of the speed of the electrons; since they are not, the hypothesis falls. The reference to the "line-gratings of the surface atoms" induces me to proceed at once to one of the principal contrasts between diffraction of electrons and diffraction of X-rays. An optical grating is a sequence of parallel equidistant grooves or rulings on a surface of metal or glass. The atoms on a crystalline surface are arranged in parallel equidistant lines, and one might expect X-rays or electrons to be diffracted from them as visible light is diffracted from an optical grating. This expectation is frustrated in the case of X-rays, because their power of penetration is so great that a single layer of atoms, be it the surface-layer or any other, diffracts but an inappreciable part of the incident X-ray beam; only the cumulative effect of many layers is detectable. Electrons as slow as those that Davisson used are not nearly so penetrating. With these indeed it is possible, as he was the first to show, to get diffraction- beams produced by the surface-layer only. Such beams, however, are detect- able only when the incident (or the emerging) beam of electrons almost grazes the surface; and nearly always, when a beam is observed, it is due to the cumulative effect of many atom-layers as is the rule with X-rays. But the cumulative effect requires more specific conditions than does diffrac- tion by the surface-layer: if the incident beam falls at a given angle upon the surface, the momentum of the electrons and the wavelength of their waves must be adjusted until it is just right, and, reversely, if the momen- tum of the electrons has a given value the angle of incidence must be ad- justed until it is just right. This also Davisson verified. As soon as Davisson made known his demonstration of electron-waves, he was bombarded by entreaties for speeches on his work and for descrip- tions to be published in periodicals less advanced and specialized than Physical Review. To a number of these he yielded, and I recommend espe- cially the talk which in the autumn of 1929 he gave before the Michelson Meeting of the Optical Society of America; one finds it in print in volume THE SCIENTIFIC WORK OF C. J. DAVISSON 795 18 of the Journal of that Society. It is written with such clarity, grace and humor as to make one regret that Davisson was not oftener tempted to employ his talents for the benefit not of laymen precisely, but of scientists who were laymen in respect to the field of his researches. I quote the first two sentences: "When I discovered on looking over the announcement of this meeting that Arthur Compton is to speak on 'X-rays as a Branch of Optics' I realized that I had not made the most of my opportunities. I should have made a similar appeal to the attention of the Society by choos- ing as my subject 'Electrons as a Branch of Optics.' " Though in this period his duties as expositor took a good deal of his time, Davisson found opportunity to prosecute his work and to begin on certain applications. One obvious development may be dismissed rather curtly, as being less important than it might reasonably seem. One might have ex- pected Davisson to strive to verify de Broglie's law X = h/p to five or six significant figures. This would have been difficult if not impossible, since the diffraction-beams of electrons are much less sharp than those of X-rays; this is a consequence of the fact that the diffraction is performed by only a few layers of atoms, the primary beam being absorbed before it can pene- trate deeply into the crystal structure. But even if it had been easy the enterprise would probably have been considered futile, for de Broglie's law quickly achieved the status of being regarded as self-evidently true. Such a belief is sometimes dangerous, but in this case it is almost certainly sound: the law is involved in the theories of so many phenomena, that, if it were in error by only a small fraction of a per cent, the discrepancy would have been noted by now in more ways than one. Davisson established the law within one per cent, and there are few who would not regard this as amply satisfactory. The greatest of the uses of electron-diffraction lies in the study of the arrangement of atoms in crystals and in non-crystalline bodies. Here it supplements the similar use of X-ray diffraction, for it serves where X-ray diffraction does not, and vice versa. Once more I quote from a lecture of Davisson's: "Electrons are no more suitable for examining sheets of metal by transmission than metal sheets are suitable for replacing glass in windows. To be suitable for examination by electrons by transmission, a specimen must be no more than a few hundred angstroms in thickness. It must be just the sort of specimen which cannot be examined by X-rays. Massive specimens can be examined by electrons by reflection. The beam is directed onto the surface at near-grazing incidence, and the half-pattern which is produced reveals the crystalline state of a surface-layer of excessive thin- ness. . . . Invisible films of material, different chemically from the bulk of the specimen, are frequently discovered by this method." Many experi- 796 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 ments of this type were done at Bell Telephone Laboratories by L. H. Germer; they do not fall within the scope of this article, but we may be sure that Davisson was interested in them. Davisson also studied the refraction of electrons at the surface of nickel, and this is work which in my opinion has never received the attention that it merits. Let us consider its importance. I have already spoken of the work which an electron must do in order to quit a metal, and have mentioned two ways employed by Davisson (and by others) to ascertain its value — the measurement of the constant b which figures in Richardson's equation, and the measurement of the quantity 0 by the calorimetric method. It is customary to ascribe this work of egress to the presence of a "surface potential-barrier," usually imagined as an infinitely sudden potential-drop occurring at the surface of the metal: the potential immediately outside the metal is supposed to be less than the potential immediately inside by a non-zero amount, which I will denote by X. One is tempted to identify X with 0 and with kb/e\ but this is an over- simplification. By the classical theory there is a difference which is small but not quite negligible. By the new theory there is a difference which is neither small nor by any means negligible. By the new theory, in fact, X is greater than <^ by an amount which is equal to the so-called "Fermi energy" — the kinetic energy of the electrons which, if the metal were at the absolute zero of temperature, would be the fastest-moving electrons in the metal. Now, this last amount is of the order of half-a-dozen electron-volts for the metals of major interest in thermionic experiments, and so also is the value of 0. Thus, if there were a method for determining the height of the surface potential-barrier, this would be expected to yield a value of the order of six volts if the old theory were right and a value of the order of twelve volts if the new theory were correct. Well, there is such a method, and it consists precisely in observing and measuring the refraction of the electron-waves as they pass through the sur- face of the metal. This refraction has a deceptive effect; it alters the orient- ations of the diffraction-beams as though the crystal were contracted in the direction normal to its surface. Once this is comprehended, the refractive index may be calculated from the observations, and from the refractive index the value of X the surface potential drop. This was done by Davisson and Germer for nickel, and published in the Proceedings of the National Academy of Sciences for 1928. The value which they found for the surface potential-drop was 18 volts — three times as great as the value prescribed by the old theory, half again as great as the value afforded by the new. Thus the experiments speak for the new theory over the old, yet not with unambiguous support of the new. This has been described to me, by a dis- THE SCIENTIFIC WORK OF C. J. DAVISSON 797 tinguished physicist, as one of the situations in which the concept of a single sharp potential-drop becomes most palpably inadequate. Work of this kind continued to be done, especially in Germany, until the later thir- ties, and then regrettably flickered out. In 1937 the Nobel prize was conferred on Davisson, and he had the opportunity of enjoying the ceremonies and festivities which are lavished upon those who go to Stockholm and receive it. He shared the prize with G. P. Thomson, who must not be entirely neglected even in an article dedicated explicitly to Davisson. There was little in common between their techniques, for Thomson consistently used much faster electrons which transpierced very thin polycrystalline films of metal and produced glorious diffraction-rings. He too founded a school of crystal analysts. Finally I mention three notes — two abstracts of papers given before the American Physical Society in 1931 and 1934, and one Letter to the Editor of Physical Review — bearing on what has been described to me, by an ex- pert in the field, as the first publication of the principle of the ''electrostatic lens" useful in electron-microscopy. These are joint papers of Davisson and C. J. Calbick. They report, in very condensed form, the outcome of an analysis which showed that a slit in a metal cylinder treats electrons as a cylindrical lens treats light, and a circular hole in a metal plate treats elec- trons as a spherical lens treats light : in both cases the field-strengths on the two sides of the metal surface (cylinder or plate) must be different. Experi- ments were performed to test the theory, and succeeded; and in the latest of the notes we read that Calbick and Davisson used a two-lens system to form a magnified image of a ribbon-filament upon a fluorescent screen. Cal- bick recalls that the magnification was of the order of twentyfold. During the time of his researches on electron-waves, Davisson's office was on the seventh floor of the West Street building, on the north side about seventy-five paces back from the west facade: his laboratories were at times beside it, at times across the corridor. This illustrates a disadvantage of our modern architecture. If Davisson had done his work in a mediaeval cathe- dral, we could mount a plaque upon a wall which had overlooked his appa- ratus, and plaque and wall would stand for centuries. But the inner walls of Davisson's rooms are all gone, and the outer wall consisted entirely of windows; and nothing remains the same except the north light steaming through the windows, which we may take as a symbol of the light which Davisson cast upon the transactions between electrons and crystals. Inorganic Replication in Electron Microscopy By C. J. CALBICK Contrast and resolution in electron micrographs from thin replica films are determined by the geometrical relationships between the directions of incidence of the condensing atom beam and the local surface normal, during film formation by evaporation in vacuo, and the direction of incidence of the electron beam, during subsequent exposure in the microscope. Rephca films may be formed of any material suitable for vacuum evaporation. Metal atoms in general tend to stick where they strike, moving only short distances, 100 A or less, to nucle- ating centers where they form small crystallites. Oxides such as silica and silicon monoxide, and also the semi-metal germanium, form amorphous films. A portion of the incident material, about 50% in the case of silica, migrates large dis- tances, 5000 A or more, before finally condensing; the remainder sticks where it first strikes the surface. The existence of a minimum perceptible mass thickness difference, about 0.7 Mg/cm^ for 50 kv electrons, results in an optimum replica mass thickness of about 10 /iig/cm^. The resolution of the replica film is proportional to its linear thickness and hence is inversely proportional to its density. Micrographs of silica, chro- mium, gold-manganin, aluminum, aluminum-platinum-chromium and germanium replicas are shown. The importance of stereoscopic methods in interpretation of micrographs is discussed. THE basic purpose of micrography of surfaces is to exhibit structural topography. Present day electron microscopes are transmission-type instruments. Practical limitations of experimental technique establish a voltage of the order of 50 kv as the most useful accelerating potential for the electrons used for illumination. In bright field transmission microscopy, the image consists of a field with local variations of intensity produced because the object has partially absorbed, or scattered, the incident radia- tion. In electron imaging scattering is the predominant factor, limiting direct examination to objects whose mass thickness does not exceed about 50 ng/crri^* Thicker specimens can be examined only in profile. Optical microscopy of surfaces is concerned with their appearance as seen by reflected light, the counterpart of which is not practicable^ with electrons. The electron microscopist has therefore devised means of trans- ferring surface structural details to thin films called replicas. ^ These films must present to the electron beam locally varying thickness corresponding to the surface details. A simple type is the plastic replica^ consisting of an appropriately thin plastic film stripped from the surface. A second type * Some microscopes provide a range of accelerating potentials, up to 100 kv or more, permitting direct examination of thicker objects. 1 Zworykin et al. "Electron Optics and the Electron Microscope," pp. 98-106. 2 /. Roy. Micro. Soc, 70, 1950, "The Practise of Electron Microscopy," ed, by D. G. Drummond, see Chapters II and V. » V. J. Schaefer and D. Harker, //. App. PJiys., 13, 427 (1942). 798 INORGANIC REPLICATION IN ELECTRON MICROSCOPY 799 is the oxide film,- produced by controlled oxidation of the surface when it is aluminum or another suitable metal. For other materials, a pressure mold of the surface in pure aluminum may be utilized as an intermediate repHca in a two-step process.'* A third type is the silica replica,^ ^ produced by the condensation of silica vaporized by a hot source in vacuo, either on the surface in a one-step, or on a plastic mold of the surface in a two-step, process. A fourth type is the shadow-cast plastic rephca,^- ^ produced by similar deposition of a suitable metal at near-glancing incidence upon a plastic replica. The purpose of this paper is to discuss the process of evaporated film formation as it is related to properties important in microscopy. The resolu- tion and range of contrast available in the finished micrograph determine the faithfulness with which the original surface is depicted, and depend on the relative orientation of the surface, vapor source, and electron beam, on the density and average thickness of the repHca, and on the mechanism of condensation. In principle, it is pointed out that any material of suitable physical and chemical properties may be used for evaporated repHca films, and a number of examples are shown in micrographs. Inorganic repHca films retain the third or vertical dimension, a fundamental advantage which permits stereoscopic study. The material presented perhaps provides a uni- fied view of repHca tion techniques and a method for the evaluation of micrographs relative to the faithfulness of portrayal of the original surface. 1. Local Thickness of Condensed Material Figure 1 illustrates how the thickness te in the direction of the electron beam is dependent on the local surface normal n. The thickness /« in the direction of the atom source is constant, depending only on the amount of material reaching the surface. The thicknesses due to two or more sources obviously may be vectorially added, and hence an arbitrary assembly of sources may be replaced by a single source properly located, since each yields the same thickness distribution on the surface S. A simple analogy is the shading produced when ordinary objects are illuminated by direct Hght. It is clear that atom source and electron beam must differ in direction for shading to occur. The atoms or molecules of some materials, notably silica and silicon monoxide, do not all stick where they strike, but some wander over the surface^ as a ''two-dimensional gas" before condensing. This * J. Hunger and R. Seeliger, Metallfarschung, 2, 65 (1947). 6R. D. Heidenreich and V. G. Peck, //. App. Phys., 13, 427 (1943). 6 C. H. Gerould, //. App. Phys., 17, 23 (1947). 7 H. Mahl, Konosion u. Metallsclmtz, 20, 225 (1945). 8R. C. Williams and R. W. G. Wyckoff, //. App. Phys., 17, 23 (1946). 9 R. D. Heidenreich, //. App. Phys., 14, 312 (1943). 800 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 results in a somewhat different shading distribution. The distributions are mathematically formulated in Appendix I. 1.1 Shadows In certain regions the local surface is not exposed to the source, resulting in "shadows" within which te is zero. These shadows are bounded by two lines, the shadow-casting profile and the shadow edge. The shape of the shadow edge depends both on the shadow profile and on the topography in the vicinity of the edge and in consequence interpretation of shadowing is DIRECTION OF ELECTRON SOURCE WHEN FILM IS LATER MOUNTED IN MICROSCOPE Fig. 1 — Diagrammatic representation of thin film replicas produced when every atom sticks where it strikes. difficult unless one of the surfaces is smooth.'" With multiple or extended sources, partial shadows and shading due to partial shadowing occur. 1.12 Negative shadows There may be other regions of the surface which are exposed to the atom source, but not to the subsequently incident electron beam. When the replica film is mounted in the microscope, these regions appear reentrant to the electron beam, which must pass through three rather than one layer of replica. These regions appear as very hghtly exposed areas in micro- graphs, and since they are essentially ''negative shadows" are subject to the same considerations of shape and interpretation as ordinary shadows. »» "Physical xMethods in Chemical Analysis," Vol. 1, 1950. On pp. 571-3, R. D. Heiden- reich reports some unpublished work of S. G. Ellis and W. G. Gross, showing great differ- ences in appearance of shadow-cast replicas as the azimuth of the atom source is varied. INORGANIC REPLICATION IN ELECTRON MICROSCOPY 801 2. Intrinsic Resolution of Replica Films In the vicinity of a sharp change in surface gradient, the local thickness te does not change abruptly, but the change occurs over a short distance d as illustrated in Fig. 2. A mathematical formulation for this intrinsic resolu- tion d is given in Appendix II, with some detailed discussion. Intrinsic resolution varies locally over the surface, dependent on the geometrical relationship between atom source, electron beam, and local surface to- pography. Observable resolution includes also instrumental resolution and contrast factors. Except at shadow boundaries it is probably never less than J/e, where ie is the average value of /g, and perhaps may be as poor as ELECTRON BEAM Fig. 2 — Diagram showing resolution of replica film at a sharp corner, (a) Every atom sticks where it strikes, (b) All atoms diffuse, finally condensing into film of uniform local thickness. several times \lc- Shadow profiles and edges often show short lengths of extreme sharpness. The resolution across these portions of shadows may often beassumed to bethe instrumental resolution. The reasons for this are developed in the Appendix. 2.1 Efect of Film Thickness The average linear thickness h is a factor in the expressions for resolution. To reduce d and thereby improve the resolution, the most effective method is to reduce h. With a given material, as the repUca film is made thinner, the contrast is reduced also, so that, just as in photography a feature that is visible in a properly exposed negative may be lost in a thin negative, some features may not be repHcated with sufficient contrast to be detectable. For 50 kv electrons, the optimum average thickness of a replica lies between S and 10 /xg/cm^. This is 7-15 times the minimum perceptible thickness 802 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 difference, a rule applicable for electrons of any energy. The local thickness of the replica varies from a fraction of to several times its average thickness, and a repHca of near optimum thickness provides a range of 20-40 detectably different shades of contrast. Although for special purposes a replica film may be made thinner or thicker, usually the average thickness should be selected in the optimum range. The resolution is then determined by its density, or more precisely, by its electron scattering power. Because the denser materials are composed of elements of higher atomic number which are more efficient scatters, scattering powerf tends to increase rather faster than density, but the difference is not sufficiently great to invahdate for Table I Resolutions of Replica Films 10 ij.s:/cm^ Film Material Density Z Resolution Plastic 1 1000 A 500 A* Silicon 2.4 416 208 Silica (Silicon Monoxide) 2.5 400 200 Aluminum 2.7 370 165 Aluminum oxide 3.7 270 135 Germanium 5.4 185 92 Chromium 6.9 144 72 Gold 50%**, Manganin 50% 14 72 36 Gold 67%**, Manganin 33% 16 62 31 Uranium 18.7 50 25*** Gold 19.3 50 25 Platinum 21.5 44 22 * Included for comparison only, ** By volume. *** On exposure to air, U oxidizes. the present purposes the assumption that the two are proportional. The existence of an optimum average mass thickness then implies that intrinsic resolution of replica films is inversely proportional to the density of the material of which they are composed. Table I presents a comparison of the resolutions associated with various materials, based on the assumption that the resolution is Yte. As discussed above, this is about the best observable resolution, for favorable topo- graphic features. The resolution of plastic films is not susceptible to calcula- tion, and is probably greater than indicated. The resolutions of evaporated films decrease from about 200 A for silicon and silica to about 25 A for the very heavy metals. However, it is difficult to process the exceedingly thin films of these metals particularly if they recrystallize as does gold. Although t Ref. 1, Chap. 19 and p. 158. See also C. E. Hall, Jl App. Phys. 22, 658, 1951. INORGANIC REPLICATION IN ELECTRON MICROSCOPY 803 gold-manganin films are only slightly thicker, they are not particularly difficult to process, especially if 500-mesh supporting screen is used. 2.2 Granularity Resolution is also affected by the short-range migration which culminates in recrystalhzation of many metallic films.^^- ^^' ^^' ^^ If the crystaUite size is smaller than the resolution, i.e. less than J/e, this effect is not too important, even though the granularity may be objectionable at high magnification from an esthetic viewpoint. A fairly extreme example of recrystalhzation is shown by the aluminimi repHca in Fig. 9. A second source of granularity is due to properties of plastics when plastic molds are used as intermediate replicas. Because plastic molecules are large, and because they associate into domains,^^ the plastic surface is actually granular on a scale of the order of 100 A. Plastic granularity is not observed in siKca replicas because of insufficient resolution, but it becomes very evident in shadow-cast repHcas on account of the near-glancing inci- dence of the shadowing material.^^- ^^ The occurrence of granularity due to this cause in replica films of denser materials is an indication of their good resolution. Since this granularity is real on the plastic surface, it shows clearly the azimuth of the incident atom beam, whereas granularity due to recrystalhzation shows no directional effect. 3. Experimental Observations The foregoing material presents a rather idealized picture of the process of replica film formation by condensation of inorganic substances evaporated under good vacuum, i.e. at pressures preferably less than 10~^ mm, and certainly not greater than lO"'' mm of mercury. Subsequent to film forma- tion in the vacuum, it must be subjected to gross physical and chemical processing to prepare it for electron microscopic examination. It must be exposed to air, which may cause oxidation. Uranium films, for example, appear to oxidize completely, and it is beheved that SiO films oxidize to Si02. Most metal films yield good electron diffraction patterns characteristic of the metal, although this does not preclude the possibihty of surface oxidation, since the oxides are usually amorphous and diffuse rings due to thin oxide layers would be difficult to detect. Then the films must be sepa- ls R. G. Picard and O. S. Duffendack, //. App. Phys., 14, 291 (1943). 12 H. A. Stahl. //. App. Phvs., 20, 1, (1949). 13 H. Levinstein, Jl. App. Phys., 20, 306 (1949). 14 R. S. Sennett and G. D. Scott, //. Opt. Soc. Am., 40, 203 (1950). 15 C. C. Hsiao and J. A. Sauer, //. App. Phys., 21, 1070 (1950). i« R. C. Williams and R. C. Backus, Jl. App. Phys., 20, 98 (1949). 1^ Metallurg:ical Applications of the Electron Microscope, p. 11, Symp. of Inst, of Met., November 1949. 804 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 rated from the surface replicated, usually by dissolution of the latter. This process subjects the film to considerable strain. Finally it must be removed from the solvent, usually on a piece of 200-mesh screen, rinsed at least once, and finally allowed to dry. It is not surprising that films sometimes Fig. 3 — Silica replica of particles and associated shadows, da = 60". Diffusing component replicates particles within shadows. Oval hole shows presence of film in shadow. Black lines = 1 At. exhibit cracks and holes. Stereoscopic examination of good replicas show that despite all the processing violence, a faithful picture of surface to- pography is obtained, at least for features up to a few microns in size. The nature of silica condensation is indicated by the micrographs of Fig. 3, of a silica replica of particles of an alkaline earth carbonate. These were dispersed on a plastic-coated microscope slide, and silica evaporated at INORGANIC REPLICATION IN ELECTRON MICROSCOPY 805 da = 60°. The plastic film was then ''floated off" on water and picked up on 200-mesh screen; the plastic and particles were successively dissolved, leaving the siHca replica.f The micrographs clearly show (a) shadow-edges and (b) a fihn in the shadows. The enlargement shows a shadow within which there exists a hole in the film and replication of completely shadowed particles by the diffusing component. It follows from (a) that a part of the incident material must stick where it strikes, and from (b) that a part must diffuse into the shadows, somewhat in the manner diagrammatically illustrated in Fig. 4. Densitometer traces through shadow edges show that the film thins down a little as the edge is approached from the unshadowed region, drops more or less abruptly at the edge, and continues to thin down within the shadow^ as illustrated. Now the diffusing part must finally con- diffusing SHADOW EDGE ORIGINAL SURFACE Fig. 4 — Diagram illustrating diffusion of silica into shadowed regions. dense, and it is natural to assume that at each collision with the surface the probabihty of sticking is a, and of diffusing is (1 — a), and that the average molecule travels between collisions a small distance. Analysis of densitometer curves on these assumptions leads to a value of a of about J, and a range of about ^ /x, with a rather wide spread of values. ^^ However, these assumptions would require the film to be vanishingly thin at distances more than 3 ju from the shadow-edge. In fact, an extremely thin film is found at even greater distances. The probability of sticking upon collision, and the distance a molecule moves as a two-dimensional gas molecule between colhsions with the surface, thus must be assumed to depend on such factors as angle of impingement, energy of molecule, and perhaps the nature of the surface. This latter initially is a plastic, probably covered t In particle study, a second evaporation of silica 180° in azimuth from the first pro- duces a "thin-shell" replica more suitable for stereoscopic study of the particles. 18 C. J. Calbick, //. App. P/tys., 19, 119 (1948). 806 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 with adsorbed gas, and later during the deposition is freshly condensed silica. Films are also found in shadows of replicas made of other materials such as silicon monoxide, germanium, gold-manganin, and even chromium. Whether the interpretation should always be the same as for silica, or whether in some cases the diffusing component is different from the sticking component, is uncertain. A high degree of contrast is commonly attributed to siUca replicas, which are supposedly deposited at near-normal incidence. In the writer's experi- ence, distortion of the conical-tungsten-basket siUca evaporator often re- sults in values of Ba greater than 10°. If normal incidence, characterized by absence of shadows, is actually attained, the resulting repHca exhibits Fig. 5 — Silica replica of natural surface of thermistor flake heated to 1425 °C. Note difference in contrast between the two pictures of the stereogram. poor contrast unless steep slopes are present. An example is shown in Fig. 5, in which difference in contrast due to the fact that da differs for the two pictures of the pair by approximately 8°, the stereoscopic angle, is evident. Note that the shadow in the surface feature in the center of the grain at the right is more pronounced in the left-hand picture which shows the greater contrast. The replica is from the surface of a thermistor flake, sintered briefly at 1425°C. Figure 6 is from a silica replica about 400 A thick, of a portion of the surface of a thermistor disk sintered 6 hrs. at 1175°C. The white line is 0.1 /i long. The striations show a minimum separation of about 250 A, and the character of the shading indicates that this is near the limit of resolu- tion of the micrograph, about 200 A (Table I). Higher resolutions claimed^- ^ are probably due either to shadow effects, to special situations on the sides of steep slopes, or perhaps to the use of extremely thin replicas. INORGANIC REPLICATION IN ELECTRON MICROSCOPY 807 The natural surfaces of sintered thermistor flakes, prepared by heating in air thin (10 ju) sheets of a mixture of NiO and Mn^Os powders, exhibit well defined planes of sizes suitable for electron micrographic study.'^ Flakes sintered briefly at 1175°C were selected as suitable objects for experimental study of replication. They were molded into the surface of Incite blocks at 150-160°C and 2500 Ib/in^. They were then dissolved in HC1,§ and replica Fig. 6 — A striated region on the surface of a thermistor disk. White line = 0.1 yu. Striations are near the limit of resolution of the silica replica, which is about 400A thick. fihns deposited on the plastic molds at pressures not greater than lO""* mm (usually about 2 X 10~^ mm). The replica surface was then scored into small (about 1.5 mm) squares and immersed in ethyl bromide.^f In a few minutes the repHca films drift free and are then ''fished" from the solvent 19 H. Christensen and C. J. Calbick, Phys.Rev., 74, 1219 (1948). § A one-step process was precluded because some of the replicating materials are soluble in HCl. ^ Ethyl bromide is not a good solvent for lucite, while chloroform is. Extended tests have produced better results when a poor solvent, which perhaps frees the replica by creeping between it and the plastic mold without appreciable dissolution, is used. 808 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 on pieces of 200- or 500-mesh screen. After drying, the screen is immersed in chloroform to remove the last traces of plastic, and is then ready for electron microscope use. The electron micrographs of Figs. 7-11 are presented as stereoscopic pairs and enlargements of selected areas, the scale being given by dark lines of 1 At length. Figure 7 is a micrograph from a chromium replica^" for which Fig. 7 — Chromium replica Qe = lOOA, da = 30**) of surface of a thermistor flake. Resolution about 50A. Granularity is due to plastic mold. ie = 100 A, da = vSO°. The shadows show that the azimuth of incidence was to the right at about vSO° above the horizontal. The granularity evident in the enlargement shows evidence of this direction, and may be ascribed to plastic granularity, except for a few of the larger hills or pits which are *« J. Ames, T. L. Cottrell and A. M. D. Sampson, Trans. Far. Soc. 46, 938 (1950). This paper, which appeared while the present paper was in preparation, exhibits micro- graphs of chromium and other metallic replicas of surfaces of crystals grown from solu- tion. The characteristic surface structures reported are in some ways similar to those of the sintered thermistor flakes here shown. INORGANIC REPLICATION IN ELECTRON MICROSCOPY 809 probably due to features of the original surface. Resolution ranges upward from about 50 A. The detection of films in shadows is difficult when these films are so thin as to approach the minimum perceptible thickness difference. The film may- be flawless and present, or ruptured during processing and completely eliminated, and the difference between these two conditions is difficult to Fig. 8 — Chromium replica (h = 150A, da = 30°) produced by two evaporations differ- ing in azimuth by 90°. Region within the circle shows partial shadows. discern. Only when structure or edges due to partial rupture appear is it easily detectable. Some shadows in the rephca from which Fig. 7 was made showed such a fikn, which was estimated to be less than 10 A in thickness, but in most of the shadows no evidence of a film could be seen. A chromium replica produced by two evaporations, from azimuths 90° apart, was the subject of the micrograph of Fig. 8. This repHca was not washed in chloroform, which accounts for the presence of the residual plastic rings. This particular micrograph was selected to show the partial 810 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 shadowing effect shown clearly in the enlargement, but is not suitable for determination of resolution or exhibition of plastic granularity on account of the slightly imperfect focus, noticeable in the enlargement. Because the replica was about 150 A thick, this granularity was scarcely evident even in a perfectly focused micrograph, from which the resolution was estimated as ranging upward from about 100 A. It should be observed that the direction Fig. 9— Aluminum replica (te = 180A, da = 30°) showing granularity due to recrystal- lization. Local curling of replica has jesulted in "negative shadows" in upper left region of stereogram. Resolution about lOOA. of maximum contrast in shading is as if a single source were toward the lower right, about midway between the two actual sources whose azimuths can be determined in the stereogram. The appearance of a micrograph of a replica which has undergone re- crystallization on a scale comparable to h is shown in Fig. 9. The replica was of aluminum; h was about 180 A, the lower limit of the optimum range; da was 30°. The non-directional character of the granularity is evident. The micrograph selected shows an area near a torn edge which has curled up- INORGANIC REPLICATION IN ELECTRON MICROSCOPY 811 ward, thus tilting the repHca to various angles. In the extreme upper left, this tilt produces negative shadows, regions where the electrons pass through three thicknesses of replica. In none of the more usual positive shadows observed in other parts of the rephca was any film observed, or in a replica twice as thick also studied. The conclusion is that aluminum does not diffuse. It is tempting to speculate that the short-range forces responsible Fig. 10— Gold-manganin replica (ie = 150A, da = 20°). Resolution about lOOA. Rep- lica is much thicker than optimum. A film in the shadow, clearly evident in the original micrograph, does not show except for two whitish areas where it has torn and curled. for recrystallization do not permit diffusion and, that when diffusion does occur with materials such as chromium, it is due to some other component such as an oxide. Resolution, although compHcated by the granular structure, appears to be about 100 A. The micrograph of Fig. 10 is from a gold-manganin replica, produced by simultaneous evaporation of two volumes of gold and one of manganin (alloy, 84% Cu, 12% Mn, 4% Ni) at da = 20°. The total thickness was about 150 A, so mass thickness, about 24 Aig/cm^, was much greater than the 812 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 optimum. Crystallite size is probably less than 50 A. As in Fig. 10, the granu- larity is probably due to plastic. A thin, torn film appears in the shadow. From the extreme sharpness of a portion of one edge of the shadow, al- though slightly complicated by granularity, one concludes that instrumental resolution is better than 50 A. Replica resolution is about 100 A. Despite the smaller value of da, the thick replica provides a greater range of tone Fig. 11 — Composite replica of Al, Mg/cm^. Resolution about lOOA. Pt, Cr.^a = 30°. Mass thickness probably 10-12 values, as compared with Fig. 7, although this may not be evident in the reproductions. Figure 11 shows a micrograph from a composite replica of aluminum, platinum, and chromium. Aluminum and platinum were simultaneously evaporated from a tungsten wire which burned out before the evaporation was complete. If all the aluminum evaporated before the platinum, its thickness was about 50 A. The amount of Pt is problematical, but the chromium, evaporated after the tungsten wire was replaced, had a thickness of about 100 A. The same angle, Ba — 30°, was used in the two evaporations. INORGANIC REPLICATION IN ELECTRON MICROSCOPY 813 The granularity barely discernible in the enlargement, which again shows a slight imperfection in focusing, is attributable to plastic. Resolution is perhaps 100 A. Metallic film replicas could easily be used to replicate surfaces in sealed- off tubes. For example, chromium can be plated on a tungsten wire which is suitably mounted in the tube, and thoroughly outgassed during pumping, the surface to be replicated being shielded from the Cr source during the process. Later it is evaporated to form the repHca. As an illustration, Fig. 12 is from a Cr repHca of the activated surface of an oxide-coated cathode. It was actually prepared by evaporation at a pressure of 2 X 10~^ mm and not in a sealed-off tube, but the suggested technique is certainly practicable. No films were observed in shadows in this replica, which was less than '•4 Fig. 12 — Chromium replica (te = lOOA, da = 30°) of surface of an oxide-coated cathode. One-step repUca. Whitish areas are due to impurity in the oxide (probably silica) re- deposited on the replica. 100 A thick with da = 30°. However, the film was very flimsy and exhibited a large number of cracks, usually originating in shadows (e.g., the elongated black area). The film was freed from the surface by dissolving the oxide in dilute acid; since no plastic mold was involved, the fine scale features are characteristic of the oxide surface. The whitish areas (near bottom) are due to some impurity in the oxide redeposited on the rephca, probably silica from the ball-milling process to which the original barium carbonate powder had been subjected. RepHca resolution is perhaps 100 A, although suitable features to test higher resolving power are not present. Shadow edges indi- cate instrumental resolution less than 50 A. In Figs. 13 and 14 the use of germanium as a repHca ting material is il- lustrated. Germanium is easily evaporated from a conical carbon crucible supported and heated by a conical helix of tungsten. As in the case of silica and silicon monoxide, the thickness of the resulting film is only roughly known. For the repHca of Fig. 13, 2 mg of Ge at 8 cm distance, 6a = 30°, 814 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 was used, and ie is estimated to lie between 200 and 300 A. For that of Fig. 14, 1 mg at 8 cm with 6a = 35° was used and h, between 100 and 150 A, is in the optimum thickness range. The micrograph has the appearance of a correctly exposed photographic negative, whereas Fig. 13 resembles an over-exposed negative. Since germanium films are amorphous unless heated to temperatures higher than 300°C, the fine structure is perhaps due to Fig. 13 — Germanium replica (/,. ~ 3(X)A, da = 30°) of thermistor flake surface. Reso- lution about 150A. Over-exposed appearance shows replica is thicker than optimum. plastic granularity, although some features are probably real in the ther- mistor flake surface. Resolutions are perhaps 150 A (Fig. 13) and 75 A (Fig. 14). A film clearly appears in the shadow in Fig. 14. Germanium shadow films are relatively thinner than silica, indicating that a is greater than 0.5 (perhaps 0.7 to 0.8), but thicker than chromium or gold-manganin shadow films. Germanium has many advantages as a replicating material. It is easily INORGANIC REPLICATION IN ELECTRON MICROSCOPY 815 evaporated; the films are substantially amorphous; they are fully as rugged as silica films in processing and, in contrast to silica films, are easily seen during the "fishing" part of this procedure. Because they are conducting and do not tend to charge up in the microscope, germanium films are more stable than sihca. Finally, and most important, because germanium is ^ Fig. 14 — Germanium replica (h ~ 150A, da = 35°) of near optimum thickness. Resolu- tion about 75A. Ruptured film evident in shadow. twice as dense as siHca, the intrinsic resolution (Table I) is better by a factor of two. Many of these remarks apply also to chromium and gold-manganin replicas; however, they are not amorphous and are less rugged in processing, even though they are perhaps even more stable in the microscope. Stereo- scopic pairs from germanium replicas are not shown only because it is desired to present the more extensive enlargements of Figs. 13 and 14. 816 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Figure 15 shows electron diffraction patterns obtained from the several replica films, indicating that crystallite size ranges from greater than 100 A for aluminum down to almost amorphous for germanium and amorphous for silica. /■ ALUMINUM GOLD-MANGAHIN CHROMIUM GE, AFTER HEATING GE, AS EVAPORATED SILICA Fig. 15 — Electron dilTraction patterns of evaporated materials, in order of decreasing crystallite size. The aluminum pattern is due to crystallites of about lOOA. The gold- manganin pattern shows at least two sharp rings not due to gold and diffuse bands due to very small crystallites with the structure of gold. The chromium pattern is due to very small crystallites of Cr. The pattern of a germanium replica film after heating in air to 390° shows partial recrystallization, with rings due to quite small crystallites super- posed on the amorphous pattern of the Ge as evaporated. 4. Interpretation of Micrographs of Replicas The electron image pattern due to the repHca is reproduced by the ex- posure of a photographic plate. The complex problems associated with photographic reproduction^^ cannot be discussed here. For a number of reasons, blackening of the plate is not linearly related to repHca film thick- ness. The number of electrons scattered out of the beam* is proportional to thickness only as a first approximation, the blackening vs. exposure curve of the plate is not linear, and there is also a roughly uniform back- ground due to inelastically scattered electrons. At the lower electronic magnifications, field distortion is also a factor affecting local intensity in the electron image. Furthermore, the geometrical relation between the electron beam incident upon the thin mesh-supported film and the atom- beam is usually not known accurately, and indeed may vary locally over the replica in the manner of which Fig. 9 is an extreme example. In con- " W. T. Wintringham, Proc. I. R. E., 38, 1284 (1950). ♦Ref. l,ch. 19orref. 7, p. 541. INORGANIC REPLICATION IN ELECTRON MICROSCOPY 817 sequence of these factors, the precise interpretation of density variations in micrographs is not practicable. Also many replicas contain artifacts, i.e., features in the micrograph not due to the original surface, but introduced somewhere in the processing. RecrystalUzation, plastic granularity, specks of dirt or other foreign material, tears in the replica films, and defects in the photographic emulsion are examples of artifacts. Few micrographs are completely free of these effects. The interpretation of micrographs therefore has as its object not so much a detailed topographical map of the surface, but rather its characteristic features, repeated in many micrographs. For example, the micrographs presented show that sintered NiO-Mn203 flakes develop grains with exten- sive crystallographic planar surfaces but that thick disks develop a striated or hill-and-valley surface structure on individual crystallites. In both cases the structure is very compact, pores between grains being ahnost non- existent. (Incidentally, these materials can be subjected to a heating cycle in which pores are a predominant feature.) Naturally, the greater the range of contrast and the better the resolution, the more surely can characteristic features on an exceedingly fine scale be detected. In general, the method of rephcation which portrays best the characteristic features under study should be selected. Even in the study of a single material, more than one method may be desirable. For example, a porous structure is probably most easily reproduced by a silica replica using the two-step process, on account of the fact that the diffusing component forms films over reentrant regions not exposed directly to the source; but fine surface detail might best be revealed by a germanium or chromium replica using the one-step process. 5. Stereoscopy Electron microscopy has a fundamental advantage in that, because of great depth of focus, stereoscopic study of surfaces at high magnification is possible. This advantage is sometimes indispensable; for example, porous structures result in complex micrograms which can be understood only by stereograms. More generally, stereographic portrayal, by fully delineating surface topography, achieves the chief purpose of microscopy and makes un- necessary the precise interpretation of density variations. However, resolution and contrast are important factors in stereograms.^^ It is obvious that the replica must retain the third dimension; inorganic replicas in general do, but thin film plastic replicas, unless heavily shadow-cast to make them effec- tively inorganic, change under the electron bombardment and draw down to a planar film of variable thickness.^ 22 A. W. Judge, "Stereoscopic Photography," p. 28. 23 C. J. Calbick, //. App. Phys., 19, 1186 (1948). 818 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Many artifacts are also detectable by stereoscopy. Since two pictures of the same field are available, photographic emulsion flaws are readily de- tected. The three-dimensional view also helps to identify many other arti- facts, such as foreign material present on the replica or local wrinkling of the replica film. Unfortunately, half-tone reproductions are not suitable for stereograms, because half-tone detail is objectionably enlarged by the viewing stereo- scope. Despite this, some idea of the value of stereograms may be obtained from the figures. Conclusions A unified picture of replication by evaporated films has been presented. Thin-film replicas may be made by any material which can be evaporated in vactw and whose physical and chemical properties are suitable. For good contrast, a considerable angle should separate the directions of incidence of atom- and electron-beams. The intrinsic resolution of the replica is about half the film thickness and is therefore inversely proportional to the density of the repHcating material. Multiple point sources and sources of extended area are equivalent from a shading standpoint to a single point source properly placed. The oxides SiO and Si02, and presumably many others, form amorphous films, whereas the metals tend to recrystaUize although the crystallite size may be less than 50 A for some metals. Germanium, a semi-metal, forms an amorphous film. Although not dense compared to the heavy metals, it is more than twice as dense as Si02, and should be valuable as a replicating material because it combines electrical conductivity and high resolving power in an amorphous fihn and is chemically rather inert. Among the metals, chromium appears to be the most generally useful repU- cating material. Gold-manganin has sufficiently small crystallite size for many purposes, and is very easy to evaporate. The platinum group suffers from the disadvantage of being very difficult to evaporate. Finally, all inorganic repUca films studied retain the third dimension. Electron stereo-micrograms may be used to reveal three-dimensional topog- raphy, largely eliminating the need for correlation of photographic density variations with the surface structure. APPENDIX I CONTRAST IN REPLICA FILMS (a) Local Thickness When Every Atom Sticks Where It Strikes. Referring to Fig. 1, it is evident that: /f == /a r-= = U cos 6a (1 -\- tan da cos f^ s n 1 1 1 1 1 1 1 M 75° 75" 60° 45° 30° 15° 0° 15° 30° 45° 60° e. COLATITUDE OF LOCAL SURFACE NORMAL Fig. 16 — Contrast-determining curves. (1) Qa =30", every atom sticks where it strikes. (2) ea = 0**, half the atoms diffuse. (3) Q^ = 30°, half the atoms diffuse. (4) B^ = 0**, all atoms diffuse over surface. duce detectable differences in shading can be displayed. To make the curves more general, relative thickness rather than /, is plotted in Fig. 16 for azi- muth ipa — 0. The four curves are, respectively, for (1) 9„ = 30°, «= 1, (2) 0„ = 0°, « = i, (3) 9, = 30°, « = i (4) e„ = 0°, a = 0. AqIA has been chosen as 0.833. Let us assume that pi, when 0 = 0 is 7 /xg/cm'^. Then a thickness difference of 0.1 on the ordinate scale is barely perceptible. For incidence shading, INORGANIC REPLICATION IN ELECTRON MICROSCOPY 821 curve (1) shows that two adjacent planes differing in colatitude angle by not less than 7° in the azimuth of incidence are detectable. For pure diffu- sion shading,* curve (4) shows that considerably larger differences in angle are required near 6 = 0; moreover, planes differing by large angles but symmetrical with respect to the electron beam yield the same /, and hence, if adjacent, cannot be detected. This difference between diffusion and inci- dence shading is even more pronounced, because curve (4) is independent of azimuth, whereas for curve (1), (1 — te/te,e=o) is proportional to cos 45°), and that incidence at an angle is much to be preferred for general surface portrayal. APPENDIX II RESOLUTION OF REPLICA FILMS a) Incidence Shading Figure 2 (a) shows, for the case of pure incidence shading, the repUca film formed at the intersection of two surfacial planes with normals wi and W2. The distance d over which the thickness changes from te\ to te2 is d = ta sin da. (5) The figure is drawn for the case (p2 = 0, 60°) and are not too far apart in azimuth (^2 ^^ = f/ to obtain a vertical shadow-edge, whose intrinsic resolution would be zero. Actual sources are neither of proper geometry nor of uniform intensity, resulting in shadow- edges such as that of Fig. 17(c). If one takes into account a profile angle 824 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 /8, and if h is so large that p > dj then somewhere along the side of the profile there should be a very sharp length of shadow-edge. In Fig. 3 the sharpest length of shadow-edge is neither at top nor at bottom of the side, but in an intermediate position. In repUcas other than those of particles which are dispersed on flat sub- strate surfaces, the topography of the surface in the shadow region is usu- ally not planar. In general the form of the shadow-edge is a compHcated function of n, of the finite source, and of the profile casting the shadow. Its intrinsic resolution may vary from large values down to nearly zero. This last fact is important since it implies that the intrinsic resolution of the sharpest portions of shadow-edges may often he assumed to be so small that the observed resolution is that of the microscope itself. These remarks also apply to shadow profiles, for which the special conditions required for extreme sharpness probably occur more frequently than for shadow-edges. d) Total Resolution The intrinsic resolution of the film is only part of the total resolution, which includes also the resolution of the electron microscope. This is de- termined theoretically by the wave-length of the electrons (about O.OSA) and the numerical aperture of the microscope (about 0.003) as modified by lens aberrations. The theoretical value of 10 A is seldom attained in practice because of lens imperfections associated with use of the microscope. Prac- tically, microscope resolution usually lies in the range 30-50 A, for the RCA type EMU microscope with which the micrographs were taken. In the X 30,000 enlargements shown, d>^ A becomes 10"^ cm, just the limit of resolution of the eye. In general the resolution of the micrographs is not this good, in part because the intrinsic resolution is larger but also because it is necessary to find suitable fine-scale features to test the resolution. A Gun for Starting Electrons Straight in a Magnetic Field By J. R. PIERCE In a simple electron gun consisting of a cathode and two apertured planes held at different potentials the apertures act as electron lenses. When the gun is immersed in a uniform axial magnetic field the aperture spacings and poten- tials can be chosen so that the emerging electrons have no radial velocities. IN 1931 Davisson and Calbick showed^ that a circular aperture in a con- ducting plate which separates regions with different electric gradients normal to the surfaces acts as an electron lens of focal length F given by F = — (1) Here V is the potential of the plate with respect to the cathode which suppUes the electrons and VJ and Vi are the electric gradients on the far and near sides of the aperture respectively. When an electron beam is produced by means of a plane cathode and an opposed plane positive apertured anode, the fields about the anode aper- ture form a diverging lens and cause the emerging beam to spread. Sometimes this is very undesirable. A strong uniform magnetic field parallel to the direction of electron flow may be used to reduce such spreading of the beam, as well as the spreading caused by space charge and by thermal velocities. The magnetic field does not completely overcome the widening of the beam caused by the lens action of the anode aperture, for the radial veloc- ities which the electrons have on emerging from the aperture cause them to spiral in the magnetic field, and the beam produced is alternately narrow and broad along its length. This paper describes an electron gun consisting of a cathode and two apertured plates together with a uniform axial magnetic field. The gun is designed so that the net lens action is zero and the electrons emerge traveling parallel to the magnetic field. The electrode system is shown in Fig. 1. The electrons travel from the plane cathode to the aperture in plane electrode Ai in parallel lines. At Ai they receive a radial velocity approximately vn, given by Vri = — fr n (2) ^ C. J. Davisson and C. J. Calbick, "Electron Lenses," Phys. Rev., vol. 38, p. 585, Aug. 1931; vol. 42, p. 580, Nov. 1932. 825 S^6 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Here r is the radial position of the electron, Fi is the focal length of the lens at ^1, and Vi is the longitudinal velocity at ^i. CATHODE l«-Lr*'*-— -Lg — J Fig. 1 — The gun consists of a planar cathode and two apertured plane electrodes Ai and Ai , with the spacings and the voltages with respect to cathode which are shown above. ^Ct^N ;.^ ,/ \'-y \ APERTURE V Fig. 2 — Between electrodes Ai and i4a of Fig. 1, an electron path as seen looking paral- lel to the axis is a sector of a circle of angular extent *. The magnetic field strength is so adjusted as to return the electrons to the radius r at v4 2. Figure 2 shows the motion of an outer electron between Ai and Aij seen looking along the axis. Since there is no radial electric field GUN FOR STARTING ELECTRONS STRAIGHT IN MAGNETIC FIELD 827 between Ai and A 2, the electron will move in a circular arc of some radius fm, and at A 2 the radial velocity will be equal and opposite to that at ri; that is, it will be — vn. The change in radial velocity of the electron in passing through the aperture in A 2, Vr2, is Vr2= - ^ V2 (3) P2 where F2 is the focal length of the lens at A 2 and V2 is the longitudinal electron velocity at A2. F2 is made such that Vr2 = Vrl (4) Hence, the radial velocity —Vri of the approaching electrons is overcome in passing through the aperture in A 2 and the electrons move parallel to the axis to the right of A2. For temperature-limited emission and small space charge, we may assume a uniform gradient between the cathode and Ai, and between Ai and A2. Further, we may use the relation V^i = VK/Vi (5) From (l)-(5) we easily find that the required relation between Li, the spac- ing from cathode to Ai, L2, the spacing between Ai and A2, and Vi and F2, the potentials of Ai and A 2 with respect to the cathode, is L2/L1 = (VFV^2 + 1)(F2/Fi - 1) (6) In case of space-charge-Hmited emission, the space charge will cause the gradient to the left of ^1 to be 3 times as great as in the absence of space charge. If space charge is taken into account in this region only, L2/L1 as obtained from (6) should be multiplied by f . We have still to determine the magnetic field required to return the elec- trons leaving ^1 at a radius r to the radius r a,t A2. From Fig. 2 we see that the electrons turn through an angle $. Since the angular velocity of electrons in a magnetic field is (e/m)B, $ = {e/m)B T (7) where r is the transit time between Ai and ^2. As the electron moves between Ai and A 2 with a constant acceleration 2L. 2L2 V2{e/m)V2 (1 + VTV^) (8) 828 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Now, from Fig. 2 we see also that Now so f«sin((?/2) = rsin(7r/2 - 0/2) = r cos{d/2) tan (0/2) = r/fm 0 = 27r - $ tan (tt - (/2)) = r/fr, tan (#/2) = - r/rm (9) For circular motion with, an angular velocity {e/m)B and a circum- ferential speed V = vn = ?;r2, the radius of motion rm is (10) 3.6 -J 5 3.4 :?^3- Tm = Vr2/ie/m)B "" — ^^ U-Z ■ a. ( ) 0 .1 0 2 0 3 0 VOLT 4 0 AGE R 5 0 ATIO, 6 0 .7 0 8 0 9 1. Fig. 3 — The ratio L2/L: of the electrode spacings shown in Fig. 1 should satisfy equa- tion (6). When this is so, the angle f>, measured in radians, is a function of the voltage ratio Fi/F2 , and this function is shown above. From (1), (3), (9) and (10) we obtain (e/m)BL2 tan ($/2) = y^^^^ (1 + Vv,/v,) (1 - Vv^/v,) From (7) and (8) we see that this may be written 4 ta„(*/2)=-(*/2)(j-Z^7==) Fi/Fj = (1 + 4(*/2)/tan(*/2))' (11) We note that $ must lie in the third or fourth quadrant. In Fig. 3, ^ is plotted vs. F1/F2. GUN FOR STARTING ELECTRONS STRAIGHT IN MAGNETIC FIELD 829 We now have both Li/Lx and $ expressed in terms V1/V2, by (6) and (11). From $ and L2 we can obtain the proper value of B from (7) and (8) B = ^/(e/m)T B = ($vlV^2V^?^)(i + \/f7F2) (12) We see from Fig. 3 that there will be little error in assuming that $ = tt. If we assume complete space charge between the cathode and Ai and neglect space charge between Ai and ^2, nothing is altered save the ratio L2/L1', as was explained previously, this becomes f times the value given by (6). In the case of slits L2/L1 is the same function of F2/F1 as for apertures; the correction for space charge is the same, and (12) will give the correct magnetic field with = tt. Electron Streams in a Diode* By FRANK GRAY A general solution of the electron stream equations is developed for a parallel plane diode, under the assumption that the electron velocity is single valued. This solution contains all particular solutions. It serves to unify the wave theory and the particle theory of electron flow, and it is an approximation for multi- velocity streams over a wide range of conditions. Introduction THE theory of an electron stream flowing in a diode has received much attention ;^~^^ because the tetrodes, pentodes and other modern tubes are cascade arrangements of individual diodes. The theory of the diode is the foundation for considering the circuit characteristics and the noise characteristics of these tubes. In earlier days when communication channels were confined to relatively low frequencies, an electron could traverse a diode in a short period of time compared to an oscillation of any electrical signal, and the theory could be developed rather simply from the known d-c equations. But in these days of high and ultra-high frequencies, the situation is quite different. A signal voltage may oscillate several times while an electron is traversing a diode, and the electron stream flows in bunches or waves. The present article is primarily concerned with this more compUcated type of flow. It is confined to the case of parallel plane electrodes, and developed under the usual assumption that the electron velocity is a single valued function of space and time. It is shown to be an approximate solution for physical electron streams over a wide range of conditions. Particular solutions for an electron stream under small signal conditions are given in various published articles. These theories approach the subject in two different manners. In one approach attention is confined to the motions of electrons as individual particles,^"^ and the other approach may best be described as a wave theory of electron streams. But the two lines of approach have not hitherto given identical results, and the disagreement can probably be attributed to neglected factors in the wave theory. The present article considers electron streams without regard to any other than a mathematical approach to the subject. The differential equations are linear in the derivatives, and they should therefore have a general solution that contains all particular solutions. The theory seeks and obtains * The paper was presented at a meeting of the American Physical Society in Columbus, Ohio in 1945. 830 ELECTRON STREAMS IN A DIODE S31 this general solution, f It involves a wave equation, and the results are in exact agreement with the small-signal calculations for the motions of electrons as individual particles. It is therefore believed that the general solution reconciles the two lines of approach to the theory of electron streams. With this solution available, the situation is comparable to that encount- ered in two-dimensional potential theory; assignment of definite functions to two arbitrary functions gives a solution for a particular problem in electron streams, but it is then difficult to determine just what problem has been solved. In the case of small signals the general solution does not greatly shorten the calculations, and it probably should not be regarded as a labor saving tool in comparison to any particular solution when the latter is already known. It is more probable that the broader solution will serve as a guide for general reasonings about electron streams, and as a guide to approximations that can be used in particular problems. 1. The Parallel Plane Diode The diode of this article is shown in Fig. 1. It is two parallel planes indi- cated as (a) and (b), and separated by a distance /. The first plane (a) may be a thermionic cathode that emits electrons, or it may be a grid through which a stream of electrons is injected into the diode. The second plane (b) may be a metallic plate that receives the electrons after they have traversed the diode space, or it may be a grid that permits the electron stream to pass out of the diode. The dimensions of the diode are assumed small compared to the electromagnetic wave-length at any frequency involved, that is, small compared to the velocity of Hght divided by the frequency; and the separation of the planes is assumed small compared to their lateral dimen- sions. Under these conditions the electric intensity is parallel to the x-axis, and the electrons move in that direction only. The electron stream injected through the first plane may vary with time, both in charge density and electron velocity; and the voltages at the two planes may also vary with time. The total current flowing in the diode space is then the sum of two components : a conduction current resulting from the motion of electrons, and a displacement current arising from the time rate of change of electric intensity. The displacement current can flow even when there are no electrons in the diode space; it is then the familiar a-c. current, flowing between two plates of a condenser. But, when electrons are present, the two currents interact with each other and they both flow in a compli- cated manner. t H. W. Konig also demonstrated the existence of a general solution; and he developed the solution for the particular case of a sinusoidal current.^ 832 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 The determining conditions that can be measured in any physical circuit associated with the diode are: the total current, the conduction current at the first plane, and the electron velocity at that plane. Then, for conveniently considering the diode as a circuit element, it has been shown by others^ that we should be able to calculate the conduction current at the second plane, the electron velocity at that plane, and the resultant voltage across the diode. From the viewpoint of circuit theory, these last three quantities may be considered as dependent variables whose solutions should be sought in terms of the initial conditions. But an electron stream flows according to its own nature, with little regard for circuit theory, its fundamental equa- CURRENT FLOW ELECTRON MOTION PLANE , , PLANE [ x-„-> I I I I I I I [<_ z J Fig. I — Parallel plane diode with a first plane (a) and a second plane (b), tions involve electric intensity and electron velocity as the dependent variables, and the general theory must therefore be developed in terms of these naturally occurring quantities. But it should be noted that the desired circuit relations can always be calculated from these fundamental variables. 1.1 Units and Symbols The equations are written in practical electrical units, centimeters, grams and seconds. In this system of units, the permittivity € of a vacuum is 10-^^ ^— — , and the acceleration constant -n of an electron is approximately oox 1.77 '10*^. To conform with circuit convention, the total current and the conduction current are measured in the negative :r-direction, that is, opposite to the motion of the electrons; all other directed quantities are measured in the positive x-direction. ELECTRON STREAMS IN A DIODE 833 The symbols are introduced and defined as needed. The following partial list is included to give the reader a general idea of the symbolism : General Symbols a,b Subscripts referring to the diode planes X Distance from the first plane / Length of diode space t Time T D-c. transit time to x T D-c. transit-time across the diode CO 2ir Frequency p Space-charge density f D-c. space-charge factor € Permittivity of vacuum, ztt— oott ri Acceleration constant of an electron 1.77-10^*. Symbols in Section 2 — The General Solution V Voltage E Electric intensity U Idealized electron velocity Q Conduction current density / Total current density Id D-c. component of / I A Oscillating component of / Idt eE+l I'" S ^ + / ^^^^ Fi{S), FiiS) Arbitrary functions of S A{S), B{S) Finite arbitrary functions of S. Symbols in Section 3 — Small Signal Theory In this section the capital letters V, E, U, Q and / change their meaning and indicate only the d-c. components of their quantities; and the small letters v, e, u, q and i then indicate the ampUtudes of the corresponding a-c. components. This section also uses the following special symbols: A, B Arbitrary constants A* B*. . . .1* Coefficients for the circuit theory of a diode. 834 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Symbols in Section 4 — Physical Electron Streams This section returns to the symboHsm of the general theory; and the capital letters jE, t/, Q and I indicate total quantities. It also uses the following special symbols: V Actual electron velocity U Average of v N Mass density of electrons n Partial density in a range dv P Momentum density of electrons K Kinetic energy density of electrons. 2. The General Solution for an Electron Stream The present theory of electron streams is a solution of two partial dif- ferential equations, in which electron velocity U and electric intensity E appear as the dependent variables. ^- The equation for electron velocity U is based on an idealism that is com- monly used in vacuum tube theory. It assumes that the electron velocity is a single-valued function of space and time or, stated in other words, it assumes that all electrons in any plane normal to the ic-axis have the same velocity. The variable U may then be regarded as a continuous function of X and t, which is everywhere equal to the velocities of the individual elec- trons. The differential equation for U follows at once from the fundamental mechanics of electron motion, which states that for any individual electron where 17 is the acceleration constant of an electron, and the small relativity terms are neglected. Then, since U is regarded as a continuous function of Xy its total derivatives may be written in terms of partial derivatives, and vf + %^-r,E (2) dx dt which is here regarded as the fundamental equation for electron velocity. It is of course based on an idealizing assumption that imposes limitations on the general theory, and these limitations are discussed in a concluding section of the article, where it is shown that the idealized velocity is an ap- proximation for the average velocity in physical electron streams. The differential equation for the electric intensity E is given by the theory of electromagnetism. It follows from this fundamental theory that ELECTRON STREAMS IN A DIODE 835 the total current density / flowing in the diode is a function of time alone; it has the same value at all planes along the ic-axis, and is given by /=-pi;-,g (3) at The first term is the conduction current density, the second term is the displacement current density, and I is measured according to circuit con- ventions in the direction opposite to the motion of the electrons. The charge density p is P=.g (4) and its substitution in (3) gives u'^ + '4=-l (5) dx dt e which is the differential equation for electric intensity. Before passing, it should be noted that the conduction current density Qy measured according to circuit conventions, is Q= -pU = -.U^^ (6) dx The two differential equations for U and E are now repeated as a group I,|^ + f=_,£ (2) dx dt U^ + ^=-l (5) dx dt € and in this group the total current density / may be regarded as any known or arbitrarily assigned function of time. These are the basic equations whose solution is sought in the present theory of electron streams. They are a de- scription of the whole diode space, and they tell how U and E occur and vary with time throughout that whole space. They are first order equations, linear in their derivatives, and it is known from the theory of differential equations that their general solution is the complete solution, and that it will contain two arbitrary functions. So if we find a solution containing two arbitrary functions, we may be quite sure that it is the complete solution. The equations can be solved by the Lagrange method, as outlined in Ap- pendix I. But that is a rather abstract operation, and the solution is here obtained by another method that has more physical meaning and is really equivalent to the Lagrange method. 836 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 For any individual electron, (2) and (5) may be written in the form of total differential equations (7) and (8) where for that individual electron at and X is the coordinate of the electron. This group of total differential equa' tions describes U and E only in the immediate vicinity of the one moving electron, and it is therefore a restricted picture in comparison to the one given by the original partial differential equations. It should, however, be clearly understood that we are not seeking the solution of this group of total differential equations; we are merely using them as aids for solving the original equations. Equation (8) may be written in the form f^[e£+//i.] = 0 (10) the bracketed term is regarded as a new variable 5, that is, S = eE + j I dt (11) and (10) says that S is an invariant for any individual electron, it remains constant as the electron moves along. The solution of (10) is S = Ci (12) where Ci is any arbitrary constant. Turning now to (7) it may be written in the form §--![-/'-] (13) and its solution for any particular electron — remembering that S is an in- variant for that electron — is U = C2 --Isi - jj I dtl (14) ELECTRON STREAMS IN A DIODE 837 where C2 is an arbitrary constant. [In repeated integrations with respect to time, the increment dt is written only once, it being understood that dt is repeated in each integration.] Now any arbitrary function Fi of 5 is a constant for the particular electron under consideration, so we may replace C2 by Fi{S) and write U = Fr{S) -}\^^ - jl I ^M U5) , (9) may now be written in th For the same electron, (9) may now be written in the form dx dt and its solution is x = C, + F^{S)I - ; [§ - llfldtj (17) where Cz is an arbitrary constant that may again be replaced by an arbi- trary function F2 of 5, and X = F, (5) + Fi {S)t - ^ [f - /// I dl'j (18) By considering one individual electron we have thus arrived at two gen- eral relations (15) and (18) which, taken together, describe U and E as functions of x and t. Now the reader will probably be much surprised, as was the writer, to learn that these two equations when standing alone are not solutions of the group of total differential equations (7), (8) and (9). The solution of that group is (12), (15) and (18). In other words, the two general relations are solutions of the total differential equations only in the very special case of S equal to a constant. But this constant may have any value, and the general relations therefore apply to all electrons in the diode space. We are therefore practically forced to the conclusion that (15) and (18) are the solution of the broader group of partial differential equations (2) and (5), and this turns out to be true. This solution, which is here rewritten, U = F,{S) --\s^- 11 ^ ^^1 (15) X = F,(S) + F,{S)t - - [f - /// I dt'] (18) S = eE + j Idi 838 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 moreover contains two arbitrary functions, and it is therefore the general and complete solution for an idealized stream flowing in a diode. As the solution stands, / is an arbitrary function of time, and Fi{S) and F2{S) are perfectly arbitrary. They correspond to all possible determining conditions: to all the d-c, a-c. and transient conditions that are possible in the idealized diode, and to all the purely mathematical conditions that cannot be realized in any physical sense. With this complete solution available, the situation is analogous in many respects to that encountered in the solution of potential problems in two- dimensional space. We can find a particular solution by merely assigning definite functions to the three arbitrary functions /(/), Fi{S) and ^2(6*); but we then encounter the difficult task of finding out just what problem has been solved. As a simple example of the general method, the reader may be interested in arbitrarily setting 7, Fi{S) and F2{S) equal to zero. He will then find that the resulting expressions, (15) and (18), are actual solutions of the partial differential equations, and that they represent a transient electron stream that can flow for a short period of time in a diode space. 2.1 The General Solution in the Presence of a Direct Current In the majority of circuits that are of practical interest, there is a continu" ous direct current flowing in a diode, and the arbitrary functions then as" sume a more restricted form. In such cases the total current density / may be considered as the sum of a d-c. component, which for the time being is indicated as Id, and a transient or alternating component Ia- Then we have the condition that Id>0 (19) and also the condition that U and x must be finite in any physical tube' Now consider (15) for U and note that f I dt = lDt+ f Ia di (20) jjlH^I^ + jjl^i, The bracketed factor in (15) thus contains power terms in /, which becomes infinite as / approaches infinity. The function Fi{S) must therefore be of such form that it cancels these terms and causes U to remain finite. Inspec- tion shows that Fi(5) must consequently be of the form F,{S) ^ A(S) + g + g,S-\- g^ (21) ELECTRON STREAMS IN A DIODE 839 where A (5) is an arbitrary finite function of S, g is an arbitrary constant, and the coefficients gi and g2 have such values that the power terms in / cancel out in (15). The finite function may, for example, be a sinusoidal function of 5, or a series of such sinusoidal terms. The values of the coefi&- cients are easily calculated, and when the resultant expression forFi(5) is substituted in (15), it may be written: U=, + A^S)+l[g.^+IJl.dt] (22) where 5 is 5 with the Id term omitted, that is, S = eE^ j I^dt (23) £n a similar manner it may be shown that, for x to be finite, (18) assumes the form X = k + B{S) - '-^ *-?[£-///"'] « where k is an arbitrary constant, and B(S) is any arbitrary finite function of S. Then (22) and (24) constitute the general solution when a continuous direct current is flowing in the diode. They are mathematical means for shortening the calculations in the presence of the direct current. It is believed that the general solution presented in this section will serve as a guide for reasoning about electron streams, and as a guide that can be used in particular problems. It should also be an aid for considering the large signal theory of electron streams. But it is here advisable to confine attention to a less ambitious program, and apply the method to the case of small signals. The results will not be entirely new, but they will bring out certain important features of the general solution. 3. The Small Signal Theory oe Electron Streams The small signal theory is developed as follows : The value of each depend- ent variable, in any plane normal to the rc-axis, is regarded as the sum of two components: a value that does not vary with time and is therefore called the d-c. component, and a value that does vary with time and is called the a-c. component. All of these components may vary with x, that is, with the exception of the total current density which is a function of time alone. Corresponding to small signal circuit theory, it is also assumed that the a-c. quantities are small compared to the d-c. quantities, and that the squares and products of the a-c. quantities are negligible in comparison to their first order values. For such signals the circuit equivalent of a diode 840 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 is completely determined by its performance at single frequencies, and this permits the solution to be developed in terms of simple sinusoidal functions of time. New symbols are needed for the small signal theory, and to avoid an undue number of subscripts they are introduced in the following manner : In the preceding general equations the dependent variables were indicated by capital letters; in the following small signal theory, the same capital letters are used to indicate the d-c. components, and the corresponding small letters then indicate the complex ampHtudes of the a-c. components. This gives the following list of symbols : Amplitude of AC mponent Total current density Conduction current density Voltage Electric intensity Electron velocity This symbolism has the disadvantage of using e to indicate both electric intensity and the base of the natural logarithms, but the duplication causes no serious confusion, for the meaning of the symbol is always evident from the text. As examples of the new nomenclature, the conduction current density is now Q + ^e^"*, and the electron velocity is Z7 + ue"^ . It should be noted that the a-c. amplitude in each of these expressions is a complex space-varying amplitude, which is sometimes called the space part of the a-c. component. Before passing it is well to write the following useful relations, which follow immediately from the fundamental equations (5) and (6) : 9 = ^ + ^coee (25) e — ceo their substitution in (11) and (23) give S ^ ^E^Ii-^S e^"* 5 = e£ - ^^ e^"' (26) With this introduction to the change in symbolism, we now express the general solution (22) and (24) in terms of the new symbols, and neglect all ELECTRON STREAMS IN A DIODE 841 second order terms in the oscillating components. Each part of the general solution then separates into two equations, one for the d-c. quantities, and another for the a-c. quantities. The resulting equations for the d-c. com- ponents are f-j+Sf (27) and the equations for the a-c. components are ue'"' = ^(5) - ^ [^ ? + -i] e"" (29) 0 = B{S) - '-^ A{S) + i[-J q+ £-3 »] e'"' (30) where in the last equation g has been replaced by its value from (27). 3.1 The D-c. Components of the Electron Stream We first consider the d-c. components in (27) and (28). It is easily shown that they obey the primitive differential equations dx (31) f/ 1^ = -/A dx which are the static equations for a diode, when it is idling in the absence of an a-c. signal. Their solutions are given in various pubHshed articles, and they are available without further calculations.'^- ^ These d-c. components are involved in the subsequent development of the a-c. theory, and the latter requires certain d-c. relations. These relations are briefly presented without derivations as follows: The current density / and the d-c. voltages at the two diode planes are assumed to be known quantities. Then the d-c. velocities at those planes are also known quantities, because their values are given by the simple relations Ua = VWa , Ub = V2v^b (32) where it is assumed that the original source of electrons is at zero voltage. The d-c. transit time plays an important role in the small signal theory. 842 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 The transit time r from the first plane to any coordinate x is and The total transit time T across the diode space also plays an important role; it is usually expressed in terms of a so-called space charge factor f, whose value is given by^ (■ - 0 tk Here / is the actual d-c. current; and Im is the maximum current that could be projected across the diode when its planes are at the voltages Va and Vb, that is, Im is the space charge Hmited current ^3 r = ^ , /2 (VVa + VVl>y " 9 y 77" p Then the total transit time T is given by 21 T = {i-Q[u.+ u.) (36) (37) It also follows that I can be expressed in the form / = % {Ua + U,) (38) Certain equations for the d-c. electric intensity are also required. They are rjl 2€ £» = ^ (f/a - i/6) - J They complete the list of d-c. relations required in the following small signal theory. electron streams in a diode 843 3.2 The A-c. Components of the Electron Stream We now return to the a-c. equations for the electron stream, (29) and (30). In (29), the arbitrary function AiS) must obviously involve an ex- ponential function oijcot, and it must therefore be of the form A{S) = Ae^-^ (40) where A is an arbitrary constant. Then the substitution of (26) gives A{S) =A exp. [y« (/ + f^) + I e'"'] (41) The term in q/I is a second-order term that may be neglected, and -=- can be replaced by its value from (39) that is, ^ = '-^-r (42) where r is the d-c. transit time to any coordinate x. The resultant exponential factor in -y- can then be included in the arbitrary constant A, and this gives A{S) = Ae''''^'-'^ (43) The substitution of this function in (29) now gives the following relation for the amplitudes of the a-c. components « = ^,--_M5_JLi (44) The arbitrary function B{S) may be treated in a similar manner, and (30) then gives the complex amplitude of the conduction current density ,=i^(.-.f^).-_^^, (45) where B is another arbitrary constant. The substitution of this value of q in (25) and (44) also gives the ampli- tudes of electron velocity and electric intensity. = -L[.-.f]e- + i[l+-^] (47) 844 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 The amplitude of the a-c. voltage in the diode space is also required, and it is derived from its expression Jo edx (48) where e has its value (47), and the integration can be performed by remem- dr bering that — is \/U. This gives dx V = Va -\- L \^,AE -A^- jBI^ {e-^^' - 1) (49) We are now in a position to examine the character of the electron stream, and for this purpose we write the conduction current density in its complete form qe^" , that is. qe^'-' ^■§{b-A ^) e-^'-> - -^ t.-' (50) The phase angle of the first term involves the d-c. transit time r, which is a function of x, so this term is a wave traveling in the ic-direction. Its ampli- tude involves the d-c. quantities U and E, and its amplitude varies with x. The velocity of the wave is given by Wave velocity = (j-) (51) and from (34) Wave Velocity = U (52) That is the velocity of the conduction current wave is equal to the d-c. com- ponent of electron velocity. The second term in (50) is an oscillation that has the same phase through- out the diode space, and its amplitude also varies with x. The a-c. conduction current is thus a wave of electric charge traveling at a finite velocity plus an oscillating charge that is in phase over the entire diode space. An inspection of equations (46), (47) and (49) shows that the other a-c. components are of the same general form; each of them is a wave traveling in the rc-direction plus an oscillation that is in phase over the entire diode. This clear-cut disclosure of the dual nature of an electron stream is an im- portant contribution of the general theory. ELECTRON STREAMS IN A DIODE 845 The formal solution for small signals is really completed with the deriva- tion of the preceding general equations for the a-c. amplitudes. But there still remains the rather tedious process of deriving the relations for circuit calculations as outlined in the following section, and they give a direct comparison with previous theories of electron streams. 3.3 Small Signal Equations for Circuit Calculations Llewellyn^ has shown that the treatment of a diode as a circuit element requires certain variables at the second plane to be expressed in terms of their values at the first plane ; that is, the circuit theory requires three equations of the form Vb — Va = AH -\- B*qa + C*Ua qj, = DH + E*qa + F*Ua (53) Ub = G*i + H*qa + I*Ua where the starred coelB&cients are known functions of the d-c. components. The derivation of these relations from the preceding general equations is outUned as follows : the first step is the evaluation of the arbitrary constants A and B. This is done by substituting the values at the first plane in (44) and (45), and then solving for A and B, which gives (54) (55) These expressions, and the values at the second plane, are then substituted in the equations for the a-c. amplitudes (45), (46) and (49); and they im- mediately give the desired relations. They do, however, involve the incon- venient electric intensities Ea and £&, and these quantities are replaced by their values from (39). These simple but rather tedious substitutions are illustrated by the fol- lowing derivation of qb—, which is brief enough to be included for that purpose. The first step is the substitution of the values at the second plane in (45); this gives where j8 isjcoT. It is now advantageous to replace B by its value from (55), and ,. = >e {^) Ae-^ + ^; e-V + J,^ (e^ - l)i (57) A = Ua +'S-'- + i' B = I ■-'5 qa -&> 846 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 The inconvenient electric intensities are now easily eliminated by substitu- tions from the d-c. equations (39), which give g,= l^A+^ e-% + -^ (e-^ - l)i (58) Ub Ub ecc^Ub The value of A is now introduced from (54), with Ea again ehminated by (39), and a grouping of terms then gives the final equation This equation gives tlie following values of starred coefficients: D* = -^ (fie-f + «"" - i) (60) 2eUt/ These coefficients may now be rewritten in any desired form; and, to con- form with previous articles on electron streams, we replace co by its equiva- lent expression — ^; and we also express / in terms of the space charge factor r from (38), that is, I-^%{Ua+ Ub) (61) These substitutions then give the coefficients in the form £* = -1 [Ui, - ma + Ui)]e-' (62) ft F* = 2j£ (U. + U.\ . This is obviously a longer mode of expression, but it has two advantages: it is convenient for circuit calculations, and it permits a direct comparison with previous articles on electron streams. The equations for ut and (vb — Va) are obtained by similar substitutions in (46) and (49) ; and the three equations are then written in the symbolic ELECTRON STREAMS IN A DIODE 847 form (53), with the values of the starred coefficients abbreviated and as- sembled as follows: ai = 1 - e~^ - ^e~^ a2 = 1 - c~^ (63) A* = 2e^ az= 2 - 2e~' - ^ - ^e~^ D* 2^ 2^ (C/„ + U,) E* = 4- [Ui - aUa + Ui;)]e-^ (64) '■'UH^)"-' G* = - -^ [(ai - 0:2^) C^6 - ciiUa + «ir(£^a + C/ft)] H* = Ub With the exception of a difference in symbols, these coefficients are iden- tically the same as those obtained by Llewellyn and Peterson^- ^ from cal- culations on the motions of electrons as individual particles, and this cor- respondence apparently reconciles the wave theory and the particle theory of electron streams. The correspondence is largely the result of a new feature in the wave theory, that is, the expression of the electron stream as the sum of two components, a wave traveUing with a finite velocity and an oscillation that is in phase over the entire diode space. Llewellyn and Peterson have derived the circuit equivalents of electronic tubes from the values of the starred coefficients, and these equivalents are well known in the electronic art.* The present section confirms these rela- tions, as derived for an ideaUzed electron stream. The validity of this idealization is considered in the following section. 848 the bell system technical journal, october 1951 4. Physical Electron Streams [This section returns to the symbolism of the general theory; and the capital letters, F, -E, Z7, Q and / now indicate total values.] The preceding general solution for an electron stream is based on ideal- ism, namely, the assumption that the electron velocity is a single-valued function of space and time. The stream then obeys the differential equations (2) and (5), and the theory is a general solution of these fundamental equations. But it is well known that the velocity in a physical electron stream is not single valued :^^^^ Electrons are emitted from their original source with shghtly different velocities; and some electrons acquire energy from the high-frequency electric field and overtake their slower neighbors. These factors cause the velocity to be a multi-valued function of space, and the electrons have various velocities in any plane normal to the axis of the diode. The present section derives the differential equations for a multi- velocity stream, and compares them with the idealized equations (2) and (5). For this purpose, the actual velocity of an electron is indicated as v. It is also convenient to develop the equations in terms of mass, so we let A^ equal the mass density of electrons at any coordinate x. The fractional mass density of electrons with velocities lying in any range from u to u + dv may likewise be expressed as ndv^ where w is a function of u, x and /; and it fol- lows that ■"L +00 ndv. (65) The momentum density P of the electrons is then given by P = / nvdv (66) J— 00 and their kinetic energy density K is K= r^dv (67) J— 00 ^ It also follows that the average electron velocity U is given by U = ? (68) TTiis is the new mechanical variable in the theory of physical electron streams. The differential equation for the electric intensity is now easily derived from the fundamental electromagnetic equation ELECTRON STREAMS IN A DIODE 849 .f -Q= -/ (69) The con 'uction current density Q is Q^-'I^-V'-^^-U^'^ (70) m m dx an(i its substitution in (69) gives OX ot e which is the analogue of (5) . The mechanical equation for the physical stream is obtained from the Liouville theorem. In the diode regions with which we shall be concerned, the individual electrons are so far apart that their microscopic forces are negligible, the electrons flow freely under the action of the macroscopic forces, and they therefore obey the Liouville theorem for particle motion. This theorem states that J = 0 (72) at that is, n remains constant as we travel along with any particular electron. This equation may also be written in terms of partial derivatives of n dn dx ,8ndv, bn _ .^ . Yxdi'^ b'vdt'^ U "^ ^' ^ and the substitution of the values of the total derivatives then gives bn ^bn , bn ^ .^.^ u - - ryE - + r- = 0 (74) ox bv bt The mechanical relations are obtained by integrating this equation with respect to u. It is first multiplied by dv and then integrated as follows: / - vdv - riE r^i^ + / 77 ^^ = ^ (75) , J— 00 ox J-oo tU J—ao ot The second integral reduces to the difference in the values of w at u = +00, and V = — 00 . It vanishes because there are no electrons with infinite velocities. The differential operators may also be moved outside the other integrals, to give nvdv + - / ndv = 0 (76) 00 5/ J— 00 b_ bx 850 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 then from (65) and (66) 8N _ U 8P 8x (77) Equation (74) i? 5 next multiplied by vdv, and ; 1 similar integration gives SP = - 7]NE : - 2 8K (78) With these relations we are now in a position to derive the differential equation for U. This mechanical equation is obtained by first writing the obvious equality Then partial differentiation of the last term gives Sx SI Sx N 51 N^ St and, when the resultant time derivatives are replaced by (77) and (78) jjiU SU _j-SU 2 SK P dP , . the substitution of NU for F then gives the final differential equation for ilj which may be written in the form It is the analogue of equation (2). The two sets of equations are now assembled and written in a form suit- able for comparison. The equations for the idealized stream are ox Ot 6 18U'8U „ . ,.. 2 dx 8t and the analogous equations for the physical stream are 6/6/6 16^ 2 6:*; -it[^-m-'^'-'^ (82) ELECTRON STREAMS IN A DIODE 851 When U is set equal to U, the first equations in the two sets are identical ; and in this respect the theory of the idealized stream corresponds to that of the physical stream. But the second equation for the physical stream then differs from its analogue by the inclusion of an additional term The bracketed quantity in this term is the difference between the actual kinetic energy density and the kinetic energy density calculated as if the electrons were all moving with their average velocity U. It is often a small term that can be neglected, and the physical stream is then approximately described by the idealized equations (2) and (5). It is, however, rather obvious that there are cases in which this approxi- mation cannot be made. It is invalid in the region between a thermionic cathode and its voltage minimum, where the electrons are travehng in both Nm directions along the a:-axis, and cause K and — — to have appreciably dif- ferent values. So, when the first plane of the diode is a space-change-Hmited cathode, the idealized theory can apply only in the region beyond the voltage minimum. This difficulty is usually overcome by considering the virtual cathode as the first plane of the diode. In all other regions the electrons are normally traveling in one direction only, and the idealized equations are then an approximation for the physical stream over a wide range of conditions. The nature of this approximation is seen more clearly by considering the electrons to be uniformly distributed over a velocity range s, where 5 is a function of x and /. Then the mechanical equation (82) is Under the usual conditions encountered in electronic tubes, - is small compared to — , and its gradient may be neglected in comparison to that of g^ 2 • The approximation can also be considered in a more rigorous manner as follows: The velocity spread s may be expressed in electron volts by the relation 852 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 where is the spread measured in electron volts, and V is the voltage in the stream. Then (84) may be written in the form 8V The last term is small compared to rj — and may be neglected, and it fol- ox lows that the idealized theory is an approximation for physical electron streams when it being understood that the inequality holds for the gradients of the d-c. components, and also for the gradients of the a-c. components of and V. This requirement is satisfied over a wide range of conditions, and the ideal- ized equations are applicable in a corresponding manner.* It is thought that these considerations explain why the single-velocity theory of electron streams is so successful in explaining the characteristics of electronic tubes. ^' ^ Conclusion It is believed that the preceding pages serve to unify our theories of elec- tron streams in some such manner as follows: (1) They develop the general solution for a single velocity stream, and this solution contains all particular solutions. (2) The small signal theory is considered in detail as a special case of the general solution, and the a-c. stream is shown to be the sum of two com- ponents: a wave traveling with a finite velocity plus an oscillation that is in phase over the entire diode space. (3) The wave expression gives identically the same results as previous calculations based on the motions of electrons as individual particles. (4) The idealized stream is shown to be an approximation for multi- velocity streams over a wide range of conditions, and this correspondence explains why the single velocity theory is so successful in describing the characteristics of electronic tubes. Acknowledgments The writer wishes to thank F. B. Llewellyn and L. C. Peterson for their assistance in the study of electron streams, and to thank R. K. Potter for his encouragement in writing the article at this time. * It should be noted that this requirement is not satisfied by a velocity-modulated stream of small current density in a long, field-free drift space. ELECTRON STREAMS IN A DIODE 85vS APPENDIX I— THE LAGRANGE SOLUTION Lagrange has shown that any partial differential equation of the first order, linear in its derivatives, is equivalent to a group of total differential equations. The Lagrange equations corresponding to (2) and (5) are (88) (89) (90) Now we can find three independent solutions of this group. One solution is e£ + / Idt = ci (91) The first member of this solution is indicated as 5; then the other solutions dx dt dU U 1 -r,E dx dt edE U ~ 1 ~ -1 or, taken together, dx dt dU edE U 1 -vE -I are U -{- rjSt -1 jj Idt = C2 (92) -^'-f +!['//^*-///H=^' (93) Since each of these quantities is a constant, we may set any one of them equal to an arbitrary function of another, and the resulting equation is also a solution of (90). We can, however, obtain only two independent solutions in this manner, and we naturally choose the two simplest combinations, that is, U ■i-'^t -"^Ij Idt = FiiS) (94) Ut-I^f + I [^ // ^"^^ ~ /// ^"^^1 ^ ^' ^^^ ^^^^ where Fi{S) and F^iS) are arbitrary functions of S. These equations contain two arbitrary functions; they are solutions of the Lagrange equations (88) and (89), and they therefore constitute the general and complete solution of the partial differential equations (2) and (5). With the exception of a slight 854 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 difiference in form, this solution is identically the same as the one given in Section 2. References 1. "Theory of the Internal Action of Thermionic Systems at Moderately High Fre- quencies," W. E. Benham, Phil. Mag., 5, 641, 1928 and 11, 457, 1931. 2. "Electronenschwingungen im Hockvacuum", J. Muller, Hockfreguenztech u. Elec- troakusiik, 41, 156, 1933; and 43, 195, 1934. 3. "Electron Inertia Effects," F. B. Llewellyn, Cambridge University Press, 1941, 4. "Space Charge and Field Waves in an Electron Beam," S. Ramo, Phys. Rev., 56, 276, 1939. 5. "On the Behavior of Electron Currents in Longitudinal Electric Fields," H. W. Konig, Hockfreguenztech u. Electroakuslik, 62, 76, 1943. 6. "Theory of Parallel Plane Diode" A. H. Traub and Nelson Wax, //. Applied Physics, 21, 974, 1950. 7. "On the Theory of Space Charge Between Parallel Plane Electrodes," C. E. Fay, A. L. Samuel and W. Shockley, B.S.TJ., 17, 49, 1938. 8. "Vacuum Tube Networks," F. B. Llewellyn and L. C. Peterson, Proc. I.R.E., 32, 144, 1944. 9. "Space Charge and Transit-Time Effects on Signal and Noise in Microwave Tetrodes," L. C. Peterson, Proc. I.R.E., 35, IKA, 1947. 10. "Theory of Space Charge Effects," P. S. Epstein, Verk. d. Deut. Phys. Ges., 21, 85, 1919, 11. "Thermionic Current between Parallel Plane Electrodes: Velocities of Emission Distributed According to Maxwell's Law," T. C. Fry, Phys. Rev., 17, 441, 1921; and 22, 445, 1923. 12. "The Effect of Space Charge and Initial Velocities on the Potential Distribution and Thermionic Current between Parallel Plane Electrodes," I. Langmuir, Phys. Rev., 21, 419, 1923. 13. "On the Velocity — Dependent Characteristics of High Frequency Tubes," J. K. Knipp, //. Applied Physics, 20, 425, 1949. The Davisson Cathode Ray Television Tube Using Deflection Modulation By A. G. JENSEN The paper describes a cathode ray television receiving tube incorporating sev- eral unique features. The tube was designed and constructed by Dr. C. J. Davis- son and was used in some of the early demonstrations of television transmission over the coaxial cable. THE present day coaxial cable broad-band transmission system was developed during the early 1930's, and was originally conceived as a means for multi-channel telephone transmission. During the same period the rapidly developing television art was producing video signals requiring wider and wider frequency bands. It was very soon realized, therefore, that this coaxial system would also lend itself admirably to the transmission of such wide band television signals. The early development culminated in the installation of a coaxial cable route from New York to Philadelphia. This system was designed to provide 240 telephone channels or a single 800 kc television channel, and both types of transmission were successfully accomplished during a series of demonstrations in 1937.^ The scanning equipment used for producing the television signals for these demonstrations was developed under the direction of Dr. H. E. Ives at the Bell Telephone Laboratories. It was designed to scan standard 35 mm motion picture film and consisted of a six-foot steel disk rotating at 1440 rpm and having 240 lenses mounted around the periphery. It thus produced a television signal of 240 lines and 24 frames per second, occupy- ing a bandwidth of about 800 kilocycles. From this same period came the well known work of Dr. Davisson in tHe field of electron diffraction. ^ This work had resulted also in important advances in electron optics and in the development of the sharply focussed, well defined electron beam. It was natural, therefore, that Dr. Ives should discuss with Dr. Davisson the possibility of designing a cathode ray tube capable of adequately displaying a picture from the television signals speci- fied above. The outcome of these discussions was that Dr. Davisson, with the close and able collaboration of C. J. Calbick, undertook to design and construct the tube described in the following pages. In this connection it should also be mentioned that the first experimental samples of the tube were built by G. E. Reitter, while the later engineering for limited produc- tion was carried out by H. W. Weinhart. 855 856 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 The disk scanner was a linear transmitter, since the ampUtude of the signal was directly proportional to the film brightness. The fundamental requirement for a receiving tube was therefore as stated by Dr. Davisson in an early memorandum: "If screen brightness is proportional to beam current, as for most screens it is, then beam current in the receiving tube should be proportional to sig- nal voltage; the modulations of beam current by signal voltage should be linear. Failure to meet this requirement results in falsification of tone values in reproduction, and when departures from linearity are marked [it leads] to unsatisfactory pictures." s' V M, (a) (b) (c) s' M? M? Ml' Fig. I — Principle of deflection modulation. It was this fundamental concept of a beam current directly proportional to input voltage, which led to the development of a tube employing deflec- tion modulation. This is a type of modulation in which the modulating voltage causes the electron beam to be deflected across a defining aperture in such a manner that increasing modulating voltage will cause a larger area of the beam to pass through the aperture and thus increase the bright- ness of the screen proportionally to the modulating voltage. The principle of this type of modulation is illustrated in Fig. 1. Figure 1(a) shows a narrow beam of electrons passing through the slit S (perpendicular to the plane of the paper) and arranged to form a sharp image of the ^lit in the plane of the square aperture S\ The relation of the slit image to the square aperture is shown in Fig. 1(b). A bias voltage is applied across the modulator plates Mi and Mi so that the slit image falls just off the square aperture for no signal voltage. As signal voltage is ap- plied across the modulator plates the slit image will move across the aper- ture in such a manner that the cross-sectional area of the beam beyond the aperture is proportional to signal voltage (for small angles of deflection, such as used here). DAVISSON CATHODE RAY TELEVISION TUBE 857 Beyond the aperture 5' the electron beam enters a projection lens sys- tem designed to project an enlarged electron image of 5' onto the fluores- cent screen of the tube. In order to avoid further modulation of the beam VERTICALLY DEFLECTING PLATES HORIZONTALLY DEFLECTING o PLATES APERTURE S--^ APERTURE S- M2+0 MODULATING PLATES,, ^ Mi+o- P2"— i:t = APERTURE S- P,___, *-oP2±0V OP4-66OOV ±200V -0M2- ■oM,'- ^ Pa -7500 V± 200 V ■oCP,CC-200V CC; ^ |U oCP2«* 200V +100V J] |W— ^-<'CP,«^-200V ±100V a^^ with the result that the diffracted beams are removed from the optical system and not focused in the image plane. In Fig. 1, crys- tals 1 and 3 are suitably oriented to diffract and so will appear dark in the final image since electrons have been removed from these regions by Bragg reflection. The calculations of the intensities for this case (the Laue case) were first made by Bethe.^ A similar treatment^ -^ employing the zone theory of crystals can be given which yields the same final results. The procedure consists in solving the Schrodinger equation for an electron moving in the INCIDENT BEAM CONJUGATE FOCAL PLANE POLYCRYSTALLINE FILM OBJECTIVE DIAPHRAGM Fig. 1 — Diffraction of electrons outside objective aperture by suitably oriented crystals in polycrystalline film. Crystals 1 and 3 would appear dark in final image. periodic potential inside the crystal and then fitting the solutions so ob- tained to the plane wave solution found for the vacuum incident and dif- fracted waves. The first result of the solution inside the crystal is that the total energy of the electron, E, is not a continuous function of the wave 27r number K {\ K\ = — ) as it is in field-free space, but exhibits discontinuities A as illustrated in Fig. 2. These discontinuities occur whenever the Bragg or Laue condition is satisfied; i.e., if g is a vector of the reciprocal lattice, then discontinuities in the E ys K curve occur when \K\ = \ K -{- 2Tg\ which is equivalent to the Bragg formula. The magnitude of the energy ^H. A. Bethe, Ann. d. Physik 87, 55 (1928). This treatment was intended to explain the results of Davisson and Germer which were published about a year before. Had Bethe examined the behavior of the total energy in his solution of the Schrodinger equation he would have discovered the band theory of crystals. 870 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 gap^ is A£ = 2 I Kg I where Vg is the Fourier coefficient of potential. The discontinuities in energy are the Brillouin zone boundaries and form a family of polyhedra in reciprocal or K space. For example, a simple square lattice gives rise to a square reciprocal lattice as seen in Fig. 3. One reciprocal lattice point is taken as the origin, 0, and the remainder of the lattice is generated by the vector g where \ g\ = -, the reciprocal of the cell constant of the original, direct lattice. The Brillouin zone boundaries are the per- pendicular bisectors of the reciprocal lattice vectors^ and define the series of zones shown in Fig. 3a. Whenever the incident electron wave vector, K^ AE=2|Vg| ■^K |K| = |K+277-g| Fig. 2 — Plot of energy, E, vs. wave number \K\, along K vector showing discontinuity when \K\ = \K -\- lirg] or when Bragg condition is realized. terminates on a Brillouin zone boundary, a diffracted wave is possible. However, when the boundary conditions at the surfaces of the crystal are apphed, it turns out that for a fixed total energy, jE, there are two incident crystal wave vectors kI and K\ which must be considered. Consequently there are also two diffracted wave vectors KI and KI with kI = kI + lirg and Kg = Ko -\- Irg as shown in Fig. 3b. KI and KI are related by a beat wave vector AK or K], = kI -{- AK. The net result is two waves of slightly different wave length traveling nearly parallel which may undergo inter- ference. This beating of the diffracted waves makes itself known by passing the energy back and forth between the incident and diffracted beams. This is the motivation for the name ''dynamical" theory. The intensity of a diffracted beam for the case when the incident wave vector terminates near a Brillouin zone boundary but far from an edge or corner is found to be^: ' This treatment is the case of loose binding which is applicable for fast electrons. It turns out that for the valence electrons in a crystal, this approximation is not very good and that the value AE - 2\Vg\ is not correct. • L. Brillouin, "Wave Propagation in Periodic Structures," McGraw-Hill Book Com- pany, Inc., New York (1946). ELECTRON TRANSMISSION THROUGH THIN METAL SECTIONS 871 □ 1ST ZONE ^ 2ND ZONE S3RD ZONE BRILLOUIN /ZONE / BOUNDARY AK VACUUM I CRYSTAL I VACUUM (b) Fig. 3 — (a). First three Brillouin zones for a simple square lattice. In an actual case, I K\ \g\ is of the order of 0.5yl~^ and — about 19A~^. \2ir\ (b). Relation among wave vectors in reciprocal space for the kinematic and for the dynamical theories. The wave vectors must satisfy the Bragg condition and the boundary conditions at the crystal faces. The dynamical theory introduces the beat wave vector AK. Kv is the vacuum incident wave vector. h- \Vg[ m sin^ ^AKz + \Vg\' (1) where Vg = Fourier coefficient of potential Ag = deviation from the Laue condition in volts 872 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 = 2E^e sin IBq E = total energy of incident electrons in volts ^0 = Bragg angle A^ = angular deviation from Bragg condition , AK = beat wave vector = r.(' +!•'''■)' z = penetration measured normal to surface of crystal D = thickness of crystal It is evident from equation (1) that the intensity of the diffracted beam is periodic with penetration in the crystal and with the deviation, Ag. This dependence of intensity upon thickness and deviation accounts for most of the image detail seen in electron micrographs of thin crystalline sections. Inelastic scattering and crystal imperfections are neglected in the deriva- tion of equation (1). Experience with thin sections of pure aluminum has indicated that it is nearly impossible to prepare and handle them without introducing some bending or rumpling of the thin area. This bending in conjunction with thickness variations gives rise to the major features of the electron images in the form of intensity maxima and minima called "extinction contours." Those arising through bending of the section are of chief interest in the uni- form area where thickness changes are very gradual. The extinction con- tours are determined by the maxima of equation (1) or where AKD = mr to give As=±((^'-4|Fsry »= 1,3,5,... (2) Equation (2) predicts that for a bent crystal offering a continuous range of Ag a series of intensity maxima or fringes will be observed. In an electron image of a bent crystal the spacing of the fringes is the only quantity which can be measured other than relative intensity. The central fringe corre- sponds to Ag = 0 with subsidiary maxima occurring at a distance s from the central fringe given by^ where R is the radius of curvature of the bending. If two crystallites in a thin section differ only slightly in orientation and the bending is favorable, then a series of fringes will occur in the two crystals with a displacement at the boundary as sketched in Fig. 4. The displacement / is related to the orientation difference Aa and the ELECTRON TRANSMISSION THROUGH THIN METAL SECTIONS 873 radius of curvature R by Aa = -^ (4) If the situation is such that R can be determined from equation (3), then the misorientation Aa can be calculated from (4). This combination of cir- cumstances is at present one of chance and does not occur frequently in images of thin sections. An example will be shown. The image contrast between adjacent regions of a thin metal section com- posed of small misoriented domains as depicted in Fig. 1 is determined by the rocking curve of equation (1). This is simply a plot of the intensity given by (1) against Ag or A^. As an example, a rocking curve for the (200) GRAIN BOUNDARY Fig, 4 — Displacement (/) at a grain boundary of extinction contours due to bending as predicted by equations (3) and (4). reflection of aluminum is shown in Fig. 5. The Fourier coefficient Vg is computed from the relation.* Vm = 300 ^' X) (^y - 0)^'"' (h^i + kvj + Iwj) volts (5) TTU j with e = charge on the electron = 4.80 X 10~^° esu Q = volume of the unit cell = 70.4 A^ for aluminum df.ki = interplanar spacing Zj = atomic number of atom species j fj = atom form factor (uj, Vj, wj) = atomic coordinates of atom species j For aluminum, F(2oo) = 5.13 volts. Using 50KV electrons: £ = 5 X 10'*, X = 0.055A, sin 2^o = 0.0272 radian and a reasonable value oi D = 250A, the intensity can be computed from (1) as a function of Ag as shown in Fig. 5. * Reference 1, Appendix I. 874 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 It will be realized that the detailed shapes and location of the maxima are quite sensitive to thickness and more often than not a calculation from the fringe spacings cannot be made with certainty. The limiting value of the fringe separation is found from (2) to be given by -^ for large values of the integer n. The fringe pattern indicated in Fig. 4 is simply a rocking curve for the crystallites with a displacement due to their difference in orientation. The absence of extinction contours from the electron image of a crystal may indicate that one or more of the following conditions exists: (1) No bending or thickness changes. (2) The thickness is sufl&ciently small that the argument of the sin^ in 0 n = 2 DEVIATION IN DEGREES Fig. 5- electrons. -(200) rocking curve calculated for an aluminum crystal 250-4 thick for 50KV (1) can replace the sine function thus suppressing the periodic fea- tures; this can occur for D less than about lOOA. (3) The crystal is sufficiently distorted that the assumption of a periodic potential function in the Schrodinger equation is not valid. Of these causes for the absence of extinction contours, the first is very unlikely as mentioned previously. The second is quite obvious since a sec- tion too thin to produce contours would give a very high transmitted in- tensity and would be immediately apparent. The third is the most likely reason and is thought to be the case in all the thin sections examined to date. This is particularly important here since crystals that have been sub- jected to plastic deformation are of primary interest. The incorporation of strains or lattice disortion into the potential function for the Schrodinger equation appears to be a formidable task and will not even be attempted. A more or less semi-quantitative approach to the effect of lattice distortion ELECTRON TRANSMISSION THROUGH THIN METAL SECTIONS 875 can be had by considering the expression for the diffracted intensity (equa- tion (1)). If dislocations are introduced into a crystal the effect is that of producing a mosaic or block structure^ the units of which will scatter incoherently. If there are a sufficient number of dislocations to reduce the coherent penetration path z to a value z' such that AiTz' is small, then equa- tion (1) will become (fj The important part in considering equation (6) is the disappearance of the periodic, dynamic term. If the model obtained by introducing dislocations into the crystal even roughly approximates the actual situation then it would be expected from equation (6) that the extinction contours will vanish. Actually, starting with a perfect crystal and adding dislocations, the dynam- ical effects will not be noticeably effected until the coherent penetration %' \P becomes much smaller than — . For 50 KV electrons in aluminum, z' would have to be something of the order of 150A or less before the dynamical effects would disappear. If the model is carried still further, it can be spec- ulated that z' is the mean separation of dislocations in the crystal indicating that a distance of separation of the order of 150 A is required to extinguish the extinction contours. This would correspond to a dislocation density of about 5 X 10" lines/cm^. This is admittedly a very crude approximation and, although the dislocation density is of the right order of magnitude, too much significance should not be attached to it. It does seem fairly safe to conclude that the extinction contours will disappear when the dislocation density reaches a high enough value. This fact in itself greatly broadens the interpretation of the electron micrographs to be presented. Preparation of Thin Aluminum Sections The details of the preparation of the thin sections used for electron mi- croscopy have been published^ and are not vital to the discussion. Suffice it to say that the sections are produced from 0.005" sheet by an electro- poUshing technique using a special holder. The central portion of the metal disc is thinned down to several hundred Angstroms or less while maintain- ing a smooth surface. A rinsing procedure is necessary to prevent the forma- tion of corrosion layers. ^ R. D. Heidenreich and W. Shockley, Report of a Conference on Strength of Solids, p. 57 (Physical Society, London, 1948). 876 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 The metal used in all this work was 99.993% French aluminum rolled into 0.005" sheet. Recovery of Cold Worked Aluminum Having briefly discussed the essential phenomena in interpreting electron images of crystals, the application of the thin section method to self-recovery in deformed aluminum can be demonstrated. This type of investigation is based to a considerable extent upon comparison of images of the metal Fig. 6 — Extinction contours due to rumpling in an annealed high purity (99.993) aluminum section. under various conditions of anneal and plastic deformation. The standard state for comparison is a well annealed specimen in which the crystals are reasonably perfect. The bending or rumpling produces the extinction con- tour patterns quite unique to the annealed condition. The chief charac- teristics of the contours for an annealed crystal are their general continuity and extension over relatively large areas. Figure 6 illustrates a contour pattern with an unusually high density of lines obtained from an aluminum section annealed 30 min. at 335°C. The dark regions are those of electron deficiency. At a grain boundary in an annealed section the contours end abruptly ELECTRON TRANSMISSION THROUGH THIN METAL SECTIONS 877 as seen in Fig. 7a. Figure 7b illustrates a case in which the contour family can be identified on either side of a grain boundary with the displacement very much in evidence at the boundary. This situation was anticipated in Fig. 4. Proof that the dark contour lines seen in Fig. 6 are due to diffraction from those regions was given in reference (1) where both the transmitted and diffracted beams were imaged in an electron shadow microscope. The usual transmission electron diffraction patterns from annealed sections generally exhibit an array of spots characteristic of a single crystal. Sometimes weak, broad Kikuchi lines are obtained but generally the bending of the section and the area of the incident electron beam are such as not to favor Kikuchi lines. The effect of cold working on the images of the sections was studied by lightly pounding the center region of a f diameter disc (0.005'' thick) with a small, rounded and poHshed steel rod against an anvil. The disc was then electro-thinned and examined in the electron microscope. Originally it was hoped that further information regarding laminar slip^ might be obtained in this manner. However, no details of slip have been observed in the cold worked sections, the general appearance being that seen in Fig. 8(a). Figure 8 was obtained from a section cold worked by pounding at room tempera- ture and shows the recovery domains or early stage of polygonization.^ These domains are not made visible by etching a polished surface and are observed only by electron transmission. The domains are slightly dis- oriented one with respect to the other and are made visible by the differences in diffracted intensity. Since the extinction contours are absent in Fig. 8a it is concluded that there is considerable internal strain in the domains as previously mentioned. Figure 8b is a transmission electron diffraction pat- tern of this section and shows arced rings made up of discrete spots. It is concluded that each spot on an arc corresponds to a domain. Insufficient domains are included in the primary beam to produce continuous rings. The electron diffraction pattern of Fig. 8b is very similar to microbeam x-ray patterns published by Kellar'^ et al and the domain size of about 2/x from the electron micrographs is in excellent agreement with the results of Kellar for pure aluminum. That domains sufficiently free of strain to yield extinction contours can be obtained is illustrated in Fig. 9. Figure 9a is from a section prepared 36 hours after a block of the high purity, aluminum had been rolled to 0.005" sheet with some annealing between passes. The contours are very much in * Recovery domains are not found in aluminum deformed by simple extension. Appar- ently inhomogeneous strain is necessary. Extinction contours are observed in specimens deformed in tension but the slip bands are not in evidence. 8 J. N. Kellar, P. H. Hirsch and J. S. Thorp, Nature 165, 554 (1950). 878 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Fig. 7 — Grain boundaries in a thin section of high purity, recrystallized aluminum. The displacement of a family of contours at the boundary is evident in (b). ELECTRON TRANSMISSION THROUGH THIN METAL SECTIONS 879 Fig.' 8 — Thin section of high purity aluminum cold worked by pounding. The recovery domains are evident in (a), (b) is an ordinary electron diffraction pattern (transmission) of the section and shows the discrete spots on the arced rings. Fig, 9 — Recovery domains in roll,<|, liigh purity aluniinuni annealed between passes through the rolls. (a). 36 hrs. after rolling showing extinction contours in the domains. (b). 1 year after rolling. The domain boundaries are evident now only through the dis- continuities of the extinction contours. 880 ELECTRON TRANSMISSION THROUGH THIN METAL SECTIONS 881 evidence indicating that the internal strain is less than in Fig. 8. Another section was prepared after the rolled sheet had stood for about one year with the result shown in Fig. 9b. The domain boundaries in this section are made visible chiefly through the discontinuities in the extinction con- tours rather than overall contrast between domains. Apparently the do- mains slowly reUeve their internal strains and become less distinct as re- covery proceeds at room temperature. A possible complication in the study of thin sections in the electron microscope is the effect of rather intense electron bombardment. There are several possible ways in which the sections might be changed by bombard- ment. One of these is simply annealing due to heating by bombardment. However, the metal is a good conductor of heat and is in contact with the heavy brass specimen holder so that high local temperatures would not be expected as with thermal insulators or isolated particles. Another phenome- non that is quite common is the deposition of a carbonaceous layer on the areas exposed to the electron beam. This is generally due to the residual hydrocarbon atmosphere in the vacuum system and is visible to the naked eye as a black deposit. The remaining possibility is that of producing lattice defects or vacancies by colUsion with the incident electrons. The cross- section for this process is not known but it would be expected that for 50 KV electrons it would be quite small. Many thin sections of aluminum have been examined in the RCA EMU instrument at moderate intensities using the biased electron gun with little evidence for any changes occurring over the normal times required for ob- taining pictures. However, if the peak intensity attainable with the biased is used, quite significant changes occur as illustrated in Fig. 10. These im- ages are taken from a sequence and show the effect of time of bombardment on the recovery domains. The loss of contrast and irreversible changes in details with time of bombardment are evident. Part of the effect is due to heating and part to deposition but in general the behavior is not under- stood. An outstanding feature of the domains in cold worked, high purity alu- minum has been the relatively uniform size exhibited over a great many samples prepared at room temperature. The deformations have ranged from the order of about 30% to several hundred percent with the domain size consistently in the neighborhood of 2/x. At low deformations of the order of a few percent the domains are not found. No growth or change in size of any consequence has been found after months at room temperature. The relief of internal strains seems to be the only significant change with time. A short anneal at or above the recrystallization temperature removes the domains and gives rise to new crystals which exhibit extinction contours. Observations such as this tie the domain structure quite firmly to recovery. Fig. 10 — Effect of intense electron bombardment {50KV electrons) on the domain structure. (a) 45 seconds bombardment (b). 125 seconds bombardment 882 ELECTRON TRANSMISSION THllOtJGH THIN METAL SECTIONS 883 As previously pointed out, the formation of recovery domains upon cold working represents an early stage of polygonization with a much smaller size than that observed at low deformation.^" This suggests a nucleation and growth process^^ for recovery during and following plastic deformation. Cahn^^ j^as pubHshed a detailed nucleation theory to account for recrystal- Hzation grain size. He considers the nuclei to be regions in the crystal witfi large curvature brought about by cold working. It would be expected that both the nucleation and growth rates would be effected by changes in tem- perature and by additions of alloying elements which reduce the rate of diffusion of dislocations. The latter was tried first by adding about 4% copper to the high purity aluminum and rolling the alloy to 0.005'' sheet. A section prepared from the rolled sheet with no anneal gave the results shown in Figure 11. It will be noted in Fig. 11a that the large, well defined domains seen in Figs. 8 and 9 are not present in the alloy. The structure is much smaller and is strung out in the direction of rolling. The electron dif- fraction pattern, (Fig. 11 (b)) exhibits arced rings with the arcs being contin- uous rather than showing the discrete spots seen for the pure metal (Fig. 8b). The number of recovery domains produced in the alloy is thus much greater than in the base metal which checks with the much smaller recovery exhibited by cold worked aluminum alloys as compared to pure aluminum. It is concluded that the addition of copper has produced ''knots" in the aluminum lattice which impede the rate of growth of domains. ^^ The effect of temperature is of much interest since nucleation processes A generally involve a temperature dependent term of the form e — —- where KI A is an activation energy^^ A plot of nucleation rate against temperature should yield a curve exhibiting a maximum at some temperature Tc. For T > Tc, only a portion of the embryos are able to exceed the critical size, the smaller ones dissociating. For T< Tc, the thermal diffusion rates are sufficiently low to impede embryo formation. The maximum nucleation rate is thus a balance between the diffusion rate and the number of embryos able to exceed the critical size and grow. In order to investigate the effect of temperature, high purity aluminum specimens were cold worked by pounding at — 78°C (dry ice) and at — 196°C (liquid nitrogen) and then allowing the specimen to warm up slowly to room temperature. It was thought that if the working was done at a temperature below that at which 10 A. Guinier and J. Tennevin, C. R. Acad, of Sci., Paris 226, 1530 (1948). 11 R. D. Heidenreich, "Cold Working of Metals," page 57 (American Society for Metals, Cleveland, 1949. 12 R. W. Cahn, Froc. Phys. Soc. A 63, 323 (1950). 1^ If this alloy is given a 10 min. anneal at 300°C, recovery domains very similar to Fig. 8 are obtained. "D, Tumbull, A.I.M.M.E. Gech. Pub. #2365 (1948). 884 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Fig. 11 — Thin section of rolled aluminum — 4% copper showing the very small domains. (b) is a transmission electron diffraction pattern. Compare with Fig. 8. Fig. 12 — Effect of temperature at which recovery proceeds on domain size in high purity aluminum. (a). Dry ice (-78°C) (b). Liquid nitrogen (-196°C) 885 886 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 the nucleation rate is a maximum, then as the specimen warmed slowly it would pass through the maximum and result in a larger number of nuclei. The time for recovery at the low temperature was varied from 15 minutes to several hours before bringing the specimen to room temperature but the results did not reflect any dependence on the time at low temperature. Even so, a primary weakness in the experiment lies in the fact that the structure could not be observed at the temperature of working. The results of cold working at — 78°C and — 196°C are shown in Fig. 12. Surprisingly enough, the domain size after cold working at — 78°C is practically the same as at room temperature as seen in Fig. 12a. It was thought that this simply meant that the structure had reverted to the room temperature configura- tion until the results were obtained at — 196°. The domain size resulting from the — 196°C treatment is slightly less than half that obtained from the — 76°C treatment, indicating that the effect of recovery temperature can be seen after bringing the specimen up to room temperature.^^ This is consistent with low temperature rolling experiments^^ on pure copper performed by W. C. EUis and E. Greiner of Bell Telephone Laboratories in which the amount of work hardening was considerably increased over that obtained by rolling at room temperature. Thus, at present it appears that the re- covery domains seen in Fig. 12 are a fair approximation to those produced at the low temperatures. More work on low temperatures is certainly justi- fied since it appears that the recovery mechanism involves a process with a very low activation energy, at least in the case of pure aluminum. General Remarks The conclusions drawn from the electron images of cold worked alumi- num are, in review, (1) During and immediately following cold working of pure aluminum self -recovery takes place by the formation of recovery domains about 2jLi in size. (2) The recovery domains produced at room temperature and below at first possess sufficient internal strains to prohibit extinction contours. These strains are slowly relieved at room temperature. (3) The addition of copper to the aluminum inhibits the growth of re- covery domains resulting in a recovery domain size much smaller than for the pure metal. Thus, aluminum-copper work hardens to a far greater extent than does pure aluminum. (4) Recovery in pure aluminum is reduced only by going to relatively " The microbeam x-ray technique (reference 9) should be invaluable in checking this point since the entire experiment could be done at the low temperature. "To be published. ELECTRON TRANSMISSION THROUGH THIN METAL SECTIONS 887 low temperatures; i.e., of the order of that of liquid nitrogen (—196 °C). (5) The recovery domains do not show (at least not readily) on etched surfaces. The overall rate of etching is much higher than in the an- nealed state, however. (6) Deformation by simple extension does not produce the recovery domains such as seen in Fig. 8. Neither domains nor slip bands are visible. These conclusions and observations suggest explanations for several well known phenomena in cold worked metals. One is the fact that slip lines are not visible on a surface etched after cold working, which has always been rather puzzHng. It seems clear now that this is simply due to an immediate rearrangement giving rise to recovery so that the slip band exists as such only during the actual deformation process. The traces left on polished sur- faces are actually only traces of the displacements that occurred during deformation and do not indicate where the energy of cold work resides when slipping has stopped but only where the energy was introduced. The energy would reside in the slip bands only if no recovery whatever took place. Another point of interest is that of recrystalHzation. In one sense the re- covery domains constitute recrystallization on a smaller scale than is usually meant. However, in view of the fact that the domains do not etch preferen- tially (probably due to internal strains) and that they disappear at the re- crystallization temperature, it would seem more accurate to view the re- covery domains as distinct from recrystallization. It would seem logical to consider the recovery domains as embryos for recrystallization. When the temperature is raised sufficiently those recovery domains which most rapidly relieve their internal strains would serve as nuclei for new grains and con- sume the surrounding embryos or domains. In a sense, then, it is the least strained material from which new grains spring. However, the embryo for the new grain very probably sprang from a region that was very highly strained. Between the actual slip process and final recrystallization grains there are actually two nucleation and growth processes. The author is grateful to Mr. W. T. Read and Dr. W. Shockley for valuable criticisms and discussions of the subject matter presented in this paper. On the Reflection of Electrons by Metallic Crystals By L. A. Mac COLL This paper gives the results of some calculations of the reflection coefficient for electrons incident normally on a plane face of a metallic crystal. The physical situation is treated as being one-dimensional; and it is assumed that the potential energy of an electron is a sinusoidal function of distance inside the crystal, and obeys the classical image force law outside the crystal. The reflection coefficient is computed as a function of the energy of the incident electrons, over the range from 0 to 20 electron volts, for a variety of values of the parameters which define • the model of the crystal. 1. Foreword ^TT^HE work which is presented in this paper was undertaken as a result -*- of conversations had with Dr. C. J. Davisson at various times during the years 1938 and 1939, when he was investigating the reflection of elec- trons impinging on the surface of a metal Uc crystal. The results for a simple special case of the general problem were pubhshed in 1939^ Thereafter the work on the general problem continued intermittently, and it was almost completed by the early part of 1942, when it was brought to a halt by the onset of wartime activities. Since then nothing has been done on the prob- lem, and the results already obtained have never been published in extenso. However, C. Herring and M. H. Nichols have included an illuminating dis- cussion of some of the more significant of the results in their recent mono- graph on thermionic emission^. Although the intervening years, by bringing new problems in physics to the fore, have caused this work to lose some of the interest which it possessed at the time it was being done, it still seems to be worth while to put the full results upon record. The present occasion, when his friends and former col- leagues are celebrating Dr. Davisson's seventieth birthday, is an especially appropriate one for this purpose. 2. Formulation of the Problem We consider electrons moving with energy E and impinging on a plane face of a metallic crystal. (Fig. 1.) According to quantum mechanics there is certain probability R, generally neither 0 nor 1, that an electron will be reflected by the crystal, and caused to move backwards toward the source; and there is the complementary probability 1 — R that the electron will ^ Physical Review, v. 56, pp. 699-702. This paper will be referred to henceforth as (LAM, 1939]. 2 Reviews of Modern Physics, v. 21, pp. 185-270 (1949). 888 ON REFLECTION OF ELECTRONS BY METALLIC CRYSTALS 889 penetrate the crystal, and flow away through the remainder of the circuit. We call R the reflection coefficient, and we can define it alternatively as the ratio of the intensity of the reflected electron beam to the intensity of the incident beam. We wish to calculate i? as a function of E. In order to be able to do this effectively, it is necessary to idealize the actual physical situation quite drastically. (However, the idealization which we shall use preserves what seem to be the most important features of the physical situation.) On the other hand, once the idealization has been set up, the mathematical calcula- tions themselves will be carried through without approximations^. Hence, INCIDENT ELECTRONS REFLECTED ELECTRONS Fig. 1 — Reflection of an electron beam by a crystal. (Schematic representation). any discrepancies between the theoretical results and the results of experi- ment are to be attributed to the inadequacy of the model, and not to il- legitimate steps in the mathematical work. Our idealization of the physical situation can be described in the form of the three following assumptions : Assumption I. The problem may be treated as one concerning one-dimen- sional motion of electrons. Thus, we set up a rectangular coordinate system in space; and we assume that the crystal occupies the half-space x < 0, and that all of the point functions with which we are concerned depend solely upon the coordinate x. Assumption II. There exists a function V{x), such that an electron at the point X has potential energy V{x) ; and the behavior of an electron is gov- erned by the Schrodinger wave equation ^ Except, of course, simple arithmetical approximations, such as are involved in almost all calculations. 890 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 k^ [E - Vix)U = 0. (1) (Here k^ — WmlW-, where h is Planck's constant, and m is the mass of an electron.) This assumption deals in a summary way with various compli- cated processes involving electrons in crystals. Discussions of the vaUdity of the assumption are to be found in various works on the electron theory of metals. Fig. 2 — Assumed potential energy as a function of the coordinate x. Assumption III. Specifically, the function V(x) is given by the formulae V{x) = — Fo + Fi sin a(x — Xo), x < Xq = — €V(4x), X > Xq xo = eV(4Fo), (2) where e is the absolute value of the electronic charge, and Fo, Vi and a are suitable non-negative constants. (A graph of this function V(x) is shown in Fig. 2.) According to this assumption, an electron in the region X > ^0 is subjected to the classical image force. This is known to be in good agreement with the facts, at least if x is not too small.* Also, according to the assumption, the potential energy of an electron in the depths of the crystal is a periodic point function with a negative mean value. This part of the assumption is as correct as any assumption can be which attempts to account for the complicated actual processes in terms of a potential energy function. However, our particular choice of a periodic function is based largely upon mere considerations of mathematical convenience. Finally, we * See Herring and Nichols, footnote 2, p. 245 et seq. ON REFLECTION OF ELECTRONS BY METALLIC CRYSTALS 89l observe that our V{x) is continuous, as physical considerations indicate that it should be. We can now state the mathematical problem before us in the following terms : V{x) being defined by (2), we are to obtain a solution }f/{x) of (1) satis- fying the following conditions: (a) In the region x > xo the function \p{x) exp {—2iriEt/h) represents an incident beam of electrons moving toward the left, and a reflected beam of electrons moving toward the right. (b) In the region x < xq the average electron flow, if it is not zero, is direc- ted toward the left. (c) The function \p{x) and its derivative \l/'{x) are everywhere continuous. Having obtained such a solution ypix), we are then to compute the ratio of the intensity of the reflected electron beam to the intensity of the incident beam. In particular, we are to study the dependence of this ratio upon the quantities E, Fo, and Fi. The paper [LAM, 1939] already referred to dealt with the special case in which Fi = 0, i.e. the case in which V{x) is assumed to be constant in the region x < xq. Consequently, we are now concerned chiefly with the cases in which Fi > 0. 3. Generalities Concerning the Calculation of R In the region x > xq the wave equation (1) takes the form dx"" The general solution of this equation is of the form yp{x) = AUx) + BUoo), where A and B are arbitrary constants, and ^i(x) and yp2{x) are two particu- lar solutions which we choose so that the functions ypi{x) exp {—liriEt/h) and ^2^ exp {—liriEt/h) represent beams of electrons, of unit intensity, moving to the left and right, respectively. In the region x < xq the wave equation takes the form ^ + k\E + Fo - Fi sin a{x - x,)]yp = 0. (3) We are concerned with a solution of this equation of the form ^P{x) = CUx\ where C is a constant, and \l^z(x) is a particular solution such that the func- + e[E + Q, = 0. 892 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 tion \l/-i{x) exp {—2wiEt/h) represents a state in which the average flow of electrons in the crystal either vanishes or is directed toward the left. The actual forms of the functions \l/i(x), 1^2 W, 1^3 W will be discussed presently. Now the continuity of the functions \f/(x) and \l/'ix) gives us the system of equations A\l/i{xo) + B\l/2(xo) = C4/z(xq) Axf^i'ixo) + B^P2'(xo) = Ch'M, from which we can calculate the ratio B/A in terms of the \l/t{xo), ^/(xo). Our required reflection coefficient R is | B/A |^ and so we obtain the for- mula R = 1^3(^0) ^3(Xo) (4) It was shown in [LAM, 1939] that the functions i/'i(x) and \p2{x) are given by the formiilae ^iW = w,,m, Moo) = Tr_xj(-^), where and the symbols W\,{{^), W-\,\{—^) denote the usual functions occurring in the theory of the confluent hypergeometric functions'*. The earher work gives us all the information concerning ^i(x) and ^2(x) that we shall require. Hence, in order to calculate R, we have, in effect, only to identify a suitable f.olution \J/z(x) of equation (3), and then to calculate \l/z{xo)/\l/z{xo). 4. The Solution of Equation (3) In order to facilitate the use of known results, it is convenient to write a2 Then equation (3) takes the form 2'+ (^2 + 2^1 cos 22)^^ = 0. (30 This is one of the canonical forms of Mathieu's differential equation, for * E. T. Whittaker and G. N. Watson, "Modern Analysis" (Chapter XVI), Cambridge Univ. Press, 4th Ed., 1927. ON REFLECTION OF ELECTRONS BY METALLIC CRYSTALS 893 which an extensive theory exists. We shall recall a few of the chief facts brought out in this theory, f Unless the constants ^o and Oi satisfy some one of certain special rela- tions, the general solution of equation (3') is of the form lA = K.e^iiz) + K^e-'^^fi-z), where /x is a constant determined by do and di, f{z) is a function which is periodic with the period r, and the i^'s are constants of integration. In certain ranges of values of the ^'s, the constant ^ is real, and in other ranges it is pure imaginary. When /x is real we can obviously take it to be positive; and then, in order that yl/z{x) may be bounded in the range x < Xo, we must choose i/'sW to be the function e^^f^z). When /z is pure imaginary, we can take it to be ^ | /x | ; and then, in order that ^3 W shall represent a state in which the flow of electrons is to the left in the crystal, we must choose ^sW to be the function e~>'^f{—z). When 11 is pure imaginary we have a non- vanishing flow of electrons to the left in the crystal. Consequently, the intensity of the reflected beam must be less than the intensity of the incident beam. Hence, under this condition we must have R < \. On the other hand, when ju is real there is no average electron flow in the crystal. Consequently, under this condition the inten- sities of the incident and reflected beams must be equal, so that R = \. These considerations point to the importance of discussing, first of all, the conditions under which /x is real or pure imaginary. Figure 3 shows a well known diagram, modified slightly to suit our present purposes^. Here ^0 and ^i are taken to be rectangular coordinates of a point in a plane, and the plane is divided into regions of two kinds (shaded and unshaded) by a system of curves. If the point (^0, ^1) is in the interior of one of the shaded regions, the above /x is real; if the point is in the interior of one of the unshaded regions, /x is pure imaginary. (If (^0, ^1) lies exactly on the boundary of one of the regions, we have a somewhat more compli- cated situation, which we do not need to consider here.) This diagram en- ables us easily to determine, for any fixed values of Vq and Fi, the ranges of values of E in which we have R = \. We shall call these ranges of values of E the dif Taction hands. Now our problem has been reduced to that of computing R for values of E which do not lie in diffraction bands. In treating this phase of the subject we shall follow the course of the actual calculations, without any examina- tion of ways in which the work might have been done more efficiently. t See, for instance, E. T. Whittaker and G. N. Watson, footnote 4, Chapter XIX. ^ See, for instance, N. W. McLachlan, "Theory and Application of Mathieu Func- tions" (p. 40), Oxford University Press, 1947. 894 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Of the many methods which have been devised for finding solutions of Mathieu's differential equation, the one which is conceptually simplest is that due to Bruns. This method can be described as follows: Vlvti M W:"} • '.;'■':'•: ':::^<]: {f::S\ SM m W- ••.•.•■•.■••■ •;^:i^ m \ 01- ••.•*•'•■.•■••• '}}':•;':% 9 ;/:::Vv: 1 ''■■[•'.':'■■•■ ^•:-;v: 1 W / m 1 '■:■•/::'■[ :1 •::":'.•; ■}■^'^:/ ■ '■::•}: ■.•••■.• ^:- f :••■••;•:•: '•/•■•;;• ':^^M W:[::] V '•'.'■'■'•'■ };i;i;;: r •;':•:•: r Ni^'S m •:•;/::: Y "••'•":•! r f :>-\^ M •■.•.■•:':> \ w r f Ik •m r f 01 234 5678 Fig. 3 — Stability diagram for Mathieu's differential equation 10 11 12 13 Under the transformation exp J en the Mathieu equation (3') goes over into the Riccati equation d

)0^ (1 _ ^2)3(4 _ ^2)^3 4(15 + 18^0 + 56>g)g"'" (1 + doYil - e,){2 + ^o)2(3 + ^o)^o (11 + 5^o)e"'" ]■ (1 + 0o)K2 + ^c)H3 + ^o)(4+ W, The functions w 896 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 settled upon a method due to Whittaker, and this was used to complete the calculations. Whittaker's method is described briefly in Whittaker and Watson's "Modern Analysis," 4th Edition, p. 424. The method is developed more fully in papers by Ince^. We shall confine ourselves here to some summary indications of the nature of the method. The method leads to representations of the solutions of Mathieu's equa- tion by formulae which differ in structure depending upon the part of the (^0, ^i) plane in which we are working. We shall give the formulae suitable for use in the neighborhood of the point ^o = 1, ^i = 0; the formulae for use in other parts of the plane are given by Ince. Given the values of ^o and 6i, we first determine a number a by means of the implicit equation el = 1 -\- di cos 2(7 + ^' (-2 + cos 4(7) - f^ cos 2(7 8 64 + 5Y2( ^- 11 cos 4(7) + 12\3 Then we seek a solution of equation (3') in the form 00 \f/ = e'" Y^ {a2n+i cos[(2n + l)z - (7] + ign+i sin [(2n + l)z - (7]), n=0 where ju, the o's, and the 6's are constants. We substitute the expression for ^ into the differential equation, and determine values of the constants by imposing the condition that the resulting relation shall be an identity in z. After some rather intricate algebraic manipulations we finally arrive at the following results: a, = 0, 61 = 1 fl3 = T^ sin 2o- -f z-^ sin ^<^ + 04 ( ~ -9- sin 2(7 + 9 sin 6(7 j + • • • 14^J . _ , uet . ^ , 35^; . _ , ^=(T08)(8^^^^2"+'-- ^ Monthly Notices, Royal Astronomical Society of London: v. 75, pp. 436-448; v. 76, pp. 431^142. ON REFLECTION OF ELECTRONS BY METALLIC CRYSTALS 897 (h = o{el) ,3 4. + geos2.4-|(-^V5cos4.) + ^4 ( - ^ COS 2(7+7 cos 6o- j + • . . el , 461 . , dt /82 , 155\ , ^' 192 ■ (9)(83) ^' = (I8)V) "^ (12^^ ' (180) (8^) "^ The calculated terms which are exhibited here enable us to calculate the solution ^(z) to a certain accuracy, and this accuracy proved to be sufficient for our purposes. Although this method is very complicated analytically, it was found to be quite convenient for purposes of numerical calculation. 5. The Reflection Coefficient for Large Values of E This work is concerned chiefly with the reflection coefficient for small values of E (actually up to 20 electron volts). However, it is interesting that we can obtain a simple approximate formula for R for indefinitely large values of E in the intervals between the diffraction bands. For this purpose we go back to Brun's method, and we write the dependent variable in equation (5) in the form (p = — i6o -{- o). We find that the new dependent variable co satisfies the equation -^ - lidoo) + 60^ + 2(9i cos 2z = 0, dz and we seek a solution of this equation in the form ccijz) CC2(Z) 0) ^= coo KZ) -r a + ""^2" -h • • • . VO VQ The functions con(3) are easily computed, and we finally arrive, in an entirely straight-forward way, at the result o(^/4) = -ido + ^i + %+ '". (7) 898 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 In pLAM, 1939] we derived an approximate formula for R when E is large for the case in which Fi = 0. The work involved in that derivation, together with the equation (7), enables us to obtain the desired formula by a simple calculation. The result obtained is the following: R= ^[l-il^l. (8) Vife2£3 L 4^ J The range of validity of the approximate formula (8) has not been de- termined. The nature of the derivation, and also the form of the result, leads us to suspect that the approximation is good only so long as the ratio Vi/Fo does not exceed some bound depending upon the other quantities entering into the expression for R. The approximation certainly breaks down when Fi/Fo reaches the value Wo/(ae^). However, this value is well above any of the values with which we deal with in this work. Consequently, we suspect that the formula can be used, to extrapolate our calculations of R to higher values of E, without serious danger of error in the cases which we consider here. 6. The Calculated Results The reflection coefficient depends upon the independent variable E, and upon the three parameters Vo, Vi, and a. The effects upon R of taking vari- ous values of Vo and Vi seemed to be of greater interest than the effect of taking various values of a; and, consequently, we confined ourselves in the calculations to a single value of a, namely, a = tt X 10"^ cm~^ This value of a makes the period of V{x) in the crystal equal to 2 X 10~^ cm. We took six values of Vo, proceeding in equal steps from 10 electron volts to 20 electron volts inclusive. These values adequately cover the range which is of interest in connection with actual metals. Including the calculations reported in [LAM, 1939], we have taken, for each of the values of Vo, five values of Vi, proceeding in equal steps from 0 to 0.4 Vo. Although it is somewhat difficult to say just what value of Vi is most appropriate to the case of a specific actual metal, it appears that these values cover the range of values of interest adequately. The results of the calculations are shown in a self-explanatory form by the curves given in Figs. 4 to 9 inclusive. For the sake of unity, we have included the results which were previously published in [LAM, 1939]. 7. Physical Discussion of the Results The results do not call for much discussion, especially in view of the dis- cussion which Herring and Nichols have given in the paper already referred to. However, there are a few observations which should be made. ON REFLECTION OF ELECTRONS BY METALLIC CRYSTALS 899 ■~~ ~~" ~~" ^~~ -^ O (VI (0 _J lU 2 II 00 , (>~ to •^ ID "ti (0 if) ii 1 — 1 (JUJ ii Q ai 0.2 0 , 0.34 0.3 0, 0.82 0.4 0, 1.30 (vjU -ai z " if) o -'ii ai Z lU 9 z / .S / (^ . / a: UJ J UJ / 4 y 4 ^ ^ ^ -^ '/ o^ V ~5r ' ^-' / / X d — ' -^ ^ — "■^ ^ ^ ^ X I =^ ^ — — \ — ~"~" ~~" ^ 1 ^' 1 ( ( 5 6 < ( n 5 < < < N3I D Did d3C 6 )D 1 < ( NOI n LD3 ( nd3 6 H < < 0 3 < ( 3 3 3 < 3 o° 900 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 — — > u UJ -J U) (M II >° j^ T Tj r f ' 1 ' / \ 4-1 TT , Pj2 ^L 1 / J 1 7 / 't / J r , / 1 / f 1 1 y / ■^ V / / /o ^ t y\ 1 ^ ^ •^ z _l UJ II 1 ■ j 1_ . ^il' tt ft ' _i jjT YtT TTj2 t^t^ 1 I \ III i 7-J / /^~[I7 / -4 l4^ / T /^T / f f f / / ^ / f / ~1_ ./ / Jv/- '*' ^ y / / f 7 ^ o y / I ^ y / -L X- ^ y^ / i it ^ y^ ^ I ^^ (0 z o >- tr lU HI d i d o d d d d a 'iN3IDIdd30D d d NOIiD3-|d3d 01 o d o 5 d d 902 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 i O liJ _l lU 2 II sJA /I / 11 In _/T J^ T T / T o> <2 mO 1 — 1 (JOI ^? ten tu >° :>■ 0.1 19.410, 19.454 0.2 19.388, 19.561 0.3 19.353, 19.738 0.4 19.302, 19.984 / \ / / /ill i , / * / / / / / / / / ) ' 1 / ' / 1 i / / / i i r / / / J 7 ' / / ]j i 1 / / / J_ / / / / ~f / / / / T / / / T / / / L oV / / L / f 7 oV 1 ' / / 7 o7 ^■1 / / / ^ y / / y / y / / / / / ^ '^ y /' / f ^ x' y ^ / y'' y A 8 § »n o s 8 8 § § o o o o d d o o d 'lN313l=Jd300 N01i03-ld3a 904 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 dodo a 'iN3IOIdd30D NOIiOaidab ON REFLECTION OF ELECTRONS BY METALLIC CRYSTALS 905 For fixed values of Vo and Fi, the reflection coefficient tends to decrease with increasing E over most of the range between any two successive diffraction bands. For fixed values of Vo and E, E being in a range between two diffraction bands, R tends to decrease with increasing Vi. This is a re- sult which was not anticipated when the work was begun. As was expected, we find a tendency for R to increase with Vo when E and Fi/Fo are held fixed. The most interesting feature of the results is the behavior of R in the neigh- borhoods of the edges of the diffraction bands. Unfortunately, the range of values of E considered is not great enough to reveal this behavior very com- pletely. (The failure to consider a greater range of values of E was the result of our reluctance to embark again on the difficult numerical computations relating to the PF±x,i(±^) functions. Since the necessary computations had been performed earlier for values of E up to 20 electron volts, we de- cided, unfortunately as it now appears, to confine ourselves to this range.) The behavior of the curves near the edges of the diffraction bands which occur in the neighborhood oi E = 19 electron volts (when Fo is 18 or 20 electron volts) does not require much discussion. The reader will observe a small dip in the curves for Vi = Fo/10 just below these diffraction bands. The accuracy of the computations is believed to be high enough that we are justified in taking this dip to be entirely genuine. When Vo is 10, 12, or 14 electron volts the behavior of the curves for values of E in the neighborhood of zero is rather complicated. Herring and Nichols consider this behavior to be one of the most significant features of the results, and they have given a full discussion of it from the physical point of view.* In view of the availability of their discussion, we may con- fine ourselves here to a few brief remarks. In some of the cases which we are referring to now there are diffraction bands extending from £ = 0 to certain positive values of E. (These dif- fraction bands are shown in a self-explanatory way in the figures.) When such a diffraction band exists the complicated behavior of R for small val- ues of £ is a result of the existence of the diffraction band, and it is com- parable with the behavior of R in the upper part of the range of values of E in the case in which Fo = 20 electron volts. In the cases in which we do not have diffraction bands extending upward from £ = 0 we have to explain the complicated behavior of R in somewhat different terms. Assuming that we have such a case, let us momentarily ignore the fact that the physically significant values of £ are non-negative, and consider £ as an unrestricted real parameter. Under this convention concerning £, * Herring and Nichols, footnote 2, pp. 248-249. 906 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 we find that there is a diffraction band lying in the range of negative values of £, and extending more or less near to the point E = 0^. We shall call this di fictitious di fraction hand. Now it is immediately clear that the complicated behavior of our curves arises from the fact that the small positive (and hence physically significant) values of E concerned are near the upper edge of the fictitious diffraction band. 8 Specifically, what is meant is that there is such a range of values of E in which the exponent n is real. The Use of the Field Emission Electron Microscope in Adsorp- tion Studies of W on W and Ba on W By J. A. BECKER The chief conclusions from these studies are given in the Introduction. Table II summarizes the adsorption properties oi W on W and Ba on W. These properties vary with the crystal plane and are given for five planes. The extent to which these planes develop depends on T and the applied field, F. The tem- perature at which W atoms migrate on W at detectable rates depends on the plane and on F, and varies from 800 to 1200°K. The adsorption properties of Ba on W are quite different for the first layer than they are for subsequent layers. In the first layer for which 6 < 1, Ba forms two phases: a condensed phase in which the Ba forms clusters or islands having a median diameter of 100 X 10~* cm, and a dispersed phase consisting of indi- vidual atoms. The temperature at which Ba migrates at detectable rates varies from 370 to 800°K from the 110 to the 100 plane. The evaporation rate depends on d. At d near 1.0 it is detectable at 1050°K. At 1600°K practically all the Ba is evaporated. For more than one layer of Ba on W, the Ba forms crystallites which grow outward from the W surface even at room T. Their median diameter is about 400 X 10-8 cm and they disappear between 600 and 800°K. Introduction and Conclusions T? W. MULLER,^ in 1936, described a tube in which the field emission -^— ' electrons from a very sharp tungsten point were made to impinge on a fluorescent screen and there portray a magnified image of the variation in emission density from different regions on the point. He showed that magni- fications approaching a million fold could be obtained. In subsequent papers^ he showed how such a tube can yield direct and striking information on the surface structure and on the effects of adsorbed films. Jenkins, ^ in 1943, summarized the progress to that date and showed that fields of the order of 10^ volts/cm produced pronounced changes in the surface configuration. More recently F. Ashworth^ has reviewed the field emission from clean metal- lic surfaces. In Fig. 2, (a) and (b) are two examples of photographs of the screen when field emission electrons are drawn from a single crystal of tungsten. The bright and dark regions are caused by variations in the intensity of elec- tron emission from different regions of the tungsten surface. From such photographs it is possible to deduce how the electron work function varies for different crystallographic planes, how adsorbed atoms change this work function, and how the surface deviates from a smooth hemisphere when the tungsten is subjected to a range of temperatures and fields. It is quite apparent that this new and powerful tool will reveal, on an 907 908 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 almost atomic scale, the nature of adsorption phenomena which are basic to thermionic, photoelectric and secondary electron emission, to catalysis and also to biological processes. Unfortunately, in most of the early work the residual gas pressure in the tube was such that the surface was contaminated in a few minutes and hence the results were probably affected by this con- tamination. In the present investigation the vacuum conditions were im- proved to such an extent that the residual gas produced only barely detec- table effects after about one week. Under such conditions the following observations and conclusions Have been made: (1) When a sharp point of a single crystal of tungsten is held at 2400°K until a steady state is reached, most of the surface is approximately hemis- pherical or more precisely paraboloidal. About 20% of the surface consists of three atomic planes which in decreasing order of size are 110, 211, and 100 planes. This is also the order of increasing intensity of field emission. The greatest intensity of emission is from the 611 direction and other directions surrounding the 100 direction. The next greatest intensity comes from the 111 direction and neighboring regions. (2) For temperatures > 2400°K the area of the 110, 211, and 100 planes decreases ; between 2400 and 1050°K the 211 and 100 planes increase steadily in size ; below 1050°K the rate of change of area is so slow that no changes are observed in one hour. These changes are ascribed to migration of W atoms on W. (3) From 1050 to 1200°K, W atoms migrate most easily in the 111 direc- tion on the 211 plane. In this direction the atoms in the outermost layer contact their nearest neighbors but the rows of atoms are separated by 1.635 atom diameters. The migrated W atoms are deposited on the hemis- pherical surface adjoining the 211 plane and form a crescent shaped mound resulting in an abnormally high field and enhanced emission. In the region between the 211 and 110 planes, W atoms are also mobile in the 111 direc- tion and form a series of step-like planes. In other regions the W atoms show no large scale migration. Above 1200°K, W atoms are mobile every- where. (4) When fields of the order of 40 million volts/cm are applied to the sur- face the rate of change of the surface configuration is greatly increased and migration of W atoms can be observed in one hour on the 211 planes and near-by regions at 800^K. These changes are the same for electron accelerat- ing and electron retarding fields. The rate of change increases rapidly with the strength of the field, perhaps as the square or cube of the field. At T = 1400°K and for fields of 40 X W volts/cm applied for hours, over half of the surface consists of planes: the 211 planes almost meet the 110 planes, and HI and 310 planes develop. Subsequent glowing without an applied field undoes the effects produced by the field. USE OP FIELD EMISSION ELECTRON MICROSCOPE 909 (5) When Ba is deposited on clean W, the average work function ^ decreases from about 4.4 volts to about 2.1 volts when an optimum amount is reached at somewhere near a monomolecular layer. Further deposition increases (p to that of bulk Ba for which (p is 2.5 volts. For convenience we define the average coverage, 6, as the Ba concentration divided by the con- centration when (^ is a minimum. (6) For 0 from 0 to 1.0, the emission comes largely from aggregates or clusters of Ba, approximately circular in shape with diameters ranging from 40 to 200 A and a median diameter of about 100 A. Between 600 and 900°K these clusters are in violent agitation with the centers of a cluster appearing to shift about half a diameter. Sometimes one cluster may dis- appear and another one near by appear. We propose that this means that the Ba forms two phases on the tungsten surface: a condensed phase of clusters and a gaseous phase of individual Ba atoms. We propose that the centers of these clusters are irregularities on the tungsten surface where small atomic planes or facets meet to form a valley. Even a clean tungsten surface shows evidence of such irregularities whose distribution in numbers and sizes is about the same as for Ba on W but in which the variation in emission density is much less pronounced. (7) For ^ > 1.0, the emission comes mostly from larger aggregates which range in size from 200 to 600 A or more. They produce spots which are intensely bright and are in continuous agitation of flicker even at room tem- perature. We associate these larger bright spots with crystallites because we believe them to be caused by Ba crystals which grow out normal to the tungsten surface and thus produce extra large local fields and hence en- hanced local emission. These crystallites disappear, presumably due to migration or evaporation, at temperatures from 400 to 600°K. (8) For ^ < 1.0 and r between 600 and 1000°K, the chief effects are due to migration of Ba from one region to another. From 600 to 700°K this migration is restricted to the 211 planes and adjoining regions in the 111 zones; the regions near 100 do not yet show migration. In any region migra- tion starts when the Ba clusters show noticeable agitation. At 800°K cluster agitation and migration occur in all regions and Ba atoms migrate from one side of the point to the other side for a distance of 3000 A in about 5 min- utes. At 900°K the migration rate is more rapid. (9) For ^ < 1.0 and r between 1050 and 1600°K the chief effect is that of evaporation. This is deduced from the fact that, as the temperature is in- creased progressively in about 100° steps and maintained at each T for about 5 min., the voltage or field required to obtain an emission of say 10 microamps becomes progressively higher, presumably because 6 decreases and (p increases. At any one temperature, the rate of evaporation is at first quite rapid but decreases as d decreases. After five minutes the rate is much 5H0 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 less than it was in the first minute, and after about 20 minutes the rate of evaporation is so small that d has nearly reached a steady state. To reduce 6 still more it is necessary to increase T. At 1600°K nearly all the Ba has evaporated and the emission pattern looks like that of clean W. Subsequent glowing at still higher temperatures produces only small increases in ip and small changes in the emission pattern. (10) For e = about .18 and T = 800°K we have observed a marked redistribution of Ba when a high field is applied: some Ba leaves the 211 and 111 regions and accumulates near the 100 regions. If the surface is then held at 800°K with zero field, some Ba leaves the 100 region and returns to FLUORESCENT SCREEN \ AQUADAG ANODE ■" r = RADIUS OF CURVATURE = 3 X lO-S CM MAGNIFICATION = 3 X 10^ V = ANODE VOLTAGES = 6000-9000 F=FIELD=5000 X V FIELD CURRENT =AF^f F (b) Fig. 1 — (a). Cross-section of tube. (b). Enlarged cross-section of tip of W point and values of constants. the 211 and 111 regions. This indicates that the adsorption forces can be modified appreciably by high applied fields. PART I Description of Field Emission Microscope Tube Figure 1(a) is a cross-section of the tube. The loop which was used to heat the point consisted of W wire 5.7 cm long and .0165 cm diameter. The W point projected about 1 mm beyond the loop. It was formed by repeatedly heating the W wire in a gas flame to oxidize it and removing the oxide with sodium nitrite. Two tantalum wire loops of 2.0 X 10"^ cm diameter wire are not shown. They were used to evaporate a tantalum film over most of the glass surface in order to adsorb residual gases and thus decrease the pressure. This proved to be very effective and estimated pressures of lO"^'^ to 10"^* mm Hg. were obtained. The tube also contained a source of Ba which could be deposited on part of the W point and loop. It consisted of a coil of .020 tantalum wire heavily coated with BaO + BeO. The coil con- USE OF FIELD EMISSION ELECTRON MICROSCOPE 911 sisted of 8 turns, .3 cm diameter. The center of the coil was 2 cm from the point, and the axis of the coil formed an angle of about 30° with the axis of the tube. Since the composition of the source is essentially that of Batalum getters which are known to evaporate Ba, it is assumed that nearly pure Ba evaporated from it. There is, however, the possibiHty that some BaO evaporated with the Ba. The tube has been in an operable condition for about 12 years. The tube was baked at 400°C for one hour. Then all the parts were glowed or heated to outgas them. It was rebaked at 410°C for three hrs. The W loop, Ta filaments, and Ba coil were heated so hot that further heating did not increase the pressure. The tube was sealed off at a pressure of 2 X 10"^ mm with both Ta filaments at a high temperature. Soon after the tube was sealed off the patterns for clean W and Ba on W were quite unsteady: there were rapid variations in intensity of small bright spots or flickering and there were more gradual changes in the pattern over large areas. After glowing the W loop, Ta filaments, and Ba coil many times and at successively higher temperatures, the flickering disappeared completely and the slow large-area changes became less pronounced or required a longer time to appear. Characteristic patterns could be reproduced at will for any particular treatment. In the early stages the clean W pattern changed notice- ably in one minute; later, the time required for a definite change to occur increased to ten minutes, then one hour, then one day, and finally one week or even one month. The effect of the residual gas was to enlarge the 211 planes and darken the 111 zone. The effect of this residual gas could be re- moved at r = 8{X)°K in a minute. We suspect that the residual gas is mostly CO. During the course of many experiments, the W loop was raised from 2200 to 2800°K. Gradually the voltage required to obtain a field emission of 10 microamps from clean W increased from 6000 to 9000 volts. In accordance with Mueller's results^ we ascribe this to an increase in the radius of curva- ture of the point from 2 to 3 X 10~^ cm. The lower portion of Fig. la shows an enlarged view of the W point and indicates that the tip of the point consists of a single crystal. Hence all possible crystal orientations should be represented on the surface. Figure lb shows a still further enlargement of the tip of the point. We assume that near the tip of the point the surface is a paraboloid. If the origin is taken at the vertex, and y is measured along the axis and x perpendicular thereto, the equation for the paraboloid is y = ^/2r (1) where r is the radius of curvature of the "point." The field near such a sur- 912 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 face can be calculated if the anode is a larger paraboloid whose equation is given by y = xyiild + r) (2) provided the origin is at its vertex, d is the distance between the two ver- tices, and the axes of the two paraboloids are the same. The field Fh for points at which 3; = A, is given by* Fn = KkV = ^(1 ^ 2h/r)Hn{\ + 2d/r) ^^^ where h is distance along the axis of the small paraboloid. At the tip or ver- tex of the W point, /? = 0 and Hence F^ = P,/U + ^V (5) For an angle of 60° with the axis, h/r = .47 and Fn = .72 Fo For clean W, this predicts that the emission density at an angle of 60° with the axis should be .008 of the emission density along the axis. For angles less than 10° the field and emission densities should differ only slightly from that for the axis values. Experiment shows that these predictions are qualitatively fulfilled. Subsequent photographs will show that for clean W most of the emission comes from regions which surround the 100 plane. For the 611 plane (p = 4.4 volts.^ The area of these highly emitting regions corresponds to about \ of the area of the screen which in turn corresponds to about wr^ crn^ on the W point. Hence we have taken the highly emitting area to be r^ cm^. The highest emitting areas make an angle of about 25° with the axis of the W point or with the 110 direction. From Eq. (3) we calculate that the field is about .924 that at the tip of the point. In order to obtain a value of r, the radius of curvature of our W point, we proceeded as follows: We observed the emission current i as a function of the applied voltage V and plotted log i — 2 log V vs \/V. Straight lines were obtained whose slopes and intercepts for clean W depended on the highest temperature and time at which the W loop was glowed. We then plotted a similar family of theoretical lines for various assumed values of r. The ex- * We are indebted to our colleague S. P. Morgan for Eqs. (1) to (4). USE OF FIELD EMISSION ELECTRON MICROSCOPE 913 perimental curves agreed fairly well with the theoretical ones for both slope and intercept. The values of r, deduced from the location of the experimental Hnes, ranged from 2 X 10-^ cm for low temperature treatment to 3 X 10"^ cm after repeated glowing at 2800°K. The theoretical family of curves was based on the Fowler-Nordheim equation modified for the electron image effect :^ i(amps/cm^) = ^-^ X 10"^ i^^F^ ^-(,3/./^,)6.8 x io7/(x) (^) in which the field = KXV volts/cm and x = ^'^^ ^ ^^-^KV ^ ^^^^_ heim* gives a table of /(x) vs x. From this we plotted f{x) ws KV ior (p = 4.4 volts, and found that for values of the field KV from 15 million to 95 milUon volts/ cm, f(x) was given by fix) = .968 - 5.54 X 10-» KV (7) This range of field covers nearly all values which are usually encountered in field emission. By substituting Eq. (7) in Eq. (6) and putting (p = 4.4 we obtain j = 3A2XiO-' K'V'.'"r'''^ ''""""'' (8) For a W point in which the major part of the current comes from an area of about r^ cm^ having a work function (p of 4.4 volts, and making an angle of about 25° with the axis, the current i in amperes is given by log i = -5.00 + .04 + 2 log r + 2 log /^ + 2 log V - """^^ '"^ (9) in which K is sl function of r, h, and d given by Eq. (3). For the experimental tube the point to anode distance was 4.0 cm. Since the field at the point will vary only shghtly with the exact shape of the anode we have put d = 4.0 cm. For r = 3 X 10"^ cm Ko = 5300 cm-i. K;, = .924 Ko = 4900 cm-i and logi = -7 + .41 + 2 log F - 5.40 X lOVF (10) Similar equations can be deduced for other values of r. From Eq. (6) it follows that the current density and hence the screen brightness depend on the work function tiA 2/5 SECOND Fig. 5 — Effect of high fields at 1400*K on size and shape of principal planes for clean W, 920 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 in the early stages the intensity increases in the 111 zone "steps" and in the region beyond the 211 plane going toward the 111 plane. j^ We have repeated similar experiments, about 20 times, varying the tem- perature and field. The rate at which the changes take place increases with temperature and with field. The rate increases more rapidly than the first power, perhaps as the square or cube of the field. In one experiment the direction of the field was reversed; this did not affect the kind of changes nor the rates. In another experiment, the temperature was reduced to 800°K while a field of about 40 million volts/cm was applied; in one hour the 211 planes enlarged perceptibly, the intensity increased just beyond this plane in the 111 direction, and the "steps" in the 111 zone appeared. For fields >40 X 10® volts/cm and T = 1500 to 1600°K, most of the surface can be developed into planes; the highest emission comes from broad lines where the planes intersect; and the voltage necessary to obtain a given current is greatly reduced. Many of these observations can be explained readily if we postulate that W atoms can be polarized and that such atoms will tend to move from low to high fields. The effects of such polarization forces will of course be super- imposed on the forces which tend to hold the W atoms in certain crystalline positions. Consider normal clean tungsten after glowing at 2400°K, and concentrate attention on the 211 plane. In the previous section we con- cluded that above 1050°K, W atoms are mobile on the surface and travel in the 111 direction until they reach the adjoining paraboloidal surface. A model of the 211 plane for W shows that, in the 111 direction, the atoms touch each other but the rows of atoms are separated by 1 .635 atom diam- eters; hence we would expect that atoms on this plane could move quite readily in the 111 direction. Now consider the effects of a high field. At the edge of the 211 plane the field will be larger than average, while at the cen- ter it will be less than average so that the field must increase toward the edge. Hence there should be a net force due to the field tending to take atoms off the edge of the plane, and the rate at which the planes develop should be greater with a field than without. Furthermore the extent to which the plane develops should be greater with a field. Since the polarization and the field gradient are probably proportional to the field, and the force is the product of the two, one would expect the field effect to increase with the square of the field. Because the force on the polarized atom due to the field is away from the surface for both positive and negative fields, the field effects should be independent of the direction of the field. The polarization postulate also explains the observation that after 39 minutes of applied field most of the emission comes from the 111 region and regions surrounding the 211 and 110 planes; and that the emission from USE OF MELD EMISSION ELECTRON MICROSCOPE 921 the regions surrounding the 100 plane, such as the 611 or 310 regions, is greatly reduced. Since the mobihty of W atoms on 211 and 110 planes is greater than that on 100 planes, we conclude that the forces required to move a W atom on a 211 or 110 plane from a position of equilibrium to a neighboring position of equilibrium are less than those required to move an atom on a 100 plane. A study of models of these planes leads to the same conclusion. The field effect reduces the displacement work on all these planes, and hence we would expect that the 211 and 110 planes would change their shape faster than the 100 plane. The W atoms involved in such changes pile up in regions near their respective planes and thus increase the local field in such regions. Since the rate of migration increases rapidly with the field, these regions will grow at a still faster rate than before. Hence we would expect that such regions would pile up W atoms at the ex- pense of other regions in which the migration rate started out more slowly. The experimental results, interpreted in this way, lead to the conclusion that high fields can result in movement of W atoms over distances of several thousand Angstroms. We have made about five observations in which this effect continued even at room temperature. If by temperature and field treatment one obtains a pattern in which the emission from a few small spots materially exceeds that of other regions, and if the temperature is then reduced to 300°K while the voltage is kept on for hours, it is found that one or two of these spots will grow in size and intensity while other spots and regions get relatively less intense. In such cases and in all cases of enhanced local field emission, the pattern can be brought back toward the normal condition by merely glowing the point at temperatures near 1000°K. The more the pattern differed from the normal one, the lower the temperature required to observe changes back toward the normal. One instance of the tendency to approach a normal pat- tern is that of the last photo in Fig. 5. A series of photos showing this tend- ency is given in Fig. 6. Effect of Temperature in Changing an Abnormal to a Normal Pattern Figure 6 shows first a pattern of normal clean W for 2400°K; then fol- lows a pattern produced by treatment at 1200°K with 8900 volts applied for 90 min. During this time the emission increased from 15 to 31 micro- amps; the next four patterns show the effect of glowing at successively higher temperatures for about an hour. A comparison of photos b and c shows that at 900°K the changes are shght : only a few of the brighter spots near the perimeter of the 110 and 211 planes have decreased in intensity. 922 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 T = 2400°K V = 0 3 MINUTES 7=9250, L = 14.5M Vs SECOND T = 1000°K V = 0 90 MINUTES V=8940. l=21/6^ Vs SECOND T = 1200*'K L = 15T0 31M V=8900 90 MINUTES V = 8840 L = 31 fl/K V5 SECOND T = 1100°K V = 0 60 MINUTES V = 8970, l-M.5ilfK V5 SECOND T= 900° K V =0 60 MINUTES V= 8870, l-2StlA V5 SECOND T=1210''K V=0 60 MINUTES V=9000. [.-\5HA V5 SECOND Fig. 6 — Effect of temperature in changing an abnormal to a normal pattern. USE OF FIELD EMISSION ELECTRON MICROSCOPE 923 That the surface has changed detectably is shown by the fact that at room T the emission decreased from 31 to 28 ^la even though V increased from 8840 to 8870 volts. This means that the abnormal "bumps" have decreased sHghtly. These effects get progressively more pronounced as the glowing T was increased to 1200°K. The 611 region is now the brightest; the small 310 and HI planes are still poor emitters. A continuation of the test showed that the HI plane became normal after one hour at 1300°K. The 310 plane became normal after one hour at 1500°K. After one hour at 1600°K, the pattern looked like normal clean W except that the 100 and 211 planes were larger than in photo a of Fig. 6; it was similar to Fig. 4, photo d, after glowing at 1600°K. PART II: EMISSION AND ADSORPTION PROPERTIES OF Ba ON W Field Emission from Ba on W Figure 7 shows a series of photographs in which successive units or "shots" of Ba were vaporized onto the W point. The geometry of the tube was such that the greatest rate of deposition occurred on the upper right 611 region (Fig. 3b) and tapered off to zero on an "arc" which passes slightly to the left of the upper left 211, central 110, and lower right 211 planes. (Photo f of Fig. 7) In this series a "shot" of Ba was produced by heating the Ba coil with 2.4 amps for one minute. Later calculations will show that one "shot" deposited about 0.5 to 0.7 of a monolayer in the 611 region so that 7 shots deposited 3 to 5 layers in this region and deposited about 1 layer near the "arc" region. The first photo shows clean tungsten treated so as to enlarge the 100 and 211 planes and to modify the shape of the 110 plane; the remainder of the surface is approximately on a paraboloid. In these latter regions the emis- sion density is nearly uniform. In the 110 plane on the negative, there is a clear but faint ellipse. This elUpse is enhanced by the Ba in photos b, c, and d. We believe this ellipse to be due to the edge of a 110 plane which extends over only part of the larger underlying 110 plane. At this edge the local field is larger than in nearby regions and hence produces slightly greater emis- sions even on clean W. When Ba is deposited on this plane the edge serves as a nucleation center for Ba clusters even at 300°K. Prominent clusters also appear on the edges of the 211 planes in photos b, c, and d. Clusters also appear on the paraboloidal surfaces. The existence of these clusters shows that Ba atoms can move over a short distance — about 200 A — even at room temperature. ^24 TSK BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 T = 1430" K V = 0 3 MINUTES V = 8500 ^ L = 30 /£A 2/5 SECOND Ba COIL 2.4 AMPERES 3 MINUTES V= 3150 ^ L= 50/tA 2/5 SECOND Ba COIL 2.4 AMPERES 1 MINUTE V=5000^ L=70/tA 2/5 SECOND Ba COIL 2.4 AMPERES 5 MINUTES V=3000^ L=50>M.A 2/5 SECOND Ba COIL 2.4 AMPERES 2 MINUTES V=3370^ L = 50mA 2/5 SECOND Ba COIL 2.4 AMPERES 7 MINUTES V = 3100 _ L = 50 iCtA 2/5 SECOND Fig. 7 — Patterns for successively increasing amounts of Ba on W with enlarged planes. use of field emission electron microscope 925 Formation and Disappearance of Crystallites As the number of Ba shots increases in Fig. 7, a large dark region develops and enlarges from the right 100 region. This is due to the well known fact that when the Ba concentration exceeds one monolayer the work function increases. If the Ba atoms remained where they were deposited, one would expect the patterns to consist of broad bright arcs whose centers were at the region of greatest deposition and whose radii would increase with amount deposited ; for 7 shots of Ba one would expect a narrow bright arc of nearly maximum possible radius. Such an arc does indeed appear after 6 and 7 shots; but the regions with more than a monolayer are not dark as expected; instead there appear in these regions intensely bright large area emission centers. These just begin to show after 3 shots and become more prominent for 4 to 7 shots. These bright emission centers have properties different from those of the clusters previously described; they are larger, may ap- pear on any plane, are in a continuous state of flicker even at 300°K, dis- appear at much lower glowing temperatures and can be observed at much lower applied voltages. In accord with Haefer,^ we believe that they are due to Ba crystals which grow normal to the surface; hence the term crystallites seems appropriate. At the crystallites the local field should be much greater than the average field and hence they should be observable at low applied voltages. Different crystallites should have a range of sizes and hence a range of spot sizes. Crystallites should occur only for Ba concentrations greater than monolayers and hence should be nearly independent of the underlying tungsten. Because of the very high current densities through a crystallite, one would expect a considerable increase in local temperature, perhaps even to the melting point of Ba which would change the size and shape of the crystalHte and hence the emission; this accounts for the flickering and agrees with the observation that the amount of flickering increases with the applied voltage and emission current. If the crystalHtes are solid Ba they should evaporate more easily than Ba clusters adsorbed on W. Furthermore the existence of similar crystallites for evaporated films has been deduced from electron diffraction experiments. Hence the evidence for crystaUites is quite good. Figure 8 shows the evidence for the disappearance of crystallites in the temperature range 370 to 615°K. Note that, as T increases from 370 to 510°K, the voltage required to get 50 microamps decreases from 3150 to 2500. Note also that up to 615°K no detectable amount of Ba migrates into the region beyond the outermost arc. The intensity of this arc decreases, presumably because V is decreased. 926 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 T = 370'*K V = 2500 4 MINUTES V = 2950 L= 50i^A 2/5 SECOND T = 450-K V = 0 5 MINUTES V=2650 L= 50/iA 2/5 SECOND T = 400°K V = 2500 5 MINUTES V= 2900^ L= 50 uA 2/5 SECOND T = 510°K V= 2300 6 MINUTES V = 2500 L=50uA 2/5 SECOND T = 420''K V=2400 10 MINUTES V=2900^ L=70aA 2/5 SECOND 2300 T = 615°K V: 5 MINUTES V= 2570 ^ L= 50 ^A 2/^ SECOND Fig. 8— The disappearance of crystallites from 370 to 615**K. USE or FIELD EMISSION ELECTRON MICROSCOPE 927 Migration of Ba on W Starting at about 800°K, Ba migrates over large distances — from one side of the paraboloid to the other or about 4000 A. Figure 9 shows the steps in the migration process and the early stages of evaporation. The migration process can be followed continuously by observing the screen for moderate V between 800 and 1000°K. Migration is essentially complete after five minutes at 1045°K. By then the crystallites have disappeared completely and with them abnormally high local fields. It is therefore possible to compute the field from the appHed voltage. Then, as explained above, values of (p and 6 averaged for the whole surface can be computed. In this way we find that for photos c and d in Fig. 9,

1200° evaporation can be observed in five minutes. This is evi- denced by the fact that after such glowing the value of V required for a given current increases. The details of the evaporation are continued in Fig. 10. From the values of V and i, values of (p and 6 have been calculated and are shown in Table I. From this table it appears that nearly all the Ba is evaporated in five minutes at 1600°K. Further information on how the evaporation rate at a given T varies with d can be deduced from experiments for which no photos are shown. Suppose, in the above series of experiments, the point had been glowed for twenty minutes instead of five minutes, the calculated Ba concentration 6 would have reached a somewhat lower value than .80, say .75. Still further glowing would have reduced 0 only sHghtly. From this we conclude that at T = 1200 and ^ = .75 the rate of evaporation or dS/dt is so small that additional glowing for twenty minutes reduces 6 by small amounts. If now T is raised to 1300°K for one minute, 6 is substantially reduced, perhaps to .65. After five minutes at 1300°K, 6 might be .55. After twenty minutes at 1300, 0 might be .51. Long times at 1300°K might reduce 0 to .50. Only by raising T above 1300°K could 0 be substantially reduced below .50. These observa- tions suggest that the rate of evaporation of Ba on W depends not only on T but also on 0: for a constant T it is substantially 0 for all values of 0 less than a critical value 0c. Above 0c, the evaporation rate increases rapidly with 0, perhaps exponentiaUy. Hence the probability of evaporation of a particular Ba atom depends on the proximity of neighboring atoms. This must mean that the forces between adsorbed Ba atoms are comparable to though smaller than the forces between Ba and W. A plot of the 0 values in Table I vs T would show that 0c varies linearly with T between 1130 and 1430 or between 0 = 1.00 and .18. 928 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 T = 800* K V = 2400 6.5 MINUTES V = 2800 ^ L=50/4A 2/5 SECOND T= 940''K V = 0 5 MINUTES V = 2650 _^ L= 50 aA 24 SECOND T = 1045'*K V = 0 5 MINUTES V= 2800 ^ L= 50 ^A 2/5 SECOND T=1130°K V=VARIED 5 MINUTES V = 2850^ L= 50 /^A 2/5 SECOND T = 1210° K V = 0 5 MINUTES V= 3250 ^ L= 50 /iA 2/5 SECOND T = 1275°K V = 0 6 MINUTES V= 4400 ^ L= 50 flA 2/5 SECOND Fig. 9— Migration of Ba on W from 800 to 1045*'K. Evaporation of Ba on W from 1130 to 127! JS^K. USE OF FIELD EMISSION ELECTRON MICROSCOPE 929 1330° K V 5 MINUTES V= 5000^ L= 50/iA 2/5 SECOND T = 1515°K V = 0 5 MINUTES V= 8350 L= lOfjifK 1/5 SECOND T=:1380°K V=0 5 MINUTES V=6000 L=50/iA 2/5 SECOND T=1670°K V = 0 3 MINUTES V = 9250 L = 27/£A 2/5 SECOND T = 1430»K V = 0 5 MINUTES V=7130 1 = 10 fjLA I/5 SECOND 9000 L= 30 /iA 2/5 SECOND Fig. 10— Evaporation of Ba on W from 1330 to 1670°K. 930 the bell system technical journal, october 1951 Temperature Effect on Clusters The photos in Figs. 9 and 10 show that, for all values of 0 from 1.0 to .10, the emission comes largely from clusters. It is interesting to observe, but difficult to portray in photographs, what happens if the temperature is raised above room T but kept below that at which it had previously been heated to reduce 6. As a specific instance we choose a case in which the treatment T was 1380°K for five minutes — photo b in Fig. 10 — for which 6 = .28. With an applied voltage at T = 300°K, the whole pattern and the clusters in particular are very steady. If T is now raised to about 700°K, the clusters bordering on the 211 planes and those in the 111 zone appear to be agitated: the brightness of any one cluster fluctuates up and down and the center of the cluster moves over about half a cluster diameter. Clusters in other regions are perfectly steady. As T is raised the 211 clusters agitate more violently and the clusters in nearby regions begin to agitate. At still higher T, the clusters in the 111 region begin to agitate but those surround- Table I Dependence of

volts 1.98 2.00 2.20 2.47 2.81 3.30 3.70 4.10 4.53 4.40 d ~1.0 -^1.0 .80 .62 .46 .28 .18 .08^.00 .Oq ing the 100 plane are still steady. For T near 800°K all clusters show some agitation. At 1045°K, the clusters near the 110, 211, and 111 planes agitate so violently that individual clusters can no longer be distinguished but merge into one another producing bright bands which presumably reveal contours on the tungsten surface. However, the clusters in the regions sur- rounding the 100 plane agitate so slowly that in a photo of J sec exposure they appear to be stationary. Photo a. Fig. 11 shows the result. Photo b shows the pattern immediately afterward at T = 300°K. These observations can be repeated as often as one pleases. Effect of Field on the Redistribution of Ba on W Photos c to f of Fig. 11 show that fields of 30 to 40 million volts/cm can redistribute some Ba from the 110, 211 and HI regions to the regions sur- rounding 100. Photo c shows the pattern after glowing at 1430°K for five minutes with V = 0. Photo d shows the pattern at T = 800°K after 3 min. with T = 800°K and V = 7380 volts. When T was reduced to 300°K, the pattern did not change appreciably. However, when T was kept at 800°K for three minutes with F = 0, the pattern changed drastically as shown in photo e. Photo f shows that the redistribution is not the result of glowing T =1380°K T = 1045° K V=0 V = 6900 , L = 70 /iA Vs SECOND 5 MINUTES 5 MINUTES V = 7100 T = 800° K V = 7380 3 MINUTES T = 1045° K T = 800° K 1= 70 fiA V = 8000 Vs SECOND NO TREATMENT T= 800°K V=0 3 MINUTES T=300°K L=70/zA Vs SECOND V = 7750 , 1=70 fiA 1/5 SECOND V = 7370 T = 1430° K V = 0 5 MINUTES 1 MINUTE 3 MINUTES T=300°K L = 70 JU.A 1/5 SECOND V = 7130 T = 300° K L= 70 /^A 1/5 SECOND V=7320 Fig. 11 — Effect of temperature and field on the agitation of clusters and the redistribu- tion of Ba. At 800 to lOOO^K, Ba clusters are violently agitated near 211 and 111 planes but relatively stationary near 100 planes. High fields cause Ba to migrate from 111 and 211 regions to 100 regions. 931 932 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 at 800°K. To get the redistribution effect it is necessary to have both a high T and a high V. It is fascinating and instructive to watch this redistribution progress slowly. To do this we start with a pattern Hke that in photo e with T = 300°K and V = 7370 volts. The clusters are steady everywhere. T is then raised to 800°K and the pattern observed for three to ten minutes. At first the clusters in the 110, 211, and 111 regions are in violent agitation while Table II Summary of Adsorption Properties tor Five Planes ON A Single Crystal Plane no 211 100 111 611 Clean W Approximate

4.9 4.8 4.6 4.40 1700 X 1300 400 260 <20 1700 X 1100 750 500 75 Changes shape 1300 800 400 1050 1050 1200 800 800 4.2 <20 <20 <20 Baon W:0 <1 Size of clusters in A °K for cluster formation °K for cluster disappearance °K for Ba migration °K for evaporation: depends on 50 to 200; median 100 300 370 300 370 420 370 420 800 -'500 1050 to 1600 300 —600 Baon W;0 >1 Size of crystallites in A °K for crystal formation .... °K for crystal disappearance. 200 to 600; median 400 300 300 300 600 600 800 300 800 the few clusters in the 100 region are stationary. In ten seconds a few more clusters appear in the 100 region. When a new cluster appears it seems to do so suddenly. One gets the impression that one cluster pushed a neighboring one closer to the 100 plane or that one cluster grew at the expense of material from a neighboring one. Gradually as the concentration of clusters in the 100 region increases, the brightness of this region increases while the bright- ness in the 110, 211, and HI regions decreases. A steady state is reached in three to five minutes. References 1. E. W. MUller, Pliys. Zs. 37, 838, 1836. 2. E. W. Muller, Zs.f. P/iysik 106, 541, 1937; 126, (Al, 1949; Naturwissenschajten, July 1950. 3. R. O. Jenkins, Reports on Progress in Physics 9, 177, 1942-43. 4. F. Ashworth, Advances in Electronics, 3, Feb. 1951. 5. M. H. Nichols, Phys. Rev., 57, 1940 p. 297. 6. Nordheim, Proc. Roy. Soc. 121, 1928 p. 638. 7. R. Haefer, ZeUs. f. Physik 116, 604, (1940). Heat Dissipation at the Electrodes of a Short Electric Arc By L. H. GERMER Platinum contacts are brought together 60 times a second, discharging on each closure a condenser of 0.01 mf capacity charged to 40 volts. The heat flowing along each electrode is calculated from a temperature diiTerence measured by thermocouples, and from this is determined the energy dissipated at each con- tact. If there is no arc on closure, the energy is the same on the two contacts, and is small. If there is an arc between the contacts before they touch, about 58 per cent of its energy is dissipated upon the anode and about 42 per cent upon the cathode. The distribution is the same in an arc between clean "inac- tive" electrodes and in the entirely different kind of arc occurring between car- bonized "active" electrodes. This information may be significant in developing an understanding of closure arcs which are the sole cause of the erosion of elec- trical contacts on closure. THIS paper is an account of direct calorimetric measurements of the energy dissipated at positive and negative electrodes when they are brought together to discharge a condenser. The experiments are called for by the fact that the erosion at the closure of electrical contacts is due to arcing/ and understanding how the energy of a closure arc is distributed between the electrodes is likely to help in developing a comprehensive theory of this arc which in turn may aid in the control of contact erosion. The experimental method is an adaptation to the present problem of a procedure^ used earlier in which crossed wires are separated and brought together 60 times per second by means of a magnetic loudspeaker unit, each closure discharging a condenser which is recharged after the wires have been separated. For the present experiments the two wires are made of platinum and are rather heavy, and the flow of heat in each of them is measured by a pair of thermocouples. There is a known length of wire between the two thermocouples of each pair which are connected in series to oppose each other, so that a galvanometer in either circuit will give a deflection proportional to the difference in temperature across the wire.'* The flow of heat along each wire is calculated from this temperature dif- ference and the thermal conductivity and dimensions of the wire. After making some corrections this gives the amount of energy dissipated upon the electrode at each discharge of the condenser. The two platinum test wires have diameters of 0.0635 cm and each is about 2.2 cm long from its end to the point where it is clamped in a very iL. H. Germer, //. App. Phys. 22, 955 (1951). 2 J. J. Lander and L. H. Germer, //. App. Phys. 19, 910 (1948), pp. 918-919. 3 This is the experimental arrangement used by J. J. Lander in measuring heat flow in his determinations of Thomson coefficients. Phys. Rev. 74, 479 (1948), Fig. 3. 933 934 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 heavy copper block. The thermocouples are Chromel-Alumel wires of 0.012 cm diameter and one couple of each pair is welded to its platinum wire 2.0 cm from the point where the wire is clamped in its copper block; the other couple of the pair is electrically insulated by a glass coating and is buried in a deep hole in the block. The electrical contact is made between points of the platinum wires a little beyond the welded thermocouples, and opening and closing of the circuit is achieved by striking one of the platinum wires beyond the point of electrical contact with the insulated armature of a speaker unit vibrating at 60 cycles. Each heavy copper block with its plati- num wire is mounted on a cantilever bar, the end of which can be moved by a screw to permit fine adjustment of the contacts. Adjustment can be made also by varying the voltage supplied to the speaker unit. In order to minimize thermal disturbances this equipment is mounted on a heavy steel base, and the speaker unit, which dissipates about 0.01 watt during operation, is thermally insulated from the contacts by three concentric heavy aluminum covers each in very good thermal contact with the steel base. All of this equipment is covered by a silvered bell jar of 21 cm inside diameter. An aluminum covered Celotex housing surrounds the bell jar and the thermocouple galvanometer, except for a small glass window for reading the galvanometer. The galvanometer light is turned on for only about one second at the time of each reading. The experiments are made in a constant temperature room. All of the significant tests consist in measurements of the heat flow along the platinum wires when they are brought together 60 times per second discharging at each closure a capacity of 10~^ f charged to a potential of 40 volts. At this potential an arc occurs between clean platinum electrodes if the circuit inductance is less than about 10~^ h, but there is no arc if the inductance is much higher than this.^ If the electrodes are operated in the presence of any one of various organic vapors they become coated with car- bonaceous material and arcing then occurs at every closure even when the inductance is quite high,^ Measurements have been carried out under three different experimental conditions: (1) clean electrodes with a circuit induc- tance of 0.05 X 10~* h and an arc at every closure, (2) clean electrodes with a circuit inductance of lOX 10"® h and no arcing, and (3) electrodes slightly carbonized by d-limonene vapor with a circuit inductance of 10 X 10~^ h and an arc at every closure. The condition of arcing on every closure, or of complete absence of all arcing, was readily determined for each experiment by continuous oscilloscopic observation.* The potential of 40 volts was chosen as the highest at which there is never a second arc (in the reverse *See reference 1, Fig. 1. HEAT DISSIPATION AT ELECTRODES OF SHORT ELECTRIC ARC 935 direction) which would impossibly complicate interpretation of the data. Experiments under conditions 3 were carried out with the limonene vapor pressure maintained at about the lowest value at which activation can be produced (0.06 mm Hg in most experiments). At this low pressure activa- tion does not develop until the electrodes have been operating for some time, but when it develops the open circuit potential after an arc is —5 volts 10 12 14 TIME IN MINUTES Fig. 1 — Readings of the galvanometer in series with the thermocouples in the moving electrode, when the electrode was positive and when it was negative. Electrodes activated by vapor of (/-limonene at a pressure of 0,06 mm Hg with 60 closures per second and an arc at every closure. Condenser of 0.01 mf charged to 40 volts, discharged on each closure through an inductance of 10 X 10~^h. Galvanometer deflections in mm are transformed into ergs per closure by multiplying by 0.510. The experimental points obtained from this figure are marked by small arrows on Fig. 2. which is also the value reached after arcing in the inactive condition. The observance of this open circuit voltage is proof that each arc is an arc in platinum vapor, and not carbon. An example of data taken upon active (carbonized) electrodes with a circuit inductance of 10 X 10"^ h (conditions 3), and an arc at every closure ending in an open circuit potential of —5 volts as verified by continuous observation of the oscilloscope recording the potential across the contacts, 936 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 is given in Fig. 1. The ordinates are readings of the galvanometer when it was in series with the thermocouples in the moving contact. The circuit for charging the condenser to 40 volts prior to each closure was turned on at 4 minutes with the potential of the moving contact positive. The potential was reversed at intervals of If minutes and finally turned off at 15 minutes. The deflections of 43.9 and 55.1 mm occasioned by the energy dissipated at the contact by the discharge of the condenser respectively when the contact was negative and when it was positive are translated into tempera- ture differences of AT = 0.1213 and ^T = 0.1523°C by multiplying by ar^ where a = 3.36 X 10~^ amp/mm of the galvanometer deflection, r = 33.7 ohms circuit resistance, and jS = 2.44 X 10^°C/volt thermocouple sensitiv- ity. Neglecting for the moment small corrections due to radiation and con- vection losses, these temperature differences are converted into heat flow along the wire of 22.4 and 28.1 ergs per closure by multiplying them by the factor B = 184.5 obtained from the dimensions of the wire, the thermal con- ductivity of platinum k = 0.699 watt/cm°C, and the factor 60 representing the number of closures per second. The heat flow in one of the wires differs from the heat dissipated by the arcs upon that wire because of radiation and convection losses, and because the higher temperature of the positive electrode results in some conduc- tion of heat to the negative electrode at their point of contact. It has been found expedient first to obtain data which are intended to be free from the last of these three sources of error and then to correct for radiation and con- vection losses as obtained by calculation. The energy in the electrode wires corresponding to the average excess temperature of the wires above their surroundings (0.07°C) represents the total energy of about 500 arcs. Thus the large scale temperature distribu- tion in one wire is inappreciably changed during the time the wires are in contact after an arc, and the transfer of heat from one to the other can be corrected for by making measurements of Ar across each wire for different fractions x of each cycle during which the wires are in contact and extra- polating the values so obtained to find ATq for zero time of contact. Data of this sort for experimental conditions listed as (1) above are plotted at the lower left side of Fig. 2, and for conditions (3) at the lower right side of the figure; the AT^o values from these curves are written downj on the first line of Table 1. On the upper half of the figure is plotted the total heat flowing along both wires as calculated by multiplying Ar by the factor B = 184.5 (not correcting for radiation and convection losses). All the solid circles on Fig. 2 (and Fig. 3 also) represent measurements upon the moving electrode, and the open circles measurements upon the stationary electrode. Differences between the solid circles and the open HEAT DISSIPATION AT ELECTKODES OF SHORT ELECTRIC ARC 937 F o t) 1 '-J O "^^ r- O -H II ro en ^i 3 1 13 * l' d '^" '^ 1 ^ 1 w ^— o > u -"w > 1 < 1 .1587°C ,0010 ,1597 ,48 ,12 ,71 = 31.31 a < + go-^. 00 ^ rrj «S 1 »o • ~» 1 1 -rt* O fC PC fN *^ f 6 1 1 O fO CD fO t^ '-^ o^ ' 00 do 00 II ^X^ ^ ESo< ^ •-< o II !^ <: 1 1 ■■^ i lO 1 1 -5 '-H fO fM O 2 < 1 1 0 dW O II ca ^^Ocg ^ IH G 28i^S3:^3£8 < '+ '^^^^ ro rt OT3 •s'i \^ si < o-^E-H--- c rt : cv AT^o fr for con rom A ■ection rrectio final V sure. . .^2'B'^g8c;'§ S .2 2i S o -5 g £? orrect roCor rgs/cl adiati onvec rgs/cl otal e :od 938 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 IMACTIVE ELECTRODES ACTIVE ELECTRODES 54 O QC I-IH 48 46 ~-^ - 1 -±--^4^-- 0.16 0.15 0.14 0.13 0.12 o.n 0.10 • 1 1 I • POSITIVE • o c 1 o ,, ( NEGATIVE — i - 1 > o 0.2 • ■—J K-J ^_c „. o POSITIVE ^ ^ ^ o NEGATIVE 1 . o 1 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 X, FRACTION OF TIME CLOSED Fig. 2 — Heat flow data at different values of x, the fraction of the time the electrodes are closed. Left hand curves, inactive electrodes, inductance 0.05 X 10"^/^, closing at 3.3 cm/sec. Right hand curves, active electrodes, inductance 10 X 10~^h, closing at 2.5 cm/sec. INACTIVE ELECTRODES ACTIVE ELECTRODES 50 «0 UJ 40 tr z) ^ *^ ^ ^ _,c 46 < -• hO Oq: 44 Q. 42 0.16 0.15 ? 0.13 I- < 0.12 0.11 0.10 o • ii:zzzzz Z^--r o — - 0 — •1 POSITIVE 1 * '^ -^ • 0 % GAT VE^ ^ 0 — l^ "^ ~~i — r POSITIVE NEGATIVE 0.2 0.4 0.6 0.8 0 0.2 CONTACT VELOCITY IN CM PER SECOND 0.6 Fig. 3— Data for different velocities at closure, all for x = 0.5. Left hand curves, in- active electrodes, inductance 0.05 X IQ-^h. Right hand curves, active electrodes, in- ductance 10 X 10-«A. HEAT DISSIPATION AT ELECTRODES OF SHORT ELECTRIC ARC 939 circles are to be attributed to differences between the electrodes, probably in the effective mean diameter. For observations in the active condition the solid circles of Fig. 2 are consistently higher than the open circles, but the opposite is true for measurements upon inactive surfaces. This reversal is not significant; it was brought about by an accident which necessitated rewelding the thermocouple to the moving electrode after the measure- ments upon the active surfaces had been completed and before the measure- ments upon the inactive surfaces. In earlier preliminary tests there was no difference of this sort; one must conclude that the welding operation altered the moving electrode. (In the case of the plots at the left of Fig. 3 below, some of the data were taken before the rewelding operation and some after.) The continuous curves drawn on the lower half of Fig. 2 have the ordi- nates Wex/B for the positive electrode and W(l — €x)/B for the negative, where W is the total energy per closure represented by the horizontal lines at the top of the figure and €x is the fraction of the energy flowing down the positive electrode. (0.5 < e^ < 1). The energy lost by the positive to the negative electrode by conduction per closure is clearly (co — ex)W. The temperature difference between the wires near the point of contact is (W/B) (2ex — 1) and, from analogy with the electrical formula for the spreading resistance of a circular contact of diameter /, the heat flow from one elec- trode to the other per second is found by multiplying this temperature difference by Ikx and the heat flow per closure by further dividing by 60. Equating the two expressions for heat flow one obtains ex = (60 Bea + Ikx)/ (60 B + 2lkx). The curves drawn on Fig. 2 have shapes determined by this expression with the two parameters €o and / chosen to fit the experimental points. The resulting values of €o and / are: €o = 0.58, / = 11 X 10~^ cm for the inactive electrodes and €o = 0.57, / = 3.3 X 10""* cm for the active electrodes. If the area of contact were truly circular and the contacting electrodes were crossed cy finders of perfect cross-section, these values of / would be simply related by elastic theory to the forces F holding the electrodes together when they are in contact. The formula^ is / = [6FD(1 — 'i^)/E]^ where D is the diameter of the wires, E is Young's modulus for platinum and V is Poisson's ratio. If we take^ E = 13 X 10^ gm/cm^, the above values of / correspond respectively to forces of 5 and 0.1 grams weight. No signifi- cance can, of course, be attached to these values of force other than to ob- serve that they are not wildly unreasonable. The average lapse of time between the end of each arc and contact of 5 A. E. H. Love, "The Mathematical Theory of Elasticity," Cambridge, fourth edition, 1927, page 197, equation 56. « R. Holm, "Electric Contacts," Hugo Gebers, Stockholm, 1946, p. 389. 940 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 the electrodes at or near the place where the arc occurred can be calculated from the velocity of the moving electrode at contact and the average sepa- ration of the electrodes when the arc took place. Measurements of this separation have been made earlier J Rough calculation of the local tempera- tures of the electrodes near the point of contact, making use of this average elapsed time, have shown that when contact is made these local tempera- tures are still far above the mean temperatures at the ends of the wires (perhaps higher by 10°C). The local temperatures reach the mean tem- peratures in a time which is very short in comparison with 1/60 second, and thus the conduction of heat from the positive to the negative electrode due to this local high temperature is not corrected for by the extrapolations of the curves of Fig. 2. This correction can be made by obtaining AT meas- urements for different electrode velocities and extrapolating to zero velocity. Such data are plotted in Fig. 3. It is obvious that the curves of the lower half of this figure must become horizontal as they approach zero velocity, but no other theoretical deduction has been made regarding their shapes. The differences between the AT values at the velocities of the data of Fig. 2 and at zero velocity are the required corrections, and these are written down on Hne 2 of Table 1. The correction seems to be small (0.001°C), or perhaps zero, for the active electrodes (right-hand side of Fig. 3) but amounting to about d= 0.005°C for the inactive electrodes (left-hand side). That the former should be smaller than the latter is in line with our knowl- edge that an arc between electrodes which are approaching each other will occur when they are farther apart if the electrodes are active than if they are inactive.*^ The values of ^Tq after applying the corrections of line 2 of Table I are written down on line 3. On line 3 are given also (columns 2) measured values of Ar for inactive electrodes in a circuit containing an inductance of 10 X 10~* h which completely prevented any arcing. On line 4 are values of the energy dissipated upon the electrodes per closure calculated from the ^Tq values of line 3. One must still consider corrections due to radiation and con- vection losses from the surfaces of the wires and radiation loss from the arc itself. These are taken up one at a time in the following paragraphs. If the only correction were due to radiation from the surfaces of the warm wires, the heat put into the end of a wire per second w would be related to Aro by the equation w = kwATo/L + HAATq/3, (1) where k is thermal conductivity, co , L and A are respectively the cross- sectional area, length and surface area of the wire, and H = 4^0 (re, the ' L. H. Germer, Jl.App. Phys. September 1951, Table I, line 3. (in press) HEAT DISSIPATION AT ELECTRODES OF SHORT ELECTRIC ARC 941 "outer conduction."^ For Tq = 300°K and the emissivity € = 0.05 at room temperature,® the second term of this expression reduced to ergs per closure has the values listed as "radiation correction" on line 5 of Table I; these corrections are negligible. The convection loss from a horizontal cylinder of diameter D has been givenio ^s 0.27^(Ar)^/VD'^^ in B.T.U. per hour with AT in °F, D in feet and A in square feet. For our system of units this becomes 4180^(Ar)^'V^^''* ergs/sec. To make the differential equation for heat flow linear this can be written approximately ^\mA{^TQ/2y'^^T/D^l\ and the heat put into the end of the wire per second taking account of convection loss would then be given by equation (1) with H = AlSOi^To/lDY'*. The second term of this expression reduced to ergs per closure has the values listed as "convection correction" on line 6 of the table. That the heat lost from the arc itself is quite negligible is clear from estimates of the duration of the arc and of its superficial area. The arc time is iriLCy^ which has the values 0.07 and 1.0 X lO"® sec respectively for the inactive and for the active surfaces. The average area of the arc which is effective in radiating is probably a great deal less than the area of the pit formed on one of the electrodes Tr(P/4:. In some experiments it was found^^ that d^ = 3.8 X 10"" cmVerg. If this estimate of pit diameter is right for the present tests, and we take the arc temperature to be the boiling point of platinum^^ 4803°C and the duration of the arc 1 X 10"* sec, the radiation loss comes out to be 0.01 erg. This is a gross upper limit. Reduction or the Data Not all of the energy in the charged condenser is dissipated in an arc on closure. During the arc some energy is dissipated by current flowing through circuit resistance, including spreading resistance in the electrodes at the site of the arc, and after the arc is over aU of the remaining energy is so dissi- pated. We need to sort out the amounts of energy which are spent in these different ways in order to make a careful analysis of the data represented by the numbers on lines 7 and 8 of Table I. The total energy is eo = CVl/2 where C = lO-^/and Vo = 40 volts in all of the experiments of this paper (eo = 80 ergs). The energy dissipated in an arc is Ca = C(Vq — Vi)v, where Vi = —S volts is the potential across the 8 H. S. Carslaw and J. C. Jaeger, "Conduction of Heat on Solids," Oxford, 1948, equa- tion (6), p 119. ^ This low value seems to be well established. See the paper by A. G. Worthing in a book "Temperature," Reinhold Pub. Co., 1941, Fig. 7 on p. 1175. 1° W. H. McAdams, "Heat Transmission," McGraw-Hill, 1942, equations (13a) and (19), pp. 240-241. " L. H. Germer and F. E. Haworth, //. App. Phys. 20, 1085 (1949), Fig. 5 on page 1088. ^ Reference 2, Table H on page 914. 942 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 open electrodes when the arc is over and ?' = 15 (for platinum)^"' is the arc voltage assumed to be strictly constant during the life of each arc which is very closely true. The energy left in the circuit after an arc is over is CVl/2. The total energy dissipated in the circuit is C[Vl/2 - (Fo - Vi)v - Vl/2] during the arc, plus CVi/2 afterwards. When closure occurs without an arc (conditions 2) the total initial energy CVo/2 is dissipated in the cir- cuit. Some of the circuit energy appears in the electrode wires and is meas- ured, as shown by the numbers of lines 7 and 8 of columns 2. It can probably be safely assumed that the fraction of the circuit energy which appears in the electrode wires is the same whether or not there is an arc. With this assumption, and knowledge of Vi and v, we can use the data of columns 2 and 3 to calculate two parameters, 77, the fraction of the circuit energy which appears in the electrode wires, and 6, the fraction of the arc energy which is dissipated upon the positive electrode for the active condition. The data of columns 1 are not to be used with those of columns 2 and 3 because of a different electrical circuit and in consequence a different (and no doubt larger) value of rj. Quantities of interest are defined here: total energy eo = CVJ2 arc energy ea = C{Vo — Vi)v energy which is measured | arc, Ca + 17(^0 — ^a) (true value) | no arc, r}eo factor by which all energy measurements are in error (i.e., experimental error) ^ fraction of arc energy at positive electrode 6 values obtained | arc, positive electrode, w+ by measurement | arc, negative electrode, w_ I no arc, total energy, wq From the way these definitions have been given it is clear that Wo = ^eo w+ = ^UaO + (eo — ea)r//2] These equations yield ^ = \(w+-\- W-)eo — (eo — e^w^jeoCa rj = 'Woea/{{w+ + W-)eo — (eo — ea)wo] 0 = [2w+ - (eo - ea)^]/2^ea. The known numerical values of C, Fo, Vi and v give, in ergs, eo = 80, Ca = 67.5, circuit energy dissipated during an arc = 11.25, circuit energy dis- " Reference 1, Table II, page 957. HEAT DISSIPATION AT ELECTRODES OF SHORT ELECTRIC ARC 943 sipated after an arc = 1.25. We identify w^ and w- with the numbers so designated in Table I. When the value of wq is taken from the table we im- plicitly assume that the electrical spreading resistance at the contact is so much larger than the rest of the resistance of the electrode wires that sub- stantially all of the heat wo is generated in the spreading resistance and not along the wires. With this assumption we obtain, ^ = 0.765 rj = 0.282 d = 0.580. The final result of the experiment is represented by the number 6 = .58 which means that a metal vapor arc between activated platinum electrodes dis- sipates 58 per cent of its energy upon the positive electrode and 42 per cent upon the negative electrode. This result differs only slightly from w^/{w^ -f- w-) = 0.577, the difference being the correction due to resistive heat de- veloped equally in the two electrodes. For the inactive electrodes we ob- tain w+/(w+ + W-) = 0.572 which is in close agreement, and it too must differ only slightly from the value which would be obtained if data were available for making the correction due to resistive heat. Reliability of Results The fact that the experiments account for only rj = 0.765 of the total energy need not be disturbing. It seems most likely that an inaccurate value for the thermal conductivity of the platinum wires and imperfect geometry of the wires account for this. The low resistance of the thermo- couple circuits does not affect the indications of temperature difference which they give. The large corrections of line 2 in columns 1 are highly uncertain as one sees readily by inspection of the corresponding curves of Fig. 3. If these corrections were taken to be zero one would obtain d = 0.556. It certainly seems unlikely that 0 for inactive platinum electrodes can be less than this value. Interpretation There are previous observations upon closure arcs between inactive elec- trodes which must be correlated with the results of these measurements There are no corresponding earher data upon active electrodes. A single closure arc between inactive platinum electrodes produces a pit on the positive electrode having a volume which is comparable with that to be expected if all of the energy of the arc is dissipated upon that electrode and is used there in melting and vaporizing metal with all of the 944 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 molten metal blown out from the arc crater by the pressure of metal vapor. ^"^ The metal from the crater is deposited in a rim about it and upon the negative electrode. There is considerable roughening of the negative elec- trode but none of its metal has been found upon the anode. This roughen- ing indicates, no doubt, that a small fraction of the energy is dissipated directly upon the cathode. Estimates of the amount of metal transferred from positive to negative, made after many thousands of closure arcs, have shown that about 1 per cent of the metal from an anode crater reaches the cathode. Microscopic examination of the surfaces after a single arc reveals that the transferred metal upon the cathode seems to be much greater in amount than the 1 per cent found after many arcs. There is thus a distinct disagreement between the results of transfer measurements after many arcs and what one sees upon the surface of the cathode after a single arc. Measurements of the present paper could be accounted for by assuming that most of the energy of a closure arc is dissipated upon the anode in melting and boiling metal, and that the energy is then located in this dis- placed metal with 58 per cent of it finally freezing on the anode and 42 per cent on the cathode. This tentative conclusion agrees with microscopic ob- servations upon the electrodes after a single closure arc but is in sharp disagreement with the results of measurements of transfer of metal resulting from many arcs. At the time this paper is being written it is felt that more penetrating experiments are called for, and in particular transfer measurements upon both active and inactive surfaces under experimental conditions which are better controlled than any which have been made previously. " L. H. Germer andF. E. Haworth, Phys. Rev. 73, 1121 (1948) and Reference 11, Figs. 5 and 6. Detwinning Ferroelectric Crystals By ELIZABETH A. WOOD Unstrained single crystals of barium titanate can be detwinned under the influence of an electric field at elevated temperature, but strained crystals can- not. It seems probable that this is also true of crystals in a polycrystalline body such as a ceramic. EACH of the ferroelectric^ crystals so far discovered has a structure which closely approaches a more symmetrical structure into which it transforms at the Curie temperature. In all of them, the deviation from the more symmetrical structure is so slight (Table I) that the application of mechanical stress or electric field can produce a shift from one orientation of the lower symmetry structure to another. Since, in crystals grown from the melt, such as barium titanate, inhomogeneous mechanical stresses re- sulting from inhomogeneous cooling or differential thermal contraction of the surrounding flux material are present in the crystals as they pass through the Curie temperature, these crystals commonly comprise regions of two or more orientations of the lower-symmetry structure, symmetrically related. They are, in other words, twinned. In this condition the electrically polar direction differs in orientation from one individual of the twin to another^. Since it is frequently desirable to have the polar direction oriented uniformly throughout the crystal, it is of interest to determine under what conditions this state can be achieved. It is not possible in all crystals. The discussion in this paper will be confined to barium titanate because more experimental data are available for this crystal, but it is probable that similar considerations are applicable to the other ferroelectric crystals. The process of causing the polar axis in a ferroelectric crystal to have the same orientation throughout the crystal has been called "poling." It is the process of detwinning the crystal. As C. J. Davisson and others pointed out in connection with the problem of detwinning quartz crystals during World War II, if the crystal is subjected to a stress which will be lessened if the "misoriented" regions change to the desired orientation and if the activa- tion energy of the change is not too great, the crystal will be detwinned. ^ Ferroelectric crystals are those crj'stals which exhibit, with respect to an electric field, most of the phenomena exhibited by ferromagnetic crystals with respect to a mag- netic field, such as spontaneous polarization, domain structure, hysteresis of response to an alternating field and a Curie temperature above which these unusual characteristics are not present. ' By the ferromagnetic analogy each twin individual is called a ferroelectric "domain." 945 946 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Table I Substance Barium titanate Potassium niobate Rochelle Salt Potassium dihy- drogen phos- phate Stable Structure at lower temperature Tetragonal c = 4.04, a 4.00 Orthorhombic a = 5.70, b = 5.74, c = 3.98 equiva- lent to special case of monoclinic in which a = c = 4.04, b = 3.98, /3 = 90°, 20' dz 5' Monoclinic Orthorhombic Closely allied more sym- metrical structure and the Curie Temperature above which it is the stable structure Cubic, 00= 4.00 Tc = ca. 120°C Cubic, ao = 4.04 Tc = ca. 435°C Orthorhombic Tc = ca. 24°C Tetragonal Tc = ca. -152°C Difference 1% of the length of the c axis 1.5% of the length of the c axis -f a shear angle of about 20' A shear angle of about 3' Small shear Fig. 1 — A. Crystal a as received from the melt. Edges at 45° to polarization direc- tions of crossed nicols. Dimensions of surface: .2 x .2 mm. B. Crystal b as received from the melt. Edges at 45** to polarization directions of crossed nicols. Dimensions of surface: .15 x .2 mm. With barium titanate as with quartz, the activation energy of this change can be reduced to zero by heating the crystal through a polymorphic transi- tion above which its symmetry is such that the twinning can no longer exist. It is then cooled through the transition under the influence of the applied stress which favors one of the possible twin-orientations. DETWINNING FERROELECTRIC CRYSTALS 947 Single-crystal Experiments Parts A and B of Fig. 1 are photomicrographs of barium titanate crystals, both grown from the same melt by B. T. Matthias. The composition of the melt was 26 grams BaCOs , 6.5 grams Ti02 , 50 grams BaCl2 , and the method followed was that described by Matthias in 1948^. Each of the crystals shows several domains and some inhomogeneous strain as indicated by birefringence evident between crossed nicols when the crystal is at the extinction position, Fig. 2, A and B, i.e. when its edges are parallel to the polarization directions in the polarizer and analyzer. An unstrained crystal in this position appears black between crossed nicols. Fig 2 — A. Same as Fig. lA, but at extinction position. B. Same as Fig. IB, but at extinction position. Optical Evidence of the Effect of a High Field However, crystal a can be made to assume essentially a single orientation throughout by the application of a high field at elevated temperature as shown in Fig. 3A, but the same treatment applied to crystal h results only in the formation of a large number of domains, as shown in Fig. 3B. A field of 16000 volts per cm. was applied across each crystal at 125°C. and continued until the crystal had cooled to less than 50°C. Parts A and B of Fig. 4 are the extinction-position photographs corresponding to Parts A and B of Fig. 3. X-RAY Evidence of Inhomogeneous Strain The reason for the difference in behavior of the two crystals is suggested by their back-reflection Laue photographs. Parts A and B of Fig. 5 are Laue • Matthias, B. T., Phys. Rev. 73, 808-9, 1948. 948 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 photographs taken before the attempt was made to pole the crystals. Whereas a Laue photograph of a perfect single crystal would show a pat- tern of single spots, crystal a shows a pattern of groups of spots joined by Fig. 3 — A. Crystal a after the application of a high field at elevated temperature. Edges at 45° to polarization directions of crossed nicols B. Crystal h after application of a high field at elevated temperature. Edges at 45° to polarization directions of crossed nicols. Fig. 4 — A. Same as Fig. 3A, but at extinction position. B. Same as Fig. 3B, but at extinction position. fainter streaks and crystal b shows a pattern of short streaks. In both cases, the streaks indicate crystal material of continuously varying orientation, but in the case of crystal a it is transitional in orientation between two or Fig. 5 — Laue photographs of the two crystals before treatment. The symmetrical half of each photograph has been removed to facilitate close comparison. A: from crystal a; B : from crystal b. 949 950 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 more twin-related orientations and is probably twin-boundary material, whereas crystal 6 is a bent crystal. The evidence for this interpretation lies in the facts that (1) the streaks in Fig. 5 A converge at the reflections from the various (101) planes which are twin planes, whereas those in Fig. 5B do not; (2) the streaks in Fig. 5B show only that variation in length which is due to the use of a flat film whereas those in Fig. 5 A show greater variation; and, finally, (3) the streaks in Fig. 5B are of nearly uniform intensity throughout, whereas those in Fig. 5A are faint streaks between strong end points. These three points are discussed in the following section. Distinction between Twin-Boundary and Other Inhomogeneous Strains in Crystals The spots on a back-reflection Laue photograph may be considered as the intersections of the film with normals to atomic planes in the crystal, modified by a non-linear scale factor. The position of any spot is inde- pendent of the wave-length of the x-rays producing it and dependent only on the orientation of the reflecting plane. When the x-ray beam falls on a twin boundary two families of twin- related spots appear on the fihn. In barium titanate twin-related spots from equivalent planes are close to each other. If the two spots of such a pair are joined by a line these lines will all converge toward the spot from the (101) plane which is the twin plane, the plane across which reflection of the struc- ture would produce the twin configuration. (See Fig. 6, a back-reflection Laue photograph of a barium titanate crystal with only 2 twin-related orientations.) That this must be so will be clear from Fig. 7. With the exception of the twinning plane the planes in this figure represent zonal planes, planes containing two or more atomic-plane normals. The zonal planes on the two sides of the twin plane represent the zonal plane orienta- tions in the two parts of the twin. The only zonal plane directions common to both parts of the twin are those normal to the twin plane since these are the only directions not changed by reflection across the twinning plane. The one direction common to all these unchanged zonal planes is the nor- mal to the twin plane. Thus the zonal arcs on the plane photograph which are common to spots from both parts of the twin intersect in the reflection from the twin plane. Referring now to Parts A and B of Fig. 5, we see that the streaks in Fig. 5A lie along the zonal arcs common to both parts of any given twin pair and are intermediate between the spots of the twin pair. They are therefore reflections from material transitional in orientation between the two twin orientations. The streaks in Fig. 5B, however, do not converge toward a DETWINNING FERROELECTRIC CRYSTALS 951 (101) plane-normal, but rather, when the non-Hnear scale factor has been taken into account, are all normal to the (100) axis which lies parallel to the film in a top-to-bottom direction. They therefore come from crystal planes bent around this axis of a twinned barium titanate crystal. Fig. 6 — Laue photograph of a barium titanate crystal with only two twin-related orientations. A section through the reciprocal lattice of a twinned barium titanate crystal is shown in Fig. 8A: that of a bent crystal, in 8B. In the reciprocal lattice of a tetragonal crystal the direction of each point from the origin is the same as the direction of the normal to the set of planes it represents and the distance of each point from the origin is proportional to the recip- rocal of their interplanar spacmg. Since the back reflection Laue photograph shows only orientations of the atomic planes it may be thought of as a 952 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 shadowgraph of the reciprocal lattice, illuminated by a point source of light at the origin, as indicated by the dashed lines in Figs. 8A and 8B. TWINNING PLANE "^ NORMAL TO TWINNING PLANE Fig. 7 — Diagram of zonal relations between the two parts of a twinned crystal, o y ////I r ! // //ri 6 I \\ / / / I FILM / / / / / / / / / / / / ; an 1 1 ■UJ- (a] (b) Fig. 8 — A. Section of the reciprocal lattice of a twinned crystal and its Laue photo- graph. B. Section of the reciprocal lattice of a strained crystal and its Laue photograph. From these figures the second point of difference between Laue photo- graphs 5A and 5B becomes clear, namely, that in the case of the bent crystal viewed normal to the bending axis the streaks appear rather uni- form in length, whereas the streaks from the inter-twin oriented material DETWINNING FERROELECTRIC CRYSTALS 953 Fig. 9 — Laue photographs of the two crystals after treatment, paired as in Fig. 5. A: from crystal a;B: from crystal b. 954 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 diminish in length as they approach the twin-plane normal. This is perhaps more obvious in Fig. 6 where only one pair of twins is shown. Finally, the streaks from bent crystals are more uniform in intensity than those with intertwin-oriented material, but if the bending were non- uniform or the intertwin material more abundant this might not be so. X-RAY Evidence of Effect of High Field The Laue photograph of crystal a, taken after the poling process had caused it to become a single untwinned crystal. Figs. 3A and 4A, is shown in Fig. 9A. It shows a pattern of single spots. The absence of streaks agrees with the paucity of birefringent regions in Fig. 4A in indi- cating very little inhomogeneous strain in the crystal. The Laue photograph of crystal 6, taken after the poling attempt had produced only a regular multiple-twin pattern in it, Figs. 3B and 4B, is shown in Fig. 9B. The inhomogeneous strain has not disappeared, as indicated also by the birefringent regions in the photograph of Fig. 4B. Summary of Results of Single-Crystal Experiments From the experiments described above it is concluded that barium- titanate crystals with only twin-boundary strain can, under the influence of a high field at elevated temperatures, be caused to have a single crystal- lographic orientation whereas barium titanate crystals otherwise strained cannot. Application to Barium Titanate Ceramics Single crystals of barium titanate large enough for practical applications have not yet been grown. Therefore all practical applications using barium titanate have so far used it in the ceramic form. Ceramics have been made for two dififerent applications: condensers and electromechanical transducers. For the first, the maximum electrical po- larizability for a given applied electric field is desired, since this results in a high dielectric constant. For the second application, however, it is desira- ble to have a ceramic which will deform mechanically in an electric field according to its own polarity. With this end in view, ceramics intended for electromechanical transducers have been poled by being subjected to a high field (roughly 15000 v/cm.) as they were cooled through the Curie tempera- ture to room temperature. In a series of unpublished experiments W. P. Mason and R. F. Wick of the Bell Laboratories have found that certain barium titanate ceramics, when poled in this way, retain their polarization in spite of high reverse fields (J to J the poling fields), i.e. require a high coercive force to change DETWINNING FERROELECTRIC CRYSTALS ^55 the direction of their polarization. Such ceramics can be used iri piezo- electric devices with high alternating fields without "depolarization" and can therefore achieve electro-mechanical coupling at higher power levels than ceramics that do not retain their polarization under the influence of a reverse field. Only a small proportion of ceramic specimens could be poled in this way and the factor common to these has not yet been ascertained. In the light of the single-crystal experiments reported in this paper, it seems apparent that ceramics composed of inhomogeneously strained crys- tals (excluding twin-boundary strain) could not be poled. Three ceramic specimens whose poling history was known were available. Of these only one could be poled. X-ray diffraction photographs of the two unpolable ceramics showed streaked reflections from the individual grains, indicating strain. The grain-size of the polable specimen was much smaller, so small that reflections from individual grains could not be identified. It is anticipated that ceramics for different uses should be differently fired and perhaps even differently composed as well as subjected to different electrical treatment subsequent to their formation. Longitudinal Modes of Elastic Waves in Isotropic Cylinders and Slabs By A. N. HOLDEN The general properties of the longitudinal modes in cylinders and slabs are de- veloped with the aid of the close formal analogy between the dispersion equations for the two cases. 1. Introduction THE classical exact treatments of the modes of propagation of elastic waves in isotropic media having stress-free surfaces but extending indefinitely in at least one dimension are those of Rayleigh^ for semi- infinite media bounded by one plane, of Lamb^ for slabs bounded by two parallel planes, and of Pochhammer^ for sohd cyhnders. Rayleigh showed that a wave could be propagated without attenuation parallel to the sur- face, in which the displacement amphtude of the medium decreased expo- nentially with distance from the surface, at a velocity independent of fre- quency and somewhat lower than that of either the plane longitudinal or plane transverse waves in the infinite medium. Such ''Rayleigh surface waves" have received appUcation in earthquake theory. For slabs or cyhnders the treatments lead to a transcendental secular equation, estabhshing a relation (the "geometrical dispersion") between the frequency and the phase velocity, which for some time received only asymp- totic appUcation in justifying simpler approximate treatments. The past decade, however, has seen a revival of interest in the exact results'*- ^ stimu- lated by experimental appUcation of ultrasonic techniques to rods^- ® and slabs,' by the use of rods and the like as acoustic transmission media, and perhaps by curiosity as to what quaUtative correspondence may exist be- tween such waves and the more intensively studied electromagnetic waves in wave guides. That this correspondence might not be close could be antici- pated l^y observing that an attempt to build up modes by the superposition of plane waves in the medium reflected from boundaries would encounter an essential difference between the two cases: the elastic medium supports plane waves of two types (longitudinal and transverse) with different veloc- ities, and reflection from a boundary transforms a wave of either type into a mixture of both. On grounds both formal and physical it may be expected that solutions to the equations of smaU motion of the medium with a stress-free cyUndrical boundary can be found with any integral number of diametral nodes of the 956 LONGITUDINAL MODES IN CYLINDERS AND SLABS 957 component of displacement along the rod, as well as for the "torsional" modes in which there is no displacement along the rod whatever. The clas- sical results are for no such nodes, the "longitudinal" (or "elongational") modes, and for one such node, the "flexural" modes. The secular equation for modes with any number of such nodes has been exhibited by Hudson.^ For any one of these types of mode, it may be expected that the secular equation will define a many-branched relation* between frequency and phase velocity, and that a different number of interior cylindrical nodal surfaces for the displacement components might be associated with each branch. Apart from the relatively simple torsional modes, the only branches whose properties have been intensively studied are the lowest branch of the longitudinal'* and the lowest of the flexural^ modes, because they (and the lowest torsional branch) are the only ones extending to zero frequency, the others exhibiting "cut-off" frequencies at which their phase velocities become infinite and below which they are rapidly attenuated as they prog- ress through the medium. Three qualitative results of these studies are of especial interest. In the first place, with increasing frequency the phase velocity in the lowest lon- gitudinal and flexural branches approaches the velocity of the Rayleigh surface wave, and the disturbance becomes increasingly confined to the surface of the cyUnder. In the second place, the dispersion is not monotonic as it is in the electromagnetic case: the phase velocity exhibits a minimum in the lowest longitudinal branch* and a maximum in the lowest flexural branch^ with varying frequency. Finally, in the lowest longitudinal branch at least, the cyUndrical nodes of the displacement components vary not only in radius but even in number with the frequency.* The last result suggests that it would be difficult in practice to drive a cyUndrical rod in that pure mode represented by its lowest longitudinal branch over any extended frequency range, since it is difficult to visualize a driving mechanism having suitable nodal properties. Longitudinal drivers which can be readily constructed may be expected to deUver energy to all longitudinal branches, in proportions varying with frequency. How satis- factory such a transmission device could be would depend importantly on how much the phase velocities at any one frequency differed from branch to branch. This paper sketches the behavior of the higher longitudinal branches. That behavior could, of course, be determined exactly; Hudson^ has shown how the calculation of the roots of the secular equations can be facilitated, * This is true in particular of the flexural type of mode, and in his otherwise excellent treatment of flexure Hudson's statement to the contrary must be disregarded. Recent writings in this field have tended to distinguish as "branches" what in allied problems are commonly called "modes". 958 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 and Hueter* has used graphical methods. The alternative adopted here is a semi-quantitative treatment, assisted by extensive reference to the be- havior of longitudinal waves in slabs,* for which the secular equation is simpler and closely analogous. The analogy in the case of flexural modes is considerably less close and will not be discussed. The general consequences of the inquiry are that the higher longitudinal branches have phase velocities which are not necessarily monotonic func- tions of frequency. With increasing frequency, however, those velocities all approach that of the plane transverse wave,** not that of the Rayleigh sur- face wave (nor that of the plane longitudinal wave, as some investigators had guessed), a fact reflected perhaps in the experimental observation that driving a rod transversely usually provides purer transmission than driving it longitudinally. t Variation of nodal cylinders in location and number with frequency persists in the higher branches. 2. The Slab The slab extends to infinity in the y, z plane and has a thickness 2a in the ^-direction. The displacements of its parts in the x, y, z directions are w, v, w. Its material has density p and Lame elastic constants X and /x, so that its longitudinal wave velocity is ■\/{2y. + X)/p and its transverse wave veloc- ity is y/n/p. That ju should be positive is a stability requirement of ener- getics; X will also be taken as positive since no material with negative X is known. The equations of small motion are, in vector form, (2/x -j- X) grad div (w, v^w) — ji curl curl (w, v, w) = p —z («, v^ w). or Solutions representing longitudinal waves propagated in the z direction can be of the form where U is an odd function, and W an even function, of x alone, co is the frequency in radians per second, and 7 = co/c where c is the phase velocity. Solutions independent of y are chosen here because they provide the simplest analogues to the case of the cylinder. Substitution shows that U = Ae "" ^ * I am indebted to Dr. W. Shockley for the suggestion that this behavior might dis- play a close enough analogy to that of the cylinder to provide insight; the work of Morse bears out the analogy. ** The fact is noted by Bancroft. t Private communication from H. J. McSkimin. LONGITUDINAL MODES IN CYLINDERS AND SLABS 959 W = Be* *, is a solution (where A and B are constants measuring the am- plitude), if either (0 kl = -^ -y' and y A, = hB,, 2 or (ii) ^2 = — — 7^ and ^2^2 = —7^2- M When solutions of both types are so superposed as to make U odd and W even U = iAi sin hx -{- iA2 sin ^2^, (1) 'Y kv W = Ai - COS kix — A2 — cos ^2:*^. (2) ki 7 The normal and tangential stresses on planes perpendicular to x are du X.= (2. + X)?^ + x(g4-g), X. = .(£ + g) /aw aa>\ and the requirement that they vanish 2X x — dtza leads to the boundary conditions -4i(X7^ + (2/x + X)^i) cos ^la + 2^2M^i^2 cos ^2^ = 0, 2^117^ sin kia -\- ^2(7^ — ^2) sin kza = 0, the vanishing of whose eliminant with regard to A\ and ^2 is the secular equation. Although in principle that equation establishes a relation be- tween 7 and CO, it is more conveniently examined when expressed in terms of a = kia and /8 = kia, which are quadratically related to co and 7 by (i) and (ii). In those terms it becomes (Xi82 + (2m + \)o?Y cos a sin j8 (3) -f 4(m + X)Q:/3(Mi8'^ - (2m + \W) sin a cos iS = 0. The physically interesting quantities can be expressed in terms of a ard /8, with the aid of (i) and (ii). Thus P"^ = 4roV (^ - "'>> ^»d (4) a^M + X) 2 MiS' - (2m + \)a /.x '>' = 2/ _L A\ • ^^^ 960 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Hence, denoting / = jS/a, the phase velocity c = w/y is given by where £ is an "effective stiffness", a function of the elastic constants and /. Since jS = 0 is a trivial root of equation (3), it can be divided by j8, and the expression on the left then becomes even in both a and /5 and (3) can be regarded as an equation in a^ and jS^. From (4) and (5) it is evident that, if CO and y are both to be real, o? and ^"^ must be real and must obey the ine- quaHties )S2 > a\ M/32 > (2m + X)c^, (7) and thus the root /3 = a can be neglected. The general character of the desired roots can consequently be exhibited on a plot of ^ against o?. Evi- dently on that plot lines of slope unity are lines of constant frequency (equation 4), and lines radiating from the origin are Unes of constant veloc- ity (equation 6). As will appear later, however, it is more convenient to use a Unear rather than a quadratic plot, real a being measured to the right, imaginary a to the left, of the vertical axis, and real jS upward, imaginary j8 downward, from the horizontal axis. Here radial lines are still lines of constant velocity, but lines of constant frequency are no longer simple. In Fig. 2 such a plot has been sketched for the first few modes of a mate- rial obeying the Cauchy condition X = /*; the properties shown are restricted to those derived in the following paragraphs, and are lettered in Fig. 1 to correspond with those paragraphs. (a) By virtue of (7), the significant portions of the roots lie above and to the left of the lines ^ = a^ ^l^ = (2/^ -f \)o?. Setting /z/S^ = (2;x -f X)^^ in (3) reveals the cut-offs at sin /8 = 0 and at cos a = 0: in other words at /32 = «V, c^ = — ^ «V, and also at 0" = '^±±1 (n + -\ ir\ 2/i 4- X M \ 2/ / iv o? = V^~^9/ ^» where n is any integer. (b) Setting a = 0 in (3), it can be seen that the roots intersect the line a^ = 0 at the points sin /3 = 0. By calculating the derivative of ^ with re- spect to o?j those points (at which a changes from pure real to pure imaginary) dQ can be shown not to be multiple points, and the branches to have 3- = 0 da and •Tr4s — ^rs > independent of branch number and negative for d\fi^) X^ LONGITUDINAL MODES IN CYLINDERS AND SLABS c g b f 961 A Cor IMAGINARY) 0 TT a REAL Fig. 1 — ^Lines and intersections, discussed in the correspondingly lettered paragraphs of the text, which determine the properties of the first five branches of the longitudinal modes for a material obeying the Cauchy condition. Two coincident pairs of points are marked (2). Z=i2fI7p c=V(277+X)^ = 00 A (or IMAGINARY) a REAL Fig. 2 — A rough sketch of the branches determined by the properties illustrated in Fig. 1. 962 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 all materials. At those points the phase velocity is that of a plane longi- tudinal wave. (c) Setting sin i3 = 0 reduces (3) to a^Qi^^ - {2n + \)a^) sin a = 0, and hence in the region of positive /S^ and negative c^ the roots do not inter- sect the horizontal Unes /3^ = wV (n f^ 0). As can be seen from (6) this confinement imphes that the velocity is asymptotic to -x/ji/p, that of a plane transverse wave, with increasing frequency. Notice that, in the re- gion of positive jS^ and negative oi^, /3 takes the values Cos /3 = 0 only where XjS^ + (2)Li + X)«^ = 0 and that the roots have zero slope there. At those points the waves have a phase velocity \/2 times that of a plane transverse wave. (d) In the region of positive jS^ and positive a^ the roots exhibit a some- what more complicated behavior, but confining lines can again be found: the diagonal fines ^ = {n + J)^ — a. It is the nature of such critical lines as these which can be better exhibited on the linear than on the quadratic plot. Alternatively those lines can be written cos a cos jS — sin a sin ]8 = 0 (and thus will be shown to have analogues in the case of the cylinder), and substitution of this expression into (3) shows that if the roots intersect these lines they must do so for values of a and (3 satisfying the relation 40i + X)a|8(iUi82 - (2)u ^- X)^^) = -(XjS^ + (2/x + \)a'y cot^ a. But the inequahties (7) make such values impossible. (e) This suggests that in that region the roots may osciUate in a some- what irregular manner about the diagonal fines /3 = wtt — a. Indeed it is immediately evident that they pass through the points cos jS = cos a = 0 and sin /8 = sin a = 0. (f) Expressing those fines as sin a cos /S + cos a sin /8 = 0, and sub- stituting into (3), shows that additional intersections may be afforded by any roots of the quartic equation (X^ + (2m + X)a2)2 - 40u -I- X)a/30u^2 _ (2^ + x)o;2) = 0 which obey the inequalities (7). Discarding the root a + /3 = 0, and dividing by o^, yields the cubic equation X2/3 - {2n -h XyP + (2m + X)(2m + S\)l + (2m + \y = 0, (8) whose roots are the negatives of the roots of the cubic equation for the Rayleigh surface wave velocity. It is weU known that the Rayleigh cubic always yields one and only one significant positive root, and hence equation (8) can afford at most two additional significant intersections of any root of the secular equation with the fine about which it oscillates. Although it LONGITUDINAL MODES IN CYLINDERS AND SLABS 963 is not feasible to exhibit the roots of the Rayleigh cubic explicitly for arbi- trary fi and X, it is of some interest to exhibit its discriminant Z) = ^ \\2n + X)'(m + X)'(11X' + 4XV - 9Xm' - 10m'), and to note that for real positive values of X and n it changes sign only once, at approximately X//x = 10/9. Hence for \/fx > 10/9 two roots of the Ray- leigh cubic are complex, while for \/ii < 10/9 two roots are real and nega- tive. For a material obeying the Cauchy condition X//i = 1, the roots of the Rayleigh cubic are —3, —3 db 2\/3; thus I = 3^ 3 + 2\/3, both of which obey the inequalities (7), are relevant to intersections of each branch of the roots of the secular equation with the hne about which it oscillates. (g) The results of (e) and (f) suggest the value of a similar investigation in the region of imaginary a. Here (denoting a ^ iA and L = ^/A where A is taken positive and real) intersections occur between the branches and the Hnes sinh A cos ^ — cosh A sin ^ = 0 when (XL^ — (2^ + X))^ = 4(jLi + \)L{p.D -\r (2m + X)). Clearly this quartic in L has two and only two positive real roots, one greater and one less than \/(2m + X)/X. In the case X = Mj those roots are approximately 9 and 1/3. This information, taken with that of (c), establishes that the branches are confined in the region of imaginary a to bands determined by wx < j8 < (w + J)7r, having one tangency to the Hnes /3 = (« + Dtt; and that at values of A greater than correspond to the smaller root of /, the branches lie in the bands mr < /?<(»+ i)7r. It is convenient to obtain assurance that in general the branches do not intersect at any point by noting that the confining lines of paragraphs (c) and (d) define bands within each of which in general one and only one cut- off point falls. Pivoting a ruler about the origin of Fig. 1, and recalling the cut-off conditions, avails. Degenerate cases arise when the elastic constants satisfy a condition 2m + X = «V where n is an integer; in those cases some cut-off points coincide in pairs on some confining lines. Calculation of de- rivatives at those points shows that the cases are not otherwise exceptional: the pair of roots forms a continuous curve which is tangent to the cut-off Hne at the double cut-off point. From (6) it follows that the phase velocity will have a maximum or a minimum with frequency if -jrr-r. = -5 . That condition requires . 2 ^ _ (X/3^ + (2m + xWfi'K'^' + (2m + X)(2m + S\W) ^^"^ " 4(m + X)(2m + X)V(^2 _ ^2) (^^2 « (2^ 4. x)«2) • 964 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 In the region of positive ^' and a^ and of the inequalities (7), this is impos- sible, but when a^ is negative the condition may be satisfied. If it is satis- fied in the higher branches, however, it must be satisfied an even number of times in any branch, so that the branch exhibits as many maxima as 3.0 1.5 2.0 2.5 3.0 3.5 r( PROPORTIONAL TO FREQUENCY) 5.0 Fig. 3 — The beginnings of the dispersion curves inferred from Figs. 1 and 2. The solid shaded lines are the curves about which the branches oscillate, intersecting them at the triangles and lying on the shaded side of them elsewhere, and the dashed extensions are the branches themselves. For increasing t these branches all become asymptotic to the base line. The dashed lines at the top are the true cut-off frequencies; the solid "cut-off" line^ are the asymptotes of the shaded curves. The beginning of the lowest branch is shown at the lower left; it becomes asymptotic to a line below this plot. i-^/'- 2 after passing through a shallow minimum. minima, for clearly the phase velocity is a decreasing function of frequency near the cut-off, and the velocity can also be shown to approach its asymp- totic value at high frequencies from above in the higher branches. In finally displaying the dispersion curves (Fig. 3) it is convenient to use as reduced variables r, the number of plane transverse wave lengths in LONGITUDINAL MODES IN CYLINDERS AND SLABS 965 one slab thickness (which is proportional to the frequency), and ~~, the Co ratio of the velocity to that of a plane transverse wave. Evidently 2 _ fccaV _ 1 2m + X,^2 2^ AV (2m + X)(/'-1) _{coaV 1 2M + X..2 2. fcV nP - (2m + X) ' where Co = 'x/fi/p. For completeness, the lowest branch will be briefly sketched: that which originates at a = /8 = 0. A calculation of -j^^ at that point yields only one non-trivial root, — (2 /z + X)(2/i + 3X)/X2, and thus the phase velocity at low frequencies is found to correspond, as would be expected, with that given by the stiffness (a semi-Young's modulus, so to speak) of a material displacement-free in the ic-direction but not in the 3;-direction, E = 4/xOu + X)/(2 /i + X). Since lines radiating from the origin of the (/S^, a^) plot are lines of constant velocity, the dispersion curve for this branch starts with zero slope. The root curves over, intersecting the line X/32 + (2m + \W = 0 at /3 = |, and intersects the line jS^ = 0 again at A^ (a = iA) where (2^ + X) ^4 cosh A = 4(m + X) sinh A. For large negative o^ and /S^, equation (3) approaches \H* + 4m(m + X)/3 -f 2X(2m + \)P - 4(2m -f X)(m + \)l + (2m + X)^ = 0, which after discarding the trivial root 1=1 leaves the Rayleigh cubic. In the case of this one branch, the phase velocity approaches its as3anptotic value at high frequencies from below, and hence the dispersion curve must have an odd number of maxima and minima, and in particular at least one minimum, as was discovered by numerical calculation for the corresponding branch in the case of the cylinder by Bancroft.** The complicated behavior of the displacements in the higher'branches is sufficiently illustrated by a brief consideration of their nodes: the values of X at which the displacement is entirely along or entirely across the slab. From (1) and the boundary conditions, the rr-dependence U of the displace- ment component perpendicular to the slab will be given by Ki U = {\^^ + (2m + \W) sin ^ sin — a (la) + 2{jjl(^ - (2,1 + X)a')sin a sin ^ 966 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 or by K2U = 2{fjL + \)(x^ cos jS sin ax - (\^ + (2/x + X)«') cos OL sin ^ (lb) where Ki = (XjS'- + (2/1 + \)a^)K sin /3, 2^2=20* + \)a^K cos /8, at aU points (a, jS) satisfying (3). Similarly from (2) and the boundary conditions, the a;-dependence W of the displacement component along the slab will be given by K^W = {\^ + (2/1 + \W) sin jS cos ~ - 2(/i + X)a/3 sin a cos — (2a) a a or by iTiTF = 2{tM^ - (2/x + X)a') cos i8 cos — + (XjS" + (2/1 + X)a') cos a cos ^, a (2b) iTa = iana{)x + X) ^, "j^ |^|^ [j^ ^^^ K sin ^, 7^4 = 2ioaa{}x + X)2r cos /3. Examine now, for example, a material for which X = /i, in the branch whose cut-off is at j9 = 27r, a = lir/y/lt. It can be verified at once that the nodes of the two components at some of the values of (a, /3) discussed ear- lier are described by the following table ( in which / = cos — 1 : a /3 Values of x/a for nodes of U Values of */a for nodes of W 2t/V3 2ir 0, =h two values given by 2/>/3 sin 27ra;/aV3 = cos lir/y/l sin 2rjf/a ±i,±f X 2t 0, ±1, ± one value given by ± two values given by 14/ 4- 8 = 0 14/2 - 2/ - 7 = 0 x/2 5t/2 0, ± two values given by 22/ 2 -f- zbl, ± one value given by 11/ -2 = 0 5/» - 15/ - 11 = 0 0 3t 0, db§, =fc§, ±1 no nodes M/IVZ 7x/2 0, =t^„db . zfc^ 0, =hi ±1, ±1 =t;^, db?, ±?, ±1 *00 3t =fci,±«,=fct It is to be noted in general that the nodal variations become less extreme at high frequencies, since for all branches except the lowest V and W tend LONGITUDINAL MODES IN CYLINDERS AND SLABS 967 to become proportional to sin — and cos — respectively, and jS approaches a a the value nw where n is the branch number in order of increasing cut-off frequency, with « = 0 ascribed to the lowest branch. Thus the feeling, de- rived from more familiar cases of wave motion, that the order in which the branches arrange themselves should be correlated with the number of nodes they display retains an asymptotic vaUdity here, in respect of each displacement component. Nodes of absolute displacement will occur only at special frequencies. OCX 8x With the notation a' = — , /8' = — , the conditions for their occurrence can a a be written Oui8'2 - (2iu + X)a'2) sin ^' cos a' + (JX + X)a'/3' cos |8' sin a' = 0, sin 2a' sin 2^' ff j8 sin 2a sin 2^ ' taken together with (3). ^' < ^, «' < a, 3. The Cylinder Procedures analogous to those of the preceding section, and presented by Love®, lead to Pochhammer*s secular equation, which in the pressnt notation* is (XjS2 + (2m + \)o?yj,{a)jm + 40z + X)c^(Mi82 - (2/x + \W)Ji{a)Jo(fi) (9) + 20z + X)(2m + X)a(a2 - 0^)J,(a)J,(fi) = 0, where (4), (5) and (6) still hold, with a signifying the radius of the rod. The analogy between (3) and the first two terms of (9) is striking. Again the roots jS = 0 and ^ = a can be neglected, and the equation when divided by |8 becomes even in a and /3, and a plot of p!^ against a^ becomes appro- priate, with the restrictions (7) as to regions of significance. The following paragraphs are lettered to correspond with their analogues of the preceding section, (a) Setting fi^ = (2 /x -f X)^^ in (9) reveals the cut-offs at Ji(fi) = 0 and at (2/x .+ X)a/o(«) = 2fiJi{a). (b) Setting o: = 0 in (9), it can be seen that the roots intersect the line * In comparing this treatment with that of Hudson^, interpret his symbols . (MX 2u 968 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 o^ = 0 at the points Ji{l3) = 0, traversing them with -^^ = -4m(m + X) a{a-) X^ or half that of their analogues. Again it is only at those points that the phase velocity has the value 's/(2/i + X)/p- (c) Setting /i(/3) = 0 reduces (9) to a/30xi8' - {2fi + \)a'')Ji{a) = 0, and hence the roots are confined between the horizontal lines /i(j8) = 0 in the region of positive 13^ and negative a^, and the velocity is asymptotic to \//x/p with increasing frequency. They meet the line XjS^ + (2n + \)c^ = 0 at the points /3/o(/3) — Jiifi) = 0, or in other words at the maxima and minima of Ji(0),* where again the phase velocity is \/2ju/p. (d) In the case of the cy Under confining lines** are since substitution shows that intersection of (9) with these lines would re- quire 40i 4- X)a^(M^' - (2m + \)a) . ,. . (Xi82+ (2M + X)aT •'^^"^ which cannot be satisfied by permitted values of a^ and jSl (e) This suggests that in that region the roots may oscillate about the lines J.MfM + A(^) [j'M + ,(,/f(;;\)„, -^.(«)] = 0. In fact, in view of the equivalence fi{x) = Jo{x) Ji{x), those lines X can be seen to have points in common with the roots of the secular equation at Ji{a) = 0, Ji(j3) = 0, and at (f) Substituting the expression for the lines of (e) into (9) shows that again additional intersections may be afforded by suitable roots of the cubic equation (8). * The analogy to the corresponding intersections for the slab at the maxima and minima of sin /3 is noted by Lamb, ref. 2, p. 122, footnote. ** There are infinitely many such families of lines but none carries the analogy with the slab to the point of being independent of the elastic constants. The families used in (d) and (e) serve the present purpose as simply as any. LONGITUDINAL MODES IN CYLINDERS AND SLABS 969 (g) In the region a = iAy the analogous lines are given by iMiA)m + M,) [aha) - ^,J^li\,^.^ iMiA)] = 0, with which intersections occur for the same values of ^/A as in the slab. These results pennit visualization of a counterpart to Fig. 1 for the cylin- drical case. In it the critical Hnes radiating from the origin are the same. The horizontal Hnes, instead of being evenly spaced by 7r/2, are spaced as the zeros, maxima, and minima of Ji(j3). The vertical hnes, again no longer evenly spaced, are replaced alternately by straight vertical hnes /i(a) = 0 2(m + \)a and by the curved "vertical" hnes Joia) = —;—, — jz — rm JiM which X/3^ + (2ai -t \)ot He between their straight companions and approach /o(«) = 0 as /3 be- comes large. FinaUy the confining Hnes, and the Hnes about which the branches oscillate, become the curves defined in (d) and (e), which can be seen to foUow a course not dissimilar to the diagonal course of their prede- cessors, passing through the intersections of the new horizontals and verticals. Again the branches do not intersect, except for pair-wise coincidence of cut-offs on one or another of the Hnes (d) when the elastic constants obey special relations. Thus the dispersion curves to which Hudson^ assigns certain of Shear and Focke's data cannot be taken (and indeed Hudson does not suggest that they must be taken) as corresponding to higher branches of the longitudinal modes, since the former curves intersect one another, and the latter cannot unless anisotropy modifies their behavior quahtatively. The assignments could represent modes other than longitu- dinal. The more recent results of Hueter^ show essentiaUy the behavior of Fig. 3. In view of the closeness of the analogy thus revealed, it may be taken as probable that quahtative correspondence wiU obtain quite generally be- tween the longitudinal modes of the slab and those of the cyHnder. References 1. Lord Rayleigh, Proc. Lond. Math. Soc. 17, 4 (1885). 2. H. Lamb, Proc. Roy. Soc. Lond. A, 93, 114 (1917). 3. L. Pochhammer, /. reine angew. Math. (Crelle) 81, 33 (1875). 4. D. Bancroft, Phys. Rev. 59, 588 (1941). 5. G. E. Hudson, Phys. Rev. 63, 46 (1943). 6. S. K. Shear and A. B. Focke, Phys. Rev. 57, 532 (1940). 7. R. W. Morse, //. Acous. Soc. Am. 20, 833 (1948). 8. A. E. H. Love, "Mathematical Theory of Elasticity," Cambridge 1927, 4th Ed., p. 287. 9. T. F. Hueter, Jl. Acous. Soc. Am. 22, 514 (1950); Zeit. angew. Phys. 1, 274 (1949). Frequency Dependence of Elastic Constants and Losses in Nickel By R. M. BOZORTH, W. P. MASON and H. J. McSKIMIN The elastic constants of nickel crystals, and their variation with magnetic field (AE effect), have been measured by a 10-megacycle ultrasonic pulsing method. The constants of three crystals agree well with one another when the crystals are magnetically saturated, but vary with domain distribution when demagnetized. The maximum ZLE effect observed is much less (3%) than has been observed at lower frequencies (20%). By measuring the A£ effect and the decrement of poly- crystalline rods at low frequencies, it is shown that the small effect observed at 10 megacycles is due to a relaxation in the domain wall motion due to micro- eddy-current damping. From the initial slope of the decrement-frequency curve, and also from the frequency of maximum decrement, the size of the average domain is found to be about 0.04 mm. Actual domains in single nickel crystals have been observed optically by Williams, who finds domain widths of 0.02 to 0.2 mm. THE three elastic constants of nickel have been determined in several single crystals by measuring the velocity of pulses of elastic waves of frequency 10 mc/s and duration 0.001 sec. The method has been described by McSkimin^ and the preliminary results on nickel have already been re- ported briefly .2 It is well known that Young's modulus, E, increases with magnetization, and changes in E (the "A£ effect") by 15 to 30 per cent have been observed at room temperature and changes by greater amounts at higher tempera- tures.^ It was surprising to find then, in our own experiments at 10 mc, that the greatest change was only about 3 per cent. It then occurred to us that, at such a high frequency, relaxation of the domain wall motion by micro- eddy-current damping might be expected. This led to the investigation of the frequency dependence of A£ and of the logarithmic decrement, 5, in polycrystalline nickel, and the results obtained support the theory and give information about domain size, as described below. Calculations'* based on the equations of domain wall motion give results which agree with the ex- periments. A number of experiments' have already established the existence of micro- eddy-current losses in magnetic materials subjected to elastic vibrations. These losses have their origin in the local stress-induced changes of mag- netization of the domains of which magnetic materials are composed. The change in magnetization of one domain will give rise to eddy-currents around it and in it, and the consequent loss in energy depends on the frequency / and the resistivity i?, and on the size and shape of the region in which the change in magnetization occurs. These losses are in addition to the macro- 970 ELASTIC CONSTANTS AND LOSSES IN NICKEL 971 eddy-current losses, due to the relatively uniform changes in magnetization of a magnetized specimen that occur during a change in stress. Calculations of the logarithmic decrement, 8i , attributable to micro- eddy-currents, have been made by Becker and Doring^ and by one of the writers.* According to these calculations when the material is composed of plate-like domains of thickness /, in which magnetization changes by bound- ary displacement, the decrement for nickel, which has its directions of easy magnetization parallel to [ill] directions, is given by the relation ^ Mo Es Xni r 5c44 T f/fo /.N Sn Icn - Cn + Scu] 1 + P/fl irR where /o , the relaxation frequency for domain wall motion is /o = ^ . ,3 Is is the saturation magnetization, Es is the saturated value of Young's modulus. Ho is the initial permeability, R the electrical resistivity, Xm the saturation magnetostriction along the [111] direction, and Cn , Cn and Cu the three elastic constants of nickel which are evaluated in this paper. For low frequencies the initial slope of the decrement vs frequency curve is 8^ ^ 24£, 111 t Xni f 5^44 T ,r.\ J SirRPs \_cii — cu -\- 3C44J As the frequency is increased the decrement rises to a maximum and then declines asymptotically to zero. Both the initial slope of the 5 vs/ curve and the frequency at which the maximum occurs are measures of the domain size. The initial slope has already been used to evaluate the size of the domains in 68 Permalloy.^ It is shown in the present work that the maximum occurs in polycrystalline nickel at a frequency consistent with the dimensions of domains observed by Williams and Walker® in single crystals of nickel. Elastic Constants and Damping in Single Crystals The nickel crystals used here were grown by slow cooling of the melt in a molybdenum wound resistance furnace, by a method previously described.^ They were cut with major surfaces parallel to (110) planes and were placed between two fused quartz rods as shown in Fig. 1. Measurements of the elastic constants were made as described in detail by McSkimin,^ by meas- uring the velocity of propagation of 10 mc pulses. In order to obtain a num- ber of reflections in the crystal, films of polystyrene approximately J wave- length thick are placed between the rods and the nickel crystal. This has the effect of lowering the impedances next to the nickel to small values and hence nearly perfect reflections at the two surfaces are obtained. The fre- quency is varied until successive reflections occur in phase, and the velocity is then calculated from the frequency and the dimensions of the crystal. 972 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 MAGNET W -^FUSED QUARTZ / RODS X r SPECIMEN / \""^^ -^POLYSTYRENE SEALS GATE N0.1 CONTINUOUS WAVE OSCILLATOR GATE NO. 2 VARIABLE MERCURY DELAY LINE TO DETECTOR Fig. 1 — Experimental arrangement for determining the elastic constants and AE effect in single nickel crystals. Table I Orientation and Elastic Constants §1 ill s hi III Type of Vibration 110 no Longitu- dinal no no Shear 1 no 001 Shear 2 Equation for Velocity V(cu + cii + 2cu)/2p •^(cii — cii)/2p Measured Velocity (cm/sec) 6.03 X 10»* 2.26 X 10» 3.65 X 10* Elastic constants (dynes/cm*) CXI +cii+2cu=- 6.47 X 10>* cii - cit= 0.90 X 10>2 c«= 1.185 X 10« A slight correction has been made for this value. The velocities for one demagnetized crystal' were found to have the values shown by Table I. These values of velocity, and a density of 8.90 for the single crystal, give values for the demagnetized elastic constants of Cll 2.50, cn = 1.60, Cu = 1.185 (3) all in 10'^ dynes/cm'^. To obtain the AE effect, the whole unit was placed between the jaws of a large electromagnet. Since the crystal was about 2.5 centimeters in diam- eter but only 0.472 cm thick, saturation could be obtained more easily along the long directions of the crystal. Figure 2 shows the changes in velocity of propagation along the [110] direction, caused by magnetization ELASTIC CONSTANTS AND LOSSES IN NICKEL 973 along tool), for tlie shear mode with particle motion along [lIO]. Fields of about 10,000 were attainable but a maximum field of about 6000 was usu- ally used. The velocity increases by 2.6 per cent at the saturated value. On decreasing the field to zero the velocity drops below the original value 2.8 2.4 2.0 1.6 5I>° 1.2 0.6 0.4 -0.4 f •' HII [oOl] ell [no] VII [no] Vo=2.26xio5 ' » ' ^ / ' ' d 1000 2000 3000 4000 5000 MAGNETIC FIELD STRENGH,H,IN OERSTEDS 6000 Fig. 2 — Change in velocity in percent from demagnetized value as a function of the magnetizing field for a shear wave in a (110) section when the particle velocity e is along the [iTOl direction and the field H along the [001] direction. for the demagnetized state, but it has practically the initial value when the crystal is again demagnetized. The lower value of velocity for the return curve indicates that the free energy is lower for some arrangement of the elementary domains other than the demagnetized state. Figure 3 shows the attenuation in decibels per trip as a function of mag- 974 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 netization. The loss drops from about 7 db to 1 db as the crystal becomes magnetized. The low value is the remanent loss caused by the energy lost to the terminations, so that one can say that the losses due to micro- eddy-current and micro-hysteresis are 6 db per trip or 12.7 db per centimeter for this mode of motion. The Q of the crystal can be shown to be equal to / 1 \ 6 ^ \ \ \ \ 5 \ \ \ Q. a: \ <\ on u \ in _i u \ uj 3 U UJ o o kw 0 400 800 1200 1600 MAGNETIC FIELD STRENGTH, H,IN OERSTEDS 2000 Fig. 3 — Loss per trip (0.472 cm) as a function of magnetizing field for shear wave of Fig. 2. the phase shift in radians divided by twice the attenuation in nepers per cm, or Q = 2ir//i> 2 (rfi per cm)/8.68 (4) and our results give Q = 94, corresponding to a decrement of ir/Q = 0.033. Figure 4 shows a measurement of the same mode when the field is applied along the [110] direction. The velocity approaches a slightly different ELASTIC CONSTANTS AND LOSSES IN NICKEL 975 limit on account of the "morphic" effect discussed in another paper.* If we average the two values the effective elastic constant for saturation be- comes c'n - cU = 0.954 X 10" dynes/cm«. (5) Measurements for the field along the thickness did not produce saturation and are not shown. 2.4 2.0 1.6 1.2 0.8 0.4 •0.4 } J 1 HII [no] €\\ [iTo] VII [no] Vq= 2.26X105 i 1 i n i\ 1 7 /I 1 1 / 1 /i / 1000 2000 3000 4000 5000 MAGNETIC FIELD STRENGTH, H, IN OERSTEDS 6000 Fig. 4 — Change in velocity in percent from demagnetized value as a function of the magnetizing field for a shear wave in a (110)_ section when the particle velocity is along the [110] direction and the field along the [110] direction. Figures 5 and 6 show similar measurements for the other shear mode (Shear 2 of Table I) for two directions of the magnetic field. Averaging the two limiting values, the constant Ca at saturation becomes cIa = 1.22 X 10^2 dynes/cm^ (6) The Q and decrement for this case become approximately 110 and 0.028. 976 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Figures 7 and 8 show measurements for the longitudinal mode. Variations of about 0.6 per cent in the velocity are obtained, and the saturated elastic constants, Q and decrement are c'n + cU + 2cU = 6.55 X lO^^, Q = 390, 5 = 0.008 (7) ^>° 1.2 1.0 0.8 0.6 0.2 •02 •04 J/y^ *- "■^ — < 1 i // f 1 1 H II [ooi] f II [ooi] VII [110] \/0= 3.65 X 10^ '' 9 t 1 1 [\ ]' f /« 'f 1 1 1 1 1 0 1000 2000 3000 4000 5000 6000 MAGNETIC FIELD STRENGTHEN, IN OERSTEDS Fig. 5— Change in velocity in percent from demagnetized values as a function of the magnetizing field for a shear wave in a (110) section when the particle velocity is along the [001] direction and the field along the [001] direction. Combining the elastic constants, the saturated elastic constants are evalu- ated: c'n = 2.53, c'i2 = 1.58, cU = 1.22, (8) all in 10" dynes/cm*. ELASTIC CONSTANTS AND LOSSES IN NICKEL 977 It is obvious from the measurements of Figs. 4 to 8 that the changes in the elastic constants with magnetization are much smaller at the high fre- quencies (10 mc) than they are at the lower frequencies of 10 to 50 kilo- 1.2 1.0 0.8 0.6 0.4 0.2 •0.2 -0.4 ^ / / Hll [no] fll [001] \/ll [no] Vo= 3.65X105 , < f p \ h \ ] \ 1 1 4 t 0 1000 2000 3000 4000 5000 6000 MAGNETIC FIELD STRENGTH,H, IN OERSTEDS Fig, 6 — Change in velocity in percent from demagnetized value as a function of the magnetizing field for a shear wave in a (110) section when the particle velocity is along the [OOlJ direction and the field along the [110] direction. cycles where changes of 15 to 30 per cent have been observed in polycrystal- line material.' A rough comparison of the low-frequency values with the 10 megacycle values can be obtained if we convert the observed changes in the c's to the equivalent change in £. This can be done if we use the method 978 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 0.7 0.6 0.5 D.4 0.3 %\> 0.2 0.1 0.1 0.2 1 1 y^o fo o / ^ 1 I ' T 1 1 1 Hll [OOI] €\\ [no] Vll [no] Vo=6.03 X105 1 1 1 1 / 1 1 / 1 , L / >} 1 I ( I -V i 0 1000 2000 3000 4000 5000 6000 MAGNETIC FIELD STRENGTH, H, IN OERSTEDS Fig, 7 — Change in velocity in percent from demagnetized value as a function of the magnetizing field for a longitudinal wave in a (110) section when the particle velocity is along the [110] direction and the field along the [001] direction. « developed by one of the writers^ for obtaining the elastic constants of a polycrystalline rod from the cubic elastic constants. In this case the Lame elastic constants are given by the formulas 3 . Cii — Ci2 " = 5^" + — 5 (9) ELASTIC CONSTANTS AND LOSSES IN NICKEL 970 0.7 0.6 0.5 0.4 0.3 5> 0.2 0.1 -0.1 ■0.2 •• — •-0- / / / Hll [no] fll [no] VII [no] Vq = 6.03X10S 1 i h J / 1000 2000 3000 4000 5000 MAGNETIC FIELD STRENGTH, H, IN OERSTEDS 6000 Fig. 8 — Change in velocity in percent from demagnetized value as a function of the magnetizing field for a longitudinal wave in a (110) section when the particle velocity is along the [1 10] direction and the field along the [110] direction. Since in terms of the Lam6 elastic constants, the value of Young's modulus is Eo "(:-m) (10) one finds that the difference between the saturated and demagnetized value of Young's modulus divided by the demagnetized value is 980 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 A£ ^ Es - £o ^ 2.381 - 2.312 Kq Eq 2.312 = 0.03 = 3% (11) which is much smaller than that given by low frequency measurements. To check our results, and be sure that the crystals were free from imper- fections and strains, two other crystals were prepared and carefully an- nealed at 1100°C. The values found for the changes in elastic constants were considerably less for these crystals. The Q's of the crystal were also higher. Table II shows the measured values and the equivalent AE/E values. The table shows also the measurements for the demagnetized crystal of two Japanese workers^^-" and the equivalent AE/E assuming that the saturated elastic constants are the same as those found for the other three crystals. Since these vary by only ±0.5 per cent among themselves, this appears to be a good approximation. Table II Elastic Constants (in 10" dynes/cm^) and A^-Effect in Single Crystals of Nickel Magnetically Saturated Demagnetized Ciystal AE/E cn Cit £44 Cn eii Cu 1 2.53 1.58 1.22 2.50 1.60 1.185 0.03 2 2.524 1.538 1.23 2.52 1.54 1.229 0.0017 3 2.523 1.566 1.23 2.517 1.574 1.226 0.0046 Yamamoto" 2.44 1.58 1.02 0.16 Honda and 2.52 1.51 1.04 0.11 Shirakavvai" The lower values of AE/E for the second and third crystals are probably due to larger domain sizes, caused by the longer anneal. Damping and A£-Efeect in Polycrystalline Rods To test the theory of micro-eddy-current shielding (see Introduction), the velocity and attenuation of elastic vibrations in well-annealed poly- crystalline nickel rods were measured over the frequency range of 5 kilo- cycles to 150 kilocycles. In the method of measurement,^^ shown by Fig. 9, two matched piezoelectric crystals of resonance frequency corresponding to integral half wavelengths along the rod, are attached to the ends of the rod. Phase-amplitude balance was obtained by critical adjustment of fre- quency and output of the calibrated attenuator. The corresponding level was then compared with that obtained when the two crystals were cemented directly together. With little error, the velocity of propagation is given by V — 2//o n= 1, 2, 3 (12) ELASTIC CONSTANTS AND LOSSES IN NICKEL 981 The attenuation A (and hence the Q of the rod) was obtained by solving the equation sinh Alo = (r — cosh AlQ)nirM( (13) in which r is the ratio of output with crystals together to output with specimen attached, lo is the length of rod, Mc the mass of either crystal, Mr the mass of the rod, and Qc the Q of the crystal as determined by reso- nance response method. For this equation to apply accurately, the terminating impedance pre- sented to the rod by the crystals at resonance must be small compared to the characteristic impedance of the rod, and the Q of the rod should be > 10. This method may be used even when the total loss in the rod is so high that well defined resonances no longer exist. At the lower frequencies, however. TEST ROD r BUFFER AMPLIFIER J TO DETECTOR INPUT P^ Kt 3 R,5 \ CRYSTAL CRYSTAL ^ I nRIVFR Dr/-ci\/rD 1 ATTENUATOR Fig. 9 — Experimental arrangement for measuring the AE effect and associated loss in a polycrystalline rod at low frequencies. a useful check may be made by the resonance response method of determin- ing Q which involves determining the frequency separation A/ for two fre- quencies 3 db from the maximum response frequency, and using the formula e = Jmax A/ (14) Correction for the mass and dissipation of the piezoelectric crystals must of course be made. Both methods have been found to agree within about 10% — the probable error to be expected. The Appendix lists formulae to be used when the resonance frequency of the crystal driver differs from the frequency at which phase balance is ob- tained. This condition of necessity occurred when the rods were subjected to a magnetic field, which caused an increase in the velocity of propagation. Figure 10 shows a typical measurement of change in frequency and change in decrement with magnetizing field excited in a solenoid surround- 982 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 ing the nickel rod. Saturation is not quite obtained so that the A£ effect measured is shghtly lower than the true value, but for relative frequency comparisons this is not important. The first rod measured was 0.320 cm in diameter and 10.16 cm long and was annealed at 1100°C. Five frequencies ranging from 22.5 kilocycles were 0.14 0 12 2 0.10 2 o Si^O.08 o z /) *^ 0.04 0.02 AE/Eo^ \ — r~^ — ' y r^ \ ^ O INCREASING FIELD • DECREASING FIELD fo=95.73KC Vq= 4.64 XIO^ CM/SEC Eo= 1.92X10^2 DYNES '^ Cm2 V i /\d^ f ^^-^^^ ^< ' i —J 25 175 50 75 100 125 150 MAGNETIC FIELD STRENGTH, H, IN OERSTEDS Fig. 10 — Typical change in velocity and decrement of a polycrystalline rod as a func- tion of the magnetizing field. 0.18 o LLl ;^o.i6 < > "^^ / O 0.14 S^-0.12 ZO.10 kJ |o.08 0 0.06 u J 0 02 ^^^ AE/Eo ■o- ^SAT = ^-^^ ^ '°^ cm/ SEC Es=2.22 X10'2 0YNES/Cm2 < > 0 20 40 60 80 100 120 140 FREQUENCY IN KILOCYCLES PER SECOND 160 Fig. 11 — Fractional change in Young's modulus, and the decrement, plotted as a func- tion of frequency for rod No. 1 . used and the ratio of the change in Young's modulus to the value of Young's modulus for the demagnetized rod is shown plotted in Fig. 11. This figure shows also the decrement 5 = -k/Q. It is obvious that the decrement even- tually decreases as the frequency rises, and this is contrary to the simple theory of the micro-eddy-current effect,^ which indicates that the decrement ELASTIC CONSTANTS AND LOSSES IN NICKEL 983 should increase linearly with the frequency. The indicated maximum for this rod is below 120 kilocycles. In order to obtain the first part of the decrement vs frequency curve, a rod of 46.05 cm length and 0.637 cm diameter was next used. This rod was annealed at 1050°C and presumably has a smaller average domain size than the first one, so that the important variations occur in a more favorable frequency range. The changes in elastic constant and the decrement for this rod are shown by Fig. 12 for frequencies from 5 kilocycles to 96 kilocycles. At the lower frequencies the decrement increases in proportion to the frequency in 0.22 0 20 ■^0.,8 ^0.6 Q < 0.14 h- 0.12 z u ^0.10 a. o LJ 0 08 o 3 0.04 0.02 \ \ VsAT =5.00X10^ CM/ SEC Es = 2.22 X 10^2 DYNES/CM 2 V .^ "^ AE/Eo 6 ^ y / / / 20 40 60 80 100 120 140 160 FREQUENCY IN KILOCYCLES PER SECOND Fig. 12 — Fractional change in Young's modulus, and the decrement, plotted as a function of frequency for rod No. 2. agreement with the simple theory. By extending this curve down to zero frequency it is seen that a micro-hysteresis effect (which is independent of the frequency) gives an initial decrement of about 0.010. The decrement rises to an indicated maximum at somewhat more than 100 kilocycles and the change in elastic constant with saturation decreases with frequency. The data on these two rods taken together indicate that there is a fre- quency of maximum decrement and for frequencies above and below this the decrement is smaller. The A£ change in the elastic constant decreases as the frequency increases and for very high frequencies the A£ effect be- comes very small. As shown by the discussion in the next section, the fre- 984 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 quency of the maximum value of 5 and the initial slope of the decrement frequency curve are connected with definite domain sizes which can be calculated approximately and compared with magnetic domain powder patterns. Discussion Our determinations of the elastic constants may be discussed in relation to the values obtained by others. The results reported by Honda and Shira- kawa^° and Yamamoto" were unlcnown to us and unavailable at the time of our preliminary communication. The data of the Japanese, converted from 5-constants to c-constants by the relations: ^11 + ^12 ^11 — 2 . r, 2 5il -r SiiSu — ^Si2 _ -^12 (15) '^12 — 2 I o 2 ^11 + ^11^12 — ^^12 Cu — 1/544 are included with our data in Table II. As our experiments show, the 10 mc pulses that we used are so rapid that micro-eddy-currents largely prevent the stress-induced changes in mag- netization from penetrating the domains. Therefore the constants deter- mined by this method are those for material almost saturated. The values at saturation are independent of the initial domain distribution, and of the ease with which the magnetization in the separate domains can be changed by stress, consequently they are the more fundamental elastic constants of the material. The variety of values for unmagnetized nickel is made evident from the scatter in the ratios of LE/E that have been reported.' The varia- tion in the values of the c-constants recently published is thus not surprising. The values at saturation of the three crystals examined by us are in sub- stantial agreement, as shown in Table II. They cannot be compared directly with the results of the Japanese workers because the latter reported data for unmagnetized crystals only and then E is sensitive to heat treatment and domain configuration. As mentioned in the introduction, the damping of elastic vibrations by micro-eddy-currents is proportional to the frequency at low frequencies (Eq. 1) and it rises with frequency to a maximum and then declines toward zero. The frequency at which the maximum occurs has been calculated^ by using the equation of domain wall motion and evaluating the constants from the initial permeability and the power loss caused by domain wall motion. The maximum value of b comes at the same value as that calculated ELASTIC CONSTANTS AND LOSSES IN NICKEL 985 for eddy current losses in sheets having the same thickness as the domain, namely r-ix,fJR = Q,U ' (16) / being the thickness of the slieet, juo the initial permeability, and R the resistivity of the material (all in c.g.s. units). As noted below, the domain sizes calculated from the initial slope of the b vs/ curve of Fig. 12, and from the frequency at which the maximum decre- ment occurs, are respectively 0.035 mm and 0.045 mm (for plates). These values agree quite well. The decrement curve is broader than would be cal- culated from equation (1) for a single domain size. This agrees with the optical measurements of domain size by WiUiams,^ which are shown by Fig. 13. This indicates domain sizes from 0.01 to 0.2 mm. The maximum value for the decrement calculated from equation (1), using the measured values, is 0.35 compared to the observed value of 0.11. Part of this is due to the broadening of the peak caused by a distribution of domain sizes, but part may also be due to the deviation of the actual domain shape from a sheet which has been assumed in making the cal- culations. The calculations of domain size are made in more detail as follows: According to Doring^^ the change in Young's modulus for nickel contain- ing only small internal strains is related to the initial permeability, 7x0 , as folio ws; A£ \\n (no - \)Es \_Cn — C12 4- 'icuj provided the averaging over all crystallites is carried out with constant strain. (If constant stress is assumed, the fraction in brackets, equal to 1.76, is omitted.) For nickel Xm is 25 X 10~^, /« is 484, and the c's are the elastic constants given in Table I. This equation holds for low frequencies at which the shielding in single domains is negligibly small. When the re- laxation effect of domain wall motion is considered* equation (18) has to be multiphed by the factor 1/(1 +/'//») " (19) The data of Fig. 12 give the values: AE Eo = 1.83 X 10^2^ E, = 2.22 X lO^^ dynes/cm^ — = 0.21 (20) is for low frequencies. Using these in the above equation, the calculated value of juo is 320. A direct measurement* of no has been made for this rod and found to be 340, in good agreement with that deduced from the AE effect. * Measurements were made independently by Miss M. Goertz and Mr, P. P. Cioffi in order to check this unusually high value. 986 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Since the permeability is much higher than can be accounted for by domain rotation it is obvious that domain boundary motion is occurring. Hence in determining the domain sizes from the slope of the decrement vs Fig. 13— Photograph of domains in a single nickel crystal (after Williams). Field of view, 0.5 mm. frequency curve, equations (1) and (2) for domain boundary motion are appropriate. When the data of Fig. 12 are extrapolated to zero frequency it appears that there is a microhysteresis loss (which is independent of the frequency) giving a decrement of 0.01. The initial slope of the 8i vs/ curve is then about ELASTIC CONSTANTS AND LOSSES IN NICKEL 987 2.5 X 10~^, and use of equation (2) with this and other appropriate values indicates that the domain size is I = 0.035 mm, (21) as reported above. A check on this value can be obtained from the frequency, fm , corre- sponding to the maximum of the 5 vs/ curve. If we use equation (16), /^o/n./^ = 0.13, (22) with/ = 1.5 X 10^ (Fig. 11), we find / = 0.045 mm, in reasonable agreement. An actual photograph of domains in a single crystal of nickel, taken by H. J. Wilhams and reproduced in Fig. 13, shows the presence of domains of various sizes ranging from about 0.01 to 0.2 mm. Any such range in domain sizes will naturally tend to flatten the maximum of the 6 vs / curve and, on account of the form of the 6 vs / function, will push the maximum to a higher frequency than that corresponding to the initial slope, and will give a lower maximum value to the decrement frequency curve. The average domain size derived from our experiments is somewhat larger than that previously obtained in 68 Permalloy.^ This may be expected, for nickel has a very high magnetostriction and the movement of domain boundaries by stress will be relatively large, possibly so large that the re- gions swept over by the domain walls will correspond to whole domains of the original domain structure, when the stresses are equal to those used in our experiments. The domain size which we have determined is based on this interpretation. APPENDIX METHOD OF MEASUREMENT— FORMULAE From transmission line theory (see reference of footnote 12) the ratio of outputs, r, defined in the text and appHcable to the circuit of Fig. 9 is given by r = cosh e/o + i (g + ^) sinh % (24) where Q = A -\- jB = propagation constant jSpco Zq = - — , — — = characteristic impedance of rod A -\r jB Zt = resistive terminating impedance provided by crystals 5 = area of rod This expression may be expanded into real and imaginary parts and the latter term set to zero in accordance with the condition of phase balance. 98S THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 B Assuming that | Zo | » Zt and that Q = "TT > 10, the ratio r which is now a real number determines the attenuation A in accordance with equation (13) of the text. If the crystal resonance frequency /^ is slightly different from the balance frequency /x obtained with the rod specimen in place, correction may be made by considering a new terminating resistance Zt formed by the crystal driver and a small section of the rod sufficient to make the combined reso- nance equal to /x . A slightly different length, /o, of rod is then used to compulc velocities and attenuation. Also a different mass M tt and ratio r' result. The equation applicable provided /x= Jc , is . / iiZ't (/ — cosh Al'n) ..,>. smh AIo = -—7 (2:)) JxMr where r — 1 + 2f //f-M 2(2 v. fJ "■-"■['-sd-')] ^ = '['-|-(|-0] In the above a sufficiently accurate value of Q is ordinarily obtained by assuming fe=fx. Further accuracy, if needed, can be obtained by recal- culation, using the corrected value of Q. We are glad to acknowledge the cooperation of Mr. J. G. Walker in grow- ing and processing the single crystals used,^ and in preparing also the poly- crystalline specimens. References 1. H. J. McSkimin, //. Aeons. Soc. Anier., 22, 413 (1050), particularly method K. 2. R. M. Bozorlh, W. P. Mason, H. J. McSkimin, J. G. Walker, PJtys. Rev., 75, 1954 (1949). 3. Summarizefl by (a) R. Becker, and W. Dorinp;, Ferromacrnelismus, Springer, Berlin (1939), and by (b) R. M. Bozorth, Ferromagnctism, Van Nostrand, New York (1951). 4. W. P. .Mason, Phyx. Rev. 83, 683 (1951). 5. H. J. Williams and R. M. Bozorlh, Phys. Rev., 59, 939 (1941), and reference 3b. 6. H. J. Williams and J. G. Walker, Phys. Rev. 83, 634 (1951). ELASTIC CONSTANTS AND LOSSES EST NICKEL 989 7. J. G. Walker, H. J. Williams and R. M. Bozorth, Rev. Set. Instruments, 20, 947 (1949) and reference 2. 8. W. P. Mason, P/tys. Rev. 82, 715, (1951). 9. W. P. Mason, Piezoelectric Crystals and Their Application to Ultrasonics, Van Nostrand, New York (1950). 10. K. Honda and Y. Shirakawa, Nippon Kinzoku Gakkai-Si (//. Inst. Metals, Japan) ;, 217 (1937), and Sci. Re/). Res. Insl., Tohoku Univ. J, 9 (1949). 11. M. Yamamoto, //. Inst. Melds, Japan 6, 331 (1942) and P/iys. Rev., 77, 566 (1950). 12. This method is a modification of one described in "Electromechanical Transducers and Wave Filters," W. P. Mason, D. Van Nostrand (1942) pages 244-247. For frequencies above 20 kc, 45° Z-cut ammonium dihydrogen phosphate crystals were used. Below 20 kc the crystals were cemented on square brass rods which were placed at the ends of the nickel rods in place of the piezoelectric crystals alone. 13. W. Doring, Z. Pliysik, 114, 579 (1939). Hot Electrons in Germanium and Ohm's Law By W. SHOCKLEY The data of E. J. Ryder on the mobility of electrons in electric fields up to 40,000 volts per cm are analyzed. The mobility decreases many fold due to the influence of scattering by optical modes and due to increases of electron energy. It is estimated that electron "temperatures" as high as 4000°K have been pro- duced in specimens having temperatures of atomic vibration of 300° K. The critical drift velocity above which there are deviations from Ohm's law is about 2.6 X 10^ cm/sec. This is three times higher than the elementary theory and an explanation in terms of complex energy surfaces is proposed. Table of Contents 1. Introduction: Fundamental Deviations from Ohm's Law 2. E. J. Ryder's Experimental Results 3. Theory of Deviations From Ohm's Law a. Electrons in »-Type Germanium b. The Phonons c. The Selection Rules d. Energy Exchange and the Equivalent Sphere Problem e. Acoustical Phonons and Electric Fields 4. Comparison Between Theory and Experiment a. Discrepancy in Critical Field b. The Effect of the Optical Modes c. Electron "Temperatures" 5. An Explanation of the Low Field Discrepancy Appendices AL Introduction and Notation A2. The Probability of Transition into Energy Range Sea A3. The Allowed Ranges for Py A4. The Matrix Element and the Mean Free Path A5, Approximate Equivalence to Elastic Sphere Model A6. Approximate Treatments of MobiUty in High Fields A7. The Effect of the Optical Modes 1. Introduction: Fundamental Deviations from Ohm's Law ^TT^HE starting point of many branches of physics is a linear relation. -■- Among the most prominent of these are Hooke's law, which relates stress and strain for solid bodies, Newton's second law of motion F = ma and Ohm's law. In all of these cases, the linear relation is only an ap- proximation that may be regarded as the first term in a Taylor's expansion of the functional relationship between the two variables. Important physi- cal principles are brought to attention when the nonlinear range is reached. Of the three laws mentioned, Newton's is, of course, the one in which the failure of linearity is the most significant representing as it does the en- trance of relativistic effects into the laws of motion. The failure of Hooke's law may be of either a primary or secondary form. 990 HOT ELECTRONS IN GERMANIUM AND OHM's LAW 991 If a solid contains voids, then under a certain pressure it will crumble and fill the voids. This is a secondary effect. If the sample is homogeneous, however, high pressures will produce fundamental deviations from Hooke's law, these deviations arising from the nonlinearity of the forces between atoms. Studies of these nonlinear effects by Bridgman have, among other things, put on a firmer basis the understanding of the forces between ions in ionic crystals and the pressures of electron gases in metals. Deviations from Ohm's law for electronic conduction in semiconductors are almost the rule rather than the exception, but the most familiar cases are secondary rather than primary. The primary linear relation for the conduction process is that between the drift velocity of an electron, or hole, and the electric field that drives it. This relationship is va = MO (r) E, (1.1) where the mobility /xo(?^) is a function of the temperature T of the specimen. By di. fundamental deviation from Ohm's law we shall mean a deviation in this linear relationship arising from the largeness of E rather than other causes. Thermistor action is typical of a secondary deviation from Ohm's law. A thermistor is usually a two-terminal circuit element in which the current flows through an electronic semiconductor. The semiconductor has the property that its resistance decreases rapidly as the temperature increases; and the physical basis for this decrease is an increase in the number of con- ducting electrons (or holes or both) with increasing temperature. The passage of current heats the thermistor and its resistance changes; conse- quently the Hnear relation between current and voltage fails and in fact there may result a decrease of voltage with increasing current so that a differential negative resistance is observed. The electric fields are so low, however, that equation (1.1) is vahd provided the dependence of /zo on the temperature is taken into account. An experimental proof that no funda- mental deviation of Ohm's law occurs is furnished by applying a small a-c. test signal on top of a d-c. bias that produces heating. If the frequency is much higher than the thermal relaxation rate, the a-c. resistance is found to be simply that expected for the observed temperature. The principal nonhnearities of crystal rectifiers, or varistors, and of tran- sistors are also secondary and are associated with changing numbers of current carriers. In this article we shall discuss some experimental evidence of funda- mental deviations in Ohm's law for electrons in «-type germanium obtained by E. J. Ryder of Bell Telephone Laboratories.^ We shall describe his ex- 1 E. J. Ryder and W. Shockley, Phys. Rev. 81, 139 (1951). 992 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 perimental techniques and results briefly in the next section and shall then present some aspects of the quantitative theory that explains them, leaving the bulk of the mathematical manipulations for the appendices. Before discussing Ryder's results, we may indicate why his procedure succeeded whereas previous attempts, of which there have apparently been a number, largely unpubhshed, have failed. Ryder's work takes advantage of three factors: (1) the availabihty of electrical pulses of microsecond dura- tion, (2) the high resistivity of germanium, and (3) the high mobihty of electrons in germanium. Because of (3), it is possible to dehver energy to electrons at relatively high rates by electric fields. In effect this "heats" the electrons above the temperature of the crystal and lowers their mobility. The generalized equation is then V, = n{T, E)E (1.2) where the fact that /x depends on E represents the fundamental nonlinear- ity. We shall show that Ryder's techniques raise the "temperature" of the electrons by a factor of about thirteen fold to above 4000°K. Since the re- sistivity is high, say 10 ohm cm, the power delivered to the specimen is sufficiently low that the heating in one pulse is negligible. The pulse repeti- tion rate is then kept so low that accumulated heat is negligible also. These conditions are enormously more favorable than those met with in metals. In a metal the average electron energy is several electron volts; in order to double this energy, each electron would acquire an added energy roughly equal to the cohesive energy per atom of the crystal. Furthermore, in a metal there is about one conduction electron per atom, compared with 10"^ per atom in Ryder's samples. Thus the stored energy due to "hot" electrons in a metal would be enough to vaporize it, whereas in germanium, or a similar semiconductor, a temperature of 10,000°K for the electrons would be enough to raise the crystal less than 0.01°K. From this reasoning it appears that it will be extremely difficult, if not impossible, to produce significant fundamental deviations from Ohm's law in metals and certainly impossible to produce effects of the magnitude described below. It should be pointed out that the behavior of electrons in crystals in fields so high that equation (1) fails have been subject to both experimental and theoretical investigation in connection with dielectric breakdown.^ The work does not apply to cases in which the specimens obey Ohm's law at low fields, however, and the experiments do not permit accurate deter- 2 See, for example, H. Frfthlich and F. Seitz, Phys. Rev. 79, 526 (1950) and F. Seitz» Phys. Rev. 76, 1376 (1950). Much of the treatment presented in the Appendices is essen- tially equivalent to that given in Seitz. In our Appendices, however, we give much more emphasis to the low field case. The Seitz paper also contains a review of the literature to which the reader is referred. HOT ELECTRONS IN GERMANIUM AND OHm's LAW 993 minations of va as a function of E. From the theoretical side also the empha- sis has been on fields so high that the linear range is neglected so that the transition from linear to nonhnear is not stressed. The current theories of dielectric breakdown are based on the principle of "secondary generation" or "electron multiplication." Thus if an electron acquires enough energy from the electric field, it will be capable of pro- ducing secondaries by collision with bound electrons, and the repetition of this process will lead to an avalanche. Our theory indicates that in ger- manium, even at fields as high as 200,000 volts/ cm, few electrons will have enough energy to produce secondaries. At about those fields, however, another phenomenon occurs. In 1934 C. Zener' proposed that dielectric breakdown was due to a pri- mary effect: the field induced generation of hole-electron pairs. His mathe- matical theory is similar to that for field emission from cold metal points and to that for radioactive decay. It involves the "tunneUing" of electrons through regions in which their wave functions are attenuated, rather than running, waves. Zener's theory does not seem to apply to breakdown; however, it does apply to the high electric fields produced in rectifying p-n junctions in ger- manium when these are biased in the reverse direction. Under these condi- tions fields of the order of 200,000 volts/cm are produced. The mobiHties of electrons, or holes, in these fields have not been measured. It has been shown,"* however, that secondary production is very small. At these fields a sort of "breakdown" effect occurs and above a critical value of the volt- age a very rapid increase in current is observed. This current appears to be of the nature predicted by Zener. It is stable at a given voltage, has a small temperature coefficient and will probably be useful in semiconductor analogues of "voltage regulator tubes" and protective devices. As is shown in the treatment given in quaUtative terms in Section 3 and in more detail in the Appendices, the explanation of the fundamental devia- tions from Ohm's law is based on the theory of electron waves. The investi- gations described in this paper may thus be regarded as furnishing evidence for the wave nature of conduction electrons in germanium and are thus re- lated to the researches of C. J. Davisson, to whom this volume is dedicated, and his collaborator, L. H. Germer. The Davisson-Germer experiments were concerned chiefly with electron waves in free space and with high energy electrons in crystals. Both of these cases are simpler than that dealt with in this paper. Electrons in the conduction band in germanium appear to behave as though they were in a multiply refracting medium in which they may have 8 C. Zener, Proc. Roy. Soc. 145, 523 (1934). * K. C. McAfee, E. J. Ryder, W. Shockley and M. Sparks, Phys. Rev. 83, 650 (1951). 994 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 several velocities of propagation for any specified direction of propagation and frequency. It is to be hoped that more detailed analyses of the data ob- tained by Ryder, together with quantitative interpretations of certain ob- servations of magnetoresistance, may lead to a unique evaluation of the ''refractive constants" of the medium for the electron waves; this possibility is discussed briefly in Section 5. The phenomena in the Zener current range afford another new opportunity to study electron waves in crystals. The waves involved in this effect are those with energies in the energy gap be- tween the conduction band and the valence band; waves in this range have received little attention from either the experimental or theoretical side. 2. E. J. Ryder's Results One of germanium's most noted attributes is its abihty to give am- plification of electrical signals when made into a transistor. The basic phe- nomenon for many types of transistors is that of "carrier injection." As is PULSER T X Fig. 1— The principles of E. J. Ryder's technique for observing conductivity in high electric fields. well known, germanium may carry current either by the electron mecha- nism in which case it is called w-type germanium, or by the mechanism of hole conduction in which case it is called ^-type. If a suitably prepared electrode is placed on an w-type specimen and current is caused to flow in the sense that removes electrons from the specimen, then the process may cause "hole injection." In this case in addition to removing conduction electrons from the germanium, electrons are removed from the valence bonds so that holes are injected. This leads to nonlinear effects because, as the current passes through the specimen, the number of carriers in the specimen changes and so does its resistivity. In order to avoid the secondary deviations from Ohm's law due to carrier injection, Ryder has designed specimens of the form shown in Fig. 1. These specimens have large ends to which the metal electrodes are attached. The resistance arises chiefly from a thin section of the material connecting the HOT ELECTRONS m GERMANIUM AND OHM*S LAW 995 large ends. Since the fields at the large ends are small, carrier injection is largely suppressed; furthermore, the electric fields are applied for such a short time during the pulse that, even if holes were injected at one of the ends, they would not have time to reach the narrow section of the bridge and modulate its conductivity during the period of the pulse. Further causes of non-linearity can arise from inhomogeneities in the germanium material itself. For example grain boundaries in polycrystalline germanium are known to have added electrical resistance. Difficulties due ?0 30 40 60 80 100 200 400 600 1000 2000 4000 10,000 ELECTRIC FIELD IN THIN SECTION IN VOLTS PER CENTIMETER Fig. 2 — Currents and estimated drift velocities deduced from E. J. Ryder's pulse data on a specimen of »-type germanium of 2.7 ohm-cm resistivity. [The fact that the numeri- cal values of current density and drift velocity have the same digits is a consequence of the accident that ^stals to describe the opposed form of motion, although no polarization accompanies the dis- placement in the latter case. 3c. The Selection Rules We shall next consider the laws which govern the interchange of energy between an electron and the phonons. There are two important laws, closely analogous to the laws of conservation of energy and momentum for two masses in colhsion. The quantity analogous to momentum for the phonon is a vector, called Py , directed along the direction of propagation of the phonon, and having a magnitude given by the relationship between mo- mentum and wavelength - Py = h{l/X) = h/\ Py II propagation direction (3.3) In a transition in which an electron exchanges energy with the phonons, and changes its momentum from Pi to P2 , so that diiy = dzl for one of the modes, one selection rule requires that P2- Pl+ bUyPy = 0. (3.4) This is analogous to conservation of momentum; actually it is based on far more subtle effects. The conservation of energy requires that 82 + dityhvy = 81 (3.5) where 82 = Pl/2m, 81 = Pl/lm (3.6) are the electron's energies before and after collision. The mass m need not be the mass of an electron but may instead be the "effective mass," a mass- like quantity of the same order as the electron mass which takes into ac- count the influence of the periodic potential of the crystal structure upon the electron wave packet. The effective mass concept represents a simplification that may not HOT ELECTRONS IN GERMANIUM AND OHM S LAW 1001 necessarily be correct. In a cubic semiconductor, the electron waves can be "refracted" as are the longitudinal and transverse acoustical waves. The deviations from Ohm's law of Fig. 2 furnish evidence that the simpli- fied assumption of equation (3.6) must in fact be replaced by the more general possibility. We shall return briefly to this point in Section 5. In addition to the conservation of energy and momentum, there are two other approximate selection rules which, while not exact, are so nearly fulfilled that no appreciable error is introduced by using them: PHONON absgrptionN PHONON N EMISSION' CONSTANT /•'ENERGY AVERAGE ENERGY 'AFTER SCATTERING 8 mc \ \ / / '\^,i— j^ --,/ 6 4 \/%^ :^\ 2 Py 0 -2 -4 -6 ( ((( ^ \^ ^ -8 1 1 ; 1 1 r ENERGY AFTER ^SCATTERING -6 -4 -2 0 2 4* 6 SmC Px (a) SCATTERING BY PHONONS 6 smc (b) SCATTERING BY ELASTIC COLLISION OF MASSES Fig. 4— Comparison of the scattering by acoustical phonons with the scattering of a small mass in elastic collision with a larger mass. Only bUy = zbl is allowed. For the acoustical modes, only the longitudinal modes interact with electrons. (This restriction does not apply to optical phonons.) Figure 4 shows the allowed transitions for an electron with initial mo- mentum Pi in the x-direction. If the energy of the phonons were zero, the allowed transitions would be to points on the sphere (or circle in Fig. 4) with Pi = P\ . Since the energy of a phonon is hvy = hc/\ = cPy = c\P2- Pi (3.7) however, the end points lie on the surfaces shown. These surfaces do not differ much from the sphere, as may be seen by considering the final energy for an electron that reverses its motion by phonon absorption. For this case Py = P2 + P1 and t _ (Pl- Pl)/2m = cP. 1002 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 (3.8) (3.9) SO that the change in magnitude of momentum is P2 - Pi = 2mc. (3.10) For an electron with energy kT and "thermal velocity" Vt = {2kT/myi\ (3.11) corresponding to 10' cm/sec at 300°i and the end surface is a sphere with S2 = Si — hvox> . (3.13) We shall neglect the role of the optical phonons until after a comparison between acoustical phonon processes and experiment has been made. We shall then show that they play an essential role in explaining Ryder's data. 3d. Energy Exchange and The Equivalent Sphere Problem We shall here give in brief some results derived in the Appendices which permit us to show the equivalence of the problem of acoustical phonon scat- tering to a problem in gas discharges. This has two advantages: it enables us to take over the solution to the statistical problem from gas discharge theory, the second problem mentioned at the end of Section 3a, and to concentrate on the problem of the mechanism. In addition the equivalence makes it much easier to visualize the mechanism of energy losses. According to the theory of phonon scattering, an electron is equally hkely to be scattered from its initial direction of motion to any other. This implies that after an interaction the electron is equally likely to end in any unit HOT ELECTRONS IN GERMANIUM AND OHM's LAW lOOvS area of the surfaces of Fig. 4. The probabihty of being scattered per unit time is simply 1/ri = v^ll (3.14) where Vx is the speed and / the mean free path ; according to the theory I is a function of the temperature T of the phonon system and is independent of V\ . The time r\ is the mean free time or average time between coUisions. Figure 4 shows the average energy after collision. The Figure represents a case in which the average energy is somewhat smaller than the initial energy. This will be the case for a high energy electron, that is one with an energy greater than kT for the acoustical modes. The average loss in energy for a high energy electron is found to be (5£) = -c'PyikT (3.15) where Py is the momentum change in the coUision. This formula is analogous to the formula for energy loss if a light mass m strikes a heavy stationary mass M and transfers a momentum P2 — Pi = Py to it. The energy transfer is given by (3.15) if M = kTl& (3.16) since then the kinetic energy of the large mass is simply P\I1M = c'P^/lkT. (3.17) The value of the mass which satisfies equation (3.16) for room temperature may be calculated from the previously quoted values of Vt and c: M = kT/c" = mvfllc = 170m, (3.18) a value which may certainly be considered large compared to m. Equation (3.15) is not the complete expression for average energy change for a coUision with momentum change Py and another term representing energy gain also occurs. If the complete expression is averaged over all final directions of motion, it is found that the average change of energy, which is obviously the average energy change per coUision, is (58) = 4mc\l - Pl/4mkT) = {4mkT/M) - {P\/M). (3.19) This is the correct expression for the average gain in energy per collision of a light mass m colliding with a heavy mass M which is moving with the thermal energy appropriate to temperature T. This corresponds to a thermal velocity of Vtm = (IkT/My/'' = 2i/2c (3.20) 1004 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 for the large mass. The second term in (3.19) is just the average of (3.15) over all directions of motion after collision and represents the energy loss that would arise if M were initially stationary. The first term represents an energy transfer from M to m due to the thermal motion of the large mass. Furthermore, if the light and heavy masses are perfectly elastic spheres, the scattering of m will be isotropic, just as is the case for the phonons. This shows that there is an almost perfect correspondence between the two mechanisms of scattering so that we are justified in using previously derived results for the sphere case and applying them to the phonon case. To complete the equivalence we should introduce a density of large spheres so as to get the correct mean free path. There is nothing unique about this procedure, as there is about the mass M and temperature T, and we may make a large selection of choices for number of M-spheres per unit volume and radii of interaction so as to obtain the desired mean free path. Once any choice is made, of course, it will give the same mean free path inde- pendent of electron energy and may be held constant independent of the electric field. 3e. Acoustical Phonons and Electric Fields We shall next give a very approximate treatment of mobility in low and high electric fields. The emphasis will be upon the interplay of the physical forces, the mathematical details being left to the Appendices or to references. In the Ohm's law range, the field E is so small that the electrons have the temperature of the lattice. They have a velocity of motion of approxi- mately Vt = (2kT/my'' (3.21) and a mean free time between collisions of r = ^/vt . (3.22) The electric field accelerates the electron at a rate a = qE/m (3.23) and imparts a velocity ar in one mean free time. Since the collisions are spherical, the effect of the field is wiped out after each collision. The drift velocity is thus approximately Vd = ar = {qt/mvT)E. (3.24) An exact treatment which averages over the Maxwellian velocity distribu- tion gives a value smaller by 25% and leads to /io = ^qt/Sr^'^rnvT . (3.25) 1005 Since theory shows that t varies as r~\ the mobihty should vary as T~ . This prediction is in good agreement with experimental findings over the range of conditions for which the dominant scattering processes are those considered here. Next we consider the effect of very large fields. Under these conditions an electron drifting in the direction of the field with drift velocity Vd acquires energy from the field at an average rate {dZ/dl)c^no toB = VaqE. (3.26) If this power is large enough, the electrons will be unable to dissipate energy sufficiently rapidly to the phonons that they can maintain their normal tem- perature. As a result their average energy mounts, after the field is initially appHed, until they can furnish energy to the phonons fast enough to main- tain a steady state. Under these conditions the sum of the two rates is zero {d&/dl)axio to B -\- {dS^/dl)dMo to phonons = 0. (3.27) If the field is high enough, there may be no steady state solution. This can occur if the ability of the phonons to remove energy decreases with increasing energy. Such cases play an essential role in the theory of dielectric breakdown.* In them it is concluded that electrons will gain sufficient energy from the field so that they can produce secondary electrons which repeat the process thus producing avalanches. For the cases with which we are con- cerned, theory indicates that the energy losses increase rapidly with the energy of the electron while the power input decreases because of decreasing mobility so that a steady state will thus occur. In order to estimate the drift velocity for the steady state we must intro- duce expressions for the two powers involved. For this purpose we assume that an electron has on the average a speed Vi and we calculate the power to phonons as the average energy loss per collision for this velocity times the rate of collision, Vi/t For vi » Vt , we can neglect the effect of motion of the M spheres and thus obtain from (3.19) (^SM)phonons = -(z;i/^) mhl/M. (3.28) The mobility will be less because of the higher collision rate so that the drift velocity in the field will be approximately Vd = {qf/mv,)E. (3.29) The power furnished by E will be idZ/dl)a.e toB== (q''C/mvi)E?. (3.30) 8 See the references to Frohlich and Seitz in Section 1. 1006 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 The steady state condition then leads to vi = {qlElmf'iMlmf^ (3.31) and to n = {qeE/m)"\m/My'' (3 32) = iV^cqCE/rnvTY'^ ^ (cuoEY'^ The treatment^ based on accurate statistics for the equivalent sphere model leads to Vd = L23{cfioEy'\ (3.33) The transition between the high field behavior and low field behavior should occur in the neighborhood of a critical field Ec at which both Umiting forms give the same Vd : Vd = noEc = 1.23{cuLoEcy'\ (3.34) leading to Ec= 1.51 c/fjLo (3.35) and to a drift velocity, which shall be referred to as the critical velocity, of Vdc = 1.51c (3.36) if Ohm's law held to a field as high as Ec . The drift velocity can be ex- pressed in terms of Ec by the equation Vd = noiEEcY'' (3.37) for values of E much greater than Ec. It is interesting to note that this initial field is just that which would give electrons a drift velocity corresponding to the thermal motion of M-masses. This seems a natural critical field. For it the effect of random motion of M would be suppressed by the systematic drift velocity so that the transfer of thermal energy to the electrons would be much reduced. This value of Ec corresponds to much smaller initial fields than are sometimes proposed. For example, one frequently encounters proposals that Ohm's law should hold up to the condition that Vd = Vt . This would correspond to 10 times higher field at 300°K than that obtained. Another criterion is that the energy gained in one mean free path, qtE, should be equal to kT. This is substantially equivalent and corresponds to Vd = Vt/2. ' Druyvesleyn Physica 10, 61, 1930. This paper is reviewed by S. Chapman and T. G Cowling in "The Mathematical Theory of Non-Uniform Gases," Cambridge at the Uni- versity Press, 1939, page 347. (The factor is 0.897 (187r/8)i^* = 1.23.) HOT ELECTRONS IN GERMANIUM AND OHM*S LAW 1007 For comparison with experiment we note that for a value of £ = 4£, = 6.04<;/mo (3.37) such that if Ohm's law held Vd = 6.04c, (3.38) the value of Vd should be less than half the value predicted by Ohm's law. We shall shortly discuss the discrepancy between this prediction and ex- periment. The "temperature" of the electrons may be conveniently expressed in terms of the ratio E/Ec . Since the electrons for the high field case are not in a Maxwellian distribution of velocities, one cannot define their ''tem- perature" unambiguously. As a measure of their temperature we shall take their average kinetic energy divided by k. This leads to a ratio of electron temperature T{E) to crystal temperature T of 2vi/3vt . Since to a first approximation the ratio of mobihties at low and high fields is Avi/Sir^'hr , the ratio of temperatures is r(£)_3xr MO ?_3x£ This ratio may also be thought of in terms of the square of the ratio of drift velocity on the extrapolated Ohm's law line to the drift velocity on the £1/2 line: nE)/T = {3T/S)yoEME)]\ (3.41) Either of these equations may be used to estimate electron temperature from the data in the range in which the E^''^ formula is a good approximation. 4. Comparison Between Theory and Experiment 4a. Discrepancy in Critical Field In Fig. 5 we repeat Ryder's data of Fig. 2 together with data on an addi- tional sample at 77°K. This new sample is considered more reliable than the first since its low field resistivity varies in just the proper ratio [see (3.25) and subsequent text] of (298/77)^/^ compared to its valua at room temperature. Also we show the theoretical curves that will be discussed below. The deviations of the data from Ohm's law do not occur at fields as low as those predicted in Section 3e. For c = 5.4 X 10^ cm/sec, the critical drift velocity should be Vdc = 1.5k = 8.2 X 105 cm/sec. (4.1) 1008 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 It is seen that Ohm's law is followed to several times higher velocities with negligible deviations. The deviations should be a factor of 2 at the field corresponding to Vd = 6.04c = 3.26 X W cm/sec. (4.2) on the Ohm's law Hne. The deviations are actually much less. Another important difference between the data and the theory of Section 3 is that the experimental points do not continue on a straight Hne with slope 1/2 but instead tend to flatten out with a roughly constant drift velocity. 10' _ — — — n. 1 .^ — M- -^ = - 1 T ^ A- A- rr — 4 ^c 4^ > ^ ^> ^' On A ^> y^ >^ O J I f' / °.y / /r ^ y ^1 D y /^ infi / < 4 / / ^ / /* c - o^. / o / / c - y / ^ / r A \ J / / / p / / / j> "*-. / o / / 1 f 10^ / / / ^ _i_ _L. 1 1 20 30 40 60 80100 200 400 600 1000 E IN VOLTS PER CENTIMETER 2000 4000 10,000 Fig. 5 — Comparison of E. J. Ryder's experimental data and the statistical theory of Appendix A7. Three theoretical curves are shown. These are based on an approximate treatment that includes the effect of the optical transitions. Due to the ap- proximation, the optical modes are neglected below the points marked Op on the Figure. This approximation also leads to a discontinuity in slope at these points; in a more accurate treatment, this bump would be smoothed out. The optical modes play the least role for the curve at 77°K and for this theory fits experiment within experimental accuracy if a value of Vdc « 2.6 X 10« cm/sec. (4.3) HOT ELECTRONS IN GERMANIUM AND OHM'S LAW 1009 is used. This value is 3.2 times larger than the value given by equation (3.36) using c = 5.4 X 10^ cm/sec, the value appropriate for longitudinal phonons.^'^ The interpretation of this discrepancy, which we refer to as the 'low field" discrepancy, is discussed in Section 5. It does not, of course, imply an error in the value of the sound velocity, but instead an error in the theory leading to the formula for critical velocity in terms of sound velocity. Although an exact theory along the lines discussed in Section 5 has not been developed, it appears evident that its chief effect will be to increase energy interchange with the phonons by a factor of 3.2 squared or approxi- mately 10. This increase can be effected in a mathematically equivalent way by introducing an ejfeclive velocity for dealing with phonon energies which is 3.2 times larger than the true velocity of longitudinal waves. The approxi- mate theory in the Appendices uses this procedure. We may remark in passing that only two constants were arbitrarily chosen to fit the curves to the data. One of these was the effective velocity c = 1.73 X 10^ cm/sec. which is 3.2 times larger than the speed of longitudinal waves. The other was the mobihty of electrons at room temperature. Three other constants were chosen from independent estimates of the properties of the crystal. One of these is Jiv for the optical modes for which a value of ^520°K was used; another is the effective electron mass, for which the free electron mass was used; and a third was the interaction constant for optical modes, which was set equal to that for the acoustical modes. The meaning of these terms is discussed in the Appendices. 4b. The Effect of the Optical Modes We shall next discuss briefly the role of the optical modes before remark- ing on a theory of the low field discrepancy. As discussed above the optical modes can act only if 8i > hvop . Theory indicates, however, that when they do come into action they are much more effective than the acoustical modes. On the basis of these ideas, we can see how they can act to give a limiting drift velocity that does not increase with increasing electric field. For purposes of this illustration we shall imagine that so high an electric field is applied that an electron may be accelerated from Pi = 0 to P2 = {Irnhvox^y^i at which its energy equals //I'op, in so short a time that it is not scattered by acoustical modes. As soon as it reaches P2 , we assume that it is scattered by the optical modes, loses all its energy and returns to zero energy. This process then repeats, the period being 1" This is the velocity of longitudinal vaves in the fl 10] direction as reported by W. L. Bond, VV. P. Mason, H. J. McSkimin, K. M. Olsen and G. K. Teal, Pliys. Rev. 73, 549 (1948>. See "Electrons and Holes in Semiconductors," page 528, for the reason for using this wave. 1010 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 FilqE since dP^/dt = qE. The average momentum is evidently P2/2 and the average velocity is va = Pillm = {hvojlmyi'' (4.4) and is independent of E. The optical modes correspond to a temperature of about 520°K and this leads to Vd = 6.3 X 10« cm/sec. (4.5) in general agreement with the observed value. The theory in the appendices indicates that both optical and acoustical modes are active simultaneously and their interplay leads to the theoretical curves shown. (In the Appendices a further discussion is presented and some additional data are compared with theory.) The tendency of the theoretical curves to fall below the data for 193°K and 298°K for field values below the optical point is thought to arise largely from the approximations employed in the theory. The approximations neglect the ability of the optical modes to enable the electrons to lose energy for fields below the indicated value. Actually some electrons will be scattered by the optical modes and this will contribute in an important way to hold- ing the temperature down and the mobility up. A correct treatment would, therefore, raise the theoretical curve appreciably in the region where it deviates most from the data. 4c. Electron ''Temperatures'' From the theory it follows that the average electron energies correspond to about 520°K at the points marked Op on Fig. 5. The highest point on the 298°K curve corresponds to '^700°K and the highest point on the 77°K curve corresponds to 550°K. For this last case the electron temperature is more than seven times as high as that of the atomic vibrations. In the ap- pendix we quote some other earlier data of Ryder's that indicates electron temperatures of about 4000°K while the crystal itself remains at room temperature. 5. An Explanation of the Low Field Discrepancy The failure to deviate from Ohm's law at the low fields predicted indicates that the electrons can dissipate their excess energy more effectively than would be expected on the basis of their mobihty. This conclusion is forced on us by the observation that they apparently retain their thermal dis- tribution and normal mobility to higher fields than predicted. It is not pos- sible to explain the discrepancy by assuming a large or a small value for the effective mass, since the value of the effective mass does not enter into the final comparison with experiment. HOT ELECTRONS IN GERMANIUM AND OHM's LAW 1011 It is possible, however, to explain the discrepancy by assuming that the effective mass is not single valued. This assumption corresponds to the case in which the surface in the Brillouin zone belonging to a single energy is not a sphere but instead a complex surface of two or three sheets. Such surfaces have been found as a result of numerical calculations for certain crystals^^ and it has also been shown that such surfaces are to be expected in generaP^ if the energy at the bottom of the conduction band is degenerate. It appears necessary to assume that such complex surfaces occur in order to explain magnetoresistance effects.^^ In terms of Fig. 4, this theory replaces the circular energy contours by deeply re-entrant curves. Transitions from peak to peak of the curves result in large energy transfers to the phonons and hence more effective energy losses. This effect can occur without a compensating change in the effective mass involved in the mobihty and, as a result, the critical field may be increased by a large factor. A preHminary analysis indicates that in order to increase the critical field by a factor of 3 a value of about 3 is also required for the ratio of maximum to minimum momentum for the energy surface. A similar analysis of magnetoresistance leads to a factor about 50% larger in order to account for the increases in transverse resistance of about 7-fold observed by Suhl.^* At the time of writing, therefore, the author feels that both the critical field data at low fields and the magnetoresistance data require a modification of the effective mass picture and that the same modi- fication may well explain both sets of data. I am indebted to E. J. Ryder, whose experimental results provoked the analysis presented in this paper, to F. Seitz and J. Bardeen for several helpful discussions, to Gregory Wannier for an introduction to the analogous case in gas discharge theory and to Esther Conwell for help with the manuscript. I shall also take this opportunity to express my appreciation to C. J. Davisson. The opportunity to work in his group was a large factor in my decision to come to Bell Telephone Laboratories, where I enjoyed his stimu- lating companionship while assigned to his group, and later as well. APPENDICES A.l Introduction and Notation The problem of energy exchange between the electrons and the phonons requires a somewhat more sophisticated treatment than does the problem of mobihty at low fields. In order to present the theory of energy exchange, II W. Shocklev, Phys. Rev. 50, 754 (1936). 12 W. Shockley, Phys. Rev. 78, 173 (1950). WW. Shocklev, Phys. Rev. 79, 191 (1950). i*H. Suhl, Phys. Rev. 78, 646 (1950). Suhl finds increases in resistance in transverse fields as high as 7-fold. 1012 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 it is necessary to reproduce a large amount of the material dealt with in or- dinary conductivity theory. We do this in a somewhat abbreviated form ex- panding the exposition on the points particularly pertinent to the theory of energy losses. For convenience we reproduce here a number of the more important sym- bols. The references indicated refer to places where they are discussed in the text. a = lattice constant; Fig. 3. c = speed of longitudinal acoustical wave; Equ. (3.2). C(e = average longitudinal elastic constant; Equ. (A4.1). e = base of Naperian logarithms. E = electric field. 8 = energy. Sin and Son; Equ. (A4.1) and (A7.9). h = Iw h = Planck's constant. k = Boltzmann's constant. / = mean free path for electron due to scattering by acoustic phonons; (A4.3). Z^op = describes scattering by optical phonons; (A7.19). m = e£Fective mass of electron. M = mass in equivalent mass treatment; (A5.8). P = "crystal momentum" of electron = It times its wave number. V = volume of crystal. A = dilation; (A4.1) and (A7.10). V = frequency of normal mode, j/op = frequency of optical mode (used in Section 4 only); Equ. (4.5). A 2 The Probability of Transition into Energy Range 5S2 In this section we consider an electron initially with energy Z\ and mo- mentum Pi, which for convenience we take to be along the P^-axis, and we evaluate the probability that it make a transition to states with ener- gies in the range S2 to S2 + 5S2. We shall assume that the crystal is elas- tically isotropic so that for the spherical energy surface approximation employed, i.e. equation 3.6, the scattering will be symmetrical about the Pz-axis. The end states, P2, may, therefore, be considered in groups lying in the range dZi, dd where 6 is the angle between Pi and P2. These states lie in a ring in P-space whose volume is 27rP2 sin 6 P2 dd dP^ = 27rmP2 sin 6 dd dSz (A2.1) HOT ELECTRONS IN GERMANIUM AND OHM'S LAW 1013 The number of end states in dB d&2 space is thus^* (V/h^) lirmPi sin 6 dd dZi = p dd J82 (A2.2) (The density p introduced above is used below in calculating the transition probability; since spin is conserved in the transitions of interest, the den- sity of possible end states in phase space is 1/h^ instead of 2//^^) The transitions will occur between states of the entire system, electron plus phonons, which conserve energy. The transition of the electron from K to P2 requires a compensating change in the phonon field.^^ The con- servation laws allow two possibilities: (I) phonon emission; the longitudinal acoustical mode with P, ^ hk = -CP2 - K) (A2.3) undergoes a change «a -> ?Ja + 1 (A2.4) with a change in energy for the electron of 82 - Si = -h coa = -h c/\ = -cPa (A2.5) where c is the velocity of the longitudinal phonons that are chiefly respon- sible for the scattering. These relationships lead to conservation of the sum of P for the electron plus Yl f^a Pa for the phonons. The other pos- sibihty is (II) phonon absorption, for this case fp^kkp^ (K - K) (A2.6) np -^np- 1 (A2.7) £2 - Si = +cPp (A2.8) again with conservation of the sum of P vectors. If we denote by S the energy of the electron after collision plus the change in phonon energy, then the requirement of equaUty for energy before and after coUision gives S = S2 + dnycPy = Si (A2.9) where 8ny = +1 is the phonon emission or a surface and 8ny = — 1 is the phonon absorption or jS surface of Fig. 4. ^5 The notation in this appendix follows closely that of W. Shockley, "Electrons and Holes in Semiconductors," D. van Nostrand (1950) to which we shall refer as E and H in S. See page 253 for a similar treatment of p. 1^ This condition is anaio'^ous to one for the conservation of momentum but has a different interpretation. See for example E and H in S, p. 519 equation (15). 1014 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 We shall next insert these symbols into the conventional expression for transition probability. We consider a system described by one or more sets of quantum numbers, say JCi , X2 , • • • , Xn which may take on discrete but closely spaced values so that the numbers of states lying in a range dxi , • • • , dxn is p{xi J • ' ' , Xn) dxi • • • dXn' (A2.10) The system may make a transition from an initial state cpo and energy 80 to another state i/dxi)] Jx2 , • • • , dXn (A2.11) where d8>i/dxi is evaluated where &i = 80; if for the range dx2, • • • , dXn of the other quantum numbers there is no Xi value that gives 8^ = 80, then the transition does not occur. We shall apply this to our case letting 0 = Xi and 82 = X2. The expres- sion d&i/dxi then becomes dx :-(a. — (fl, <-"' where = Pi P2 sin e/Py, 1/2 (A2.13) We then obtain, for Wn d8>2 , the probability per unit time of transition of the electron from Pi to states with energies between 82 and 82 + ^^82 , the expression Wu de>2 = {27r/h) | U f {V/h^)2TmP2 sin 0 X (Py/c8nyPiP2 sin 0) de>2 = {V/2Trh*)m I U p (Py/c8ny Pi) de,2 (A2.14) = (V/27^h')m\UnPy/Pi){-dPy); where the negative coefficient of dPy is without significance except for its relationship to the selection of the limits of integration. In subsequent equa- tions we shall disregard the sign convention which relates d8>2 to dPy] no "See L. I. Schiff "Quantum Mechanics," McGraw-Hill Book Co. (1949), equation (29.12). The additional factor 1/(36»/9.ti) converts thep used here to that of Schiff, which latter is number of states per unit energy range. HOT ELECTRONS IN GERMANIUM AND OHM's LAW 1015 error is introduced provided the subsequent integrations are always in the direction of increasing values for the variables concerned. A. 3 The Allowed Ranges for Py An electron with an energy corresponding to room temperature can change its energy by only a small fraction in a one phonon transition. The extremes occur for ^ = tt corresponding to complete reversal of direction. For this case we have Si = (pI - p\)/2m = -dftycP^ = -dnyc{P2-{- Pi) (A3.1) so that P2 - Pi = -dfiy 2mc = - 28ny Po. (A3.2) Thus the limiting values of P2 differ from Pi by ±2Po = ± 2mc (A3.3) in keeping with the results shown in Fig. 4. [For Vi = Pi/m = 10 cm/ sec, corresponding to Si = 0.025 electron volts, andc = 5.4 X 10^ cm/ sec, it is seen that P2 and Pi differ by 10%.] For this case the range of Py is phonon emission, 8na = +1, Pa from 0 to 2 (Pi — Po) (A3. 4) phonon absorption, dnp = — 1, P^ from 0 to 2(Pi + Po). (A3. 5) A singularity occurs for Pi = Pq. For this case phonon emission becomes impossible and the inner curve of Fig. 4 shrinks to zero; in Fig. Al we show the sequence of shrinkage. The value of 81 for this condition corresponds to thermal energy for a temperature of less than 1°K. Under the conditions for which we shall compare theory and experiment, a negligible number of electrons lie in this range. Accordingly we shall use the above limits in cal- culations and neglect the small errors introduced. A A The Matrix Element and the Mean Free Path The matrix element may be written in the form \U f = SL {2ny + 1 + 8ny)Pyc/4Vca (A4.1) where 8in is the derivative of the edge of the conduction band in respect to dilatation of the crystal and cu is the elastic constant for longitudinal ^8 See E and H in S, page 528, equation 31. The second expression in equation 31 of this reference is in error by omission of a factor hujka = cPy. 1016 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 -8 _ (a) ^^^ if ^' lP,| = 6mc yj -8 -6 mc -4 -2 0 smc 6 amc 8 6 4- (c) 5n=-i J L lPil= mc © J L -8-6-4-2 0 2 4 6 8mC -8 -6-4-2 0 2 4 Px-^ Px-*^ CRYSTAL MOMENTUM amc Fig. Al— Initial and Final Values of P for Transitions which conserve energy. (a) The two nearly spherical surfaces for | K I = 6 mc. (b) The two surfaces for | /-*, | = 3 mc. (c) For an electron with \P^\ = mc, energy loss is impossible. (d) The case of | K I = 0. waves. Inserting this in the expression (A2.14) for PF12 dZi, we obtain Wx. J82 = (F/27rM) m \^inP-,cl\Vcu\ X (2;h + 1 + ^ny){Py/P,) dPy (A4.2) = (1/0(1/8WP1)(2«^ + 1 + 8ny){cPy/kT)PydPy where we have used the symbol / to represent ^ = irh* culrrC-^xn kT (A4.3) because, as we shall shortly show, t is the mean free path for electrons. HOT ELECTRONS IN GERMAISTIUM AND OHM's LAW 1017 For the cases with which we shall be concerned, the values of ity may- be approximated by classical equipartition. This may be seen from the fact that largest energy phonons correspond approximately to an energy of cPy = 2cPi = (Acm/Pi)Pl/2m (A4.4) = WvOkT. Their energies will, therefore, be considerably less than kT. For large in- creases in electron energy in high fields, however, this approximation may not be adequate. At room temperature cPy/kT = 0.2 and the critical range will correspond approximately to an increase of about 10 fold of electron temperature above the temperature of the crystal. Under these conditions cPy deduced from equation (A4.4) will be about 2kT for the most energetic phonons; for this condition, however, Py lies at the edge of the Brillouin zone and dispersive effects must be considered. In this treat- ment we shall not investigate further these limits and shall in general assume that cPy < kT. We shall next derive an expression for the mean free path and verify that the scattering is isotropic. These results can be derived more simply and directly from the matrix element by neglecting (Pq/Pi) and (cPa/kT) from the outset. For the treatment of energy losses that follows, we cannot make these approximations. We shall, however, make them in the re- mainder of this section thus establishing that our more general formulation reduces correctly to the more convenient and simpler formulation usually used. For the condition under which equilibrium apphes we may approximate ity as follows: ny = l/[(exp cPy/kT) -1] = (kT/cPy) - i (A4.5) Then, for the phonon emission or a case, the contribution to Wu d&2 be- comes Wi2d&2 = (4w^Pi)-i[l + {cPa/2kT)]Pa dPa (A4.6a) and for the phonon absorption case, it becomes Wi2d&2 = (4w^Pi)-'[l - {cPfi/2kT)\PfidPfi. (A4.6b) We shall use these expressions later for the calculation of energy exchange, in which case the terms in cPj2kT, which favor phonon emission, play an important role. In order to check the expression for mean free path we neg- lect these terms, however, and also approximate the integral of Pa dPa by 2P\ rather than 2 (Pi — Po)'. The total probability of transition from state 1018 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Pi, which should be taken to be l/n where n is the mean free time, is then - \lr^ = W^i = (4m^Pi)-i 4P'i = {Pi/m)/t = Vi/t. {M.I) This is just the relationship appropriate to the interpretation of / as a mean free path between colUsions/^ It does not follow that ri is the relaxation time for the current, however, unless the average velocity after collision is zero. We shall next show that the average velocity after collision is zero to the same degree of approximation used above by showing that scatter- ing into any solid angle of directions is simply proportional to the solid angle, i.e. the direction of motion after collision is random. The conclusion that the scattering is nearly isotropic follows from the approximate proportionality of probability to PydPy. Since P2 is nearly equal to Pi and substantially independent of 0, we may write Pa dPa = i d(PaY = ^d {2P\ - 2P\ COS o) = - Pld COS e = Pi sin e dd. (A4.8) The last term is simply proportional to the soHd angle lying in range dd; hence the end states are distributed with uniform probability over all direc- tions and the scattering is isotropic. A5. Approximate Equivalence to Elastic Sphere Model In this section we shall show that on the average the energy exchange between the electron and the phonons when the electron is scattered through an angle 6 is very similar in form to that corresponding to elastic collisions between spheres with the phonons represented by a mass much greater than the electrons. If dPa and dPp correspond to scattering through angles between 6 and 6 -\- dd, then the energy loss for phonon emission is cPa and the energy gain for absorption is cP^. The relative probabilities of loss and gain are given by equations (A4.6) and from these it is found that the average energy gain is / V ^ cPp[l - (cP0/2kT)]P0 dPp - cPall + (cPj2kT)]PadP„ ^^^^ [1 - {cP,/2kT)]P^ dP^ + [1 + {cPj2kT)]P^ dPa , ^ , (A5.1) ^ C[PI dPff - Pi dPg] - (cy2kT){Pl dPff -h Pi dPg) [1 - (cP0/2kT)]Pp dPff + [1 + {cPa/2kT)]Pa dPa ' Since we are concerned chiefly with cases in which Po <3C Pi , P2 — Pi , and cPfi/kT </dl)no\d + (^S/^/)phonons = 0. (A6.3) In order to calculate the average rate of energy loss to the phonons, we consider the average energy gain of an electron of momentum Pi. As given by(A5.12): {8S)p, = 4wc2 [1 - (mv\/^kT)]. (A6.4) According to our assumption, the number of electrons in the velocity range V to V -{- dv is N{v) dv = A exp {—mv /2kTe)v-dv. These electrons suffer collision at a rate v/^. Hence the average rate of energy gain is WS/(//)phonon3 = / {5S)p{v/{)N{v) dv^ Jn{v) dv = (8/>/x)(mcV0[l - ive/vr?] where we have introduced Vt = {2kT/myi\ Ve = {2kTe/myi\ (A6.6) (A6.5) (A6.8) 1022 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 We see that for thermal equilibrium, with T = Te and v = Ve , this equation gives correctly the result that there is no net interchange of energy be- tween electrons and phonons. The equation for mobility for the case of phonon scattering is /xo = ^qt/diy/irVim. (A6.7) This expression may be used to reduce the steady state equation: 0 = (cte/i/)field — {d8>/dt) phonons = {vT/ve)qfJLoE^ + {S/'\/T){mchT/-C){Ve/vT) [1 — {Vc/VtY to (ve/vr)' - (ve/vr)' = (St/ S2) (ji^/ cf . (A6.9) This equation may be solved for Ve/vri (ve/vr = a/(4)(1 + [1 + (STr/SKnoE/cWy' (A6.10) The drift velocity then becomes Vi = nE = Mofi V2/(l + [1 + {d>ir/^){n,E/cni''Yi\ (A6.11) For E < hv and it seems unlikely that analytic solutions can be obtained. Even the Maxwellian distribution leads to somewhat complicated integrals. A.7b. Estimate of the Matrix Element In order to proceed further we must estimate the order of magnitude of the optical scattering matrix element. For this purpose we introduce a deformation potential" coefficient for the optical modes by the equation S2n = de>c/d{x/Xo) (A7.9) where x is the displacement parallel to the :r-axis of one sublattice in respect to the other and Xq is the a;-component of relative displacement of the sub- lattices for equilibrium conditions. The same reasoning as used in treating mobility by deformation potentials may then be applied and the matrix element evaluated by analogy with the dilatation waves. For the latter the matrix element may be written in the form \Ua\' = e,ln{A')/2 (A7.10) where A is the dilatation and (A^) is the average (dilatation)^ for the mode before and after transition. Since half the energy in a running wave is potential i c^^(A2) V = ihvX [average of (n -f J)] (A7.11) = hpi2n+ 1 + 5w)/4. This leads to the form introduced in equation (A4.1). By analogy, for the optical modes we should take I Uo, \' = e>ln{{x/xoy)/2 (A7.12) 26 W. Shockley and J. Bardeen Phys. Rev. 77, 407-408 (1950) and J. Bardeen and W. Shockley, Phys. Rev. 80, 72 (1950). 27 See E and H in S, page 528. 1028 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 where the stored energy for deformation {x/xo) is J ^00 (x/xoY V (A7.13) and the average value for a transition from n = 0 to n = 1 is hv for the total energy and (i)hv for potential. This leads to |C/op|2 = e>Lhv/2cooV (A7.14) As a first approximation we may take the stiffness between the planes of atoms separated by xq as the same as the macroscopic value. This leads to Coo = C(( (A7.15) Furthermore, jequal relative displacements of neighbors are produced by equal values of A and x/xq. Hence approximately equal changes in energy may occur so that we may assume that S2„ = Si„. (A7.16) Under these conditions I Uo^ p = (hv/kT) I f/A p. (A7.17) Since the energy of the optical modes is a maximum for Py = 0, it will change only a small fraction for values of Py comparable to Pi. (See Fig. 3.) Consequently, conservation of energy leads to transitions between Pi and a sphere with P2 — [2m(8i — hv)Y'^. The probability is equal to each point on the sphere and the transition probability is readily found" to be lAop = {V I C/op |WM^)z;2 (A7.18) where Vi = P2/W is the speed after collision. If we assume relationship (A7.17) between matrix elements and introduce C as defined in (A4.3), then 1/rop = {hv/m V2/I ^ V4p (A7.19) where 4p is a sort of mean free path for optical scattering. The dependence of V2 upon the velocity before collision vi is obtained as follows: 82 = Si - hv (A7.20) V2 = [2(Si - hv)/mYi'' ) , (A7.21) » See F. Seitz, "Modern Theory of Solids," McGraw-Hill Book Co., 1940, p. 122. * See E and 11 in S of A. 2, p. 493, for a similar treatment. HOT ELECTRONS IN GERMANIUM AND OHM*S LAW 1029 where Vi> is the velocity corresponding to hv: V, = {2hv/myf\ (A7.22) The rate of energy loss to the optical modes is simply hm/fov (A7.23) A. 7c. Approximate Steady State Treatment In order to test whether or not the role of optical modes can explain Ryder's data, we shall use a very crude method. We shall assume that the electrons all have the same energy and shall calculate their mobility on the basis of the mean free time at that energy; from this we calculate the power input. We shall also calculate the power loss in the same way. It is obvious that this treatment is a very poor approximation to the actual situation. An electron which loses energy to the optical modes will, under most cir- cumstances, have only a small fraction of its energy left afterwards; thus to assume a monoenergetic distribution is unrealistic. However, the treatment does bring into the analytic expressions the principal mechanisms and, as we shall show, appears to account for the main experimental features. The collision frequency or relaxation time for transitions involving the optical modes is given in (A7.19) and the energy loss in (A7.23). We must introduce corresponding expressions for the effect of the acoustical modes. Since the single energy distribution is to be used over the entire range of electric fields, we must introduce some approximations like those discussed in connection with (A6.25) in order to make it converge on the correct be- havior at £ = 0. The particular choice selected is a compromise between the energy loss formulae for the Maxwellian and single energy distributions: idS>/dt) acous.phonons = (4 WcV/)[l " (^'lAr)"]. (A7.24) A simplified expression is also used for the mobihty: fx = qC/mvi = hoVt/v. (A7.25) The relationship between /zo and t given by this differs by 25 per cent from the correct relationship (A6.7); since /zo is an adjustable parameter in the comparison between theory and experiment, (A7.25) does not introduce any error at low fields. Equations (A7.24) and (A7.25) cause fi to converge on /xo and 8i on kT as E approaches zero. (It is probable that a slightly better fit to the data would be obtained by using the procedure described with equa- tion (A6.25) ; the calculations based on (A7.24) and (A7.25) were made be- fore the (A6.25) procedure was worked out, however, and it was not consid- ered worth while to rework them for this article.) 1030 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Rewriting the equation for mobility in terms of the coUision frequencies l/r = v-Jl and 1/rop, the power input from the electric field is {dS/dOncia = qn^^ = q'E'/m [(l/r) + (l/rop)] (A7.26) = qn^/Mvr) [1 + Wlo;)Mv,)] where the »2 term is omitted if Vi < Vy. The power delivered by phonons is (J8/J/)phonons = 4mc2 {Vi/ ^) [1 - (Vi/VtY] " km/ Lr> = (4qc'/noKvi/vT) (A7.27) X [1 - {vi/vtY - {hp/4mc')W^o^){v2M]. The two coefficients of (i'2/2'i) are both larger than unity according to the analysis given above. We shall introduce the symbols A and B for them: Accordingly A = //4p = hp/kT, (A7.28) the last equahty following from (A7.19), and B = hvl^ mc\ (A7.29) If we take hv = k S20°K, m = the electron mass and c = 5 X 10^ cm/ sec, we find B = 87. (A7.30) As discussed in the text, the losses appear to be larger than can be ac- counted for by these values of m and c. The critical drift velocity used in the fit of Fig. 4 was 2.6 X 10® cm/sec and this corresponds to a value of c of c = Vc/l.Sl = 1.72 X W cm/sec (A7.31) according to the exact treatment based on the sphere model. (As stated in the text this means an effectiveness of energy interchange about (1.72 X 10V5 X 10^)2 = 10 times larger than the simple theory.) Our simplified energy loss equation (A7.27) leads to Vc = 2c (A7.32) so that we shall take c = 1.3 X 10« (A7.33) HOT ELECTRONS IN GERMANIUM AND OHM's LAW 1031 in this section so as to agree with the critical velocities observed in Fig. 2. This leads to a value for B of B = k 520°K/^m (1.3 X 10«)2 (A7.34) = 12.8 For A we shall take A = 520/r (A7.35) The only other adjustable parameter is /zq. For this we shall use the value based on Haynes' drift mobility and acoustical scattering. ^o(r) = ^0 (298°i^)(298°i^/r)3/2 (A7.36) = 3600 {29S°K/Tyi^ This value automatically fits the room temperature data in the Ohm's law range. The T~^'^ dependence then extrapolates it to the other ranges. The steady state condition may then be written in the form x2(l + Ay){ABy + Ax"^ - 1) = z^ (A7.37) where V, = {2hv/myi^ (A7.38) X = v,/v., y = v,/v, = (1 - x-^yi^ (A7.39) A = hv/kT = (v./vtY (A7.40) B = 12.8 (A7.41) z = MO {T)E/2cA''\ (A7.42) This form lends itself to calculation of z as a function of x. The drift velocity is then found to be given by u = Vd/2c = z/x{l + Ay) (A7.43) = [(ABy + Ax' -1)/(1 + Ay)Y'' If ^ » 1, there are three distinct ranges of behavior for u versus z: Range (/) u = z/A"'' For z — > 0, x^ ^ 1/A , y = 0 and consequently, u = zA"' = Vd/2c = Mo E/2c (A7.44) 1032 THE BELL SYSTEM TECffiSTICAL JOURNAL, OCTOBER 1951 SO that the low field relationship Vd = fJioE (A7.45) is correctly given. Range II, Ax- » 1 and x < 1 In this range the electrons are at high temperature but not high enough to excite tlie optical modes. For it 22 = ^^.4^ ^ = sV2/^i/4 (A7.46) u = z'l'^A"' or Vd = {2cix,Eyi\ {M Al) This corresponds to the square root range with a critical field of Ec = 2c/fjLo and Vc = 2c. Range III, x> 1 When X is greater than unity, the optical modes enter the picture. For the three cases considered the values of A and AB are: 77% A = 6.75, AB = 87, 193% A = 2.69, AB = 34.5, (A7.48) 296% A = 1.74, AB = 22.3. The large value oi AB means that as soon as y is appreciably greater than zero, say 0.5 corresponding to x — 1.15, energy losses to optical modes dominate. As y approaches unity, the value of u is approximately u = [AB/{\ + A)]'i^ (A7.49) = {iiv/^mc'yiy{\ + A-'yi^ leading to vM. B) = {hu/myf'/(l + A-'yi' (A7.50) = z;./[2(l + A-')Y'\ For the values of A and B given above, the ranges are not completely sepa- rated. In Fig. A2 we show the theoretical curves used in Fig. 5, together with the limiting lines just discussed. For the middle or 193°K curve, we also show the fit that would be ob- tained if c = 5 X 10^ cm/sec, corresponding to i5 = 87 as for (A7.30). It is seen that this deviates much more from the data than does the curve based HOT ELECTRONS IN GERMANIUM AND OHM'S LAW 1033 one = 1.3 X W corresponding to B = 12.8. The deviation between theory and experiment would be still worse at 77°K, for which temperature the curve of Figure A2 fits the data well, as is shown in Figure 5. ',03 ' - " -10' E IN VOLTS PER CENTIMETER Fig. A2— The theoretical curves and their limiting forms. Some of the data from Fig. 2 are repeated here and some additional data from the original publication (Ryder and Shockley loc. cit.) are shown by crosses. A scale of values of x and of approximate "tem- peratures" is also shown. The dashed curve for T = \9^°K is drawn for the case of the simple theory with c = 5 X 10» cm/sec; the change at 77°K would be even more marked. Above range III, the Ax"^ term makes an appreciable contribution. When Ax- becomes large compared to B, the approximation of taking the acoustical modes to be fully excited becomes questionable. This effect may be estimated by comparing kT and the energy in an acoustical transition. The ratio is approximately Pre kT mxVyC 2c kT kT V 520 ^ 2 -1.3 -10' 300 * 1.26-10^ (A7.51) X = x/3. 1034 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOHKK 1051 On Fig. A2 we show the values of x. Equ. (A7.51) leads to values of ac < 3 for 29S°K and x < 2ior .193°A'. Although tlie approximation of Iiv (acousti- cal) < kT breaks down, extraj)()laliiig the acoustical scattering into the higher range involves some comj)cnsating cfTects. The effective "temperature" 7\. of (he electrons may be taken on the basis of this approximate treatment to be pn)i)()rti()nal to vi. In order to make Tt become equal to T for zero field, we (\c\\\\c Tehy the equation Te = Tvl/vl = x^ hv/k (A7.52) = 520 x'. Some temperatures deduced from this equation are also shown on Fig. A2. Some of the data of Fig. 2 are also repeated in Fig. A2. In addition some earlier data''^ are also shown. These data extend to a somewhat higher range and appear to show the upward tendency predicted by the theory. The scale of temperatures indicates that for the extreme conditions experi- enced electron "temperatures" of about 4000°iir have been produced. w E. J. Ryder and W. Shockley, Phys. Rev. 81, 139 (1950). Published writings of C. J. Davisson Note on Radiation due to Impact of Beta Particles upon Solid Matter. Abstract. Phys. Rev., v. 28, ser. 1, pp. 469-470, June 1909. Positive Thermions from Salts of Alkali Earths. Phil Mag., V. 23, pp. 121-139, Jan. 1912. Role Played by Gases in the Emission of Positive Thermions from Salts. Phil. Mag., V. 23, pp. 139-147, Jan. 1912. Dispersion of Hydrogen and Helium on Bohr's Theory. Phys. Rev., v. 8, ser. 2, pp. 20-27, July 1916. Gravitation and Electrical Action. Science, v. 43, p. 929, June 30, 1916. The Emission of Electrons from Oxide-coated Filaments under Positive Bombardment, (with Germer, L. H.) Phys. Rev., v. 15, ser. 2, pp. 330-332, April 1920. The Electro-magnetic Mass of the Parson Magnetron. Abstract. Phys. Rev., v. 9, ser. 2, pp. 570-571, June 1917. The Emission of Electrons from Oxide-Coated Filaments, (with Pidgeon, H. A.) Phys. Rev., v. 15, ser. 2, pp. 553-555, June 1920. The Relation between the Emissive Power of a Metal and its Electrical Resistivity, (with Weeks, J. R.) Abstract. Phys. Rev., v. 17, pp. 261-263, February 1921. Scattering of Electrons by Nickel, (with Kunsman, C. H.) Science, v. 54, pp. 522-524, Nov. 25, 1921. The Scattering of Electrons by Aluminum, (with Kunsman, C. H.) Abstract. Phys. Rev., v. 19, ser. 2, pp. 534-535, May 1922. Secondary Electron Emission from Nickel, (with Kunsman, C. H.) Abstract. Phys. Rev., v. 20, ser. 2, page 110, July 1922. Thermionic Work Function of Tungsten, (with Germer, L. H.) Phys. Rev., v. 20, ser. 2, pp. 300-330, Oct. 1922. Scattering of Electrons by a Positive Nucleus of Limited Field. Phys. Rev., v. 21, ser 2, pp. 637-649, June 1923. 1035 1036 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Scattering of Low Speed Electrons by Platinum and Magnesium, (with Kunsman, C. H.) Phys. Rev., v. 22, ser. 2, pp. 242-258, Sept. 1923. The Thermionic Work Function of Oxide-coated Platinum, (with Germer, L. H.) Abstract. Phys. Rev., v. 21, ser. 2, page 208, February 1923. Note on the Thermodynamics of Thermionic Emission. Phil. Mag., V. 47, ser. 6, pp. 544-549, Mar. 1924. The Relation between Thermionic Emission and Contact Difference of Potential. Abstract. Phys. Rev., v. 23, page 299, January 1924. Relation between the Total Thermal Emissive Power of a Metal and its Electrical Resistivity, (with Weeks, J. R.) Opl. Soc. Am.y Jl. and Rev. Sci. Inslrnmenls, v. 8, pp. 581-^05, May 1924. Thermionic Work Function of Oxide-coated Platinum, (with Germer, L. H.) Phys. Rev., v. 24, ser. 2, pp. 666-682, Dec. 1924. Note on Schottky's Method of Determining the Distribution of Velocities among Thermionic Electrons. Phys. Rev., v. 25, pp. 808-811, June 1925. Are Electrons Waves? Bell Lab. Record, v. 4, no. 2. pp. 257-260. Apr. 1927. Diffraction of Electrons, (with Germer, L. H.) Phys. Rev., v. 30. pp. 705-740, Dec. 1927. Note on the Thermionic Work. Function of Tungsten, (with Germer, L. H.) Phys. Rev., v. 30, ser. 2, pp. 634-638, Nov. 1927. Scattering of Electrons by a Single Cr}^stal of Nickel, (with Germer, L. H.) Nalure, v. 119, pp. 558-560, Apr. 16, 1927. Are Electrons Waves? Franklin Inst., Jl, v. 205, pp. 597-623, May 1928. Attempt to Polarize Electron Waves by Reflection, (with Germer, L. H.) Nalure, v. 122, p. 809, Nov. 24, 1928. Diffraction of Electrons by a Crystal of Nickel. Bell Sys. Tech. Jl, v. 7, pp. 90-105, Jan. 1928. Reflection and Refraction of Electrons by a Crystal of Nickel, (with Germer, L. H.) NaCl Acad. Sci., Proc, v. 14, pp. 619-627, Aug. 1928. Reflection of Electrons by a Crystal of Nickel, (with Germer, L. H.). NaCl Acad. Sci., Proc, v. 14, pp. 317-322, Apr. 1928. "Anomalous Dispersion" of Electron Waves by Nickel, (with Germer, L. H.) *> r Phys. Rev., v. 33, pp. 292-293, Feb,, 1929. PUBLISHED WRITINGS OF C. J. DAVISSON 1037 Electron Waves. Franklin Inst., JL, v. 208, pp. 595-604, Nov. 1929. Electrons and Quanta. OpL Soc. Amer., JL, v. 18, pp. 193-201, Mar. 1929. Scattering of Electrons by Crystals. Sci. Monthly, v. 28, pp. 41-51, Jan. 1929. Test for Polarization of Electron Waves by Reflection, (with Germer, L. H.) Phys. Rev., v. 33, pp. 760-772, May 1929. Wave Properties of Electrons. Science, v. 71, pp. 651-654, June 27, 1930. Sir Chandrasekhara Venkata Raman, Nobel Laureate. Bell Lab Record, v. 9, pp 354-357, Apr. 1931. Conception and Demonstration of Electron Waves. Bell Sys. Tech. JL, v. 11, pp. 546-562, Oct. 1932. Diffraction of Electrons by Metal Surfaces, (with Germer, L. H.) Abstract. Phys. Rev., v. 40, p. 124, Apr. 1932. Electron Lenses, (with Calbick, C. J.) Letter to the editor. Phys. Rev., v. 42, p. 580, Nov. 15, 1932. Electron Particles as Waves, (with Germer, L. H.) Abstract. Science, v. 75, supp. pp. 10, 12, Mar. 4, 1932, Electron Microscope, (with Calbick, C. J.) Abstract. Phys. Rev., v. 45, p. 764, May 15, 1934. Electron Optics. ScL Monthly, v. 39, pp. 265-268, Sept. 1934. What Electrons can Tell us About Metals. //. Applied Phys., v. 8, pp. 391-397, June 1937. Discovery of Electron Waves. Nobel Lecture. Bell Sys. Tech. JL, v. 17, pp. 475-482, July 1938. Laureation in Stockholm. Bell Lab. Record, v. 16, pp. VII-XII, Feb. 1938. Theory of the Transverse Doppler Effect. Phys. Rev., v. 54, pp. 90-91, July 1, 1938. Double Bragg Reflections of X-rays in a Single Crystal, (with Ha worth, F. E.) Letter to the Editor. Phys. Rev., v. 66, pp. 351-352, Dec. 1 & 15, 1944. Double Bragg Reflections of X-rays in a Single Crystal. Letter to the Editor. Phys. Rev., v. 67, page 120, February 1 and 15, 1945. Contributors to This Issue Joseph A. Becker, A.B., Cornell University, 1918; Ph.D., Cornell University, 1922. National Research Fellow, California Institute of Tech- nology, 1922-24; Assistant Professor of Physics, Stanford University, 1924. Engineering Department, Western Electric Company, 1924-25; Bell Tele- phone Laboratories, 1925-. Dr. Becker has worked in the fields of X-rays, magnetism, thermionic emission and adsorption, particularly in oxide coated filaments, and the properties of semiconductors as applied in varistors, ther- mistors and transistors. R. M. BozoRTH, A.B., Reed College, 1917; U. S. Army, 1917-19; Ph.D. in Physical Chemistry, California Institute of Technology, 1922; Research Fellow in the Institute, 1922-23. Bell Telephone Laboratories, 1923-. As Research Physicist, Dr. Bozorth is engaged in research work in magnetics. C. J. Calbick, B.Sc. in E.E., State College of Washington, 1925; M.A. in Physics, Columbia, 1928. Bell Telephone Laboratories, 1925-. Here he has been engaged in the study of thin films on thermionic cathodes, electron diffraction problems, electron optics and microscopy, and in the development of high quahty cathode-ray tubes for television reception. Member of American Physical Society, American Crystallographic Association, the Electron Microscope Society of America, the New York Microscopical Society and the I.R.E. Karl K. Darrow, B.S., University of Chicago, 1911; University of Paris, 1911-12; University of Berlin, 1912; Ph.D., University of Chicago, 1917. Western Electric Company, 1917-25; Bell Telephone Laboratories, 1925-. As Research Physicist, Dr. Darrow has been engaged largely in writing on various fields of physics and the allied sciences. L. H. Germer, B.A., Cornell, 1917; M.A., Columbia, 1927; Ph.D., Colum- bia, 1927. Bell Telephone Laboratories, 191 7-. With the Research Depart- ment, Dr. Germer has been concerned with studies in electron scattering and diffraction, surface chemistry, order-disorder phenomena, contact physics and physics of arc formation. Member of American Physical Society, the American Crystallographic Society of which he was president in 1944, the A.A.A.S., the New York Academy of Sciences and Sigma Xi. 1038 CONTRIBUTORS TO THIS ISSUE 1039 Frank Gray, B.S., Purdue, 1911; M.A., Wisconsin University, 1913; Ph.D., 1916. U. S. Navy, 1917-19; Bell Telephone Laboratories, 1919- His work has been chiefly research in microphone and relay contacts, gas dis- charge tubes, television, electron beam tubes, microwave tubes, PCM sys- tems, and transistors. Fellow of American Physical Society and the A.A.A.S.; member of Gamma Alpha and Sigma XI; and Associate, I.R.E. R. D. Heidenreich, B.S., Case School of Applied Science, 1938; M.S., 1940. Dow Chemical Company, 1940-45; Bell Telephone Laboratories, 1945-. Here he has worked chiefly on problems of surface metallurgy. Fellow of American Physical Society; member of A.A.A.S., the Electron Microscope Society of America and Sigma Xi. A. N. HoLDEN, B.S., Harvard, 1925. Bell Telephone Laboratories, 1925-. In the Research Department his work has been chiefly in chemistry and solid state physics, primarily in originating new piezoelectric materials and in perfecting methods of growing crystals. A. G. Jensen, E.E., Royal Technical College, Copenhagen, 1920; instruc- tor, 1921. Bell Telephone Laboratories, 1922-. He has been occupied chiefly in radio receiving studies, short-wave transatlantic telephony, coaxial cable development and television research. Fellow of I.R.E. and member of Society of Motion Picture and Television Engineers. M. J. Kelly, B.S., Missouri School of Mines and Metallurgy, 1914; M.S., University of Kentucky, 1915; Ph.D., University of Chicago, 1918. Joining Bell Telephone Laboratories in 1918, Dr. Kelly became Director of Vacuum Tube Development in 1928; Director of Research, 1936; Executive Vice President, 1944; President, 1951. For the past year he has also served in an advisory capacity to the Air Force to assist in organizing its research and development. He holds honorary doctors' degrees from the University of Kentucky and the University of Missouri. In 1944 Dr. Kelly was awarded a Presidential Certificate of Merit and in 1945 was elected to the National Academy of Sciences. Member of Franklin Institute; Fellow of American Physical Society, I.R.E., Acoustical Society of America, A.I.E.E., and the American Association for the Advancement of Science. L. A. MacColl, A.B., University of Colorado, 1919; M A., Columbia, 1925; Ph.D., 1934. Bell Telephone Laboratories, 1919-. He has been con- cerned chiefly with mathematical research and consultation. Visiting lec- turer, Princeton, 1948-49 ; author of "Fundamental Theory of Servomecha- 1040 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 nisms" (1945); member of American Mathematical Society, the Mathematical Association of America, the Edinburgh Mathematical Society, the American Physical Society, Phi Beta Kappa and Sigma Xi; and Fellow of New York Academy of Sciences. W. P. Mason, B.S. in E.E., University of Kansas, 1921; M.A., Ph.D., Columbia, 1928. Bell Telephone Laboratories, 1921-. Dr. Mason has been engaged principally in investigating the properties and applications of piezo- electric crystals and in the study of ultrasonics. H. J McSkimin, B.S., University of Illinois, 1937; M.S., New York Uni- versity, 1940. Bell Telephone Laboratories, 193 7-. Here he has worked chiefly on crystal filters, piezoelectric elements, ADP crystals, studies of the acoustic properties of liquids and solids. Member of Acoustical Society of America, Eta Kappa Nu, and Sigma Xi. J. R. Pierce, B.S., in Electrical Engineering, California Institute of Technology, 1933; Ph.D., 1936. Bell Telephone Laboratories, 1936-. Dr. Pierce has been engaged in the study of vacuum tubes. W. ScHOCKLEY, 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 solid state physics. Elizabeth A. Wood (Mrs. Ira E.), A.B., Barnard, 1933; M.A., Bryn Mawr, 1934; Ph.D., Bryn Mawr, 1939. Research Assistant, Columbia, 1941. The next year she was awarded a National Research Fellowship and spent two years studying quartz deposits in the United States. Bell Telephone Laboratories, 1943-. Her work has been chiefly in X-ray diffraction, and the X-ray and optical investigation of crystals. Delegate to the Second Interna- tional Congress of Crystallography in Stockholm in 1951. Member of Ameri- can Physical Society, American Crystal lographic Association, the New York Mineralogical Club, Phi Beta Kappa, Sigma Xi; and a Fellow of the Min- eralogical Society of America. HE BELL SYSTE^ mcai ourna I E^OTED TO THE SCIENTIFIC ^^^ AND ENGINEERIN SPECTS OF ELECTRICAL COMMUNICATION GLUME XXX OCTOBER 1951 NUMBER 4 PART ] The TD-2 Microwave Radio Relay System A. A. ROETKEN, K. D. SMITH and R. W. FRIIS 1041 Deterioration of Organic Polymers B. S. BIGGS 1078 Electron Tubes for a Coaxial System G. T. FORD and E. J. WALSH 1103 Telephone Traffic Time Averages JOHN RIORDAN 1129 Reproduction of Magnetically Recorded Signals R. L. WALLACE, JR. 1145 Flow of Holes and Electrons in Semiconductors R. C. PRLM, III 1174 Instantaneous Compandors on Narrow Band Speech Channels J. C. LOZIER 1214 Evolution of Inductive Loading (Concluded) THOMAS SHAW 1221 Abstracts of Bell System Technical Papers Not PubUshed in This Journal 1244 Contributors to This Issue 1254 COPYRIGHT 1951 AMERICAN TELEPHONE AND TELEGRAPH COMPANY THE BELL SYSTEM TECHNICAL JOURNAL PUBLISHED QUARTERLY BY THE AMERICAN TELEPHONE AND TELEGRAPH COMPANY 195 BROADWAY, NEW YORK 7, N. Y. CLEO F. CRAIG, President CARROLL O. BICKELHAUPT, Secretary DONALD R. BELCHER, Treasurer EDITORIAL BOARD F. R. KAPPEL O. E. BUCKLEY H.S.OSBORNE M.J.KELLY J. J. PILLIOD A.B.CLARK R. BOWN D. A. QUARLES F. J. FE E LY P. C. JONES, Editor M. E. STRIEBY, Managing Editor S U H S C R I r T I O N S Subscriptions are accepted at $1.50 per year. Single copies are 50 cents each. The foreign postage is .35 cents per year or 9 cents per copy. PRINTED IN U.S.A. The TD-2 Microwave Radio Relay System By A. A. ROETKEN, K. D. SMITH and R. W. FRIIS (Manuscript Received July 5, 1951) The TD-2 microwave radio relay system is a recent addition to the tele- phone plant facilities for long distance communication. It is designed to supple- ment the coaxial system and to provide greatly expanded facilities for nationwide transmission of broad-band signals such as television pictures or large groups of message circuits. The system makes use of many microwave repeaters located 25 to 30 miles apart in line-of-sight steps. The great variety and number of components which make up such a system require the engineering of all com- ponents to close tolerances. This paper describes the system in some detail from the standpoints of overall objectives, component designs to meet such objectives and facilities for the maintenance of overall performance. I. Introduction SUPER-HIGH or microwave frequencies began to attract the interest of communication research engineers during the late '30s. The practical application of microwaves to commercial communication circuits was delayed by the outbreak of World War II, but the microwave techniques which had already been developed were employed to advantage in the prosecution of the war. The concentrated development effort and mass production of microwave equipment for mihtary applications greatly expanded the engi- neering knowledge and production skill in this relatively new communica- tions field. After termination of the war, it was possible again to devote the necessary development effort toward application of microwave techniques to commercial purposes. In the Bell System this effort was applied to the development and construction of a long-haul radio relay system. A broad-band multi-channel radio relay system now connecting some of the main communication centers of the United States, as shown in Fig. 1, represents the combined efforts of a Bell System team since- 1945.^ This chain of stations carrying hundreds of message circuits or a television picture on each broad-band channel, in giant 25 to 30-mile strides across the country, has opened up a new radio field. The first step was the development of an experimental system placed in service in November 1947 between New York and Boston.^ Upon the successful completion of this project objectives were estabhshed for a system, which is called the TD-2 Radio System, capable of extension to at least 4000 miles with upwards of 12vS repeaters. The TD-2 Radio System provides no new types of service but will sup- plement existing facihties such as the coaxial system. Therefore, TD-2 must provide comparable reliability, economy and quality of service. It is 1041 1042 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 TD-2 MICROWAVE RADIO RELAY SYSTEM 1043 contemplated that by the end of 1951 there will be over 20,000 broad-band channel miles of radio relay in operation in the Bell System. Of this, about two-thirds will be used for television service and one-third to provide over 600,000 circuit miles of telephone circuits. II. TD-2 System — General A radio relay system designed for long distances involves many problems new to radio but not new to long distance wire circuits. These problems are chiefly those of systems engineering to close transmission tolerances be- 4200 r— Q O 4150 ai - u < 4000 O UJ Z 3950 o < 3900 5 3850 < O 2 3800 O 2 2 3750 O U 3700 4170 4130 4090 4050 4010 3970 3850 3810 3770 STATION A STATION B 3930 ^ stfLj'i '^M ^^^^^H K 1 ■ Fig. 12 — Transmitter modulator. The transmitter modulator is shown in Fig. 12. The oscillator power is applied to the cathode grid cavity through a tuner, a bandpass filter and a waveguide spacer. The IF power is applied between cathode and grid through a network which is mounted within a cyUndrical compartment around the tube socket. The desired output sideband of the modulator is selected by a bandpass filter. Following this filter is a tuner unit which provides a means for adjusting the output impedance for a match with the following ampHfier. A conversion gain of 9 db is reahzed in the process of shifting the IF frequency to the microwave band. The modulator assembly is directly connected to the input of the trans- mitter ampHfier, as may be seen in Fig. 8. An amphfier shown in Fig. 13 consists of three stages of 416A triodes mounted in cavity structures as 1056 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 described above. The three stages are connected together in cascade through waveguide spacers and reactance tuners of such dimensions that the joining of each output cavity with the following input cavity (or filter section in the case of the output stage) forms a double-tuned critically coupled transformer. A flat over-all transmission characteristic is thereby obtained which is about 20 megacycles wide between points 0.1 db down. While capable of greater gain, the amphfier is adjusted to a gain of 18 db at an output power level of 0.5 watt. A double directional coupler in the waveguide between the trans- mitting amplifier and the transmitter channel separation filter provides monitoring and output alarm signals. Fig. 13— Transmitter amplifier. E. Microwave Sources and Control Circuits The receiver control unit may be seen in Fig. 8. It contains a stabilized d-c amplifier for IF automatic gain control and level adjustments, and test- ing facihties for checking the performance of the receiver. The control unit also contains power controls and protection devices for the plate and fila- ment circuits. The transmitter control unit contains controls for the applica- tion of power and bias to the transmitter and a means for metering various circuits. The microwave generator, which furnishes about 200 milliwatts of beating oscillator power for the transmitter and receiver, is a stable microwave frequency source developed by harmonic generation from a quartz crystal in the vicinity of 18 megacycles. The multiplication takes place in six har- TD-2 MICROWAVE RADIO RELAY SYSTEM 1057 monic generator stages, three doublers and three triplers. Only a few miUi- watts of output power is required where the generator is used for the re- ceiver beating oscillator alone, as in main stations or terminals. Here the final multiplier is operated as a sextupler, thereby permitting the ehmination of the penultimate stage. At an auxiliary repeater, the receiving beating oscillator source is obtained from a 40-megacycle shifter converter, one input of which is from a part of the microwave generator output, and the other is from a crystal controlled 40-megacycle generator. F. Transmitter-Receiver Interconnections At auxiliary stations the IF output of the receiver is connected by a short coaxial line and 5 db resistance pad directly to the transmitting modulator in the same bay. This resistance pad is used as an impedance matching aid. At main repeater stations the IF receiver output and the transmitter input are carried in coaxial lines to IF patching and switching equipment. With 30 to 60 feet of coaxial line between the receiver and transmitter, impedance match requirements are more severe than for short coaxial Hne connections. Here, a 6 db resistance pad is connected in the output line of the receiver and a 3 db resistance pad and buffer amplifier are connected in the input line of the transmitter modulator. The buffer amplifier consists of a single stage using a 418A tetrode and its gain may be set manually to provide — 1 dbm to +5 dbm of signal power into the transmitter modulator as required. The bandwidth of the amplifier is approximately 20 megacycles and is sloped in such a manner as to approximately compensate for the small variation of loss over the band in the patching coaxial lines. G. IF Switching* IF switching circuits are provided at terminals and main repeater points to facilitate maintenance operations as well as to provide flexibiUty for the changing requirements of network distribution. These switching and dis- tributing operations are obtained by the use of unity gain amplifiers which are designated IF switching amplifiers and IF distributing amplifiers. An IF switching amplifier functions as a single-pole double-throw switch for connection between intermediate frequency circuits of 75-ohm impedance. It has two input networks, each connected to a grid of a 404A pentode. The plates of the two tubes are connected in parallel to the output. Trans- mission through one or the other of the tubes is prevented by the apphca- tion of a high negative grid bias to that tube. Switching the bias from one tube to the other thus permits the selection of either input signal. In most * Prepared by T. R. D. Collins. 1058 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 applications of the switching ampUfier, signaUng facilities are provided so that the switching operation can be controlled remotely. An IF distributing amphfier provides three outputs from a single input, all at 75-ohm impedance. It consists of four 404A pentodes, the plate of one tube being connected to the grids of the other three tubes through an interstage network. Individual networks from the three output stages pro- vide the desired distributing branches which are well isolated from each other electrically. Switching and distributing amplifiers and a mounting framework are shown in Fig. 14. The two amplifiers have the same physical size and as many as five such units may be mounted in a frame on a plug-in basis. A number of such mounting frames are grouped and mounted on duct type bays to meet the needs of each switching and distributing location. Jack :## Fig. 14— Switching and distribution amplifiers. fields associated with the mounting frames terminate the interbay coaxial trunks through which the switching and distributing connections are made. Various combinations of switching and distributing amplifiers perform a large variety of interconnection functions within the system. Figure 15 indicates how these amplifiers may be used to replace a circuit which has failed by a spare circuit. At a transmitting terminal, the regular and spare channels may be paralleled. If a transmission failure occurs in channel 1 at one of the auxiliary repeater stations east of the main station, the failure of this channel is noted at the end of the system and service is switched to the spare channel 2. Since channel 1 is good except for the break east of the main station, the remote control for the switching amplifier in channel 1 is operated to switch output A of the channel 2 distributing amplifier to channel 1 radio transmitter. Thus channel 1 is connected in parallel with TD-2 MICROWAVE RADIO RELAY SYSTEM 1059 channel 2 at this station and both a regular and a spare circuit are now available at succeeding stations. H. Automatic IF Switching* At present IF switching is handled on a manual basis by attendants at the main stations or on a remote control basis over the order wire facilities. This type of switching is satisfactory for maintenance purposes but ob- viously is not fast enough to avoid a circuit interruption in replacing a circuit which has failed. The reliabihty of wire circuits will be difficult to meet in a long radio relay system without standby facilities because of vacuum tube failures and fading. Work is now under way to develop auto- matic IF switching facihties which will detect instantaneously a circuit AUXILIARY REPEATERS AUXILIARY REPEATERS Fig. 15 — IF switching and distributing amplifier. Interconnection diagram. failure or an increase in noise on a radio channel and switch in a spare circuit for the poor section without circuit interruption. Fading data indicate that nrost deep fades which go beyond the range of the AGC circuit are of the selective type. Thus switching to a spare channel will provide frequency diversity advantages. With automatic switching it is believed the TD-2 System circuit outage time will not exceed that of wire circuits. I. Television Monitoring Visual monitoring facilities are provided at terminal and main repeater stations for observing circuit performance. Auxiliary repeater stations may also be so equipped in special cases. At transmitting or receiving terminals, monitoring connections are bridged to the video cables which run to operat- * Prepared by T. R. D. Collins. 1060 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 ing centers. The equipment units which make up the monitoring facilities are an auxihary IF ampHfier, an FM receiver, a video ampHfier and a video monitor. A combination of these units is assembled in a bay to fit the needs of each monitoring location. IV. FM Terminal Equipment A. General The TD-2 System will transmit a standard RMA black and white tele- vision signal or a band of message channels built up on a frequency division basis as provided by the coaxial cable message terminals. The FM terminal transmitter converts either of these signals to a frequency-modulated signal centered at 70 megacycles for application to the radio transmitter. The FM terminal receiver recovers the television or carrier signal from a frequency- modulated 70-megacycle signal. Thus the FM terminal equipment provides the connecting links between the TD-2 radio equipment and other facilities. In a long system it may be necessary to bring the radio signal down to voice and back up to radio frequency many times in order to add and drop message groups. Each such process will require FM receiving and transmit- ting terminal equipment which consequently estabHshes severe linearity requirements for this equipment. An objective in the development of the terminals was to meet long haul systems performance requirements with sixteen pairs of terminals in tandem. B. FM Transmitter A functional diagram of the FM terminal transmitter is shown in Fig. 16. It accepts a signal from an unbalanced 75-ohm line and delivers an FM signal centered at 70 megacycles to the radio transmitter. The input level may be adjusted from 0.2 volt to 2.5 volts peak-to-peak with an output level of 13 dbm at an impedance of 75 ohms. For television transmission with a ±4 megacycle swing the tips of the synchronizing pulses are at 74 megacycles and the picture white at 66 megacycles. For message service the nominal deviation is centered about 70 megacycles. For television transmission the output is automatically clamped to a predetermined frequency during each synchronizing pulse. These differences in operation are described in more detail below. 1. Description The input signal to the FM transmitter is applied through an adjustable attenuator to a video amplifier consisting of two similar three-stage feed- back amplifiers in tandem which have a combined gain of 42 db. The video TD-2 MICROWAVE RADIO RELAY SYSTEM 1061 amplifier output is applied to the repeller of a deviation oscillator described below. A microwave heterodyne method of generating a 70-megacycle FM signal was selected because it was found possible to design a highly linear deviator in the microwave region. It also allows separate tests to be made of the transmitter and receiver linearity and thus facilitates maintenance, A reflex klystron oscillator may be frequency-modulated by superim- posing a modulating signal on the repeller d-c voltage. The rate of frequency change with change of repeller voltage passes through a minimum near the BASEBAND INPUT Wv VIDEO AMPLI FtER LINEARITY ADJUSTMENTS ^'ggS;iTr.^i-#To qTd ] Fig." 16— Block diagram of FM terminal transmitter. point of maximum power output. At a deviation of =t4 megacycles, the difference in FM sensitivity over the 8-megacycle swing would normally be sufficient to produce intolerable distortion. However, the operating fre- quency of a reflex oscillator is subject to modification by the load impedance seen by the oscillator. This effect is commonly called "pulling." In the de- viation oscillator, this effect is made use of to provide deviation linearity over a range of more than 10 megacycles. The load circuit for the 4280- megacycle deviation oscillator consists of a variable attentuator, a short length of line, and a variable position short circuit. Adjustments of these two variables allows complete control of the reactance seen at the output 1062 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 of the deviation oscillator. The length of circuit to the movable short is so chosen (about 35 inches) to provide the optimum rate of change of reactance with frequency. At optimum adjustment, the reactive component of the load pulls the frequency of the generator by just the amount necessary to straighten out the deviation curve. The deviation sensitivity is at the same time increased about 25%, which reduces the required video driving voltage. A portion of the output signal of the deviation oscillator is fed through a directional coupler to a crystal microwave converter where it is mixed with a 4210-megacycle signal from another klystron to produce a 70-megacycle FM signal. The microwave output from the deviation oscillator is about 50 milHwatts, and after losses in the directional coupler and converter about one milliwatt of 70-megacycle FM output is available. This signal is amplified in a broad-band limiter-amplifier for application directly to the radio transmitter or indirectly through appropriate switching circuits. 2. Clamper and AFC Circuit For television transmission the voltage suppHed to the repeller of the deviation oscillator is clamped to a predetermined negative value during each synchronizing pulse in a conventional manner. This clamping action enables the transmission of video signal components down to direct current. For message telephone transmission the clamping circuit is disabled. The automatic frequency control circuit used to control the frequency of the beat oscillator provides a high gain and stable AFC without a d-c ampli- fier. As shown in Fig. 16, a portion of the 70-megacycle output signal is diverted and after passing through a gated amplifier is appHed to a dis- criminator. The discriminator network is of conventional design and the detector elements are germanium diodes. The direct-current output voltages are applied to the grids of two triodes acting as a pulse modulator. The anodes of these triodes are supplied with a high level positive pulse used for gating from a blocking oscillator associated with the clamper circuit. This oscillator is free running for message signals but is triggered by the synchronizing pulses when video signals are being transmitted. The un- balance voltage on the triode grids controls the amplitude and polarity of the pulse produced by this modulator. After two stages of a-c. amplification this error signal is combined with a second high level pulse from the same blocking oscillator source in a phase detecting circuit, and, after integration, the d-c. output of this detector is used for AFC. With television operation the gated amplifier operates only during synchronizing pulses, and the discriminator is adjusted for an output frequency of 74 megacycles. With multi-channel message operation, the gated amplifier is operated as a straight-through amplifier, and the discriminator is adjusted to hold an average output frequency of 70 megacycles. TD-2 MICROWAVE RADIO RELAY SYSTEM 1063 C. FM Receiver The FM receiver contains an IF amplifier, limiter, discriminator, and video amplifier, as indicated in Fig. 17. The input ampUfier consists of two stages, each using a 404A pentode, with broad-band interstage networks. The two-stage instantaneous amplitude limiter has biased siUcon varistors shunt- ing the single-tuned plate loads of each of the 41 8A tubes. The bias voltages are so adjusted that the load impedance is high for signal voltages less than about one volt, and very low for any larger signal. 1. Discriminator The discriminator circuit follows early conventional practice, in that two separately driven antiresonant circuits are used. The signal at the limiter output is fed to two 404A amplifier stages, one tuned above the signal band, DISCRIMINATOR VIDEO AMPLIFIERS Fig. 17— Block diagram of FM terminal receiver. the other below. The frequency-modulated signals produce amplitude varia- tions of the voltage across these tuned circuits which are detected by diode rectifiers and applied to the video amplifier. A potentiometer in the cathode interconnection of the amplifier tubes provides a balance adjustment for the discriminator. 2. Video Amplifier The video amplifier is a three-stage resistance-capacity coupled unit having negative feedback in each symmetrical half, and negative feedback to longitudinal voltages through a common cathode resistor. The gain is adjustable over a range of several db by means of a dual potentiometer which varies the common cathode resistance in each half of the ampUfier. Whenever such an adjustment is made, a constant loop gain is maintained in the feedback system by varying simultaneously the local cathode de- 1064 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 generation in the middle stages of the amplifier. A peak-to-peak voltmeter connected across one side of the balanced output is used to monitor the transmission level of television signals. V. System Maintenance and Test Equipment A. General Most TD-2 stations are operated on an unattended basis. Test equipment is provided at each terminal, auxiliary and main station to perform the necessary maintenance functions. This consists of a radio test bay as shown in Fig. 18 for each auxiliary, main and terminal station, and an FM test console as shown in Fig. 19 at terminals and main stations where FM termi- nal equipment is provided. The philosophy is to provide sufficient test equipment at each station to isolate the trouble. When the unit in trouble requires extensive tests or repair, a station spare is substituted and the faulty unit is returned to a maintenance center. Maintenance centers are usually located in existing telephone offices along the route. In maintaining the radio equipment each repeater bay is adjusted to provide a transmission band 20 megacycles wide, flat to within two-tenths of a db and centered about the assigned channel frequency. Trimming ad- justments are provided on the receiver and transmitter to obtain this characteristic. This test involves the use of a swept signal source which is divided into a reference path and a path through the equipment under test, each of which is terminated in an identical detector. The outputs of these detectors are alternately appHed to the vertical deflection amplifier of an oscilloscope at a 30-cycle rate, while a voltage proportional to the frequency excursion is appUed to the horizontal amplifier. Generally, the vertical gain of the oscilloscope is adjusted so that a separation of one inch between the test and reference traces corresponds to a level difference of 1 db and the horizontal gain is adjusted so that one inch corresponds to a 10-megacycle frequency excursion. The reference trace is then matched to the test trace by adjustments of the equipment under test. The waveguide attenuators and directional couplers shown in Fig. 18 provide for testing over a wide range of levels. B. Radio Test Bay The radio test bay contains a microwave swept frequency oscillator, a combined microwave and IF power meter, a cathode ray oscilloscope, RF and IF wave meters, detectors and attenuators and associated power supplies. The microwave sweep oscillator is adjustable in sweep range up to 70 megacycles over the 3700 to 4200 megacycle band. The frequency is swept TD-2 MICROWAVE RADIO RELAY SYSTEM 1065 POWER SUPPLY RF SWEEP OSC IF & RF POWER METER 1500 VOLT RECT, OSCILLOSCOPE IF ATT. PANEL IF DETECTOR PANEL IF SWEEP OSC. (OR 30 CYCLE SWITCH) METER 8. CONTROL PANEL ATTENUATOR (AT 2) ATTENUATOR CABLE TRANSDUCER WAVEMETER CRYSTAL MONITOR DIRECTIONAL COUPLER TERMINATIONS Fig. 18 — Radio test bay. by a motor driven reactive element in one of two cavities associated with the 402A velocity variation oscillator tube. 1066 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 The RF and IF power meter consists of a temperature compensated thermistor bridge unit. It has separate input arrangements for the 3700 to 4200-megacycle and 50 to 90-megacycle bands. Accurate measurements of power may be made in the range from — 10 dbm to +6 dbm. The test bay used at maintenance centers has, in addition to the above equipment, a 50- to 90-megacycle swept frequency oscillator and associated detectors for the testing of intermediate frequency components. The opera- Fig. 19 — FM terminal test console. tions carried out at the maintenance center include the repair and realignment of defective equipment returned from the radio stations. The maintenance center test equipment includes facilities for accurate impedance match measurement in the microwave and IF range, for varistor matching tests, vacuum tube transconductance tests and general component tests which cannot be made at the radio station. Usually the maintenance centers are operated by the same staff that maintains the radio stations in the section. TD-2 MICROWAVE RADIO RELAY SYSTEM 1067 C. FM Terminal Test Console The terminal test console shown in Fig. 19 is used to measure FM de- viation, Hnearity of the FM transmitter and receiver and for routine moni- toring of wave forms at video frequencies. The equipment includes a con- ventional CW signal generator covering the range of 50 to 90 megacycles, a video '^A" scope, an electronic switch and patching and terminating facili- ties. A rather unique linearity test set described below and an FM terminal receiver are also included. 1. Deviation Measurement For deviation measurements, the IF signal being monitored is patched into one input of the IF electronic switch which switches between inputs at a 1200-cycle rate, and the CW signal generator into the other input. After detection by the FM receiver, the signals are applied to the oscilloscope and a straight line corresponding to the CW generator frequency is displayed superimposed on the video signal. By adjustment of the CW reference frequency, the instantaneous frequency of any signal component may be determined. 2. FM Receiver Linearity For a measurement of linearity of the receiver discriminator, the linearity test set is connected to an FM transmitter which is patched to the receiver under test. The linearity test set supplies a low level 100 kc modulating voltage to the deviation oscillator of the transmitter and a high level 60- cycle voltage to the transmitter beat oscillator. For this test the transmitter AFC circuit is disabled. Under these conditions the signal applied to the receiver discriminator swings over approximately 10 megacycles at a 60- cycle rate and over a small range of less than one megacycle at a 100 kc rate. The 100 kc video component in the receiver output is then proportional to the slope of the discriminator response curve. The envelope of this 100 kc amplitude is recovered in the linearity test set and the a-c. component is applied to the oscilloscope vertical amplifier. The horizontal deflection is synchronized with the 60-cycle deviation. A 30-cycle switch changes the amplitude of the 100 kc signal by a calibrated amount to provide two sepa- rated traces on the screen and make the device self-calibrating. 3. FM Transmitter Linearity For a measurement of transmitter linearity, the same setup used in the receiver test is made use of except that both the 100 kc small signal and 60- cycle large signal are applied to the deviation oscillator of the transmitter under test. The beat oscillator AFC circuit is allowed to operate with a time constant sufficiently rapid to follow the 60-cycle fluctuation of the deviation oscillator, but not the 100 kc component. Thus the 100 kc modula- tion component is applied over a 10-megacycle range of the deviation oscil- 1068 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 lator characteristic, but is applied to the receiver at a fixed (70-megacycle) frequency, so that the receiver discriminator does not enter the measurement except as a fixed gain detector. While the transmitter is being tested as above, the magnitude and phase adjustments of the deviation oscillator load impedances are made as required to meet the desired linearity of devia- tion which is normally 1% over the 10-megacycle range. VI. CI Alarm and Control System* The operation and maintenance of unattended repeater stations require a flexible and rehable alarm system whose performance is commensurate with the importance of the toll and television program services handled by the TD-2 System. The CI alarm and control system has been developed for this purpose and, as its name implies, it serves two functions. The first is that of transmitting detailed alarm information from unattended repeater stations to the responsible alarm centers. The second function is that of transmitting orders, or remote control signals, from alarm centers to unattended stations. The salient features of the CI system may be summarized as follows: 1. It is a voice-frequency system, thus permitting its use with equal facility on cable pairs, open wire fines, or radio channels (or combina- tions thereof) capable of transmitting a 3000-cycle voice band. 2. It transmits a maximum of 42 separate alarms or indications from each unattended station to its associated alarm center. 3. It transmits a maximum of ten remote control orders in the opposite direction, that is, from an alarm center to each unattended station for whose operation it is responsible. 4. A maximum of twelve unattended stations may be associated with one alarm center. A typical section of the TD-2 Radio Relay System is shown in Fig. 4. The alarm center for the section indicated is at Cuyahoga Falls, which in this case, is also a maintenance center. Alarm centers and maintenance centers may be located at any attended central office or repeater station on existing cable and open wire routes. Alarm signals are transmitted to the alarm center from the unattended station over a one-way, two-wire circuit as shown in Fig. 20. A four-wire local order circuit is used for voice communication between adjacent main radio stations and the intermediate unattended auxiliary repeater stations. The alarm centers and maintenance centers in that alarm section are also bridged on it. Remote control order signals from the alarm center are of such short duration that they can be transmitted without objectionable interference over one side of this four-wire local order circuit. An express * Prepared by C. E. Clutts and G. A. Pullis. TD-2 MICROWAVE RADIO RELAY SYSTEM 1069 illC KEYS FOR SELECTING STATIONS AND ORDERS ^<2 lt5>< ii|3 >3lSi 1 t t t i < -I a. {^Sp Oiu"* sen 1 ZUJ ujq: ^5 • 5« q:"-1: < -J < I s-^?« ■ 1 t f t SCD(0 = - I s ^5UJ Jffig UJ w < h to ^^ii ■"^ Q.U UJ QC 2 ' KIT E<°^ E<°^ 0 t t t \ i S - J3 U LU tr-i 55 - 05 ° ^ HOC .5 UJ -0 1 q: ip lit $0 8 zz U-=) t3 iQ « -1 ^5i bib CXj *{ t t t i \ sis ii UJ cr z aUZm -^ -^ ^•/^ t3 D q: a > tr > VL 0 °?s III Ou,0 0 u lU>:iiJ,n "•■*. U sip "^^--' ^91 ^^^'^■"^Y^^^ i4^i|ippiiiiiimi I t;- " •»'»«VAH fcj?^ /Ti l'-^-..-- ^^^^^H|^^^^^^^^^^ ^^^JL^^^ Fig. 3— Samples of rubber in various stages of weathering. 1080 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Fig. 4— Cellulose acetate panels exposed in Florida for six months. Fig. 5— Samples of rubber garden hose cracked by ozone. DETERIORATION OF ORGANIC POLYMERS 1081 The value of polymers as structural materials is derived entirely from the fact that they are composed of very large molecules. They are generally classified in two broad groups, the essentially linear or chain-like polymers comprising the thermoplastics and rubbers, and the very highly branched three-dimensional networks which are called thermoset materials. The fundamental difference between these groups is shown diagrammatically in Fig. 6 in which, for convenience, the linear polymers are shown as straight lines instead of in their usual randomly kinked shape. The linear polymers are made up of molecules of finite average size, from a hundred to a thousand or more times as long as they are wide^ and the SCHEMATIC REPRESENTATION OF A LINEAR POLYMER SCHEMATIC REPRESENTATION OF A THERMOSET POLYMER Fig. 6— Schematic representation of a linear polymer, above, and of a thermoset ])olymer, below. Strength of the material is dependent on the size of these molecules much as the strength of a cotton thread is dependent on the length of the individual fibers of which it is composed. The forces holding the aggregate together are the cumulative interchain forces. In thermoplastics these forces may be quite strong. In rubbers they are weak until the rubber is vulcanized. Vulcanization connects the chain-like molecules into a loose three-dimen- sional network, but the number of cross-links is very low compared to typical thermoset polymers being only about one or two for every hundred chain atoms.* Vulcanized rubbers are therefore still largely linear polymers and their deterioration follows the pattern of the thermoplastics. The 1082 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 theraioset materials, of which the phenolic resins are typical examples, are so highly interconnected that the molecular weight can be considered to be infinite. Each molding, for example, may consist of a single molecule. Be- cause of their extensive internal cross-bracing their deterioration is usually a surface phenomenon.^ It will be discussed later in this memorandum. The paragraphs which follow immediately will refer to Hnear polymers. Any material chosen for an engineering apphcation obviously must pos- sess desirable characteristics and "corrosion" or deterioration changes these characteristics in some undesirable way. There are three ways in which a system of chain-like molecules can change: 1) the chains may be cut into smaller pieces, 2) the chains may be tied together by cross-links, and 3) the nature of any side groups along the chain may be modified. All of these changes have been found to occur during normal weathering of polymers and the properties of the product are determined by the extent of each change.® The first type, chain scission, is usually the most serious because it cuts at the very essence of polymeric nature which is high molecular weight. As molecular weight is lowered, strength is lowered and ultimately is lost com- pletely. To continue the analogy to a cotton thread, the individual fibers become so short that they cease to overlap each other adequately. Tough horny polyethylene, for example, deteriorates to something akin to paraffin wax. If chain scission occurs extensively in rubbers, portions of chains are cut loose from the relatively few cross-links and the product will appear to have become unvulcanized. This phenomenon is well known with natural rubber and is called "reversion".'^ (Fig. 7) The second type of change caused by aging, the introduction of ties or cross-Hnks, is not usually of great importance in plastics unless carried to an extreme when the rigidity and brittleness of thermoset polymers might result. As a matter of fact, the introduction of a few cross-links in a thermo- plastic, without accompanying chain scission, probably serves to toughen the material. In rubbers, however, where high elongation is a desired prop- erty and is derived from the uncoiling of the molecules under stress, in- troduction of cross-links beyond those necessary for vulcanization tends to ''shorten" the material and can eventually stiffen it to the point that it loses serviceabiHty. The introduction of cross-hnks increases the density, and frequently when the surface of a plastic or rubber has been cross-linked extensively it develops an "alligator" or "mud crack" pattern resulting from excessive shrinkage. The third type of change, the modification of side groups, normally has little effect on the strength of a polymer, but may have a pronounced effect on the dielectric properties, solubility, moisture absorption, etc., depending DETERIORATION OF ORGANIC POLYMERS 1083 '^ Fig. 7— Natural rubber tapes before and after oxygen bomb treatment. on the nature of the groups introduced or modified. As indicated above, during normal deterioration all of these types of change are proceeding 1084 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 simultaneously to greater or less extent. The rates of the reactions vary from one material to another, and the same conditions which degrade natural rubber to a soft gum may cause neoprene or GR-S to become harder and stiffer. Returning now to the thermoset polymers, one sees that neither occasional chain scission nor occasional cross-linking can have an important effect on the mechanical properties of a thermoset polymer since every part of the structure is tied to the rest of it by many bonds. For this reason the most conspicuous changes of thermoset materials on exposure to weather are on the surface and are of the third type discussed above. From the viewpoint of physical structure all of the elements of deteriora- tion are covered in the above paragraphs. However, nothing has been said about the agencies which cause the chemical changes or the mechanisms by which they are brought about. These agencies and mechanisms become the most important objects of study. One type of change — the cross-linking of molecules — in certain cases can occur by self -reaction under the influence of heat or light in complete absence of other chemicals. Self-reaction is not, however, an important effect in materials which are in engineering use. The changes which lead to the loss of utility of polymers during aging are caused by chemical reaction with the environment. Usually this environment is the atmosphere. There are normally three substances in the atmosphere which under various circumstances may be considered reactive toward or- ganic compounds, namely water vapor, ozone, and oxygen. The next section^ will discuss the ways in which these chemicals bring about the destruction or organic polymers. Water The chemical reaction of water with organic compounds is limited to materials which contain hydrolyzable groups either as part of their original composition or as a result of oxidation. Examples of such groups are esters, amides, nitriles, acetals, and certain types of ketones. The reaction is illus- trated with an amide Unkage, the unaffected portions of the molecule being represented by the letter P: N O I II P— CH2— H— C— CH2— P + H2O -^ O II P— CH2— NH2 + HOC— CH2— P When these vulnerable groups are present as substituents on a polymer chain composed exclusively of carbon-to-carbon bonds their hydrolysis DETERIORATION OF ORGANIC POLYMERS 1085 may affect certain properties of the material (dielectric constant, power factor, insulation resistance, water absorption) but in general the molecular weight of the polymer is unaffected. When the vulnerable group is a link in the skeletal chain, however, the result of hydrolysis is much more serious because it constitutes scission of the primary chain and hence a lowering of molecular weight. Polymers which are subject to this kind of scission are polyesters, polyamides, cellulose and cellulose derivatives (ethers and esters). Hydrolysis is accelerated by high temperature and is catalyzed by acids and alkahes, and hence many polymers of the classes listed are stable only when kept neutral. Polyesters in particular are usually easily hydrolyzed and it is this fact w^hich has been the main barrier to their greater commercial utilization. Hydrolysis as such is a well known reaction and is taken into account in current engineering with materials which are subject to it. For example, nylon molding powder is shipped dry in sealed containers to keep the moisture content low until after the molding operation which requires that the nylon be heated to a high temperature,* and cellulose esters undergo repeated careful neutralizations and washes after esterification to reduce acidity.^ The extent to which water plays a role in the deterioration of hydro- carbon materials which are first attacked by oxidation is not yet known, but it is certainly secondary to the oxidation itself. An important effect of rain in outdoor weathering is the washing awaiy of water soluble oxidation prod- ucts with consequent exposure of new surface. Another effect is the removal of water soluble compounding ingredients. This may be distinctly beneficial as in the case of polyester rubbers vulcanized by acid-producing catalysts,^" or harmful as in certain polyvinyl chloride formulations which contain water soluble protective agents. Ozone Ozone is an extremely reactive chemical which is present in the air in extremely small amounts, ranging from 0 to 10 parts per hundred million. In this low concentration it has not been shown to have any effect on chem- ically saturated materials, but it is a very serious hazard for unsaturated compounds. Natural rubber and several synthetic rubbers fall in this class (Fig. 8). Ozone is a specific reagent for carbon-to-carbon double bonds, forming an ozonide which undergoes rearrangement resulting in chain scis- sion.^^ When rubber is not being stretched the attack of ozone appears to be negligible, but when it is under stress the attack has very serious conse- quences resulting in transverse cuts which may sever the piece of rubber.^^ • '' Apparently the initial attack, starting in regions of highest local stress, cuts enough chains to cause a crack to open, and this exposes new surface and concentrates the stress so that the crack grows. 1086 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 The practical significance of the reaction of ozone on rubber is very great since ahnost all rubber articles which undergo any appreciable stretching in service are in some degree subject to attack. Exceptions are articles com- posed of certain specialty rubbers such as silicones, Hypalon*, and some Thiokols. These are saturated materials and hence are not attacked. Neo- prene and Butyl rubber are more resistant than natural rubber or GR-S, Butyl because it is only slightly unsaturated, and neoprene because its double bond is considerably deactivated by the adjacent chlorine atom.^* CI H — C=C— Fig. 8— Samples of various rubber compounds after exposure to ozone. (1) Silicone; (2) Hypalon; (3) Buna-N; (4) natural rubber; (5) & (6) Neoprene; (7) GR-S; (8) Butyl. Large additions of pigments or plasticizers lower the ozone resistance of neoprene. The measure which has been found most effective for protecting rubber compounds from ozone is the inclusion of several percent of wax. The amount required varies with the type of wax, the polymer, and the other compounding ingredients, the absorptive power of any pigments present being an important factor. By proper compounding neoprene can be made extremely resistant to the attack of ozone, and the other unsaturated rubbers can be greatly improved. The chief effect of temperature changes on the cracking of rubber by ozone is in changing the solubility of wax in the rubber. At elevated temperature the wax fibn may redissolve and leave the rubber unprotected. This is illustrated in Fig. 9 which shows a tape wrapping which has been attacked on the sunny side, not by the light, but by ozone enabled to reach the rubber because the sun's heat had redissolved the wax in it. * A chlorinated, sulphonated polyethylene manufactured by the Du Pont Company. DETERIORATION OF ORGANIC POLYMERS 1087 Oxygen The degradative agent of most general attack and of greatest economic importance is oxygen, which is capable sooner or later of bringing about change in almost any organic material. Even disregarding the oxidation of dead organic matter in nature, which is aided by bacteria and fungi, one finds many examples of oxidation familiar to the layman. The development of rancidity in foods is a common one. The production of sludge-forming acids in engine oils, and the spontaneous combustion of rags soaked with hnseed oil are others. The loss of strength of cotton cloth after a few years of service is very largely due to oxidation although mildew or other fungus attack may have played a part depending on circumstances.^^- ^^' ^^ That changes lig. 9 — A Ldpc-wiappcu splice after 6-weeks of exposure outdoors. An example of the acceleration of the ozone reaction by heat. in polymers are indeed the result of oxidation is easily demonstrated in the laboratory by exposing samples to heat or to ultraviolet light in the presence and in the absence of oxygen The results of such an experiment are shown in Table I, in which solution viscosity is used as a measure of molecular weight. It is seen that in nitrogen neither heat nor light brought about any serious loss of molecular weight. Similar work has been reported with natural rubber with the conclusion that in an inert atmosphere rubber would retain its original properties "for at least thirty years". ^^ Gross Effects of Oxidation of Polymers Severe oxidation of organic polymers results in the drastic changes men- tioned in the introduction and is easily detected. Photo-oxidation of poly- 1088 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 ethylene/^ nylon and cellulose esters,^** for example, causes crazing, cracking, embrittlement, and in extreme cases granulation of the sample. (Fig. 10) In polyvinyl chloride it leads to hardening and discoloration.^^ In natural rubber, GR-S, and neoprene it causes the development of "mud-crack" pat- terns or "alligatoring" of the surface and loss of elongation. Thermal oxida- tion leads to embrittlement of thermoplastics, to "shortening" or loss of elongation in neoprene,^^- ^^ nitrile rubbers, and GR-S, and to reversion or the development of tackiness in Butyl rubber and sometimes in natural rubber. As pointed out earher, these varying effects result from the relative rates of cross-linking and chain-scission reactions. The mechanisms by which oxygen can attack polymers are discussed in the next paragraphs. Table I Solution Viscosity or Cellulose Acetate Butyrate Original 1.77 After 4 Weeks Exposure to UV Light at Room Temperature In Nitropjen 1.60 In Oxygen ... ... .15 After 150 hrs. at 150°C In Nitrogen * 1.78 .52 In Oxygen . . Mechanism of Oxidation Leading to Chain Scission The reaction of organic compounds with atmospheric oxygen, frequently called "auto-oxidation" or "autoxidation", has been of interest to chemists for a long time and a voluminous literature on the subject has accumu- lated.^-^^' ^® While most of the work done hks been on small molecules rather than on polymers it is becoming apparent that much of the mecha- nism of oxidation is the same and what has been learned on small molecules can be applied to large.^^- ^^' ^^ This is fortunate since polymers do not lend themselves readily to normal chemical manipulations. While it might be expected that different compounds would be attacked by oxygen in different ways a general mechanism has emerged which appears to be characteristic for aliphatic hydrocarbon structures and is probably applicable to many of the polymeric materials in current engineering use. It can be described as an autocatalytic free radical chain reaction.^" • ^^ • '^ The sequence of events is believed to be as follows: Free radicals are produced in the substrate from the energy of heat or of light. They may arise from the decomposition of unstable groupings such as the — O — O — DETERIORATION OF ORGANIC POLYMERS 1089 bond in peroxides or by the dissociation of a relatively more stable bond such as — C — C — or — C— H. Needless to say, the ease with which such cracking occurs is influenced by chemical structure. These free radicals, which may be produced in very minute amount, react with oxygen to form Fig. 10— (1) Cellulose acetate exposed six months at Murray Hill, N, J. (2) Nylon test panels exposed 5 months at Yuma, Arizona. (3) Clear Polyethylene sheet exposed 3 years at Murray Hill, N. J. (4) Clear polyethylene coated wire exposed 3 years at Murray Hill, N. J. peroxidic radicals. This is illustrated by the following chemical equation in which the radical is represented by the letter R and the fact that it is "free" or reactive is indicated by the dot. R- + O, R— O— O 1090 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 The peroxidic radicals are also reactive entities, but their afl&nity is for hydrogen atoms and they tend to abstract hydrogen from some other molecule of substrate, thus: ROO- + RH -> ROOH + R- (These equations were written by Backstrom for the oxidation of benzalde- hyde'° and have been adopted by many others.)^^- ^' ^^ The latter reaction results from molecular collision with formation of intermediate additive complexes which decompose into the indicated products and in general many ineffective colHsions will occur before reaction takes place. The molecule of substrate which loses hydrogen in this way is now a free radical and it repeats the process, reacting first with oxygen and then with another molecule of substrate. This linear chain reaction continues until two radicals unite by coUision with each other, thus terminating two chains. The word hnear is itaUcized in the previous sentence to emphasize that this part of the reaction is not in itself autocatalytic. The autocatalytic nature of the oxidation stems from the fact that the product of the reaction as outlined is a hydroperoxide, ROOH. Such compounds are relatively unstable and slowly decompose into free radicals which -initiate new chains. This might go as follows: ROOH -^ RO- + OH RO- + RH -^ ROH + R- and OH + RH ^ HOH + R- Thus, though the original rate of generation of free radicals from cracking might have been very low, the combined rate increases quite rapidly since each molecule of peroxide produced in the chain reaction becomes a po- tential source of new radicals. Eventually the rate reaches what appears to be a steady state and finally levels off. A typical oxygen absorption curve for a liquid hydrocarbon is shown in Fig. 11. The region of fast reaction has received attention from those interested in the oxidation of small molecules but it is unimportant to people interested in polymers because it has been shown by various workers that only shght oxidation is required to destroy the useful properties of a polymer.^^ By the time oxidation has proceeded far enough to be getting into a rapid rate it has already resulted in enough chain scissions to have lowered the molecular weight below useful levels. (A simple calculation will illustrate this point. Suppose a polymer molecule whose molecular weight is 32,000 reacts with one molecule of oxygen (mol. wt. 32) and a chain scission results. The molecular weight of the polymer molecule will have been halved by reaction with .1% of its weight of oxygen. Not every reaction with oxygen results in chain scission of course;^ but, even so, the amount of oxygen required to ruin the polymer is very small.) DETERIORATION OF ORGANIC POLYMERS 1091 The principal effect of the reactions described above is to introduce the hydroperoxide group into the polymer at various points. It is in the decom- position of these peroxides that chain scission occurs. Studies of the decom- position of the tertiary peroxides produced by oxidation of various dialkyl OCTAOECANE IN OXYGEN AT I05°C (2.4 g SAMPLE) 130 20 40 60 80 100 120 TIME IN HOURS Fig. 11— Octadecane in oxygen at 105° C. (2.4 g sample) 140 phenyl methanes have shown that the product is invariably an alkyl phenyl ketone in which the alkyl group is the shorter of the two originally present.'^ CHs Thus: <^^J>— C— C2H, OOH 5 goes to + -OH 1092 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 the C — C bond attaching the ethyl group having been broken. The decom- position of tertiary butyl hydroperoxide has been shown similarly to proceed by the following reactions:^®- ^^ CH3 CH3 I I CH3— C— OOH -^ CH3— C— O- + OH -> I I CH3 CH3 CH3 I C=0 + CH3- + -OH I "• CH3 Here again a carbon-to-carbon bond has been broken. The impHcation of this work for a substituted polyethylene, for example, is quite clear. If oxidation occurred at a tertiary hydrogen as it most probably would,^^' ^^" ^^ the decomposition of the resulting tertiary peroxide would be as follows (the unaffected portions of the polyethylene chain being represented by the letter P): CH3 CH3 I I P— CH2— C— CH2— P -> P— CH2— C— CH2— P -^ ! I OOH O + OH P— CH2— C— CH3 + •CH2— P + OH II o Thus the polyethylene chain would be cut. The course of events is less clear for secondary peroxides. Here at least two paths are possible: P— CH2— C— CH2— P H / 0 + H2O P~CH2— C— CH2— P 1 \ H OOH \ 1 P—CH2— C + .CH2— P + •OH O If the decomposition proceeds according to the top arrow, no chain scission results, whereas if it takes the lower course the polymer is divided. The alde- hyde is subsequently oxidized to acid. The fact that short fatty acids are produced in the oxidation of straight chain hydrocarbons such as octadecane DETERIORATION OF ORGANIC POLYMERS 1093 is proof that secondary peroxides or peroxidic radicals can decompose by the chain spHtting process. That they do not decompose exclusively by that mechanism is shown by the high yield of tetralone obtained from the de- composition of tetralin hydroperoxide. The mechanisms outhned, while certainly not complete, are adequate to account for the chain scission type of oxidative deterioration of many plastics and rubbers. The degradation of chlorine bearing plastics such as polyvinyl chloride and polyvinylidene chloride, while also being caused by oxygen and being energized by light and heat, is not believed to follow the patterns out- Table II Field Results on Samples of Naturally Aged Neoprene Jacketing (From Drop Wire)* Origmal Months Exposure at Tensile Strength psi 2218 Elongation, % 330 Chester, N. J. 15 31 57 2635 2655 2510 215 225 205 Stone Harbor, N. J 21 64 78 1990 2485 2615 190 185 175 Miami, Fla. 14 48 60 74 87 109 2540 2215 2260 2410 2450 2520 195 140 125 150 130 120 San Antonio, Tex. 11 22 34 45 2395 2300 2585 2165 160 145 180 135 Brawley, Cal. 15 58 1980 2405 165 165 * From a paper by G. N. Vacca, R. H. Erickson and C. V. Lundberg^**) lined above. The first step here is reported^^ •'*^ "^ to be the elimination of hydrogen chloride with introduction of a double bond, which makes the loss of more HCl easier and also increases the oxidizability. Cross-Linking Resulting from Oxidation The second important effect of oxidation of polymers is cross-Unking. This is of great consequence only with unsaturated compounds and these are principally the rubbers. If cross-linking is the dominant reaction (as it usually is on neoprene, GR-S, and the nitrile rubbers) the result is a decrease in elongation and an increase in hardness without a loss in tensile strength. 1094 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 The strength may actually increase as shown in Table II. The rubber tends to "shorten" and ultimately ceases to be rubbery. Carried to an extreme condition, oxidized rubbers can resemble hard rubber or the phenolic resins. The detailed mechanisms of cross-linking are not worked out but certain deductions can be made about the reaction. That it is not just a polymeriza- tion of the double bonds can be shown by the fact that its rate in the absence of oxygen is extremely slow. That it is probably induced by free radicals can be inferred from the work on "vulcanization" of unsaturated polyesters with peroxides in which it was evident that a free radical attacking a double bond initiated the cross-linking reaction.^^- ^ The sequence might be as follows:^ H H P— CH2— C CH2— P -^ P— CH2— C— CH2— P OOH O • + OH H P— CH2— C— CH2— P + P— CH2— C=C— CH2— P -> 0 H H H P— CH2— C— CH2— P I O I H P— CH2— C— C— CH2— P H • Thus a link has been introduced. The new radical can react with another radical, it can react with oxygen to form another peroxide group, it caii react with a double bond in another chain to form an additional cross-link, or when antioxidant is present it can react with antioxidant. The hydroxy radical resulting in the original decomposition of the peroxide could initiate a similar series of reactions resulting in one or more cross-links as follows: •OH + P— CH2— C=C— CH2— P -^ H H H H OH OH P— CH2— C— C— CH2— P P— CH2— C— C— CH2— P + H • H . H O H P— CH2— C=C— CH2— P -> P— CH2— C— C— CH2— P H H H H P— CH2— C— C— CH2— P H . DETERIORATION OF ORGANIC POLYMERS 1095 The factor that determines whether or not cross-hnking will be dominant in the aging of an unsaturated material must be the chemical structure of the polymer (and its peroxide.) The mode of decomposition of the peroxide which, of course, is a function of structure probably has the most important effect. While cross-Hnking can occur in saturated materials, as shown by the vulcanization of saturated polyester rubbers with peroxides, its rate is never high enough to result in a condition that could be called deterioration. Both polyethylene and cellulose acetate butyrate can undergo enough gelation on outdoor exposure to become insoluble, but if this were the only change occurring their toughness would be improved rather than degraded by it. Their deterioration in strength is due entirely to chain scission. Modification of Side Groups by Oxidation All the oxidation reactions discussed result in the introduction of oxygen into the polymer composition. If the polymer is one which already contains a high percentage of oxygen such as cellulose or even nylon, this may have little effect. If the polymer is a hydrocarbon, however, its power factor will be raised markedly. As a matter of fact the measurement of power factor is a very sensitive way of detecting the addition of oxygen to polyethylene. Ex- cept where the polymer is being used for its low power factor, however, the change in side groups will be secondary to the change resulting from chain scission and cross-linking. Acceleration of Oxidation The foregoing description of the mechanisms of auto-oxidation makes apparent several ways in which oxidation may be accelerated beyond what might be called the natural rate for a pure material. Since oxidation is a free radical process an obvious way to accelerate it is to add free radicals or materials which produce free radicals. Addition of peroxides to organic compounds generally accelerates the rate of oxidation.^^ Similarly the oxidation of a relatively stable material is accelerated if there is left in it a small amount of a chemical which itself is easily oxidized to peroxides. For example, an addition of turpentine greatly accelerates the air-oxidation of paraffin wax.^ The addition to polyethylene of an unsaturated polymer such as natural rubber would probably have a similar effect. It is apparent that the amount by which the rate of oxidation of a sub- strate is accelerated by peroxides, whether the latter are added as such or are self -generated, is dependent on the rate of decomposition of the peroxide. The latter rate can be accelerated by the presence of certain metallic ions and hence they act as catalysts for oxidation reactions. Copper is particu- larly active in this regard in natural rubber, and the rubber industry long ago learned to avoid it^^ (Fig. 12). Other metals which have been found to 1096 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Fig. 12 — Various samples oi natural rubiK-r oven aged on tin,* above; and on copper, below. DETERIORATION OF ORGANIC POLYMERS 1097 cause poor aging at various times are cobalt, manganese, and iron.^^ Since the "drying" of paint is an oxidative reaction, and since rapid drying is a desirable feature, the paint industry has found it advantageous, to use certain metaUic salts as ''paint dryers".''^ Retardation of Oxidation Antioxidants It was discovered by Moureu and Dufraisse about IQIS''^ that the oxida- tion of many organic compounds could be very greatly retarded by the addition of small quantities of certain other chemicals, which they called "antioxygens." Although the mechanisms which they postulated for the action of these materials were later found to be incorrect, their discovery led to the wide use of such protective agents in industry, particularly in rubber which needs this protection badly. The action of what are now called "antioxidants" becomes clear when one understands the free radical chain mechanism of oxidation outhned above. Antioxidants are chain stoppers.'* By interposing themselves in the chain reaction they terminate it by giving rise to relatively inert free radicals^"- ^^ (stabiUzed by resonance). For ex- ample, the antioxidant, designated HA, could act in the following way: ROO- + HA — ROOH + A In this case the antioxidant satisfies the peroxidic radical by giving it the hydrogen atom it needs, but the residual radical • A is not sufficiently reactive toward oxygen to continue the chain. A typical antioxidant is |8-phenyl naphthylamine. It was pointed out earlier that many ineffective collisions of the radical ROO- with substrate molecules occur before reaction takes place. If the reactivity of ROO- toward HA is sufficient that few ineffective collisions take place, then small concentrations of HA in the substrate will be ade- quate to stop each chain at a very early stage. This not only saves all those substrate molecules which would otherwise have become links in these chains but, by so doing, it limits the number of molecules of peroxide pro- duced and thus keeps the rate of initiation of new chains at a low level. The degree of protection by antioxidants varies with the length of the "natural" chain reaction (which is a function of the ratio of effective to 1098 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 ineffective collisions in the absence of an inhibitor and depends on chemical structure) and on the efficiency of the antioxidant but, in some cases, par- ticularly with Hquids, very remarkable protection is obtainable as shown in Fig. 13. (The oxidation of the control sample is so fast at this high tempera- ture that the autocatalytic period is not evident.) The effect is less in solids but is still of great value. Antioxidants are of the greatest benefit where the rate of initiation is low, a condition usually true of thermal oxidation. The POLYETHYLENE IN OXYGEN AT 150 °C I g SAMPLES IN BOATS 5/ 8" X 4" 1JO ! /unprotected f o -90 UJ r < 70 Z 1 f 0.05% /antioxidant 0.20 °/o antioxidant i t • / X o / o UJ 2 40 §30 20 10 1 / / / / J / / _/ y ^ ) 2 0 4 0 e T 0 IME 1 8 n ho 0 URS l( )0 1 20 U Fig. 13-Polethylene in oxygen at 150° C, 1 g samples in boats f X V. reason is that since antioxidant is consumed^^- ^ in doing its job the rather limited amounts which can be added from a practical point of view (usually not over 1 or 2%) do not last long if the rate of chain formation is very high. This explains the oft stated fact that an antioxidant is far more effective if added before oxidation starts, than if added after oxidation has proceeded for a while." In the latter case enough peroxide will have been produced to overwhelm the antioxidant relatively quickly. This is also the explanation of DETERIORATION OF ORGANIC POLYMERS 1099 the fact that antioxidants are limited in their effectiveness against photo- oxidation. The rate of initiation of chains in a material exposed to sunlight is so great that any antioxidant present is used up relatively fast. Further- more, the oxidation of the antioxidant itself is rapid in sunhght and hence if it were not removed in the one way it would be in the other. There are many chemicals in current use as antioxidants and more are being created all the time. Most of them are either phenols or aromatic amines. It is frequently asked why one antioxidant is more effective than another, if indeed such differences do exist. The answer is not altogether clear but certain statements can be made about it. In the first place, for any given substrate there are usually several antioxidants which are equally good. However, gradations of effectiveness of many commercial antioxidants can be demonstrated. Many factors can exert an influence on this. Some are solubiHty in the substrate, volatihty, inertness toward the substrate. Beyond these are the reactivity of the antioxidant toward free radicals, both hydrocarbon and peroxidic, and the relative stability of the free radical left when the antioxidant reacts. Undoubtedly, some intermediate level of reactivity is desirable in an antioxidant^^ • ^^ and this desired level probably varies from one substrate to another. Light Screens It was mentioned above that antioxidants are of Httle effect against rela- tively strong photooxidation because of the overwhelming rate of generation of chains. The most serious problems of deterioration in the Bell System are, of course, in outdoor applications, and it is quite clear that this is be- cause of exposure to short wave light. The extensive commerical use of unprotected material outdoors came about because of a lack of appreciation of this fact. Once this vulnerability or organic materials to Hght is appreci- ated the remedy is obvious, at least in principle, and that is to shut off the light. For this purpose there are many pigments available as well as many light-absorbing organic compounds. A great deal of work' has been done with various substrates in testing the effects of the absorbers, and this can be summarized as follows: In the class of light colored pigments, none offers complete protection. Most of them have a sHght effect; a few are fairly helpful; and a few are actually harmful, acting as photosensitizers. Of the darker pigments several are quite effective but the outstanding ones are lead chromates, iron oxides and carbon black, the last being the best. A study of the effect of various types of carbon black in various concentrations in polyethylene has been reported^^ wherein it is shown that under the most favorable conditions the useful life of polyethylene, as judged by accelerated tests, can be extended 1100 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 at least 30 fold. It was shown in this work that for best results the carbon black should be finely divided and well dispersed. The use of polyethylene as a sheath material on outdoor cable would not have been practical without the protective effect of carbon black. The efficacy of carbon black as a light screen is apparently quite general although detailed studies have been made only with polyethylene, rubber,^^ cellulose esters,^^ and polyvinyl chloride, ^^ in all of which it is effective. Fig. 14— Cellulose Ace late Butyrate panels exposed to concentrated beams of UV light filtered through pyrex bottles filled with water. Sample at left contains 1% carbon black. Sample at right contains 1% Salol. In many applications of plastics and rubbers, colors are desirable and for these the use of carbon black is, of course, precluded. Some success has resulted from the use of organic materials which are transparent to visible light but which absorb in the ultraviolet. For example, phenyl salicylate, known as Salol, at a concentration of 1% is a fairly effective protective agent for transparent cellulose esters.^" Such effects appear to be quite specific, since Salol is not nearly so effective in most other polymers (it is reported to be effective in Saran^*), and many other compounds which are even better DETERIORATION OF ORGANIC POLYMERS 1101 absorbers of ultraviolet light are much less effective in cellulose esters. Some of them actually are sensitizers. Even in cellulose esters Salol at a concentra- tion of 1% is a poor second to carbon black, giving in accelerated tests less than half the life imparted by 1% of a well dispersed, finely divided carbon black.^7 (Fig 14) References 1. G. T. Kohman, /. Phys. Chem. 33, 226 (1929). 2. R. Burns, A. S. T. M. Bulletin #134, pg. 27 (May 1950). 3. T. Alfrey, "Mechanical Behavior of High Polymers," pp. 464-465, Intersciencc Publishers, (1948). 4. P. J. Flory, Chem. Reviews, 35, 51 (1944). 5. L. H. Campbell, A. H. Falk, R. Bums, Proc. A.S.T. M. 46, 1465 (1946). 6. R. B. Mesrobian and A. V. Tobolsky, //, Polymer Science, 2, 463 (1947). 7. C. C. Davis and J. T. Blake, "Chemistry & Technology of Rubber," pp. 538, Rein- hold Publishing Co., N. Y. (1937). 8. Du Pont Technical Service Bulletin No. SB, March 1950. 9. C. J. Malm and C. L. Crane, U. S. Patent #2,346,498. 10. B. S. Biggs, R. H. Erickson and C. S. Fuller, Ind. and Eng. Chem., 39, 1096 (1947). 11. J. Crabtree and A. R. Kemp, Ind. and Eng. Chem. 38, 278 (1946). 12. A. Rieche, R. Meister, H. Santhoff, H. Pfeiffer, Liehig's Ann. Chem., 553, 187 (1942). 13. R. G. Newton, //. of Rubber Research, 14, 27 (1945). 14. C. R. Noller, J. F. Carson, H. Martin, K. S. Hawkins, //. Am. Chem. Sac. 58, 24 (1936). 15. J. D. Dean et al. Am. Dyestuf Reporter 36, 705 (1947). 16. J. D. Dean and R. K. Worner, Am. Dyestuf Reporter 36, 405 (1947). 17. G. S. Egerton, Am. Dyestuf Reporter 36, 561 (1947). 18. Admiralty Engineering Lab., Journal of Rubber Research 15, 737 (1946). 19. V. T. Wallder, W. J. Clarke, J. B. DeCoste and J. B. Howard, Ind. and Eng. Chem. 42, 2320 (1950). 20. L. W. A. Meyer and W. M. Gearhart, Ind. and Eng. Chem. 37, 232 (1945). 21. V. W. Fox, J. G. Hendricks, H. F. Ratti, Ind. and Eng. Chem. 41, 1774 (1949). 22. G. N. Vacca, R. H. Erickson, and C. V. Lundberg, Ind. and Eng. Chem. 43, 443 (1951). 23. D. C. Thompson and N. L. Cotton, Ind. and Eng. Chem. 42, 892 (1950). 24. Symposium on Oxidation, Trans. Faraday Soc. 42 (1946). 25. K. C. Bailey, Retardation of Chemical Reactions, Longmans, N. Y. (1937). 26. H. H. Zuidema, Chem. Reviews 38, 197 (1946). 27. L. Bateman, Trans, of Inst, of Rubber Ind. 26, 246 (1950). 28. A. V. Tobolsky, India Rubber World 118, 363 (1948). 29. J. L. Bolland and P. TenHave, Trans Faraday Soc. 45, 93 (1949). 30. H. L. J. Backstrom, Zeit.fur Physichalische Chem. B25, 99 (1934). 31. L. Bateman and G. Gee, Proc. Royal Soc. 195, 376 (1949). 32. E. H. Farmer, G. F. Bloomfield, A. Sundralingham, and D. A. Sutton, Trans. Faraday Soc. 38, 348 (1942). iZ. J. L. Boland, Proc. Royal Soc. 186, 218 (1946). 34. R. Houwink, Kautschuk 17, 67 (1941). 35. H. N. Stephens, //. Am. Chem. Soc. 50, 2523 (1928); 57, 2380 (1935). 36. J. H. Raley, F. F. Rust and W. E. Vaughn, //. Am. Chem. Soc. 70, 1336 (1948). 37. N. A. Milas and D. M. Surgenor, J I. Am. Chem. Soc. 68, 205 (1946). 38. H. S. Taylor and J. O. Smith, //. CJtem. Physics 8, 543 (1940). 39. A. D. Walsh, Trans. Faraday Soc. 42, 269 (1946). 40. P. George and A. D. Walsh, Trans. Faraday Soc. 42, 272 (1946). 41. R. F. Boyer, //. Phys. and Colloid Chem. 51, 80 (1947). 42. P. I. Pavlovich, Legkaya Prom. (1945). 23 C.A. 40, 7699 (1946). 43. W. O. Baker, //. Am. Chem. Soc. 69, 1125 (1947). 44. F. E. Francis, //. Chem. Soc. 121, 502 (1922). 45. C. O. Weber, "The Chemistry of India Rubber," pp. 220 and 299, Charles Griffin and Co., London, 1902. 1102 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 46. A. Van Rosse and P. Dekker, Ind. and Eng. Chem. 18, 1152 (1926). 47. Proc. of the Scientific Sec. Nat. Paint, Varnish and Lacquer Assoc, Circ. 546, pp. 307 (1938). 48. C. Moureu and C. Dufraisse, Chem. Reviews 3, 113 and ref. cited therein (1926). 49. J. A. Christianson, //. Phys. Chem. 28, 145 (1924). 50. J. L. Bolland and P. TenHave, Trans. Faraday Soc. 43, 201 (1947). 51. H. S. Taylor, A.S.T. M. Proc. 32 Part II, 9 (1932). 52. H. N. Alyea and H. L. J. Backstrom, //. Am. Chem. Soc. 51, 90 (1929). 53. A. M. Wagner and J. C. Brier, Ind. and Eng. Chem. 23, 46 (1931). 54. L. F. Fieser, //. Am. Chem. Soc. 52, 5204 (1930). 55. C. D. Lowry, C. G. Dryer, G. Eglofif, and J. C. Morrell, Ind. and Eng. Chem. 24 1375 (1932). 56. W. N. Lister, Trans. Inst, of Rubber Ind. 8, 241 (1932). 57. R. H. Erickson, unpublished work. 58. V. T. Wallder and J. B. DeCoste, unpublished work. 59. R. F. Boyer, U. S. Patent 2,429,155. , The Development of Electron Tubes for a New Coaxial Transmission System By G. T. FORD and E. J. WALSH (Manuscript Received July 27, 1951) 1. Introduction As THE demand for long distance telephone circuits has increased, -^ ^ new transmission systems capable of handling more channels per con- ductor have been developed. Also the advent of television has created a demand for broad band channels for network facilities. One of the latest developments now nearing completion is the L3 Coaxial System. Three new tubes have been developed specifically to meet the exacting requirements of this system: two tetrodes, the W.E. 435 A and W.E. 436A, and a triode, the W.E. 437A. All three types are used in the line and office amplifiers. The new tubes make possible a substantially higher level of broad band amplifier performance compared to their predecessors. They represent the result of improvements made by applying well known basic principles through new tube-making techniques. These techniques have been developed largely within the framework of existing conventional tel- ephone tube manufacturing methods. The development of special, small, low power vacuum tubes for high fre- quency application in the Bell System began in 1934. The tube program was instituted originally as part of a research project in the field of radio communications. When the development of the LI Coaxial System began it was recognized that similar tubes would be needed. Part of the tube development effort was therefore directed toward the coaxial requirements. Work on the W.E. 384A and W.E. 386A tubes used in the LI system was completed in 1939 as an outgrowth of this program. The demand for amplification over wider frequency bands resulted in further development work along the same lines. During World War II this effort was applied to the development of the 6AK5 tube which became available early in 1943 and was used widely in IF amplifiers in radar equip- ment. Shortly after the war the W.E. 408A tube was developed for tele- phone repeater uses. This is a long life version of the 6AK5 tube having the same electrical characteristics except for the heater voltage and current. The W.E. 404A tube appeared in telephone circuits in 1949. This tube, having a higher figure of merit than the W.E. 408A, provided improved performance in the IF amplifiers used in the New York to Boston radio 1103 1104 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 relay system and in the TD2 radio relay system. The W.E. 435A, W.E. 436A and W.E. 437A tubes are the latest types to come out of this long range program. It will be seen in what follows that the key to continued development along these lines has been improvements in the techniques of grid making to meet the basic objective of providing a grid which can be spaced very close to the cathode and which, in effect, acts as a uniform potential plane controlling the current drawn from the cathode without offering any physi- cal obstruction. This objective is approached by using many turns of very small diameter wire for the grid winding. The reason for the close grid- cathode spacing is that the transconductance or sensitivity depends on this factor. Although the increase in input capacitance which results is a dis- advantage because of its effects on the interstage circuits, this disadvantage is more than compensated for by the higher transconductance obtained. 2. Principles of Design 2.1 Requirements The overall requirements for the L3 system, and the manner in which they are related to the tube parameters, are very complex. However, in its simplest terms, the objective for the L3 system is to provide on one coaxial p'pe a facility suitable for the simultaneous transmission over a 40(X)-mile circuit of a television signal and 600 one-way telephone channels or, alternatively, 1800 one-way telephone channels when no television channel is required. The transmission band being provided is from approxi- mately 0.3 MC to approximately 8 MC. The amplifier needed to compen- sate for the cable attenuation must meet very exacting requirements with respect to gain-frequency characteristics, stability, noise, and linearity. The design features necessary to provide suitable electron tubes for use in the L3 amplifiers are closely related to the requirements mentioned above for the amplifiers. In general terms, the tube design objectives are: (1) high transconductance-capacitance ratio (figure of merit), (2) minimum excess phase shift or phase delay, (3) low noise, (4) well controlled modu- lation, (5) long life, (6) interchangeability, and (7) lowest cost consistent with the first six objectives. In the material which follows, each of these objectives will be discussed in detail and its relationship to the system objectives brought out. 2.2 Figure of Merit Figure of merit is of particular importance. It is a direct measure of the bandwidth over which the required amplification can be obtained. In gen- ELECTRON TUBES FOR A COAXIAL SYSTEM 1105 eral, a given factor of improvement in the figure of merit can be translated directly into a wider transmission band providing more communication channels. For a two-terminal type of interstage such as that used in the L3 ampli- fier, the figure of merit is F = GB = KGm (1) 2t(C, + C2) where F is the figure of merit, G is the voltage amplification, B is the band- width between the frequencies where the gain is 3 db below that at the center frequency, K is a, constant whose value depends on the particular interstage design, Gm is the transconductance of the tube, Ci is the input Q-*\ Tir ^1 ^. b — 2r T CONTROL GRID 1 SCREEN I GRID -CATHODE COATING Fig. 1 — Geometry of the 436A tube. capacitance, and C2 is the output capacitance. This figure of merit is di- rectly applicable to a tetrode operated as a small-signal voltage amplifier and is a well known relationship.^ It will be used to show how the tube design factors influence the figure of merit of the W.E. 435A and W.E. 436A tubes. Using equation (1) and applying certain simplifying assumptions which can be made without materially affecting the results, expressions are de- rived in the appendix showing the relationship between the figure of merit and the tube parameters. Equations (2) and (4) in the appendix show how the figure of merit is affected by the grid-cathode spacing "a", the grid- screen spacing "b", the screen-plate spacing "c", and the grid wire radius "r". See Fig. 1. Equation 3 gives the required screen voltage for the as- ^ "Characteristics of Vacuum Tubes for Radar Intermediate Frequency Amplifiers," G. T. Ford, B.S.TJ., Vol. XXV, p. 389, July, 1946. 1106 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 sumed current density and geometry. Since these expressions are rather involved, the manner in which the various factors influence the figure of merit can be brought out best by a series of curves. Figures 2,3, and 4 show how F is affected by changes in "a", "6", and "c". Figures 6 and 7 show how the screen voltage required to get the assumed current density with a given bias Ed varies with "a" and "6" (equation 3). The screen voltage is essentially independent of "c". These relationships are also applicable to the W.E. 437A tube with minor modifications. 2.21 Design Considerations How the various factors in equations (2), (3), and (4) affect the figure of merit will be discussed in detail. They are listed in Table I. The factor M is the ratio of the plate current to the cathode current. The figure of merit is directly proportional to this factor. M can be increased Table I Factor Design Values Practical Design Considerations M 0.75 Mechanical, plate-grid capacitance /o 50 MA/cm2 Stability of emission, life a 0.00635 cm Mechanical b 0.0444 cm Screen voltage, mechanical c 0.150 cm Formation of potential min. r 0.00038 cm Mechanical Ed -1.5 volts Grid current Ec2 150 volts Dissipation, life by using smaller wire in the screen grid, the minimum practical wire size being determined by the mechanical rigidity and heat dissipation capa- bility required. M can also be increased by reducing the number of turns on the screen, but this is limited by the necessity for sufficient shielding effect to meet the requirement that the plate-grid capacitance be less than a speci- fied value. Since the figure of merit is directly proportional to the cube root of the cathode current density /o , the improvement with increasing /o is not very rapid. The problems of obtaining uniform initial performance and long life are aggravated by increasing the current density, for several rea- sons. There is no direct evidence to show that high current density per se causes accelerated loss of available emission. In fact there is some evi- dence to the contrary.^ However, there is ample evidence that phenomena ' "Influence of Density of Emission on the Life of Oxide Cathodes," S. Wagener, Nature, p. 357, Aug. 27, 1949. ELECTRON TUBES FOR A COAXIAL SYSTEM 1107 usually associated with high current density tend to shorten the life. Higher electrode temperatures, higher potentials, and the production of more ions are the major items in this category. It is presumed that the shorter life found under these conditions is due to the greater rate of contamination of the cathode by material from the other parts of the tube. Great efforts have been made to find and to use processing techniques which will mini- mize this kind of limitation and to introduce constituents into the cathode which will counteract such deterioration. The situation at the time the L3 1200 1100 1000 900 800 700 600 500 ft 2 400 300 O 200 u. 100 1^ % Io= 0.05 AMP/CM2 M = 0.75 r = 0.000381 CM C = 0.150 CM Ec,= -1.5 VOLTS V K \ \^ V \ \ \^ 5^ \ \: ^^ F^:> 05)- X ^^ ^^^ $? /f "^^ 'Oo - 0.0/ e?"-"^ - 12 3 4 5 6 7 8 GRID-TO -CATHODE SPACING "a" IN CENTIMETERS Fig. 2 — Figure-of-merit vs. grid-to-cathode spacing. 9 10x10"^ tubes were being developed was that 50 MA/cm^ was as high a current density as seemed to be consistent with the long life required. It is apparent from the curves in Fig. 2 that the figure of merit increases rapidly as the grid-cathode spacing "a'' is reduced. The limitation here is mechanical and manifests itself in two ways. One is the practical difficulty of spacing the parts so closely with sufficient accuracy. The other is the problems associated with fabricating grids wound with wire of small enough diameter to make effective use of the close grid-cathode spacing. This part of the subject will be discussed in detail later. It is one of the most important aspects of the design of the L3 tubes. 1108 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 It would appear from Fig. 3 that the grid-screen spacing ''ft" should be as large as possible. However, the required screen voltage increases as "6" increases, and it is desirable to keep the screen voltage low. Therefore, "6" is made as low as possible without causing too much penalty on figure of merit. A good compromise value for "6" depends on the range of grid- cathode spacing ''o" being considered, but it will usually be from 0.005 cm to 0.020 cm for close spaced tubes. Figure 4 shows that the figure of merit increases as "c" increases, but there is very little advantage in making it more than 0.040-0.050 cm. Making it much larger also increases the outside dimensions of the struc- 1200 1 1 1100 oiooo — • p-" a= 0.00127 CM / ^ 0.00254 1 - — Seoo 2 """■" ^ 0.00381 / ^ ■ — — y y 1 0.00635 —ir~ ,^ ^ ■ ' ' ' 0.00889 ^400 °300 Hi O 200 100 0 — y y _,^-> - lo = 0.05 AMP/CM^ M = 0.75 r = 0.000381 CM C = 0.150 CM Ec, = -1.5 VOLTS / ^ / 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 SOxlO"^ GRID -TO- SCREEN SPACING ^'b' IN CENTIMETERS Fig. 3 — Figure-of-merit vs. grid-to-screen spacing. ture unnecessarily, and eventually leads to a spacing which will cause ir- regularities in the plate current-plate voltage characteristic due to space charge effects in the screen-plate space. Although it is not apparent from the curves or from what has been said above, it is desirable to have 'V" as small as possible. It is obvious that "r" must be less than — , otherwise the grid is completely closed. Under the assumption that na - \, this means that 'V" must be less than 0.5a if there is to be open space between the grid wires. Actually, it is desirable to have not more than 30% of the projected area of the grid closed, which ELECTRON TUBES FOR A COAXIAL SYSTEM 1109 means that 'V" should be less than 0.15a. In addition to this consideration, it is desirable to have "r" considerably less than 0.15a so that the required screen voltage will be as low as possible. This comes about because the amplification factor /x increases as 'V" is increased, other quantities held constant, and equation (3) shows that £^2 increases as n increases. The diagram shown in Fig. 5 illustrates the trend in grid-cathode spacings and grid wire sizes. The W.E. 416A tube (formerly BTL 1553) represents the 800 700 600 500 U < CD ?8 400 300 200 100 1 — - a = 0.00381 CM 1 1 0.00635 • — ■ ' 1 0.00889 — " ■ Io= 0.05 AMP/CM2 M = 0.75 r = 0.000381 CM b = 0.0444 CM Ec,= -1.5 VOLTS 20 40 60 80 100 120 140 160 180 200 220 240 260 xlO'^ SCREEN-TO-PLATE SPACING ''c" IN CENTIMETERS Fig. 4 — Figure-of-merit vs. screen-to-plate spacing. GRID wires' 1 0.001" Dl A. CATHODE COATING 0 0.0003" DIA. 0.0025" yO-OOOa^DIA. 386A, 6AK5 404A,435A, 436A, 437A Fig. 5 — Trend in spacing and grid wire size. 416A greatest extension of this trend reported as far as grid-cathode spacing is concerned.^ The figure of merit increases as the absolute value of the bias Ed is reduced, since Iq increases. However, a minimum bias value of about —1.5 volts is usually necessary in order to avoid undesirable effects due to the ' "Design Factors of the Bell Telephone Laboratories 1553 Triode," J. A. Morton and R. M. Ryder, B.S.T.J., Oct. 1950. 1110 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 collection of electrons of high initial velocity by the control grid. Such grid currents contribute to the noise, cause input loading, and may also cause excessive signal distortion. Since h increases as the screen voltage Ec2 is increased, the figure of merit likewise increases. It is desirable to keep £c2 as low as possible for at least three reasons. The most important is that high screen voltage will generally have an adverse effect on tube life. The second is that low power consump- tion is desirable for economic reasons and the third is that it helps from the standpoint of maintaining low temperatures of the components in an 260 240 220 200 180 "i.60 ^ 140 1 \ \ lo = 0.05 AMP/ CM 2 \ \ \ M = 0.75 r = 0.000381 CM C = 0.150 CM Ec,= -1.5 VOLTS v \ ' \ \ feo \ k \ 1 \ \ \ \ \ ^ \ \ s, \ ^^ ^ z '" Ui ^100 80 60 40 20 0 V \ V ^. \ \ \ V \ ^ •^ *^^ — \J V \ S^o V \ N° 4? ^~ ^ --- 1. h^ -- _ ^"^ ■" 2 3 4 5 6 7 GRID-TO-CATHODE SPACING "a" IN CENTIMETERS Fig. 6 — Screen voltage vs. grid-to-cathode spacing. 9X10"3 amplifier. Figures 6 and 7 show how Eci depends on "a" and requirement that £^2 be kept low means that the range of ''o' which can be used is restricted. 'V\ The "6" 2.3 Phase Shift The effects of electron transit time and lead inductance in the tubes must be taken into account in order to meet the amplifier requirements with respect to phase margin. In order to maintain stable operation over ELECTRON TUBES FOR A COAXIAL SYSTEM nil the desired transmission band, the gain and phase characteristics must be controlled up to about 200 MC. The amount of phase shift at the frequency where the gain becomes unity ("cross-over point") is of particular interest. In the L3 amplifier this frequency is about 40 MC. Phase shift introduced by electron transit time and by lead inductance is referred to as "excess phase." Ideally, of course, the excess phase would be zero. The time required for an electron to travel from the cathode to the plate is of the order of 10~^^ seconds. This corresponds to about 5° of excess phase at 40 MC. Close spacings and high electrode potentials tend to reduce the 260 240 220 200 180 M J heo r : 140 gioo if) 20 / f Io= 0.05 AMP/ CM 2 / / M = 0.75 r = 0.000381 CM C = 0.150 CM Ec,= -1.5 VOLTS / a = 0.00381 CM / ^^ ^ / / y ^ / ,X / / 0.00635 / ^ ^ ^ / f y / ^^^ ^ ^ J / ^ y 0.00889 / / ^ / ,y y ^ ^ 5 20 25 30 35 40 45 50 55 60 65 GRID-TO-SCREEN SPACING "b" IN CENTIMETERS Fig. 7 — Screen voltage vs. grid-to-screen spacing. 70 transit time. However, the considerations discussed in Section 2.2 have been the major factors in setting the spacings and potentials because the transit time, though important, is far less so than the figure of merit. By using relatively heavy lead wires and mounting the tube structure in such a way as to make the lead wires as short as possible, the additional excess phase due to the lead wires has been minimized so that it amounts to about 5° at 40 MC. In order to insure adequate margin against a singing condition, the amplifier has been designed to have about 20°-30° less phase shift at 40 MC 1112 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 with these tubes than that which will cause singing. With this situation, it can be seen that any substantial factor of increase in the excess phase introduced by the tubes, or any other components, could begin to reduce the phase margin seriously. 2.4 Noise Fluctuation noise is an important factor in the W.E. 435 A used in the first stage of the input amplifier and in the W.E. 436A used in the first stage of the output amplifier. There is adequate margin against the effect of low frequency noise components such as microphonics, power frequency hum, and "sputter noise" if reasonable precautions in tube and circuit design are taken. From a design standpoint, the fluctuation noise is min"mized by adopting a combination of cathode temperature and current density drawn such that, with a normally active cathode, the space current is substan- tially space charge limited, with ample margin for some loss of cathode activity in service before the temperature limited condition is approached. When the temperature limited region is reached, the noise is substantially higher than for the space charge limited condition. The temperature and the cathode current density ratings for these tubes have been set at values which take these considerations into account. 2.5 Modulation Since a major purpose of using feedback is to reduce the modulation products arising in the amplifiers, the more nearly an ideal linear transfer characteristic can be approached in the tube design the better, because less feedback is required to obtain a given grade of system performance. Unfortunately, however, a conventional triode or tetrode type of vacuum tube operating under normal space charge limited conditions necessarily has a transfer characteristic which is non-linear. Several possible special structures which might give less modulation were explored, but none were found which would provide the required figure of merit and be sufficiently stable and reproducible. Considerable emphasis was placed on the problem of controlling the variation in modulation from tube to tube. The most important factors are grid-cathode spacing, uniformity of grid pitch, and cathode activity. Al- though these factors must be well controlled for other reasons also, the special requirements on modulation necessitated a thorough investigation. The effect of the grid-cathode spacing can be expressed in terms of the d-c. plate current and the signal level. For a triode having an idealized dii three-halves-power transfer characteristic with ttt" = 0 as in Section 2.2, ELECTRON TUBES FOR A COAXIAL SYSTEM 1113 and for small signals, the ratio of the fundamental signal current to the second harmonic component for the case of a very small load impedance is 7^ = 12 — (see appendix for derivation) (11) i2p Ip This means that, for a given signal current amplitude Ip in the output, a tube having the assumed characteristics will give a ratio which depends only on the d-c. plate current, which in turn is very sensitive to changes in grid-cathode spacing. A study of the variations in grid pitch and their effects on modulation in a particular experiment showed that reducing the standard deviation of the pitch distance from 16% to about 7% reduced the second-order modulation by 4 db. Since the second-order modulation must be reduced by feedback which is at a premium in the L3 system, this experiment showed that control of the grid pitch was important, and that periodic checks on this factor would be desirable in manufacture. The effect of cathode activity on modulation was studied in diodes so as to eliminate the effects of grid variations. The variations in modulation from tube to tube were found to be about the same as when grids were present. The geometry of the diodes was so closely controlled that dimen- sional variations could not account for the differences in the modulation levels. This part of the investigation led to a recognition of the importance of obtaining the best possible uniformity of cathode activity. It also became apparent that the surface condition of the anode was a factor, and that it is therefore desirable to maintain a high degree of cleanliness of the elec- trodes to which positive potentials are applied. 2.6 Life Long tube life is a very important requirement in the L3 system. The most important consideration is the effect of the life on the reliability of the system. There is also the obvious effect of the life on maintenance costs. Short life tends to reduce the reliability of a system which contains a great number of tubes because the potential failures cannot be predicted so accurately as when the life is long, without a prohibitively costly amount of testing. , Even with the most frequent and accurate testing procedure which might be considered, it would be amazing if more than 90% of the potential failures were replaced before causing transmission trouble. To illustrate the effect of short life, consider a 100-mile section of L3 line. There will be five tubes in each of 24 amplifiers. If the performance of any one of the total of 120 tubes becomes poor enough to make the circuit un- commercial, that section must be taken out of service until the defective 1114 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 tube (or amplifier) is replaced. Now, for a going system, with 120 tubes, and assuming an abnormally short life of say 1200 hours, a tube will fail every ten hours on the average unless preventative testing is used. Even if very frequent testing be done in order to replace 90% of the potential failures before they occur, one circuit interruption every 100 hours may be expected. It is evident that a life many times greater than that assumed in this illustration is imperative if reliable service is to be obtained and costly maintenance avoided. Laboratory life tests predict that a tube life of at least 15,000 hours may be expected in the L3 system. The actual results will depend on the extent to which the operating conditions are closely controlled, the severity of the field rejection limits, and the ability of the tube factory to control the processing. 2.7 Interchangeability The objective is to make the characteristics of the tubes sufficiently uniform so that tubes may be replaced at will without circuit adjustments being needed. In the L3 amplifiers, the circuits have been designed so that a relatively wide range of characteristics can be accepted for individual tubes. However, it is essential that the average characteristics be held in close control from one manufacturing lot to another. This has been pro- vided for by setting up distribution requirements which will be discussed further in a later section. 2.8 Cost As will be seen from the description which follows, it has been possible to meet the L3 requirements with tube designs which do not require too great departures from the manufacturing methods employed for conven- tional telephone tubes. With a reasonable demand, it is accordingly ex- pected that the tube costs should be moderate. 3. Design Description and Characteristics 3.1 Mechanical Description and Mechanical Problems Figure 8 shows the three L3 tubes along with some of the earlier high figure of merit tubes. The W.E. 386A (left hand side) was designed to be soldered directly into the circuits and had its input lead at the stem end while the output lead came out through the top of the bulb. The flexible leads used for soldering purposes, and the double-ended lead construction, ELECTRON TUBES FOR A COAXIAL SYSTEM 1115 add materially to the cost of tube construction and testing. Early in the L3 tube development the question of factory cost compared with circuit per- formance was weighed and it was decided that the advantage of lower tube cost plus the very large advantage of simple plug-in tubes would outweigh (1939) (J943) (1949) Fig. 8— The 386A, 408A,, actual size. 404A, 435A, 436A and the 437A tubes approximately the cost in performance. Accordingly, all three L3 tubes are of the stiff pin, plug-in type designed to fit existing sockets. The price paid for obtain- ing the advantages of lowered cost and interchangeability has been a loss in feedback of approximately 2 db per amplifier. 1116 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 roiA. GETTER END SHIELD MICA DISK PLATE CONVENTIONAL SCREEN GRID MICA DISK FRAME GRID Fig. 9 — Cutaway view of the 435A. Figures 9, 10, and 11 are the cutaway views of the 435 A, 436A, and 43 7 A tubes. The overall dimensions of the L3 tubes are: 435A 436A 437A Max. seated height ir 9 ir 9 Max. diameter Number of pins Pin circle diameter H" Conventional construction for small repeater tubes may be thought of as two mica wafers between which are assembled the active elements of the tube. The mica wafers serve to support and space the tube elements. This ELECTRON TUBES FOR A COAXIAL SYSTEM 1117 mica and element assembly is then mounted upon a glass stem or platform which is next sealed into a glass bulb after which the exhaust and activation procedures complete the tube. These cutaway views show that these L3 system tubes are very similar to conventional tubes. The reason for want- ing to continue with the conventional type structures is simply that of tube END SHIELD CONVENTIONAL SCREEN GRID -MICA DISK FRAME GRID Fig. 10 — Cutaway view of the 436A. cost. A production line such as that for the W.E. 408A or 6AK5 tubes could very readily be changed over to any one of these tubes. The only change needed would be in the control grid supply and in the dimensional control procedures. The principal distinctive design feature in these tubes, compared to earlier repeater tubes, is the "frame" type of control grid which was first introduced in a somewhat different form in the W.E. 404A4 and W.E. 4 ''The 404A- A Broadband Amplifier Tube," G. T. Ford, Bell Laboratories Record, Vol. XXVII Feb. 1949. 1118 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 418A tube. The L3 frame grids are illustrated in Fig. 12, together with a conventional control grid from the 6AK5 tube and the control grid from the 404A vacuum tube. The conventional grid consists of two large side rods, usually of nickel, around which is spirally wound the grid lateral wire. The lateral wire is joined to the side rod at each intersecting point by first knifing a groove into the side rod, laying the lateral wire into the groove, GETTER CATHODE -• PT--MICA DISK PLATE -FRAME GRID ■rh MICA DISK Fig. 11 — Cutaway view of the 437A. and then swaging the groove closed. Since, in these conventional grids, the lateral wire is usually larger than 0.0008" diameter, the grid is self support- ing and needs no strengthening members. For the high figure of merit tubes, control grid lateral wires of the order of 0.0003" diameter are needed. Wire of this diameter is not self supporting in the necessary lengths and for that reason the two large side rods are first joined together by the cross straps ELECTRON TUBES FOR A COAXIAL SYSTEM 1119 which are located at the ends of the grid proper. These then form a rigid frame around which the very fine lateral wire can be spiraled without any danger of having laterals out of place. It can be seen that this technique produces the extremely fiat grid plane which is necessary for the desired 6AK5 CONVENTIONAL NOTCHED AND SWAGED GRID 404 A BRAZED FRAME GRID 435 A GLAZED FRAME GRID 436 A AND 437A GLAZED FRAME GRID '^-GLAZE Fig. 12 — Control grids for the 408A or 6AK5, the 404A and the L3 carrier tubes. tube performance, and which is the real difference between these high figure of merit tubes and the more conventional tubes. The fabrication of the 404A frame grid has been discussed in a previous article.^ That article also mentioned the 418A grid which is a side rod type 5 "Fine-Wire Type Vacuum Tube Grid," E. J. Walsh, Bell Laboratories Record, Vol. XXVIII AprU 1950. 1120 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 frame grid. The L3 grids are a further development. The major difference between the earlier frame grids and these is in the method of bonding the 0.0003'' lateral wire to the side rods. In the earlier grids a gold braze was used to bond the laterals to the side rods. This necessitated heating the unit to approximately 1070°C to flow the gold. The newer grids have the lateral wires bonded by a glass glaze which allows the process to be carried out at approximately 700°C. There is a differential expansion between molybdenum and tungsten of about five to four. The net result of the reduction of temperature in this process is that the tungsten wires are stretched less at the lower temperature and thus when returned to room temperature have higher residual tensions. This is important because the higher the residual tension the higher the resonant frequency of the lateral wires. This in turn means that the noise level of the tube due to vibration or shock will be reduced since loose grid wires will give rise to microphonic noises. Tighter wires also decrease the possibility of grid to cathode shorts. Tests have shown that an increase of about 25% in the resonant frequencies of the lateral wires can be expected as a result of using the glass glazing technique as compared to the gold brazing technique. It is interesting to note that the residual stress in the lateral wires of these grids is of the order of 200,000 pounds per square inch. This figure is roughly ten times as great as the allowable working stress for steel beams such as are used in the construction industry. When the glazing technique is used, the grid is gold plated after the glazing operation has been completed. The gold is used to inhibit thermionic emission from the grid wires. This is a necessity for tubes of this type when used in the circuits for which they were designed. The need for the plating exists because of the proximity of the grid wires to the hot cathode and their unfortunately favorable position for receiving a deposition of active material from the cathode during its processing and operation. The desired amount of gold on the grid wires is that which will cause a diameter in- crease of about 0,00002". This is an extremely difficult increase to measure because the measurement must be non-destructive, since it is made on the finished grid and is used as a production control. The method used to date has been an optical measurement at a magnification of about 500 X. A very high degree of precision, compared to that previously available, has been obtained for some of the parts whose dimensions are critical. The cathode sleeve is now obtainable with minor axis limits of ±0.0003''. The mica discs are now made with the critical holes to that same tolerance. The frame grid side rod is made to ±0.0001". These are the basic elements of the tube and, after inspection has shown them to be acceptable, their assembly becomes close to that of a conventional tube. The inspection of ELECTRON TUBES FOR A COAXIAL SYSTEM 1121 these parts is difficult when production numbers are considered. The micas in particular presented a serious problem. Mica sheet is comf)osed of a large number of laminations many of which are of the order of 0.0001" in thick- ness. When the mica discs are punched out, these laminations leave, not smooth edge holes as do metal stampings, but rather a large number of minute jagged edges. The method used to check these was an optical one in which the mica was projected at about 40 times size onto a glass screen on which engraved lines acted as go-no-go gages. This reduced tool and human error considerably. The cooperation of several industrial concerns which supply some of the critical parts and the measuring instruments was very helpful in obtaining the desired tolerances. It was evident from the start of the development of the L3 tubes that the performance requirements for high gain conventional structure tubes would be pushing to the limit the available process controls and measuring techniques. A statistical quality control program was put into effect on the tubes after the final laboratory design had been crystallized. The statistical study covered the tube dimensions and the data collected from those tubes after they had been processed. The net result of the study was to indicate that better measuring methods and process controls are needed. With the amount of d-c. feedback employed in the working circuits, the space current does not vary too rapidly with tube geometry. In the case of the most critical spacing, that between the grid and the cathode, a 10% change in the spacing would be expected to cause only about 2.5% change in space current. However, the transconductance is more sensitive to the grid-cathode spacing, with a 14% change in transconductance to be ex- pected for a 10% change in the spacing. This comes about because the trans- conductance is a function of the spacing, even at a fixed space current. Since a 10% change in spacing is only 0.00025 inch, the importance of close tolerances on the parts dimensions controlling it is evident. The test specification limits on transconductance permit a variation of about ±25%, so that the 0.00025 inch change in spacing would use up over half of the allowed deviation. Preproduction runs at the Laboratories have shown that the tubes are practical and that their performance in the amplifier circuits has justified their design. 3.2 Electrical Characteristics The nominal electrical characteristics are shown in Table II. The corre- sponding characteristics for the earlier types 386A, 6AK5 and 404A are also given for comparison. The last row in the table shows figure of merit values which are a measure of the circuit performance. The tabulated values for the figure of merit were calculated, taking into account the effect of 1122 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 space charge on the input capacitance, and include a total allowance of 3 mmf. for socket and wiring capacitance (input plus output). The L3 tubes are somewhat better than the 404A and substantially better than the 6AK5. The figures of merit tabulated will not check with the values shown in Figs. 2-4 since the curves were calculated for cold tube capacitances and zero socket and circuit capacitances. Table II Classification Heater voltage Heater current Plate current Screen current Transconductance Input capacitance* Output capacitance* Plate-grid capaci- tance* Figure of merit** 386A Pentode 6.3 0.150 7.5 2.5 4000 3.6 2.6 0.025 61 6.3 0.175 6AK5 408A Pentodes 20.0 .05 7.5 2.5 5000 3.9 2.85 0.01 72 404A 43SA 436A Pentode Tetrode Tetrode 6.3 6.3 6.3 0.30 0.30 0.45 13 13 25 4.5 3.5 8 12500 15000 28000 7.0 7.8 15.2 2.5 2.5 3.3 0.03 0.025 0.05 123 146 165 437A Triode 6.3 volts 0.45 amps 40 ma — ma 45000 Mmhos 11.5 mmf 0.9 mmf 3.5 mmf — mc * Cold capacitances. ** This is the frequency at which unity voltage amplification would occur with a simple parallel tuned circuit interstage. Allowances have been made for stray capacitances and for the increase in input capacitance when a tube is energized. No figure is given for the 437A tube because the relations derived for the earlier stages in the amplifier do not apply to the output stage. 3.3 Performance in Repeater The positions of the tubes in an auxiliary repeater are indicated in the diagram of Fig. 13. The overall insertion gain is a little over 30 db at 4 mc. While the noise contributions of the first 435A tube and the 436A tube are important, they have been reduced to 48 db below one volt and 62 db below one volt, respectively, for 1200 repeaters. The second 435 A tube and the "lower" 437A tube appearing in Fig. 13 are the major contributors to the modulation. The expected modulation levels from these tubes are those associated with single tone ratios of about 34 db for the fundamental to second harmonic ratio and 70 db for the fundamental to third harmonic ratio, with a grid signal level of 0.1 volt r.m.s. INPUT AMPLIFIER OUTPUT AMPLIFIER TETRODE TETRODE 435A 435A TETRODE 436A TRIODE 437A TRIODE 437A Fig. 13 — Position of tubes in the input and output amplifiers for the L3 carrier system. ELECTRON TUBES FOR A COAXIAL SYSTEM 1123 The gain-band performance in this repeater, or in any other circuit, will be less than that shown in the curves in Figs. 2-4 since the total shunt capacitances in a working circuit are always larger than the cold tube capacitances used in calculating the inherent figure of merit. 3.4 Test Specifications The test specifications for the L3 tubes were written with the L3 system requirements as the prime consideration. In addition to the usual tests made on small tubes, a modulation test was included for the 435A and 437A tubes because of the importance of this characteristic in terms of system performance. In order to avoid penalties which can result from unwanted systematic deviations which pile up in a long system, requirements have been set up which will control the distribution of transconductance, modula- tion, and some of the most critical interelectrode capacitances. By the application of suitable quality control methods, it is expected that these requirements can be met economically and that such measures will prevent the manufacture of large numbers of tubes having average characteristics far off the design values. When simple go, no-go limits are used, it is not economical to set close enough limits to attain the desired control of the average characteristics. 4. Conclusions and Future Possibilities The fundamental problem in the development of repeater tubes for broad band coaxial systems has been to devise means for utilizing closer and closer grid-cathode spacings without sacrificing life performance. The closer spacings have been made possible by devising rigid control grid supporting structures which can be wound with very small diameter wire. The wire is held under tension by the supporting frame so that a flat winding is produced which can be spaced very close to a flat cathode. The possibilities for the development of tubes which will provide still better broad band amplification depend to a great extent upon the kind of system design to be considered. If higher figure of merit, as defined in this article, can be utilized, considerable improvement can be realized with space charge controlled tubes such as the 435A, 436A and 437A by using mounting arrangements which provide more precise means of establishing and maintaining the critical dimensions. Acknowledgements Several members of the technical staff and their assistants have con- tributed materially in solving the numerous technical problems which arose during the development of these tubes. In addition, those who fabricated 1124 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 the grids and assembled the experimental tube models made important contributions in terms of skill and painstaking effort. It is not practical to name all of the persons involved. The development of broad band tubes over the last fifteen years was under the direction of the late Dr. H. A. Pidgeon until 1943, and Mr. J. O. McNally from 1943 to date. The writers wish to acknowledge the impor- tance of their helpful guidance and encouragement. APPENDIX Meanings of Symbols F = Figure of merit G = Voltage amplification B = Bandwidth between 3 db points K = Interstage circuit constant Gm = Grid-plate transconductance C\ = Input capacitance C2 = Output capacitance n = Turns per unit distance on grid a = Grid-cathode spacing b = Grid-screen spacing c = Screen-plate spacing A = Area of active structure h = Plate current, d-c M = Ratio of plate current to cathode current Eel = Grid-cathode voltage Er2 = Screen-cathode voltage M = Grid-screen amplification factor /o = Cathode current density, d-c r = Grid wire radius Ip = Amplitude of fundamental component of a-c plate current hp = Amplitude of second harmonic component of a-c plate current ip = Fundamental a-c plate current component iip = Second harmonic plate current component Go = Perveance factor Eg = Amplitude of grid signal voltage p = Frequency X 27r / = Time i = a-c plate current Units: length in cms; practical electrical units; time in seconds. ELECTRON TUBES FOR A COAXIAL SYSTEM! 1125 Assumptions I na = 1 The ratio of the pitch distance to the grid-cathode spacing is held constant. This is done so that the effect of the variation in field along the cathode surface resulting from the finite grid pitch distance will be small and the same throughout the discussion. II Ci = 0.0885 X 10' ■"-(M) 0.0885 X 10"''^ The input and output spaces are treated as if they can be represented by ideal condensers. This amounts to assuming that the grids are per- fect planes and that there are no end effects. The effects of space charge on the capacitances are neglected, and the socket and wiring capaci- tances are also neglected. This means that the resulting calculated figure of merit represents the limiting value inherent in the tube structure. /F V^ 2.33 X lO-'M^ — + Eci) III ^fi ~ 7 : ; r73j2 •■(■-r-f'j The expression for plate current assumed is an idealized one, but holds fairly well for these tubes. It is assumed that the triode amplification factor is independent of the control-grid voltage. This holds fairly well under the conditions of assumption I. V When the interstage consists of a single parallel tuned circuit, K = 1. This case is assumed. Derivations Beginning with the above assumptions, and substituting in equation (1), equations (2), (3) and (4) can be derived. The procedure will be outlined below : KGrn 2t(Ci -h C2) (1) 1126 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 _ 4.74 X WMIl'^ \a 0 c/\ /x a / £,, = ^ [5/8 X rn'o^'^ll" (1 + i ^) - £., 2.73- - log,„cosh(27r-V a \ a/ (3) logio coth (-0 (4) Substitutions for Ci , C2 , and K in (1) are made from assumptions II and V. Gn is found by differentiating the plate current expression (assump- tion III) with respect to Ed , remembering that /x is independent of Ed according to assumption IV. .1/2 ^ 2.33 X IQ-'MA ^"^ = 2 ^ . _^ ? r\ 3/2 (5) (6) From assumption III we can write .1/32/3A , la + A^'^ (IP \l/2 Ib 0' I 1 T- I )u "^ '7 (2.33 X lo-'y'm^'^A'i' Substituting in (5) , (2.33 X 10-')M.1/!,'V" f 1 + 1 ''~±^) ^ _ o ^ \ IX a / a'^ ( 1 + 1 e-±i ) (2.33 X 10-«)^^^M^^^^ 1.5(2.33 X 10-")'^^^'^'^'/^^^ Crm — 7 r \ yi a / Since /« = M/(v4 by defmition, ^ 2.64 X IQ-V^/J^' ,o^ t'w = ; r yfi) 1/2 (7) ELECTRON TUBES FOR A COAXIAL SYSTEM 1127 Substituting in (1), p ^ 2.64 X lO-'MAll"' ,^. a ('+r-f>"H^'»""^(M^')] Collecting the constants and cancelling the A's, F = 4.74 X lO'Mll" ^2) \a b c/ \ n a / The expression for Ec2 can be found by substituting Ib = MIqA in assump- tion III and solving for Ec2 . 3/2 2.33 X 10""^^ ' "^ MIqA = ^ + £cl M 1.76 X 10-* £.. = M [5.68 X 10V»/S" (1+ ^ ^*) - £..] (3) The expression for fx can be found by applying assumption / and substitut ing n = - in the Vogdes-Elder formula* for a plane structure. Or _ lirnb logio cosh (27rwr) ^ ~ 2.303 log 1 Substituting n = 2.303 logio coth (iTrnr) logio coth (lirnr) 1 a (10) 2.73 - logio cosh f27r -j logio coth ( 27r - j logio coth ( 27r - j (4) Equation (11) can be derived by considering a particular structure and introducing a small sinusoidal signal Eg cos pi added to the d-c. voltage in the plate current expression, Assumption III. This can be written as Is + i =Gc (— + Eel + Eg cos ptj (12) * F. B. Vogdes and Frank R. Elder, Phys. Rev., 24, pp. 683-689, Dec, 1924. 1128 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 For zero signal this becomes /b = Go (y + £.1)"* (13) For a pure resistance load which is small compared to the plate resistance, the fundamental component, neglecting contributions from third and higher order terms, is ip = Gm Eg cos pt (14) Neglecting the contributions of fourth and higher order terms, the second harmonic component is 3 E^ ^2P == Ib72 77^ 7-2 cos 2pt (15) 16/£.. V M / This is found by expanding (12) into the binomial series. From Assumption III and equation (5), The amplitude of the second harmonic component, from (15) is h. = l ,J"^' .. (17) Substituting for (y + '^-.)' From (14), Substituting from (19) in (18), This can be written ''(^--•.) from (16) in (17) T _ CiEg GlE] = II I - '' ''' \2Is It, 1, (18) (19) (20) (11) Telephone TraflSc Time Averages By JOHN RIORDAN (Manuscript Received April 25, 1951) This paper describes the determination of the first four semi-invariants of the distribution of the average, over an arbitrary time interval, of traffic carried by a telephone system with an infinite number of trunks, during a period of statistical equilibrium. Both finite and infinite numbers of independent call sources are con- sidered, and the distribution function of call holding times is left general. 1. Introduction T?OR mathematical studies of telephone traffic, like those of call loss or ^ delay which are used in trunking engineering, the traffic is considered as a flow of probability in time. In the period of most importance, the busy hour, this flow is usually regarded as stationary; that is to say, the proba- bility of a given number of busy trunks, or the probability of delay of an incoming call (or any other probability of the system which comes in ques- tion) is taken as independent of the particular moment in the busy hour at which the system is examined. The system is said to be in statistical equilib- rium. For such theoretical studies, the statistical quantities which determine these probabilities, like the rate at which calls appear, are of course taken as given, but in the application they must be determined by observations, such as those being taken in the current extensive program of traffic meas- urements. Here a difficulty appears. To abridge the extensive amount of observational material, either measurements are made of traffic averages over periods small compared to the busy hour (but not small enough to be neglected) or the measurements of continuous recorders are averaged by hand. It may be noticed here that for application of the results given below the traffic averages obtained by measurements must be those of a con- tinuous device which records all traffic changes and not, as in some measuring devices, those obtained from a number of ''looks" at points within the averaging interval. But to use these measurements in determining the traffic parameters by standard sampling theory, a corresponding theoretical study of the averages is necessary. Such a study, within limits to be described presently, is given here. No attempt is made to describe the sampling studies possible from the results reached. These seem to be of many kinds, not necessary to describe, but for 1129 1130 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 concreteness it may be mentioned that the most important, at the moment, seems to be that of setting confidence limits for the average traffic. The most important of the Umits to this study are those impHed by the assumptions of statistical equihbrium with fixed average, and an infinite number of trunks. The former Umits appHcation to periods in which, roughly speaking, average traffic is neither rising nor falling; the latter is justified only by the extreme mathematical difficulties produced by assuming other- wise. The traffic variable is the number of busy trunks in a period of statisti- cal equilibrium. For pure chance call input, the call holding time character- istic is left arbitrary throughout the development, but main interest lies in the two extreme cases of constant holding time and exponential holding time, which are examined in detail,* For calls from a limited number of sources, results are obtained only for exponential holding time. More precisely, if N{t) is the random variable for the number of busy trunks at time t, the variable studied, the average number of calls in an interval of length T, is M{T) =\, f N{t) dt (1) 1 Jo The question is: What are the statistical properties of M{T)? The results given are the first four cumulants (semi-invariants) of M{T), which seem to have the simplest expressions. For the convenience of the reader it may be noticed that the first cumulant is the mean, the second the second moment about the mean which is the variance, the third the third moment about the mean, and the fourth the fourth moment about the mean less three times the square of the variance. In all cases the mean of M{T) is the mean of N(t) and for pure chance call input is called b, the average number of calls in unit average holding time, h. The other cumulants for pure chance call input, kn , have the general expression k. = b "^"^7 ^^ jj dxgix) {T - x)x"-'; « = 2, 3, 4 with * F. W. Rabe [6] has reported results for these two cases for relatively long averaging intervals, which are verified below. I owe my interest in this problem to a report on Rabe's work made by Messrs. Gibson, Hayward and Seckler in a probability colloquium at Bell Telephone Laboratories initiated and directed by Roger Wilkinson. TELEPHONE TRAFFIC TIME AVERAGES 1131 and /(/) the probability that a call lasts at least /, that is, the distribution function of holding times. The specializations of this, for constant holding time and exponential holding time, appear in section 4. The results for finite source input have a similar character. The procedure in obtaining these is as follows. The cumulants are de- termined from the ordinary moments (about the origin) and the latter are determined by the integration of expectations. Thus the first moment, the m^an is determined from E\M{T)] = 1; jf '^ mH)] dt = E[Nit)] (2) where E(x) is written for the expectation or mean of x. Similarly the second moment is given by E[M\T)] = ^[ [ E{N{t)mu)] dt du (3) and so on for higher moments. Correlation effects appear in (3) in E[N(t)N(u)] and are included in the development by formulation of transi- tion probabilities, that is, those probabilities determining the traffic flow in time. The transition probability Pjk{t) is defined as the probability of transition in t from j calls in progress (busy trunks) to k calls in progress, and fixes the inter-relatedness of call probabilities at different time epochs. Only for large values of / are these probabiHties independent. Hence, the first task is to determine these simple transition probabilities, then those of double and triple transitions, then the expected values of pairs, triples and quadruples of numbers of busy trunks, and finally the moments. 2. Transition Probabilities For exponential holding time, and infinite sources, infinite trunks, these probabilities have already been determined by Conny Palm [5]. Palm's work has been summarized both by Feller [1] and by Jensen [3], and de- scribes the whole process, not merely the equilibrium condition. For the equilibrium condition, a different procedure,* similar to that used by Newland [4] for another purpose, allows the assumption of a more general holding time characteristic. * Thanks are due S. O. Rice for suggesting this, as well as for many corrections and improvements. I also have had the advantage of a careful reading of the mss. by E. L. Kaplan. 1132 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 For infinite sources, and calls arriving individually and collectively at random with average density a, the well-known formula for the probability that exactly k calls arrive in time interval / is the Poisson TT.W = e-'^Xatf/kl (4) Then, if P,y(/; k) is the conditional probabiUty of transition from i to j when k calls arrive in time /, Piiit) = IlPij(t;kUk{t) ' (5) fc=0 Consider Pij{t; 0), that is the (conditional) transition probabilities when no calls arrive. Let the probabiUty that a call lasts at least t be/(/), so that the average holding time h is given by h = f u[-f(u)] du = f f{u) du (6) Jo Jq The i calls initially in process are independent of each other. Select one of them and suppose the time from its arrival (its age) is h . Then the proba- biUty that it will also exist / units later is the conditional proba- biUty/(/ + ti)/f{ti). Since in equilibrium conditions all moments of arrival have equal probability, the corresponding probability for an arbitrary call is git) = j[ f{t + h) dh ^ jf m dt=^-j^ fiu) du (7) Hence the transitional probability Pij(t', 0) is the binomial expression i>,,(/;0) = (j)g'(l-g)-' (8) and its generating function is Piit, x; 0) = ZPiiii; 0)x^ = [1 + (,: - l)gY (9) In (8) and (9), for brevity, the argument of g is omitted. Now, suppose one call arrives in interval /. The moment of arrival is uniformly distributed in /; that is, if Ui is the moment of arrival, Pr(u < Ui < u -\- du) = du/i and the probability that a caU arriving at an arbitrary moment wiU be in existence at time t is, say, QU) = ('f{t-u)^ = \ /"/(«) d« = 7 (1 - ««)) Jo t I Jo t (10) TELEPHONE TRAFFIC TIME AVERAGES 1133 The corresponding generating function is 1 - (?(/) + xQ{t) = 1 + {x - l)Q{t) and, since calls arriving are independent, the generating function for k calls arriving is [1 + {x- 1)())^ and PS, x; *) = [1 + (x - l)g]«[l Jr(x- Dei' (11) Hence, finally by (5), = [1 + U - \)gV E [1 + (^ - \)Q\' '^^- = [1 + (:*; - l)g]*exp(a:- 1) at g = [1 + (:«: - DgV exp {x - 1) ah (1 - g) (12) The last step uses (10). This is the generating function for the simplest transition probabilities, and is quite like Pahn's result; indeed, for exponential holding time g = f = e~^'^. The probabilities themselves are obtained by expansion of the generat- ing function in powers of x, or by substituting g for e~^'^ in Palm's result. But they are not needed here; the generating function is most apt for deter- mining the averages of interest, as will appear. Before going on to the other transition probabihties, it is interesting to notice certain checks of equation (12). In statistical equilibrium the traffic has Poisson density (Palm I.e.) that is, in the present notation Pr(N(t) = k) = e-^b'/kl where b = ah. This of course is independent of time. Then, if A^(0) has this density, so should N{t) as determined from iV(0) and the transition proba- bihties impHcit in (12). This is verified by E Pi(t,x)e-'byi\ = exp (x - l)b(l - g) E [1 + ix - ^)gV^-jr = exp [{x - \)b{\ -g)-b + b + {x- \)bg\ (13) = exp {x — \)b. 1134 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Also, ^(0) = 1 and g(oo) = 0 so that Pi{0,x) = [1 + (:^- 1)]^ = x' (14) Fi{,x) = exp (x - l)b - (15) showing that in zero time no transit to another state is possible, and in infinite time the equihbrium probabiHties are reached no matter what the initial state has been. Finally, in a Markov process (cf. Feller [2], Chap. 15) the simple transi- tion probabilities alone are needed since Pijkit, U) = P^J{t)PJk{u) A test for this is the Chapman-Kolomogorov equation, namely Pikit + u) =J2 Pij{t)Pjk{u) j Using (12), the corresponding relation of generating functions is [l+{x- \)g{t + «)]^ exp h{x - 1)[1 - g{t + u)] = [1 + (:. - \)g{t)g{u)Ytx^h{x - 1)[1 - g{i)g{u)]', so the process is Markovian only if g{t + w) = g{t)g[u) which is true only for exponential holding time. For the next transition probability Pijk{t, u), consider first the condition in which no call arrives in the whole interval / + w. As before '.vw = (*y,(i - g.)'-' where for convenience gt is written for g{t). For the next transit, however, there is a difference, namely J-k '*> = (i)(t)'0-T)' since gt+u/gt is the conditional probability that -a, call which has lasted / will last u more; Pjk{u) is the conditional probability of a transit from j to k in «, given the transit i toj in /. The generating function for the double transition probabilities in this case is, then, E L Piy*(/,w;0)xy = [! + (:,- \)g, + x{y - l)gt+uY (16) j * Now suppose a single call arrives at random in interval /. As before, the probability that it will occupy a trunk at time / is Q{t) = htr^(l — g(t)) TELEPHONE TRAFFIC TIME AVERAGES 1135 and the conditional probability that it will also occupy a trunk at time t -\- uis I ff{t + u-x)dx-^Q{l) t Jo (17) / Jo or ^^^^^ - m,uX s.y. The corresponding generating function, with x and y the indicators of calls at / and / + u, resp. is 1 - eW + Qim - R(t, u)]x + Q{t)R(t, u)xy or 1 + (:*: - 1)(1 - g(t))h/t + x{y - iMu) - g(t + u)]h/t The generating function for c calls in this interval is this expression raised to the c'th power, since calls arrive independently; and since c calls arrive with probabihty e~°'\aty/c\, the generating function for calls arriving in this interval is Z [1 + (^ - i)e + 1 e.h.t. g{x) = e-* and the results are as follows: Constant Holding Time Cumulant T < 1 T > 1 k2 b(l - T/3) bT-\\ - l/Sr) h 6(1 - T/2) bT-\\ - \/2T) ki h{\ - 3T/5) bT-\l - 3/5T) Exponential Holding Time ki 2bT-\T - 1 + e-^] h 6bT-^[T - 2 + (r + 2)e-T] ki 12bT-'[2T - 6+ (T+ 4T + 6)e-^] It may be worth noting that, if the surmise is correct, for constant holding time r *. _ 1 1 T < 1 TELEPHONE TRAFFIC TIME AVERAGES 1141 1.0 HI O.J z5 I- 0.6 0.4 0.2 \ N, ^ v^ \ ^ ^ EXPONENTIAL .^JHOLDING TIME CONSTANT HOLDING TIME ^ ~^ 0.5 1.0 2.0 2.5 3.0 3.5 4.0 HOLDING TIME UNITS, T 5.0 Fig. 1. — Comparison of variances of average traffic for constant and exponential hold- ing times. 1.0 0.8 z < uj 0, to Ol- P 0. < \ ^w ^ ^ \ \ N n=2 \^ V -^ 4 — 0.5 1.5 2.0 2.5 3.0 3.5 4.0 HOLDING TIME UNITS, T 4.5 •6.0 Fig. 2. — Cumulants kz, ka, and k4 for constant holding time. 1.0 1— < 0.8 i< HI 0.4 lo O 1- \ S^ N "^ V X -^ ^s?^^ ^n=2 ^ \ .. — 0 r~ 0.5 2.0 2.5 3.0 3.5 4.0 HOLDING TIME UNITS,! 5.5 Fig. 3. — Cumulants k2, ka and k4 for exponential holding time. 1142 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 and for exponential holding time k^ = b "-^^^^ [(n - 2)! r - (» - 1)! + e-' {T + a)-'] where in the last term {T + a:)"~^ is a symboHc expression or shorthand for (r + ay-' = Z f" ~ ^) r-^- «„ 0 \ w / and«« = (w + 1)!; e.g. (r + ay = T' + 6^ + 1ST + 24 For small values of T, the two cases coalesce (e~' ^ 1 — x) and at T = 0 approach b as they should. For large values of T, and constant holding time, kn^b/T-\ {n= 2,3,4); for exponential holding time kn^n\b/T''-\ (n= 2,3,4). For w = 2, these results agree with Rabe [6]. As T increases, for either holding time, the cumulants are progressively smaller, and the approximation of the distribution of M{T) by a normal curve (which has all cumulants, except the first and second, zero) improves. This is what follows from the central limit theorem if the subdivision of T into a large number of intervals results in mutually independent random variables (cf. Rice [7] 3.9). Figure 1 shows a comparison of the variances (^2) for the two holding time cases. Figure 2 shows a comparison of the cumulants ^2 , h and ki for constant holding time, and Fig. 3 shows the same thing for exponential holding time. 5. Finite Sources — Exponential Holding Time The generating function for transitional probabilities for N subscribers, each originating calls independently with probabihty X, and for exponential holding time, as given by Jensen (l.c.) is as follows: Piit. ^) = [1 + qi{x - 1)]»[1 + qo{x - l)]^-» (31) with ?■ = /> + 9 " p = l-q = \/{\+y) 7= 1/h TELEPHONE TRAFFIC TIME AVERAGES 1143 It should be noticed that for / = co ^ q^ = q^ = p and Pi{<^,x) = [\-\-p{x- \)Y (32) The right hand side is the binomial generating function and, as independent of i, is the generating function for the statistical equilibrium probabilities; that is ■ Pr mo = *] = (^) / q"-" Also the process is Markovian since Z ^' Z PiAt)Pik{u) = JlPiM^ + qUx - \)V [1 + qou{x - 1)]^-^' k j j = [1 4- (.qou + quQiu — quqou)(^ — 1)]* [1 + (qou + qotqiu — qotqou){x — l)]^~* and qcu + qitqiu — qitqou = qi,t+u qou ~\~ qotqiu ~ qotqou = qo.t+u Here it has been convenient to indicate by the double subscript the de- pendence of go and qi on a time variable. Moments are obtained by the process given in detail for the infinite source case. For brevity it is convenient to use the binomial cumulants which are as follows K2 = Npq K3 = Npqiq - p) Ki = Npq(\ — 6pq) and the modified time variable Ti = (X + y)T. Then the results are k2 = 2IT%[Ti - 1 + e-'''] k, = 67T^3[ri -2+ (Ti+ 2)6-^^] k, = 127T'((/c4 + kIN-')[2Ti - 6+iTl + 4^ + 6)^-^^] - .^^^[1 - {Tl + 2)6-'^ + e-''^]) These of course bear a strong resemblance to the infinite source case (ex- ponential holding time), to which they converge. 1144 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Bibliography 1. VV. Feller, "On the theory of stochastic processes with particular reference to applica- tions," Proc. Berkeley Symposium on Math. Statistics and Probability, Univ. of California Press, 1949. 2. W. Feller, "An introduction to probability theory and its applications," New York, 1950. 3. A. Jensen, An elucidation of Erlang's statistical works through the theory of stochastic processes, "The Life and Works of A. K. Erlang," Copenhagen, 1948. 4. W. F. Newland, A method of approach and solution to some fundamental traffic problems, P.O.E.E. JL, 25, 119-131 (1932-3). 5. Conny Palm, "Intensitatsschwangungen in fernsprechverkehr," Ericsson Technics, 44, 1-189 (1943). 6. F. W. Rabe, "Variations of telephone traffic," Elec. Comm. 26, 243-248 (1949). 7. S. O. Rice, "Mathematical analysis of random noise," Bell System Technical Journal, 23, 282-332 (1944); 24, 46-156 (1945). The Reproduction of Magnetically Recorded Signals R. L. WALLACE. JR. (Manuscript Received July P, 1951) For certain speech studies at the Bell Telephone Laboratories, it has been necessary to design some rather specialized magnetic recording equipment. In connection with this work, it has been found experimentally and theo- retically that introducing a spacing of d inches between the reproducing head and the recording medium decreases the reproduced voltage by 54.6 {d/\) decibels when the recorded wavelength is X inches. For short wavelengths this loss is many decibels even when the effective spacing is only a few ten- thousandths of an inch. On this basis it is argued that imperfect magnetic con- tact between reproducing head and recording medium may account for much of the high-frequency loss which is experimentally observed. Introduction WITHIN the last few years there has been increasing use of magnetic recording in various telephone research applications (examples are various versions of the sound spectrograph used in studies of speech and noise). Some of these uses^ have required a reproducing head spaced slightly out of contact with the recording medium. Experimental studies were made to determine the effect of such spacing and the results were found to be expressible in an unexpectedly simple form. The general equation derived is believed to be fundamental to the recording problem and to account for much of the high-frequency loss that is found in both in- and out-of-contact systems. This paper discusses results of the experimental study and presents for comparison some theoretical calculations based on an idealized model. Measurements of Spacing Loss In order to measure the effect of spacing between the reproducing head and the medium, an experiment was set up as indicated in Fig. 1. The recording medium used was a 0.0003 inch plating of cobalt-nickel alloy- on the flat surface of a brass disc approximately 13 inches in diameter by J inch thick. This disc was made with considerable care to insure that the recording surface was as nearly plane and smooth as possible and that it would turn reasonably true in its bearings. Speeds of 25 and 78 rpm were provided. iR. C. Mathes, A. C. Norwine, and K. H. Davis, "Cathode-Ray Sound Spectro- scope," //. Acous. Soc. Am., 21, 527 (1949). 2 Plating was done by the Brush Development Company. 1145 1146 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 The ring-type record-reproduce head shown in Fig. 1 was lapped sHghtly to obtain a reasonably good fit with the surface of the disc. A single-frequency recording was made with the head in contact with the disc using a-c. bias in the usual way. Then the open circuit reproduced signal level was measured, first with the head in contact, and then after introducing paper shims of various thickness between the reproducing head and the medium. Thus the effect of spacing was measured at a particular frequency and recording speed. The signal was then erased and the process was repeated for other recorded frequencies and for several record-repro- duce speeds. Measurements were also made for cases in which the recording and reproducing speeds were different. Considerable care was required to keep the disc and head sufficiently clean so that reproducible results could be obtained. HIGHLY POLISHED PLANE SURFACE PLATED WITH 0.0003" COBALT NICKEL ALLOY \ RECORDED TRACK ^ /^ 0.1 18" WIDE PIVOT / RECORD- REPRODUCE HEAD (brush BK9n) -BRASS DISC Fig. 1— Mechanical arrangement of recording set up. The one head served for re- cording, playback, and erase. Figure 2 shows typical response curves measured at 21 in./sec. with the reproducing head in contact and with 0.004 inch spacing. The difference between these two curves will be called the spacing loss corresponding to this spacing and speed. From these data and more of the same sort it is found that, within experimental error, spacing loss can be very simply re- lated to spacing and the recorded wavelength, X, by the empirical equation, Spacing loss = 55{d/\) decibels (1) where spacing loss is the number of decibels by which the reproduced level is decreased when a spacing of d inches is introduced between the repro- ducing head and a magnetic medium on which a signal of wavelength X inches has been recorded. The fact that this expression fits the experimental data reasonably well is indicated in Fig. 3 where spacing loss data measured at a number of dif- ferent speeds, frequencies, and spacings are plotted against d/\. REPRODUCTION OF MAGNETICALLY RECORDED SIGNALS 1147 IN MECHANICAL CONTACT --.^ ^ """^"^ \ ^ s ^ ^ ^ ^' 1 SPACING LOSS 1 1 ^ Vc - - "7 .^ ^ 0.004" / SPACING '\ N V REPRODUCE HEAD \ \ N I \ H \ "^^d MEDIUM-^ \ 1 _L ^ 100 200 300 400 600 1000 2000 3000 FREQUENCY IN CYCLES PER SECOND 5000 Fig. 2 — Response curves taken at 21 in./sec. Recordings were made with head in contact and were played back first with head in contact and then with a spacing of 4 mils between head and disc. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 SPACING IN WAVELENGTHS , Cl/\ Fig. 3— Data obtained as in Fig. 2 show spacing loss approximately equal to 55{d/\) decibels. 1148 the bell system technical journal, october 1951 Implications of the Experiment In this section it will be assumed that equation (1) holds true in all cases where the spacing d is sufficiently small and the recorded track is sufficiently wide so that end effects are negligible. If this is true, as it seems experi- mentally to be, then it is indeed surprising how great can be the effect of even a very small spacing when the recorded wavelength is small. For example, take the case of a 7500 cps signal recorded at 7.5 in./sec. in which case the wavelength is 0.001 inch. A particle of dust which separated the tape from the reproducing head by one-thousandth of an inch would de- crease the reproduced level by 55 db. A spacing of 0.0001 inch would pro- duce a quite noticeable 5.5 db effect and even at 0.00001 inch spacing the 0.55 db loss would be measurable in a carefully controlled experiment. In view of the magnitudes involved, it seems probable that this spacing loss may play a significant role even in cases where the reproducing head is supposed to be in contact with the medium. For example, it has been known for some time that chattering of the tape on the reproducing head or changes in the degree of contact due to imperfect smoothness of the tape can result in amplitude modulation of the reproduced signal and thereby give rise to "modulation noise" or "noise behind the signal." With the aid of equation (1) it is possible to estimate the magnitude of the noise provided some assumption is made about the wave form of the modulation. To take a simple case, suppose that the roughness of the tape were such as to sinusoidally modulate the spacing by a very small amount and at a low frequency. The reproduced signal would then be modulated and would contain a sideband on each side of the center frequency. The energy in these two sidebands constitutes the modulation noise in this case. If it is required that this noise be 40 db down on the signal, then one can calculate the maximum permissible excursion of the tape away from the reproducing head. This turns out to be 1.1(10)-^ cm. or about one-sixth of the wavelength of the red cadmium line ! Of course, the one mil wavelength assumed in this example is about as short as is often used and the effect becomes less severe as the wavelength is increased. This is one of the rea- sons that speeds greater than 7.5 in./sec. are used for highest quality reproduction. One can also make some rough qualitative inferences about the effect of the thickness of the recording medium on the shape of the response curve. As can be seen from equation (1) or from Fig. 2, low frequencies can be reproduced with very little loss in amplitude in spite of considerable spacing between the reproducing head and the medium while high frequencies (i.e. short wavelengths) may be appreciably attenuated by even 0.0001 inch REPRODUCTION OF MAGNETICALLY RECORDED SIGNALS 1149 spacing between the head and the medium. With this in mind it is easy to see that at high frequencies only a thin layer of the medium nearest the reproducing head will contribute to the reproduced signal. In this case (short X) increasing the thickness of the medium beyond a certain amount can have no effect on the reproduced level simply because the added part of the tape is too far from the head to make its effect felt. Consider the effect of increasing the thickness of the medium from 0.3 mil to 0.6 mil when the wavelength is one mil. Since the spacing loss for 0.3 mil spacing at X = 1 mil is 16.5 db, the signal contributed by the lower half of a medium 0.6 mils thick cannot be less than 16.5 db lower than that contributed by the upper half and hence the increase in thickness can do no more than to raise the reproduced level by 1.2 db. At a lower frequency for which X = 100 mil, however, the corresponding spacing loss is only 0.165 db and in this case the two halves of the tape can contribute almost equally with the result that doubling the thickness of the medium can almost double the reproduced signal voltage. Qualitatively, then, one might expect that increasing the thickness of the recording medium, other things being equal, would increase the response to low frequencies and leave the high frequency response relatively unal- tered. This is in agreement with data published by Kornei.^ The estimates of magnitudes just given rest on assumptions which cannot be proved except by further experiments. It has been implicitly assumed, for example, that the medium is uniformly magnetized throughout its thickness and this may not be the case. It does seem perfectly safe, how- ever, to conclude that at a wavelength of one mil that part of the medium which lies deeper than about 0.3 mil from the surface cannot contribute appreciably to the reproduced signal. Furthermore, as the wavelength is decreased beyond this point the thickness of the effective part of the tape decreases in inverse proportion to X with the result that the available flux also decreases. For this reason the "ideal" response curve cannot continue indefinitely to rise at 6 db per octave as it does at low frequencies. In fact, when the effective part of the tape becomes thin enough, the available flux will decrease at 6 db per octave and just cancel the usual 6 db per octave rise, giving an "ideal" response curve which rises 6 db per octave at low fre- quencies but which eventually becomes flat, neither rising nor falling with further increase in frequency. Spacing loss may contribute in still another way to the frequency response characteristic of a magnetic recording system in which the reproducing head makes contact with the medium. It is well known to those who work 'Otto Kornei, "Frequency Response of Magnetic Recording," Electronics, p. 124, August, 1947. 1150 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 with magnetic structures such as are used in transformers and the Hke that intimate mechanical contact between two parts of a magnetic circuit does not imply intimate magnetic contact. In fact, even when great care is taken in fitting such parts together, measurements invariably show an effective air gap between them and the effective width of this gap usually amounts to appreciably more than one mil. One reason for this is that the permeability of soft materials such as are used in the cores of transformers and reproducing heads is very sensitive to strain. Even the light cold work- ing which a surface receives in being ground flat is sufficient to impair very seriously the permeability of a thin surface layer. In view of this it is to be expected that the magnetic contact between reproducing head and medium is less than perfect. If cold working during the fabrication of the head or due to abrasion by the recording medium should result in an effective air space between head and medium amounting to as much as one mil, the effect on frequency response would be pro- nounced indeed. At a recording speed of 7.5 in./sec. this amount of spacing would cause a loss of 7.3 db at 1000 cps, 14.6 db at 2000 cps, 21.9 db at 3000 cps, 29.2 db at 4000 cps, etc. It seems certain that in a practical recording system some loss of this sort must occur. The problem of determining the magnitude of the loss or in other words the amount of the effective spacing in a practical case is, however, a difficult one. So far, no direct experimental method for its deter- mination has been found. Theoretical Calculations for an Idealized Case In the preceding section an experimentally determined spacing loss func- tion has been discussed. It was shown that as the reproducing head is moved away from the recording medium the reproduced signal level decreases. This means that the magnetic flux through the head decreases. If the dis- tribution of magnetization in the recording medium were known, it should be possible to compute the flux through the head and thereby to derive the spacing loss function on a theoretical basis. Unfortunately it seems almost impossible to do this calculation in an exact way because very little is known about the magnetization pattern in the medium and because the geometry of the usual ring type head makes the boundary value problem an exceedingly difficult one to solve. It is possible, however, to obtain a solution for an idealized case which bears at least some resemblance to the practical situation and this solution will be presented. The results must, of course, be viewed with due skepti- cism until they can be proved experimentally or else recalculated on the basis of better initial assumptions. It is hoped, however, that in some REPRODUCTION OF MAGNETICALLY RECORDED SIGNALS 1151 measure they may serve as a guide to a better understanding of the mag- netic reproducing process. The Idealized Recording Medium The problem will be reduced to two dimensions by assuming an infinitely wide and infinitely long tape of finite thickness d. A rectangular coordinate system will be chosen in such a way that the central plane midway between the upper and lower surfaces of the recording medium lies in the x-y plane. It will be assumed that the medium is sinusoidally magnetized in such a way that in the medium the intensity of magnetization is given by Ix = Im sin {lirx/X) Iv = h = 0. (2) Equations (2) say that the recording is purely longitudinal. In a prac- tical case, of course, the recorded signal is neither purely longitudinal nor purely perpendicular but rather contains components of both sorts. In Appendix I it is shown that the frequency response does not depend on the relative amounts of these two components and hence that the computed results are equally valid whether the recorded signal is purely longitudinal, purely perpendicular, or a mixture of the two. Appendix II contains calculations for the case of a round wire sinusoi- dally magnetized along its axis, and for a plated wire. These results, though much different in mathematical form, are shown to be very similar to the results for a flat medium. The Idealized Reproducing Head Figure 4 shows a semi-practical version of the sort of idealized repro- ducing head which will be treated. It consists of a bar of core material with a single turn of exceedingly fine wire around it. This head is imagined to be spaced d inches above the sur- face of the recording medium. If the dimensions of the bar are made large enough, the amount of flux through it will obviously be as great as could be made to pass through any sort of head which makes contact with only one side of the tape and so the open circuit reproduced voltage per turn is as high as can be obtained with any practical head. Suppose a very narrow gap is introduced in this head where the single turn coil was and that the magnetic circuit is completed by a ring of core material as shown in Fig. 5. If the permeability of the head is very high and the gap very small then the flux which passed through the single turn coil of Fig. 4 will now pass 1152 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 through the ring of Fig. 5 and can be made to thread through a coil of many turns wound on the ring. In so far as this is true, calculations based on this bar type head are applicable to ring type heads. If the bar of Fig. 4 is now allowed to become infinite in length, width, and thickness, the flux density in it can be computed and the flux per unit width can be evaluated. This calculation is outlined in Appendix I. If the tape moves past the head with a velocity v in the x direction, the repro- SINGLE TURN OF VERY FINE WIRE \ BAR OF PERMEABLE MATERIAL SPACING d Fig. 4 — Idealized bar-type reproducing head. Fig. 5 — Idealized ring- type reproducing head. duced voltage should be proportional to the rate of change of flux. In the appendix this is shown to be dt 2t«/X\ -2-Kdl\ M+1 ^irlVvIrr^iX - e-''"le cos (co/) (3) d4>x . where ^ is the rate of change of flux in W cm. width of the reproducing dt head measured in Maxwells per sec, H is the permeability of the reproducing head, W is the width in cm. of the reproducing head (and of the recorded track in a practical case), REPRODUCTION OF MAGNETICALLY RECORDED SIGNALS 1153 V is the velocity in cm./sec. with which the recording medium passes the reproducing head. Im is the peak value of the sinusoidal intensity of magnetization in the recording medium measured in gauss, 8 is the thickness of the recording medium measured in the same units as X, X is the recorded wavelength measured in any convenient units, d is the eflfective spacing between the reproducing head and the surface of the recording medium measured in the same units as X, and CO is 27r times the reproduced frequency in cycles per sec. Note that equation (3) applies to a ring type head with no back gap. If the head has a back gap then not all the available flux will thread through the ring. Some of it will return to the medium through the scanning gap and hence will not contribute to the reproduced voltage. This does not aflfect the shape of the frequency response curve but does contribute a constant multiplying factor (less than unity) to the right hand side of equation (3). The value of this factor depends on the reluctances of the gaps and of the magnetic parts of the reproducing head. If the reluctance of the magnetic parts is negligible and the reluctance of the back gap is equal to the reluctance of the front gap then the available flux will divide equally in the two gaps and the factor will be one-half. This factor will not be con- sidered further in this paper because it does not contribute to the shape of the response curve but only to the absolute magnitude of the repro- duced voltage. It could be interpreted as reducing the effective number of turns on the reproducing head to a value somewhat lower than the actual number of turns. Spacing Loss The term e~^''^'^ tells how the reproduced voltage depends on spacing. In order to compare this computed effect with the experimentally observed one it is necessary to put it in decibel form by computing twenty times the logio of e-2'^'^/\ This gives Spacing Loss = 54.6 {d/\) decibels . This agrees very well indeed with the experimentally determined equation (1) in which the constant is 55 instead of the computed 54.6. The com- puted spacing loss function is plotted in Fig. 6. 1154 the bell system technical journal, october 1951 Thickness Loss The effect of the thickness of the recording medium shows up in the term (1 — ^"^tS/x)^ ^^ Jq^ frequencies for which the wavelength is much greater than the thickness of the medium this reduces to lird/X. In this case the reproduced voltage is proportional to the thickness of the medium and to frequency. This is the familiar six db per octave characteristic. At high frequencies, however, when X ^ 5 the term reduces to unity 10 15 20 25 30 35 40 45 50 55 60 - -^ .^^ \, 27rd SPACING LOSS = 20 LOG G K = 54.64 DB A \ \ > \ \ \ REPRODUCE HEAD > V \ T\ ^iJ^SPACING \ y V_ic: a MEDIUM-^ \ \ _i_ _1_ 0.8 1.0 0.01 a02 0.03 0.05 0.1 0.2 03 0.4 0.5 SPACING IN WAVELENGTHS, d/A, Fig. 6 — Computed spacing loss as a function of d/\. and the computed "ideal" response is flat with frequency and independent of the thickness of the medium. If the term (1 — g-2»«/^) is rewritten as then the part in parenthesis accounts for a 6 db per octave characteristic and the part in brackets accounts for a loss wilh respect to this 6 db per octave characteristic. This loss, which will be called Thickness Loss*, is given by * It seems somewhat awkward to speak of "Thickness Loss" when nothing is actually lost by making the medium thick. The only excuse for this way of splitting the terms is that it makes for ease in comparing measured and computed curves. REPRODUCTION OF MAGNETICALLY RECORDED SIGNALS 1155 Thickness Loss = 20 logio 27r5/X ,-2rhl\ db (5) where X is the recorded wavelength and 5 is the thickness of the recording medium. This function is plotted in Fig. 7. Comparison with Experiment The most elementary consideration of the magnetic recording process indicates that when the recording signal current is held constant the open circuit reproduced voltage should be a function of frequency, increasing by 6 db for each octave increase in frequency. Experimental response curves tend to show this 6 db per octave characteristic when the recorded wave- ■^ ^..^ •V^ v \ w \^ ' THICKNESS LOSS = 277 6 20 LOG Kjf— DECIBELS <5= THICKNESS OF MEDIUM X= WAVELENGTH \ N, X s. V N s» \ 1 1 .!_ 1 1 , _l_ 1 -_ i _!_ _L X, 10 15 20 25 30 35 40 45 0.02 0.04 0.06 0.10 0.2 0.4 0.6 0.8 1.0 2 4 6 8 10 6/\ Fig. 7 — Computed thickness loss as a function of 5/X. 20 length is moderately long and the frequency moderately low. This makes it possible to draw a 6 db per octave line on the measured response char- acteristic in such a way as to coincide with the low-frequency part of the measured response characteristic. As the frequency is increased the meas- ured curve tends to fall more and more below the 6 db per octave line. This is because several kinds of loss come into play as the wavelength decreases or as the frequency increases. Among these losses are: 1. Self demagnetization, 2. Eddy current and other losses in the recording and reproducing heads, and 3. Gap loss due to the finite scanning slit in the reproducing head. The work presented in the first sections of this paper indicates that the 1156 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 following two kinds of loss should be added to this list: 4. Spacing loss due to imperfect magnetic contact between the repro- ducing head and the recording medium, and 5. Thickness loss. Of these five losses three can be evaluated quantitatively either by direct measurement or by calculation from theory. The remaining two are self- demagnetization and spacing loss. In this section the known losses will be evaluated for a particular re- cording system. This leads to a response curve which can be compared with the measured curve. The difference between the two curves should be due to self-demagnetization and to spacing loss provided the above list of losses is complete. -35 -40 EDDY LOSS ^ J,C — [d -so ^^ "N V. \ o ■-> -55 0; X «+- O -60 O i -65 i i- /^ > ■r]^ \ ^ \ ^ m/ \ -70 -75 i_ -L. 1 — L_ -1- -1- 1 ...1,._ -L- _L 0.6 0.8 1.0 2 4 6 8 10 20 40 FREQUENCY IN KILOCYCLES PER SECOND 60 80 100 200 Fig. 8 — Measured eddy current loss as a function of frequency. The recording system used is the one shown in Fig. 1 with the speed set at 15.5 in./sec. for both recording and reproducing. A constant signal cur- rent of 0.1 ma was used for recording with the 55 kc bias adjusted to give maximum open circuit reproduced voltage. Eddy current losses were measured as indicated in Fig. 8 by sending a measured constant current i through a small auxiliary winding around the pole tip and measuring the open circuit voltage developed across the normal winding of the head. Any departure of this measured voltage from a 6 db per octave increase with increasing frequency is due to losses in the head which will be loosely called eddy current losses. Other kinds of loss may enter into this measurement (as, for example, loss due to the self-capaci- tance of the winding) but in the frequency range of interest, eddy losses predominate. REPRODUCTION OF MAGNETICALLY RECORDED SIGNALS 1157 By a completely different sort of measurement,^ J. R. Anderson has arrived at a similar value for eddy current loss in this type of head and has shown that approximately the same loss occurs in both the recording and the reproducing process. For this reason it seems proper to assume that eddy currents account for just twice the loss measured by the method of Fig. 8. The loss due to the finite gap in the reproducing head is computed from the well known relation.^ Gap loss = 20 logi- '^^^^ sin irg/X) where g is the effective gap width in inches and.X is the recorded wave- length in inches. Thickness loss is computed from equation (5). It must be remembered that this loss was derived on the assumption of uniform magnetization throughout the thickness of the recording medium. This may be a fairly good approximation to the actual state of affairs for a thin medium such as the one being considered, but obviously if the thickness of the medium is large compared with the width of the recording gap then the recording field will not penetrate uniformly through the medium and the derived thickness loss function will not apply. The derived equation (3) indicates that at low frequencies the reproduced voltage should be proportional to the thickness of the medium. If the thick- ness of the medium is increased beyond the limit to which the recording field can penetrate, this will no longer be the case and further increase in thickness will have no effect on the response. Data presented by Kornei^ on the cobalt-nickel plating being considered here shows that the low-frequency response is approximately proportional to the thickness of the medium for values of thickness between 0.075 mil and 0.5 mil. This may be taken as an indication of approximately uniform penetration through these thicknesses and hence tends to indicate that the derived thickness loss function should be applicable in the case of the 0.3 mil plating being considered here. The effects of these losses are shown in Fig. 9 along with measured fre- quency response data. Consider first the experimentally measured response 5 In unpublished work, J. R. Anderson of the Bell Telephone Laboratories has made use of the fact that eddy losses depend on frequency while all other magnetic recording losses depend on wavelength. By recording a single frequency and playing back at vari- ous speeds he determined the loss on playback. By recording various frequencies with recording speed adjusted to give constant recorded wavelength and using a single play- back speed he evaluates the eddy loss in the recording process. 6 S. J. Begun, "Magnetic Recording," p. 84, Murray Hill Books, Inc., New York. 1158 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 data shown as circles falling near the lowest curve. Some of the measured points have been omitted to avoid crowding but enough remain to show the trend. At low frequencies these points fall along a line of approximately 6 db per octave. A straight 6 db per octave line labeled 1 has been drawn through these points and extended as shown in the figure. This line is the base from which the various losses must be subtracted. Curve 2 shows the effect of sub- tracting the computed thickness loss. When eddy losses and gap loss are 50 45 35 30 LOSS d =0.23 MIL -d = 0.36MIL -d = 0.81MIL 0.3 0.4 0.6 0.8 1.0 2 3 4 FREQUENCY IN KILOCYCLES PER SECOND 6 a 10 20 Fig. 9 — Computed response curves and measured response points. also taken into account, curve 4 is obtained. The difference between this curve and the lowest measured response points is presumably due either to self-demagnetization, to spacing loss, or perhaps to both. There is one clue which may be of help in deciding how much of this loss should be attributed to self-demagnetization and how much to spacing loss. This clue comes from the fact that the form of the spacing loss function is known. Any part of the loss which is due to spacing must follow the equa- tion Spacing Loss = 54.6 ((//X) db REPRODUCTION OF MAGNETICALLY RECORDED SIGNALS 1159 whereas there is reason to believe that the effects of self-demagnetization cannot possibly account for more than something like ten or fifteen db loss and hence could not follow the equation given above. In view of this it seems reasonable to try as a first guess the assumption that all the unexplained loss is due to spacing. If this assumption properly accounts for the shape of the measured re- sponse curve there will be at least some reason to suppose it may be correct; particularly so if the required amount of effective spacing seems reasonable. The lowest solid curve, No. 7 of Fig, 9, has been computed on this basis. That is, a spacing loss corresponding to 0.81 mil effective spacing has been subtracted from curve 4. It is seen that this computed response curve fits reasonably well with the measured points. Furthermore, 0.81 mil effective spacing corresponds to quite reasonably good magnetic contact. If this interpretation of the measured data is correct then it is obvious that the high-frequency response could be improved a great deal if more intimate magnetic contact between the reproducing head and the recording medium could be achieved. To this end an attempt was made to lap the surface of the head in such a way as to remove material very gently and slowly. After lapping, the response was appreciably improved as indicated by the set of measured points around curve 6. This curve was computed assuming an effective spacing of 0.36 mil. Note that the computed curve now fits the measured points very well indeed. After still more lapping,^ the measured response points around curve 5 were obtained. In this case it is necessary to assume only 0.23 mil effective spacing in order to account for the measured curve. Further lapping failed to give further improvement in response but a defect in the head which may account for this has since been found and it is believed that with great care one might actually measure something very close to curve 4. To summarize, this is what seems to have been found. It is possible to compute a response curve taking into account gap loss, eddy current losses, and thickness loss. If this curve is compared with the final measured re- sponse curve it is found that the measured curve gives less high-frequency response than was computed. The difference between the two curves is just the right sort of function of frequency and of just the right magnitude to be accounted for by an effective spacing of 0.00023 inch between the reproducing head and the recording medium. It seems probable that the effective spacing could not have been much smaller than this value and therefore it may be correct to assume that practically all the unexplained ' After each lapping it was found that smaller values of bias current sufficed to give maximum reproduced voltage. This is presumably because the improved magnetic con- tact made the bias current more effective. 1160 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 high-frequency loss is due to spacing. This would imply that, under the conditions of this experiment, self-demagnetization has a negligible effect on frequency response. In any case it seems clear that the intimacy of magnetic contact between the reproducing head and the medium can have a very pronounced effect on high-frequency response. The condition of the surface of the reproducing head (and of the tape) may have more effect on high-frequency response than any other single factor. In a very fine piece of pioneering work Liibeck found empirically that a term of the form e~^^^^ was needed to account for the shape of measured response curves. Guckenburg^ has recently written more on this subject. Both authors have assumed that this term has to do with self-demagnetiza- tion and that Xi is determined by the magnetic properties of the recording medium. The experiment just discussed and the theory presented in this paper suggest, on the other hand, that Xi is not a function of the magnetic properties of the recording medium but rather is determined by the intimacy of magnetic contact between reproducing head and medium. If this is the case then Lubeck's Xi is related to the d of this paper through the equation Xi = Iwd. Guckenburg reports Xi = lOO^u for the best available medium. This cor- responds to d = 0.625 mil and yields a response curve a little better than the poorest measured curve of Fig. 9. The best measured curve of Fig. 9. corresponds to Xi = 37//. ACKNOWLEDGEMENTS The author wishes to express his appreciation for the encouragement and guidance of Mr. R. K. Potter, Mr. J. C. Steinberg, and Mr. W. E. Kock. APPENDIX I THE FIELD DUE TO A FLAT SINUSOID ALLY MAGNETIZED MEDIUM The Field in Free Space It is convenient to begin by evaluating the field inside and outside the recording medium when the medium is in free space. By making use of the •H. Ltibeck, "Magnetische Schallaufzeichnung mit Filmen und Ringkopfen," Aku- sticheZeit., 2,27$ (1937). ' W. Guckenburg, "Die Wechselbeziehungen zwichen Magnettonband und Ringkipf bie der Wiedergabe," Funk und Ton, 4, 24 (1950). REPRODUCTION OF MAGNETICALLY RECORDED SIGNALS 1161 method if images, this solution can be used to find the fields which exist when the medium is under an ideaHzed reproducing head of permeability /x. Also, the free space solution may be of use in evaluating the effect of self demagnetization since the demagnetizing field is computed. Let the recording medium be an infinite plane sheet of thickness 5 and choose rectangular coordinates so that the central plane of the medium lies in the x~y plane as shown in Fig. 10. Let the permeability of the recording medium be unity and let the inten- sity of magnetization inside it be given by (6) h = Im sin (2irx/\) Iv = Iz = 0 z A dH/ dHz (■^fii^o) y w ^y^ dHx' \ \ 1 (x.z) CZJ dz / dx ( 1 i 1 RECORDING MEDIUM Fig. 10 — Coordinate system for flat tape calculations. This is equivalent to a volume density of "magnetic charge" given by p = — div / ^ __ dh dx - (ItIJX) cos (27rVX) (7) The problem then is to compute the field at a point (xo , So) due to this charge. Consider the field at (.to , zo) due to the element f/.v dz at {x, z). This element amounts to an infinitely long line of uniform charge density. The field due to such a distribution is directed perpendicular to the line and has a magnitude equal to twice the linear charge density divided by the distance from the point to the line. 1162 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 In the present case this leads to dH, = -(47r/^/X) J %-T-T^ T^ cos (27rx/X) dx dz (xo - xY + (zo - zY (8) dH, = -(4irIm/\) -, ^^. 7 f r2 COS {lirx/X) dx dz {xq - xY + (zo - z)^ The total field at {xq , Zo) is obtained by integrating with respect to x over the range — <» to + oo and with respect to z over the range —5/2 to +5/2. In carrying out the integration over x it is convenient to make the substitution (xo - x)/{zo - z) = p (9) dx = — (zo — z) dp Neglecting terms which obviously integrate to zero, this gives H, = (4x/„A) sin (2xVX) f' [ O sin [M., - .) j>Al I ^^ S. = {4xWX) COS (2WX) /■"' r r '"" t^"^^-/^^/^J dJrf. J-«/2 Uoo 1 + ^^ J 20 > 2 The integrals in brackets can be found in tables. ^° Carrying out the inte- gration gives a/2 -a/2 .a/2 H, = -{4tIJ\) sin (27r:x^/X) f £r. = -(47rVx) cos (27rVX) / e-''^''-'^'^ Zo > z (11) dz J-S/2 which integrate to H. = -2^/„ sin (27rVX)^"'"°^'[e'*^' - ^"''^1 £r, = -2x7^ cos (27rVX)«"'"°^'[«'*^' - ^"'*^'l 2o > 5/2 (12) '» D. Bierens de Haan, "Nouvelles Tables D'Integrales D^finies," p. 223, Leide, En- gels, 1867. REPRODUCTION OF MAGNETICALLY RECORDED SIGNALS 1163 Below the recording medium, that is for Zq < —6/ 2, H. = -lirlrr, sin (27rVX)^'"'"°^'[e"'' - e"'*^'] zo < - 8/2 (13) SEMI- INFINITE BLOCK OF PERMEABILITY /I d ^RECORDING MEDIUM I / (14) Fig. 11 — Flat tape under idealized reproducing head. Inside the recording medium, H, = - (4x /^/X) sin (2t^/X) r r ^-2x(«o-.)/x ^^ _^ f"" ^+2,(.o-.)/x ^1 L**-«/2 Jzo J H, = - {ArljX) cos (27raK,/X) which integrate to Zr, = - 27r/^ sin (2irXo/\)l2 - ^-'^/^(g-^-o/x _^ ^2«o/x>^j H, = 2irlm cos (2xVX)e"''''(e-''^»'' - e'^''"") 8/2 > zo > -5/2 The Fields in and Under the Reproducing Head The idealized reproducing head amounts simply to a semi-infinite block of high permeability material with a flat face spaced a distance d above the surface of the recording medium as shown in Fig. 11. (15) 1164 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 The problem of most interest is that of finding the x component of mag- netic induction, Bx , at any point {xo , Zo) in the ideahzed head and inte- grating this with respect to Zo to determine the total flux passing through unit width (in the y direction) of a plane x = xo . This plane will then be allowed to move with a velocity v by putting Xq = vt and the time rate of change of flux will be computed. Except for the effects of eddy currents, self demagnetization, gap loss, etc. (which are treated separately) this rate of change of flux should be proportional to the open circuit reproduced voltage. This is the only result of which direct use will be made but for the sake of completeness all the field components will be evaluated not only in the idealized head but also at all other points. This problem is completely analogous to the problem of a point charge in front of a semi-infinite dielectric treated by Abraham and Becker^^ and can be solved by use of the method of images. The Field Inside the High Permeability Head By analogy with the treatment of Abraham and Becker, the value of B in the high permeability head is computed as though this head filled all space and as though the recording medium were polarized to a value 2/i/(/Li +1) times the actual value of polarization present. This gives di- rectly from equations (12), B. = -[2m/(m + mTTlm sin (2TXo/\)e-''''''\e''"^ - e""^) B, = -[2/z/(m + m^Im cos (27rVX)^"''^'^''(^'^''' - ^"'''') Zo > ^ + 8/2 The Field Below the Reproducing Head Again by analogy with the treatment of Abraham and Becker, the field outside the idealized head is computed as though no head were present. The field is that due to the actual magnetized medium plus the field due to an image of the medium (centered about z = 2d -{- 8). The intensity of magnetization of the image medium is — (/u — 1)/(m + 1) times the in- tensity of magnetization of the actual medium. The field due to the image medium is computed from equations (13) after suitable modification. The required modifications are: 1. Multiply the right hand sides by — (/x — 1)/(m + 1) to take account of the magnitude and sign of the image magnetization as just dis- cussed, and 2. Replace zc by So — (2d -\- 8) io take account of the position of the image. " M. Abraham and R. Becker, The Classical Theory of Eleclricily and Magnetism. |). 77, Blackie and Son Limited, London, 1937. REPRODUCTION OF MAGNETICALLY RECORDED SIGNALS 1165 This gives the field due to the image plane as //xi = 27r/m , , sin {2'KXQ/K)e " {e ' - e ) " + ' (17) Hzi = — lirlm ' — ;— 7 COS (27r.r()/X)e (e — e ) M + 1 2o < (/ + 5/2 To this must be added the field due to the real medium which is given by equations (12) when h/2 < Zq < d -{- 5/2, by equations (15) when —5/2 < Zo ^ 5/2, and by equations (13) when Zq < —5/2. Performing this addition gives the following results: Between the head and the recording medium, H. = -2irl„. sin {2irXo/\)e-'''''\e^''^ - e'^"^) [. M -" 1^ -2T(2d+4-2zo)/X (18) d -{- d/2 > Zo > 5/2 Inside the recording medium, Hx = — 2irlm sin {2irXo/\) [2 _ -»5/X/g2r^o/X , ^-2tjo/X\ _ M_"" J ^-2x(2d+«-zo)/X/gT5/X _ ^-'i/Xj i7, = -27r/^ cos (27rV^) (^'^) [-x6/\/ 2T20/X _ -2tzoI\\ , M ~ 1 ^-2r(2d+S-zo)/X/ »-a/X _ g-»«/X\ M 4- 1 J 5/2 > 2o > 5/2 Below the recording medium, Hx = -27r/.sin (27rWX)^''"''(^'''' - e''"') r M — 1 -2r(W4«)/xl ■ L^ " 7+"i J Z/, = 2,/„ cos (2TX,/\)e""%"" - e-'") (20) ^"r+"i' J 2« < -V2 1166 the bell system technical journal, october 1951 The Flux per Unit Width in the Idealized Reproducing Head The desired flux per unit width is computed from x = f B^dz (21) Jd+hl2 where Bx is given by equation (16). Performing the indicated integration gives /, d(i>x At . T /I -2irdl\\ -27rd/X dt M + 1 iwviM - e-'^'ne-'''''" cos (coO (23) where co is lir times the reproduced frequency. This is the result for unit width of the reproducing head. For a width of W cm., % : f- iTWviM - .-^'*'^)e-^'^'^ COS (<./) (24) The Case of Perpendicular Magnetization Equation (23) was derived for the case of pure longitudinal magnetiza- tion as defined by equations (6). It will now be shown that this same result is obtained for dx/dt if the magnetization is purely perpendicular, that is if /« = —Im cos (27rxA) (25) Ix= ly = 0 In this case the divergence of I is zero except at the surface of the tape and this magnetization is equivalent to a surface distribution of magnetic charge on the top and bottom surfaces of the tape. The magnitude of this charge density is just equal to Ig so that on the top surface of the tape there is a surface density of charge given by a = -Im cos (27rx/X) at z = 6/2 (26) and on the bottom surface of the tape there is a surface density of charge given by 0- = /m cos (2WX) at z = -5/2 (27) Since the permeability of the recording medium is assumed to be unity, this problem reduces to that of finding d^x/dt due to two infinitely thin REPRODUCTION OF MAGNETICALLY RECORDED SIGNALS 1167 tapes of the sort to which equation (23) applies. One of these tapes is at z = 8/2 and the other at z = —8/2. The problem then is to rewrite equation (23) for a very thin tape and in terms of surface density of charge. As 5 approaches zero, equation (23) reduces to % = - ^ 4^/.(2,r6/X).-^''^^^ cos (co/) (28) at M + 1 From equation (7), the volume density of charge in this tape is p = - {lirlm/X) cos (Ittx/X) But as 5 approaches zero, the longitudinally magnetized tape to which equation (28) applies becomes equivalent to a surface distribution of mag- netic charge of surface density equal to 8p. This amounts, for the thin longitudinally magnetized tape, to a surface charge density of (71 = -(27r5A) cos (Ittx/X) (29) But the charge density on the top side of the perpendicularly magnetized tape is given by equation (26). Comparing these two values shows that the surface charge density in the thin longitudinally magnetized tape is just 27r5/X times as great as the surface charge density on top of the perpendicu- larly magnetized medium. This means that d4>x/dt due to the top side of the perpendicularly magnetized tape can be obtained by dividing the right hand side of equation (28) by 2t8/\. This gives dt M + 1 ^irvln.e-'''"' cos (a,/) (30) due to the top side of the tape. The contribution from the bottom side is obtained from equation (30) by replacing d by d -\- 8 (since the bottom side is spaced d -\- 8 from the reproducing head) and changing the sign. Adding these two contributions gives for the total '^= --JL- i^Ui - e-""\-'"" cos (0,0 (31) dt M + 1 This is the same as equation (23) and so the desired result has been established. Note from equations (6) and (24) that in order to get the same result for the perpendicular and longitudinal cases it was necessary to assume a 90- degree phase difference between 7^ and 7, . The usual type of recording head lays down a pattern of magnetization which is neither purely per- 1168 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 pendicular nor purely longitudinal but the two components are always in phase. This means that the two contributions to dx/dt add as vectors at 90 degrees. If the intensity of magnetization in the recording medium is held constant while the relative values of perpendicular and longitudinal components are changed, the only effect on the reproduced signal is a change of phase. APPENDIX II THE FIELD DUE TO A ROUND WIRE In Appendix I the field due to a sinusoidally magnetized fiat medium such as a tape has been calculated and the rate of change of flux in an MAGNETIC PLATING ON NONMAGNETIC CORE Fig. 12 — Coordinate system for round wire calculations. idealized reproducing head has been evaluated. The analogous calculations for a round wire have also been carried through and it is the purpose of this section to present some of the results. The derivation of these results seems too tedious and long to be presented here. The Recording Medium Let the recording medium be a wire, the axis of which lies along the x axis as shown in Fig. 12. Let the radius of the wire be a. To take account of plated wires as well as solid magnetic ones, let the wire have a nonmag- netic core of radius ao . Let the cylindrical shell between Oo and a be mag- netized sinusoidally in the x direction so that /x = Im Sin (27rVX) By putting a© = 0 in the expressions which follow it wil obtain the result for a solid magnetic wire. (32) be possible to REPRODUCTION OF MAGNETICALLY RECORDED SIGNALS 1169 The Field in Free Space If no reproducing head is present to disturb the field distribution, the computed field components at a point (ocq , ro) are H^ = -4TrIm Sin (27rVX)^o(27rro/X)[(27ra/X)/i(2ira/X) -(27raoA)/i(27raoA)] (33) Hr = -^irlm Cos (2irVX)i^i(27rro/X)[(27ra/X)/i(27ro/X) -(27rao/X)/i(27rao/X)] ro > a A discussion and tabulation of the I and K functions can be found in Watson's "Theory of Bessel Functions. "^^ The field due to a solid magnetic wire is obtained by setting Oo = 0 in equations {33). This gives H, = -^Im Sin (27rVX)(27ra/X)A:o(2WX)/i(27ra/X) Hr = -^Im Cos (27rVX)(2xa/X)i^i(27rro/X)/i(27rflA) ro> a The Rate of Change of Flux in an Idealized Head It has not been possible to carry out the calculations for an idealized head which is a satisfactory approximation to the grooved ring-type head often used in wire recording. The results presented below will apply only to repro- ducing heads which completely surround the wire. In this case the idealized head is an infinitely large block of core material of permeability m pierced by a cylindrical hole of radius R in which the wire is centered as shown in Fig. 13. At any point (xq , ro) in the permeable medium the components of flux density can be shown to be (35) Br= oHr ro>R where a = (36) (m - l){2irR/\)lo{2irR/\)Ki{2irR/\) + 1 and Hx and Hr are given by equation (33). 12 G. N. Watson, "A Treatise on the Theory of Bessel Functions," p. 79, 361, 698, Cambridge Univ. Press, 1922. 1170 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 The total flux through a plane x = ocq in the permeable medium is ob- tained by integrating 0« = / B^irr) dr Jr This gives ^ = -2\^odm sin (2TXQ/\){2wR/\)Ki{2TrR/\)[{2Ta/\)Ii(2Ta/\) -(2xaoA)/i(2TaoA)] (37) (38) ^^^~>^^^ '^ S\^ U ^^ ^— -^^^ ^ >^^^^^^/.^ ^ " f^^ ^ r/r7f~-^ "'' L pU aVTjrj---^ 1 '/^i^y -^ 1 // ' 1 ^^^>^ ^\^ CYLINDRICAL HOLE OF RADIUS R IN INFINITE BLOCK OF PERMEABILITY /t Fig. 13 — Round wire surrounded by idealized reproducing head consisting of an infinite block of core material of permeability /x. K the plane x = ocq moves with a velocity v with respect to the wire so that xq = vty then ^ = -iirXavIm cos M{2wR/\)Kii2'!rR/\)[(2Tra/\)Ii{2Ta/\) d^ (39) - (2iraoA)/i(27raoA)] where w = 2^-/ and / is the reproduced frequency. Speclal Cases Equation (39) can be used to compute the response of a simple repro- ducing head consisting of a single turn of very fine^' wire as shown in Fig. 14. In this case m = 1 and equation (36) shows that a = \. Furthermore if the wire is solid so that oo = 0, equation (39) reduces to " Unless the diameter of the wire is small compared to the recorded wavelength there will be additional loss not accounted for by 39. REPRODUCTION OF MAGNETICALLY RECORDED SIGNALS 1171 ^ = -^TrXvIm COS M{2TR/\){2Ta/X)Ki{2wR/\)li{2Tra/\) (40) As X approaches infinity, Ki{2irR/\) approaches \/2'kR and Ii{2ira/\) approaches ira/X so that, for very long wavelengths, equation (40) reduces to % = -Mmv{2'K/\){W) COS (coO (41) at This relation (which could have been derived in a much simpler manner) should be useful for the experimental determination of the intensity of magnetization, Im . SINGLE TURN OF RADIUS R CONCENTRIC WITH WIRE WIRE OF RADIUS a Fig. 14 — Elementary reproducing head consisting of a single turn of wire. Another case of some interest corresponds to a high permeability repro- ducing head which surrounds the wire. In this case m is great enough so that equation (36) reduces to " " {2TR/\)h{2TR/\)K,{27rR/\) ^^^^ If it is assumed, in addition, that the wire is solid so that flo = 0, then equa- tions (42) and (39) give ^ = -^TrXvIm cos (co/)(27ra/X)7i(2xa/X)//o(2Ti?/X) (43) dt Comparison between Round Wire and Flat Medium Response It is interesting to compare equation (43) with equation (24) to see how the response characteristic of a round wire compares with that of a tape. Assuming m » 1, the appropriate equation for the flat medium is ^' = -ArWvI^ cos (coOd - e-''^"'')e-''"' (44) at 1172 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 To compare equations (43) and (44), consider first the limiting cases of very long and very short wavelength. As X approaches infinity they re- duce to at for the wire and dt = -dW(STv/\)Im cos M (45) (46) for the tape. These two expressions are identical provided the cross section area of the wire, (tta^), is the same as that of the recorded track on the tape, {8W). -5 -10 -15 -20 -25 -30 -35 -40 -45 WIRE^. ^^^* <" "' >K ■ y "--TAPE \ V ^ \ \ ^ ^ DIMENSIONS IN MILS TAPE j WIRE WIDTH =25.13 1 DIAMETER =8.00 THICKNESS = 2.00 i SPACING =0.50 SPACING = 0.50 1 V = 12.56" PER SEC. \ V > y \ y \ \ 1 1_ „,1. 1 1 , .^ 1— 1 ^ \ 0.02 0.1 0.2 0.4 0.6 0.8 1.0 2 4 FREQUENCY IN KILOCYCLES PER SECOND Fig. 15 — Computed responses for wire and tape showing that the responses are very similar provided the dimensions of the wire and tape are suitably related. As X approaches zero, the two expressions reduce to dt for the wire, and Im COS (co/) d^ dt = -47rt^(l4^)g-'"^'X COS (co/) (47) (48) for the tape. Suppose that the reproducing head makes reasonably good contact with the wire so that s/ R/a = 1. In this case equations (47) and (48) are identical provided the circumference of the wire, {lira), is the same as the width of the recorded track on the tape and p)rovided also the effective spacing be- tween reproducing head and medium is the same in the two cases, {d = R — a).\n both cases only a thin surface layer of the recording me- dium is effective in producing high frequency response. For this reason the REPRODUCTION OF MAGNETICALLY RECORDED SIGNALS .1173 high-frequency response is independent of the "thickness" of the medium and is directly proportional to the ''width" of the track provided 2ira is interpreted as the width of track on a wire. The comparisons which have just been made indicate that if the dimen- sions of a wire and of a tape are suitably related, the two media should give identical response at very high and very low frequencies provided they are equally magnetized. The dimensional requirements are 7ra2 = 8W, 2Tca = W, and (49) R- a = d In order to show how the computed responses compare at intermediate frequencies, numerical calculations have been made for a special case in which equations (49) are satisfied. The case chosen is that of a wire 8 mils in diameter moving at a velocity of 12.56 in./sec. past a reproducing head which is effectively one half mil out of contact with the wire {R — a = 0.5(10)"^ in.). By equations (49) the corresponding flat medium is a tape which is 2 mils thick and 25.13 mils wide. The tape is assumed to be moving with a velocity of 12.56 in./sec. past a reproducing head which is also effectively one half mil out of contact (d = 0.5(10)~^ in.). In this case the numerical constants in equations (43) and (44) are equal. That is, S-n^av = 4TrWv = 25.6 cm.Vsec. and the quantity to be computed and compared for the two cases is 2^^"^^"2T67; The computed curves are shown in Fig. 15 from which it can be seen that they coincide at low and high frequencies as planned and that further- more they differ by no more than 1.5 db in the middle range of frequencies. As has been pointed out, equation (43) applies only to the unusual case in which the head completely surrounds the wire. The similarity of the two curves of Fig. 15, however, suggests a way of computing approximately the response to be expected when the wire head makes contact with only a part of the circumference of the wire. It suggests that the computation be carried out as though the wire were a flat medium of suitably chosen dimen- sions. In order to make the high frequency end come out right one would expect that W in equation (44) should be given a value equal to the length of the arc of contact between the wire and the head. To make the low frequency end come out right, 5 must be given a value which makes the cross section area of the tape equal to that of the wire, i.e. such that 8W = 7ra2. Some Results Concerning the Partial Differential Equations Describing the Flow of Holes and Electrons in Semiconductors By R. C. Prim, III (Manuscript Received June 22, 1951) The subject equations are investigated with the aim of establishing some general properties of the flow fields which they describe, including the existence or non-existence of classes of exact solutions having certain formal properties. The results include a number of geometric characteristics of the vector fields involved, a suggestive reformulation of the partial differential equations re- stricting carrier concentration and electrostatic potential, and several classes of exact solutions involving arbitrary constants and/or functions. Of particular interest is a family of solutions in closed form for the steady-state, no-recom- bination case involving an arbitrary harmonic function in three dimensions. Table of Contents A. Introduction 1174 B. Some Properties of the Current Density Vector Fields 1177 C. Formulation of Partial Differential Equation System Restricting (P and V 1180 D. The Recombination Rate Function (R 1182f E. Addition of Arbitrary Time Functions to V and 3C 1183 F. Summary of Solutions for No Recombination or Time Variation 1183 G. Solutions With V = V(t) 1185 H. Solutions With (P = (P(t), N y^ 0 1187 I. Solutions With (P = (P(t), N = 0 1188 J. Solutions With 3C = SC(t), N ^0 1188 K. Solutions With V = t)((P, t), grad (9^0 1189 L. Solutions With V = vlh, t), (P = (?ih, t), gradCP j^ 0, div grad /f = 0, iV 5^ 0 . 1191 M. Solutions With V = V{h,t),(9 = (?{h, /), grad (P 9^ 0, div grad h = 0, N = 0 . 1198 N. Construction of Solutions from Orthogonal Harmonic Fields, N 9^ 0 1202 O. Construction of Solutions from Orthogonal Harmonic Fields, iV = 0 1202 P. Superposition of a Harmonic 5C Field, N 9^ 0 1203 Q. A Partial Differential Equation in Terms of 3C Alone, N 9^ 0 1203 R. Sample Application of the Results of Section L: Spherical Symmetry, iV 5«^ 0 . . . 1205 S. Sample Application of the Results of Section M: Spherical Symmetry, N = 0 . . 1210 T, Summary List of Symbols 1212 U. References 1213 A. Introduction THIS paper is concerned with the system of relations describing the flow of holes and electrons in the interior of a homogeneous semiconductor subject to the assumption of constant temperature, electrical neutrality, and constant difference in concentrations of ionized donor and acceptor centers. These relations are: div II. --,[« + If] (1) div||„ = el(R + ^^| (2) 1174 FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1175 lip = -Upe^p grad V + ~ grad p] (3) o r j^j- ~\ ||n = — Mn e n grad V — — grad n (4) n — p = fiQ — po = N (a, constant) (5) n, p > 0 (6) ll = ll+l|n (7) wherein n: concentration of negative carriers (electrons) p: concentration of positive carriers (holes) no: thermal equilibrium value of n pQi thermal equilibrium value of p o lip! hole current density vector o ||„: electron current density vector o 1 1 : total current density vector /: time variable e: magnitude of electronic charge k: Boltzmann's constant Hpi hole mobility constant * fin- electron mobility constant T: absolute temperature (assumed constant with time and uniform) V : potential of electrical intensity field (R: electron-hole recombination rate function (will usually be regarded as depending on p — po and « — «o or equivalent variables). These relations have fundamental application to transistor electronics, photoelectric effects, and related phenomena. Detailed discussions of their physical bases will be found in References 1 and 3. In brief, (1) and (2) are conservation conditions for the positive and negative carriers; (3) and (4) express the dependence of the local current densities on the electrostatic potential gradient and on the carrier concentration gradients (i.e., on con- duction and diffusion); (5) expresses the condition of electrical neutraUty under the assumption of a constant difference in concentrations of ionized donor and acceptor centers; and (6) and (7) are self evident. The present study is directed toward the discovery of (1) general proper- ties of the flow fields inside semiconductors and (2) families of exact solu- tions to the flow equations. The approach to the latter objective is through 1176 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 the ^'inverse method" which has proved very useful in the study of vari- ous non-Hnear partial differential equation systems in mechanics. In the inverse method, one proceeds by formal devices suggested by the equations under study to try to find families of solutions to the equations which in- volve arbitrary constants or, preferably, arbitrary functions. This is done without reference to any preconceived boundary value problems. After a pool of such families of solutions is available, it can be examined from the point of view of finding boundary value problems of interest consistent with any of the solutions in hand. The likelihood of finding solutions of interest in this way is of course greatly enhanced when the solutions in- volve arbitrary functions. Aside from providing solutions of some useful boundary value problems, the solutions found by the inverse method constitute a reference bank of non-trivial exact solutions against which to check numerical methods and approximation schemes (based, for ex- ample, on the assumption that a particular term can be neglected) for solving problems of more immediate practical interest. J. Bardeen has demonstrated (in Reference 2) how the steady-state be- havior of contact-semiconductor combinations can be explained on the basis of the characteristics of (1) the flow field inside the semiconductor and (2) those of the barrier layer at the contact. The present study is con- cerned in this connection only with the first of these influences. It provides, for example, a complete solution for the spherically symmetric flow field without recombination for arbitrary currents^ — a generalization of the zero- total current solution given by Bardeen. In the absence of surface recom- bination this spherically symmetric solution provides the hemispherically symmetric flow field in the neighborhood of a point contact on a plane surface and remote from other electrodes or surfaces. This spherically sym- metric solution is contained as a particular case in a family of solutions involving an arbitrary harmonic function in three dimensions. Other choices of the harmonic function can be made to yield flow fields associated with numerous electrode configurations of immediate practical interest, for ex- ample that of the type-A transistor. The objective of the present paper is to find (or establish the non-exist- ence of) broad classes of solutions, and not to undertake detailed studies of any particular solutions. Such detailed studies of particular cases from the family of solutions mentioned above (and from other families found in this study) will form the subject matter of papers dealing with specific flow field configurations. However, in order to illustrate the interpretation of mathematical arbitrary constants in terms of basic physical parameters, the analysis of the spherically symmetric solution mentioned above is car- FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1177 ried up to the point of actual substitution of numerical values in the formulae. Note: In the following, functions and constants described as "arbitrary" are to be considered as being subject nevertheless to the restrictions implied by (6). In any particular case it is an elementary matter to determine these restrictions and we shall not usually carry out this detail. Also, ''arbitrary" functions are subject to appropriate dif- ferentiability conditions readily evident in any particular case. B. Some Properties of the Current Density Vector Fields o o Several interesting properties of the current density vector fields || p ,|| n , o and II are easily found from {S)-{5). It is evident that (3) and (4) can be rewritten as \\v = -envP grad (t) + ^ in p\ (8) and c / j^J- \ !|n = — ^Mn n grad [y — — In w j . (9) From (3), (4), and (7) we have II = -eiyLnfi + ixpp) grad V ^- kT grad (jinfi - Upp) (10) which because of (5) can be rewritten as fl = -e (Mn « + MP P) grad \v - ^"t^" In (m„ » + Mp p)\. (11) L ^ Mn I Mp J Now (8), (9) and (11) are all of the form U = <^ grad ^ and hence obviously satisfy the condition U • curl u = 0. Therefore we have CO o Theorem 1: || p , || n , and || are surface-normal vector fields. From (8)-(10) we find, using (5) curl iIp = -e/zp grad p X grad V, (12) 1178 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 o curl I In = — e/i«grad/> X grad "0, ^ (13) o curl II = —e(jin + Mp) grad p X grad V, (14) and whence Theorem 2: curl |L curl IL curl !! Mp Mn At' -r ^p o c o That is, curl ||p , curl ||n , and curl j| are constant multiples of one another, and o o o Theorem 3: | |p , | |n , and 1 1 are irrotational if and only if grad /> = 0 {p = pit)) or grad'U = 0 fU = V{t)) or V = V{p, t). The following interesting relations can be obtained from (8) and (9) (they are really consequences of Theorem 1) : o o curl Up = grad In /> X ||p (15 and o o curl Ijn = grad In w X ||n. (16) Now from (3) — (5) we find lip X fin = e^nHpkT{n + p) grad p X grad V (17a) = innHpkT(n + p) grad {n + p) X grad V (17b) = iennUpkT grad (n + pY X grad V (17c) = WnUpkT curl [(« + pY grad V] (I7d) and and L^ _ II- = grad \nv - - (n + p)\ (18) Mj)« line \_ e J Jl? + Ik ^ -{« + /,) grad U (19) FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1179 [Note: As is suggested by (18) and (19), the total carrier concentration (P = n-\- p = N + 2p = 2n- N {(P>\N\) will frequently appear as the "natural" concentration variable in the relations with which we shall be working. Hence, expressions involving p, or p and n will often be replaced in the sequel by their equivalents in terms of the variable (P. It will be noted that grad (P = 2 grad p = 2 grad n.] Equations (17) and (19) yield at once the following theorems: Theorem 4: The vector field ll X ||„ = II X ||„ = ll X II is solenoidal. Theorem 5: The vector field ' o o / IIp _ lU j jg irrotational with a potential (-eNV + kT(P). Theorem 6: The vector field o o / IIp _l_ Lb J is surface-normal (to the surfaces of constant V). [Theorem 7: ||p, ||n, || , grad "0, and grad p are coplanar vectors. o o o Theorem 8: The flow lines of any two of the fields l|p ,||n , and || coincide if and only if grad /> = 0 {p = pit)) or grad '0 = 0 fU = •U(/)) or V = V{p, /). Also, from (17) and (19) we obtain the curious relations: ^grad(PX (^^+'^) (20a) 2 \Mp M«/ If V 11? = Mp M» o o = -*?(Pcurl(i' + ^") (20b) = -f-[44:)]- 1180 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Finally, by taking the divergence of (7) and making use first of (1) and (2) and then of (5), we obtain: o [Theorem 9: The vector field 1 1 is solenoidal. C. Formulation of Partial Differential Equation System Restricting (P and V A very convenient formulation of the partial differential equations re- stricting (P and V is suggested by (18) and (19). Taking the divergence of these equations and substituting (1) and (2) into the results we obtain: div grad [nv-^-^(9'^= -a{si + Yf\ (21) and div ((P grad V) = ^ U + 1 ^ j (22) wherein for brevity we have set a = f- — Mp Mn and and shall henceforth assume /J ?^ 0, i.e., Hp 9^ fin . Equations (21) and (22) yield immediately a derived equation not containing explicitly the terms introduced by recombination and time variations: div grad f iVT) - — (P j = - - div ((P grad V) (23a) div (^ + ^ (P) grad V -— grad (P 1 = 0 (23b) or or Either the set (21) and (22) or one of the forms of (23) together with either (21) or (22) constitutes a basic set of two partial differential equations deter- mining (P and V. We are here considering (R as CR((P). FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1181 It will be observed that (23) is equivalent to the condition div 11 = 0 (24) established as Theorem 9. (In terms of (P, (10) becomes ,°, ^ _ eU- M.) [fa ^ ^ \ _^ ,^ _ kT Lvi ^ + ^) Srad "^ - Y ^""^"^ ^)1 • (25) In most of the following sections we shall find it expedient to consider separately the cases N 9^ 0 and N = 0 (associated respectively with semi- conductors of the extrinsic and intrinsic conductivity types). For the case y ^ 0, use will be made frequently of new dependent variables ^ and 3C defined by: ■a^^(P (26) kT 3Q, = V- — iS> = V-'\l, (27) That is, (P-gnt (28) t) = ni + 3C (29) will be substituted into relations involving (P and V to obtain the corre- sponding relations in terms of "U and 3C. Incidentally, it will be noted that 11 and 3C have the dimensions of voltage. In terms of *U and JC the basic equations (21)-(23) can be written: divgrad.= -^[cH + |^,^] (30) div[^grad(at+ac)]=f:[cR + g;^^] (31) div [grad 3C + ^ ai grad (U + JC) J = 0 (32) wherein (R will be considered as (R(^). It will be observed that, in the absence of recombination and time varia- tion, (30)-(32) reduce to div grad OC = 0 (33) and [A^ ^ 0] div [ai grad (ni -h OC)] = 0 (34) 1182 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 The elegant form of this set of equations furnished the original motivation for the introduction of the variables 11 and JC. The comparable equations for iV = Oare div grad (P = 0 (35) [N = 0] div [(? grad V] = 0. (36) D. The Recombination Rate Function (R In order to avoid undue confusion in the sequel we shall at this point make some clarifying remarks concerning the function (R. As was stated in the Introduction, we basically regard (R as a function oi p — po and n — no , However, because of (5), any expression in p — po and n — no can be re- placed by one in which (say) p is the only field variable quantity. It is then convenient to regard 61 as a function of p and write it 6{(p). When dealing with expressions in terms of (P and of *U, it is convenient to regard (R as a function of one of these variables and to indicate this fact by writing (R((P) or (R(aL). When we do this we do not mean that (R((P) (say) is the same algebraic function of (P as (R{p) is of p, but rather that (R{p) is the function of p obtained when one substitutes (P = N -{- 2p into (R((P). For example, for constant mean lifetime recombination (Si{p) =i{p - p^) (37a) To (R((P) = ri- ((P - (Po) (37b) (RCa) - ^ (ai - - ^'""^ FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1183 E. Addition of Arbitrary Time Functions to V and OC Since only the gradient of V appears in the basic equations (21) and (22), it is evident that if V = V(x, y, z, /) and (P = (P{x, y, z, 0 are a pair of functions satisfying (21) and (22), then so also are V = Vix, y, z, t) + mit) and 6> = (P(x, y, z, t) where m{t) is an arbitrary time function. And since 1) = 01 + 5C, if 5C = 3C(x, y, z, /) and 01 = Ol(a:, y, z, /) are a pair of functions satisfying (30)-(32), so also are dC = 3C(:r, y, z, /) + w(/) and 01 = Ol(:r, y, z, t). These arbitrary additive functions with zero gradients are physically trivial in that they merely reflect the arbitrariness of the reference voltage level. They will, however, be retained for the sake of formal completeness whenever they appear in the subsequent analyses. F. Summary of Solutions for No Recombination or Time Variation The next ten sections of this paj)er (Sections G-Q) contain a sequence of detailed analyses in which is determined the existence or non-existence of solution fields having certain prescribed formal properties. In most of these studies time variability and recombination are admitted and the analysis includes the establishment of the class of recombination rate functions (R consistent with the property under consideration. In those cases where solutions are found to exist, they are expressed in the simplest convenient 1184 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 terms: in closed form, or as solutions of an ordinary differential equation, or as solutions of a single partial differential equation. The solutions found usually involve arbitrary constants and/or arbitrary functions of various kinds. The present section is intended to provide a skimpy but compact sam- pling of the results obtained in the next ten sections. It will be confined to a simple listing of solutions found and furthermore will contain only the forms to which these solutions reduce when recombination and time varia- tion are excluded. (Some solutions are lost under this reduction.) A heading will indicate the section (s) from which the solution comes as well as the formal property associated with each solution. For the sake of conciseness and simplicity the symbols denoting arbi- trary constants and functions in this section are independent of those em- ployed in the later sections. They are to be interpreted as follows: A , B: arbitrary constants h(x, y^ z) : any harmonic function (or with subscript) {Vf ^): any given solution field [G. grad V = 0] [H, I. grad (P = 0] [J. grad X = 0, .V 9^ 0] rv = A L(P = h(x, y, [V = hix, y, l(P = A 'V = A + Vh{x,y,z) ^ Ne /—, r^ = ^V/^(x,y,z) [K, L. -U = ^{(9), N 9^ 01 7/ \ I ^ A r^ ~ /i(a;, y, z)"] •U = h{x, y, 2) + ^A -^ — {A 9^0) FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1185 (For definition of function A see Equation (87) and Figs. 1 and 2 ) [K, M. -U = 1)((P), .V = 0) 'V = A\n h(x, y,z) -\- B _(P = h(x, y, z) [N, O. gradCP-grad'U = 0] 'V = h{x, y, z) (P = h{x, y, z) provided _grad hi{x, y, s)-grad h{x, y^ z) = ^ [N. grad 01 • grad 5C = 0, N 9^ 0] '"U = \/h^{x, y, z) H- A^(:c, y, z) Ne , — ^ = Yr ^^'^""^ ^» ^^ provided _grad hi{x, y, s) -grad hi{.x, 3;, s) = 0 [P. grad (P- grad ^ = OJ "t) = li + h{x, y, z) (P = ^ provided grad (P-grad h{x^ y, z) = 0. G. Solutions with V = Vit) Our point of view in general is that (P and V (or *U and 3C) are functions of three space coordinates and time, so that V = V(l) implies for example that — = — = — =0. That is to say, we now seek solutions for which dx dy dz everywhere grad •U = 0. (39) From (21) and (22) this condition gives us the following restrictions on 1186 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 (P (and noneon*U(/)): - div grad (P = 0 (40) and Ol((P)+i^ = 0. (41) By operating with div grad on (41) we obtain (R''((P) = 0 (we consistently use primes to denote differentiation with respect to the argument of a function of a single variable — e.g., whence, 2(R((P) = A(P + B (42) (A, B: arbitrary constants). Substituting (42) into (41) we obtain whence or (P = c{x, y, z)e"^' - B/A (A 9^ 0) (43a) (P = c(x, y, z) - Bt {A =Q). (43b) From (36) it follows that div grad c{x, y, z) = 0, (44) that is, c must be harmonic. In brief, if (R((P) is of the form given in (42), any V{t) and (43) constitute solutions to the flow equations for any harmonic c{x, y, z). Other forms of (R((P) admit no solutions with V = V{t). It is evident that when recombination is absent time variation is also absent, and vice versa. The solutions reduce in this case to: "U = C (C: arbitrary constant) (45) (P = c{x, y, z). (46) FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1187 H. Solutions with (P = (P(/), N 9^ O The condition grad (P = 0 (47) yields from (21) and (22) f ^' + ^ (PJ div grad V =- 0 (48) and (P div grad V = ^ UCCP) + ^ ^1 • (49) Two cases arise for (R 7^ 0: Case 1: , 0 = gW + ^ In ae (P + ^— a The restriction on (P is then provided by the result of substituting (67) into (21): divgrad[(P-f ln|5. + ^|] = {(R((P)+i^^]. (68) Any (P satisfying (68) constitutes with (67) a solution having the property desired. If (65) is substituted into (25) it will be found that the condition \ iS /d(P e is equivalent to 1 1 = 0, so that Case 1 is characterized by zero total current. Case 2: V i8 / acP e In this case (66) can be written in the form divg«d^^_ a r/ a V_t)_«:i (grad (P)2 d(9 W ^ / d(9 e ] ^ ' From (69) it follows that (P must be of the form (P {h, t) with div grad h{x, y, z, /) = 0. (70) In summary we have o V Theorem 10: liV = 'U((P, /) with grad (P 5^ 0, then either || = 0 or %) = L V{h, t) and (P = (P(A, I) with div grad h{x, y, z, /) = 0. We shall investigate the restrictions on the functions /f(x, y, z, /), V{h, /), and (P(/f, 0 in the next two sections. Theorem 10 remains unchanged if recombination is absent. If time varia- tion is absent, it simply drops t as a variable in the functions mentioned in the theorem. If both recombination and time variation are absent, the theorem can be strengthened to: [Theorem 11: If both recombination and time variation are absent and •0 = V((9), then V = V{h) and (P = (P(A) with div grad h{x, y, z) = 0. FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1191 L. Solutions with v = Vih, t), (P = (P(/r, /), grad (P t^ 0, Div grad h = Oy N 9^ 0 For formal reasons we shall work, not with the conditions (P = (P(A, /) and V = V{h, t), but with the equivalent conditions ^ = aL(/r, /) and 5C = JC(A, /). (71) The condition grad (? 9^ 0 now implies — r 5*^ 0. dfi Substitution of (79) into (30) and (32) yields— after use of (70): — (gradW =-_[_(R(cu)+__- + ___J and (Vm^ dh\\_ ae ^ I a/i dh ■]S+-S) = ' (72) (73) From (73) we get a^ ^W-^ar ah m^^ ae (74) (y(/) : arbitrary function) which yields upon substitution into (72) : a _ ae (grad «' (75) in which ni, — r , and -rr are, of course, functions of h and of /. dh dh^ In determining the combined implications of (75) and (70) three cases arise accordmg to whether or not -— - = 0 or grad (grad hY = 0. Case 1: dh^ ^ ' grad (grad hY j^ 0. 1192 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 In this case no satisfactory interpretation has been found when time variability is present. When time variation is absent, we work with the conditions (76) m = ni(/?); 5C = 3Q{h) with div grad h(x, y, z) = 0 and arrive : at counterparts of (74) and (75) : 3C' = H - mm' 7 + *a {^-^) {H:3i and {H : arbitrary constant) (77) 3C" (grad hT = (^p^y (grad hf = - ^ (R(ni). (78) From (78) it is evident that (R 9^ 0 implies K" ^ 0 and grad h ^ 0. So we have W + 11 / which is of the form [grad h{x, y, z)f = 4>{h). (79a) Now from (79a) follows grad h X grad (grad hY = 0 (80) which implies that the vector lines of the field grad h are all straight. Since h is harmonic, this restricts the choice of h to the potential fields associated with a uniform parallel flow, a straight line source, or a point source. Hence, for suitably chosen rectangular coordinates (x, y, z), circular cylindrical co- ordinates (p, dj z) or spherical polar coordinates (r, 6, 0), the only possibili- ties, are respectively h= x-^ (grad hf = 1 (81a) or A = In 1 -^ (grad hf = - = e^ (81b) P P^ FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1193 or A = i ^ (grad hf = 1 = h\ (81c) The possibility h = x violates one defining condition for the present case (i.e., grad (grad h)- ^ 0) and hence will be left for consideration in Case 3. The remaining two possibilities lead respectively to the following forms of ordinary differential equation for the determination of ai(A): or (S - 'g-u'V ^ - "^"^^'V + «1^ «,(<,) =0. (82c) Given any 11 (A) satisfying one of these equations, the associated 3€(A) is obtained by integration from (77): '^W = / (tT^) " + ' (/: arbitrary constant). ^^^^ It is evident from (72) that Case 1 does not exist if both recombination and time variation are absent. Case 2: In considering this case we shall exclude the condition -77- = 0 because it on has been included in Section J. From the condition — — = 0 we have 3C = k{t)h + /(/) {k{t), l{t): arbitrary functions) (84) with kr^O. This shows that JC itself is a harmonic function and we can with- out loss of generality use it in place of h. Equations (74) and (75) now yield the two conditions on ni(3C, /), (R(ni), and3C(:*:, y^ z, t): ^^'^ - "^ ax ^ . (85) 11 + T 1194 and THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 0. (86) A(x)o -3 ^^ ^ ^ ^- " — ■ ~^ J .y^ / y A+£n|A-i| =x > y ■3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 X Fig. 1 — The transcendental function A {x). 8 ^ ' ^^ "" <.)0 -4 ~in> A2- > -y / y A+£n|A-i| =x -1? A3 •14 -12 Fig. 2 — The transcendental function A (x). For the integration of (85) we need the transcendental algebraic function of a single real variable defined by A{x) + In I A{x) - 1 I = :r. (87) This function is plotted in Figs. 1 and 2. It will be observed that x is always a single-valued function of A; while A is a single- valued function of x for X > 0, a, double-valued function for x — 0, and a triple-valued function for I'LOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1195 X < 0. The single- valued monotone functions Ai , A2 , and A3 are defined respectively by the restrictions A > 1, 1 > A > 0, and A < 0. When A is used without subscript it is implied that either Ai , A2 , or A3 can be used. It will be useful to remember that A'W = ^^%:fi. (88) A{x) In terms of the function A, (85) integrates to /< -(QtKM-y)) [r + »»'« + M^ -w] (i/ (96) (97) (98) where u(xj y, z) is any harmonic function. In the absence of recombination, Possibilities 1 and 2 lead to the same result: Equation (97) and X,{x, y, z, /) = u{x, y, z) + m(f). (99) FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1197 In the absence of time variation, (86) shows that recombination is neces- sarily absent, too, so the results reduce to (t^) OLCOC) = ^A l^-:^] (100) with 3C(x, y, z) any harmonic function and A and B arbitrary constants. This solution for the case grad 3C f^ 0, together with that given by (59b) and (60) (with G = 0) for the case grad 3C = 0, constitute a veritable gold mine of useful solutions because of the arbitrary harmonic function involved. An example involving a particular choice of JC will be examined in Section R. Case 3: ^ ?^ 0, grad (grad h)' = 0. In this case (grad hY is a function of t so that (75) can be written in the form From this it follows (because div grad ^ = 0) that h{x, y, z, t) = a{t)h{x, y, z) + c{l) (101) with div grad b{x, y, z) = 0. (102) The condition grad (grad hY = 0 now requires further that grad (grad hf = 0. (103) But any h{x, y, z) satisfying both (100) and (101) can, by suitable choice of axes, be written h = Sx (S: constant). This leaves us with exactly the same totality of solutions as we could have obtained by setting^ = ^(x, /), 3C = 3C(x, /) in the first place. So we replace /r by X in (74) and (75) and obtain: dX^!r__!^ (104) dx 7 + 'It 1198 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 and dx ox ![■ + ii «<* + £?] = »■ ""' Any 1l(x, /) satisfying (105) can be substituted into (104) to obtain 3C{x, I) from 5C(x, /) = 7(0 + / ^-^-^^^^"^a^ ^^ (106) 7 + It (/(/): arbitrary function). If recombination is absent, (R(*U) disappears from (105). If time variation is absent, — disappears from (103) andjXO and/(/) are replaced by arbitrary dt constants. In the latter case, the standard change of variables WCU) for g 'W('l^)^ f°^ Tx ^^°^^ reduces the solution of the second order equation (105) to the solution of a first-order equation followed by a quadrature. If both recombination and time variation are absent, the substitution (107) reduces the solution of (105) to two quadratures. A set of equations equivalent to the steady-state f — = 0 j forms of (104) and (105) has been the subject of an extensive numerical investigation by W. van Roosbroeck (Reference 1) for the recombination rate functions given in (37) and (38). M. Solutions with V = V{h, /), (P = (P{h, /), Grad (9 9^ 0, Div Grad /? = 0, .V = 0 For these conditions (21) and (23b) yield -(grad/.) =_L(R((P)+-(^__ + _jJ I' and (107) 5 e-,Tr-S] *-«•=»■ »««' FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1199 Since we do not here allow grad h = 0, (108) implies .'[S-*'] dV ' Idh ^^^J ^kT .... ,. . . . (109) rr = :;^ y = KgW ' arbitrary function) on (y ae Case 1: 9^ 0, grad (grad hY 7^ 0. In this case, as in the associated case in Section L, the implications of (107) together with div grad h{x^ y, z, /) = 0 are not known when time variation is present. When time variation is absent, we work with the conditions (P = (9{h) and V = V{h) with div grad h{x, y, z) = 0 and arrive at counterparts of (107) and (108): (P"-(grad/>)' = ^(R((P) (110) ((P' - i (P^'V = 0. (Ill) Proceeding as in the analysis of Case 1 of Section L, we infer that h must be of the kind given by (81b) or (81c). The associated second-order differ- ential equations restricting (9{h) are then, respectively: and and (P"-^r^(R((P) =0 (112a) Kl ft The V{h) associated with any solution of (112) can be obtained by integra- tion from V{h) = C + f y^ ~ ^ dh (C, 5: arbitrary constants). (113) J iy 1200 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 It will be noted from (110) that simultaneous absence of recombination and time variation is inconsistent with the defining conditions of this case. Case 2: ^ = 0. We shall exclude the possibility o^ tt = 0 because it is included in Section I. Then, proceeding as in Case 2 of Section L, we conclude that (P itself is a harmonic function and can be used in place of h. (107) and (109) then become- (5l((P)+^^ = 0 (114) and dV ^ 7(1 - git)] d(9 (P or V{(9, t) = y[\ - !(/)] In (P + }(/) (}(/): arbitrary function). (116) Because — - is harmonic and a function of (P, we have dt 2(R((P) = -""-Z = E(P - F dt (£, F: arbitrary constants) whence 2(R((P) = E(P - F (117) (115) and or (9(x, y, z, /) = e-'"m(x, y, z) - t (E ^ C) (118a) (P(jc, y, 2, 0 = m(x, y, z) + Ft {E = 0) (118b) where m{x, y, z) is an arbitrary harmonic function. If recombination is absent, these results specialize to (116) and (118b) FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1201 with F = 0. If time variation is absent it follows from (114) that recom- bination is absent, too, and the results specialize to •0((P) = G + #ln(P (119) with (9{x, y, z) any harmonic function and G and R arbitrary constants. These solutions play the same role for the intrinsic semiconductor {N = 0) that (100) does for the extrinsic {N 9^ 0). Case 3: ^ F^ 0, grad (grad hf = 0. In this case it can be shown, just as in Case 3 of Section L, that no gen- erality is lost by considering (P = (9{x, t) and V = V{x, I) in place of (P(A, /) and V{h, t). Equations (107) and (109) then become and dv _ la^~^^^^J (121) dx (P Any solution of (120) when substituted into (121) gives an associated V from (X) dx ^'^' ^ (122) -iw V(x, t) = q{t) +y f ^-^ dx If recombination is absent, (R((P) merely vanishes from (120). If time varia- tion is absent, the functions g{t) and q(/) are replaced by arbitrary constants and the standard change of variables U((P) for ^ ax (123) u((P) -7:z for — d(P dx leads to a solution of (120) in two quadratures. An equivalent solution is given by W. van Roosbroeck in Reference 1. From (120) it follows that recombination and time variation cannot simultaneously be absent for Case 3. 1202 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 N. Construction of Solutions from Orthogonal Harmonic Fields, N 7^0 There are many known examples of pairs of harmonic functions hi{x, y, z) and hix, y, z) that have orthogonal vector fields — that is, for which grad /fi-grad h2 = 0 (124) with grad hiT^O and grad /?2 7^ 0. [E.g., the real and imaginary parts of any analytic function of a complex variable.] From any such pair of functions we can construct the following solutions of (33) and (34) : "il = hi; 5C= h2- hi (125) and (126) ■ (127) (128) The validity of the solution (125) is seen from (33) and this expanded form of (34): ni div grad ni + grad ^-grad ('a + 3C) = 0. (129) Similarly, the validity of (126) follows from (33) together with a different expansion of (34): div grad ^24-2 grad ai-grad 3C = 0. (130) It is evident that a given hi and ^2 can be interchanged in the above solutions to yield different solutions, and also that any given hi or ho can be replaced by an arbitrary constant multiple of itself plus a second arbitrary constant. O. Construction of Solutions from Orthogonal Harmonic Fields, N = 0 We can write the differential equation system for the intrinsic semi- conductor [(35) and (36)] in the form: div grad (P = 0 (131) (P div grad V + grad (P-grad V = 0. (132) 01 = Vhi; 5C = = h. In terms of (P and V these solutions are and (P Ne , V = h. (P Ne kT Vh\ V = Vhi + h2 FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1203 From these we verify the solution: (9 = h) V = h2 (133) for any harmonic hi and h2 satisfying (124). The solutions given by (127) and (133) have the property grad (P-gradl) = 0 and so may be considered, in a sense, complementary to the solutions in Sections L and M for which grad (P X grad V = 0. - • P. Superposition of a Harmonic 3C Field, N. 5^ 0 Inspection of the equation system [(33), (130)] reveals the following superposition theorem for obtaining new solutions from some known solu- tions for the case of no recombination or time variation: Theorem 12: If [ii, 5C] is a known solution and if h is any harmonic func- tion such that grad il-grad h = 0, then [ix, 5q.-\- h]is also a solution. Or, in terms of (P and V : [Theorem 12': If [^, V] is a known solution and if h is any harmonic function such that grad ^-grad h = 0, then [5, V -{- h]is also a solution. In the latter form it is evident from Section O that the theorem holds also for iV = 0, but does not extend the results of Section O. Q. A Partial Differential Equation in Terms of 3C Alone, N 9^ 0 For N = 0, (21) provides a differential equation involving only one de- pendent variable — (P. We shall now derive an analogous — ^but vastly more complicated — differential equation for the case N 9^ 0, -— = 0. ot For this case (30) and (32) become div grad OC = - ^ (R(ai) and div grad OC + - 01 grad (Ol -f 5C) = 0, or in terms of a familiar vector symbolism 1204 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 V'OC = - ^ (RCll) (134) and V. vac + - OlVC^ + 3C) = 0. (135) Now let S(1L) be the inverse function to (R(1l), i.e. the function such that S((R(^)) = 01. Then from (134) we have 01 = s(- -V'ocV (136) Substitution of (136) into (135) yields after some computation ss'v^(v^ac) - - (ss" + s'')(vv^3c)' (137) + SVOC- VV^OC - ^ (S + 7)V'5C = 0 where s'(^) = — S(^), etc. / N \ S, S', S" are considered as given functions of I — - V^OC I . The simplest meaningful choice of S is (138) (/, K : prescribed constants) corresponding to constant mean lifetime recombination. For this S, (137) specializes to J(K - 7V25C)V2(V23C) - 72(vv2ac)2 (139) ■f JV3C'W5Q, - {y + K - 7V23C)V2aC = 0. If any 3C can be found satisfying (139), the associated 11 is given (from (136)) by FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1205 R. Sample Application of the Results of Section L: Sphekicai. Symmetry, N 9^ 0 As an example of the solutions included in the results of Section L we consider the case of a spherically symmetric field about a point (or spherical) source of current. We take, as the most general harmonic function having spherical symmetry, 3C = Zi+ if (140) r (I, M: arbitrary constants). For the time being we shall assume Z 5^ 0 and M ^ 0. Then from (10(J) and (28) and (29) we have L and •0 = Ia(^-^-^/-)+M+^ (141) 0 which is equivalent to (P>\N\. (171) This implies first of all that (?«, must be chosen > | iV | . It is instructive to look first at the case Z = 0. Equation (165) shows immediately that (171) requires the choice of the positive sign for the radical for A^ > 0 and the negative f or iV^ < 0 to avoid (?« < | A^ | . We further find by substitution of (166) and (169) into (165) that (171) requires Nip. (172) -lnkT^p{(Pl-\N\')_ The bracketed factor is positive. Since we are interested only in non-negative values of r, (172) imposes no restriction if Ip is zero or not of the same sign as N. However, for N and Ip of the same sign, (172) establishes an inner radius inside which the solution does not satisfy (171). This may be regarded as establishing the minimum radius for an inner spherical electrode for FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1209 prescribed Ip and (?«, , or alternatively as limiting the possible choices of Ip and (Poo for prescribed inner electrode radius. Had we chosen the con- stants Q, R and 5 so as to obtain prescribed values of (P and D at a pre- selected electrode radius tq , restrictions analogous to (172) on the maximum radius would appear. For the case ^4 = 0 the restriction analogous to (172) is Since the bracketed factor is positive, (173) provides no restriction for Ip > 0, but for Ip < 0 establishes a minimum radius of the kind just dis- cussed. For L,A^O, the analog of (172) and (173) is Z/1 -1 (^I^\ _ .-1 (kT\N\\ (174) \NeA) \ NeA ) r > where A and L are given by (153) and (154) and K~^ denotes the inverse function of A — i.e., A-i[A(x)] ^ X or A-HA) = A + In I A - 1 I . Equation (174) is a minimum radius restriction of the same kind as those obtaining for yl = 0, and Z = 0, but the relationship between the minimum radius tq and (?«, , Ip and In is considerably more complicated than in the more degenerate cases. It will be noted that the relation eN A \ A ) (with I, B, M given in terms of (?« , /p , h by (152), (153), and (154)) deter- mines which function (Ai , A2 , or A3) is to be used for A in any given case, because any assigned value (p^ 0) is taken on by one and only one of (Ai , A2 , A3). If surface recombination is negligible as well as interior recombination, this spherically symmetric solution is of use in the study of "point" con- tacts on a plane surface of a semiconductor. [Fig. 3 and Ref. 2.] The results of this section can easily be duplicated for any other choice of the harmonic function 3C to obtain a great variety of specimen solutions. 1210 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Solutions based on 5C's having a single source singularity (such as the ex- ample above) will contain four mathematical parameters, and hence will permit arbitrary selection (subject to (6)) of the physical parameters, Ip , /„,(?«,, and "Uoo • However, solutions based on 5C's having more than one source singularity will provide only a subset of the possible assignments of the physical parameters. For example, the harmonic function associated with the electrostatic field produced by two separate point charges each equi- distant from two parallel infinite plane conductors provides solutions of \ ! / / \ i / / Fig. 3— Point source flow field, useful in connection with point contact theory Fig. 4 — Two source flow field between conducting planes, useful in connection with Type A transistor theory. interest in connection with the type A transistor configuration (Fig. 4). However, the family of solutions obtained contains only a five-parameter subset of the six-parameter family obtainable by arbitrary assignment of I pi , I pi , In\ , /n2 , (Pee , and V^ . S. Sample Application of the Results of Section M: Spherical Symmetry, A^ = 0 We now round out the considerations of Section R by exhibiting the related solutions for AT = 0 (i.e., the intrinsic semiconductor). and FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1211 In accordance with the results of Section M, we choose for (P the most general harmonic function with spherical symmetry: (P = A--}- B {A,B: arbitrary constants). (175) From (119) then, for A 7^ 0 V = H \n(A--i- b\ + G (176) and from (175), (176), (143), and (144) /, = ifiMp.i(5+^) (177) /n = ^UnneA(S-^\ (178) I = ^QeA ^{^JLn + ^ip)H - inn - Mp) y] • From (177) and (178) we obtain (179) A = '^ ^" (180) QfJLptlnkT fj = ^^ ^i-nlp + l^pln (181) e Unlp — y^pln and from (175) and (176) for \)« = 0: B = (9^ (182) and G= -HlnB = -^^i4^±^ln(P«. (183) e fJin^p — ^p^n The condition (Poo > UV | = 0 introduces the restriction (for A 9^ 0): Evidently this implies no real restriction for ju„/p — txjjn < 0 (i.e., ^ < 0), but introduces a minimum radius — of the same kind we have already dis- cussed—when nJp — f^pln > 0 (i.e., A > 0). 1212 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 For il = 0, (P is constant and, by Section I, V is harmonic. So we set (P = (Poo > 0 (185) and •U = (? i + 5 (186) r and obtain from (143) and (144) /p = il2/xp ^CCPoo (187) and In = h^HneC(S>^ . (188) From (187) and (188):' ~ 12)Upe(P^ ~ ^lJLne(?^ ~ QfJLnfJ^pe(P^ and from (186) for "Uoo = 0, D = 0. (190) Evidently A = 0 is associated with the condition flnlp ~~ fJLpIn = 0. T. Summary List of Symbols Coordinate Systems: (^) >'j 2): ordinary rectangular cartesian coordinates, (p, 6, z) : ordinary circular cylindrical coordinates, (r, d, ) : ordinary spherical polar coordinates. Ti : unit radial vector in {r, d, <])). t : time variable. Physical Variables: n : concentration of negative carriers (electrons). p : concentration of positive carriers (holes). (P: total carrier concentration = »+/>. cu:^^(p (yv^^o). eN (R: recombination rate function. V: electrostatic potential. FLOW OF HOLES AND ELECTRONS IN SEMICONDUCTORS 1213 kT dZ\ = V - ^ = V - 4-^(9 (N 9^ 0). o el\ II : total current density vector. o ||»: electron current density vector. o ||p: hole current density vector. subscript "0": designates thermal equilibrium values. subscript "oo": designates values ''at infinity". Physical Constants: T: absolute temperature. e : magnitude of electronic charge. k : Boltzmann's constant. ju„: electron mobility constant. Hpi hole mobility constant. a : = 1/fip + 1/fjin . ^ : = l//xp - 1/Mn . (Assumed p^ 0) y : = - — ae N: = no — po. Other Constants and Functions: A,B, • • • , Z ((except /, N, and T)), A,B,",Z, A, B, • • • , Z: arbitrary constants a,b, ■" ,z ((except e, h, k, n, p, r, t, x, y, z)), d,h, • • • , z: arbitrary functions of variables designated (e.g., j(t)). h, hi , h2 : harmonic functions of variables designated at place of usage. A: A{x) is defined by the relation A(:r) + In | A(x) — 1 \ = x. (See Figs. 1 and 2.) S: S(ni) is defined by S[(R(ni)] = U Acknowledgment The author is indebted to J. Bardeen and W. van Roosbroeck for a critical reading of the manuscript and a number of valuable comments. References 1. W. van Roosbroeck, "Theory of the Flow of Electrons and Holes in Germanium and Other Semiconductors," Bell System Technical Journal, 29, 4, 560-607 (October 1950). 2. J. Bardeen, "Theory of Relation Between Hole Concentration and Characteristics of Germanium Point Contacts," Bell System Technical Journal, 29, 4, 469-495 (October 1950). 3. VV. Shockley, Electrons and Holes in Semiconductors, New York, 1950. Instantaneous Compandors on Narrow Band Speech Channels By J. C. LOZIER (Manuscript Received Aug. 15, 1951) If speech is passed through an instantaneous compressor, the original speech frequency spectrum is substantially widened. It is known that instantaneously compressed speech can be transmitted over a medium with a passband no wider than that occupied by the uncompressed speech, and the original signals re- covered without distortion. The conditions required for such distortionless transmission are examined. The analysis indicates that more severe requirements must be imposed on the attenuation and phase characteristics of the system when this reduced bandwidth mode of operation is used. The practical value of this ex- change of transmission requirements is a matter for experimental determination. Introduction WHEN a signal such as speech is instantaneously compressed in ampli- tude, harmonics and cross modulation products are generated which extend the frequency spectrum of the original signal by many octaves. It is proposed to demonstrate that the additional products thus generated are necessary for the distortionless recovery of the original signal. Then the conditions will be examined under which this broadband signal can be transmitted without distortion through a bandwidth no wider than that occupied by the spectrum of the uncompressed speech. Finally, some of the practical aspects of using intantaneous compandors on narrow band speech channels will be considered, with emphasis on the nature of the trans- mission requirements placed on the medium. The advantages to be obtained from the use of instantaneous compandors have already been presented by Mallinckrodt.^ Bandwidth vs Distortion If a single frequency tone is compressed by a 2 to 1 compressor,^ and then the fundamental alone is expanded, it can be shown that the resultant 3rd harmonic distortion is only 13 db below the fundamental. Expansion of both the fundamental and the 3rd harmonic output of the compressor will reduce this 3rd harmonic distortion to 29 db below the fundamental. Ex- pansion of the fundamental plus the 3rd and 5th harmonics will reduce the 3rd harmonic distortion in the recovered signal to 45 db below the funda- ^C. O. Mallinckrodt "Instantaneous Compandors," B.S.TJ., Vol. XXX, No. 3, July 1951. * In a 2 to 1 com[)ressor, the outi)Ut amplitude is the sciuare root of the input amplitude. The name comes from the fact tnat, in such a compressor, the output amplitude will increase 1 db for each 2 db increase in input amplitude. 1214 COMPANDORS ON NARROW BAND SPEECH CHANNELS 1215 mental. These results are indicative of the significance of such components in the compressor output spectrum to distortion in the recovered signal. Frequency Analysis of Transmission under Reduced Bandwidth Conditions It might be concluded from the results quoted above that a wideband channel is required for the d compressed speech. However, stortionless transmission of instantaneously f the compressed speech is properly sampled (a) ASSUMED SPECTRUM OF ORIGINAL SIGNAL (b) SIGNAL AFTER INSTANTANEOUS COMPRESSION (C) INSTANTANEOUS SAMPLER SPECTRUM (d) SIGNAL AFTER COMPRESSING AND SAMPLING 20 0 4 8 12 16 FREQUENCY IN KILOCYCLES PER SECOND Fig. 1 — Frequency analysis of instantaneous compressing and sampling of origina signal. before transmission, and the received signals are again sampled at the re- ceiver, the bandwidth of the intervening medium can be restricted to that of the original speech, and still the transmission can be distortionless. Hence, the sampling must transform the broadband spectrum of the com- pressed speech in such a way that it can be successfully transmitted over a relatively narrow band. A steady state frequency analysis will serve to illustrate this phenomenon. Figure 1(a) shows the 4 kc frequency spectrum assumed for the original 1216 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 signal, and Fig. 1(b) shows a 10 kc portion of this signal after instantaneous compression. Now the minimum sampling rate required to handle a 4 kc signal band is 8 kc. It is also the sampling rate that will allow the maxi- mum band reduction in this case, as further analysis will show. The fre- quency spectrum of a sampling function with an 8 kc repetition rate has a d-c. component, an 8 kc fundamental, and all the harmonics of this repetition rate as shown in Fig. 1(c). These harmonics are all of equal ampHtude and all are phased so as to add up every 125 microseconds to form the charac- teristic sampling waveform. Figure 1(d) shows the frequency spectrum formed by sampling the 10 kc portion of the compressed speech signal. It 8 10___ 1 8 4L,_ 1 10 KC PORTION OF I 1 COMPRESSED SIGNAL' —'' FOLDED* INTO ,4 KC BASEBAND 1 1 1 1 ' I 1 1 1 1 (a) FREQUENCY SPECTRUM OF 1 4KC BASEBAND SECTION OF 1 { SIGNAL AFTER COMPRESS- 1 ING AND SAMPLING 0 41 1 1 1 1 1 8 10 ! 8 4J4 10 8 1 1 1 . 8 10 1 10 8 8 10 8 8 4!4 8 8 4! (b) EFFECT OF RESAMPLING 1 t 1 IN FIGURE 2(a) 0 4[4 0 0 4l4 0 0 41 1 1 1 1 1 ORIGINAL ^^SIGNAL * ,!, [ 1 1 (C) EFFECT OF EXPANDING ^1 , FIGURE 1(Cl)(0R FIGURE 2(b) 1 1 1 1 1 ZATION) 4 8 12 16 FREQUENCY IN KILOCYCLES PER SECOND Fig. 2 — Frequency analysis of instantaneous sampling and expanding of transmitted signal. represents the product of the spectra of Fig. 1(b) and 1(c). As such, it is composed of the various component frequencies in the sampling spectrum as carrier frequencies, with the 10 kc portion of the compressed speech signals as amplitude modulated sidebands about these carriers. Figure 2(a) shows the resulting spectrum that falls in the 4 kc baseband of Fig. 1(d). It represents that part of the compressed and sampled spectrum that would be received over an ideal 4 kc baseband channel. This spectrum is worth examining because it illustrates how the addition of instantaneous sampling makes it possible to transmit all the components in the compressed speech over a 4 kc channel. The effect may be described as a linear "folding" of the broadband spectrum back and forth over the 4 kc band. However, COMPANDORS ON NARROW BAND SPEECH CHANNELS 1217 although any broadband signal can be similarly folded into a 4 kc band by an instantaneous sampler with an 8 kc repetition rate, the process is not fully reversible. For example, there is no means of telling whether a 3 kc component in the folded signal comes from a 3 kc, a 5 kc, an 11 kc, or a 13 kc, etc. component in the original signal. Hence it is only a very special class of signals that can be recovered after their frequency spectra have been condensed in this fashion. To recover the original speech in this case, the spectrum shown in Fig. 2(a) can be sampled at an 8 kc rate to produce the spectrum shown in Fig. 2(b). Now an examination of the spectra involved will show that when the second sampling is properly synchronized with the transmitting sampler, the two spectra shown in 1(d) and 2(b) will be identical. The spectrum in Fig. 1(d) represents the 8000 samples per second of the compressed speech gen- erated at the transmitter. Thus, when the spectra of Figs. 1(d) and 2(b) are identical, samples will be recovered at the receiver which are identical to those that were generated at the transmitter. These can be converted to samples of the uncompressed speech by complementary instantaneous ex- pansion. The spectrum of these samples is shown in Fig. 2(c). All that is necessary at this point to recover the original speech without distortion is to pass these samples through a 4 kc. low-pass filter. Requirements for Distortionless Transmission on Reduced Bandwidth Basis Thus the criterion for distortionless transmission of compressed and sampled speech under these conditions is that the samples recovered at the receiver be the same as the samples of compressed speech that were generated at the transmitter. This means sending 8000 pulses per second over a 4 kc band without intersymbol interference. Nyquist' has shown that this is the maximum rate at which independent pulses can be transmitted over a 4 kc band and still be recovered at the receiver. At this maximum rate, the bandwidth employed does not give the transient response of one pulse time to die out before the next pulse is received. Therefore the transient response in this case must be such that, when one pulse is at its peak, the transient responses of all other pulses will be going through zero. The infinitely sharp cut-ofif at 4 kc, which is required to separate out the spectrum shown in Fig. 2(a) from that in Fig. 1(d), will have the required zeros in its pulse response, provided the attenuation is constant and the phase is linear with frequency. This is the familiar shape of transient response. Nyquist has shown x 3H. Nyquist, "Certain Topics in Telegraph Transmission Theory," A.LE.E. Trans- actions, Vol. 47, Pages 617 to 644, April 1928. 1218 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 also that this is just one of a whole family of transmission characteristics with a specified symmetry about the cut-off frequency, all of which have the required transient zeros. However, there is no reason to suppose that any of them would prove less sensitive to variation of the transmission characteristics from the ideal than the one described above. It is apparent that synchronization of the transmitting and receiving samplers is required to insure that the receiving sampling is done at the exact instant that all transient responses but the desired one are zero. Effect of Variations from Ideal Transmission Characteristics ON Distortion In practice of course a certain amount of distortion is tolerable. To get some measure of the practicability of such reduced bandwidth transmission of compressed speech, the first step is to determine how much intersymbol interference can be tolerated in this type of signal, and then to translate this tolerance into allowable variations in the frequency characteristics of the transmission medium from the assumed ideal. However, it is hard to estimate what the allowable intersymbol interference might be in this case. In a single channel system, intersymbol interference produces a form of distortion, and the sensitivity of such signals to distortion is primarily a matter for subjec- tive determination. For computational purposes it will be assumed, however, that this inter- symbol interference should be 20 db down in the output. It is apparent that a 5% variation in the amplitude of a sample before expansion will produce a 10% variation in the expanded sample. On this basis 5% intersymbol interference in the medium between transmitter and receiver is the maximum allowable. Using Wheeler's theory of paired echoes'*, it can readily be shown that a sinusoidal variation in the phase vs. frequency characteristics of the medium, with an amplitude of ^^ of a radian (5.7 degrees), will cause a pair of echoes each of which will have a peak equal to 5% of the original sample. Similarly a sinusoidal deviation in the attenuation vs. frequency characteristic of 0.9 db from the ideal will also cause a pair of echoes with an amplitude of 5%. In estimating the average effect of such echoes, it cannot be expected that the intersymbol interference from a given echo will be appreciably less than its peak amplitude would indicate. The principal reason is that, in order to realize the savings in bandwidth, the pulses are 125 microseconds apart, which is as close together as the 4 kc band will permit. Reference to the *H A. Wheeler,The Interpretation of Amj)litu(ie and Phase Distortion in Terms of Paired Echoes, I.R.R., June 1939. COMPANDORS ON NARROW BAND SPEECH CHANNELS 1219 form of transient response indicates that the width of pulses (and hence of echoes) received over a 4 kc band, is such that they will be within 65% of their peak amplitude for a full 125 microseconds. Thus such echoes will cause at least 65% of their peak interference to at least one subsequent pulse. This illustrates why it is so difficult to control intersymbol interference in pulse systems operating under minimum bandwidth conditions. Assuming from this argument that the interference from echoes should be taken at their peak values, the tolerable phase deviations from linearity must be measured in tenths of a radian in this case. On ordinary speech channels the tolerable phase deviations from linearity are measured in radians, which represents a difference of one or two orders of magnitude. Another estimate of the allowable intersymbol interference may be ob- tained by comparing it to quantizing noise on a PCM system. A 5-digit PCM system has 32 quantizing levels, and the average uncertainty in the recovered pulse amplitude is one half of a quantum step, or approximately 1.6%. The 10% intersymbol interference requirement chosen above repre- sents approximately 6 times as much deviation in recovered pulse amplitude. Again only subjective measurements can tell whether intersymbol inter- ference in this case is six times more tolerable than quantizing noise. How- ever, a 5-digit PCM system is not a high quality circuit by Bell System standards. The distortion effects due to lack of synchronization of the transmitting and receiving samplers have been ignored in the discussion so far, on the assumption that it would not prove too difficult in practice to make it a relatively negligible source of intersymbol interference. However, it may not prove to be a negligible factor from the economic standpoint, when an at- tempt is made to prove in a system of this type. Multichannel Aspects In the case of multichannel time division systems, the addition of in- stantaneous campandors seldom requires an increase in the transmission requirements of the medium. In multichannel PAM and PPM systems, for example, intersymbol interference causes intelligible crosstalk between chan- nels, and the requirements on such crosstalk usually calls for the intersymbol interference to be some 60 db down in the recovered speech. In such cases the addition of an instantaneous compandor can serve to reduce this re- quirement on the line to some 40 db, through the so-called "Compandor Advantage"^ It is fair to point out, however, that such systems are seldom, if ever, operated as minimum band pulse systems. *€. O. Mallinckrodt, "Instantaneous Compandors," B.S.T.J., Vol. XXX, No. 3, July 1951. 1220 the bell system technical joubnal, october 1951 Conclusions It has been shown that distortionless transmission of instantaneously compressed speech over a frequency band no wider than that required for the uncompressed speech does involve the transmission of a broad-band signal over a relatively narrow-band channel. This is made possible by the use of an instantaneous sampler which serves to "fold" the spectrum of the compressed speech at the transmitting end so that the entire spectrum is contained within the desired bandwidth. The criterion for distortionless transmission of these "folded" signals is shown to be one of recovering at the receiving end the precise samples of compressed speech that were gener- ated at the transmitter. To accomplish this distortionless recovery of the transmitted pulses it is necessary, first, that the transmission medium cause no intersymbol interference, and, second, that the signals at the receiver must be sampled in synchronism with the sampling at the transmitter. It was also shown that the full reduction in bandwidth can be realized only by pulse operation under minimum bandwidth conditions. It was esti- mated that the accuracy of control of the steady state phase and attenuation vs. frequency characteristics that would be required to maintain the inter- symbol interference below an acceptable level would be hard to meet in practice, primarily because of having to operate under such minimum band- width conditions. The Evolution of Inductive Loading for Bell System Telephone Facilities By THOMAS SHAW {Concluded from July J 95 J issue) PART VI: CONTINUOUS LOADING General CONTINUOUS loading, i.e., the addition of uniformly distributed in- ductance, was studied theoretically in the Bell System several years before theoretical work started on coil loading. This early work of John Stone Stone, then a member of the headquarters technical staff of the American Bell Telephone Company, resulted in the issue to him on March 2, 1897 of a U.S. Patenl (575,275) describing a "bi-metallic" wire cable. Later on, when the commercial development was authorized, cost con- siderations made it desirable to start with laboratory experiments on an "electrically equivalent" artificial line using small lumped inductances. In planning these experiments, it soon became apparent that only a small amount of distributed inductance could be obtained with the best magnetic material then available, namely, iron. Recognition of the important ad- vantages inherent in the use of large amounts of inductance, and of the absence of limitations regarding the magnitude of inductance that could be provided in coil form, then shifted the development emphasis to the as yet unsolved problem of spacing inductance coils in relation to wavelength. This theoretical problem was quickly solved by G. A. Campbell, who was then in charge of the project, and accordingly the laboratory artificial line was designed to demonstrate the practicability of coil-loading (early in 1899). The Bell System development work on continuous loading was then sus- pended for some time. During the next two decades, coil loading was found to be economicaUy suited to all Bell System needs for inductive loading, even on short inter- mediate submarine cables required at shallow water crossings of rivers and bays. Shortly after the First World War, however, it became necessary to undertake the development of continuously loaded cable to meet an urgent demand for telephone communication with Cuba. Exploratory theoretical studies and laboratory investigations had been started shortly before the war, but were discontinued during the war. The exploratory work included consideration of the possible use of a new nickel-iron magnetic alloy which 1221 1222 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 was then under development by the Research Department of the Western Electric Company, and which later on became widely known as permalloy .^^ Key West-Havana Submarine Telephone Cable System This project required three different submarine cables ranging in length from about 100 to 105 nautical miles, each being a great deal longer than any previously designed for telephone transmission, and a large fraction of the route was in deep water, reaching a maximum depth somewhat over 6000 ft. The difficulties to be expected in protecting loading coils from injury under the great hydrostatic pressure involved, and the complications that would be encountered during installation and in subsequent maintenance work, prevented coil loading from receiving consideration. Moreover, the great water pressure also eliminated consideration of paper insulated cable. Since the cables were intended for use in telephone circuits connecting remote points in the United States with Havana and remote points in Cuba, the over-all system design requirements were very formidable. In addition to a two-way telephone circuit in each cable, provision also was made for three carrier telegraph circuits above the voice range, and for direct current grounded telegraphy below the voice. These complex requirements brought in difficult problems regarding telegraph flutter interference and other types of non-linear distortion. The fundamental design studies resulted in a decision to install single core, continuously loaded, cables using gutta-percha insulation, and having a concentric system of copper tapes wrapped around the insulated conductor, for use as a return conductor. (These cables were the first to be installed with this feature.) Iron-wire type continuous loading was chosen largely because the desired project in-service dates did not allow sufficient time for the additional research and development work, and the additional manu- facturing preparations, that would have been necessary in order to use permalloy tape loading. The manufacturing situation presented serious problems, because it was necessary to plan for manufacture abroad, since no American company had facilities for making deep-sea submarine cable. Moreover, iron-wire type continuous loading (as proposed by C. E. Krarup* of Denmark) was old in the European telephone art, having been used in several short submarine cables, and some underground cables. In the Cuban Straits cables under discussion, the central copper conductor had a diameter of about 0.140 inch. About this was closely wrapped a single layer of 0.008 inch soft iron wire and three layers of gutta-percha type insulation having a total thickness of about 0.135 inch. A thin copper tape directly on this core furnished protection against damage by the teredo, *E.T.Z., April 17, 1902. EVOLUTION OF INDUCTIVE LOADING 1223 and was part of the system of copper tapes previously mentioned which served as a return conductor. The effective permeability of the iron-wire loading material was about 115. The distributed inductance of about 4.35 millihenrys per nautical mile resulted in a low nominal impedance of about 115 ohms. The energy losses in the loading material were the principal factors in limiting the top of the working frequency band to about 4000 cycles. At KXX) cycles per second, the bare line equivalent was of the order of about 22 db (for the mean value of the longest and shortest cable). At 4000 cycles it was about 2.2 times as great. Space limitations prevent a more complete description and discussion here. Comprehensive information regarding all features of the project is given in a 1922 A. I.E. E. Paper'^^ prepared by Messrs. W. H. Martin, G. A. Anderegg and B. W. Kendall. Engineers of the A. T. &. T. Co. and W. E. Co. were responsible for the electrical design of the cables, method of opera- tion, and arrangement of the repeaters and other terminal apparatus. The cables were manufactured late in 1920 and installed early in 1921 by The Telegraph Construction and Maintenance Co. Ltd. of London, for the Cu- ban-American Telephone and Telegraph Company. The latter organization is jointly owned by the A. T. &. T. Co. and the Cuban Telephone Co. (a subsidiary of the International T. &. T. Co.) 1930 Non-Loaded Cable: Since the 1921 cables were not suitable for carrier telephone operation (largely because of excessive losses and non-linear distortion at high frequencies), it became necessary during 1930 to install a fourth cable between Key West and Havana in order to meet the demand for additional facilities. Advantage was taken of advances in the communica- tion art, notably an improved cable insulation (paragutta), improved re- peaters and carrier telephone systems, to design a non-loaded cable system which would be suitable for carrier operation. The initial carrier set-up provided three carrier telephone circuits, using a type C4 system which had originally been developed for open-wire lines. Early in 1942, a seven-channel system was substituted. Comprehensive information regarding the 1930 cable and its use of the 3-channel carrier telephone system is given in a 1932 A.I. E. E. paper by Messrs. Affel, Gorton and Chesnut.'*^ High Speed Transoceanic Loaded Telegraph Cables During the First World War when the need for increasing the message- carrying capacity of existing non-loaded transoceanic telegraph cables be- came urgent, the Bell System engineers who worked on this problem finally came to the conclusion that to obtain a great advance in the existing art it would be necessary to have much better cables. 1224 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 In July 1919 the continuing interest in this problem crystallized in a Western Electric proposal to use permalloy continuous loading in new transoceanic telegraph cables. Since this remarkable new magnetic alloy-^ had been invented and developed by Western Electric engineers, they were already familiar with its extraordinary high permeability characteristics, and had confidence in their ability to use it in providing a high impedance loading which would make practicable a great increase in message-carrying capacity. Loading with iron-wire would not have any advantage in tele- graph speed, because of its low permeability. Intensive research work quickly started on the permalloy loaded cable design and installation prob- lems, and on the related terminal apparatus and operating problems. The success attained in these efforts resulted in disclosures to the Western Union Telegraph Company regarding the great increase in telegraph signaling speed that could be obtained with the proposed new permalloy loading. In due course the Telegraph Company made arrangements with the Telegraph Construction and Maintenance Company Ltd. of London for the manu- facture and installation of a 120-mile trial length, using loading material supplied by the Western Electric Company and applied and treated under the direction of Western Electric engineers. In October 1923 this experi- mental length was laid in deep water near the south shore of Bermuda. The trial installation tests were so satisfactory that the Western Union company arranged for the manufacture and installation of a 2300-mile cable to connect New York with Horta in the Azores. As with the trial length, the loading material was supplied by the Western Electric Company, and it was ap- plied and treated under Western Electric supervision. The new cable was laid during September 1924. After refined adjust- ments in the terminal apparatus, a speed of over 1900 letters per minute was obtained. This speed is about four times the carrying capacity of an ordinary non-loaded cable of the same length. At this point a brief state- ment of general theory is indicated: The effect of the inductance is to oppose the setting up of a current and to maintain it once it has been established, thus preserving a definite wave front as the signal impulse travels over the cable. The individuality of the signal impulses is retained, and thus the much higher speed becomes possible. The permalloy loading material was applied in tape form in a close helix around a stranded copper conductor. The tape was 0.006 inch thick and 0.125 inch wide. The alloy was composed of about 79% of nickel and 21% of iron and a small amount of manganese, suitably heat treated. It provided an inductance of about 54 millihenrys per mile, slightly over 12 times that obtained by the use of iron wire in the Cuba cables previously described. The permeability of the loading was about 2300, or about 20 times that of EVOLUTION OF INDUCTIVE LOADING 1225 the iron wire used on the Cuba cables. An important feature of the cable not previously mentioned was a layer of viscous insulating material (under the regular gutta-percha insulation) which protected the strain-sensitive permalloy from the stresses caused by hydrostatic pressure in the great depths of the ocean. Demand for other high-speed loaded submarine cables quickly followed the successful demonstration of the New York-Horta cable and several were installed during 1926, reaching a total of about 15,000 miles of high-speed cables. The new installations included the Horta-Emden cable manufac- tured and installed by the Norddeutsche-Seekabelwerke A.G. for the Deutsch Atlantische Telegraphengesellschaft, and the New York-Bay Roberts-Penzance cable manufactured and installed by the T. C. & M. Company for the Western Union Telegraph Company. These particular cables used an improved form of permalloy supplied by the Western Electric Company containing about 80% nickel, 17.5% iron, 2% chromium, and 0.5% manganese. This alloy had an initial permeability of about 3700 and provided a higher impedance loading than that used on the first high-speed cable. In consequence, the newer cables were capable of speeds of about 2500 letters per minute. Other high-speed continuously loaded cables, installed in 1926 and subse- quent years, used permalloy material manufactured under Western Electric Company patent license, in some instances under a special foreign trade name. Comprehensive information regarding all features of the high-speed cable projects specifically mentioned above is given in two papers by O. E. Buckley, published in 1925^'* and 1928^^ respectively. In passing, it should be observed that the permalloy loaded cables under discussion were not intended for, and were not suitable for telephone communication. For this purpose, a new family of magnetic alloys, the perminvars, was developed.'*^ Their composition centered on 47% nickel, 25% cobalt, 20% iron, 7.5% molybdenum, and 0.5% manganese. When used as a thin loading tape, this alloy has electrical and magnetic properties especially suitable for telephone transmission, including very low hysteresis which is very advantageous in the control of all forms of non-linear dis- tortion. A Proposed Transatlantic Telephone Cable During the late 1920's, there was worked out a design of a perminvar loaded cable suitable for voice frequency telephony between Newfound- land and Ireland (1800 nautical miles). It was of the single core type with a concentric return conductor. Four layers of very thin perminvar tape 1226 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 provided the loading, and the loaded conductor was insulated with para- gutta. The suitability of the design for use in deep water was verified by temporarily dropping a 20-mile length on the sea floor in a deep water section of the Bay of Biscay. The general business depression of the early 1930's resulted in a post- ponement of the cable project because of its great cost. Later on the project was postponed indefinitely because, in the face of improvements in trans- atlantic radio telephone communicaion, so expensive a cable to carry a single conversation could no longer be justified. Additional information regarding this cable project is included in Dr. O. E. Buckley's 1942 paper, "The Future of Transoceanic Telephony," constituting the 33rd Kelvin Lecture before the Institution of Electrical Engineers.'*^ Continuous Loading for Paper Insulated Telephone Cables Tape and Wire Loading: When permalloy and perminvar first became available, theoretical studies were undertaken to determine the prospects of economic competition with coil loading on ordinary paper insulated telephone cables. Special consideration was given to the use of the mag- netic alloys in situations where coil loading is most expensive, namely, in submarine intermediate cables at river crossings, many of which involve high-frequency carrier telephone operation. None of these studies, however, gave sufficient promise to warrant commercial development work. Electroplated Permalloy Loading: During the middle 1920's, the Bell Tele- phone Laboratories started research work on a radical new concept of continuous loading using electroplated permalloy, which gave some promise of being less expensive than magnetic alloy tape or wire loading. The process involved the electrolytic deposition simultaneously of suitable pro- portions of nickel and iron on the copper conductor, and the use of special heat treatments to obtain the desired characteristic (magnetic and electrical) properties of permalloy. In due course, methods were devised for separating the concentric magnetic layer from the conductor, and for breaking it up into longitudinally discontinuous pieces, so as to secure the most advantageous properties for telephone transmission service, and to provide mechanical flexibility in handling. The experimental work was concentrated on small copper conductors, partly because of the more simple process problems, and partly because such combinations appeared to have the best prospects of competing with coil loading from the plant cost standpoint. (N.B. — The amount of permal- loy loading material required to provide a specified inductance per unit length, and its cost, is a direct function of the conductor diameter.) EVOLUTION OF INDUCTIVE LOADING 1227 The requirements for and the possibihties of using electroplated loading in the exchange area services were given priority in the theoretical cost studies — largely because of their extensive use of small conductor cables. These studies indicated some attractive possibilities of using light-weight electroplated loading on fine wires (26 and 24-gauge) as substitutes for larger size wires without loading, provided satisfactory solutions could be worked out for the circuit balance and magnetic instability problems. The balance problem arises from the difficulty of securing sufficient uniformity among the loaded conductors used as wire and mate in the individual pairs. This is complicated by the sensitivity of the permalloy continuous loading to magnetization by steady and intermittent superposed signaling currents. On the larger-size exchange cable wires that are not now used extensively without coil loading, the comparative cost estimates were not attractive for the electroplated loading. The inflexibility of continuous loading is an adverse general factor, since it is not feasible to decrease or increase the weight of the loading after manufacture, in order to accommodate changes in transmission require- ments made desirable by changes in performance standards or alterations in circuit layouts. Also, there would be inflexibility in conforming to changing requirements in complement sizes of loaded circuits in areas where it is necessary to have loaded and non-loaded circuits within the same cable sheath. Theoretically, one of the flexibility limitations of the coiitmuous loading could be reduced by using coil loading in combination with it, in order to extend its transmission range. However, this would reduce the width of the transmission band below that obtainable with the coil loading on a circuit not having continuous loading — the decrease in effective cutoff being a complex function of the ratio of distributed inductance to coil inductance. Combinations of high cutoff, low impedance, coil loading with low in- ductance continuous loading could be designed to have satisfactory band width properties. For a given grade of transmission performance, however, such combinations appear to be inherently more expensive than coil loading or continuous loading by themselves. The experimental work on electroplated continuous loading for exchange area cables was carried on somewhat intermittently during the 1930's. At no time did the prospects of securing satisfactory over-all transmission performance, at costs which would encourage competition with coil loading, appear to be sufficient to warrant an all-out sustained attack on the many difficult technical problems involved. Although the development project has not been permanently abandoned, it had to be discontinued in the late 1930's on account of the great pressure of more urgent work. 1228 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 The use of electroplated loading as a substitute for coil loading on toll cables, or on incidental cables in open-wire lines, did not appear to be attractive when the cost estimates and the complex requirements on circuit balance, stability, non-Unear distortion and flexibility were taken into account. Summary Enough has been told in the preceding pages to support the earlier statements regarding the low importance of continuous loading in the growth of the Bell System, relative to that of coil loading. Obviously, the success attained by the intensive development and in the very extensive use of economical types of coil loading is an important factor in this situa- tion. That these extent-of-use relations are not due to a lack of interest in continuous loading is well demonstrated by the Bell System initiative in developing the permalloy continuous loading that made high-speed telegraphy practicable in long submarine telegraph cables, and by the other develop- ment work summarized in this review. PART VII: EXTENT OF USE AND ECONOMIC SIGNIFICANCE Introduction Up to now, this account of coil loading has been in terms of individual developments and their significance with respect to the prior art and current developments in related fields, with occasional information regarding their importance and extent of use. It is now appropriate to supply and analyze some general statistics regarding the total amount of loading which has been used, in a rough appraisal of the importance of coil loading in the growth of the BeU Tele- phone System. Some important qualifications of the statistics are com- mented upon in advance of the presentation of actual figures. The statistics here given and discussed are for the most extensive and most important applications of coil loading, namely, for voice-frequency loading over cable circuits. They are grouped in two principal categories: (1) non-phantom type coils used on non-quadded exchange area cables, and to a relatively very small extent on toll cables, and (2) side circuit and associated phantom coils used on quadded long-distance and interurban toll cables, and to a relatively very small extent on entrance cables in open- wire lines and on long quadded exchange cables. The figures used are based on production statistics up to the end of 1949. The important significance of the production figures is that they measure at the time of manufacture the current demands for additional loaded facilities required by the growth of the telephone system, and the up-to- EVOLUTION OF INDUCTIVE LOADING 122'>> then accumulated total demand. In general, the loading coils were manu- factured to meet specific customers' orders; manufacture for merchandise stock in anticipation of future orders was seldom undertaken, except during periods of extraordinarily high, sustained, demand. On this basis practically all of the coils that were manufactured were installed in the telephone plant. The production statistics of course include a considerable number of coils w^hich were installed shortly after manufacture and which were taken out of service many years later to facilitate the use of improved transmission systems that required different types of coils, or to permit the use of carrier systems on the unloaded toll cable circuits. In general, complete potting complements were not taken out of service in preparation for carrier sys- tems operation; i.e., a large fraction of the disconnected loading coils remain in the cases in which they w^ere originally potted and installed, and the other coils in the same cases are still in service. It is important to remember that the displaced loading coils played an important part in the improve- ment and growth of telephone service in their own period of commercial use. The unavailability of statistics regarding displaced loading makes it impossible to supply accurate information regarding the total number of loading coils now being used for regular telephone service. It seems probable, however, that about 80% or more of all the toll cable coils that have been manufactured are in service, or installed in circuits which will be used as soon as trafiic growth requires them. The corresponding percentage figure for exchange area coils is probably higher. The number of loading coils taken out of service because of incipient defects that were not detected in the factory inspection tests, or which became unserviceable in consequence of service injuries, or which have been junked because of obsolescence, is a very small fraction of the total number of coils that have been manufactured lor Bell System use General Production Statistics, Voice-Frequency Cable Loading Total Production The grand total production figure (up to the end of 1949) for all types of voice-frequency loading coils for Bell System use is of the order of 20.7 million. Approximately 54% of this total (about 11,270,000 coils) are non- phantom type coils, used almost entirely on exchange area non-quadded cables. Nearly 9,500,000 coils are side circuit or phantom loading coils used on quadded toll and toll entrance cables. Approximately three-quar- ters of the grand total have been manufactured during the last two decades. The greatly varying rates in the growth of loading coil production are shown, (a) in terms of accumulated total production through 1949 in 1230 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Table XIX and (b) in annual totals during the period 1920-1949, plotted in Fig. 35. Annual Prodtiction Totals » In general, the average and peak figures of annual production prior to 1920 were very small relative to those in the 1920-1949 period covered by the chart. For example, the maximum annual production of side circuit and phantom toll cable coils prior to 1925 was in the war year 1918,* and the maximum annual production of non-phantom exchange area cable coils Table XIX Accumulated Total Production^^^— Voice Frequency Cable Loading Coils (in Millions of Coils) At End of Year Side Circuit (2) and Phantom Coils Non-Phantom Coils Total 1915 0.31 0.22 0.53 18 0.52 0.30 0.82 20 0.64 0.35 0.99 22 0.73 0.39 1.12 1924 0.95 0.53 1.48 26 1.49 0.79 2.28 28 2.69 1.32 4.01 30 5.59 2.06 7.65 1934 6.44 2.60 9.04 38 6.65 3.21 9.86 40 7.04 3.81 10.85 42 7.82 5.15 12.97 1944 8.14 5.48 13.62 46 8.49 6.69 15.18 48 9.33 9.76 19.09 49 9.46 11.27 20.72 Notes: (1) All production figures are approximate values. (2) Commercial production of side and phantom coils did not start until 1910. Up to that time non-phantom coils were used for toll cable loading (and for exchange area cables). prior to 1923 was in the war year 1917. f Thus, with occasional exceptions, the production data for the years prior to 1920 could not be accurately plotted on the chart without using a confusing s:ale. In the beginning, the use of loading was small relative to its subsequent use because the Bell System cable plant was small. For nearly a decade the expanding toll cable plant used fewer coils than the exchange plant. From then on, in the two-decade period 1913-1932, toll cable loading dominated ♦ 117,000 coil peak in 1918; 187,000 coil total in 1925. 1 33,000 coil peak in 1917; 38,000 coil total in 1923. EVOLUTION OF INDUCTIVE LOADING 1231 in the extent of use, reaching its all-time peak in growth during 1930. The four-year period of most rapid expansion of toll cable loading coincided with : (a) the full scale introduction of four-wire repeatered loaded (H44-25) circuits for long haul long-distance facilities, (b) the introduction of permalloy-core loading coils which resulted in large loading economies, and (c) the planned use of relatively large circuit-groups in order to speed up the long-distance service. The business depression of the early 1930's terminated the rapid expansion period in all types of loading. Several years later, when business conditions 1920 1922 1924 1926 1928 1930 1932 1934 1936 1938 1940 1942 1944 1946 1948 1950 YEAR (estimated) Fig. 35 — Annual production totals of voice-frequency cable loading coils for Bell Tele- phone facilities. improved sufficiently to require another large expansion in the toll cable facilities, the demand for new long-haul circuits was taken care of generally by the use of Type K carrier systems on non-loaded cable pairs and pairs from which loading was removed; and the use of new toll cable loading was largely restricted to short-haul repeatered and non-repeatered circuits. Thus it happened that, during the 1939-1942 period of rapid plant expansion, the production of exchange area loading coils substantially exceeded that for toll cable loading in the struggle to meet the demands for additional facilities required by the war effort. The post-war drive to meet the greatly mcreased demands for long- 1232 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 distance telephone service, and the provision of a tremendous amount of new exchange plant to take care of more than eleven million new Bell System telephone stations, made it necessary to build up the production rates to higher values than those during the war period. An important factor in the new heavy demands was the desire to restore the speed of service to the pre-war standards. The post-war demand for exchange area loading has been greatly in excess of that in any previous spurt in demand, reaching its peak value during 1948, and has been very large in relation to the toll cable loading requirements. The post-war rapid build-up of a backbone network of coaxial cables, together with the expanding use of carrier systems in existing and new cables of the conventional types, and the introduction of micro- wave radio relay systems have held down the demand for new toll cible loading to relatively small quantities for use on relatively short circuits. Relative Costs y Toll and Exchange Loading Production statistics by themselves do not indicate the relative economic importance of exchange area and toll cable loading. Except in the early years when coils of the same size were used for both types of loading, the toll cable loading coils have been considerably more expensive than the exchange area loading coils. During the periods of maximum production and use portrayed in Fig. 35, the average prices per potted toll cable loading coil have ranged up to about twice or three times as large as those per p)otted exchange area coil. Consequently, the total plant investment in toll cable loading is substantially greater than the total investment in exchange area loading, notwithstanding the somewhat greater total use of exchange area loading, as indicated by the production statistics. This is consistent with the fact that more expensive types of cable are used for the toll circuits and the service requirements are more difficult. Analysis in Relation to Core Materials There now follows a rough breakdown of total production in terms of core materials, in recognition of the importance of the cores in determining the coil performance characteristics and costs: In general, the production percentage figures in Table XX do not dis- criminate between types of facilities (toll or exchange area). If separate percentage-of-total figures should be derived for toll facilities and for ex- change area facilities, those for toll facilities would substantially exceed the tabulated figures for total iron-wire, iron-dust, and permalloy-powder core loading coils, especially in the case of the latter, and the percentage-of-total figure for exchange area molybdenum-permalloy core coils would greatly exceed that for toll cable loading. EVOLUTION OF INDUCTIVE LOADING 1233 In considering the two different permeability types of iron-wire and of iron-dust core-materials, it is important to note that in each case the lower permeability material had a much more extensive total use than the higher permeability material, and that it was used in the more important facilities. It is of special interest from the plant-cost standpoint that nearly two- thirds of the compressed molybdenum-permalloy powder core coils (up to the end of 1949) are the reduced cost designs using Formex-insulated conductors in their windings, this being an important factor in coil-size reduction. The other molybdenum-permalloy core coils are larger-size coils using a combination of textile and old type of enamel conductor-insulation. It is highly significant with respect to the economics of the Bell System plant growth that over one-third of all voice-frequency loading coils manu- factured up to the end of 1949 are of the lowest-cost types ever standardized Table XX Estimated Distribution of Accumulated Total Loading Coil Production Up to End of 1949 in Terms of Core Materials Core Material Fine Iron-Wire Compressed Powdered-Iron Compressed Powdered-Permalloy. . Compressed Powdered Molybdenum- Permalloy Non-Magnetic (Carrier loading) Approx. Period ^'^ of Commercial Manu- facture 1901-1927 1916-1928 1927-1938 1937- 1920- Note (1): For more definite dates in relation to different types of facilities, and in relation to the two different permeability values of the iron-wire and iron- dust materials, reference should be made to Table III (page 158). for general use. This total includes about 60% of the total production (through 1949) of all types of exchange area loading coils. Loaded Circuit Mileage Estimates To add some substance to the significance of the production statistics on voice-frequency loading, it is desirable to record some rough estimates regarding the aggregate length of the cable circuits which have been loaded. For exchange area loading, a weighted average coil-spacing between the 6000 ft. and 3000 ft. values now standard can be assumed. Considering the time elements in the evolution of loading practices, as discussed in Part III of this review, it is reasonable to assume an average coil-spacing some- what longer than the mean value of the two standard spacings, say about 5000 ft. On this assumption, the aggregate loaded cable-mileage which corresponds with an assumed production total of 11,200,000 coils is of the general order of 10,500,000 pair miles. 1234 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 The 3000-ft. spacing has been used much less extensively on toll cable circuits than in the exchange plant, on which basis the weighted average coil-spacing for quadded toll cable loading is somewhat longer than the weighted average value for exchange area loading. Within the accuracy- required for the present general estimates, 5500 ft. seems to be a reasonable estimate for the average coil spacing in quadded toll cable loading. On this basis, and assuming a production total of about 9,500,000 side circuit and phantom coils, the aggregate loaded toll cable circuit-mileage is of the order of 9,900,000 miles. Keeping in mind the substantially universal use of quadded cables and of phantom group loading for long-distance and inter- urban toll cables, the aggregate mileage of loaded toll cable quads is of the order of 3,300,000 miles. Because of the extensive installation of loaded H 44-25 four-wire repeatered circuits during the period 1925-1931, the loaded "facility** mileage-aggregate is considerably less than the loaded "circuit" mileage-figure above given. Meanwhile, much of the loaded H 44- 25 4-wire circuit mileage has been converted for short haul two-wire circuit usage, and much has been unloaded to permit the operation of Type K carrier systems. The available data on these plant changes do not permit accurate estimates regarding the mileage of loaded four-wire and two-wire types of toll cable circuits now in commercial use. It is again appropriate, however, to call attention to the important part in the growth and im- provement of the telephone service which the displaced loading coils played m their own period of commercial use. Economic Significance Since loading has been used only when it permitted the use of cheaper facilities than would otherwise have been feasible, the great economic value of loading in the growth of the Bell Telephone System is indicated by the circuit mileage-figures given above. Other factors, however, would have to receive consideration in a complete appraisal, namely, the contributions of loading to nation-wide customer satisfaction that have resulted from im- proved transmission performance and higher speed of service. In turn, these factors themselves have been greatly influenced by the unit plant-cost reductions made possible by the use of loading. For example, if loading had not been available when new or additional facilities became desirable, it is highly questionable as to whether it would have been economically feasible to work to the high-grade transmission- performance standards that have been readily achieved at reasonable costs with the cheaper loaded facilities. Moreover, it is even more questionable whether it would have been economically feasible to provide as many facilities without loading as were actually installed on a loaded basis. EVOLUTION OF INDUCTIVE LOADING 1235 Because of the speculative uncertainties involved in making assumptions regarding relative transmission-performance and relative plant-size, with and without loading, and because of the practical difficulties involved in evaluating in monetary terms the differences in transmission performance and in speed of service, no complete appraisal of the economic value of coil loading has ever been attempted for the exchange area plant. These, and additional special complications subsequently discussed, have also prevented accurate appraisals of the economic value of toll cable loading. Exchange Area Loading During the first two decades or so of the use of exchange area loading, rough estimates of its economic significance were sometimes made by comparing the total costs of the loaded faciUties with the much higher cost of the non-loaded cable plant which otherwise would have been required to meet the same trunk-loss limits at 800 or 1000 cycles. Depending on the period under study, the estimated aggregate plant-cost reduction figures ranged up to and beyond $100,000,000. These estimates included the plant-cost reductions that resulted from the use of less expensive pole fines for aerial cables, and less expensive conduit systems made possible by utilizing a smaller total number of cables, each having a larger number of pairs. If similar studies should be made now, the corresponding hypothetical plant-cost reduction figure would probably be many times as large as the figure previously mentioned. These figures ignore the superior over-all transmission in loaded trunk plant that results from the much more favorable distortion characteristics. Also they assume equal sizes of trunk plant, with and without loading. Because of these qualifications, and because of the magnitude of the cost-reduction estimates, it is difficult to define their real significance. A better understanding may perhaps be obtained from consideration of the cable data given in Table XXI, following. This compares some of the most important types of cable on which loading has been used with the types which would probably have been required for transmission reasons, if loading had not been available. The large savings which loading permitted in the use of cable copper and in the amount of lead sheath per cable pair, are indirectly indicated by the tabulated data. Moreover, with loading on finer-wire cables a given total number of facilities can be provided with a much smaller total number of cables, thus permitting the use of less expensive conduit systems. This factor is extremely important in some routes of congested sections of large metropoHtan areas such as Manhattan and the loop section in Chicago, where there might well be a question as to the physical practicability, dis- 1236 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 regarding costs, of installing enough large-conductor, non-loaded cables to provide as many facilities as those made available in existing loaded small- conductor cables. Toll Cable Loading: An accurate appraisal of the economic value of toll cable loading would have the specific complications mentioned above in the discussion of exchange area loading, and in addition certain intricate difficulties briefly discussed below. In the aggregate, a very much larger amount of loading has been used on repeatered facifities than on non-repeatered voice-frequency circuits. The over-all plant-cost reduction and the transmission and speed of service Table XXI Loaded and Non-Loaded Exchange Area Cables Relative Use or Different Types Loaded Exchange Area Cable Alternative Types of Non-Loaded Cables Degree of Use (») Conduc- tor Size B & S ga. 22 24 19 26 Copper Pair-Mile No. Pairs Full Size Cable 909(2) 1515(2) . 455(2) 2121(2) Conduc- tor Size B & S ga. Weight- Lbs. (») Pai*I?& 42.0 84.3 21.0 42.0 84.3 168.8 13.2 21.0 No. Pairs Full Size Cable Very Extensive 21.0 13.2 42.0 8.3 19 16 22 19 16 13 24 22 455(2) Very Extensive Substantial 152(3) 909(2) 455(2) 152(3) Small 75(3) 1515(2) 909(2) Notes: (1) These weights include a small allowance for the effect of pair- twist and stranding, in increasing the conductor length, relative to the cable sheath- length. (2) High-capacitance cables-(approx.) 0.082 (±) mf/mi. (3) Low -capacitance cables-(approx.) 0.066 mf/mi. (a) In the very extensive installations of exchange area loading during the 1928-1949 period, a very large fraction of the total use was on 22 and 24- gauge cables in nearly equal quantities. improvements that have resulted from the use of loading in combination with voice-frequency repeaters must of course be jointly credited to the repeaters and the loading. Since as yet no rationally acceptable procedure for allocating the pro-ratio credits has evolved, very questionable arbitrary allocations would become necessary. Moreover, very debatable uncertainties would be involved in making assumptions regarding the types of facilities which would have been employed if loading and repeaters could not have been jointly used on small-gauge toll cable conductors. In appraising the economic importance of toll cable loading it is therefore necessary to revert to general terms, namely, its great extent of use as EVOLUTION OF INDUCTIVE LOADING 1237 indicated by the previously discussed production and circuit-mileage sta- tistics. In short-haul, non-repeatered, toll cable circuits, loaded 19 ga. conductors are generally used for service which would have required 16 or 13 gauge conductors without loading. The plant-cost savings in cable, copper, and lead are much greater per unit length than the average savings realized in the loaded exchange area cables. The aggregate mileage in this type of toll plant, however, is but a small fraction of that in the loaded exchange area plant. Until the commercial exploitations of lower-cost carrier telephone systems started during the late 1930's, the loaded repeatered voice-frequency cable facilities satisfactorily met the quantitative and qualitative needs for the rapidly expanding long-distance telephone services along dense traffic routes where the use or the extension and expansion of the open-wire plant would have been unduly expensive, even on a carrier basis. In such backbone routes, and also along slow-growing tributary routes, and for short-haul toll facilities, the repeatered and non-repeatered loaded toll cables have provided more economical service than could have been obtained in an open-wire plant, and with increased dependability. Also, as previously indicated, larger circuit groups have been economically feasible, with valu- able results as regards the speed of service. In concluding this part of the review, it is noteworthy that the phantom- group loading ahnost universally used on voice-frequency repeatered and non-repeatered toll cable facilities is a major factor in the plant economies that have resulted from the commercial exploitation of the phantom working principle. These particular plant-cost savings constitute an important con- tribution to the aggregate economies achieved by toll cable loading. PART VIII: SUMMARY AND CONCLUSION General The story of coil loading told in the present review is one of continuing evolution whereby its inherent capabilities have been substantially realized in its adaptation to the growing and changing needs of exchange area facilities and of interurban and long-distance communications by wires, throughout the Bell Telephone System. Also, full advantage has been taken of the opportunities offered by the development of better core- materials and new manufacturing techniques and tools to improve the loading apparatus and reduce its cost. It was inevitable that by far the most important uses of coil loading would be for voice-frequency telephony over cable circuits. The very low 1238 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 ratio of distributed inductance to distributed capacitance, incidentally resulting in low impedances, and the relatively high conductor resistances of cable circuits, gave loading its greatest opportunities in exercising its natural functions of reducing the circuit attenuation and attenuation- frequency distortion. Clearly appreciated from the beginning, these possi- bilities have been advantageously realized to a very great extent, and they still have substantial economic importance for future voice-frequency appli- cations in the continuing growth of the exchange area non-quadded cable plant, and short, quadded interurban toll cables. Open-Wire Loading The higher ratios of distributed inductance to distributed capacitance in the open-wire lines made the reduction of attenuation-frequency distortion a relatively minor objective in the use of loading, attenuation reduction being the primary objective. Incidentally, the relatively high impedances of the non-loaded lines that resulted from their higher ratios of inductance to capacitance limited the attenuation reduction obtainable by coil loading to smaller percentage values than those obtainable on cable circuits. How- ever, full advantage of these important, though limited, possibilities was realized in the expanding open-wire plant during the decade that preceded the commercial introduction of vacuum-tube repeaters. The early uses of these repeaters on open-wire lines were on circuits having improved loading designed especially for use in conjunction with repeaters. In 1915, this combi- nation of loading and repeaters made transcontinental telephony econom- ically feasible, and for several years greatly increased the demand for loading. The importance of open-wire loading soon started to decline, however, as a result of improvements in the repeaters, their circuits, and auxiliary networks, which made it possible to secure considerably better voice-frequency transmission on long lines at a lower total cost by dis- carding loading and using more repeaters. The climactic event in this new- trend was the beginning of the operation of the first transcontinental circuits on a non-loaded basis during 1920. During the middle and late 1920's the general removal of open-wire loading was expedited to increase the plant flexibility and facilitate the commercial exploitation of carrier telephone and telegraph systems over non-loaded lines. Since, for transmission-cost reasons, it is not feasible to develop suitable loading for long lines over which carrier systems are operated, there is no reason to expect any new leases of life for open-wire coil loading. Not- withstanding its small extent of use relative to that for cable loading, and the relatively short period during which it was standard practice, open-wire loading was a necessary and a vitally important factor in the rapid expansion of long-distance telephony that began nearly five decades ago. EVOLUTION OF INDUCTIVE LOADING 1239 Toll Cable Loading The pattern of the commercial evolution of loading practices for long- distance cable systems has been generally similar to that for open-wire loading, but with important quantitative and qualitative differences, and especially in the relative time-elements. These various differences have been mainly due to the previously mentioned inherent differences in the basic transmission properties of non-loaded cables and non-loaded open-wire lines. Prior to the availability of vacuum-tube repeaters, loading was an essential factor in the establishment of a very important expanding network of storm-proof, intercity, toll cables; coarse-gauge conductors and expensive coils were used for distances ranging up to about 250 miles, 16 ga. con- ductors and less expensive coils being satisfactory for terminal business over short distances. Without using loading, these early toll cable systems would not have been economically feasible. In the early uses of repeaters on toll cables the cable circuits also used loading. These combinations permitted improved transmission performance and important extensions in transmission range. In this general connection, it is of interest to note that it was not economical to use non-loaded con- ductors for toll cable transmission until cable carrier telephone systems became available about two decades after the commercial introduction of the vacuum-tube repeater. For voice-frequency transmission, the use of repeaters without loading would have been unduly expensive, due to the high costs of the additional repeaters and the much more expensive distortion- correcting networks and regulating networks that would have been required. In the early part of the period that intervened between the introduction of vacuum-tube repeaters and of cable carrier systems, the substantially continuous development of improved loading, and of improved repeaters and auxiliary equalizing and regulating networks, provided improved fa- cilities of several different types especially proportioned on a minimum cost basis to meet the transmission-service needs of different geographical distances. High- velocity, four-wire, H 44-25 19 gauge circuits were very extensively used for long-haul facilities ranging up to about 2000 miles in length. It is of interest that the timely completion of the development of the first cable- carrier system stopped the contemporary efforts to make additional im- provements in the H 44-25 voice-frequency loaded four-wire circuits so that they would be suitable for transcontinental distances. These improvements would have involved the use of velocity distortion corrective networks. Nineteen gauge two-wire circuits having lower-velocity, higher-im- pedance, loading than that employed on the above mentioned four-wire 1240 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 circuits were very extensively used for short-haul repeatered and non- repeatered facilities. A large curtailment in the demand for loading on new long cable circuits inmiediately followed the commercial exploitation of the Type K cable- carrier system, which started during the middle 1930's. The drastic nature of this impact was subsequently increased by the standardization of a still more economical (K2) cable carrier system,^^ and by the post-war extensive installation of coaxial cable systems. The very recent development of a relatively inexpensive short-haul carrier system (Type N), which uses two pairs in the same cable for its opposite-direction paths, promises an ad- ditional substantial reduction in the need for new loaded toll cable facilities, even for short distances. However, it seems probable that the demand for new loading may continue indefinitely on a low-level basis for more or less special short-haul situations where carrier telephony may be more expensive. During the past two decades or so, loading cost-reduction has been carried so far that the prospects of further substantial cost-reductions are not now in sight. It seems improbable that any further design cost-reduction could be large enough to reverse the present general trend towards a large dependence upon carrier telephony for new short-haul toll cable facilities. Exchange Area Loading During the period covered by the present review, telephone transmission over exchange area cables has been entirely on a voice-frequency basis. Moreover, the use of vacuum-tube repeaters in conjunction with loading (or on non-loaded cables) has been statistically insignificant in comparison with the very extensive use of loading. In consequence, exchange area loading does not have to share with developments in repeaters and in carrier systems the great credit which it has earned with respect to the improvement of exchange area transmission performance and the reduction of plant cost. The simple pattern in the evolution of exchange area loading practices, relative to those for toll cable loading, is of course basically due to the shortness of the circuits and the relatively uncomplicated service-require- ments. In certain important respects, the improvements achieved by the nearly continuous development work are generally similar in the two types of loading, notably: (1) the improvement in transmission quality obtained by increasing the transmission band-width, and (2) the successive facility-cost reductions resulting from the successive developments of lower-cost loading apparatus. These plant-cost reduction activities were carried out to a greater degree in the exchange area loading. It is especially noteworthy EVOLUTION OF INDUCTIVE LOADING 1241 that the most important apparatus-cost reduction developments were com- pleted in time for exploitation during periods of peak demand for new coils. With respect to the effects of other developments in reducing the demand for exchange area loading, the introduction of improved subscriber sets during the 1930's warrants special mention. By permitting higher losses in the trunks, somewhat longer non-loaded trunks could be used. Looking towards the future, the prospective use of a new low-cost re- peater of an entirely new type (El telephone repeater) is expected to reduce the demand for the heavier weights of loading. Also, the new Type N short-haul cable carrier system, referred to on page 1240, may have some considerable use on relatively long non-loaded exchange trunks along heavy traffic routes. It is also of interest that a greatly improved telephone set (500-type) now in the final stages of development will probably reduce the need for loading on long subscriber loops. Although it is not possible at present to make accurate quantitative estimates of the ultimate effects of the just mentioned new developments upon the future demand for new exchange area loading, there is no reason to believe they will be so drastic as the effects of carrier system develop- ments upon the ultimate future demand for toll cable loading. It seems especially probable that the low-cost H-spaced loading will continue in- definitely to be an important factor in the economy of design of new exchange area cable plant to provide telephone service for a continually increasing number of subscribers. Loading for Incidental Cables in Open-Wire Lines The impedance-matching loading systems used on entrance and inter- mediate cables have made vital contributions to the excellence of the over-all performance of the open-wire transmission systems. These are of great importance relative to the amount and the cost of the loading actually used. In consequence of the increasing utilization of open-wire carrier systems, the voice-frequency loading is much less important than it was two to three decades ago. However, an indefinitely continuing, though small, demand seems certain, because of the valuable transmission improvements which the loading makes available at low cost. The demand for additional carrier loading is expected to continue in a somewhat rough proportion to the number of additional open-wire carrier systems that are installed. However, in consequence of the high cost of the loading for multi-channel systems (which is much higher than formerly in consequence of greatly increased labor and material costs), it seems probable that more and more consideration will be given (especially on **long" 1242 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 incidental cables) to the use of lower-cost transmission-improvement treat- ments, even though they are not so good as loading in certain respects. Cable Program Circuit Loading During the 1930's and early 1940's, there were extensive applications of loading on the cable sections of nation-wide chain networks used for trans- mitting AM broadcast program material. Now that high-grade program transmission circuits may be obtained by carrier methods on broadband cable carrier systems, the future demand for 8-kc loaded cable program circuits will be largely limited to special situations where the carrier program circuits are not economical. It is expected also that there will be a moderate, continuing demand for the recently developed loading that provides a 15-kc band for the trans- mission of FM program broadcast material, principally on studio-transmitter circuits, and on end links in toll cable networks, where carrier program circuits may be uneconomical. Continuotts Loading Over the years, a substantial amount of exploratory development work on continuous loading for ordinary types of paper-insulated cable has been done, but with negative results so far as commercial applications in the Bell System are concerned; it has not yet been found feasible to compete with coil loading in service performance and cost. However, continuous loading has had a few appHcations in single core submarine cables, in deep water installations where coil loading is not feasible. The three 1921 cables between Key West and Havana are the only continuously loaded cables to become a part of the Bell System. They use iron wire as the loading material. Several years later, permalloy tape continuous loading developed by the Bell Telephone Laboratories made possible a great increase in the message-carrying capacity of transoceanic telegraph cables. During the middle 1920's, an aggregate of about 15,000 nautical miles of the new type, high speed, cable was installed for use by non-affiliated telegraph and cable companies. Late in the 1920's, a perminvar type loaded cable suitable for voice- frequency telephony between Newfoundland and Ireland was developed by the Bell Telephone Laboratories. The business depression of the early 1930's intervened to cause a temporary postponement of the project; later on, an indefinite postponement resulted from improvements in transatlantic radio-telephony. From the foregoing, it is clear that the importance of continuous loading has been low relative to that of coil loading in the growth of the Bell Tele- phone System. evolution of inductive loading 1243 Conclusion During the half century that has intervened since its invention, coil loading has played a very important part in making nation-wide telephony possible and in helping to make possible the great growth in the business which has occurred. Although the application of coil loading to new circuits has now been greatly curtailed, due in large part to the development of carrier systems, coil loading still has an important field of application in exchange area telephone plant and for some rather special circuit applica- tions. The reader may take it for granted that the organization which has developed and used loading to the maximum degree of utility in the present telephone plant will be on the alert in the future to make full use of loading in situations wherever loaded circuits provide a more economical solution of the transmission service needs than the other available procedures. It is also reasonable to expect that new types of loading and new loading ap- paratus will be developed to the extent that may be economically war- ranted. Bibliography {Concluded) 23. H. D. Arnold and G. W. Elmen, "Permalloy, An Alloy of Remarkable Magnetic Properties," Journal of the Franklin Institute, Vol. 195, 1923. 42. W. H. Martin, G. A. Anderegg, and B. VV. Kendall, "Key West-Havana Submarine Cable System," Trans. A.LE.E., Vol. XLI, 1922. 43. H. A. AfTel, W. S. Gorton, and R. VV. Chesnut, "A New Key West-Havana Carrier Telephone Cable," B.S.T.J., Vol. XI, April 1932. 44. O. E. Buckley, "The Loaded Submarine Telegraph Cable," B.S.TJ., Vol. IV, July 1925; Electrical Communication, Vol. 4, No. 1, 1925, Journal AJMJE., Vol. XLIV, No. 8, 1925. 45. O. E. Buckley, "High Speed Ocean Cable Telegraphy," 5.5.7./., Vol. VII, April 1928. Presented at the International Congress of Telegraphy and Telephony in Com- memoration of Volta, Lake Como, Italy, September 1927. 46. G. W. Elmen, "Magnetic Alloys of Iron, Nickel and Cobalt," //. Franklin Institute Vol. 207, p. 583, 1929. 47. O. E. Buckley, "The Future of Transoceanic Telephony," The Thirty-third Kelvin Lecture of the Institution of Electrical Engineers, April 23, 1942; The Journal of The Institution of Electrical Engineers, Vol. 89, Part 1, 1942. (Bell Laboratories reprint, Monograph B-1346). 48. H. S. Black, F. A. Brooks, A. J. Wier and J. G. Wilson, "An Improved Cable Carrier System," Trans. AJ.E.E., Vol. 66, 1947. In addition to the published articles referred to in the text or footnotes, the following will be of interest: W. Fondiller, "Commercial Loading of Telephone Cable," Electrical Communication, Vol. 4, No. 1, July 1925. George Crisson, "Irregularities in Loaded Telephone Circuits," B.S.T.J., Vol. IV, October 1925. F. L. Rhodes, "Beginnings of Telephony," Harper and Brothers, New York, 1929. L. G. Abraham, "Circulating Currents and Singing on Two-Wire Cable Circuits," B.S.TJ., Vol. XIV, October 1935. L. L. Bouton, "Four-Wire Circuits in Retrospect," Bell Lab. Record, December 1938. S. G. Hale, "Splice Loading Developments," Bell Lab. Record, January 1951. Abstracts of Bell System Technical Papers Not Published in This Journal A Full Automatic Private Line Teletypewriter Switching System."^ W. M. Bacon^ and G. A. Locke.^ Elec. Engg., v. 70, pp. 408-413, May, 1951. Abstract — A full automatic teletypewriter message switching system has been developed for use in private line networks involving one or more switching centers and a multiplicity of local or long distance lines, each of which may have one or more stations. This system provides fast teletype- writer communication from any station to any other station or group of stations in the network. Crossbar Tandem System.* R. E. Collis.^ AJ.E.E., Trans., v. 69, pt. 2, pp. 997-1004, 1950. A Study of Nuclear and Electronic Magnetic Resonance.* K. K. Darrow.^ Elec. Engg., v. 70, pp. 401-404, May, 1951. Abstract — Since the discovery of magnetic resonance in solids, liquids, and gases in 1945, the phenomenon has been used in the determination of nuclear magnetic moments and magnetic field strengths, as well as in the study of crystal structure and relaxation times. The Genesis of Submarine Cables. L. Espenschied.^ Bibliography. Elec. Engg., 70, pp. 379-383, May, 1951. Abstract — It was a century ago that the first submarine cable was laid between Dover and Calais. To mark this centenary the author reviews some of the events leading up to this achievement which made possible further advances in the communications field, such as laying of the trans- atlantic cable by the Great Eastern escorted by four ships, as shown in the picture. Borocarbon Film Resistors. R. O. Grisdale,^ A. C. Pfister^, and G. K. Teal.^ Natl. Electronics Conference, Proc. v. 6, pp. 441-442, 1950. Abstract — The carbon film type of resistor is particularly useful at high frequencies, for not only can it be made to have small reactance but it is, in effect, all skin so that there is no increase in resistance at high frequencies due to skin effect. The film is also well cooled through its intimate contact with the core and this makes possible the dissipation of large amounts of power per unit area. While primarily developed for high frequency ap- plications in this country, the pyrolytic carbon resistor possesses other * A reprint of this article may be obtained on request. » Bell Tel. Labs. 1244 ABSTRACTS OF TECHNICAL ARTICLES 1245 characteristics which have led and are leading to greatly expanded fields of application. Principal am;)ng these are the tolerances of one per cent or better attainable in production, the stability in use, the relatively small and predictable temperature coefficient of resistance, and the low noise level. These properties result in large part from the ultimate crystalline structure of the carbon films. Some Methods of Solving Hyperbolic and Parabolic Partial Differential Equations. R. W. Hamming.^ International Business Machines Corp. Com- putation seminar. Proceedings, Dec, 1949, Ed. by C. C. Hurd. N. Y ., I.B.M., pp. 14-23, 1951. Abstract — The main purpose of this paper is to present a broad, non- mathematical introduction to the general field of computing the solutions of partial differential equations of the hyperbolic and parabolic types, as well as some related classes of equations. I hope to show that there exist methods for reducing such problems to a form suitable for formal computa- tion, with a reasonable expectation of arriving at a usable answer. I have selected four particular problems to discuss. These have been chosen and arranged to bring out certain points which I feel are important. The first problem is almost trivial as there exist well-known analytical methods for solving it, while the last is a rather complicated partial differ- ential-integral equation for which there is practically no known mathemati- cal theory. Electrography and Electro-Spot Testing.*!!. W. Hermance^ and H. V. Wadlow.^ Physical Methods in Chemical Analysis; Ed. by W. G. Berl. N. Y., Academic Press, v. 2, pp. 155-228, 1951. Correlation Energy and the Heat of Sublimation of Lithium. C. Herring.^ Letter to the editor. References. Phys. Rev., v. 82, pp. 282-283, Apr. 15, 1951. Some Theorems on the Free Energies of Crystal Surfaces.* C. Herring.^ References. Phys. Rev., v. 82, pp. 87-93, Apr. 1, 1951. Abstract — Although the interpretation of experiments in such fields as the shapes of small particles and the thermal etching of surfaces usually involves problems of kinetics rather than mere equilibrium considerations, it is suggested that a knowledge of the relative free energies of different shapes or surface configurations may provide a useful perspective. This paper presents some theorems on these relative free energies which follow from the Wulff construction for the equilibrium shape of a small particle, and some relations between atomic models of crystal surfaces and the sur- face free energy function used in this construction. Equilibrium shapes of * A reprint of this article may be obtained on request. 1 BeU Tel. Labs. 1246 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 crystals and of non-crystalline anisotropic media are classified, and it is pointed out that the possibilities for crystals include smoothly rounded as well as sharp-cornered forms. The condition is formulated for thermo- dynamic stability of a flat crystal face with respect to formation of hill-and- valley structure. A discussion is presented of the limitations on the appli- cability of the results imposed by the dependence of surface free energy on curvature; and it is concluded that these limitations are not likely to be serious for most real substances, though they are serious for certain ideal- ized theoretical models. The Crystal Stmctures of NiO-3BaO, NiO-BaO, BaNiOz and Intermediate Phases With Composition Near Ba2Ni20^ ; With a Note on NiO* J. J. Lan- der.^ References. Acta Cryst., v. 4, pp. 148-156, Mar., 1951. Abstract — ^The crystal structures of NiO-3BaO, NiO-BaO and BaNiOs have been determined from X-ray diffraction data, and data are given for phases with composition near that represented by Ba2Ni205 . In each of these structures nickel behaves in a novel fashion. A coplanar triangular arrangement of oxygen around nickel is found in NiO-3BaO. In BaNiOs nickel has a valence of four and the structure is a close-packed hexagonal stacking of planar arrangements found in perovskite 111 planes. The com- pound NiO-BaO has a magnetic moment corresponding to two unpaired electrons, whereas the deduced coplanar square arrangement of oxygen around nickel suggests that there should be no unpaired electrons. Com- pounds with composition near Ba2Ni205 contain an amount of oxygen which is a continuous function of temperature and possibly contain mixtures of bi- and tetravalent nickel. The problem of NiO having octahedral co-ordination of oxygen is con- sidered. New Ferroelectric Tartrates. B. T. Matthias^ and J. K. Hulm. Letter to the editor. Phys. Rev., v. 82, pp. 108-109, April 1, 1951. A Negative Impedance Repeater* J. L. Merrill, Jr.^ A.I.E.E., Trans., V. 69, pt. 2, pp. 1461-1466, 1950. Inter exchange Tandem Trunking in the Los Angeles Metropolitan Area. W. F. PfeifferI. A.I.E.E., Trans., v. 69, pt. 2, pp. 1071-1079, 1950. Abstract — ^Twenty-four years have elapsed since the first large-scale machine switching tandem system was designed and installed for service in Los Angeles. As an intermediate switching center, the tandem office enabled operators to use the dial method of operation for establishing inter- exchange telephone connections over the associated trunking network. During the intervening years, it has facilitated the rapid handling of tele- * A reprint of this article may be obtained on request. » Bell Tel. Labs. ABSTRACTS OF TECHNICAL ARTICLES 1247 phone calls between the various communities in and around the city. Step- by-step tandem equipment was employed and, as the volume of calls grew, the trunk capacity was increased by installing additional switching equip- ment. In 1946 it became evident that the abnormal rate of growth required additions substantially beyond the practical size limit of the step-by-step tandem unit. To solve the resulting problem, it became necessary to reor- ganize the tandem trunking system and select a multiunit tandem switch- ing plan. It also provided an opportunity to consider the application of the more recently developed crossbar tandem switching system. This paper reviews the factors affecting the general problem of interexchange trunking which have led to the development of the present tandem network in the Los Angeles metropolitan area. It describes the major elements of a system which now employs a total of five tandem switching units, three of which are crossbar tandem offices. p-n Junction Rectifier and Photo-cell. W. J. Pietenpol^ Letter to the editor. Phys. Rev., v. 82, pp. 120-121, Apr. 1, 1951. Formulas for the Determination of Residual Stress in Wires by the Layer Removal Method.* W. T. Read, Jr.^. //. Applied Phys., v. 22, pp. 415-416, Apr., 1951. Abstract — The distribution of residual axial stress in a beam or wire of circular cross section is derived as a function of the moment required to straighten the wire after removal of successive layers of material. Applica- tion of the formulas involves two graphical differentiations and integra- tions of experimental curves. ' Observation of Magnetic Domains by the Kerr Effect. H. J. Williams^ F. G. Foster!, and E. A. Wood^. Letter to the editor. Phys. Rev., v. 82, pp. 119-120, Apr. 1,1951. Particle Size in Suspension Polymerization.* F. H. Winslow^ and W. Matreyek^ Bibliography. Ind. & Engg. Chem., v. 43, pp. 1108-1112, May, 1951. Abstract — Control of size and geometrical form of densely cross-linked hydrocarbon polymers yields fluid spherical powders useful as dielectrics and in rheological studies. Such studies also bear on polymer forms impor- tant in ion exchange resins. Several significant factors influencing the preparation of polymer sphe- roids have been established on a semi-quantitative basis: Polyvmyl alcohol proved to be a highly efficient stabilizer for polymer spheroid preparations. Under comparable conditions, (a) high molecular weight grades, (b) par- tially hydrolyzed grades, and (c) high concentrations of stabilizer were * A reprint of this article may be obtained on request. 1 Bell Tel. Labs. 1248 THE BELL SYSTEM TECHNICAL JOUENAL, OCTOBER 1951 associated with spheroids of lower mean diameters. These generalizations cover suspension stabilization down to roughly 0.1% stabilizer. The con- centration limits where suspending action begins are, however, of special interest. Here it was found that the number of polyvinyl alcohol molecules present became important — that is, for equal weight concentrations in the vicinity of 0.005%, low molecular weight polymer (19,000) produced sta- bilized (although large) spheres whereas the usual high molecular weight polymer (95,000) was ineffective. Close to the maximum possible yield of well-formed spheroids was repro- ducibly obtained in narrow size distribution and with average spheroid diameters ranging from 5 microns to several millimeters in diameter — a thousand-fold variation in dimensions. Elastic and Electromechanical Coupling Coefficients of Single-Crystal Bar- ium Titanate. W. L. Bond^, W. P. Mason^, and H. J. McSkimin^ Letter to the editor. Phys. Rev., v. 82, pp. 442-443, May 1, 1951. Making Small Spheres. W. L. Bond^ Rev. Sci. Instruments, v. 22, pp. 344-345, May, 1951. Submarine Telephone Cable With Submerged Repeaters. J. J. Gilbert^. Electronics, v. 24, pp. 164, 168, 172+, June, 1951. Electrode Reactions in the Glow Discharge.* F. E. Haworth^ References. //. Applied Phys., v. 22, pp. 606-609, May, 1951. Abstract — The reactions which occur at silver electrodes in a normal glow discharge in air have been determined. These are: (1) formation of AgN02 and some Ag20 at the anode at the rate of 3.4 /zg/coulomb; (2) loss of metal from the cathode by chemical action at the rate of 3.5 /xg/coulomb (probably the same reaction as (1) with subsequent loss of the reaction products by the greater heating of the cathode, but this hypothesis has not been established); and (3) normal sputtering loss at the cathode at the rate of 0.4 /ug/coulomg. These processes result in building a conducting layer on the anode. If the electrode separation is so small that the anode extends into the region of the cathode fall, then the high electric field pulls the newly formed and not very coherent growth upon the anode across into a bridge between the electrodes. Storing Video Information.* k. L. Hopper^ Electronics, v. 24, pp. 122- 125, June, 1951. Abstract — Comparison of signal amplitudes along adjacent television scanning lines can be made by storing the video information of one line for 63.5 microseconds. Storage is done in an ultrasonic delay line employing a fused silica bar with quartz transducers. * A reprint of this article may be obtained on request. » Bell Tel, Labs. ABSTRACTS OF TECHNICAL ARTICLES 1249 Cross Sections for I on- A torn Collisions in He, Ne, and .4. J. A. Hornbeck' and G. H. Wannier^. Letter to the editor. Phys. Rev., v. 82, p. 458, May 1, 1951. Ferromagnetic Resonance.*C. Kittel^ Bibliography. //. de Physique, v. 12, pp. 291-302, Mar., 1951. Theory of Antiferroelectric Crystals. C. Kittel^ References. Phys. Rev., V. 82, pp. 729-732, June 1, 1951. Abstract — An antiferroelectric state is defined as one in which lines of ions in the crystal are spontaneously polarized, but with neighboring lines polarized in antiparallel directions. In simple cubic lattices the antiferro- electric state is likely to be more stable than the ferroelectric state. The dielectric constant above and below the antiferroelectric curie point is in- vestigated for both first- and second-order transitions. In either case the dielectric constant need not be very high; but if the transition is second order, e is continuous across the Curie point. The antiferroelectric state will not be piezoelectric. The thermal anomaly near the Curie point will be of the same nature and magnitude as in ferroelectrics. A susceptibility variation of the form C/(T + Z) as found in strontium titanate is not indicative of antiferroelectricity, unlike the corresponding situation in anti- ferromagnetism. Theory of Antiferromagnetic Resonance C. Kittel^ Letter to the editor. Phys. Rev., v. 82, p. 565, May 15, 1951. Barium-Nickel Oxides With Tri- and Tetravalent Nickel.* J. J. Lander^ and L. A. WootenI. ^^ Chem. Soc, Jl., v. 73, pp. 2452-2454, June, 1951. Abstract — The compound BaNiOa and intermediates with composition ranging between BasNiaOs and Ba2Ni205 have been prepared. BaNiOs is black, stable in alkali, and has a structure made up of layers identical with the 111 planes of a perovskite but stacked in a close-packed hexagonal fash- ion. At 730° in 730 mm. of oxygen, the structure changes to that associated with the series BasNiaOg to Ba2Ni205 in which the oxygen content appears to decrease continuously with temperature increasing to 1200°, at which point sharp melting is observed. These materials are black and stable in alkali with an hexagonal structure for which the details have not been deter- mined. Resistivities and magnetic susceptibilities are reported. A wide range in composition, temperature and reaction atmosphere was studied but only one additional compound was observed. Attempts to isolate this compound were not successful. The Phase System BaO-NiO.* J. J. Lander^ Am. Chem. Soc, JL, v. 73, pp. 2450-2452, June, 1951. * A reprint of this article may be obtained on request. 1 Bell Tel. Labs. 1250 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Abstract — ^The phase system BaO-NiO has been studied largely by means of X-ray diffraction. The two compounds NiO BaO and NiO 3BaO occur in the system. Their preparation and properties are described. NiO BaO is black, stable in air, orthorhombic, and melts at 1240°. NiO 3BaO is gray- green, unstable in air, hexagonal, and melts at 1160°. A eutectic melting at 1080° is observed between these compounds, but none between NiO 3BaO and BaO. Intersolubility of all solid phases in the system is small, even at high temperatures, but quantitative data have not been obtained. A Phenomenological Derivation of the First- and Second-Order Magneto- striction and Morphic Effects for a Nickel Crystal* W. P. Mason^ References. Phys. Rev., v. 82, pp. 715-723, June 1, 1951. Abstract — In order to account for experimental results which showed that the saturation elastic constants of a single nickel crystal varied with the direction of magnetization, a phenomenological investigation has been made of the stress, strain, and magnetic relations for single nickel crystals. The variation in elastic constants is shown to be a "morphic" effect caused by the change in the crystal symmetry due to the magnetostriction effect. In the energy equation this effect is represented by additional terms which involve squares and products of both the magnetic intensities and stresses. These terms are as large as the magnetostrictive terms when the stresses are of the order of 10^^ dynes/cm^ The energy equation has been used to derive the first- and second-order magnetostrictive effect, and the resulting terms agree with Becker and Boring's empirical constants for saturation conditions. For smaller magnetic intensities the terms divide up into first- and second- order terms which vary differently with magnetic field intensity. It is shown that the morphic effects involve six measurable constants, and some of these are evaluated experimentally. Dielectric Properties of Sodium and Potassium Niobates/^ B. T. Matthia.s^ and J. P. Remeika^ Phys. Rev., v. 82, pp. 727-729, June 1, 1951. Abstract — The following paper deals with evidence of ferroelectricity in KNbOa and NaNbOa. Temperatures at which both materials undergo crys- tallographic changes and corresponding changes in dielectric constant and loss tangent are reported. Photographs of dielectric hysteresis loops and values of saturation polarization taken at various points over a temperature range are given for KNbOa. Ferroelectricity. B. T. MATTHIAS^ Bibliography. Science, v. 113, pp. 591- 596, May 25, 1951. Abstract — Under the name of Ferroelectrics one classifies those materials which exhibit dielectric anomalies phenomenologically similar to the mag- * A reprint of this article may be obtained on request. Bell Tel. Labs. ABSTRACTS OF TECHNICAL ARTICLES 1251 netic behavior of the ferromagnetics. Perhaps it would have been more logical to use the term Rochelle electrics, thus emphasizing the similarity in the dielectric behavior to that of Rochelle salt, for which this behavior was first discovered by J. Valasek. In this discussion the known ferroelectrics will be listed, and the various theories that have been created to explain them will be examined. Theory of Ferroelectric Behavior of Barium Titanate. P. W. Anderson'. References. Ceramic Age, v. 57, pp. 29-30, 33+, April, 1951. Criterion for Superconductivity. J. Bardeen^ Letter to the Editor. Phys. Rev., V. 82, pp. 978-979, June 15, 1951. Magnetic Domain Patterns.* R. M. Bozorth^ Bibliography. //. de Phy- sique, V. 12, pp. 308-321, March, 1951. Electron Temperature vs Noise Temperature in Low Pressure Mercury- Argon Discharges. M. A. Easley' and W. W. Mumford^ Letter to the Editor. //. Applied Phys.,v. 22, pp. 846-847, June, 1951. The Origin of Bombardment-Enhanced Thermionic Emission.* J. B. John- SON^ References. Phys. Rev., v. 83, pp. 49-53, July 1, 1951. Abstract — Measurements on bombardment-enhanced thermionic emis- sion from oxide cathodes show that (a) the effect is not related to normal fading and recovery of thermionic emission; (b) the emitted electrons have energies in the thermal range rather than in the secondary range. Calcula- tions indicate that the electron bombardment releases more than enough internal secondaries to account for the effect as increased thermionic emis- sion. A more comprehensive theory is needed for explaining why the observed effect is not even larger. Dipolar Domains in Paramagnetic Crystals at Low Temperatures. C. KittellI. Letter to the Editor. Phys. Rev., v. 82, pp. 965-966, June 15, 1951. Methods of Measuring Adjacent-Band Radiation from Radio Transmitters.* N. Lund'. I.R.E. Proc, v. 39, pp. 653-656, June, 1951. Abstract — A review of three possible methods of measuring or estimating adjacent-band radiation characteristics of a radio transmitter is given. These three methods differ in the type of signal applied to the transmitter and may be termed the two-tone, normal signal, and thermal noise methods. Measurements on a multichannel single-sideband transmitter using each of these methods are presented to show that there is a good correlation between the normal signal and thermal noise methods. An empirical method for calculating the slope of the adjacent-band radia- tion as a function of frequency from the measured two-tone distortion values * A reprint of this article may be obtained on request. 1 Bell Tel. Labs. 1252 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 is given, and the measured and calculated slopes are shown to be in fairly good agreement. Microwave Spectrum in NO2. K. B. Mc Afee, Jr.^ Letter to the Editor. Phys. Rev., v. 82, p. 971, June 15, 1951. A Simple Electronic Differential Analyzer as a Demonstration and Labora- tory Aid to Instruction in Engineering. M. H. Nichols^ and D. W. Hagel- BARGER^ //. Engg. Education, v. 41, pp. 621-630, June, 1951. Telecommunications. H. S. Osborne^. Ordnance, v. 36, pp. 87-90, July- August, 1951. Triangular Permutation Numbers. J. Riordan^. References. Am. Math. Soc, Proc, V. 2, pp. 429-432, June, 1951. Measurements of Dynamic Internal Dissipation and Elasticity of Soft Plastics.* H. C. RordenI and A. Grieco^. //. Applied Phys., v. 22, pp. 842- 845, June, 1951. Abstract — In order to measure the mechanical properties of soft plastics over wide frequency and temperature ranges two new techniques have been devised. The first one, which operates in the frequency range of a few cycles, uses a horizontal oscillating pendulum. The shear impedance of the sample is measured by mounting a small pad of the material between the vibrating pendulum and a fixed platform and determining the change in frequency and the change in the decrement caused by the sample. From these measure- ments the shear mechanical resistance and reactance of the specimen can be determined. The other technique, which is applicable in the frequency range from 100 cycles to 10,000 cycles, makes use of a vibrating tuning fork. Two identical samples are mounted between a stationary weight and the moving tines, and the shear mechanical impedance is determined by deter- mining the change in frequency and change in decrement caused by the specimen. These two techniques have been applied to measuring the shear properties of a number of soft plastics including Pyralin, Koroseal, Keldur, polyvinyl butyral, Thiokol, and gum rubber. All of these show relaxation effects. The polyvinyl butyral appears to be approaching a crystalline elastic stage at the low frequency of 1000 cycles, while gum rubber remains in a quasi-co'nfigurational stage from 2 cycles to 1000 cycles. The Mobility of Electrons in Silver Chloride.* J. R. Haynes^ and W. Shockley^ References. Phys. Rev., v. 82, pp. 935-943, June 15, 1951. Abstract — Techniques are described which utilize the ''print out effect" to obtain both the direction and velocity of photoelectrons in silver chloride crystals in an electric field. Hall mobility of the electrons is calculated from their change in direction produced by crossed electric and magnetic fields. * A reprint of this article may be obtained on request. » Bell Tel. Labs. ABSTRACTS OF TECHNICAL ARTICLES 1253 Drift mobility of the electrons is obtained by measurement of their velocity in known electric fields. The value obtained for the Hall mobility (Ra) multiplied by S/Stt is 51 cmVvolt sec at 25°C. The values obtained for the drift mobility are shown to be a function of temperature. A value of 49.5 cmVvolt sec was obtained at 25°C, which is within experimental error of (8/37r)R(7, indicating that acoustical scattering is the principal mechanism and that temporary trapping is unimportant. A summary of the behavior of conduction electrons in silver chloride, calculated from the results of these experiments, is included. p-n Junction Transistors * W. Shockley^ M. Sparks^, and G. K. Teal^ References. Phys. Rev, v. 83, pp. 151-162, July 1, 1951. Abstract — The effects of diffusion of electrons through a thin p-type layer of germanium have been studied in specimens consisting of two n-type regions with the p-type region interposed. It is found that potentials applied to one n-type region are transmitted by diffusing electrons through the p-type layer although the latter is grounded through an ohmic contact. When one of the p-n junctions is biased to saturation, power gain can be obtained through the device. Used as "n-p-n transistors" these units will operate on currents as low as 10 microamperes and voltages as low as 0.1 volt, have power gains of 50 db, and noise figures of about 10 db at 1000 cps. Their current-voltage characteristics are in good agreement with the diffusion theory. * A reprint of this article may be obtained on request. 1 Bell Tel. Labs. Contributors to This Issue B. S. Biggs, B.A., Southwest Texas Teachers College, 1927; M.A., Uni- versity of Texas, 1931, Ph.D., 1933; Civil Research Laboratory, Carnegie Institute of Technology, 1933-1936. Bell Telephone Laboratories, 1936-. With the Laboratories he has worked chiefly on the synthesis of wood pre- servatives, on dielectric materials and on other phases of organic chemistry. He is a member of the American Chemical Society and of Sigma Xi. G. T. Ford, B.S., Michigan State College, 1929; M.A., Columbia, 1936. Bell Telephone Laboratories, 1929-. With the Laboratories he has worked on gas tubes, thermistors, general vacuum tube development, and electron tubes for broad band amplifiers. He is a member of the Institute of Radio Engineers. R. W. Frus, B.E.E., University of Minnesota, 1930. Bell Telephone Labo- ratories, 1930-. With the Laboratories Mr. Friis has been concerned with transoceanic and ship-to-shore radio telephone, fire-control radio trans- mitters, and the microwave radio -relay system. He is a Senior Member of the Institute of Radio Engineers. J. C. LoziER, B.A., Columbia, 1934. R.C.A. Mfg. Co., 1935-1936. Bell Telephone Laboratories, 1936-. Mr. Lozier's work with the Laboratories has been principally transmission development for radio and carrier tele- phone systems, the theory and design of servomechanisms, and the theory of feedback systems such as compandors and regulators. He is a Senior Member of the Institute of Radio Engineers. R. C. Prim, III, B.S.E.E., University of Texas, 1941; M.A. and Ph.D., Princeton, 1949. General Electric Company, 1941-44; Naval Ordnance Laboratory, 1944-49. Bell Telephone Laboratories, 1949-. Here his work has been chiefly mathematical research on non-linear partial differential equations and as a consultant on military projects. Dr. Prim is a member of the Amer. Math. Soc, the Amer. Phys. Soc, Sigma Xi and Tau Beta Pi. John Riordan, B.S., Yale, 1923. Amer. Tel. and Tel., 1926-34; Bell Telephone Laboratories, 1934-. With the American Company and subse- quently with the Laboratories, Mr. Riordan has been concerned chiefly with 1254 CONTRIBUTORS TO THIS ISSUE 1255 transmission theory, the application of Boolean algebra to switching, number theory in cable splicing, and combinatorial and probability studies of traffic. He is a member of the Amer. Math. Soc, Math. Assoc, of America, Inst, of Math. Statistics, and Fellow of the Amer. Assoc, for the Advancement of Science. A. A. RoETKiN, B.E.E., Ohio State University, 1927; M.Sc, 1929. Bell Telephone Laboratories, 1929-. With the Laboratories Mr. Roetkin has worked on overseas radio telephone receivers, ultra-high frequency, point- to-point radio telephone service, pulse multiplex microwave radio repeaters for the armed forces, and microwave radio-relay systems. He is a member of the Institute of Radio Engineers. Thomas Shaw, S.B., Massachusetts Institute of Technology, 1905. Ameri- can Telephone and Telegraph Company, Engineering Department, 1905-19; Department of Development and Research, 1919-33. Bell Telephone Labora- tories, 1933-48. Mr. Shaw's active telephone career was mainly concerned with loading problems in telephone circuits, including the transmission and economic features of the loading apparatus. The article which is concluded in this issue was started shortly before his retirement in 1948. K. D. Smith, B.A., Pomona College, 1928; M.A., Dartmouth, 1930. Bell Telephone Laboratories, 1930-. Consultant to National Defense Research Council, 1941-44. Awarded Joint Army-Navy Certificate of Appreciation for Scientific Achievement following World War II. With the Laboratories Mr. Smith has been concerned with the coaxial cable system, radar bombing equipment, broad band microwave radio system, and transistors. He is a Senior Member of the Institute of Radio Engineers. R. L. Wallace, Jr., B.A. summa cum laude, physics and mathematics, University of Texas, 1936; M.A., physics, 1939; Special Research Associate, Harvard, 1941-45. Bell Telephone Laboratories, 1946-. Mr. Wallace's work with the Laboratories has been chiefly concerned with magnetic recording and transistors. He is a member of the Acoustical Society of America, Phi Beta Kappa, and Sigma Chi. E. J. Walsh, Bell Telephone Laboratories, 1928-. Mr. Walsh's work with the Laboratories has been chiefly on vacuum tube design, magnetrons, proximity fuse tubes, reflex oscillators and close-spaced fine- wire grid tubes. THE BELL SYSTEM TECHNICAL JOURNAL VOLUME XXX, 195 1 Table of Contents January 1951 The Type N-1 Carrier Telephone System: Objectives and Transmis- sion Features — R. S. Caruthers 1 Television by Pulse Code Modulation — W. M. Goodall ?>2t Prediction and Entropy of Printed English — C. E. Shannon 50 A Submarine Telephone Cable with Submerged Repeaters — J. J. Gilbert 65 Theory of the Negative Impedance Converter — J. L. Merrill 88 The Ring Armature Telephone Receiver — E. E. Mott and R. C. Miner. . 1 10 Internal Temperatures of Relay Windings — R. L. Peek 141 The Evolution of Inductive Loading for Bell System Telephone Facilities — T. Shaw 149 April i951 The Seventy-fifth Anniversary of the Telephone 213 Seventy-five Years of the Telephone: An Evolution in Technology — W. E. Martin 215 An Improved Telephone Set — A . H. Inglis and W. L. Tuffnell 239 Pyrolytic Film Resistors: Carbon and Borocarbon — R. O. Grisdale, A. C. Pfister, and W . van Roosbroeck 271 The Potential Analogue Method of Network Synthesis — Sidney Darlington 315 Zero Temperature Coefficient Quartz Crystals for Very High Tem- peratures— W. P. Mason 366 Duality as a Guide in Transitor Circuit Design — R. L. Wallace, Jr. and G. Raisbeck 381 Some Design Features of the N-1 Carrier Telephone System — W. E. Kahl and L. Pedersen 418 The Evolution of Inductive Loading for Bell System Telephone Facili- ties (Continued) — Thomas Shaw 447 July 1951 Reduction of Skin Effect Losses by the Use of Laminated Conductors —A. M. Clogston 491 111 iv THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Some Circuit Properties and Applications of n-p-n Transistors — R. L. Wallace, Jr. and W. J. Pietenpol 530 A Photographic Method for Displaying Sound Wave and Microwave Space Patterns — W. E. Kock and F. K. Harvey 564 Some Basic Concepts of Translators and Identifiers Used in Telephone Switching Systems — H. H. SchnecUoth 588 Waves in Electron Streams and Circuits — J. R. Pierce ^26 Interaxial Spacing and Dielectric Constant of Pairs in Multipaired Cables — J. T. Maupin 652 iV-Terminal Switching Circuits — E. N. Gilbert 668 Coaxial Impedance Standards — R. A . Kempf 689 Instantaneous Compandors — C. O. Mallinckrodt 706 The Evolution of Inductive Loading for Bell System Telephone Facili- ties (Continued) — Thomas Shaw 721 October i951— part i Dr. C. J. Davisson— Af. J. Kelly 779 The Scientific Work of C. J. D^isson— i^Tar/ K. Darrow 786 Inorganic Replication in Electron Microscopy — C. /. Calbick 798 A Gun for Starting Electrons Straight in a Magnetic Field — J, R. Fierce 825 Electron Streams in a Diode — Frank Gray 830 The Davisson Cathode Ray Television Tube Using Deflection Modu- lation— A . G. Jensen 855 Electron Transmission Through Thin Metal Sections with Applica- tion to Self-Recovery in Cold Worked Aluminum — R. D. Heidenreich 867 On the Reflection of Electrons by Metallic Crystals — L. A . MacColl. ... 888 The Use of the Field Emission Electron Microscope in Adsorption Studies of W on W and Ba on W— J. A. Becker 907 Heat Dissipation at the Electrodes of a Short Electric Arc — L. H. Germer .' 933 Detwinning Ferroelectric Crystals — Elizabeth A. Wood 945 Longitudinal Modes of Elastic Waves in Isotropic Cylinders and Slabs— ^. N. Holden 956 Frequency Dependence of Elastic Constants and Losses in Nickel — R. M. Bozorth, W. P. Mason and H. J. McSkimin 970 Hot Electrons in Germanium and Ohm's Law — W. Shockley 990 October i95i— part ii The TD-2 Microwave Radio-Relay System— yl. A. Roetken, K. D. Smith and R. W. Friis 1041 CONTENTS V Deterioration of Organic Polymers — B. S. Biggs 1078 The Development of Electron Tubes for a New Coaxial Transmission System — G. T. Ford and E. J. Walsh 1103 Telephone Traffic Time Average — John Riordan 1129 The Reproduction of Magnetically Recorded Signals — R. L. Wallace, Jr 1145 Some Results Concerning the Partial Differential Equations Describ- ing the Flow of Holes and Electrons in Semi-conductors — R. C. Prim, III 1174 Instantaneous Compandors on Narrow Band Speech Channels — J. C. Lozier 1214 The Evolution of Inductive Loading for Bell System Telephone Facili- ties— Thomas Shaw 1221 Index to Volume XXX A Adsorption Studies of W on W and Ba on W, The Uee of the Field Emission Electron Microscope in, J. A. Becker, page 907. Aluminum, Cold Worked, Electron Transmission Through Thin Metal Sections with Ap- plication to Self-Recovery in, R. D. Heidenreich, page 867. Anniversary, The Seventy-fifth, of the Telephone, page 213. Applications of n-p-n Transistors, Some Circuit Properties and, R. L. Wallace, Jr., and W. J. Pietenpol, page 530. Arc, Short Electric, Heat Dissipation at the Electrodes of a, L. H. Germer, page 933. Armature, Ring, Telephone Receiver, The, E. E. Mott and R. C. Miner, page 110. Average, Telephone Traffic Time, John Riordan, page 1129. B Becker, J. A., The Use of the Field Emission Electron Microscope in Adsorption Studies of W on W and Ba on W, page 907. Biggs, B. S., Deterioration of Organic Polymer, page 1078. Borocarbon, Carbon and: Pyrolytic Film Resistors, R. O. Grisdale, A. C. Pfister, and W. vati Rooshroeck, page 271. Bozorth, R. M., Mason, W. P. and McSkimin, H. J., Frequency Dependence of Elastic Constants and Losses in Nickel, page 970. C Cable, Submarine Telephone, with Submerged Repeaters, A, /. /. Gilbert, page 65. Cables, Multipaired, Interaxial Spacing and Dielectric Constant of Pairs in, /. T. Maupin, page 652. Calbick, C. J., Inorganic Replication in Electron Microscopy, page 798. Carbon and Borocarbon: Pyrolytic Film Resistors, R. O. Grisdale, A. C. Pfister, and W. van Roosbroeck, page 271. Carrier, N-1, Telephone System, Some Design Features of the, W. E. Kahl andL. Pedersen, page 418. Carrier Telephone System Objectives and Transmission Features, The Type N-1, i?. S. Caruthers, page 1, Carutliers, R. S., The Type N-1 Carrier Telephone System Objectives and Transmission Features, page 1. Circuit Design, Transistor, Duality as a Guide in, R. L. Wallace, Jr. and G. Raisbeck, page 381. Circuit Properties and Applications of n-p-n Transistors, Some, R. L. Wallace, Jr., and W. J. Pietenpol, page 530. Circuits, Waves in Electron Streams and, /. R. Pierce, page 626. Clogston, A. M., Reduction of Skin Effect Losses by the Use of Laminated Conductors, page 491. Coaxial Impedance Standard, R. A. Kempf, page 689. Coaxial Transmission System, New, The Development of Electron Tubes for a, G. T. Ford and E. J. Walsh, page 1103. Coefficient Quartz Crystals for very High Temperatures, Zero Temperature, W. P. Mason, page 366. Compandors, Instantaneous, C 0. Mallinckrodt, page 706. Compandors, Instantaneous, on Narrow Band Speech Channels, /. C. Lozier, page 1214. Concepts of Translators and Identifiers Used in Telephone Switching Systems, Some Basic, //. H. Schneckloth, page 588. Conductors, Laminated, Reduction of Skin Effect Losses by the Use of, A. M. Clogston, page 491. Constants and Losses, Elastic, in Nickel, Frequency Dependence of, R. M. Bozorlh, W. P. Mason and H. J. McSkimin, page 970. INDEX Vll Converter, Negative Impedance , Theory of the, /. L. Merrill, page 88. Crystals, Detvvinning Ferroelectric, Elizabeth A. Wood, page 945. Crystals, Metallic, On the Reflection of Electrons by, L. A. MacColl, page 888. Crystals, Quartz, for Very High Temperatures, Zero Temperature Coefficient, W. P. Mason, page 366. Cylinders and Slabs, Isotropic, Longitudinal Modes of Elastic Waves in, A. N. Holden, page 956. Darlington, Sidney, The Potential Analogue Method of Network Synthesis, page 315. Darrow, Karl A'., The Scientific Work of C. J. Davisson, page 786. Davisson Cathode Ray Television Tube Using Deflection Modulation, The, A. G. Jensen, page 855. Davisson, C. J., The Scientific Work of, Karl K. Darrow, page 786. Davisson, Dr. C. J., M. J. Kelly, page 779. Deterioration of Organic Polymers, B. S. Biggs, page 1078. Detwinning Ferroelectric Crystals, Elizabeth A. Wood, page 945. Dielectric Constant of Pairs in Multipaired Cables, Interaxial Spacing and, /. T. Maiipin, page 652. Diode, Electron Streams in a, Frank Gray, page 830. Dissipation, Heat, at the Electrodes of a Short Electric Arc, L. H. Germer, page 933. Duality as a Guide in Transistor Circuit Design, R. L. Wallace, Jr. and G. Kaisbeck, page 381. Electron Microscope, Field Emission, in Adsorption Studies of W on W and Ba on W, The Use of the, /. A. Becker, page 907. Electron Microscopy, Inorganic Replication in, C. /. Calbick, page 798. Electron Streams and Circuits, Waves in, /. R. Pierce, page 626. Electron Streams in a Diode, Frank Gray, page 830. Electrons in Semiconductors, Some Results Concerning the Partial Differential Equations Describing the Flow of Holes and, R. C. Prim, III, page 1174. Electrons, Hot, in Germanium and Ohm's Law, W. Shockley, page 990. Electrons by Metallic Crystals, On the Reflection of, L. A. MacColl, page 888. Electrons Straight in a Magnetic Field, A Gun for Starting, J. R. Pierce, page 825. English, Printed, Prediction and Entropy of, C. E. Shannon, page 50. Entropy of Printed English, Prediction and, C. E. Shannon, page 50. Equations Describing the Flow of Holes and Electrons in Semiconductors, Some Re- sults Concerning the Partial Differential, R. C. Prim, III, page 1174. Evolution of Inductive Loading for Bell System Telephone Facilities, The, Thomas Shaw, pages 149, 447, 721, 1221. Evolution in Technology, An, Seventy-five Years of the Telephone :, W. H. Martin, [lage 215. Facilities, Bell System Telephone, The Evolution of Inductive Loading for, Thomas Shaw, pages 149, 447, 721, 1221. Ford, G. T. and Walsh, E. J., The Development of Electron Tubes for a New Coaxial Transmission System, page 1103. Friis,R. W., Roetken, A. A. and Smith, K. D., The TD-2 Microwave Radio-Relay System, page 1041. Germanium and Ohm's Law, Hot Electrons in, W. Shockley, page 990. Germer, L. H., Heat Dissipation at the Electrodes of a Short Electric Arc, page 933. Gilbert, E. N., N-Terminal Switching Circuits, page 668. Gilbert, J. J., A Submarine Telephone Cable with Submerged Repeaters, page 65. Goodall, W. M., Television by Pulse Code Modulation, page 33. Gray, Frank, Electron Streams in a Diode, page 830. viii THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Grisdale, R. 0., Pfister, A. C., and van Rooshroeck, W., Pyrolytic Film Resistors: Carbon and Borocarbon, page 271. Gun for Starting Electrons Straight in a Magnetic Field, A, /. R. Pierce, page 825. H Harvey, F. K. and Kock, W. E., A Photographic Method for Displaying Sound Wave and Microwave Space Patterns, page 564. Heidenreich, R. D., Electron Transmission Through Thin Metal Sections with Application to Self-Recovery in Cold Worked Aluminum, page 867. H olden, A. N., Longitudinal Modes of Elastic Waves in Isotropic Cylinders and Slabs, page 956. Holes and Electrons in Semiconductors, Some Results Concerning the Partial Differential Equations Describing the Flow of: R. C. Prim, III, page 1174. I Identifiers Used in Telephone Switching Systems, Some Basic Concepts of Translators and, H. H. Schneckloth, page 588. Impedance Converter, Negative, Theory of the, /. L. Merrill, page 88. Impedance Standards, Coaxial, R. A. Kempf, page 689. Improved Telephone Set, An, A. H. Inglis and W. L. Tuffnell, page 239. Inglis, A. H. and Tuffnell, W. L., An Improved Telephone Set, page 239. Inorganic Replication in Electron Microscopy, C. /. Calbick, page 798. Instantaneous Compandors, CO . Mallinckrodt, page 706. J Jensen, A. G., The Davisson Cathode Ray Television Tube Using Deflection Modulation, page 855. K Kahl, W. E. and Pedersen, L., Some Design Features of the N-1 Carrier Telephone System, page 418. Kelly, M. J., Dr. C. J. Davisson, page 779. Kempf, R. A., Coaxial Impedance Standards, page 689. Kock, W. E. and Harvey, F. K., A Photographic Method for Displaying Sound Wave and Microwave Space Patterns, page 564. L Laminated Conductors, Reduction of Skin Effect Losses by the Use of, A. M. Clogston, page 491. Loading, Inductive, for Bell System Telephone Facihties, The Evolution of, Thomas Shaw, pages 149, 477, 721, 1221. Losses in Nickel, Elastic Constants and. Frequency Dependence of, R. M. Bozorth, W. P. Mason and H. J. McSkimin, page 970. Losses, Skin Effect, by the Use of Laminated Conductors, Reduction of, A. M. Clogston, page 491. Lozier,J. C, Instantaneous Compandors on Narrow Band Speech Channels, page 1214. M MacColl, L. A., On the Reflection of Electrons by Metallic Crystals, page 888. Magnetic Field, A Gun for Starting Electrons Straight in a, /. R. Pierce, page 825. Mallinckrodt, C. O., Instantaneous Compandors, page 706. Mason, W. P., Bozorth, R. M. and McSkimin, H. J., Frequency Dependence of Elastic Constants and Losses in Nickel, page 970. Mason, W. P., Zero Temperature Coefficient Quartz Crystals for Very High Temperatures, page 366. Martin, W. H., Seventy-five Years of the Telephone: An Evolution in Technology, page 215. Maupin, J. T., Interaxial Spacing and Dielectric Constant of Pairs in Multipaired Cables, page 652. INDEX IX McSkimin, H. J., Bozorth, R. M. and Mason, W. P., Frequency Dependence of Elastic Constants and Losses in Nickel, page 970. Metal Sections, Thin, With Application to Self-Recovery in Cold Worked Aluminum, Electron Transmission Through, R. D. Heidenreich, page 867. Method of Network Synthesis, The Potential Analogue, Sidney Darlington, page 315. Merrill, J. L., Theory of the Negative Impedance Converter, page 88. Microscope, Field Emission Electron, in Adsorption Studies of W on W and Ba on W, The Use of the, /. A. Becker, page 907. Microscopy, Electron, Inorganic Replication in, C. J. Calbick, page 798. Microwave Space Patterns, A Photographic Method for Displaying Sound Wave and, W. E. Kock and F. K. Harvey, page 564. Microwave Radio-Relay System, The TD-2, A. A. Roetken, K. D. Smith and R. W. Friis, page 1041. Miner, R. C. and Molt, E. E., The Ring Armature Telephone Receiver, page 110. Modes, Longitudinal, of Elastic Weaves in Isotropic Cylinders and Slabs, A. N. Holden, page 956. Modulation, The Davisson Cathode Ray Television Tube Using Deflection, A. G. Jensen, page 855. Modulation, Pulse Code, Television by, W. M. Goodall, page 33. Mott, E. E. and Miner, R. C, The Ring Armature Telephone Receiver, page 110. N N-1 Carrier Telephone System Objectives and Transmission Features, The Type, R. S. Caruthers, page 1. N-1 Carrier Telephone System, Some Design Features of the, W. E. Kald and L. Pedersen, page 418. N-Terminal Switching Circuits, E. N. Gilbert, page 668. Network Synthesis, The Potential Analogue Method of, Sidney Darlington, page 315. Nickel, Frequency Dependence of Elastic Constants and Losses in, R. M. Bozorth, W. P. Mason and H. J. McSkimin, page 970. O Ohm's Law, Hot Electrons in Germanium and, W. Shockley, page 990. Organic Polymers, Deterioration of, B. S. Biggs, page 1078. P Patterns, Microwave Space, A Photographic Method for Displaying Sound Wave and, W. E. Kock and F. K. Harvey, page 564. Pedersen, L. and Kahl, W . E., Some Design Features of the N-1 Carrier Telephone System, page 418. Peek, R. L., Internal Temperatures of Relay Windings, page 141. Pfister, A. C, Grisdale, R. 0. and van Rooshroeck, W., Pyrolytic Film Resistors: Carbon and Borocarbon, page 271. Photographic Method for Displaying Sound Wave and Microwave Space Patterns, A, W. E. Kock and F. K. Harvey, page 564. j ^r Pierce, J. R., A Gun for Starting Electrons Straight in a Magnetic Field, page 825. Pierce, J. R., Waves in Electron Streams and Circuits, page 626. Pietenpol, W. J. and Wallace, R. L., Jr., Some Circuit Properties and Apphcations of n-p-n Transistors, page 530. Polymers, Organic Deterioration of, B. S. Biggs, page 1078. Prediction and Entropy of Printed English, C. E. Shannon, page 50. Prim, R. C, III, Some Results Concerning the Partial Differential EquaUons Descnbing the Flow of Holes and Electrons in Semiconductors, page 1174. Pulse Code Modulation, Television by, W. M. Goodall, page 33. „ „^ , „, Pyrolytic Film Resistors: Carbon and Borocarbon, R. O. Grtsdale, A. C. Pfister, and M . van Rooshroeck, page 271. Q Quartz Crystals for Very High Temperatures, Zero Temperature Coefficient, W. P. Mason, p. 366. THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 Raisbeck, G. and Wallace, R. L., Jr., Duality as a Guide in Transistor Circuit Design, page 381. Receiver, Telephone, The Ring Armature, E. E. Mott and R. C. Miner, page 110. Recorded Signals, Magnetically, The Reproduction of, R. L. Wallace, Jr., page 1145. Reflection of Electrons by Metallic Crystals, On the, L. A . MacColl, page 888. Relay Windings, Internal Temperatures of, R. L. Peek, page 141. Repeaters, Submerged, A Submarine Telephone Cable with, /. /, Gilbert, page 65. Reproduction of Magnetically Recorded Signals, The', R. L. Wallace, Jr., page 1145. Resistors, Pyrolytic Film: Carbon and Borocarbon, R. O. Grisdale, A. C. Pfister, and W. van Roosbroeck, page 271. Ring Armature Telephone Receiver, The, E. E. Mott and R. C. Miner page 110. Riordan, John, Telephone Traffic Time Average, page 1129. Roetken, A. A., Smith, K. D. and Friis, R. W., The TD-2 Microwave Radio-Relay System, page 1041. Schneckloth, H. H., Some Basic Concepts of Translators and Identifiers Used in Telephone Switching Systems, page 588. Scientific Work of C. J. Davisson, The, Karl K. Darrow, page 786. Semiconductors, Some Results Concerning the Partial Differential Equations Describing the Flow of Holes and Electrons in, R. C. Prim, III, page 1174. Set, Improved Telephone, An, A. H. Inglis and W. L. Tufnell, page 239. Seventy-fifth Anniversary of the Telephone, The, page 213. Seventy-five Years of the Telephone: An Evolution in Technology, W. H. Martin, page Sliannon, C. E., Prediction and Entropy of Printed English, page 50. Shaw, Thomas, The Evolution of Inductive Loading for Bell System Telephone FaciHties, pages 149, 447, 721, 1221. Shockley, W., Hot Electrons in Germanium and Ohm's Law, page 990, Signals, Magnetically Recorded, The Reproduction of, R. L. Wallace, Jr., page 1145. Skin Effect Losses by the Use of Laminated Conductors, Reduction of, A. M. Clogston, page 491. Slabs, Isotropic Cyhnders and, Longitudinal Modes of Elastic Waves in, A. N. H olden, page 956. Smith, K. D., Roetken, A. A. and Friis, R. W., The TD-2 Microwave Radio-Relay System, page 1041. Sound Wave and Microwave Space Patterns, A Photographic Method for Displaying, W. E. Kock and F. K. Harvey, page 564. Spacing, Interaxial, and Dielectric Constant of Pairs in Multipaired Cables, /. T. Maupin, page 652. Standards, Coaxial Impedance, R. A. Keampf, page 689. Streams, Electron, in a Diode, Frank Gray, page 830. Submarine Telephone Cable with Submerged Repeaters, A, /. /. Gilbert, page 65. Switching Circuits, N-Terminal, E. N. Gilbert, page 668. Switching Systems, Telephone, Some Basic Concepts of Translators and Identifiers Used in, H. H. Schneckloth, page 588. Synthesis, Network, The Potential Analogue Method of, Sidney Darlington, page 315. System, N-1 Carrier Telephone, Some Design Features of the, W. E. Kahl and L. Pedersen, page 418. System, New Coaxial Transmission, The Development of Electron Tubes for a, G. T, Ford and E. J. Walsh, page 1103. System, The TD-2 Microwave Radio-Relay, A. A. Roetken, K. D. Smith and R. W. Friis, page 1041. TD-2 Microwave Radio-Relay System, The, A. A. Roetken, K. D. Smith and R. W. Friis, page 1041. Technology, An Evolution in: Seventy-five Years of the Telephone, W. U. Martin, page 215. INDEX XI Telephone, Seventy-five Years of the: An Evolution in Technology, IF. //. Martin, page Telephone, The Seventy-fifth Anniversary of the, page 213. Television by Pulse Code Modulation, W. M. Goodall, page 33. Television Tube, The Davisson Cathode Ray, Using Deflection Modulation, A. G.Jensen, page 855. • Temperatures, Internal, of Relay Windings, R. L. Peek, page 141. Temperatures, Very High, for Zero Temperature Coefficient Quartz Crystals, W. P. Mason, page 366. Theory of the Negative Impedance Converter, /. L. Merrill, page 88. Traffic Time Average, Telephone, John Riordan, page 1129. Transmission, Electron, Through Thin Metal Sections with Applications to Self-Recovery in Cold Worked Aluminum, R. D. Heidenreich, page 867. Transmission Features, The Type N-1 Carrier Telephone System Objectives and, R. S. CarutJiers, page 1. Transistor Circuit Design, Duality as a Guide in, R. L. Wallace, Jr., and G. Raisbeck, page 381. Transistor: Hot Electrons in Germanium and Ohm's Law, W. Shockley, page 990. Transistor: Some Results Concerning the Partial Differential Equations Describing the Flow of Holes and Electrons in Semiconductors, R. C. Prim, III, page 1174. Transistors, n-p-n, Some Circuit Properties and Applications of, R. L. Wallace, Jr., and W. J. Pietenpol, page 530. . Translators and Identifiers Used in Telephone Switching Systems, Some Basic Concepts of, H. H. Schneckloth, page 588. Tube, The Davisson Cathode Ray Television, Using Deflection Modulation, A. G. Jensen, page 855. Tubes, Electron, for a New Coaxial Transmission System, The Development of, G. T. Ford and E. J. Walsh, page 1103. Tiiffnell, W. L. and Inglis, A. H., An Improved Telephone Set, page 239. van Roosbroeck, W., Grisdale, R.O., and Pfister, A. €., Pyrolytic Film Resistors: Carlx)n and Borocarbon, page 271. W Wallace, R. L., Jr., The Reproduction of Magnetically Recorded Signals, page 1145. Wallace, R. L., Jr. and Pietenpol, W. J., Some Circuit Properties and Applications of n-p-n Transistors, page 530. Wallace, R. L., Jr. and Raisbeck, G., Duality as a Guide in Transistor Circuit Design, page 381. Walsh, E. J. and Ford, G. T., The Development of Electron Tubes for a New Coaxial Transmission System, page 1103. Waves, Elastic, in Isotropic Cylinders and Slabs, Longitudinal Modes of, A. N. H olden, page 956. Waves in Electron Streams and Circuits, /. R. Pierce, page 626. Windings, Relay, Internal Temperatures of, R. L. Peek, page 141. Wood, Elizabeth .4., Detwinning Ferroelectric Crystals, page 945. m, ".''"A*?-*^